1 #LyX 2.0 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}
46 \renewcommand{\equationautorefname}{\hspace{-\abc}}
47 \renewcommand{\sectionautorefname}{sec.\negthinspace}
48 \renewcommand{\subsectionautorefname}{sec.\negthinspace}
49 \renewcommand{\subsubsectionautorefname}{sec.\negthinspace}}
52 % don't load packages twice
53 % see first footnote in sec. 9.3
54 \@ifundefined{textcolor}{\usepackage{color}}{}
56 % the pages of the TOC are numbered roman
57 % and a PDF-bookmark for the TOC is added
59 \let\myTOC\tableofcontents
60 \renewcommand{\tableofcontents}{%
62 \pdfbookmark[1]{\contentsname}{}
65 \pagenumbering{arabic}}
67 % insert additional vertical space of 1.5 mm between footnotes,
69 \renewcommand{\footnote}[1]{\myFoot{#1\vspace{1.5mm}}}
71 % provides caption formatting
72 \setkomafont{captionlabel}{\bfseries}
75 \usepackage[samesize]{cancel}
77 % enables calculation of values
80 % for multiple columns used in sec. 23.7
86 % for the Fourier transformation symbol
89 % define a color, used in sec.9.3
90 \definecolor{darkgreen}{cmyk}{0.5, 0, 1, 0.5}
92 % declare operators (see sec. 10.4 and sec. 15.2)
93 \DeclareMathOperator*{\Lozenge}{\blacklozenge}
94 \DeclareMathOperator{\sgn}{sgn}
96 \newcommand{\spce}{\textvisiblespace}
98 % example definitions for sec. 20.1
99 \newcommand{\gr}{\Longrightarrow}
100 \newcommand{\us}[1]{\underline{#1}}
101 \newcommand{\fb}[3]{\framebox#1#2{$#3$}}
102 \newcommand{\cb}[3][white]{\fcolorbox{#2}{#1}{$#3$}}
103 \newcommand{\fracS}[3][]{\genfrac{}{}{#1}{}{#2}{#3}}
105 % example macro from sec. 19.4
106 %\def\tagform@#1{\maketag@@@{|#1|}}
108 % macro from sec. 10.2
109 \def\clap#1{\hbox to 0pt{\hss #1\hss}}
110 \def\mathclap {\mathpalette \mathclapinternal}
111 \def\mathclapinternal #1#2{\clap{$\mathsurround =0pt #1{#2}$}}
114 % ------------------------------------
115 % used to check for needed LaTeX packages
118 % check for package eurosym
119 % used for the Euro symbol
121 \IfFileExists{eurosym.sty}
122 {\usepackage[gennarrow]{eurosym}
123 \setboolean{eurosym}{true}}
124 {\setboolean{eurosym}{false}}
126 % check for package braket
127 % used for physical vectors
129 \IfFileExists{braket.sty}
131 \setboolean{braket}{true}}
132 {\setboolean{braket}{false}}
134 % check for package cancel
136 \IfFileExists{cancel.sty}
138 \setboolean{cancel}{true}}
139 {\setboolean{cancel}{false}}
141 % check for package upgreek
143 \IfFileExists{upgreek.sty}
144 {\usepackage{upgreek}
145 \setboolean{upgreek}{true}}
146 {\setboolean{upgreek}{false}}
148 \options bibliography=totoc,index=totoc,BCOR7.5mm,titlepage,captions=tableheading
149 \use_default_options false
150 \maintain_unincluded_children false
152 \language_package default
157 \font_typewriter default
158 \font_default_family default
159 \use_non_tex_fonts false
166 \default_output_format default
168 \bibtex_command default
169 \index_command default
173 \pdf_title "LyX's Math Manual"
174 \pdf_author "LyX Team, Uwe Stöhr"
175 \pdf_subject "LyX-documentation about math"
176 \pdf_keywords "LyX, Mathed"
178 \pdf_bookmarksnumbered true
179 \pdf_bookmarksopen true
180 \pdf_bookmarksopenlevel 1
181 \pdf_breaklinks false
185 \pdf_pdfusetitle false
186 \pdf_quoted_options "linkcolor=black, citecolor=black, urlcolor=blue, filecolor=blue, pdfpagelayout=OneColumn, pdfnewwindow=true, pdfstartview=XYZ, plainpages=false"
196 \paperorientation portrait
199 \notefontcolor #0000ff
206 \paragraph_separation skip
208 \quotes_language english
211 \paperpagestyle plain
215 \tracking_changes false
216 \output_changes false
219 \html_be_strict false
225 LyX's detailed Math manual
233 \begin_layout Plain Layout
235 If you have comments or error corrections, please send them to the LyX Documenta
239 \begin_inset CommandInset href
241 name "lyx-docs@lists.lyx.org"
242 target "lyx-docs@lists.lyx.org?subject=LyX's Math manual"
253 \begin_inset Note Note
256 \begin_layout Plain Layout
263 \begin_inset Newline newline
267 \begin_inset Newline newline
275 \begin_layout Standard
276 \begin_inset CommandInset toc
277 LatexCommand tableofcontents
284 \begin_layout Standard
285 \begin_inset Note Note
288 \begin_layout Plain Layout
289 To export this document to PDF, PS or DVI the LaTeX-packages
291 braket, cancel, eurosym,
302 If they are not installed the document can be export anyway but the sections
303 where the packages are required will not appear in the output.
308 ; if it is not installed, this file cannot be exported.
311 \begin_layout Plain Layout
312 The latest PDF-version of this document can be found here:
313 \begin_inset Newline newline
318 http://wiki.lyx.org/LyX/DocumentationDevelopment#Math
326 \begin_layout Standard
327 \begin_inset Newpage newpage
333 \begin_layout Section
337 \begin_layout Standard
338 This document explains LyX's math features and is furthermore a collection
339 of LaTeX-commands used for mathematical characters and constructs.
340 The explanations are designed for the usage of commands.
341 It is therefore required that you have read the section
352 \begin_layout Standard
353 Most of the characters and many constructs explained in this manual are
354 also accessible via the menu
358 \SpecialChar \menuseparator
374 But everybody who has to write lots of formulas will notice that it is
375 much faster to use commands instead of the math toolbar.
376 Therefore this manual is focused on commands but also mentions the correspondin
377 g toolbar buttons when available.
380 \begin_layout Standard
381 If not specially mentioned the commands are only available within formulas.
382 To be able to use all commands explained in this document, the option
386 must be used in the document settings (menu
388 Document\SpecialChar \menuseparator
389 Settings\SpecialChar \menuseparator
400 \begin_layout Plain Layout
403 Use AMS math package automatically
409 \begin_layout Plain Layout
418 -math when math constructs are found that are supported by LyX.
426 \begin_layout Standard
427 This document doesn't list all
431 \begin_layout Plain Layout
444 \begin_layout Plain Layout
449 \begin_layout Plain Layout
458 -math commands is in the file
461 \begin_inset CommandInset href
464 target "ftp://ctan.tug.org/tex-archive/macros/amstex/doc/amsguide.ps"
470 , which is part of every LaTeX standard installation.
475 for lucidity reasons.
478 \begin_layout Section
482 \begin_layout Standard
483 To create an inline formula
484 \begin_inset Index idx
487 \begin_layout Plain Layout
493 that is embedded into a text line, use one of the shortcuts
499 or the toolbar button
500 \begin_inset Graphics
501 filename ../images/math-mode.png
507 \begin_inset Newline newline
510 To create a display style formula
511 \begin_inset Index idx
514 \begin_layout Plain Layout
515 Formula ! display style
520 that will appear bigger and in an own paragraph, use one of these shortcuts:
530 \begin_layout Standard
531 To change a display style formula to an inline formula, set the cursor into
532 the formula and use one of the shortcuts
540 Edit\SpecialChar \menuseparator
541 Math\SpecialChar \menuseparator
545 The same way is used to change an inline formula to a display style formula.
548 \begin_layout Standard
549 To display parts of an inline formula in the size of a display style formula,
557 \begin_inset Index idx
560 \begin_layout Plain Layout
569 Then a new blue box appears in which the desired formula part is inserted.
572 \begin_layout Standard
573 Only inline formulas are allowed inside tables.
576 \begin_layout Standard
581 can be turned on in the menu
583 View\SpecialChar \menuseparator
587 When you click there on
588 \begin_inset Quotes eld
592 \begin_inset Quotes erd
595 the toolbar will be shown permanently at the bottom; this state is visualized
600 menu with a checkmark.
601 When you click in this state again on
602 \begin_inset Quotes eld
606 \begin_inset Quotes erd
617 is only shown when the cursor is within a formula; this state is visualized
618 by the renaming of the menu entry from
619 \begin_inset Quotes eld
623 \begin_inset Quotes erd
627 \begin_inset Quotes eld
635 \begin_inset Quotes erd
641 \begin_layout Standard
643 \begin_inset Index idx
646 \begin_layout Plain Layout
652 is invoked by pressing the toolbar button
653 \begin_inset Graphics
654 filename ../images/ert-insert.png
661 Insert\SpecialChar \menuseparator
666 \begin_layout Plain Layout
682 \begin_inset Note Note
685 \begin_layout Plain Layout
686 In LyX there are three
687 \begin_inset Quotes eld
691 \begin_inset Quotes erd
694 that appear in the output with sub- and superscript letters: TeX, LaTeX
698 \begin_layout Plain Layout
699 To avoid that these names are recognized as proper names, a TeX-brace pair
708 \begin_layout Standard
709 To change the LaTeX-preamble
710 \begin_inset Index idx
713 \begin_layout Plain Layout
721 Document\SpecialChar \menuseparator
722 Settings\SpecialChar \menuseparator
727 \begin_layout Plain Layout
743 \begin_layout Standard
744 To edit matrices, case differentiations and multiline formulas subsequently,
747 Edit\SpecialChar \menuseparator
752 Edit\SpecialChar \menuseparator
754 \begin_inset space \thinspace{}
758 \begin_inset space \thinspace{}
768 When lines and columns are swapped via the menu, the column or line where
769 the cursor is in is exchanged with the column to the right or the line
771 Is the cursor in the last column or row, the exchange is done with the
772 column to the left or the line above.
775 \begin_layout Standard
776 To write text in formulas
780 \begin_layout Plain Layout
781 For multiline formulas the command
788 \begin_inset CommandInset ref
790 reference "sub:Text-in-multiline"
804 \begin_inset Index idx
807 \begin_layout Plain Layout
814 \begin_inset Index idx
817 \begin_layout Plain Layout
824 This mode is invoked with the shortcut
830 or by the insertion of the command
837 \begin_inset Index idx
840 \begin_layout Plain Layout
849 The text appears black in LyX and can therefore be distinguished from the
850 other formula parts that appear blue.
851 In the output mathematical text is set upright, in contrary to other formula
855 \begin_layout Subsection*
859 \begin_layout Standard
860 Most of the LaTeX-commands for math constructs have the following scheme:
863 \begin_layout Standard
879 \begin_layout Standard
880 A command starts always with a backslash
881 \begin_inset Quotes gld
891 \begin_inset Quotes grd
895 To omit optional arguments, also omit the associated brackets.
896 The braces around the required arguments are named in this document as
898 \begin_inset Index idx
901 \begin_layout Plain Layout
908 If you add in a formula a left brace to a command name, LyX creates automatical
910 In all other cases TeX-braces are created in formulas with the command
918 TeX-braces appear red in LyX, in contrary to normal braces that appear
920 In TeX-mode no command is needed to get TeX-braces.
921 TeX-braces don't appear in the output.
924 \begin_layout Standard
925 When commands without arguments, like commands for symbols are entered in
926 TeX-mode, a space character must
930 be behind the command to end it.
931 This space doesn't appear in the output.
932 When the space should appear in the output, the space must be followed
933 by a protected space in normal text.
936 \begin_layout Standard
937 A protected space is inserted with
940 arg "space-insert protected"
946 \begin_layout Subsection*
947 \begin_inset Newpage newpage
953 \begin_layout Itemize
958 \begin_layout Plain Layout
959 This visible space character can be created with the command
966 \begin_inset Index idx
969 \begin_layout Plain Layout
977 , inserted in TeX-mode.
986 \begin_layout Plain Layout
999 denotes a space character to be input.
1002 \begin_layout Itemize
1004 \begin_inset Formula $\to$
1007 denotes the usage of the corresponding arrow key on the keyboard.
1010 \begin_layout Subsection*
1014 \begin_layout Standard
1016 \begin_inset Float table
1022 \begin_layout Plain Layout
1024 \begin_inset Caption
1026 \begin_layout Plain Layout
1027 \begin_inset CommandInset label
1029 name "tab:Available-units"
1041 \begin_layout Plain Layout
1043 \begin_inset Tabular
1044 <lyxtabular version="3" rows="13" columns="2">
1045 <features tabularvalignment="middle">
1046 <column alignment="center" valignment="top" width="0">
1047 <column alignment="center" valignment="top" width="0">
1049 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
1052 \begin_layout Plain Layout
1058 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
1061 \begin_layout Plain Layout
1069 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
1072 \begin_layout Plain Layout
1078 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
1081 \begin_layout Plain Layout
1089 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
1092 \begin_layout Plain Layout
1098 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
1101 \begin_layout Plain Layout
1109 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
1112 \begin_layout Plain Layout
1118 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
1121 \begin_layout Plain Layout
1123 \begin_inset space \thinspace{}
1127 \begin_inset space \thinspace{}
1137 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
1140 \begin_layout Plain Layout
1146 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
1149 \begin_layout Plain Layout
1151 \begin_inset space \thinspace{}
1155 \begin_inset space \thinspace{}
1165 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
1168 \begin_layout Plain Layout
1174 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
1177 \begin_layout Plain Layout
1179 \begin_inset space \thinspace{}
1183 \begin_inset space \thinspace{}
1193 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
1196 \begin_layout Plain Layout
1202 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
1205 \begin_layout Plain Layout
1207 \begin_inset space \thinspace{}
1211 \begin_inset space \thinspace{}
1221 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
1224 \begin_layout Plain Layout
1230 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
1233 \begin_layout Plain Layout
1235 \begin_inset space \thinspace{}
1239 \begin_inset space \thinspace{}
1249 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
1252 \begin_layout Plain Layout
1258 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
1261 \begin_layout Plain Layout
1263 \begin_inset space \thinspace{}
1267 \begin_inset Formula $\approx$
1271 \begin_inset space \thinspace{}
1281 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
1284 \begin_layout Plain Layout
1290 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
1293 \begin_layout Plain Layout
1295 \begin_inset space \thinspace{}
1299 \begin_inset space \thinspace{}
1309 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
1312 \begin_layout Plain Layout
1318 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
1321 \begin_layout Plain Layout
1325 \begin_inset Quotes eld
1331 \begin_inset Quotes erd
1341 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
1344 \begin_layout Plain Layout
1350 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
1353 \begin_layout Plain Layout
1355 \begin_inset Quotes eld
1363 \begin_inset Quotes erd
1373 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
1376 \begin_layout Plain Layout
1382 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
1385 \begin_layout Plain Layout
1387 \begin_inset space \thinspace{}
1391 \begin_inset Formula $\nicefrac{1}{18}$
1395 \begin_inset space \thinspace{}
1416 \begin_layout Standard
1417 \begin_inset Newpage newpage
1423 \begin_layout Section
1427 \begin_layout Subsection
1429 \begin_inset Index idx
1432 \begin_layout Plain Layout
1439 \begin_inset Index idx
1442 \begin_layout Plain Layout
1449 \begin_inset Index idx
1452 \begin_layout Plain Layout
1457 \begin_layout Plain Layout
1468 \begin_layout Plain Layout
1481 \begin_inset Index idx
1484 \begin_layout Plain Layout
1489 \begin_layout Plain Layout
1500 \begin_layout Plain Layout
1515 \begin_layout Standard
1516 Indices are created with an underscore
1517 \begin_inset Quotes eld
1521 \begin_inset Quotes erd
1524 or via the math toolbar button
1525 \begin_inset Graphics
1526 filename ../images/math-subscript.png
1531 , exponents with a caret
1532 \begin_inset Quotes eld
1536 \begin_inset Quotes erd
1539 or via the math toolbar button
1540 \begin_inset Graphics
1541 filename ../images/math-superscript.png
1549 \begin_layout Standard
1551 \begin_inset Tabular
1552 <lyxtabular version="3" rows="4" columns="2">
1553 <features tabularvalignment="middle">
1554 <column alignment="center" valignment="top" width="0pt">
1555 <column alignment="center" valignment="top" width="0pt">
1557 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
1560 \begin_layout Plain Layout
1566 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
1569 \begin_layout Plain Layout
1571 \begin_inset Note Note
1574 \begin_layout Plain Layout
1581 is only used as spacer.
1593 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
1596 \begin_layout Plain Layout
1602 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
1605 \begin_layout Plain Layout
1606 \begin_inset Formula $B_{V}$
1616 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
1619 \begin_layout Plain Layout
1625 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
1628 \begin_layout Plain Layout
1629 \begin_inset Formula $\raisebox{5mm}{}B^{V}$
1639 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
1642 \begin_layout Plain Layout
1647 \begin_layout Plain Layout
1661 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
1664 \begin_layout Plain Layout
1665 \begin_inset Formula $\raisebox{5mm}{}B^{A}$
1681 \begin_layout Standard
1682 As the caret is in some languages an accent, vowels will be accentuated
1683 in this case and not set as exponents
1687 \begin_layout Plain Layout
1688 Depending on the used keyboard settings this can also happen for other character
1695 To get in this case exponents, press
1699 after the caret as in the last example.
1702 \begin_layout Subsection
1704 \begin_inset CommandInset label
1706 name "sub:Fractions"
1711 \begin_inset Index idx
1714 \begin_layout Plain Layout
1723 \begin_layout Standard
1724 Fractions are generated with the command
1731 \begin_inset Index idx
1734 \begin_layout Plain Layout
1742 or via the math toolbar button
1743 \begin_inset Graphics
1744 filename ../images/math/frac.png
1750 The font size is adjusted automatically, depending on whether the fraction
1751 is in an inline or display style formula.
1752 With the math toolbar button
1753 \begin_inset Graphics
1754 filename ../images/math/frac-square.png
1759 you can select different fraction types.
1762 \begin_layout Standard
1770 \begin_inset Index idx
1773 \begin_layout Plain Layout
1781 a fraction can be created that has in any case the size of a display style
1790 \begin_inset Index idx
1793 \begin_layout Plain Layout
1801 the fraction appears always with the size of an inline formula.
1805 \begin_layout Standard
1806 A line with the fraction
1807 \begin_inset Formula $\frac{1}{2}$
1810 that was created with the command
1819 \begin_layout Standard
1820 A line with the fraction
1821 \begin_inset Formula $\dfrac{1}{2}$
1824 that was created with the command
1833 \begin_layout Standard
1835 \begin_inset Tabular
1836 <lyxtabular version="3" rows="4" columns="2">
1837 <features tabularvalignment="middle">
1838 <column alignment="center" valignment="top" width="0pt">
1839 <column alignment="center" valignment="top" width="0pt">
1841 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
1844 \begin_layout Plain Layout
1850 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
1853 \begin_layout Plain Layout
1855 \begin_inset Note Note
1858 \begin_layout Plain Layout
1865 is only used as spacer.
1877 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
1880 \begin_layout Plain Layout
1887 \begin_layout Plain Layout
1897 \begin_inset Formula $\downarrow$
1905 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
1908 \begin_layout Plain Layout
1909 \begin_inset Formula $\raisebox{4.5mm}{}\frac{A}{B}\raisebox{-2.5mm}{}$
1919 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
1922 \begin_layout Plain Layout
1929 \begin_layout Plain Layout
1939 \begin_inset Formula $\downarrow$
1947 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
1950 \begin_layout Plain Layout
1951 \begin_inset Formula $\raisebox{7mm}{}\dfrac{A}{B}\raisebox{-4mm}{}$
1961 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
1964 \begin_layout Plain Layout
1971 \begin_layout Plain Layout
1984 \begin_layout Plain Layout
1999 \begin_layout Plain Layout
2009 \begin_inset Formula $\downarrow$
2013 \begin_inset Formula $\downarrow\downarrow$
2021 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
2024 \begin_layout Plain Layout
2025 \begin_inset Formula $\raisebox{8mm}{}\dfrac{e^{\frac{1}{2}}}{3}\raisebox{-4mm}{}$
2041 \begin_layout Standard
2042 \begin_inset VSpace bigskip
2046 \begin_inset Newpage newpage
2049 For nested fractions the command
2056 \begin_inset Index idx
2059 \begin_layout Plain Layout
2069 \begin_inset VSpace -3mm
2075 \begin_layout Standard
2076 \begin_inset Formula
2078 \textrm{created with \textbf{\textbackslash frac}} & & \textrm{created with \textbf{\textbackslash cfrac}}\\
2079 \frac{A}{B+\frac{C+\frac{E}{F}}{D}} & & \cfrac{A}{B+\cfrac{C+\cfrac{E}{F}}{D}}
2087 \begin_layout Standard
2088 The command for the example above is:
2091 \begin_layout Standard
2100 \begin_layout Plain Layout
2110 \begin_inset Formula $\downarrow$
2119 \begin_layout Plain Layout
2134 \begin_layout Plain Layout
2144 \begin_inset Formula $\downarrow$
2148 \begin_inset Formula $\downarrow$
2154 \begin_layout Standard
2155 \begin_inset VSpace medskip
2161 \begin_layout Standard
2168 sets the fraction always in the size of a displayed formula, also when
2169 it is part of another fraction.
2172 \begin_layout Standard
2173 It is possible to specify the alignment of the numerator.
2180 is used to left align it, the command
2193 centers the numerator.
2194 These fractions demonstrate the different alignments:
2197 \begin_layout Standard
2198 \begin_inset Formula $\cfrac[l]{A}{B+C}$
2202 \begin_inset Formula $\cfrac{A}{B+C}$
2206 \begin_inset Formula $\cfrac[r]{A}{B+C}$
2212 \begin_layout Standard
2213 \begin_inset Note Greyedout
2216 \begin_layout Plain Layout
2233 are no real LaTeX commands but represent the command
2237 cfrac[alignment]{numerator}{denominator}
2240 Therefore you cannot use them in TeX code.
2248 \begin_layout Standard
2249 \begin_inset VSpace medskip
2252 It is often advantageous to combine
2265 \begin_inset Formula
2267 \cfrac{A}{B+\cfrac{C+\frac{E}{F}}{D}}
2275 \begin_layout Standard
2276 For inline fractions with a sloped fraction stroke you can use the command
2284 \begin_inset Index idx
2287 \begin_layout Plain Layout
2296 \begin_inset Formula $\nicefrac{5}{31}$
2306 \begin_inset Index idx
2309 \begin_layout Plain Layout
2318 \begin_inset Formula $\unitfrac{5}{31}$
2321 There is furthermore the command
2327 that offers to write a fraction in combination with a number:
2328 \begin_inset Formula $\unitfrac[2]{1}{3}$
2334 \begin_layout Standard
2335 \begin_inset Note Greyedout
2338 \begin_layout Plain Layout
2349 is not a real LaTeX command but the command
2350 \begin_inset Newline newline
2357 unitfrac[number]{numerator}{denominator}
2360 Therefore you cannot use it in TeX code.
2368 \begin_layout Standard
2369 How to define own fractions where the fraction stroke can be changed, is
2371 \begin_inset CommandInset ref
2373 reference "sub:Self-defined-Fractions"
2380 \begin_layout Subsection
2382 \begin_inset Index idx
2385 \begin_layout Plain Layout
2394 \begin_layout Standard
2395 Square roots are created with
2402 \begin_inset Index idx
2405 \begin_layout Plain Layout
2413 or the math toolbar button
2414 \begin_inset Graphics
2415 filename ../images/math/sqrt.png
2420 , all other roots with the command
2427 \begin_inset Index idx
2430 \begin_layout Plain Layout
2438 or with the math toolbar button
2439 \begin_inset Graphics
2440 filename ../images/math/root.png
2448 \begin_layout Standard
2450 \begin_inset Tabular
2451 <lyxtabular version="3" rows="3" columns="2">
2452 <features tabularvalignment="middle">
2453 <column alignment="center" valignment="top" width="0pt">
2454 <column alignment="center" valignment="top" width="0pt">
2456 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
2459 \begin_layout Plain Layout
2465 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
2468 \begin_layout Plain Layout
2470 \begin_inset Note Note
2473 \begin_layout Plain Layout
2480 is only used as spacer.
2492 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
2495 \begin_layout Plain Layout
2502 \begin_layout Plain Layout
2516 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
2519 \begin_layout Plain Layout
2520 \begin_inset Formula $\raisebox{4.5mm}{}\sqrt{A-B}$
2530 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
2533 \begin_layout Plain Layout
2540 \begin_layout Plain Layout
2550 \begin_inset Formula $\downarrow$
2558 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
2561 \begin_layout Plain Layout
2562 \begin_inset Formula $\raisebox{4.5mm}{}\sqrt[3]{A-B}$
2578 \begin_layout Standard
2579 A square root can also be created with
2585 when the root index field is left empty.
2588 \begin_layout Standard
2589 With certain indices the distance to the root is too small, like in this
2591 \begin_inset Formula $\sqrt[\beta]{B}$
2595 \begin_inset Newline newline
2599 \begin_inset Formula $\beta$
2603 To avoid this, the commands
2610 \begin_inset Index idx
2613 \begin_layout Plain Layout
2628 \begin_inset Index idx
2631 \begin_layout Plain Layout
2639 are used with the following scheme:
2642 \begin_layout Standard
2656 \begin_layout Standard
2657 Distance is the number of Big Points (unit bp;
2658 \begin_inset Formula $\mathrm{72\, bp=1\, inch}$
2661 ), that the index should be moved to the left or top, resp..
2662 The commands are written to the index.
2663 This way the command
2664 \begin_inset Newline newline
2674 \begin_inset Formula $\to$
2680 \begin_inset Formula $\to$
2689 \begin_layout Plain Layout
2699 \begin_inset Formula $\to$
2703 \begin_inset Newline newline
2708 produces a correct typeset formula:
2709 \begin_inset Formula $\sqrt[\leftroot{-1}\uproot{2}\beta]{B}$
2715 \begin_layout Subsection
2716 Binomial Coefficients
2717 \begin_inset Index idx
2720 \begin_layout Plain Layout
2721 Binomial coefficients
2729 \begin_layout Standard
2730 Binomial coefficients are inserted with the command
2737 \begin_inset Index idx
2740 \begin_layout Plain Layout
2748 or with the submenu of the math toolbar button
2749 \begin_inset Graphics
2750 filename ../images/math/frac-square.png
2756 Analog to fractions (
2775 \begin_inset Index idx
2778 \begin_layout Plain Layout
2793 \begin_inset Index idx
2796 \begin_layout Plain Layout
2805 For other brackets around binomial coeficients there are the commands
2812 \begin_inset Index idx
2815 \begin_layout Plain Layout
2830 \begin_inset Index idx
2833 \begin_layout Plain Layout
2844 \begin_layout Standard
2846 \begin_inset Tabular
2847 <lyxtabular version="3" rows="6" columns="2">
2848 <features tabularvalignment="middle">
2849 <column alignment="center" valignment="top" width="0pt">
2850 <column alignment="center" valignment="top" width="0pt">
2852 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
2855 \begin_layout Plain Layout
2861 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
2864 \begin_layout Plain Layout
2866 \begin_inset Note Note
2869 \begin_layout Plain Layout
2876 is only used as spacer.
2888 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
2891 \begin_layout Plain Layout
2898 \begin_layout Plain Layout
2908 \begin_inset Formula $\downarrow$
2916 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
2919 \begin_layout Plain Layout
2920 \begin_inset Formula $\raisebox{5mm}{}\binom{A}{B}\raisebox{-2.5mm}{}$
2930 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
2933 \begin_layout Plain Layout
2940 \begin_layout Plain Layout
2950 \begin_inset Formula $\downarrow$
2958 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
2961 \begin_layout Plain Layout
2962 \begin_inset Formula $\raisebox{5mm}{}\dbinom{A}{B}\raisebox{-2.5mm}{}$
2972 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
2975 \begin_layout Plain Layout
2982 \begin_layout Plain Layout
2992 \begin_inset Formula $\downarrow$
3000 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
3003 \begin_layout Plain Layout
3004 \begin_inset Formula $\raisebox{5mm}{}\tbinom{A}{B}\raisebox{-2.5mm}{}$
3014 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
3017 \begin_layout Plain Layout
3024 \begin_layout Plain Layout
3034 \begin_inset Formula $\downarrow$
3042 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
3045 \begin_layout Plain Layout
3046 \begin_inset Formula $\raisebox{5mm}{}{A \brack B}\raisebox{-2.5mm}{}$
3056 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
3059 \begin_layout Plain Layout
3066 \begin_layout Plain Layout
3076 \begin_inset Formula $\downarrow$
3084 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
3087 \begin_layout Plain Layout
3088 \begin_inset Formula $\raisebox{5mm}{}{A \brace B}\raisebox{-2.5mm}{}$
3104 \begin_layout Subsection
3105 Case Differentiations
3106 \begin_inset Index idx
3109 \begin_layout Plain Layout
3110 Case differentiations
3118 \begin_layout Standard
3120 \begin_inset Tabular
3121 <lyxtabular version="3" rows="3" columns="2">
3122 <features tabularvalignment="middle">
3123 <column alignment="center" valignment="top" width="0pt">
3124 <column alignment="center" valignment="top" width="0pt">
3126 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
3129 \begin_layout Plain Layout
3135 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
3138 \begin_layout Plain Layout
3146 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
3149 \begin_layout Plain Layout
3156 \begin_layout Plain Layout
3166 \begin_inset Formula $\to$
3170 \begin_inset Index idx
3173 \begin_layout Plain Layout
3186 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
3189 \begin_layout Plain Layout
3190 \begin_inset Formula $\begin{cases}
3201 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
3204 \begin_layout Plain Layout
3211 \begin_layout Plain Layout
3223 arg "newline-insert newline"
3231 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
3234 \begin_layout Plain Layout
3235 \begin_inset Formula $\begin{cases}
3236 A & \textrm{for }x>0\\
3237 B & \textrm{for }x=0
3254 \begin_layout Standard
3261 or the usage of the math toolbar button
3262 \begin_inset Graphics
3263 filename ../images/math/cases.png
3268 you can create new lines with the shortcut
3271 arg "newline-insert newline"
3274 or the table toolbar button
3275 \begin_inset Graphics
3276 filename ../images/tabular-feature_append-row.png
3284 \begin_layout Standard
3291 is also available via the menu
3293 Insert\SpecialChar \menuseparator
3294 Math\SpecialChar \menuseparator
3300 \begin_layout Subsection
3302 \begin_inset Index idx
3305 \begin_layout Plain Layout
3314 \begin_layout Standard
3322 \begin_inset Index idx
3325 \begin_layout Plain Layout
3333 every character can be displayed canceled.
3334 The characters are quasi accentuated by a slash.
3337 \begin_layout Standard
3339 \begin_inset Tabular
3340 <lyxtabular version="3" rows="4" columns="2">
3341 <features tabularvalignment="middle">
3342 <column alignment="center" valignment="top" width="0pt">
3343 <column alignment="center" valignment="top" width="0pt">
3345 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
3348 \begin_layout Plain Layout
3354 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
3357 \begin_layout Plain Layout
3365 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
3368 \begin_layout Plain Layout
3376 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
3379 \begin_layout Plain Layout
3380 \begin_inset Formula $\not=$
3390 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
3393 \begin_layout Plain Layout
3403 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
3406 \begin_layout Plain Layout
3407 \begin_inset Formula $\not\le$
3417 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
3420 \begin_layout Plain Layout
3430 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
3433 \begin_layout Plain Layout
3434 \begin_inset Formula $\not\parallel$
3450 \begin_layout Standard
3451 The last example shows, that not all negations look good.
3452 Therefore there are for some negations special commands (see
3453 \begin_inset CommandInset ref
3455 reference "sub:Mathematical-Symbols"
3460 \begin_inset CommandInset ref
3462 reference "sec:Relations"
3469 \begin_layout Subsection
3471 \begin_inset CommandInset label
3473 name "sub:Placeholders"
3478 \begin_inset Index idx
3481 \begin_layout Plain Layout
3488 \begin_inset Index idx
3491 \begin_layout Plain Layout
3492 Chemical characters ! Isotopes
3498 \begin_inset Index idx
3501 \begin_layout Plain Layout
3506 \begin_layout Plain Layout
3517 \begin_layout Plain Layout
3532 \begin_layout Standard
3534 \begin_inset space \thinspace{}
3538 \begin_inset space \space{}
3545 \begin_layout Plain Layout
3546 Typesetting isotopes and chemical symbols is described in
3547 \begin_inset CommandInset ref
3549 reference "sub:Chemical-Symbols-and"
3558 the following problem occurs:
3561 \begin_layout Standard
3563 \begin_inset Tabular
3564 <lyxtabular version="3" rows="2" columns="2">
3565 <features tabularvalignment="middle">
3566 <column alignment="center" valignment="top" width="0pt">
3567 <column alignment="center" valignment="top" width="0pt">
3569 <cell alignment="center" valignment="top" usebox="none">
3572 \begin_layout Plain Layout
3573 Indices created with sub- and superscripts:
3578 <cell alignment="center" valignment="top" usebox="none">
3581 \begin_layout Plain Layout
3582 \begin_inset Formula $_{9}^{19}\mathrm{F}\raisebox{-3mm}{}$
3592 <cell alignment="center" valignment="top" usebox="none">
3595 \begin_layout Plain Layout
3601 <cell alignment="center" valignment="top" usebox="none">
3604 \begin_layout Plain Layout
3605 \begin_inset Formula $_{\phantom{1}9}^{19}\mathrm{F}$
3619 \begin_inset Note Note
3622 \begin_layout Plain Layout
3629 is only used as spacer.
3637 \begin_layout Standard
3638 The shorter index is by default placed below or above the first character
3639 of the longer index.
3640 To avoid this there is the command
3647 \begin_inset Index idx
3650 \begin_layout Plain Layout
3658 or the math toolbar button
3659 \begin_inset space \thinspace{}
3666 \begin_layout Plain Layout
3667 can be found in the submenu of the toolbar button
3668 \begin_inset Graphics
3669 filename ../images/math/space.png
3680 \begin_inset Graphics
3681 filename ../images/math/phantom.png
3686 that creates one or more phantom characters.
3693 a small blue box appears that is superposed with two red arrows.
3694 The arrows indicate that the complete width and height of the box content
3695 will be created as placeholder.
3696 Phantom characters are accordingly placeholders with the size of the characters.
3699 \begin_layout Standard
3701 \begin_inset Tabular
3702 <lyxtabular version="3" rows="4" columns="2">
3703 <features tabularvalignment="middle">
3704 <column alignment="center" valignment="top" width="0">
3705 <column alignment="center" valignment="top" width="0">
3707 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
3710 \begin_layout Plain Layout
3716 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
3719 \begin_layout Plain Layout
3721 \begin_inset Note Note
3724 \begin_layout Plain Layout
3731 is only used as spacer.
3743 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
3746 \begin_layout Plain Layout
3751 \begin_layout Plain Layout
3766 \begin_layout Plain Layout
3776 \begin_inset Formula $\to$
3783 \begin_layout Plain Layout
3797 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
3800 \begin_layout Plain Layout
3801 \begin_inset Formula $\raisebox{4.5mm}{}{}_{\phantom{1}9}^{19}\mathrm{F}\raisebox{-2.5mm}{}$
3811 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
3814 \begin_layout Plain Layout
3819 \begin_layout Plain Layout
3834 \begin_layout Plain Layout
3844 \begin_inset Formula $\to$
3851 \begin_layout Plain Layout
3865 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
3868 \begin_layout Plain Layout
3869 \begin_inset Formula $\raisebox{4.5mm}{}{}_{\phantom{23}9}^{235}\mathrm{F}\raisebox{-2.5mm}{}$
3879 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
3882 \begin_layout Plain Layout
3889 \begin_layout Plain Layout
3904 \begin_layout Plain Layout
3914 \begin_inset Formula $\to$
3921 \begin_layout Plain Layout
3935 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
3938 \begin_layout Plain Layout
3939 \begin_inset Formula $\raisebox{4.5mm}{}\Lambda_{MMt}^{\phantom{ii}t}\raisebox{-2.5mm}{}$
3955 \begin_layout Standard
3956 Furthermore there are the commands
3963 \begin_inset Index idx
3966 \begin_layout Plain Layout
3975 \begin_inset space ~
3979 \begin_inset Graphics
3980 filename ../images/math/vphantom.png
3992 \begin_inset Index idx
3995 \begin_layout Plain Layout
4004 \begin_inset space ~
4008 \begin_inset Graphics
4009 filename ../images/math/hphantom.png
4021 creates only space for the maximal height of the characters in the box
4022 but not for its width.
4029 creates only space for the width of the box content.
4030 Therefore the boxes of both commands have only one red arrow.
4033 \begin_layout Standard
4044 \begin_layout Plain Layout
4059 space for the height of the integral sign,
4063 \begin_layout Plain Layout
4070 creates an integral sign, see
4071 \begin_inset CommandInset ref
4073 reference "sub:Big-Operators"
4082 because this is the larger character.
4083 An example application is in
4084 \begin_inset CommandInset ref
4086 reference "sub:Multiline-Brackets"
4093 \begin_layout Standard
4094 Placeholders can also be used for text when it is inserted via the menu
4097 Insert\SpecialChar \menuseparator
4098 Formatting\SpecialChar \menuseparator
4104 \begin_layout Standard
4106 \begin_inset Newline newline
4110 \begin_inset Phantom Phantom
4113 \begin_layout Plain Layout
4122 \begin_layout Subsection
4124 \begin_inset Index idx
4127 \begin_layout Plain Layout
4134 \begin_inset Index idx
4137 \begin_layout Plain Layout
4138 Formula ! underlined
4146 \begin_layout Standard
4148 \begin_inset Tabular
4149 <lyxtabular version="3" rows="4" columns="2">
4150 <features tabularvalignment="middle">
4151 <column alignment="center" valignment="top" width="0pt">
4152 <column alignment="center" valignment="top" width="0pt">
4154 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
4157 \begin_layout Plain Layout
4163 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
4166 \begin_layout Plain Layout
4168 \begin_inset Note Note
4171 \begin_layout Plain Layout
4178 is only used as spacer.
4190 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
4193 \begin_layout Plain Layout
4200 \begin_layout Plain Layout
4210 \begin_inset Index idx
4213 \begin_layout Plain Layout
4226 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
4229 \begin_layout Plain Layout
4230 \begin_inset Formula $\raisebox{5mm}{}\overline{A+B}$
4240 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
4243 \begin_layout Plain Layout
4250 \begin_layout Plain Layout
4260 \begin_inset Index idx
4263 \begin_layout Plain Layout
4276 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
4279 \begin_layout Plain Layout
4280 \begin_inset Formula $\underline{A+B}\raisebox{-2.5mm}{}$
4290 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
4293 \begin_layout Plain Layout
4300 \begin_layout Plain Layout
4315 \begin_layout Plain Layout
4329 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
4332 \begin_layout Plain Layout
4333 \begin_inset Formula $\raisebox{5mm}{}\overline{\underline{A+B}}\raisebox{-2.5mm}{}$
4349 \begin_layout Standard
4350 In the last example it doesn't matter if first
4365 \begin_layout Standard
4366 To double underline e.
4367 \begin_inset space \thinspace{}
4371 \begin_inset space \space{}
4383 \begin_layout Standard
4384 It is possible to place up to 6 lines above or below characters.
4387 \begin_layout Standard
4388 \begin_inset VSpace bigskip
4391 Custom lines can be created using the command
4398 \begin_inset Index idx
4401 \begin_layout Plain Layout
4409 which has the following scheme:
4412 \begin_layout Standard
4417 rule[vertical offset]{length}{thickness}
4420 \begin_layout Standard
4421 The optional vertical offset shifts the line upwards (or downwards, when
4422 the value is negative).
4424 \begin_inset CommandInset ref
4426 reference "tab:Available-units"
4430 can be used for the values.
4431 Here are two example lines created with the commands
4432 \begin_inset Newline newline
4439 rule[-2ex]{3cm}{2pt}
4450 \begin_layout Standard
4452 \begin_inset Formula $\rule[-2ex]{3cm}{2pt}\rule{2cm}{1pt}$
4458 \begin_layout Standard
4465 can also be used for text when a line is inserted via the menu
4467 Insert\SpecialChar \menuseparator
4468 Formatting\SpecialChar \menuseparator
4470 \begin_inset space ~
4478 \begin_layout Standard
4480 \begin_inset CommandInset line
4491 \begin_layout Subsection
4493 \begin_inset CommandInset label
4500 \begin_inset Index idx
4503 \begin_layout Plain Layout
4512 \begin_layout Standard
4513 There are different types of ellipses available.
4517 \begin_layout Plain Layout
4518 In the math toolbar in the submenu of the button
4519 \begin_inset Graphics
4520 filename ../images/math/ldots.png
4530 For listings dots at the baseline are used (
4537 \begin_inset Index idx
4540 \begin_layout Plain Layout
4548 ), while for operations dots are needed that are on the same height as the
4556 \begin_inset Index idx
4559 \begin_layout Plain Layout
4568 When using the command
4575 \begin_inset Index idx
4578 \begin_layout Plain Layout
4586 , LaTeX decides on the basis of the next character what type is used.
4589 \begin_layout Standard
4591 \begin_inset Tabular
4592 <lyxtabular version="3" rows="9" columns="2">
4593 <features tabularvalignment="middle">
4594 <column alignment="center" valignment="top" width="0pt">
4595 <column alignment="center" valignment="top" width="0pt">
4597 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
4600 \begin_layout Plain Layout
4606 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
4609 \begin_layout Plain Layout
4617 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
4620 \begin_layout Plain Layout
4625 \begin_layout Plain Layout
4640 \begin_layout Plain Layout
4654 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
4657 \begin_layout Plain Layout
4658 \begin_inset Formula $A_{1},\dots,A_{n}$
4668 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
4671 \begin_layout Plain Layout
4676 \begin_layout Plain Layout
4691 \begin_layout Plain Layout
4705 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
4708 \begin_layout Plain Layout
4709 \begin_inset Formula $A_{1}+\dots+A_{n}$
4719 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
4722 \begin_layout Plain Layout
4727 \begin_layout Plain Layout
4742 \begin_layout Plain Layout
4756 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
4759 \begin_layout Plain Layout
4760 \begin_inset Formula $A_{1},\ldots,A_{n}$
4770 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
4773 \begin_layout Plain Layout
4778 \begin_layout Plain Layout
4793 \begin_layout Plain Layout
4807 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
4810 \begin_layout Plain Layout
4811 \begin_inset Formula $A_{1}+\cdots+A_{n}$
4821 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
4824 \begin_layout Plain Layout
4832 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
4835 \begin_layout Plain Layout
4836 \begin_inset Formula $\vdots$
4846 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
4849 \begin_layout Plain Layout
4857 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
4860 \begin_layout Plain Layout
4861 \begin_inset Formula $\ddots$
4871 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
4874 \begin_layout Plain Layout
4882 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
4885 \begin_layout Plain Layout
4886 \begin_inset Formula $\iddots$
4896 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
4899 \begin_layout Plain Layout
4901 \begin_inset space \thinspace{}
4904 matrix with the different dots
4909 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
4912 \begin_layout Plain Layout
4913 \begin_inset Formula $\begin{array}{ccc}
4914 A_{11} & \cdots & A_{1m}\\
4915 \vdots & \ddots & \vdots\\
4916 A_{n1} & \cdots & A_{nm}
4933 \begin_layout Standard
4934 The ellipses available in menu
4936 Insert\SpecialChar \menuseparator
4938 \begin_inset space ~
4952 \begin_layout Standard
4953 \begin_inset VSpace medskip
4962 , one of the options
4964 Use mathdots package (automatically)
4966 must be set in the document settings under
4969 \begin_inset space ~
4975 \begin_inset Newline newline
4980 Use mathdots package
4982 will improve the appearance of all dots in the documents if their font
4983 style or size is not the default.
4986 \begin_layout Standard
4987 \begin_inset VSpace medskip
4990 Specially for matrices there are ellipses that span over several columns.
4991 They are created with the command
4998 \begin_inset Index idx
5001 \begin_layout Plain Layout
5009 , that has the following scheme:
5012 \begin_layout Standard
5017 hdotsfor[distance]{number of columns}
5020 \begin_layout Standard
5021 The number of columns specifies how many columns should be spanned.
5022 Distance is a factor for the distance between the dots.
5025 \begin_layout Standard
5026 In the following matrix the command
5032 was inserted in the first box of the second line, to get an ellipsis with
5033 a dot distance twice as long as with the command
5040 \begin_inset Formula
5042 \left(\begin{array}{cccc}
5051 Note that the matrix fields that should be spanned must be empty, otherwise
5052 you get LaTeX-errors.
5055 \begin_layout Standard
5056 \begin_inset VSpace bigskip
5059 Furthermore you can fill with the command
5066 \begin_inset Index idx
5069 \begin_layout Plain Layout
5077 the rest of a line with dots.
5078 The effect of these commands is the same like with
5085 \begin_inset CommandInset ref
5087 reference "sub:Variable-Space"
5094 \begin_layout Standard
5095 For example the command
5103 \begin_layout Plain Layout
5117 \begin_layout Standard
5118 \begin_inset Formula $A\dotfill B$
5124 \begin_layout Standard
5131 there is for a line the command
5138 \begin_inset Index idx
5141 \begin_layout Plain Layout
5152 \begin_layout Standard
5153 \begin_inset Formula $A\hrulefill B$
5159 \begin_layout Standard
5160 To use the commands for text, they have to be inserted in TeX-mode.
5163 \begin_layout Section
5165 \begin_inset CommandInset label
5172 \begin_inset Index idx
5175 \begin_layout Plain Layout
5184 \begin_layout Standard
5185 Matrices can be inserted via the math toolbar button
5186 \begin_inset Graphics
5187 filename ../images/dialog-show_mathmatrix.png
5194 Insert\SpecialChar \menuseparator
5195 Math\SpecialChar \menuseparator
5199 In the matrix dialog you can specify the number of columns and rows, the
5200 alignment and the decoration.
5201 The vertical alignment is hereby only of importance for matrices in inline
5205 \begin_layout Standard
5206 The first matrix is top
5207 \begin_inset Formula $\begin{array}[t]{cccc}
5215 \begin_inset Formula $\begin{array}{cccc}
5222 and the third bottom
5223 \begin_inset Formula $\begin{array}[b]{cccc}
5233 \begin_layout Standard
5234 The horizontal alignment specifies how the column entries should be aligned.
5235 It is set by entering a letter for every column.
5240 denotes left aligned,
5249 To create for example a 4
5254 \begin_inset space ~
5257 matrix where the first column is left aligned, the second and third are
5258 centered and the last one is right aligned, one enters for the horizontal
5264 Normally are in a matrix all columns centered, therefore the default is
5265 for every column is a
5272 \begin_layout Standard
5273 Horizontal alignment:
5276 \begin_layout Standard
5282 \begin_inset Formula $\begin{array}{lll}
5294 \begin_inset Formula $\begin{array}{ccc}
5306 \begin_inset Formula $\begin{array}{rrr}
5316 \begin_layout Standard
5317 To add or delete rows and columns subsequently, the math toolbar buttons
5319 \begin_inset Graphics
5320 filename ../images/tabular-feature_append-row.png
5326 \begin_inset Graphics
5327 filename ../images/tabular-feature_delete-row.png
5333 \begin_inset space \thinspace{}
5338 Edit\SpecialChar \menuseparator
5342 New rows can also be created with
5345 arg "newline-insert newline"
5351 \begin_layout Standard
5352 \begin_inset VSpace bigskip
5359 adds parentheses in the selected style around the matrix.
5360 Alternatively, parentheses can can either be created with the commands
5368 \begin_inset Index idx
5371 \begin_layout Plain Layout
5386 \begin_inset Index idx
5389 \begin_layout Plain Layout
5400 \begin_inset space ~
5406 \begin_inset CommandInset ref
5408 reference "sub:Automatic-Bracket-Size"
5412 , or by using the following commands:
5413 \begin_inset VSpace medskip
5419 \begin_layout Standard
5420 \begin_inset space \hfill{}
5424 \begin_inset Tabular
5425 <lyxtabular version="3" rows="4" columns="2">
5426 <features tabularvalignment="middle">
5427 <column alignment="center" valignment="top" width="0">
5428 <column alignment="center" valignment="top" width="0">
5430 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
5433 \begin_layout Plain Layout
5439 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
5442 \begin_layout Plain Layout
5444 \begin_inset Note Note
5447 \begin_layout Plain Layout
5454 is only used as spacer.
5466 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
5469 \begin_layout Plain Layout
5476 \begin_layout Plain Layout
5490 \begin_inset space \thinspace{}
5498 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
5501 \begin_layout Plain Layout
5502 \begin_inset Formula $\raisebox{7.5mm}{}\begin{bmatrix}\begin{array}{cc}
5503 0 & \textrm{-}\mathrm{i}\\
5505 \end{array}\end{bmatrix}\raisebox{-5.3mm}{}$
5515 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
5518 \begin_layout Plain Layout
5525 \begin_layout Plain Layout
5539 \begin_inset space \thinspace{}
5547 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
5550 \begin_layout Plain Layout
5551 \begin_inset Formula $\raisebox{7.5mm}{}\begin{Bmatrix}\begin{array}{cc}
5552 0 & \textrm{-}\mathrm{i}\\
5554 \end{array}\end{Bmatrix}\raisebox{-5.3mm}{}$
5564 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
5567 \begin_layout Plain Layout
5574 \begin_layout Plain Layout
5588 \begin_inset space \thinspace{}
5596 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
5599 \begin_layout Plain Layout
5600 \begin_inset Formula $\raisebox{7.5mm}{}\begin{pmatrix}\begin{array}{cc}
5601 0 & \textrm{-}\mathrm{i}\\
5603 \end{array}\end{pmatrix}\raisebox{-5.3mm}{}$
5617 \begin_inset space \hfill{}
5621 \begin_inset Tabular
5622 <lyxtabular version="3" rows="4" columns="2">
5623 <features tabularvalignment="middle">
5624 <column alignment="center" valignment="top" width="0">
5625 <column alignment="center" valignment="top" width="0">
5627 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
5630 \begin_layout Plain Layout
5636 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
5639 \begin_layout Plain Layout
5647 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
5650 \begin_layout Plain Layout
5657 \begin_layout Plain Layout
5671 \begin_inset space \thinspace{}
5679 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
5682 \begin_layout Plain Layout
5683 \begin_inset Formula $\raisebox{7.5mm}{}\begin{vmatrix}\begin{array}{cc}
5684 0 & \textrm{-}\mathrm{i}\\
5686 \end{array}\end{vmatrix}\raisebox{-5.3mm}{}$
5696 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
5699 \begin_layout Plain Layout
5706 \begin_layout Plain Layout
5720 \begin_inset space \thinspace{}
5728 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
5731 \begin_layout Plain Layout
5732 \begin_inset Formula $\raisebox{7.5mm}{}\begin{Vmatrix}\begin{array}{cc}
5733 0 & \textrm{-}\mathrm{i}\\
5735 \end{array}\end{Vmatrix}\raisebox{-5.3mm}{}$
5745 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
5748 \begin_layout Plain Layout
5755 \begin_layout Plain Layout
5769 \begin_inset space \thinspace{}
5777 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
5780 \begin_layout Plain Layout
5781 \begin_inset Formula $\raisebox{7.5mm}{}\begin{matrix}\begin{array}{cc}
5782 0 & \textrm{-}\mathrm{i}\\
5784 \end{array}\end{matrix}\raisebox{-5.3mm}{}$
5798 \begin_inset space \hfill{}
5804 \begin_layout Standard
5805 \begin_inset VSpace medskip
5809 \begin_inset space \thinspace{}
5813 \begin_inset space \space{}
5822 is inserted, a blue box appears between two vertical lines where the matrix
5824 \begin_inset Newline newline
5827 Note that decorated matrices ignore the vertical alignment.
5830 \begin_layout Standard
5831 \begin_inset Note Greyedout
5834 \begin_layout Plain Layout
5839 LaTeX limits the number of matrix columns with decorations to 10.
5840 If you need more than 10
5841 \begin_inset space \thinspace{}
5844 columns, you have to add this line to the document preamble:
5847 \begin_layout Plain Layout
5852 setcounter{MaxMatrixCols}{number}
5855 \begin_layout Plain Layout
5860 is the number of columns between 11 and 99.
5868 \begin_layout Standard
5869 \begin_inset VSpace bigskip
5872 As all multiline formulas are matrices, the length
5879 \begin_inset Index idx
5882 \begin_layout Plain Layout
5890 that is described in
5891 \begin_inset CommandInset ref
5893 reference "sub:Column-Separation"
5897 can also be used to change the column separation of matrices.
5900 \begin_layout Standard
5901 To change the row separation, the command
5908 \begin_inset Index idx
5911 \begin_layout Plain Layout
5920 It is used as follows:
5923 \begin_layout Standard
5930 arraystretch}{stretch factor}
5931 \begin_inset Index idx
5934 \begin_layout Plain Layout
5945 \begin_layout Standard
5952 assigns the stretch factor to the predefined command
5960 \begin_inset space \thinspace{}
5964 \begin_inset space \space{}
5967 the row separation, use the factor 2.
5968 This is then used for all following matrices.
5969 To go back to the original separation, assign the factor 1 to
5978 \begin_layout Standard
5979 To set matrices into a text line, the command
5986 \begin_inset Index idx
5989 \begin_layout Plain Layout
5998 When it is inserted a blue box with two dashed lines appears.
5999 In this box the matrix is inserted.
6002 \begin_layout Standard
6004 \begin_inset Formula $\left(\begin{smallmatrix}A & B\\
6006 \end{smallmatrix}\right)$
6012 \begin_layout Section
6013 Brackets and Delimiters
6014 \begin_inset Index idx
6017 \begin_layout Plain Layout
6024 \begin_inset Index idx
6027 \begin_layout Plain Layout
6036 \begin_layout Subsection
6037 Vertical Brackets and Delimiters
6038 \begin_inset Index idx
6041 \begin_layout Plain Layout
6050 \begin_layout Standard
6051 \begin_inset space \hfill{}
6055 \begin_inset Tabular
6056 <lyxtabular version="3" rows="9" columns="2">
6057 <features tabularvalignment="middle">
6058 <column alignment="center" valignment="top" width="0pt">
6059 <column alignment="center" valignment="top" width="0pt">
6061 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
6064 \begin_layout Plain Layout
6070 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
6073 \begin_layout Plain Layout
6081 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
6084 \begin_layout Plain Layout
6090 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
6093 \begin_layout Plain Layout
6094 \begin_inset Formula $($
6104 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
6107 \begin_layout Plain Layout
6113 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
6116 \begin_layout Plain Layout
6117 \begin_inset Formula $\{$
6127 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
6130 \begin_layout Plain Layout
6136 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
6139 \begin_layout Plain Layout
6140 \begin_inset Formula $[$
6150 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
6153 \begin_layout Plain Layout
6161 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
6164 \begin_layout Plain Layout
6165 \begin_inset Formula $\langle$
6175 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
6178 \begin_layout Plain Layout
6186 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
6189 \begin_layout Plain Layout
6190 \begin_inset Formula $\lceil$
6200 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
6203 \begin_layout Plain Layout
6211 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
6214 \begin_layout Plain Layout
6215 \begin_inset Formula $\lfloor$
6225 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
6228 \begin_layout Plain Layout
6234 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
6237 \begin_layout Plain Layout
6238 \begin_inset Formula $/$
6248 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
6251 \begin_layout Plain Layout
6257 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
6260 \begin_layout Plain Layout
6261 \begin_inset Formula $|$
6275 \begin_inset space \hfill{}
6279 \begin_inset Tabular
6280 <lyxtabular version="3" rows="9" columns="2">
6281 <features tabularvalignment="middle">
6282 <column alignment="center" valignment="top" width="0pt">
6283 <column alignment="center" valignment="top" width="0pt">
6285 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
6288 \begin_layout Plain Layout
6294 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
6297 \begin_layout Plain Layout
6305 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
6308 \begin_layout Plain Layout
6314 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
6317 \begin_layout Plain Layout
6318 \begin_inset Formula $)$
6328 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
6331 \begin_layout Plain Layout
6337 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
6340 \begin_layout Plain Layout
6341 \begin_inset Formula $\}$
6351 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
6354 \begin_layout Plain Layout
6360 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
6363 \begin_layout Plain Layout
6364 \begin_inset Formula $]$
6374 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
6377 \begin_layout Plain Layout
6385 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
6388 \begin_layout Plain Layout
6389 \begin_inset Formula $\rangle$
6399 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
6402 \begin_layout Plain Layout
6410 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
6413 \begin_layout Plain Layout
6414 \begin_inset Formula $\rceil$
6424 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
6427 \begin_layout Plain Layout
6435 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
6438 \begin_layout Plain Layout
6439 \begin_inset Formula $\rfloor$
6449 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
6452 \begin_layout Plain Layout
6462 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
6465 \begin_layout Plain Layout
6466 \begin_inset Formula $\backslash$
6476 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
6479 \begin_layout Plain Layout
6487 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
6490 \begin_layout Plain Layout
6491 \begin_inset Formula $\|$
6505 \begin_inset space \hfill{}
6511 \begin_layout Standard
6514 \begin_inset Note Greyedout
6517 \begin_layout Plain Layout
6522 In TeX-mode the command
6529 \begin_inset Index idx
6532 \begin_layout Plain Layout
6540 must be used for the backslash, because the command
6548 produces there a line break.
6556 \begin_layout Standard
6557 For all characters listed above the size can be adjusted with the commands
6558 described in the following two subsections.
6559 When using these commands, the characters < and > can directly be used
6560 instead of the commands
6575 \begin_layout Subsubsection
6577 \begin_inset CommandInset label
6579 name "sub:Manual-Bracket-Size"
6584 \begin_inset Index idx
6587 \begin_layout Plain Layout
6588 Bracket size ! manual
6596 \begin_layout Standard
6597 The bracket size can be specified manually by the LaTeX-commands
6604 \begin_inset Index idx
6607 \begin_layout Plain Layout
6640 denotes the smallest and
6646 the largest bracket size.
6649 \begin_layout Standard
6650 These commands are used to emphasize levels of brackets:
6653 \begin_layout Standard
6655 \begin_inset Tabular
6656 <lyxtabular version="3" rows="2" columns="2">
6657 <features tabularvalignment="middle">
6658 <column alignment="center" valignment="top" width="0pt">
6659 <column alignment="center" valignment="top" width="0pt">
6661 <cell alignment="center" valignment="top" usebox="none">
6664 \begin_layout Plain Layout
6665 all brackets in the same size:
6670 <cell alignment="center" valignment="top" usebox="none">
6673 \begin_layout Plain Layout
6674 \begin_inset Formula $((A+B)(A-B))^{C}\raisebox{-4mm}{}$
6684 <cell alignment="center" valignment="top" usebox="none">
6687 \begin_layout Plain Layout
6693 <cell alignment="center" valignment="top" usebox="none">
6696 \begin_layout Plain Layout
6697 \begin_inset Formula $\Big((A+B)(A-B)\Big)^{C}$
6711 \begin_inset Note Note
6714 \begin_layout Plain Layout
6721 is only used as spacer.
6729 \begin_layout Standard
6730 For the second formula the command
6740 \begin_layout Plain Layout
6754 \begin_layout Standard
6755 Here is an overview about all bracket sizes:
6758 \begin_layout Standard
6778 \begin_layout Plain Layout
6795 \begin_layout Plain Layout
6808 \begin_layout Plain Layout
6824 \begin_layout Standard
6826 \begin_inset Formula $\Bigg(\exp\bigg<\Big[\big\{\ln(3x)\big\}^{2}\sin(x)\Big]^{A}\bigg>\Bigg)^{0,5}$
6832 \begin_layout Standard
6839 -commands there is the variant
6846 \begin_inset Index idx
6849 \begin_layout Plain Layout
6857 that adds a bit more space between the bracket and its content, and the
6871 \begin_inset Index idx
6874 \begin_layout Plain Layout
6884 , that don't add additional space.
6889 at the end of the command
6895 is for a left bracket; for a right bracket this will be replaced by an
6901 A left or right bracket can each be an opening or closing bracket.
6904 \begin_layout Standard
6905 In the following table is a comparison of the variants:
6908 \begin_layout Standard
6910 \begin_inset Tabular
6911 <lyxtabular version="3" rows="5" columns="2">
6912 <features tabularvalignment="middle">
6913 <column alignment="center" valignment="middle" width="0">
6914 <column alignment="center" valignment="middle" width="0">
6916 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
6919 \begin_layout Plain Layout
6925 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
6928 \begin_layout Plain Layout
6930 \begin_inset Note Note
6933 \begin_layout Plain Layout
6940 is only used as spacer.
6952 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
6955 \begin_layout Plain Layout
6970 \begin_layout Plain Layout
6988 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
6991 \begin_layout Plain Layout
6992 \begin_inset Formula $\raisebox{5.5mm}{}\Bigm(\bigm(\ln(3x)\bigm)^{2}\Bigm)\raisebox{-3.25mm}{}$
7002 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
7005 \begin_layout Plain Layout
7020 \begin_layout Plain Layout
7038 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
7041 \begin_layout Plain Layout
7042 \begin_inset Formula $\raisebox{5.5mm}{}\Big(\big(\ln(3x)\big)^{2}\Big)\raisebox{-3.25mm}{}$
7052 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
7055 \begin_layout Plain Layout
7070 \begin_layout Plain Layout
7088 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
7091 \begin_layout Plain Layout
7092 \begin_inset Formula $\raisebox{5.5mm}{}\Bigl(\bigl(\ln(3x)\bigr)^{2}\Bigr)\raisebox{-3.25mm}{}$
7102 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
7105 \begin_layout Plain Layout
7117 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
7120 \begin_layout Plain Layout
7121 \begin_inset Formula $\raisebox{4.5mm}{}\bigl)\ln(3x)\bigr(\raisebox{-2mm}{}$
7137 \begin_layout Subsubsection
7138 Automatic Bracket Size
7139 \begin_inset CommandInset label
7141 name "sub:Automatic-Bracket-Size"
7146 \begin_inset Index idx
7149 \begin_layout Plain Layout
7150 Bracket size ! automatic
7158 \begin_layout Standard
7159 Brackets with variable size can be inserted with the commands
7166 \begin_inset Index idx
7169 \begin_layout Plain Layout
7184 \begin_inset Index idx
7187 \begin_layout Plain Layout
7195 or via the math toolbar button
7196 \begin_inset Graphics
7197 filename ../images/dialog-show_mathdelimiter.png
7215 the wanted bracket must be inserted.
7216 The bracket size will then automatically be calculated for the output.
7219 \begin_layout Standard
7221 normal bracket: The command
7231 \begin_layout Plain Layout
7241 \begin_inset Formula $\downarrow$
7248 \begin_layout Plain Layout
7260 \begin_inset Formula
7270 \begin_layout Standard
7272 multiline bracket: The command
7284 \begin_layout Plain Layout
7294 \begin_inset Formula $\downarrow$
7301 \begin_layout Plain Layout
7315 \begin_inset Formula
7317 \ln\left(\frac{A}{C}\right)
7325 \begin_layout Standard
7341 \begin_inset space ~
7347 This has the advantage that you can see in LyX immediately the real bracket
7348 size and that the matching right bracket will be created too.
7349 \begin_inset Newline newline
7352 The command for the last example would then be:
7366 \begin_layout Plain Layout
7376 \begin_inset Formula $\downarrow$
7382 \begin_layout Standard
7383 To omit a left or right bracket, a dot is inserted for the omitted bracket.
7384 For example the command
7394 \begin_layout Plain Layout
7404 \begin_inset Formula $\downarrow$
7411 \begin_layout Plain Layout
7427 \begin_inset Formula
7429 \left.\frac{A}{B}\right\}
7448 will be converted by LyX to brackets in the right size when the document
7449 is reloaded and an omitted bracket will appear as dashed line.
7452 \begin_layout Standard
7453 \begin_inset VSpace bigskip
7456 Because all popular LaTeX-Distributions use eTeX, an extension to LaTeX,
7464 \begin_inset Index idx
7467 \begin_layout Plain Layout
7475 is additionally available for all brackets and limits.
7476 With this command the height of the following character is adapted to the
7477 one of the surrounding brackets, what is e.
7478 \begin_inset space \thinspace{}
7482 \begin_inset space \space{}
7485 needed for physical vectors:
7486 \begin_inset Formula
7488 \left\langle \phi\:\middle|\: J=\frac{3}{2}\,,\, M_{J}\right\rangle
7493 For physical vectors there is a special LaTeX-package, described in
7494 \begin_inset CommandInset ref
7496 reference "sub:Physical-Vectors"
7503 \begin_layout Subsection
7505 \begin_inset Index idx
7508 \begin_layout Plain Layout
7509 Brackets ! horizontal
7517 \begin_layout Standard
7519 \begin_inset Tabular
7520 <lyxtabular version="3" rows="4" columns="2">
7521 <features tabularvalignment="middle">
7522 <column alignment="center" valignment="top" width="0pt">
7523 <column alignment="center" valignment="top" width="0pt">
7525 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
7528 \begin_layout Plain Layout
7530 \begin_inset Note Note
7533 \begin_layout Plain Layout
7540 is only used as spacer.
7550 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
7553 \begin_layout Plain Layout
7561 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
7564 \begin_layout Plain Layout
7568 \begin_layout Plain Layout
7583 \begin_layout Plain Layout
7596 \begin_layout Plain Layout
7609 \begin_layout Plain Layout
7622 \begin_layout Plain Layout
7630 \begin_inset Index idx
7633 \begin_layout Plain Layout
7646 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
7649 \begin_layout Plain Layout
7650 \begin_inset Formula $\overbrace{A+B}^{3}$
7660 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
7663 \begin_layout Plain Layout
7667 \begin_layout Plain Layout
7682 \begin_layout Plain Layout
7695 \begin_layout Plain Layout
7708 \begin_layout Plain Layout
7716 \begin_inset Index idx
7719 \begin_layout Plain Layout
7732 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
7735 \begin_layout Plain Layout
7736 \begin_inset Formula $\underbrace{A+B}_{5}$
7746 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
7749 \begin_layout Plain Layout
7756 \begin_layout Plain Layout
7771 \begin_layout Plain Layout
7784 \begin_layout Plain Layout
7797 \begin_layout Plain Layout
7810 \begin_layout Plain Layout
7823 \begin_layout Plain Layout
7836 \begin_layout Plain Layout
7850 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
7853 \begin_layout Plain Layout
7854 \begin_inset Formula $\overbrace{\underbrace{A+B_{w}}_{7}}^{C}$
7870 \begin_layout Standard
7871 In the last example it doesn't matter if
7883 is inserted at first.
7886 \begin_layout Standard
7887 \begin_inset VSpace bigskip
7890 When brackets are needed that overlap each other, multiline formulas, as
7892 \begin_inset CommandInset ref
7894 reference "sec:Multiline-Formulas"
7899 \begin_inset Formula
7901 A & = & \underbrace{gggg+bbqq}_{r}+\: dddd\\
7902 & & \hphantom{gggg+\:}\underbrace{\hphantom{bbqq+dddd}}_{s}
7907 In the first row the formula is inserted together with the first brace.
7908 It is hereby important that the space command
7912 \begin_layout Plain Layout
7913 Space commands are explained in
7914 \begin_inset CommandInset ref
7916 reference "sub:Predefined-Space"
7931 is inserted before the first
7932 \begin_inset Formula $d$
7935 , because the brace that ends behind the
7936 \begin_inset Formula $q$
7939 prevents that the following
7940 \begin_inset Quotes eld
7944 \begin_inset Quotes erd
7947 is surrounded by space.
7951 \begin_layout Plain Layout
7952 because a bracket is not handled as character, see
7953 \begin_inset CommandInset ref
7955 reference "sub:Binary-Operators"
7964 In the second row the second brace is inserted.
7965 As it should begin before the
7966 \begin_inset Formula $b$
7981 \begin_layout Plain Layout
7989 \begin_inset CommandInset ref
7991 reference "sub:Placeholders"
8000 This space is needed because the
8001 \begin_inset Quotes eld
8005 \begin_inset Quotes erd
8008 is also surrounded by space in the formula.
8009 The brace is placed under the command
8018 \begin_layout Standard
8019 It gets more complicated when brackets overlap each other, like in the following
8024 \begin_layout Plain Layout
8036 \begin_inset Formula
8038 & & \hphantom{gggg+\:}\overbrace{\hphantom{bbqq+dddd}}^{s}\\
8039 A & = & \underbrace{gggg+bbqq}_{r}+\: dddd
8048 \begin_layout Plain Layout
8059 The first formula row is the same as the second row of the previous example,
8060 with the difference that the brace is above.
8061 The second row contains the formula together with the second brace.
8062 To avoid that there is space between the upper brace in the first row and
8063 the formula, the row spacing need to be reduced.
8064 This is not easily possible due to a bug in LyX
8068 \begin_layout Plain Layout
8069 \begin_inset CommandInset href
8071 name "LyX-bug #1505"
8072 target "http://www.lyx.org/trac/ticket/1505"
8082 As solution for the problem, the global formula row separation
8089 \begin_inset Index idx
8092 \begin_layout Plain Layout
8100 must be changed to -6
8101 \begin_inset space \thinspace{}
8104 pt before the formula with the command
8119 is set back after the formula to the standard value of 3
8120 \begin_inset space \thinspace{}
8123 pt using the same command.
8124 More about the row separation in formulas is explained in
8125 \begin_inset CommandInset ref
8127 reference "sub:Line-Separation"
8134 \begin_layout Section
8136 \begin_inset Index idx
8139 \begin_layout Plain Layout
8148 \begin_layout Standard
8149 Arrows can be inserted via the math toolbar button
8150 \begin_inset Graphics
8151 filename ../images/math/leftarrow.png
8156 or the commands listed in the following subsections.
8159 \begin_layout Subsection
8161 \begin_inset Index idx
8164 \begin_layout Plain Layout
8173 \begin_layout Standard
8174 \begin_inset space \hfill{}
8178 \begin_inset Tabular
8179 <lyxtabular version="3" rows="8" columns="2">
8180 <features tabularvalignment="middle">
8181 <column alignment="center" valignment="top" width="0pt">
8182 <column alignment="center" valignment="top" width="0pt">
8184 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
8187 \begin_layout Plain Layout
8193 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
8196 \begin_layout Plain Layout
8204 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
8207 \begin_layout Plain Layout
8215 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
8218 \begin_layout Plain Layout
8219 \begin_inset Formula $\gets$
8229 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
8232 \begin_layout Plain Layout
8240 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
8243 \begin_layout Plain Layout
8244 \begin_inset Formula $\Leftarrow$
8254 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
8257 \begin_layout Plain Layout
8265 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
8268 \begin_layout Plain Layout
8269 \begin_inset Formula $\longleftarrow$
8279 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
8282 \begin_layout Plain Layout
8290 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
8293 \begin_layout Plain Layout
8294 \begin_inset Formula $\Longleftarrow$
8304 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
8307 \begin_layout Plain Layout
8315 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
8318 \begin_layout Plain Layout
8319 \begin_inset Formula $\leftharpoonup$
8329 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
8332 \begin_layout Plain Layout
8340 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
8343 \begin_layout Plain Layout
8344 \begin_inset Formula $\leftharpoondown$
8354 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
8357 \begin_layout Plain Layout
8365 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
8368 \begin_layout Plain Layout
8369 \begin_inset Formula $\hookleftarrow$
8383 \begin_inset space \hfill{}
8387 \begin_inset Tabular
8388 <lyxtabular version="3" rows="8" columns="2">
8389 <features tabularvalignment="middle">
8390 <column alignment="center" valignment="top" width="0pt">
8391 <column alignment="center" valignment="top" width="0pt">
8393 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
8396 \begin_layout Plain Layout
8402 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
8405 \begin_layout Plain Layout
8413 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
8416 \begin_layout Plain Layout
8424 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
8427 \begin_layout Plain Layout
8428 \begin_inset Formula $\to$
8438 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
8441 \begin_layout Plain Layout
8449 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
8452 \begin_layout Plain Layout
8453 \begin_inset Formula $\Rightarrow$
8463 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
8466 \begin_layout Plain Layout
8474 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
8477 \begin_layout Plain Layout
8478 \begin_inset Formula $\longrightarrow$
8488 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
8491 \begin_layout Plain Layout
8499 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
8502 \begin_layout Plain Layout
8503 \begin_inset Formula $\Longrightarrow$
8513 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
8516 \begin_layout Plain Layout
8524 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
8527 \begin_layout Plain Layout
8528 \begin_inset Formula $\rightharpoonup$
8538 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
8541 \begin_layout Plain Layout
8549 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
8552 \begin_layout Plain Layout
8553 \begin_inset Formula $\rightharpoondown$
8563 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
8566 \begin_layout Plain Layout
8574 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
8577 \begin_layout Plain Layout
8578 \begin_inset Formula $\hookrightarrow$
8592 \begin_inset space \hfill{}
8598 \begin_layout Standard
8599 \begin_inset space \hfill{}
8603 \begin_inset Tabular
8604 <lyxtabular version="3" rows="6" columns="2">
8605 <features tabularvalignment="middle">
8606 <column alignment="center" valignment="top" width="0pt">
8607 <column alignment="center" valignment="top" width="0pt">
8609 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
8612 \begin_layout Plain Layout
8618 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
8621 \begin_layout Plain Layout
8629 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
8632 \begin_layout Plain Layout
8640 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
8643 \begin_layout Plain Layout
8644 \begin_inset Formula $\leftrightarrow$
8654 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
8657 \begin_layout Plain Layout
8665 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
8668 \begin_layout Plain Layout
8669 \begin_inset Formula $\Leftrightarrow$
8679 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
8682 \begin_layout Plain Layout
8690 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
8693 \begin_layout Plain Layout
8694 \begin_inset Formula $\longleftrightarrow$
8704 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
8707 \begin_layout Plain Layout
8715 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
8718 \begin_layout Plain Layout
8719 \begin_inset Formula $\Longleftrightarrow$
8729 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
8732 \begin_layout Plain Layout
8740 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
8743 \begin_layout Plain Layout
8744 \begin_inset Formula $\rightleftharpoons$
8758 \begin_inset space \hspace{}
8763 \begin_inset space \hfill{}
8767 \begin_inset Tabular
8768 <lyxtabular version="3" rows="5" columns="2">
8769 <features tabularvalignment="middle">
8770 <column alignment="center" valignment="top" width="0pt">
8771 <column alignment="center" valignment="top" width="0pt">
8773 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
8776 \begin_layout Plain Layout
8782 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
8785 \begin_layout Plain Layout
8793 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
8796 \begin_layout Plain Layout
8804 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
8807 \begin_layout Plain Layout
8808 \begin_inset Formula $\mapsto$
8818 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
8821 \begin_layout Plain Layout
8829 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
8832 \begin_layout Plain Layout
8833 \begin_inset Formula $\longmapsto$
8843 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
8846 \begin_layout Plain Layout
8854 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
8857 \begin_layout Plain Layout
8858 \begin_inset Formula $\leadsto$
8868 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
8871 \begin_layout Plain Layout
8879 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
8882 \begin_layout Plain Layout
8883 \begin_inset Formula $\dasharrow$
8897 \begin_inset space \hfill{}
8903 \begin_layout Standard
8904 \begin_inset VSpace medskip
8907 Arrows used as accent like e.
8908 \begin_inset space \thinspace{}
8912 \begin_inset space \space{}
8915 vector arrows are listed in
8916 \begin_inset CommandInset ref
8918 reference "sec:Accents"
8925 \begin_layout Standard
8926 \begin_inset VSpace bigskip
8929 Furthermore there are the labeled arrows
8930 \begin_inset Index idx
8933 \begin_layout Plain Layout
8946 \begin_inset Index idx
8949 \begin_layout Plain Layout
8964 \begin_inset Index idx
8967 \begin_layout Plain Layout
8974 \begin_layout Plain Layout
8989 When inserting one of these commands in a formula, an arrow with two blue
8990 boxes appear where the label can be inserted.
8991 The length of the arrow adapts to the label width.
8994 \begin_layout Standard
8996 \begin_inset Tabular
8997 <lyxtabular version="3" rows="3" columns="2">
8998 <features tabularvalignment="middle">
8999 <column alignment="center" valignment="top" width="0pt">
9000 <column alignment="center" valignment="top" width="0pt">
9002 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
9005 \begin_layout Plain Layout
9011 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
9014 \begin_layout Plain Layout
9016 \begin_inset Note Note
9019 \begin_layout Plain Layout
9026 is only used as spacer.
9038 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
9041 \begin_layout Plain Layout
9048 \begin_layout Plain Layout
9058 \begin_inset Formula $\downarrow$
9062 \begin_inset Formula $\to$
9070 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
9073 \begin_layout Plain Layout
9074 \begin_inset Formula $\raisebox{5mm}{}F(a)\xleftarrow[x>0]{x=a}F(x)\raisebox{-4mm}{}$
9084 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
9087 \begin_layout Plain Layout
9094 \begin_layout Plain Layout
9104 \begin_inset Formula $\downarrow$
9108 \begin_inset Formula $\to$
9116 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
9119 \begin_layout Plain Layout
9120 \begin_inset Formula $\raisebox{5mm}{}F(x)\xrightarrow[x>0]{x=a}F(a)\raisebox{-4mm}{}$
9136 \begin_layout Subsection
9137 Vertical and diagonal Arrows
9138 \begin_inset Index idx
9141 \begin_layout Plain Layout
9148 \begin_inset Index idx
9151 \begin_layout Plain Layout
9160 \begin_layout Standard
9161 \begin_inset space \hfill{}
9165 \begin_inset Tabular
9166 <lyxtabular version="3" rows="7" columns="2">
9167 <features tabularvalignment="middle">
9168 <column alignment="center" valignment="top" width="0pt">
9169 <column alignment="center" valignment="top" width="0pt">
9171 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
9174 \begin_layout Plain Layout
9180 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
9183 \begin_layout Plain Layout
9191 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
9194 \begin_layout Plain Layout
9202 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
9205 \begin_layout Plain Layout
9206 \begin_inset Formula $\uparrow$
9216 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
9219 \begin_layout Plain Layout
9227 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
9230 \begin_layout Plain Layout
9231 \begin_inset Formula $\Uparrow$
9241 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
9244 \begin_layout Plain Layout
9252 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
9255 \begin_layout Plain Layout
9256 \begin_inset Formula $\updownarrow$
9266 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
9269 \begin_layout Plain Layout
9277 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
9280 \begin_layout Plain Layout
9281 \begin_inset Formula $\Updownarrow$
9291 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
9294 \begin_layout Plain Layout
9302 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
9305 \begin_layout Plain Layout
9306 \begin_inset Formula $\Downarrow$
9316 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
9319 \begin_layout Plain Layout
9327 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
9330 \begin_layout Plain Layout
9331 \begin_inset Formula $\downarrow$
9345 \begin_inset space \hfill{}
9349 \begin_inset Tabular
9350 <lyxtabular version="3" rows="5" columns="2">
9351 <features tabularvalignment="middle">
9352 <column alignment="center" valignment="top" width="0pt">
9353 <column alignment="center" valignment="top" width="0pt">
9355 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
9358 \begin_layout Plain Layout
9364 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
9367 \begin_layout Plain Layout
9375 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
9378 \begin_layout Plain Layout
9386 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
9389 \begin_layout Plain Layout
9390 \begin_inset Formula $\nearrow$
9400 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
9403 \begin_layout Plain Layout
9411 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
9414 \begin_layout Plain Layout
9415 \begin_inset Formula $\searrow$
9425 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
9428 \begin_layout Plain Layout
9436 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
9439 \begin_layout Plain Layout
9440 \begin_inset Formula $\swarrow$
9450 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
9453 \begin_layout Plain Layout
9461 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
9464 \begin_layout Plain Layout
9465 \begin_inset Formula $\nwarrow$
9479 \begin_inset space \hfill{}
9485 \begin_layout Standard
9486 \begin_inset VSpace medskip
9489 Vertical arrows can be used also as delimiter together with the commands
9491 \begin_inset CommandInset ref
9493 reference "sub:Manual-Bracket-Size"
9498 \begin_inset CommandInset ref
9500 reference "sub:Automatic-Bracket-Size"
9507 \begin_layout Section
9509 \begin_inset CommandInset label
9516 \begin_inset Index idx
9519 \begin_layout Plain Layout
9528 \begin_layout Standard
9529 Accents can be inserted via the math toolbar button
9530 \begin_inset Graphics
9531 filename ../images/math/hat.png
9536 or the commands listed in the following subsections.
9539 \begin_layout Subsection
9540 Accents for one Character
9544 \begin_layout Plain Layout
9557 \begin_layout Plain Layout
9559 \begin_inset CommandInset ref
9561 reference "sub:Accents-in-Text"
9574 \begin_layout Plain Layout
9582 \begin_inset Note Note
9585 \begin_layout Plain Layout
9592 is used to avoid that the footnote appears in the PDF-bookmark.
9595 \begin_layout Plain Layout
9603 \begin_inset CommandInset ref
9605 reference "sub:Formulas-in-Section"
9615 \begin_inset CommandInset label
9617 name "sub:Accents-for-one"
9622 \begin_inset Index idx
9625 \begin_layout Plain Layout
9626 Accents ! for one character
9634 \begin_layout Standard
9635 \begin_inset space \hfill{}
9639 \begin_inset Tabular
9640 <lyxtabular version="3" rows="8" columns="2">
9641 <features tabularvalignment="middle">
9642 <column alignment="center" valignment="top" width="0pt">
9643 <column alignment="center" valignment="top" width="0pt">
9645 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
9648 \begin_layout Plain Layout
9654 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
9657 \begin_layout Plain Layout
9659 \begin_inset Note Note
9662 \begin_layout Plain Layout
9669 is only used as spacer.
9681 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
9684 \begin_layout Plain Layout
9691 \begin_layout Plain Layout
9705 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
9708 \begin_layout Plain Layout
9709 \begin_inset Formula $\raisebox{5mm}{}\dot{A}$
9719 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
9722 \begin_layout Plain Layout
9729 \begin_layout Plain Layout
9743 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
9746 \begin_layout Plain Layout
9747 \begin_inset Formula $\raisebox{5mm}{}\ddot{A}$
9757 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
9760 \begin_layout Plain Layout
9767 \begin_layout Plain Layout
9781 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
9784 \begin_layout Plain Layout
9785 \begin_inset Formula $\raisebox{5mm}{}\dddot{A}$
9795 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
9798 \begin_layout Plain Layout
9805 \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 $\raisebox{5mm}{}\ddddot{A}$
9833 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
9836 \begin_layout Plain Layout
9843 \begin_layout Plain Layout
9853 \begin_inset Index idx
9856 \begin_layout Plain Layout
9867 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
9870 \begin_layout Plain Layout
9871 \begin_inset Formula $\raisebox{5mm}{}\vec{A}$
9881 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
9884 \begin_layout Plain Layout
9891 \begin_layout Plain Layout
9905 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
9908 \begin_layout Plain Layout
9909 \begin_inset Formula $\raisebox{5mm}{}\bar{A}$
9919 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
9922 \begin_layout Plain Layout
9929 \begin_layout Plain Layout
9943 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
9946 \begin_layout Plain Layout
9947 \begin_inset Formula $\raisebox{5mm}{}\mathring{A}$
9961 \begin_inset space \hfill{}
9965 \begin_inset Tabular
9966 <lyxtabular version="3" rows="7" columns="2">
9967 <features tabularvalignment="middle">
9968 <column alignment="center" valignment="top" width="0pt">
9969 <column alignment="center" valignment="top" width="0pt">
9971 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
9974 \begin_layout Plain Layout
9980 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
9983 \begin_layout Plain Layout
9991 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
9994 \begin_layout Plain Layout
10001 \begin_layout Plain Layout
10015 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
10018 \begin_layout Plain Layout
10019 \begin_inset Formula $\raisebox{5mm}{}\tilde{A}$
10029 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
10032 \begin_layout Plain Layout
10039 \begin_layout Plain Layout
10053 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
10056 \begin_layout Plain Layout
10057 \begin_inset Formula $\raisebox{5mm}{}\hat{A}$
10067 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
10070 \begin_layout Plain Layout
10077 \begin_layout Plain Layout
10091 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
10094 \begin_layout Plain Layout
10095 \begin_inset Formula $\raisebox{5mm}{}\check{A}$
10105 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
10108 \begin_layout Plain Layout
10115 \begin_layout Plain Layout
10129 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
10132 \begin_layout Plain Layout
10133 \begin_inset Formula $\raisebox{5mm}{}\acute{A}$
10143 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
10146 \begin_layout Plain Layout
10153 \begin_layout Plain Layout
10167 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
10170 \begin_layout Plain Layout
10171 \begin_inset Formula $\raisebox{5mm}{}\grave{A}$
10181 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
10184 \begin_layout Plain Layout
10191 \begin_layout Plain Layout
10205 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
10208 \begin_layout Plain Layout
10209 \begin_inset Formula $\raisebox{5mm}{}\breve{A}$
10223 \begin_inset space \hfill{}
10229 \begin_layout Standard
10230 \begin_inset VSpace bigskip
10236 \begin_layout Standard
10237 You can directly insert accents like é to formulas.
10238 LyX will transform them to the corresponding accent command.
10240 \begin_inset Index idx
10243 \begin_layout Plain Layout
10249 it is better to insert a quotation mark before the vowel.
10250 These two characters are then treated by LaTeX as
10254 character when the formula part with the umlaut is marked as German.
10262 \begin_inset Quotes eld
10266 \begin_inset Quotes erd
10269 umlauts are created as demonstrated in the following example:
10272 \begin_layout Standard
10273 \begin_inset VSpace -2mm
10279 \begin_layout Standard
10281 \begin_inset Tabular
10282 <lyxtabular version="3" rows="3" columns="2">
10283 <features tabularvalignment="middle">
10284 <column alignment="center" valignment="top" width="0">
10285 <column alignment="center" valignment="top" width="0">
10287 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
10290 \begin_layout Plain Layout
10296 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
10299 \begin_layout Plain Layout
10301 \begin_inset Note Note
10304 \begin_layout Plain Layout
10312 \begin_inset space \thinspace{}
10315 pt space are only used as spacer.
10327 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
10330 \begin_layout Plain Layout
10333 \begin_inset Quotes grd
10341 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
10344 \begin_layout Plain Layout
10345 \begin_inset space \hspace{}
10352 \begin_inset Formula $"i$
10362 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
10365 \begin_layout Plain Layout
10372 \begin_layout Plain Layout
10386 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
10389 \begin_layout Plain Layout
10390 \begin_inset Formula $\raisebox{5mm}{}\ddot{i}$
10406 \begin_layout Standard
10407 Another advantage to
10413 is that umlauts can directly be converted to mathematical text because
10414 the accent commands above are
10420 in mathematical text
10423 To convert an accented character to mathematical text, only the character
10424 under the accent may be converted.
10425 This applies also for all other conversions, e.
10426 \begin_inset space \thinspace{}
10430 \begin_inset space \space{}
10436 \begin_layout Standard
10437 In mathematical text, umlauts and other accented characters can directly
10441 \begin_layout Subsection
10442 Accents for Operators
10443 \begin_inset Index idx
10446 \begin_layout Plain Layout
10447 Accents ! for operators
10455 \begin_layout Standard
10463 \begin_inset Index idx
10466 \begin_layout Plain Layout
10481 \begin_inset Index idx
10484 \begin_layout Plain Layout
10492 characters can be placed above or below an operator, respectively, to accent
10501 \begin_inset Index idx
10504 \begin_layout Plain Layout
10512 characters can be set before and behind an operator.
10513 The command scheme is:
10516 \begin_layout Standard
10532 \begin_layout Standard
10539 must always be before the operator that should be accented.
10540 You can accent with several characters and even with other operators and
10548 for example only characters behind an operator, write nothing between the
10549 first braces but don't omit the braces.
10552 \begin_layout Standard
10553 For example the command
10558 \begin_inset Formula $\to$
10568 \begin_inset Formula $\to$
10577 \begin_layout Plain Layout
10593 \begin_inset Formula
10595 \sideset{}{'}\sum_{k=1}^{n}
10603 \begin_layout Standard
10612 \begin_layout Plain Layout
10627 \begin_layout Plain Layout
10639 \begin_inset Formula $\uparrow$
10647 \begin_inset Formula
10649 \overset{a}{\maltese}
10654 As seen in the last example, with
10666 also symbols and characters can be accented; with
10672 this is not possible.
10675 \begin_layout Subsection
10676 Accents for several Characters
10677 \begin_inset Index idx
10680 \begin_layout Plain Layout
10681 Accents ! for several characters
10689 \begin_layout Standard
10690 \begin_inset space \hfill{}
10694 \begin_inset Tabular
10695 <lyxtabular version="3" rows="5" columns="2">
10696 <features tabularvalignment="middle">
10697 <column alignment="center" valignment="top" width="0pt">
10698 <column alignment="center" valignment="top" width="0pt">
10700 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
10703 \begin_layout Plain Layout
10709 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
10712 \begin_layout Plain Layout
10714 \begin_inset Note Note
10717 \begin_layout Plain Layout
10724 is only used as spacer.
10736 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
10739 \begin_layout Plain Layout
10746 \begin_layout Plain Layout
10760 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
10763 \begin_layout Plain Layout
10764 \begin_inset Formula $\raisebox{6mm}{}\overleftarrow{A=B}\raisebox{-2mm}{}$
10774 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
10777 \begin_layout Plain Layout
10784 \begin_layout Plain Layout
10798 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
10801 \begin_layout Plain Layout
10802 \begin_inset Formula $\raisebox{5mm}{}\underleftarrow{A=B}\raisebox{-3mm}{}$
10812 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
10815 \begin_layout Plain Layout
10822 \begin_layout Plain Layout
10836 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
10839 \begin_layout Plain Layout
10840 \begin_inset Formula $\raisebox{6mm}{}\overleftrightarrow{A=B}\raisebox{-2mm}{}$
10850 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
10853 \begin_layout Plain Layout
10856 underleftrightarrow
10860 \begin_layout Plain Layout
10874 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
10877 \begin_layout Plain Layout
10878 \begin_inset Formula $\raisebox{5mm}{}\underleftrightarrow{A=B}\raisebox{-3mm}{}$
10892 \begin_inset space \hfill{}
10896 \begin_inset Tabular
10897 <lyxtabular version="3" rows="5" columns="2">
10898 <features tabularvalignment="middle">
10899 <column alignment="center" valignment="top" width="0pt">
10900 <column alignment="center" valignment="top" width="0pt">
10902 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
10905 \begin_layout Plain Layout
10911 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
10914 \begin_layout Plain Layout
10922 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
10925 \begin_layout Plain Layout
10932 \begin_layout Plain Layout
10946 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
10949 \begin_layout Plain Layout
10950 \begin_inset Formula $\raisebox{6mm}{}\overrightarrow{A=B}\raisebox{-2mm}{}$
10960 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
10963 \begin_layout Plain Layout
10970 \begin_layout Plain Layout
10984 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
10987 \begin_layout Plain Layout
10988 \begin_inset Formula $\raisebox{5mm}{}\underrightarrow{A=B}\raisebox{-3mm}{}$
10998 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
11001 \begin_layout Plain Layout
11008 \begin_layout Plain Layout
11022 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
11025 \begin_layout Plain Layout
11026 \begin_inset Formula $\raisebox{6mm}{}\widetilde{A=B}\raisebox{-2mm}{}$
11036 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
11039 \begin_layout Plain Layout
11046 \begin_layout Plain Layout
11060 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
11063 \begin_layout Plain Layout
11064 \begin_inset Formula $\raisebox{6mm}{}\widehat{A=B}\raisebox{-2mm}{}$
11078 \begin_inset space \hfill{}
11084 \begin_layout Standard
11085 \begin_inset VSpace medskip
11088 With these commands as many characters as you like can be accented.
11101 will only be set in the output with a length of three characters, as shown
11102 in the following example:
11103 \begin_inset Formula
11105 \widetilde{A+B=C-D}
11113 \begin_layout Standard
11121 \begin_inset Index idx
11124 \begin_layout Plain Layout
11139 \begin_inset Index idx
11142 \begin_layout Plain Layout
11150 described in the previous subsection it is also possible to accent several
11160 \begin_layout Plain Layout
11170 \begin_inset Formula $\downarrow$
11176 \begin_inset Formula
11178 \underset{***}{A=B}
11186 \begin_layout Section
11188 \begin_inset CommandInset label
11195 \begin_inset Index idx
11198 \begin_layout Plain Layout
11207 \begin_layout Subsection
11209 \begin_inset CommandInset label
11211 name "sub:Predefined-Space"
11216 \begin_inset Index idx
11219 \begin_layout Plain Layout
11220 Space ! horizontal ! predefined
11228 \begin_layout Standard
11229 Sometimes it is necessary to insert horizontal space to a formula.
11230 This is done by inserting a protected space (shortcut
11233 arg "space-insert protected"
11238 \begin_inset Quotes eld
11247 \begin_layout Plain Layout
11259 \begin_inset Quotes erd
11262 appears and by pressing
11266 several times one can select one of eight different space sizes.
11267 The spaces can also be inserted using the math toolbar button
11268 \begin_inset Graphics
11269 filename ../images/math/space.png
11274 or special commands.
11275 Independent from the inserted command, one can select the size again by
11283 \begin_layout Standard
11286 \begin_inset VSpace -5mm
11290 \begin_inset Tabular
11291 <lyxtabular version="3" rows="3" columns="7">
11292 <features tabularvalignment="middle">
11293 <column alignment="center" valignment="middle" width="6.8cm">
11294 <column alignment="center" valignment="top" width="0">
11295 <column alignment="center" valignment="top" width="0">
11296 <column alignment="center" valignment="top" width="0">
11297 <column alignment="center" valignment="top" width="0">
11298 <column alignment="center" valignment="top" width="0">
11299 <column alignment="center" valignment="top" width="0">
11301 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
11304 \begin_layout Plain Layout
11310 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
11313 \begin_layout Plain Layout
11321 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
11324 \begin_layout Plain Layout
11332 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
11335 \begin_layout Plain Layout
11343 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
11346 \begin_layout Plain Layout
11354 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
11357 \begin_layout Plain Layout
11365 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
11368 \begin_layout Plain Layout
11378 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
11381 \begin_layout Plain Layout
11386 keystrokes after inserting the protected space
11391 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
11394 \begin_layout Plain Layout
11400 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
11403 \begin_layout Plain Layout
11409 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
11412 \begin_layout Plain Layout
11418 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
11421 \begin_layout Plain Layout
11427 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
11430 \begin_layout Plain Layout
11436 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
11439 \begin_layout Plain Layout
11447 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
11450 \begin_layout Plain Layout
11456 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
11459 \begin_layout Plain Layout
11460 \begin_inset Formula $A\, B$
11468 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
11471 \begin_layout Plain Layout
11472 \begin_inset Formula $A\: B$
11480 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
11483 \begin_layout Plain Layout
11484 \begin_inset Formula $A\; B$
11492 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
11495 \begin_layout Plain Layout
11496 \begin_inset Formula $A\quad B$
11504 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
11507 \begin_layout Plain Layout
11508 \begin_inset Formula $A\qquad B$
11516 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
11519 \begin_layout Plain Layout
11520 \begin_inset Formula $A\! B$
11536 \begin_layout Standard
11537 The last size seem to produce no space.
11538 It is displayed red in LyX contrary to the other sizes, because it is a
11540 There are two more negative spaces:
11543 \begin_layout Standard
11545 \begin_inset Tabular
11546 <lyxtabular version="3" rows="3" columns="3">
11547 <features tabularvalignment="middle">
11548 <column alignment="center" valignment="middle" width="6.8cm">
11549 <column alignment="center" valignment="top" width="0pt">
11550 <column alignment="center" valignment="top" width="0pt">
11552 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
11555 \begin_layout Plain Layout
11561 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
11564 \begin_layout Plain Layout
11572 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
11575 \begin_layout Plain Layout
11585 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
11588 \begin_layout Plain Layout
11593 keystrokes after inserting the protected space
11598 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
11601 \begin_layout Plain Layout
11607 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
11610 \begin_layout Plain Layout
11618 <cell multicolumn="1" alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
11621 \begin_layout Plain Layout
11627 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
11630 \begin_layout Plain Layout
11631 \begin_inset Formula $A\negmedspace B$
11639 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
11642 \begin_layout Plain Layout
11643 \begin_inset Formula $A\negthickspace B$
11659 \begin_layout Standard
11660 Negative spaces can lead to characters overlapping each other.
11661 Thus they can be used to enforce ligatures, what is e.
11662 \begin_inset space \thinspace{}
11666 \begin_inset space \space{}
11669 useful for summation operators:
11672 \begin_layout Standard
11674 \begin_inset Tabular
11675 <lyxtabular version="3" rows="3" columns="2">
11676 <features tabularvalignment="middle">
11677 <column alignment="center" valignment="top" width="0">
11678 <column alignment="center" valignment="top" width="0">
11680 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
11683 \begin_layout Plain Layout
11689 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
11692 \begin_layout Plain Layout
11694 \begin_inset Note Note
11697 \begin_layout Plain Layout
11704 is only used as spacer.
11716 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
11719 \begin_layout Plain Layout
11728 \begin_layout Plain Layout
11742 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
11745 \begin_layout Plain Layout
11746 \begin_inset Formula $\raisebox{4.5mm}{}\sum\sum f_{kl}\raisebox{-2.5mm}{}$
11756 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
11759 \begin_layout Plain Layout
11770 \begin_layout Plain Layout
11784 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
11787 \begin_layout Plain Layout
11788 \begin_inset Formula $\raisebox{4.5mm}{}\sum\negmedspace\sum f_{kl}\raisebox{-2.5mm}{}$
11804 \begin_layout Standard
11805 Relations like for example equal signs, are always surrounded by space.
11806 To suppress this, the equal sign is placed into a TeX-brace.
11807 The following example demonstrates this:
11810 \begin_layout Standard
11812 \begin_inset Tabular
11813 <lyxtabular version="3" rows="2" columns="2">
11814 <features tabularvalignment="middle">
11815 <column alignment="center" valignment="top" width="0pt">
11816 <column alignment="center" valignment="top" width="0pt">
11818 <cell alignment="center" valignment="top" usebox="none">
11821 \begin_layout Plain Layout
11827 <cell alignment="center" valignment="top" usebox="none">
11830 \begin_layout Plain Layout
11831 \begin_inset Formula $A=B$
11841 <cell alignment="center" valignment="top" usebox="none">
11844 \begin_layout Plain Layout
11845 \begin_inset Note Note
11848 \begin_layout Plain Layout
11855 is only used as spacer.
11861 \begin_inset Formula $\raisebox{5mm}{}$
11864 equation without space
11869 <cell multicolumn="1" alignment="center" valignment="top" usebox="none">
11872 \begin_layout Plain Layout
11873 \begin_inset Formula $A{=}B$
11889 \begin_layout Standard
11891 The command for the last formula is:
11896 \begin_inset Formula $\to$
11902 \begin_layout Standard
11903 \begin_inset VSpace bigskip
11906 Spaces are needed for physical units, because the space between the value
11907 and the unit is the smallest one and not a normal space.
11908 For units in text, the smallest space is inserted via the menu
11910 Insert\SpecialChar \menuseparator
11911 Formatting\SpecialChar \menuseparator
11913 \begin_inset space ~
11921 arg "space-insert thin"
11927 \begin_layout Standard
11928 An example to visualize the difference:
11931 \begin_layout Standard
11932 \begin_inset Tabular
11933 <lyxtabular version="3" rows="2" columns="2">
11934 <features tabularvalignment="middle">
11935 <column alignment="left" valignment="top" width="0">
11936 <column alignment="left" valignment="top" width="0">
11938 <cell alignment="center" valignment="top" usebox="none">
11941 \begin_layout Plain Layout
11943 \begin_inset Formula $\cdot$
11951 <cell alignment="center" valignment="top" usebox="none">
11954 \begin_layout Plain Layout
11955 space between value and unit
11962 <cell alignment="center" valignment="top" usebox="none">
11965 \begin_layout Plain Layout
11967 \begin_inset space \thinspace{}
11971 \begin_inset Formula $\cdot$
11979 <cell alignment="center" valignment="top" usebox="none">
11982 \begin_layout Plain Layout
11983 smallest space between value and unit
11996 \begin_layout Subsection
12001 \begin_layout Plain Layout
12014 \begin_layout Plain Layout
12015 for vertical space in formulas see
12016 \begin_inset CommandInset ref
12018 reference "sub:Line-Separation"
12031 \begin_layout Plain Layout
12039 \begin_inset Note Note
12042 \begin_layout Plain Layout
12045 texorpdfstring is used to avoid that the footnote appears in the PDF-bookmark.
12048 \begin_layout Plain Layout
12051 texorpdfstring is in section
12052 \begin_inset CommandInset ref
12054 reference "sub:Formulas-in-Section"
12064 \begin_inset CommandInset label
12066 name "sub:Variable-Space"
12071 \begin_inset Index idx
12074 \begin_layout Plain Layout
12075 Space ! horizontal ! variable
12083 \begin_layout Standard
12084 Space with a defined length can be inserted with the command
12091 \begin_inset Index idx
12094 \begin_layout Plain Layout
12104 \begin_inset Quotes eld
12113 \begin_layout Plain Layout
12125 \begin_inset Quotes erd
12129 The length can be specified by left-clicking on the
12130 \begin_inset Quotes eld
12139 \begin_layout Plain Layout
12151 \begin_inset Quotes erd
12155 The length may also be negative.
12156 To insert so many space that the formula uses all available space, the
12164 \begin_inset Index idx
12167 \begin_layout Plain Layout
12178 \begin_layout Standard
12179 \begin_inset VSpace -1mm
12185 \begin_layout Standard
12187 \begin_inset Tabular
12188 <lyxtabular version="3" rows="4" columns="2">
12189 <features tabularvalignment="middle">
12190 <column alignment="center" valignment="top" width="0">
12191 <column alignment="center" valignment="top" width="0">
12193 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
12196 \begin_layout Plain Layout
12204 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
12207 \begin_layout Plain Layout
12215 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
12218 \begin_layout Plain Layout
12225 \begin_layout Plain Layout
12235 \begin_inset Formula $\to$
12241 \begin_inset space \thinspace{}
12249 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
12252 \begin_layout Plain Layout
12253 \begin_inset Formula $A=B\hspace{3cm}A\not=C$
12263 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
12266 \begin_layout Plain Layout
12273 \begin_layout Plain Layout
12283 \begin_inset Formula $\to$
12289 \begin_inset space \thinspace{}
12297 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
12300 \begin_layout Plain Layout
12301 \begin_inset Formula $A\hspace{-1mm}A\not=A$
12311 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
12314 \begin_layout Plain Layout
12321 \begin_layout Plain Layout
12335 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
12338 \begin_layout Plain Layout
12339 \begin_inset Formula $A=A\hfill B=B$
12355 \begin_layout Standard
12356 In the last example the available space is given by the longest column entry
12358 In an inline formula the space depends on the length of the line in which
12366 Thus, when the line uses the full width, no space will be created.
12373 only has an effect on displayed formulas when the formula style
12378 (Formula styles are explained in
12379 \begin_inset CommandInset ref
12381 reference "sec:Formula-Styles"
12388 \begin_layout Standard
12395 , there are the commands
12407 that fill the space with a pattern, see
12408 \begin_inset CommandInset ref
12410 reference "sub:Ellipses"
12417 \begin_layout Standard
12418 For text, variable space can be inserted via the menu
12420 Insert\SpecialChar \menuseparator
12421 Formatting\SpecialChar \menuseparator
12423 \begin_inset space ~
12431 \begin_layout Standard
12432 This is a line with
12433 \begin_inset space \hspace{}
12438 \begin_inset space \thinspace{}
12444 \begin_layout Standard
12445 This is a line with
12446 \begin_inset space \hfill{}
12452 \begin_layout Subsection
12453 Space besides inline Formulas
12454 \begin_inset Index idx
12457 \begin_layout Plain Layout
12458 Space ! besides inline formulas
12466 \begin_layout Standard
12467 The space that surrounds inline formulas can be adjusted with the length
12475 \begin_inset Index idx
12478 \begin_layout Plain Layout
12487 The value of a length is set with the command
12494 \begin_inset Index idx
12497 \begin_layout Plain Layout
12505 that has the following scheme:
12508 \begin_layout Standard
12513 setlength{length name}{value}
12516 \begin_layout Standard
12524 \begin_inset space \thinspace{}
12530 \begin_layout Standard
12540 \begin_layout Standard
12541 is inserted in TeX-mode.
12543 \begin_inset space \thinspace{}
12546 mm space will now be set around all inline formulas:
12550 \begin_layout Plain Layout
12564 \begin_layout Standard
12565 This is a line with an inline formula
12566 \begin_inset Formula $A=B$
12570 \begin_inset space \thinspace{}
12573 mm surrounding space.
12577 \begin_layout Plain Layout
12591 \begin_layout Standard
12592 To return to the predefined value,
12598 is set to the value 0
12599 \begin_inset space \thinspace{}
12605 \begin_layout Section
12607 \begin_inset Index idx
12610 \begin_layout Plain Layout
12617 \begin_inset Index idx
12620 \begin_layout Plain Layout
12625 \begin_layout Plain Layout
12636 \begin_layout Plain Layout
12651 \begin_layout Standard
12652 Boxes for text are described in chapter
12659 \begin_inset space ~
12667 \begin_layout Subsection
12669 \begin_inset CommandInset label
12671 name "sub:Boxes-with-Frame"
12676 \begin_inset Index idx
12679 \begin_layout Plain Layout
12688 \begin_layout Standard
12689 It is possible to frame formulas or parts of it with the commands
12696 \begin_inset Index idx
12699 \begin_layout Plain Layout
12714 \begin_inset Index idx
12717 \begin_layout Plain Layout
12728 \begin_layout Standard
12729 When one of these commands is inserted to a formula, a blue box appears
12730 within a frame to enter formula parts.
12737 an additional formula has to be created by
12741 within this box, because the box content will otherwise be treated as mathemati
12749 is used, a new formula is automatically created inside the frame.
12752 \begin_layout Standard
12759 is not suitable to frame displayed formulas because the formula will always
12760 be set in the size of the text.
12767 is in contrary not suitable to frame inline formulas, because the formula
12768 will always be set in the size of a displayed formula.
12771 \begin_layout Standard
12778 there is the command
12785 \begin_inset Index idx
12788 \begin_layout Plain Layout
12796 where additionally the frame width and the alignment can be specified.
12803 is used in the following scheme:
12806 \begin_layout Standard
12811 framebox[frame width][position]{box content}
12814 \begin_layout Standard
12815 The position can either be
12832 right aligns the formula in the box.
12833 When no position is given, the formula will be centered.
12834 \begin_inset Newline newline
12837 Is no width given, also no position can be given.
12838 In this case the frame width is adjusted to the box content like for
12847 \begin_layout Standard
12854 is inserted, a box appears containing three blue boxes.
12855 The first two boxes are surrounded by brackets and denote the two optional
12857 The third box is for formula parts like for
12866 \begin_layout Standard
12868 \begin_inset Tabular
12869 <lyxtabular version="3" rows="5" columns="2">
12870 <features tabularvalignment="middle">
12871 <column alignment="center" valignment="top" width="0">
12872 <column alignment="center" valignment="top" width="0">
12874 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
12877 \begin_layout Plain Layout
12883 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
12886 \begin_layout Plain Layout
12888 \begin_inset Note Note
12891 \begin_layout Plain Layout
12898 is only used as spacer.
12910 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
12913 \begin_layout Plain Layout
12920 \begin_layout Plain Layout
12939 \begin_layout Plain Layout
12953 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
12956 \begin_layout Plain Layout
12957 \begin_inset Formula $\raisebox{6mm}{}\fbox{\ensuremath{\int A=B}}\raisebox{-4mm}{}$
12967 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
12970 \begin_layout Plain Layout
12977 \begin_layout Plain Layout
12992 \begin_layout Plain Layout
13006 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
13009 \begin_layout Plain Layout
13010 \begin_inset Formula $\raisebox{8.5mm}{}\boxed{\int A=B}\raisebox{-6.5mm}{}$
13020 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
13023 \begin_layout Plain Layout
13030 \begin_layout Plain Layout
13044 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
13047 \begin_layout Plain Layout
13048 \begin_inset Formula $\raisebox{6mm}{}A+\fbox{B}\raisebox{-3mm}{}$
13058 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
13061 \begin_layout Plain Layout
13068 \begin_layout Plain Layout
13078 \begin_inset Formula $\to$
13082 \begin_inset Formula $\to$
13095 \begin_layout Plain Layout
13105 \begin_inset Formula $\downarrow$
13113 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
13116 \begin_layout Plain Layout
13117 \begin_inset Formula $\raisebox{6mm}{}$
13121 \begin_inset Formula $\framebox[20mm][]{\ensuremath{\frac{A}{B}}}$
13125 \begin_inset Formula $\raisebox{-4mm}{}$
13141 \begin_layout Standard
13142 The frame thickness can also be adjusted.
13143 To do this the following commands have to be inserted in TeX-mode before
13147 \begin_layout Standard
13157 \begin_inset Quotes eld
13161 \begin_inset Quotes erd
13175 \begin_inset Quotes eld
13179 \begin_inset Quotes erd
13185 \begin_layout Standard
13186 \begin_inset Quotes eld
13190 \begin_inset Quotes erd
13193 specifies the minimal distance between the frame and the first character
13195 An example for this is the following framed formula:
13199 \begin_layout Plain Layout
13211 \begin_inset Formula
13218 Before this formula the commands
13221 \begin_layout Standard
13243 \begin_layout Standard
13244 were inserted in TeX-mode.
13245 The given values are used for all following boxes.
13248 \begin_layout Standard
13249 To return to the standard frame size, the command
13252 \begin_layout Standard
13277 \begin_layout Plain Layout
13291 \begin_layout Standard
13292 is inserted in TeX-mode before the next formula.
13295 \begin_layout Subsection
13296 Boxes without Frame
13297 \begin_inset CommandInset label
13299 name "sub:Boxes-without-Frame"
13304 \begin_inset Index idx
13307 \begin_layout Plain Layout
13308 Boxes ! without frame
13316 \begin_layout Standard
13317 For boxes without a frame there are the following box commands:
13324 \begin_inset Index idx
13327 \begin_layout Plain Layout
13342 \begin_inset Index idx
13345 \begin_layout Plain Layout
13360 \begin_inset Index idx
13363 \begin_layout Plain Layout
13374 \begin_layout Standard
13381 a box can be super- or subscripted.
13382 But in contrary to normal super- and subscripting, the characters in the
13383 box keep their font size.
13390 is used in the following scheme:
13393 \begin_layout Standard
13398 raisebox{height}{box content}
13401 \begin_layout Standard
13402 When the box should contain a formula, an extra formula is needed like for
13413 \begin_inset Note Greyedout
13416 \begin_layout Plain Layout
13427 this extra formula is created by pressing
13431 twice instead of once because LyX doesn't yet support
13445 \begin_layout Standard
13447 \begin_inset Tabular
13448 <lyxtabular version="3" rows="4" columns="2">
13449 <features tabularvalignment="middle">
13450 <column alignment="center" valignment="top" width="0">
13451 <column alignment="center" valignment="top" width="0">
13453 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
13456 \begin_layout Plain Layout
13462 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
13465 \begin_layout Plain Layout
13473 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
13476 \begin_layout Plain Layout
13480 \begin_inset Formula $\to$
13486 \begin_inset Formula $\to$
13494 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
13497 \begin_layout Plain Layout
13498 \begin_inset Formula $H\raisebox{2mm}{al}lo$
13508 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
13511 \begin_layout Plain Layout
13515 \begin_inset Formula $\to$
13521 \begin_inset Formula $\to$
13529 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
13532 \begin_layout Plain Layout
13533 \begin_inset Formula $H\raisebox{-2mm}{al}lo$
13543 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
13546 \begin_layout Plain Layout
13550 \begin_inset Formula $\to$
13569 \begin_layout Plain Layout
13583 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
13586 \begin_layout Plain Layout
13587 \begin_inset Formula $A=\raisebox{-2mm}{\mbox{\ensuremath{\sqrt{B}}}}$
13603 \begin_layout Standard
13628 , with the difference that there is no frame.
13631 \begin_layout Subsection
13633 \begin_inset CommandInset label
13635 name "sub:Colored-Boxes"
13640 \begin_inset Index idx
13643 \begin_layout Plain Layout
13652 \begin_layout Standard
13653 To be able to use all commands explained in this section, the LaTeX-package
13662 \begin_layout Plain Layout
13667 is part of every LaTeX standard installation.
13673 \begin_inset Index idx
13676 \begin_layout Plain Layout
13682 has to be loaded in the LaTeX-preamble with the line
13686 \begin_layout Plain Layout
13687 When text is colored somewhere in the document with a predefined color,
13688 LyX loads the LaTeX-package
13693 Thus it is possible that the package is loaded twice, but this doesn't
13700 \begin_inset Note Note
13703 \begin_layout Plain Layout
13704 To avoid that the package is loaded twice, a macro was inserted to the LaTeX-pre
13713 \begin_layout Standard
13721 \begin_layout Standard
13722 \begin_inset VSpace medskip
13725 To color boxes, the command
13732 \begin_inset Index idx
13735 \begin_layout Plain Layout
13743 is used in the following scheme:
13746 \begin_layout Standard
13751 colorbox{color}{box content}
13754 \begin_layout Standard
13755 The box content can also be a box and a
13761 can also be part of another box (see the 2nd and 3rd example).
13762 When the box should contain a formula, an extra formula has to be created,
13763 the same way as for
13773 \begin_layout Plain Layout
13774 This also applies for the command
13788 \begin_layout Standard
13789 One of the following predefined colors can be chosen:
13792 \begin_layout Standard
13826 \begin_layout Standard
13828 \begin_inset Tabular
13829 <lyxtabular version="3" rows="4" columns="2">
13830 <features tabularvalignment="middle">
13831 <column alignment="center" valignment="top" width="0">
13832 <column alignment="center" valignment="top" width="0">
13834 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
13837 \begin_layout Plain Layout
13843 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
13846 \begin_layout Plain Layout
13848 \begin_inset Note Note
13851 \begin_layout Plain Layout
13858 is only used as spacer.
13870 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
13873 \begin_layout Plain Layout
13877 \begin_inset Formula $\to$
13887 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
13890 \begin_layout Plain Layout
13891 \begin_inset Formula $\raisebox{6mm}{}\colorbox{yellow}{A=B}\raisebox{-3mm}{}$
13901 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
13904 \begin_layout Plain Layout
13908 \begin_inset Formula $\to$
13919 \begin_layout Plain Layout
13933 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
13936 \begin_layout Plain Layout
13937 \begin_inset Formula $\raisebox{6mm}{}\colorbox{green}{\fbox{A=B}}\raisebox{-3mm}{}$
13947 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
13950 \begin_layout Plain Layout
13957 \begin_layout Plain Layout
13969 \begin_inset Formula $\to$
13988 \begin_layout Plain Layout
14002 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
14005 \begin_layout Plain Layout
14006 \begin_inset Formula $\raisebox{7mm}{}\fbox{\colorbox{green}{\mbox{\ensuremath{\int C=D}}}}\raisebox{-5mm}{}$
14022 \begin_layout Standard
14029 only colors the box but not the characters in the box.
14030 To color all characters, the whole formula is highlighted and the wanted
14031 color is chosen in the
14034 \begin_inset space ~
14040 The dialog can be called with the toolbar button
14041 \begin_inset Graphics
14042 filename ../images/dialog-show_character.png
14049 Edit\SpecialChar \menuseparator
14051 \begin_inset space ~
14054 Style\SpecialChar \menuseparator
14058 The formula number has then the same color as the formula.
14059 When the formula number should get another color than the formula characters,
14060 the color must be changed within the formula.
14063 \begin_layout Standard
14067 \begin_layout Standard
14070 \begin_inset Formula
14072 \int A=B\label{eq:red}
14080 \begin_inset Formula
14082 \textcolor{red}{\int A=B}\label{eq:redgreen}
14090 \begin_layout Standard
14092 \begin_inset CommandInset ref
14098 is completely colored red.
14099 \begin_inset Newline newline
14103 \begin_inset CommandInset ref
14105 reference "eq:redgreen"
14109 was first completely colored green to set the color for the formula number.
14110 Subsequently the formula characters were colored red.
14113 \begin_layout Standard
14114 \begin_inset VSpace bigskip
14117 To color the frame different than the rest of the box, the command
14124 \begin_inset Index idx
14127 \begin_layout Plain Layout
14135 is used in the following scheme:
14138 \begin_layout Standard
14143 fcolorbox{frame color}{color}{box content}
14146 \begin_layout Standard
14153 is an extension of the command
14160 The frame width is set, like for
14183 \begin_layout Plain Layout
14195 \begin_inset Formula
14197 \fcolorbox{cyan}{magenta}{A=B}
14206 \begin_layout Plain Layout
14220 \begin_layout Standard
14221 This formula was created with the command
14222 \begin_inset Newline newline
14230 \begin_inset Formula $\to$
14236 \begin_inset Formula $\to$
14246 \begin_layout Standard
14247 \begin_inset VSpace bigskip
14250 To use other colors than the predefined ones, they have to be defined first.
14253 \begin_layout Standard
14254 One can for example define the color
14255 \begin_inset Quotes eld
14263 \begin_inset Quotes erd
14266 with the LaTeX-preamble line:
14269 \begin_layout Standard
14274 definecolor{darkgreen}{cmyk}{0.5,
14289 \begin_inset Index idx
14292 \begin_layout Plain Layout
14303 \begin_layout Standard
14308 is the color space that denotes the colors
14325 The four comma separated numbers are the portion factor for the corresponding
14326 colors of the color space.
14327 The factors can be in the range of 0
14328 \begin_inset space \thinspace{}
14332 \begin_inset space \thinspace{}
14340 also the color space
14344 can be used for definitions.
14361 , so that there are in this case three portion factors for the corresponding
14363 Furthermore there is the color space
14367 with one portion factor for the gray value.
14370 \begin_layout Standard
14371 As example a framed box with the new defined color
14375 where the characters have been colored
14380 \begin_inset Formula
14382 \colorbox{darkgreen}{\color{yellow}\boxed{\int A\,\mathrm{d}x=\frac{\sqrt[5]{B}}{\ln\left(\frac{1}{3}\right)}}}
14390 \begin_layout Standard
14391 Self-defined colors can also be used for text with the help of the command
14399 \begin_inset Index idx
14402 \begin_layout Plain Layout
14411 \begin_layout Standard
14415 \begin_layout Plain Layout
14419 textcolor{darkgreen}{
14425 \begin_inset Quotes eld
14429 \begin_inset Quotes erd
14436 \begin_layout Plain Layout
14446 \begin_layout Standard
14454 \begin_inset Index idx
14457 \begin_layout Plain Layout
14465 is used in the scheme
14469 textcolor{color}{characters to color}
14474 \begin_layout Subsection
14476 \begin_inset CommandInset label
14478 name "sub:Paragraph-Boxes"
14483 \begin_inset Index idx
14486 \begin_layout Plain Layout
14487 Boxes ! as paragraph
14495 \begin_layout Standard
14496 A box that can contain several lines and paragraphs, a so called paragraph
14497 box (parbox), can be created with the menu
14499 Insert\SpecialChar \menuseparator
14502 or the toolbar button
14503 \begin_inset Graphics
14504 filename ../images/box-insert.png
14512 \begin_layout Standard
14513 The following example shows a framed parbox in a line:
14516 \begin_layout Standard
14517 \begin_inset VSpace medskip
14521 \begin_inset Box Boxed
14531 height_special "totalheight"
14534 \begin_layout Plain Layout
14535 This is a paragraph box.
14537 \begin_inset space \thinspace{}
14540 cm long and can also contain formulas:
14541 \begin_inset Formula $\int A\,\mathrm{d}s=C$
14552 \begin_layout Standard
14553 \begin_inset VSpace medskip
14559 \begin_layout Standard
14560 Such a box is created by right-clicking on the gray box inset.
14561 A dialog pops up showing the box properties.
14575 \begin_inset space \thinspace{}
14580 Vertical Box Alignment
14585 \begin_layout Standard
14586 \begin_inset VSpace medskip
14589 In LaTeX a parbox is created with the command
14596 \begin_inset Index idx
14599 \begin_layout Plain Layout
14607 that has the following scheme:
14610 \begin_layout Standard
14615 parbox[position]{width}{box content}
14618 \begin_layout Standard
14632 for bottom means that the box is aligned within the surrounding text with
14638 for top this is done with the first line.
14639 When no position is given, the box will be vertically centered, see section
14647 \begin_inset space ~
14652 manual for examples.
14655 \begin_layout Standard
14656 \begin_inset VSpace bigskip
14659 To frame formulas completely, including the formula number, the formula
14660 must be set into a parbox.
14661 To do this, the command
14675 is inserted in TeX-mode before the formula.
14683 \begin_inset Index idx
14686 \begin_layout Plain Layout
14694 is hereby the line width set for the document.
14695 Because the frame is outside the parbox, 2
14696 \begin_inset space \thinspace{}
14699 times the frame separation and the frame thickness must be subtracted from
14701 As this is not automatically done by LyX due to a bug
14705 \begin_layout Plain Layout
14706 \begin_inset CommandInset href
14708 name "LyX-bug #4483"
14709 target "http://www.lyx.org/trac/ticket/4483"
14718 , TeX-mode has to be used.
14719 To be able to multiply and subtract in arguments, the LaTeX-package
14727 \begin_layout Plain Layout
14732 is part of every LaTeX standard installation.
14738 \begin_inset Index idx
14741 \begin_layout Plain Layout
14747 must be loaded in the LaTeX-preamble with the line
14750 \begin_layout Standard
14758 \begin_layout Standard
14759 Behind the formula both boxes are closed by entering
14764 Here is an example:
14768 \begin_layout Plain Layout
14782 \begin_layout Standard
14786 \begin_layout Plain Layout
14804 \begin_inset Formula
14806 \int A\,\mathrm{d}x=\frac{\sqrt[5]{B}}{\ln\left(\frac{1}{3}\right)}
14815 \begin_layout Plain Layout
14826 \begin_layout Plain Layout
14840 \begin_layout Standard
14841 \begin_inset VSpace medskip
14844 As a parbox is used as argument of
14850 , there is in this case no difference between
14865 \begin_layout Standard
14866 \begin_inset VSpace bigskip
14869 Paragraph boxes are very useful to comment formulas directly.
14876 is used in combination with the command
14890 \begin_inset CommandInset ref
14892 reference "sub:User-defined-Numbering"
14899 \begin_layout Standard
14900 An example of a formula commented with
14909 \begin_layout Standard
14913 \begin_layout Plain Layout
14926 This is a description.
14927 It is distinctly separated from the formula and multiline.
14931 \begin_layout Plain Layout
14943 \begin_layout Standard
14944 Such a formula must be inserted completely in TeX-mode because LyX does
14945 not yet support the command
14952 The formula is created with the following command sequence:
14955 \begin_layout Standard
14968 is inserted in TeX-mode.
14972 \begin_layout Plain Layout
14973 When the formula style
14985 can also be replaced by
14992 (formula styles see
14993 \begin_inset CommandInset ref
14995 reference "sec:Formula-Styles"
15004 Then the description follows as normal text and finally
15010 is inserted in TeX-mode.
15023 hereby create a displayed formula.
15026 \begin_layout Standard
15033 can be seen in this example that was
15034 \begin_inset Quotes eld
15038 \begin_inset Quotes erd
15041 using the mathematical textmode:
15042 \begin_inset Formula
15044 5x-7b=3b\textrm{This is a description. It is not separated from the formula ...}
15052 \begin_layout Section
15054 \begin_inset Index idx
15057 \begin_layout Plain Layout
15066 \begin_layout Subsection
15068 \begin_inset CommandInset label
15070 name "sub:Big-Operators"
15075 \begin_inset Index idx
15078 \begin_layout Plain Layout
15085 \begin_inset Index idx
15088 \begin_layout Plain Layout
15095 \begin_inset Index idx
15098 \begin_layout Plain Layout
15107 \begin_layout Standard
15108 To be able to use all integral operators listed here, the option
15110 Use esint package automatically
15112 must be set in the document settings under
15115 \begin_inset space ~
15123 \begin_layout Standard
15124 \begin_inset space \hfill{}
15128 \begin_inset Tabular
15129 <lyxtabular version="3" rows="11" columns="2">
15130 <features tabularvalignment="middle">
15131 <column alignment="center" valignment="top" width="0pt">
15132 <column alignment="center" valignment="top" width="0pt">
15134 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
15137 \begin_layout Plain Layout
15143 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
15146 \begin_layout Plain Layout
15154 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
15157 \begin_layout Plain Layout
15161 \begin_inset Index idx
15164 \begin_layout Plain Layout
15177 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
15180 \begin_layout Plain Layout
15181 \begin_inset Formula $\int$
15191 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
15194 \begin_layout Plain Layout
15202 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
15205 \begin_layout Plain Layout
15206 \begin_inset Formula $\oint$
15216 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
15219 \begin_layout Plain Layout
15227 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
15230 \begin_layout Plain Layout
15231 \begin_inset Formula $\ointctrclockwise$
15241 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
15244 \begin_layout Plain Layout
15252 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
15255 \begin_layout Plain Layout
15256 \begin_inset Formula $\ointclockwise$
15266 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
15269 \begin_layout Plain Layout
15277 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
15280 \begin_layout Plain Layout
15281 \begin_inset Formula $\sqint$
15291 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
15294 \begin_layout Plain Layout
15302 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
15305 \begin_layout Plain Layout
15307 \begin_inset Formula $\fint$
15317 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
15320 \begin_layout Plain Layout
15328 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
15331 \begin_layout Plain Layout
15333 \begin_inset Formula $\landupint$
15343 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
15346 \begin_layout Plain Layout
15354 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
15357 \begin_layout Plain Layout
15359 \begin_inset Formula $\landdownint$
15369 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
15372 \begin_layout Plain Layout
15380 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
15383 \begin_layout Plain Layout
15384 \begin_inset Formula $\bigcap$
15394 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
15397 \begin_layout Plain Layout
15405 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
15408 \begin_layout Plain Layout
15409 \begin_inset Formula $\bigcup$
15423 \begin_inset space \hfill{}
15427 \begin_inset Tabular
15428 <lyxtabular version="3" rows="11" columns="2">
15429 <features tabularvalignment="middle">
15430 <column alignment="center" valignment="top" width="0pt">
15431 <column alignment="center" valignment="top" width="0pt">
15433 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
15436 \begin_layout Plain Layout
15442 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
15445 \begin_layout Plain Layout
15453 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
15456 \begin_layout Plain Layout
15460 \begin_inset Index idx
15463 \begin_layout Plain Layout
15476 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
15479 \begin_layout Plain Layout
15480 \begin_inset Formula $\sum$
15490 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
15493 \begin_layout Plain Layout
15497 \begin_inset Index idx
15500 \begin_layout Plain Layout
15513 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
15516 \begin_layout Plain Layout
15517 \begin_inset Formula $\prod$
15527 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
15530 \begin_layout Plain Layout
15538 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
15541 \begin_layout Plain Layout
15542 \begin_inset Formula $\coprod$
15552 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
15555 \begin_layout Plain Layout
15563 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
15566 \begin_layout Plain Layout
15567 \begin_inset Formula $\bigodot$
15577 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
15580 \begin_layout Plain Layout
15588 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
15591 \begin_layout Plain Layout
15592 \begin_inset Formula $\bigotimes$
15602 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
15605 \begin_layout Plain Layout
15613 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
15616 \begin_layout Plain Layout
15617 \begin_inset Formula $\bigoplus$
15627 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
15630 \begin_layout Plain Layout
15638 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
15641 \begin_layout Plain Layout
15642 \begin_inset Formula $\bigwedge$
15652 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
15655 \begin_layout Plain Layout
15663 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
15666 \begin_layout Plain Layout
15667 \begin_inset Formula $\bigvee$
15677 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
15680 \begin_layout Plain Layout
15688 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
15691 \begin_layout Plain Layout
15692 \begin_inset Formula $\bigsqcup$
15702 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
15705 \begin_layout Plain Layout
15713 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
15716 \begin_layout Plain Layout
15717 \begin_inset Formula $\biguplus$
15731 \begin_inset space \hfill{}
15737 \begin_layout Standard
15738 All big operators can also be inserted via the math toolbar button
15739 \begin_inset Graphics
15740 filename ../images/math/intop.png
15748 \begin_layout Standard
15749 The operators are called big because they are bigger than the sometimes
15750 equal looking binary operators.
15751 All big operators can have limits as described in the next subsection.
15754 \begin_layout Standard
15755 For all integral operators there is a second version available, ending on
15773 These operators are different from
15780 \begin_inset space \space{}
15783 in the style the operator limits are displayed, see
15784 \begin_inset CommandInset ref
15786 reference "sub:Operator-Limits"
15794 \begin_layout Subsubsection*
15795 Advice for Integrals
15798 \begin_layout Standard
15803 in an integral is an operator, that therefore has to be set upright.
15804 This is done by highlighting the
15808 and using the keyboard shortcut
15818 \begin_layout Plain Layout
15824 \begin_inset CommandInset ref
15826 reference "sub:Font-Styles"
15836 Finally the smallest space is inserted before the
15840 , as this is usual for operators.
15844 \begin_layout Standard
15846 \begin_inset Formula $\int A(x)dx$
15850 \begin_inset Newline newline
15854 \begin_inset Phantom HPhantom
15857 \begin_layout Plain Layout
15864 \begin_inset Formula $\int A(x)\,\mathrm{d}x$
15870 \begin_layout Standard
15871 For multiple integrals there are the following commands:
15872 \begin_inset VSpace medskip
15878 \begin_layout Standard
15879 \begin_inset space \hfill{}
15883 \begin_inset Tabular
15884 <lyxtabular version="3" rows="4" columns="2">
15885 <features tabularvalignment="middle">
15886 <column alignment="center" valignment="top" width="0">
15887 <column alignment="center" valignment="top" width="0">
15889 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
15892 \begin_layout Plain Layout
15898 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
15901 \begin_layout Plain Layout
15903 \begin_inset Note Note
15906 \begin_layout Plain Layout
15913 is only used as spacer.
15925 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
15928 \begin_layout Plain Layout
15936 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
15939 \begin_layout Plain Layout
15940 \begin_inset Formula $\raisebox{4.5mm}{}\iint\raisebox{-2.5mm}{}$
15950 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
15953 \begin_layout Plain Layout
15961 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
15964 \begin_layout Plain Layout
15965 \begin_inset Formula $\raisebox{4.5mm}{}\oiint\raisebox{-2.5mm}{}$
15975 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
15978 \begin_layout Plain Layout
15986 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
15989 \begin_layout Plain Layout
15990 \begin_inset Formula $\raisebox{4.5mm}{}\sqiint\raisebox{-2.5mm}{}$
16004 \begin_inset space \hfill{}
16008 \begin_inset Tabular
16009 <lyxtabular version="3" rows="4" columns="2">
16010 <features tabularvalignment="middle">
16011 <column alignment="center" valignment="top" width="0">
16012 <column alignment="center" valignment="top" width="0">
16014 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
16017 \begin_layout Plain Layout
16023 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
16026 \begin_layout Plain Layout
16034 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
16037 \begin_layout Plain Layout
16045 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
16048 \begin_layout Plain Layout
16049 \begin_inset Formula $\raisebox{4.5mm}{}\iiint\raisebox{-2.5mm}{}$
16059 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
16062 \begin_layout Plain Layout
16070 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
16073 \begin_layout Plain Layout
16074 \begin_inset Formula $\raisebox{4.5mm}{}\iiiint\raisebox{-2.5mm}{}$
16084 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
16087 \begin_layout Plain Layout
16095 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
16098 \begin_layout Plain Layout
16099 \begin_inset Formula $\raisebox{4.5mm}{}\dotsint\raisebox{-2.5mm}{}$
16113 \begin_inset space \hfill{}
16119 \begin_layout Subsection
16121 \begin_inset CommandInset label
16123 name "sub:Operator-Limits"
16128 \begin_inset Index idx
16131 \begin_layout Plain Layout
16140 \begin_layout Standard
16141 Limits are created by super- and subscripts:
16144 \begin_layout Standard
16146 \begin_inset Tabular
16147 <lyxtabular version="3" rows="2" columns="2">
16148 <features tabularvalignment="middle">
16149 <column alignment="center" valignment="top" width="0pt">
16150 <column alignment="center" valignment="top" width="0pt">
16152 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
16155 \begin_layout Plain Layout
16161 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
16164 \begin_layout Plain Layout
16166 \begin_inset Note Note
16169 \begin_layout Plain Layout
16176 is only used as spacer.
16188 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
16191 \begin_layout Plain Layout
16200 \begin_layout Plain Layout
16210 \begin_inset Formula $\to$
16214 \begin_inset Formula $\to$
16222 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
16225 \begin_layout Plain Layout
16226 \begin_inset Formula $\raisebox{5mm}{}\prod_{0}^{\infty}A(x)\raisebox{-2.5mm}{}$
16242 \begin_layout Standard
16243 Limits of inline formulas are set right beside the operator.
16244 Limits in displayed formulas are set above or below the operator, except
16245 for integral limits.
16248 \begin_layout Standard
16249 To force that the limits are set beside the operator, the cursor is set
16250 directly behind the operator and the limits type is changed with the menu
16253 Edit\SpecialChar \menuseparator
16254 Math\SpecialChar \menuseparator
16273 \begin_layout Standard
16274 The default limits type is this:
16275 \begin_inset Formula
16277 \sum_{x=0}^{\infty}\frac{1}{x^{2}}
16282 This is how it looks when the limits type was changed to
16289 \begin_inset Formula
16291 \sum\nolimits _{x=0}^{\infty}\frac{1}{x^{2}}
16296 For integrals, except those ending with
16312 etc., the limits are by default set beside the operator.
16313 But for multiple integrals the limits are often set below the operator.
16314 In the following example the limits type was therefore set to
16318 and so set below the integrals:
16319 \begin_inset Formula
16321 \iiint\limits _{V}X\,\mathrm{d}V=U\label{eq:VolInt}
16329 \begin_layout Standard
16330 \begin_inset VSpace medskip
16333 To specify conditions for limits, the commands
16340 \begin_inset Index idx
16343 \begin_layout Plain Layout
16358 \begin_inset Index idx
16361 \begin_layout Plain Layout
16370 To create for example this expression
16371 \begin_inset Formula
16373 \sum_{\begin{subarray}{c}
16377 \end{subarray}}^{n}k^{-2}\label{eq:substack}
16385 \begin_layout Standard
16386 the following has to be done:
16387 \begin_inset Newline newline
16402 \begin_layout Plain Layout
16414 One is now in a blue box under the summation operator and insert there
16423 \begin_layout Plain Layout
16435 The blue box is now within a purple box and now several lines can be written
16437 A new line is created by inserting a line break (
16440 arg "newline-insert newline"
16445 \begin_inset Newline newline
16450 0<k<1000 Ctrl+Return
16451 \begin_inset Newline newline
16456 is typed in, a new box appears below for the new line.
16459 \begin_layout Standard
16460 The alignment of the lines can be changed to left aligned with the
16470 Edit\SpecialChar \menuseparator
16474 To get right alignment,
16482 \begin_layout Plain Layout
16493 is inserted at the beginning of the line.
16496 \begin_layout Standard
16509 with the difference that the lines are always centered.
16512 \begin_layout Standard
16513 \begin_inset VSpace bigskip
16517 \begin_inset CommandInset ref
16519 reference "eq:substack"
16523 there can be too much space beside an operator, because the characters
16524 following the operator are set beside the limits.
16527 \begin_layout Standard
16528 To avoid this, the following macro can be used in the LaTeX-preamble:
16531 \begin_layout Standard
16545 \begin_inset Newline newline
16557 \begin_inset Newline newline
16564 mathclapinternal #1#2{
16568 mathsurround =0pt #1{#2}$}}
16571 \begin_layout Standard
16572 This defines the command
16579 \begin_inset Index idx
16582 \begin_layout Plain Layout
16590 that sets the width of the limit to 0
16591 \begin_inset space \thinspace{}
16595 The command scheme is
16598 \begin_layout Standard
16606 \begin_layout Standard
16607 where the limit can consist of several conditions.
16610 \begin_layout Standard
16612 \begin_inset CommandInset ref
16614 reference "eq:substack"
16618 , one uses the command
16621 \begin_layout Standard
16634 \begin_layout Plain Layout
16643 0<k<1000 Ctrl+Return
16646 \begin_layout Standard
16647 to create the lower limit.
16648 The summand is now directly behind the summation operator:
16649 \begin_inset Formula
16651 \sum_{\mathclap{\substack{0<k<1000\\
16663 \begin_layout Standard
16664 \begin_inset VSpace bigskip
16667 How to use one limit for several operators is described in
16668 \begin_inset CommandInset ref
16670 reference "sub:Self-defined-Operators"
16677 \begin_layout Standard
16678 \begin_inset Newpage newpage
16684 \begin_layout Subsection
16686 \begin_inset CommandInset label
16688 name "sub:Binary-Operators"
16693 \begin_inset Index idx
16696 \begin_layout Plain Layout
16705 \begin_layout Standard
16706 Binary operators are surrounded by space when there is a character before
16708 \begin_inset VSpace medskip
16714 \begin_layout Standard
16715 \begin_inset space \hfill{}
16719 \begin_inset Tabular
16720 <lyxtabular version="3" rows="13" columns="2">
16721 <features tabularvalignment="middle">
16722 <column alignment="center" valignment="top" width="0pt">
16723 <column alignment="center" valignment="top" width="0pt">
16725 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
16728 \begin_layout Plain Layout
16730 \begin_inset Note Note
16733 \begin_layout Plain Layout
16740 is only used as spacer.
16750 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
16753 \begin_layout Plain Layout
16761 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
16764 \begin_layout Plain Layout
16770 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
16773 \begin_layout Plain Layout
16774 \begin_inset Formula $+$
16784 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
16787 \begin_layout Plain Layout
16793 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
16796 \begin_layout Plain Layout
16797 \begin_inset Formula $-$
16807 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
16810 \begin_layout Plain Layout
16818 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
16821 \begin_layout Plain Layout
16822 \begin_inset Formula $\pm$
16832 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
16835 \begin_layout Plain Layout
16843 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
16846 \begin_layout Plain Layout
16847 \begin_inset Formula $\mp$
16857 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
16860 \begin_layout Plain Layout
16868 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
16871 \begin_layout Plain Layout
16872 \begin_inset Formula $\cdot$
16882 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
16885 \begin_layout Plain Layout
16893 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
16896 \begin_layout Plain Layout
16897 \begin_inset Formula $\times$
16907 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
16910 \begin_layout Plain Layout
16918 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
16921 \begin_layout Plain Layout
16922 \begin_inset Formula $\div$
16932 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
16935 \begin_layout Plain Layout
16939 \begin_layout Plain Layout
16952 \begin_layout Plain Layout
16964 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
16967 \begin_layout Plain Layout
16968 \begin_inset Formula $*$
16978 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
16981 \begin_layout Plain Layout
16989 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
16992 \begin_layout Plain Layout
16993 \begin_inset Formula $\star$
17003 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
17006 \begin_layout Plain Layout
17014 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
17017 \begin_layout Plain Layout
17018 \begin_inset Formula $\circ$
17028 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
17031 \begin_layout Plain Layout
17039 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
17042 \begin_layout Plain Layout
17043 \begin_inset Formula $\diamond$
17053 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
17056 \begin_layout Plain Layout
17064 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
17067 \begin_layout Plain Layout
17068 \begin_inset Formula $\bullet$
17082 \begin_inset space \hfill{}
17086 \begin_inset Tabular
17087 <lyxtabular version="3" rows="13" columns="2">
17088 <features tabularvalignment="middle">
17089 <column alignment="center" valignment="top" width="0pt">
17090 <column alignment="center" valignment="top" width="0pt">
17092 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
17095 \begin_layout Plain Layout
17101 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
17104 \begin_layout Plain Layout
17112 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
17115 \begin_layout Plain Layout
17123 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
17126 \begin_layout Plain Layout
17127 \begin_inset Formula $\nabla$
17137 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
17140 \begin_layout Plain Layout
17148 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
17151 \begin_layout Plain Layout
17152 \begin_inset Formula $\bigtriangledown$
17162 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
17165 \begin_layout Plain Layout
17173 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
17176 \begin_layout Plain Layout
17177 \begin_inset Formula $\bigtriangleup$
17187 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
17190 \begin_layout Plain Layout
17198 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
17201 \begin_layout Plain Layout
17202 \begin_inset Formula $\Box$
17212 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
17215 \begin_layout Plain Layout
17223 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
17226 \begin_layout Plain Layout
17227 \begin_inset Formula $\cap$
17237 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
17240 \begin_layout Plain Layout
17248 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
17251 \begin_layout Plain Layout
17252 \begin_inset Formula $\cup$
17262 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
17265 \begin_layout Plain Layout
17273 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
17276 \begin_layout Plain Layout
17277 \begin_inset Formula $\dagger$
17287 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
17290 \begin_layout Plain Layout
17298 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
17301 \begin_layout Plain Layout
17302 \begin_inset Formula $\ddagger$
17312 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
17315 \begin_layout Plain Layout
17323 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
17326 \begin_layout Plain Layout
17327 \begin_inset Formula $\wr$
17337 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
17340 \begin_layout Plain Layout
17348 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
17351 \begin_layout Plain Layout
17352 \begin_inset Formula $\bigcirc$
17362 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
17365 \begin_layout Plain Layout
17373 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
17376 \begin_layout Plain Layout
17377 \begin_inset Formula $\wedge$
17387 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
17390 \begin_layout Plain Layout
17398 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
17401 \begin_layout Plain Layout
17402 \begin_inset Formula $\vee$
17416 \begin_inset space \hfill{}
17420 \begin_inset Tabular
17421 <lyxtabular version="3" rows="13" columns="2">
17422 <features tabularvalignment="middle">
17423 <column alignment="center" valignment="top" width="0pt">
17424 <column alignment="center" valignment="top" width="0pt">
17426 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
17429 \begin_layout Plain Layout
17435 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
17438 \begin_layout Plain Layout
17446 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
17449 \begin_layout Plain Layout
17457 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
17460 \begin_layout Plain Layout
17461 \begin_inset Formula $\oplus$
17471 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
17474 \begin_layout Plain Layout
17482 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
17485 \begin_layout Plain Layout
17486 \begin_inset Formula $\ominus$
17496 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
17499 \begin_layout Plain Layout
17507 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
17510 \begin_layout Plain Layout
17511 \begin_inset Formula $\otimes$
17521 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
17524 \begin_layout Plain Layout
17532 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
17535 \begin_layout Plain Layout
17536 \begin_inset Formula $\oslash$
17546 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
17549 \begin_layout Plain Layout
17557 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
17560 \begin_layout Plain Layout
17561 \begin_inset Formula $\odot$
17571 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
17574 \begin_layout Plain Layout
17582 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
17585 \begin_layout Plain Layout
17586 \begin_inset Formula $\amalg$
17596 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
17599 \begin_layout Plain Layout
17607 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
17610 \begin_layout Plain Layout
17611 \begin_inset Formula $\uplus$
17621 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
17624 \begin_layout Plain Layout
17632 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
17635 \begin_layout Plain Layout
17636 \begin_inset Formula $\setminus$
17646 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
17649 \begin_layout Plain Layout
17657 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
17660 \begin_layout Plain Layout
17661 \begin_inset Formula $\sqcap$
17671 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
17674 \begin_layout Plain Layout
17682 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
17685 \begin_layout Plain Layout
17686 \begin_inset Formula $\sqcup$
17696 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
17699 \begin_layout Plain Layout
17707 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
17710 \begin_layout Plain Layout
17711 \begin_inset Formula $\triangleleft$
17721 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
17724 \begin_layout Plain Layout
17732 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
17735 \begin_layout Plain Layout
17736 \begin_inset Formula $\triangleright$
17750 \begin_inset space \hfill{}
17756 \begin_layout Standard
17757 All binary operators can also be inserted via the math toolbar button
17758 \begin_inset Graphics
17759 filename ../images/math/pm.png
17767 \begin_layout Standard
17768 To typeset the Laplace operator also
17785 \begin_inset Formula $\nabla^{2}$
17788 ) can be used instead of
17797 \begin_layout Standard
17804 Insert\SpecialChar \menuseparator
17816 \begin_layout Subsection
17817 Self-defined Operators
17818 \begin_inset CommandInset label
17820 name "sub:Self-defined-Operators"
17825 \begin_inset Index idx
17828 \begin_layout Plain Layout
17829 Operators ! self-defined
17837 \begin_layout Standard
17838 With the help of the command
17842 DeclareMathOperator
17845 \begin_inset Index idx
17848 \begin_layout Plain Layout
17853 DeclareMathOperator
17858 custom operators can be defined in the LaTeX-preamble.
17859 Its command scheme is:
17862 \begin_layout Standard
17867 DeclareMathOperator{new command}{display}
17870 \begin_layout Standard
17871 Display can be characters or symbols that define how the operator looks
17873 To define a big operator a * is set behind the command.
17874 All self-defined big operators can have limits as described in
17875 \begin_inset CommandInset ref
17877 reference "sub:Operator-Limits"
17884 \begin_layout Standard
17885 For example the LaTeX-preamble line
17888 \begin_layout Standard
17893 DeclareMathOperator*{
17900 \begin_layout Standard
17901 defines the command
17907 , that inserts a big operator consisting of the lozenge symbol from
17908 \begin_inset CommandInset ref
17910 reference "sub:Miscellaneous-Symbols"
17915 \begin_inset Formula
17917 \Lozenge_{n=1}^{\infty}
17922 The command for this formula is:
17933 \begin_inset Formula $\to$
17939 \begin_layout Standard
17940 \begin_inset VSpace bigskip
17943 When self-defined operators are not used several times in the document,
17944 they can also be defined with the commands
17951 \begin_inset Index idx
17954 \begin_layout Plain Layout
17969 \begin_inset Index idx
17972 \begin_layout Plain Layout
17980 , which have the following scheme:
17983 \begin_layout Standard
17997 \begin_layout Standard
18004 defines big operators,
18013 \begin_layout Standard
18021 \begin_inset space \thinspace{}
18025 \begin_inset space \space{}
18028 be used to use one limit for several operators:
18031 \begin_layout Standard
18032 \begin_inset Formula
18034 \mathop{\sum\negmedspace\sum}_{i,j=1}^{N}
18042 \begin_layout Standard
18043 The command for the formula above is:
18044 \begin_inset Newline newline
18063 \begin_layout Plain Layout
18075 \begin_inset Formula $\to$
18084 \begin_layout Plain Layout
18098 \begin_layout Section
18100 \begin_inset Index idx
18103 \begin_layout Plain Layout
18112 \begin_layout Subsection
18114 \begin_inset CommandInset label
18116 name "sub:Font-Styles"
18121 \begin_inset Index idx
18124 \begin_layout Plain Layout
18133 \begin_layout Standard
18134 Latin letters in formulas can be set in one of the following font styles:
18135 \begin_inset VSpace -2mm
18141 \begin_layout Standard
18143 \begin_inset Tabular
18144 <lyxtabular version="3" rows="7" columns="3">
18145 <features tabularvalignment="middle">
18146 <column alignment="center" valignment="top" width="0">
18147 <column alignment="center" valignment="top" width="0">
18148 <column alignment="center" valignment="top" width="0">
18150 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
18153 \begin_layout Plain Layout
18159 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
18162 \begin_layout Plain Layout
18168 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
18171 \begin_layout Plain Layout
18179 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
18182 \begin_layout Plain Layout
18191 \begin_layout Plain Layout
18207 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
18210 \begin_layout Plain Layout
18211 \begin_inset Formula $\mathbb{ABC}$
18219 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
18222 \begin_layout Plain Layout
18235 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
18238 \begin_layout Plain Layout
18247 \begin_layout Plain Layout
18263 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
18266 \begin_layout Plain Layout
18267 \begin_inset Formula $\mathbf{AbC}$
18275 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
18278 \begin_layout Plain Layout
18291 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
18294 \begin_layout Plain Layout
18303 \begin_layout Plain Layout
18319 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
18322 \begin_layout Plain Layout
18323 \begin_inset Formula $\boldsymbol{AbC}$
18331 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
18334 \begin_layout Plain Layout
18337 arg "font-boldsymbol"
18347 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
18350 \begin_layout Plain Layout
18359 \begin_layout Plain Layout
18375 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
18378 \begin_layout Plain Layout
18379 \begin_inset Formula $\mathcal{ABC}$
18387 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
18390 \begin_layout Plain Layout
18403 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
18406 \begin_layout Plain Layout
18415 \begin_layout Plain Layout
18431 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
18434 \begin_layout Plain Layout
18435 \begin_inset Formula $\mathfrak{AbC}$
18443 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
18446 \begin_layout Plain Layout
18454 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
18457 \begin_layout Plain Layout
18466 \begin_layout Plain Layout
18482 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
18485 \begin_layout Plain Layout
18486 \begin_inset Formula $\mathscr{AbC}$
18494 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
18497 \begin_layout Plain Layout
18511 \begin_layout Standard
18513 \begin_inset Tabular
18514 <lyxtabular version="3" rows="5" columns="3">
18515 <features tabularvalignment="middle">
18516 <column alignment="center" valignment="top" width="0">
18517 <column alignment="center" valignment="top" width="0">
18518 <column alignment="center" valignment="top" width="0">
18520 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
18523 \begin_layout Plain Layout
18529 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
18532 \begin_layout Plain Layout
18538 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
18541 \begin_layout Plain Layout
18549 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
18552 \begin_layout Plain Layout
18561 \begin_layout Plain Layout
18577 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
18580 \begin_layout Plain Layout
18581 \begin_inset Formula $\mathit{AbC}$
18589 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
18592 \begin_layout Plain Layout
18600 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
18603 \begin_layout Plain Layout
18612 \begin_layout Plain Layout
18628 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
18631 \begin_layout Plain Layout
18632 \begin_inset Formula $\mathrm{AbC}$
18640 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
18643 \begin_layout Plain Layout
18656 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
18659 \begin_layout Plain Layout
18668 \begin_layout Plain Layout
18684 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
18687 \begin_layout Plain Layout
18688 \begin_inset Formula $\mathsf{AbC}$
18696 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
18699 \begin_layout Plain Layout
18712 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
18715 \begin_layout Plain Layout
18724 \begin_layout Plain Layout
18740 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
18743 \begin_layout Plain Layout
18744 \begin_inset Formula $\mathtt{AbC}$
18752 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
18755 \begin_layout Plain Layout
18758 arg "font-typewriter"
18774 \begin_layout Standard
18775 \begin_inset Note Greyedout
18778 \begin_layout Plain Layout
18795 can only be used for big letters.
18803 \begin_layout Standard
18804 Predefined is the style
18813 \begin_layout Standard
18814 The style commands work also for letters in mathematical constructs:
18815 \begin_inset Formula
18817 \mathfrak{A=\frac{b}{C}}
18825 \begin_layout Standard
18826 Characters in mathematical text don't appear in a math font style but in
18827 the text font style
18834 That their style can't be set correctly via the text style dialog is a
18839 \begin_layout Plain Layout
18840 \begin_inset CommandInset href
18842 name "LyX-bug #4629"
18843 target "http://www.lyx.org/trac/ticket/4629"
18855 \begin_layout Standard
18856 Instead of the style commands the dialog
18858 Edit\SpecialChar \menuseparator
18859 Math\SpecialChar \menuseparator
18862 or the toolbar button
18863 \begin_inset Graphics
18864 filename ../images/math/font.png
18872 \begin_layout Subsection
18874 \begin_inset CommandInset label
18876 name "sub:Bold-Formulas"
18881 \begin_inset Index idx
18884 \begin_layout Plain Layout
18893 \begin_layout Standard
18894 To make a complete formula bold, the command
18900 from the previous subsection cannot be used, because it doesn't work for
18901 small Greek letters.
18902 Furthermore it prints Latin letters always upright, like in the following
18906 \begin_layout Standard
18907 \begin_inset Formula
18909 \mathbf{\int_{n}^{2}f(\theta)=\Gamma}\qquad\textrm{equation with \textbackslash mathbf}
18917 \begin_layout Standard
18918 To display the formula correctly, the command
18925 \begin_inset Formula
18927 \boldsymbol{\int_{n}^{2}f(\theta)=\Gamma\qquad\textrm{equation with \textbackslash boldsymbol}}
18932 It is also possible to set the formula in a
18934 boldmath environment
18937 This environment is created by inserting the command
18944 \begin_inset Index idx
18947 \begin_layout Plain Layout
18956 To end the environment, the command
18963 \begin_inset Index idx
18966 \begin_layout Plain Layout
18974 is inserted in TeX-mode.
18978 \begin_layout Plain Layout
18988 \begin_inset Formula
18990 \int_{n}^{2}f(\theta)=\Gamma\qquad\textrm{equation in a boldmath environment}
18999 \begin_layout Plain Layout
19011 \begin_layout Subsection
19013 \begin_inset Index idx
19016 \begin_layout Plain Layout
19025 \begin_layout Standard
19026 Formulas can be colored like normal text: Highlight a formula or a formula
19032 Here is a formula in magenta:
19033 \begin_inset Formula
19035 {\color{magenta}\int A\,\mathrm{d}x=\frac{\sqrt[5]{B}}{\ln\left(\frac{1}{3}\right)}}
19043 \begin_layout Standard
19044 You can also define your own colors as described in
19045 \begin_inset CommandInset ref
19047 reference "sub:Colored-Boxes"
19052 They can be used with the TeX code command
19059 \begin_inset Index idx
19062 \begin_layout Plain Layout
19073 \begin_layout Standard
19078 textcolor{color}{characters or formula}
19081 \begin_layout Standard
19082 The following example was colored completely dark green and partly red:
19085 \begin_layout Standard
19089 \begin_layout Plain Layout
19093 textcolor{darkgreen}{
19099 \begin_inset Formula
19101 \int A\,\mathrm{d}x=\frac{{\color{red}\sqrt[5]{B}}}{\ln\left(\frac{1}{3}\right)}
19110 \begin_layout Plain Layout
19120 \begin_layout Standard
19121 Due to a bug in LyX only complete formulas can be colored with self-defined
19126 \begin_layout Plain Layout
19127 \begin_inset CommandInset href
19129 name "LyX-bug #5269"
19130 target "http://www.lyx.org/trac/ticket/5269"
19142 \begin_layout Subsection
19144 \begin_inset CommandInset label
19146 name "sub:Font-Sizes"
19151 \begin_inset Index idx
19154 \begin_layout Plain Layout
19163 \begin_layout Standard
19164 For characters in formulas there are, analog to characters in text, the
19165 following size commands:
19168 \begin_layout Standard
19212 \begin_inset Newline newline
19234 \begin_layout Standard
19235 The size produced by the commands depends on the document font size, that
19236 corresponds with the command
19243 The other commands produce smaller or larger sizes than
19250 The font size can however not exceed a certain value.
19251 Is for example the document font size 12
19252 \begin_inset space \thinspace{}
19261 switches to the same size as
19271 \begin_layout Standard
19272 A size command is inserted in TeX-mode before the formula and sets the size
19273 for all following formula and text characters.
19274 To switch back to the initial size, the command
19280 is inserted behind the formula in TeX-mode.
19283 \begin_layout Standard
19284 Within a formula the size can be changed using the following size commands:
19287 \begin_layout Standard
19290 \begin_inset Tabular
19291 <lyxtabular version="3" rows="5" columns="2">
19292 <features tabularvalignment="middle">
19293 <column alignment="center" valignment="top" width="0">
19294 <column alignment="center" valignment="top" width="0">
19296 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
19299 \begin_layout Plain Layout
19305 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
19308 \begin_layout Plain Layout
19310 \begin_inset Note Note
19313 \begin_layout Plain Layout
19320 is only used as spacer.
19332 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
19335 \begin_layout Plain Layout
19339 \begin_inset Index idx
19342 \begin_layout Plain Layout
19355 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
19358 \begin_layout Plain Layout
19359 \begin_inset Formula $\raisebox{6.5mm}{}{\displaystyle E_{\mathrm{pot_{1}}}=\frac{K}{l+\frac{m}{n_{2}}}}\raisebox{-5.5mm}{}$
19369 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
19372 \begin_layout Plain Layout
19380 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
19383 \begin_layout Plain Layout
19384 \begin_inset Formula $\raisebox{4.5mm}{}{\textstyle E_{\mathrm{pot_{1}}}=\frac{K}{l+\frac{m}{n_{2}}}}\raisebox{-4mm}{}$
19394 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
19397 \begin_layout Plain Layout
19405 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
19408 \begin_layout Plain Layout
19409 \begin_inset Formula $\raisebox{4.5mm}{}{\scriptstyle E_{\mathrm{pot_{1}}}=\frac{K}{l+\frac{m}{n_{2}}}}\raisebox{-3.5mm}{}$
19419 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
19422 \begin_layout Plain Layout
19430 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
19433 \begin_layout Plain Layout
19434 \begin_inset Formula $\raisebox{4.5mm}{}{\scriptscriptstyle E_{\mathrm{pot_{1}}}=\frac{K}{l+\frac{m}{n_{2}}}}\raisebox{-3.5mm}{}$
19450 \begin_layout Standard
19451 After entering these commands, a blue box appears in which the formula parts
19455 \begin_layout Standard
19456 There is a further method to change the font size, that though only works
19457 for symbols or letters in mathematical text.
19458 To use it, one of the above text size commands is inserted in mathematical
19460 All following characters until the end of the mathematical text or until
19461 another size command will have the selected size.
19463 \begin_inset VSpace -2mm
19469 \begin_layout Standard
19473 \begin_layout Plain Layout
19483 \begin_inset Formula
19485 A=\frac{B}{c}\cdot\maltese
19491 \begin_inset Formula
19493 \maltese A\textrm{\Large\maltese\textit{A}}\textrm{\tiny\maltese\textit{A}}
19502 \begin_layout Plain Layout
19514 \begin_layout Standard
19515 \begin_inset VSpace medskip
19518 Before both formulas the command
19525 The command for the second formula is:
19526 \begin_inset Newline newline
19537 \begin_layout Plain Layout
19552 \begin_layout Plain Layout
19567 \begin_layout Plain Layout
19582 \begin_layout Plain Layout
19592 \begin_inset Formula $\to$
19596 \begin_inset Formula $\to$
19600 \begin_inset Newline newline
19604 \begin_inset space \hspace*{}
19618 \begin_layout Plain Layout
19633 \begin_layout Plain Layout
19648 \begin_layout Plain Layout
19660 \begin_layout Standard
19661 If a symbol cannot be displayed in different sizes, it will always be displayed
19662 in the default size.
19665 \begin_layout Section
19667 \begin_inset Index idx
19670 \begin_layout Plain Layout
19679 \begin_layout Standard
19680 Greek letters can also be inserted via the toolbar button
19681 \begin_inset Graphics
19682 filename ../images/math/alpha.png
19688 All international typesetting norms purport that Greek letters in math
19689 have to be typeset italic/slanted.
19690 In some languages, like French or Russian, they are nevertheless sometimes
19694 \begin_layout Subsection
19696 \begin_inset Index idx
19699 \begin_layout Plain Layout
19700 Greek letters ! small
19708 \begin_layout Standard
19709 \begin_inset space \hfill{}
19713 \begin_inset Tabular
19714 <lyxtabular version="3" rows="11" columns="2">
19715 <features tabularvalignment="middle">
19716 <column alignment="center" valignment="top" width="0pt">
19717 <column alignment="center" valignment="top" width="0pt">
19719 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
19722 \begin_layout Plain Layout
19728 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
19731 \begin_layout Plain Layout
19739 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
19742 \begin_layout Plain Layout
19750 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
19753 \begin_layout Plain Layout
19754 \begin_inset Formula $\alpha$
19764 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
19767 \begin_layout Plain Layout
19775 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
19778 \begin_layout Plain Layout
19779 \begin_inset Formula $\beta$
19789 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
19792 \begin_layout Plain Layout
19800 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
19803 \begin_layout Plain Layout
19804 \begin_inset Formula $\gamma$
19814 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
19817 \begin_layout Plain Layout
19825 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
19828 \begin_layout Plain Layout
19829 \begin_inset Formula $\delta$
19839 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
19842 \begin_layout Plain Layout
19850 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
19853 \begin_layout Plain Layout
19854 \begin_inset Formula $\epsilon$
19864 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
19867 \begin_layout Plain Layout
19875 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
19878 \begin_layout Plain Layout
19879 \begin_inset Formula $\varepsilon$
19889 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
19892 \begin_layout Plain Layout
19900 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
19903 \begin_layout Plain Layout
19904 \begin_inset Formula $\zeta$
19914 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
19917 \begin_layout Plain Layout
19925 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
19928 \begin_layout Plain Layout
19929 \begin_inset Formula $\eta$
19939 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
19942 \begin_layout Plain Layout
19950 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
19953 \begin_layout Plain Layout
19954 \begin_inset Formula $\theta$
19964 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
19967 \begin_layout Plain Layout
19975 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
19978 \begin_layout Plain Layout
19979 \begin_inset Formula $\vartheta$
19993 \begin_inset space \hfill{}
19997 \begin_inset Tabular
19998 <lyxtabular version="3" rows="12" columns="2">
19999 <features tabularvalignment="middle">
20000 <column alignment="center" valignment="top" width="0pt">
20001 <column alignment="center" valignment="top" width="0pt">
20003 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
20006 \begin_layout Plain Layout
20012 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
20015 \begin_layout Plain Layout
20023 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
20026 \begin_layout Plain Layout
20034 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
20037 \begin_layout Plain Layout
20038 \begin_inset Formula $\iota$
20048 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
20051 \begin_layout Plain Layout
20059 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
20062 \begin_layout Plain Layout
20063 \begin_inset Formula $\kappa$
20073 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
20076 \begin_layout Plain Layout
20084 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
20087 \begin_layout Plain Layout
20088 \begin_inset Formula $\varkappa$
20098 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
20101 \begin_layout Plain Layout
20109 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
20112 \begin_layout Plain Layout
20113 \begin_inset Formula $\lambda$
20123 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
20126 \begin_layout Plain Layout
20134 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
20137 \begin_layout Plain Layout
20138 \begin_inset Formula $\mu$
20148 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
20151 \begin_layout Plain Layout
20159 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
20162 \begin_layout Plain Layout
20163 \begin_inset Formula $\nu$
20173 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
20176 \begin_layout Plain Layout
20184 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
20187 \begin_layout Plain Layout
20188 \begin_inset Formula $\xi$
20198 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
20201 \begin_layout Plain Layout
20207 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
20210 \begin_layout Plain Layout
20211 \begin_inset Formula $o$
20221 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
20224 \begin_layout Plain Layout
20232 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
20235 \begin_layout Plain Layout
20236 \begin_inset Formula $\pi$
20246 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
20249 \begin_layout Plain Layout
20257 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
20260 \begin_layout Plain Layout
20261 \begin_inset Formula $\varpi$
20271 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
20274 \begin_layout Plain Layout
20282 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
20285 \begin_layout Plain Layout
20286 \begin_inset Formula $\rho$
20300 \begin_inset space \hfill{}
20304 \begin_inset Tabular
20305 <lyxtabular version="3" rows="11" columns="2">
20306 <features tabularvalignment="middle">
20307 <column alignment="center" valignment="top" width="0pt">
20308 <column alignment="center" valignment="top" width="0pt">
20310 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
20313 \begin_layout Plain Layout
20319 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
20322 \begin_layout Plain Layout
20330 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
20333 \begin_layout Plain Layout
20341 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
20344 \begin_layout Plain Layout
20345 \begin_inset Formula $\varrho$
20355 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
20358 \begin_layout Plain Layout
20366 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
20369 \begin_layout Plain Layout
20370 \begin_inset Formula $\sigma$
20380 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
20383 \begin_layout Plain Layout
20391 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
20394 \begin_layout Plain Layout
20395 \begin_inset Formula $\varsigma$
20405 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
20408 \begin_layout Plain Layout
20416 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
20419 \begin_layout Plain Layout
20420 \begin_inset Formula $\tau$
20430 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
20433 \begin_layout Plain Layout
20441 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
20444 \begin_layout Plain Layout
20445 \begin_inset Formula $\upsilon$
20455 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
20458 \begin_layout Plain Layout
20466 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
20469 \begin_layout Plain Layout
20470 \begin_inset Formula $\phi$
20480 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
20483 \begin_layout Plain Layout
20491 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
20494 \begin_layout Plain Layout
20495 \begin_inset Formula $\varphi$
20505 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
20508 \begin_layout Plain Layout
20516 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
20519 \begin_layout Plain Layout
20520 \begin_inset Formula $\chi$
20530 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
20533 \begin_layout Plain Layout
20541 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
20544 \begin_layout Plain Layout
20545 \begin_inset Formula $\psi$
20555 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
20558 \begin_layout Plain Layout
20566 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
20569 \begin_layout Plain Layout
20570 \begin_inset Formula $\omega$
20584 \begin_inset space \hfill{}
20590 \begin_layout Standard
20591 \begin_inset VSpace medskip
20597 \begin_layout Standard
20598 How to create special upright Greek letters is explained in
20599 \begin_inset CommandInset ref
20601 reference "sub:Upright-small-Greek"
20608 \begin_layout Subsection
20610 \begin_inset Index idx
20613 \begin_layout Plain Layout
20614 Greek letters ! big
20622 \begin_layout Standard
20623 \begin_inset space \hfill{}
20627 \begin_inset Tabular
20628 <lyxtabular version="3" rows="7" columns="2">
20629 <features tabularvalignment="middle">
20630 <column alignment="center" valignment="top" width="0pt">
20631 <column alignment="center" valignment="top" width="0pt">
20633 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
20636 \begin_layout Plain Layout
20642 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
20645 \begin_layout Plain Layout
20653 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
20656 \begin_layout Plain Layout
20664 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
20667 \begin_layout Plain Layout
20668 \begin_inset Formula $\Gamma$
20678 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
20681 \begin_layout Plain Layout
20689 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
20692 \begin_layout Plain Layout
20693 \begin_inset Formula $\Delta$
20703 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
20706 \begin_layout Plain Layout
20714 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
20717 \begin_layout Plain Layout
20718 \begin_inset Formula $\Theta$
20728 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
20731 \begin_layout Plain Layout
20739 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
20742 \begin_layout Plain Layout
20743 \begin_inset Formula $\Lambda$
20753 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
20756 \begin_layout Plain Layout
20764 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
20767 \begin_layout Plain Layout
20768 \begin_inset Formula $\Xi$
20778 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
20781 \begin_layout Plain Layout
20789 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
20792 \begin_layout Plain Layout
20793 \begin_inset Formula $\Pi$
20807 \begin_inset space \hfill{}
20811 \begin_inset Tabular
20812 <lyxtabular version="3" rows="6" columns="2">
20813 <features tabularvalignment="middle">
20814 <column alignment="center" valignment="top" width="0pt">
20815 <column alignment="center" valignment="top" width="0pt">
20817 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
20820 \begin_layout Plain Layout
20826 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
20829 \begin_layout Plain Layout
20837 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
20840 \begin_layout Plain Layout
20848 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
20851 \begin_layout Plain Layout
20852 \begin_inset Formula $\Sigma$
20862 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
20865 \begin_layout Plain Layout
20873 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
20876 \begin_layout Plain Layout
20877 \begin_inset Formula $\Upsilon$
20887 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
20890 \begin_layout Plain Layout
20898 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
20901 \begin_layout Plain Layout
20902 \begin_inset Formula $\Phi$
20912 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
20915 \begin_layout Plain Layout
20923 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
20926 \begin_layout Plain Layout
20927 \begin_inset Formula $\Psi$
20937 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
20940 \begin_layout Plain Layout
20948 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
20951 \begin_layout Plain Layout
20952 \begin_inset Formula $\Omega$
20966 \begin_inset space \hfill{}
20972 \begin_layout Standard
20973 \begin_inset VSpace medskip
20976 That the big Greek letters appear upright is caused by a design bug when
20978 To get correct italic big letters, begin every command with
20983 For example the command
20990 \begin_inset Formula $\varGamma$
20994 Another way is to load the package
21002 \begin_layout Plain Layout
21007 is part of the LaTeX-package
21012 \begin_inset Index idx
21015 \begin_layout Plain Layout
21020 \begin_layout Plain Layout
21040 \begin_inset Index idx
21043 \begin_layout Plain Layout
21049 with the LaTeX-preamble line
21052 \begin_layout Standard
21057 usepackage{fixmath}
21060 \begin_layout Standard
21061 Then all big Greek letters in a document will automatically be typeset italic.
21064 \begin_layout Subsection
21066 \begin_inset Index idx
21069 \begin_layout Plain Layout
21070 Greek letters ! bold
21078 \begin_layout Standard
21079 Greek letters cannot be set with different font styles like Latin letters.
21080 They can only be made bold with the command
21087 \begin_inset Index idx
21090 \begin_layout Plain Layout
21101 \begin_layout Standard
21103 \begin_inset Tabular
21104 <lyxtabular version="3" rows="3" columns="2">
21105 <features tabularvalignment="middle">
21106 <column alignment="center" valignment="top" width="0">
21107 <column alignment="center" valignment="top" width="0">
21109 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
21112 \begin_layout Plain Layout
21118 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
21121 \begin_layout Plain Layout
21129 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
21132 \begin_layout Plain Layout
21144 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
21147 \begin_layout Plain Layout
21148 \begin_inset Formula $\Upsilon\boldsymbol{\Upsilon}$
21158 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
21161 \begin_layout Plain Layout
21173 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
21176 \begin_layout Plain Layout
21177 \begin_inset Formula $\theta\boldsymbol{\theta}$
21193 \begin_layout Standard
21194 \begin_inset Newpage newpage
21200 \begin_layout Section
21205 \begin_layout Plain Layout
21218 \begin_layout Plain Layout
21219 A list with all symbols of most of the LaTeX-packages can be found in
21220 \begin_inset CommandInset citation
21235 \begin_layout Plain Layout
21243 \begin_inset Note Note
21246 \begin_layout Plain Layout
21249 texorpdfstring is used to avoid that the footnote appears in the PDF-bookmark.
21252 \begin_layout Plain Layout
21255 texorpdfstring is in section
21256 \begin_inset CommandInset ref
21258 reference "sub:Formulas-in-Section"
21268 \begin_inset Index idx
21271 \begin_layout Plain Layout
21280 \begin_layout Standard
21281 Many of the symbols listed in this section can also be inserted via the
21283 \begin_inset Graphics
21284 filename ../images/math/nabla.png
21290 \begin_inset Graphics
21291 filename ../images/math/digamma.png
21299 \begin_layout Subsection
21300 Mathematical Symbols
21301 \begin_inset CommandInset label
21303 name "sub:Mathematical-Symbols"
21308 \begin_inset Index idx
21311 \begin_layout Plain Layout
21312 Symbols ! mathematical
21320 \begin_layout Standard
21321 \begin_inset space \hfill{}
21325 \begin_inset Tabular
21326 <lyxtabular version="3" rows="10" columns="2">
21327 <features tabularvalignment="middle">
21328 <column alignment="center" valignment="top" width="0pt">
21329 <column alignment="center" valignment="top" width="0pt">
21331 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
21334 \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
21351 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
21354 \begin_layout Plain Layout
21362 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
21365 \begin_layout Plain Layout
21366 \begin_inset Formula $\neg$
21376 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
21379 \begin_layout Plain Layout
21387 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
21390 \begin_layout Plain Layout
21391 \begin_inset Formula $\Im$
21401 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
21404 \begin_layout Plain Layout
21412 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
21415 \begin_layout Plain Layout
21416 \begin_inset Formula $\Re$
21426 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
21429 \begin_layout Plain Layout
21437 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
21440 \begin_layout Plain Layout
21441 \begin_inset Formula $\aleph$
21451 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
21454 \begin_layout Plain Layout
21462 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
21465 \begin_layout Plain Layout
21466 \begin_inset Formula $\partial$
21476 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
21479 \begin_layout Plain Layout
21487 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
21490 \begin_layout Plain Layout
21491 \begin_inset Formula $\infty$
21501 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
21504 \begin_layout Plain Layout
21512 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
21515 \begin_layout Plain Layout
21516 \begin_inset Formula $\wp$
21526 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
21529 \begin_layout Plain Layout
21537 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
21540 \begin_layout Plain Layout
21541 \begin_inset Formula $\imath$
21551 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
21554 \begin_layout Plain Layout
21562 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
21565 \begin_layout Plain Layout
21566 \begin_inset Formula $\jmath$
21580 \begin_inset space \hfill{}
21584 \begin_inset Tabular
21585 <lyxtabular version="3" rows="10" columns="2">
21586 <features tabularvalignment="middle">
21587 <column alignment="center" valignment="top" width="0pt">
21588 <column alignment="center" valignment="top" width="0pt">
21590 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
21593 \begin_layout Plain Layout
21599 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
21602 \begin_layout Plain Layout
21604 \begin_inset Note Note
21607 \begin_layout Plain Layout
21614 is only used as spacer.
21626 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
21629 \begin_layout Plain Layout
21637 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
21640 \begin_layout Plain Layout
21641 \begin_inset Formula $\forall$
21651 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
21654 \begin_layout Plain Layout
21662 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
21665 \begin_layout Plain Layout
21666 \begin_inset Formula $\exists$
21676 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
21679 \begin_layout Plain Layout
21687 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
21690 \begin_layout Plain Layout
21691 \begin_inset Formula $\nexists$
21701 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
21704 \begin_layout Plain Layout
21712 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
21715 \begin_layout Plain Layout
21716 \begin_inset Formula $\emptyset$
21726 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
21729 \begin_layout Plain Layout
21737 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
21740 \begin_layout Plain Layout
21741 \begin_inset Formula $\varnothing$
21751 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
21754 \begin_layout Plain Layout
21762 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
21765 \begin_layout Plain Layout
21766 \begin_inset Formula $\dag$
21776 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
21779 \begin_layout Plain Layout
21787 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
21790 \begin_layout Plain Layout
21791 \begin_inset Formula $\ddag$
21801 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
21804 \begin_layout Plain Layout
21812 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
21815 \begin_layout Plain Layout
21819 \begin_layout Plain Layout
21829 \begin_inset Formula $\complement$
21836 \begin_layout Plain Layout
21850 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
21853 \begin_layout Plain Layout
21861 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
21864 \begin_layout Plain Layout
21865 \begin_inset Formula $\Bbbk$
21879 \begin_inset space \hfill{}
21883 \begin_inset Tabular
21884 <lyxtabular version="3" rows="10" columns="2">
21885 <features tabularvalignment="middle">
21886 <column alignment="center" valignment="top" width="0pt">
21887 <column alignment="center" valignment="top" width="0pt">
21889 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
21892 \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
21909 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
21912 \begin_layout Plain Layout
21920 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
21923 \begin_layout Plain Layout
21924 \begin_inset Formula $\prime$
21934 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
21937 \begin_layout Plain Layout
21945 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
21948 \begin_layout Plain Layout
21949 \begin_inset Formula $\backprime$
21959 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
21962 \begin_layout Plain Layout
21970 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
21973 \begin_layout Plain Layout
21974 \begin_inset Formula $\mho$
21984 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
21987 \begin_layout Plain Layout
21995 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
21998 \begin_layout Plain Layout
21999 \begin_inset Formula $\triangle$
22009 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
22012 \begin_layout Plain Layout
22020 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
22023 \begin_layout Plain Layout
22024 \begin_inset Formula $\angle$
22034 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
22037 \begin_layout Plain Layout
22045 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
22048 \begin_layout Plain Layout
22049 \begin_inset Formula $\measuredangle$
22059 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
22062 \begin_layout Plain Layout
22070 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
22073 \begin_layout Plain Layout
22074 \begin_inset Formula $\sphericalangle$
22084 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
22087 \begin_layout Plain Layout
22095 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
22098 \begin_layout Plain Layout
22099 \begin_inset Formula $\top$
22109 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
22112 \begin_layout Plain Layout
22120 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
22123 \begin_layout Plain Layout
22124 \begin_inset Formula $\bot$
22138 \begin_inset space \hfill{}
22144 \begin_layout Subsection
22145 Miscellaneous Symbols
22146 \begin_inset CommandInset label
22148 name "sub:Miscellaneous-Symbols"
22153 \begin_inset Index idx
22156 \begin_layout Plain Layout
22157 Symbols ! miscellaneous
22165 \begin_layout Standard
22168 \begin_inset Tabular
22169 <lyxtabular version="3" rows="10" columns="2">
22170 <features tabularvalignment="middle">
22171 <column alignment="center" valignment="top" width="0pt">
22172 <column alignment="center" valignment="top" width="0pt">
22174 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
22177 \begin_layout Plain Layout
22183 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
22186 \begin_layout Plain Layout
22194 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
22197 \begin_layout Plain Layout
22205 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
22208 \begin_layout Plain Layout
22209 \begin_inset Formula $\flat$
22219 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
22222 \begin_layout Plain Layout
22230 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
22233 \begin_layout Plain Layout
22234 \begin_inset Formula $\natural$
22244 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
22247 \begin_layout Plain Layout
22255 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
22258 \begin_layout Plain Layout
22259 \begin_inset Formula $\sharp$
22269 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
22272 \begin_layout Plain Layout
22280 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
22283 \begin_layout Plain Layout
22284 \begin_inset Formula $\surd$
22294 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
22297 \begin_layout Plain Layout
22305 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
22308 \begin_layout Plain Layout
22309 \begin_inset Formula $\checkmark$
22319 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
22322 \begin_layout Plain Layout
22330 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
22333 \begin_layout Plain Layout
22334 \begin_inset Formula $\yen$
22344 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
22347 \begin_layout Plain Layout
22355 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
22358 \begin_layout Plain Layout
22359 \begin_inset Formula $\pounds$
22369 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
22372 \begin_layout Plain Layout
22378 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
22381 \begin_layout Plain Layout
22382 \begin_inset Formula $\$$
22392 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
22395 \begin_layout Plain Layout
22401 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
22404 \begin_layout Plain Layout
22405 \begin_inset Formula $§$
22419 \begin_inset Tabular
22420 <lyxtabular version="3" rows="10" columns="2">
22421 <features tabularvalignment="middle">
22422 <column alignment="center" valignment="top" width="0">
22423 <column alignment="center" valignment="top" width="0">
22425 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
22428 \begin_layout Plain Layout
22434 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
22437 \begin_layout Plain Layout
22445 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
22448 \begin_layout Plain Layout
22456 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
22459 \begin_layout Plain Layout
22460 \begin_inset Formula $\hbar$
22470 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
22473 \begin_layout Plain Layout
22481 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
22484 \begin_layout Plain Layout
22485 \begin_inset Formula $\hslash$
22495 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
22498 \begin_layout Plain Layout
22506 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
22509 \begin_layout Plain Layout
22510 \begin_inset Formula $\clubsuit$
22520 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
22523 \begin_layout Plain Layout
22531 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
22534 \begin_layout Plain Layout
22535 \begin_inset Formula $\spadesuit$
22545 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
22548 \begin_layout Plain Layout
22556 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
22559 \begin_layout Plain Layout
22560 \begin_inset Formula $\bigstar$
22570 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
22573 \begin_layout Plain Layout
22581 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
22584 \begin_layout Plain Layout
22585 \begin_inset Formula $\blacklozenge$
22595 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
22598 \begin_layout Plain Layout
22606 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
22609 \begin_layout Plain Layout
22610 \begin_inset Formula $\blacktriangle$
22620 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
22623 \begin_layout Plain Layout
22631 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
22634 \begin_layout Plain Layout
22635 \begin_inset Formula $\blacktriangledown$
22645 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
22648 \begin_layout Plain Layout
22656 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
22659 \begin_layout Plain Layout
22660 \begin_inset Formula $\bullet$
22674 \begin_inset Tabular
22675 <lyxtabular version="3" rows="10" columns="2">
22676 <features tabularvalignment="middle">
22677 <column alignment="center" valignment="top" width="0pt">
22678 <column alignment="center" valignment="top" width="0pt">
22680 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
22683 \begin_layout Plain Layout
22689 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
22692 \begin_layout Plain Layout
22700 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
22703 \begin_layout Plain Layout
22711 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
22714 \begin_layout Plain Layout
22715 \begin_inset Formula $\diamondsuit$
22725 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
22728 \begin_layout Plain Layout
22736 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
22739 \begin_layout Plain Layout
22740 \begin_inset Formula $\Diamond$
22750 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
22753 \begin_layout Plain Layout
22761 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
22764 \begin_layout Plain Layout
22765 \begin_inset Formula $\heartsuit$
22775 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
22778 \begin_layout Plain Layout
22786 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
22789 \begin_layout Plain Layout
22790 \begin_inset Formula $\P$
22800 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
22803 \begin_layout Plain Layout
22811 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
22814 \begin_layout Plain Layout
22815 \begin_inset Formula $\copyright$
22825 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
22828 \begin_layout Plain Layout
22836 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
22839 \begin_layout Plain Layout
22840 \begin_inset Formula $\circledR$
22850 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
22853 \begin_layout Plain Layout
22861 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
22864 \begin_layout Plain Layout
22865 \begin_inset Formula $\maltese$
22875 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
22878 \begin_layout Plain Layout
22886 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
22889 \begin_layout Plain Layout
22890 \begin_inset Formula $\diagup$
22900 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
22903 \begin_layout Plain Layout
22911 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
22914 \begin_layout Plain Layout
22915 \begin_inset Formula $\diagdown$
22931 \begin_layout Standard
22932 \begin_inset VSpace medskip
22935 More symbols are listed in
22936 \begin_inset CommandInset ref
22938 reference "sub:Miscellaneous-special-Characters"
22945 \begin_layout Standard
22946 Some symbols can be displayed in different sizes, see
22947 \begin_inset CommandInset ref
22949 reference "sub:Font-Sizes"
22956 \begin_layout Subsection
22958 \begin_inset Index idx
22961 \begin_layout Plain Layout
22962 Symbols ! Euro-symbol
22968 \begin_inset Index idx
22971 \begin_layout Plain Layout
22978 \begin_layout Plain Layout
22995 \begin_layout Standard
22996 To use the Euro symbol in formulas, the LaTeX-package
23001 \begin_inset Index idx
23004 \begin_layout Plain Layout
23010 must be installed and loaded with the LaTeX-preamble line
23013 \begin_layout Standard
23018 usepackage[gennarrow]{eurosym}
23021 \begin_layout Standard
23022 The Euro symbol can now be inserted with the command
23029 \begin_inset Index idx
23032 \begin_layout Plain Layout
23043 \begin_layout Standard
23044 The Euro symbol can directly be inserted with the € key in mathematical
23045 text, without having
23060 can also be inserted in TeX-mode.
23061 The official currency symbol can then be inserted with the command
23068 \begin_inset Index idx
23071 \begin_layout Plain Layout
23079 , that is only available in TeX-mode.
23082 \begin_layout Standard
23086 \begin_layout Plain Layout
23096 \begin_inset Note Note
23099 \begin_layout Plain Layout
23100 The following table will only be displayed when the LaTeX-package
23112 \begin_layout Standard
23113 An overview about the different Euro symbols:
23116 \begin_layout Standard
23118 \begin_inset Tabular
23119 <lyxtabular version="3" rows="4" columns="3">
23120 <features tabularvalignment="middle">
23121 <column alignment="center" valignment="top" width="0pt">
23122 <column alignment="center" valignment="top" width="0pt">
23123 <column alignment="center" valignment="top" width="0pt">
23125 <cell multicolumn="1" alignment="center" valignment="top" bottomline="true" usebox="none">
23128 \begin_layout Plain Layout
23134 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
23137 \begin_layout Plain Layout
23143 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
23146 \begin_layout Plain Layout
23154 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
23157 \begin_layout Plain Layout
23163 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
23166 \begin_layout Plain Layout
23174 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
23177 \begin_layout Plain Layout
23178 \begin_inset Formula $\euro$
23188 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
23191 \begin_layout Plain Layout
23197 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
23200 \begin_layout Plain Layout
23206 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
23209 \begin_layout Plain Layout
23210 \begin_inset Formula $\mbox{€}$
23220 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
23223 \begin_layout Plain Layout
23229 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
23232 \begin_layout Plain Layout
23240 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
23243 \begin_layout Plain Layout
23247 \begin_layout Plain Layout
23269 \begin_layout Standard
23273 \begin_layout Plain Layout
23283 \begin_inset Note Note
23286 \begin_layout Plain Layout
23287 The following will be displayed when the LaTeX-package
23299 \begin_layout Standard
23300 You need to install the LaTeX-package
23304 to see the rest of this subsection in the output.
23307 \begin_layout Standard
23311 \begin_layout Plain Layout
23323 \begin_layout Section
23325 \begin_inset CommandInset label
23327 name "sec:Relations"
23332 \begin_inset Index idx
23335 \begin_layout Plain Layout
23342 \begin_inset Index idx
23345 \begin_layout Plain Layout
23350 \begin_layout Plain Layout
23361 \begin_layout Plain Layout
23376 \begin_layout Standard
23377 All relations can also be inserted via the toolbar button
23378 \begin_inset Graphics
23379 filename ../images/math/leq.png
23387 \begin_layout Standard
23388 \begin_inset space \hfill{}
23392 \begin_inset Tabular
23393 <lyxtabular version="3" rows="17" columns="2">
23394 <features tabularvalignment="middle">
23395 <column alignment="center" valignment="top" width="0pt">
23396 <column alignment="center" valignment="top" width="0pt">
23398 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
23401 \begin_layout Plain Layout
23407 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
23410 \begin_layout Plain Layout
23418 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
23421 \begin_layout Plain Layout
23427 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
23430 \begin_layout Plain Layout
23431 \begin_inset Formula $<$
23441 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
23444 \begin_layout Plain Layout
23452 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
23455 \begin_layout Plain Layout
23456 \begin_inset Formula $\le$
23466 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
23469 \begin_layout Plain Layout
23477 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
23480 \begin_layout Plain Layout
23481 \begin_inset Formula $\ll$
23491 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
23494 \begin_layout Plain Layout
23502 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
23505 \begin_layout Plain Layout
23506 \begin_inset Formula $\prec$
23516 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
23519 \begin_layout Plain Layout
23527 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
23530 \begin_layout Plain Layout
23531 \begin_inset Formula $\preceq$
23541 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
23544 \begin_layout Plain Layout
23552 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
23555 \begin_layout Plain Layout
23556 \begin_inset Formula $\subset$
23566 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
23569 \begin_layout Plain Layout
23577 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
23580 \begin_layout Plain Layout
23581 \begin_inset Formula $\subseteq$
23591 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
23594 \begin_layout Plain Layout
23602 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
23605 \begin_layout Plain Layout
23606 \begin_inset Formula $\sqsubseteq$
23616 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
23619 \begin_layout Plain Layout
23627 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
23630 \begin_layout Plain Layout
23631 \begin_inset Formula $\in$
23641 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
23644 \begin_layout Plain Layout
23652 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
23655 \begin_layout Plain Layout
23656 \begin_inset Formula $\vdash$
23666 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
23669 \begin_layout Plain Layout
23677 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
23680 \begin_layout Plain Layout
23681 \begin_inset Formula $\smile$
23691 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
23694 \begin_layout Plain Layout
23702 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
23705 \begin_layout Plain Layout
23706 \begin_inset Formula $\lhd$
23716 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
23719 \begin_layout Plain Layout
23727 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
23730 \begin_layout Plain Layout
23731 \begin_inset Formula $\unlhd$
23741 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
23744 \begin_layout Plain Layout
23752 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
23755 \begin_layout Plain Layout
23756 \begin_inset Formula $\gtrless$
23766 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
23769 \begin_layout Plain Layout
23777 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
23780 \begin_layout Plain Layout
23781 \begin_inset Formula $\mid$
23791 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
23794 \begin_layout Plain Layout
23802 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
23805 \begin_layout Plain Layout
23806 \begin_inset Formula $\nmid$
23820 \begin_inset space \hfill{}
23824 \begin_inset Tabular
23825 <lyxtabular version="3" rows="17" columns="2">
23826 <features tabularvalignment="middle">
23827 <column alignment="center" valignment="top" width="0pt">
23828 <column alignment="center" valignment="top" width="0pt">
23830 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
23833 \begin_layout Plain Layout
23839 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
23842 \begin_layout Plain Layout
23850 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
23853 \begin_layout Plain Layout
23859 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
23862 \begin_layout Plain Layout
23863 \begin_inset Formula $=$
23873 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
23876 \begin_layout Plain Layout
23884 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
23887 \begin_layout Plain Layout
23888 \begin_inset Formula $\not=$
23898 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
23901 \begin_layout Plain Layout
23909 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
23912 \begin_layout Plain Layout
23913 \begin_inset Formula $\equiv$
23923 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
23926 \begin_layout Plain Layout
23934 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
23937 \begin_layout Plain Layout
23938 \begin_inset Formula $\sim$
23948 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
23951 \begin_layout Plain Layout
23959 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
23962 \begin_layout Plain Layout
23963 \begin_inset Formula $\simeq$
23973 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
23976 \begin_layout Plain Layout
23984 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
23987 \begin_layout Plain Layout
23988 \begin_inset Formula $\approx$
23998 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
24001 \begin_layout Plain Layout
24009 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
24012 \begin_layout Plain Layout
24013 \begin_inset Formula $\cong$
24023 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
24026 \begin_layout Plain Layout
24034 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
24037 \begin_layout Plain Layout
24038 \begin_inset Formula $\bowtie$
24048 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
24051 \begin_layout Plain Layout
24059 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
24062 \begin_layout Plain Layout
24063 \begin_inset Formula $\notin$
24073 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
24076 \begin_layout Plain Layout
24084 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
24087 \begin_layout Plain Layout
24088 \begin_inset Formula $\perp$
24098 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
24101 \begin_layout Plain Layout
24109 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
24112 \begin_layout Plain Layout
24113 \begin_inset Formula $\propto$
24123 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
24126 \begin_layout Plain Layout
24134 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
24137 \begin_layout Plain Layout
24138 \begin_inset Formula $\asymp$
24148 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
24151 \begin_layout Plain Layout
24159 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
24162 \begin_layout Plain Layout
24163 \begin_inset Formula $\doteq$
24173 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
24176 \begin_layout Plain Layout
24184 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
24187 \begin_layout Plain Layout
24188 \begin_inset Formula $\circeq$
24198 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
24201 \begin_layout Plain Layout
24209 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
24212 \begin_layout Plain Layout
24213 \begin_inset Formula $\models$
24223 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
24226 \begin_layout Plain Layout
24234 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
24237 \begin_layout Plain Layout
24238 \begin_inset Formula $\widehat{=}$
24252 \begin_inset space \hfill{}
24256 \begin_inset Tabular
24257 <lyxtabular version="3" rows="17" columns="2">
24258 <features tabularvalignment="middle">
24259 <column alignment="center" valignment="top" width="0pt">
24260 <column alignment="center" valignment="top" width="0pt">
24262 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
24265 \begin_layout Plain Layout
24271 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
24274 \begin_layout Plain Layout
24282 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
24285 \begin_layout Plain Layout
24291 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
24294 \begin_layout Plain Layout
24295 \begin_inset Formula $>$
24305 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
24308 \begin_layout Plain Layout
24316 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
24319 \begin_layout Plain Layout
24320 \begin_inset Formula $\ge$
24330 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
24333 \begin_layout Plain Layout
24341 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
24344 \begin_layout Plain Layout
24345 \begin_inset Formula $\gg$
24355 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
24358 \begin_layout Plain Layout
24366 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
24369 \begin_layout Plain Layout
24370 \begin_inset Formula $\succ$
24380 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
24383 \begin_layout Plain Layout
24391 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
24394 \begin_layout Plain Layout
24395 \begin_inset Formula $\succeq$
24405 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
24408 \begin_layout Plain Layout
24416 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
24419 \begin_layout Plain Layout
24420 \begin_inset Formula $\supset$
24430 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
24433 \begin_layout Plain Layout
24441 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
24444 \begin_layout Plain Layout
24445 \begin_inset Formula $\supseteq$
24455 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
24458 \begin_layout Plain Layout
24466 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
24469 \begin_layout Plain Layout
24470 \begin_inset Formula $\sqsupseteq$
24480 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
24483 \begin_layout Plain Layout
24491 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
24494 \begin_layout Plain Layout
24495 \begin_inset Formula $\ni$
24505 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
24508 \begin_layout Plain Layout
24516 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
24519 \begin_layout Plain Layout
24520 \begin_inset Formula $\dashv$
24530 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
24533 \begin_layout Plain Layout
24541 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
24544 \begin_layout Plain Layout
24545 \begin_inset Formula $\frown$
24555 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
24558 \begin_layout Plain Layout
24566 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
24569 \begin_layout Plain Layout
24570 \begin_inset Formula $\rhd$
24580 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
24583 \begin_layout Plain Layout
24591 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
24594 \begin_layout Plain Layout
24595 \begin_inset Formula $\unrhd$
24605 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
24608 \begin_layout Plain Layout
24616 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
24619 \begin_layout Plain Layout
24620 \begin_inset Formula $\lessgtr$
24630 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
24633 \begin_layout Plain Layout
24641 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
24644 \begin_layout Plain Layout
24645 \begin_inset Formula $\parallel$
24655 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
24658 \begin_layout Plain Layout
24666 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
24669 \begin_layout Plain Layout
24670 \begin_inset Formula $\nparallel$
24684 \begin_inset space \hfill{}
24690 \begin_layout Standard
24691 \begin_inset VSpace medskip
24706 are bigger than the equal looking operators
24721 \begin_layout Standard
24722 Relations are, in contrary to symbols, always surrounded by space.
24725 \begin_layout Standard
24726 Relations with labels can be created with the command
24733 \begin_inset Index idx
24736 \begin_layout Plain Layout
24747 \begin_layout Standard
24749 \begin_inset Tabular
24750 <lyxtabular version="3" rows="2" columns="2">
24751 <features tabularvalignment="middle">
24752 <column alignment="center" valignment="top" width="0">
24753 <column alignment="center" valignment="top" width="0">
24755 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
24758 \begin_layout Plain Layout
24764 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
24767 \begin_layout Plain Layout
24769 \begin_inset Note Note
24772 \begin_layout Plain Layout
24779 is only used as spacer.
24791 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
24794 \begin_layout Plain Layout
24801 \begin_layout Plain Layout
24818 \begin_layout Plain Layout
24828 \begin_inset Formula $\downarrow$
24837 \begin_layout Plain Layout
24850 \begin_layout Plain Layout
24864 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
24867 \begin_layout Plain Layout
24868 \begin_inset Formula $\raisebox{5mm}{}A(r)\stackrel{r\to\infty}{\approx}B$
24884 \begin_layout Section
24888 \begin_layout Subsection
24889 Predefined Functions
24890 \begin_inset CommandInset label
24892 name "sub:Predefined-Functions"
24897 \begin_inset Index idx
24900 \begin_layout Plain Layout
24901 Functions ! predefined
24909 \begin_layout Standard
24910 In general, variables are set
24914 in mathematical expressions, but not function names, because
24915 \begin_inset Formula $sin$
24918 could be misunderstood as
24919 \begin_inset Formula $s\cdot i\cdot n$
24923 Therefore there are predefined functions, that are additionally a bit separated
24925 They are inserted as commands starting with a backslash before their name.
24928 \begin_layout Standard
24930 \begin_inset Tabular
24931 <lyxtabular version="3" rows="2" columns="4">
24932 <features tabularvalignment="middle">
24933 <column alignment="center" valignment="top" width="0pt">
24934 <column alignment="center" valignment="top" width="0pt">
24935 <column alignment="center" valignment="top" width="0pt">
24936 <column alignment="center" valignment="top" width="0pt">
24938 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
24941 \begin_layout Plain Layout
24947 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
24950 \begin_layout Plain Layout
24956 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
24959 \begin_layout Plain Layout
24965 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
24968 \begin_layout Plain Layout
24976 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
24979 \begin_layout Plain Layout
24985 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
24988 \begin_layout Plain Layout
24989 \begin_inset Formula $Asin(x)+B$
24997 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
25000 \begin_layout Plain Layout
25008 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
25011 \begin_layout Plain Layout
25012 \begin_inset Formula $A\sin(x)+B$
25028 \begin_layout Standard
25029 The following functions are predefined:
25032 \begin_layout Standard
25033 \begin_inset VSpace -2mm
25039 \begin_layout Standard
25041 \begin_inset Tabular
25042 <lyxtabular version="3" rows="9" columns="4">
25043 <features tabularvalignment="middle">
25044 <column alignment="center" valignment="top" width="0pt">
25045 <column alignment="center" valignment="top" width="0pt">
25046 <column alignment="center" valignment="top" width="0pt">
25047 <column alignment="center" valignment="top" width="0pt">
25049 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
25052 \begin_layout Plain Layout
25058 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
25061 \begin_layout Plain Layout
25067 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
25070 \begin_layout Plain Layout
25076 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
25079 \begin_layout Plain Layout
25087 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
25090 \begin_layout Plain Layout
25098 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
25101 \begin_layout Plain Layout
25109 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
25112 \begin_layout Plain Layout
25120 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
25123 \begin_layout Plain Layout
25133 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
25136 \begin_layout Plain Layout
25144 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
25147 \begin_layout Plain Layout
25155 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
25158 \begin_layout Plain Layout
25166 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
25169 \begin_layout Plain Layout
25179 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
25182 \begin_layout Plain Layout
25190 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
25193 \begin_layout Plain Layout
25201 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
25204 \begin_layout Plain Layout
25212 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
25215 \begin_layout Plain Layout
25225 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
25228 \begin_layout Plain Layout
25236 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
25239 \begin_layout Plain Layout
25247 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
25250 \begin_layout Plain Layout
25258 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
25261 \begin_layout Plain Layout
25271 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
25274 \begin_layout Plain Layout
25282 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
25285 \begin_layout Plain Layout
25293 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
25296 \begin_layout Plain Layout
25304 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
25307 \begin_layout Plain Layout
25317 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
25320 \begin_layout Plain Layout
25328 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
25331 \begin_layout Plain Layout
25339 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
25342 \begin_layout Plain Layout
25350 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
25353 \begin_layout Plain Layout
25363 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
25366 \begin_layout Plain Layout
25374 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
25377 \begin_layout Plain Layout
25385 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
25388 \begin_layout Plain Layout
25396 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
25399 \begin_layout Plain Layout
25409 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
25412 \begin_layout Plain Layout
25420 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
25423 \begin_layout Plain Layout
25431 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
25434 \begin_layout Plain Layout
25442 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
25445 \begin_layout Plain Layout
25461 \begin_layout Standard
25462 They can also be inserted with the math toolbar button
25463 \begin_inset Graphics
25464 filename ../images/math/functions.png
25472 \begin_layout Subsection
25473 Self-defined Functions
25474 \begin_inset Index idx
25477 \begin_layout Plain Layout
25478 Functions ! self-defined
25486 \begin_layout Standard
25487 To use a function that is not predefined, like for example the sign function
25488 sgn(x), there are two possibilities:
25491 \begin_layout Itemize
25492 Define the function by inserting the following line to the LaTeX-preamble
25496 \begin_layout Plain Layout
25501 DeclareMathOperator
25504 \begin_inset CommandInset ref
25506 reference "sub:Self-defined-Operators"
25516 \begin_inset Newline newline
25520 \begin_inset VSpace -3mm
25524 \begin_inset Newline newline
25531 DeclareMathOperator{
25536 \begin_inset Index idx
25539 \begin_layout Plain Layout
25544 DeclareMathOperator
25550 \begin_inset Newline newline
25554 \begin_inset VSpace -2mm
25558 \begin_inset Newline newline
25561 Now the new defined function can be called with the command
25570 \begin_layout Itemize
25571 Write the formula as usual, mark the formula name, in our example the letters
25576 , and change it to mathematical text.
25577 At last a space is inserted between prefactor and function.
25580 \begin_layout Standard
25581 The result is the same with both methods as with a predefined function
25585 \begin_layout Plain Layout
25586 In LyX self-defined functions are displayed red, predefined ones black.
25594 \begin_layout Standard
25596 \begin_inset Tabular
25597 <lyxtabular version="3" rows="3" columns="2">
25598 <features tabularvalignment="middle">
25599 <column alignment="center" valignment="top" width="0pt">
25600 <column alignment="center" valignment="top" width="0pt">
25602 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
25605 \begin_layout Plain Layout
25611 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
25614 \begin_layout Plain Layout
25622 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
25625 \begin_layout Plain Layout
25633 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
25636 \begin_layout Plain Layout
25637 \begin_inset Formula $A\sgn(x)+B$
25647 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
25650 \begin_layout Plain Layout
25654 \begin_inset Formula $\underbrace{\textrm{sgn}}_{\textrm{Alt+M}\,\textrm{M}}$
25662 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
25665 \begin_layout Plain Layout
25666 \begin_inset Formula $A\,\textrm{sgn}(x)+B$
25682 \begin_layout Standard
25683 The first method is more suitable when the self-defined function should
25684 be used several times.
25687 \begin_layout Subsection
25689 \begin_inset Index idx
25692 \begin_layout Plain Layout
25701 \begin_layout Standard
25702 For limits there are defined besides
25709 \begin_inset Index idx
25712 \begin_layout Plain Layout
25732 furthermore the following functions:
25735 \begin_layout Standard
25737 \begin_inset Tabular
25738 <lyxtabular version="3" rows="5" columns="2">
25739 <features tabularvalignment="middle">
25740 <column alignment="center" valignment="top" width="0">
25741 <column alignment="center" valignment="top" width="0">
25743 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
25746 \begin_layout Plain Layout
25752 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
25755 \begin_layout Plain Layout
25757 \begin_inset Note Note
25760 \begin_layout Plain Layout
25767 is only used as spacer.
25779 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
25782 \begin_layout Plain Layout
25790 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
25793 \begin_layout Plain Layout
25794 \begin_inset Formula $\varliminf$
25804 <cell alignment="center" valignment="top" leftline="true" usebox="none">
25807 \begin_layout Plain Layout
25815 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
25818 \begin_layout Plain Layout
25819 \begin_inset Formula $\varlimsup$
25829 <cell alignment="center" valignment="top" leftline="true" usebox="none">
25832 \begin_layout Plain Layout
25840 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
25843 \begin_layout Plain Layout
25844 \begin_inset Formula $\varprojlim$
25854 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
25857 \begin_layout Plain Layout
25865 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
25868 \begin_layout Plain Layout
25869 \begin_inset Formula $\varinjlim$
25873 \begin_inset Formula $\raisebox{-2.5mm}{}$
25889 \begin_layout Standard
25890 \begin_inset VSpace medskip
25893 The limit is created by inserting a subscript.
25894 It is set right beside the function in an inline formula:
25897 \begin_layout Standard
25899 \begin_inset Tabular
25900 <lyxtabular version="3" rows="2" columns="2">
25901 <features tabularvalignment="middle">
25902 <column alignment="center" valignment="top" width="0pt">
25903 <column alignment="center" valignment="top" width="0pt">
25905 <cell alignment="center" valignment="top" usebox="none">
25908 \begin_layout Plain Layout
25914 <cell alignment="center" valignment="top" usebox="none">
25917 \begin_layout Plain Layout
25918 \begin_inset space \hspace{}
25923 \begin_inset Note Note
25926 \begin_layout Plain Layout
25933 are used here as spacer.
25945 <cell alignment="center" valignment="top" usebox="none">
25948 \begin_layout Plain Layout
25957 \begin_layout Plain Layout
25970 \begin_layout Plain Layout
25984 <cell alignment="center" valignment="top" usebox="none">
25987 \begin_layout Plain Layout
25988 \begin_inset Formula $\hspace{1cm}\raisebox{5mm}{}\lim_{x\to A}x=B$
26004 \begin_layout Standard
26005 In a displayed formula the limit is set below the formula, as usual:
26006 \begin_inset Formula
26016 \begin_layout Subsection
26018 \begin_inset Index idx
26021 \begin_layout Plain Layout
26022 Functions ! modulo-
26030 \begin_layout Standard
26031 The modulo-function is special, because it exists in four variants.
26034 \begin_layout Standard
26035 The variants in a displayed formula:
26036 \begin_inset Formula
26038 \underline{\textrm{Command}\raisebox{-0.9mm}{}} & & \underline{\textrm{Result}}\\
26039 \mathrm{a\backslash mod\textrm{\spce}b} & & a\mod b\\
26040 \mathrm{a\backslash pmod\textrm{\spce}b} & & a\pmod b\\
26041 \mathrm{a\backslash bmod\textrm{\spce}b} & & a\bmod b\\
26042 \mathrm{a\backslash pod\textrm{\spce}b} & & a\pod b
26050 \begin_layout Standard
26051 In an inline formula less space is set before the function names for all
26055 \begin_layout Section
26057 \begin_inset Index idx
26060 \begin_layout Plain Layout
26069 \begin_layout Subsection
26070 Special Characters in Mathematical Text
26073 \begin_layout Standard
26074 The following commands can only be used in mathematical text or in TeX-mode:
26077 \begin_layout Standard
26078 \begin_inset space \hfill{}
26082 \begin_inset Tabular
26083 <lyxtabular version="3" rows="8" columns="2">
26084 <features tabularvalignment="middle">
26085 <column alignment="block" valignment="top" width="0">
26086 <column alignment="block" valignment="top" width="0">
26088 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
26091 \begin_layout Plain Layout
26097 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
26100 \begin_layout Plain Layout
26108 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
26111 \begin_layout Plain Layout
26119 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
26122 \begin_layout Plain Layout
26123 \begin_inset Formula $\textrm{œ}$
26133 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
26136 \begin_layout Plain Layout
26144 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
26147 \begin_layout Plain Layout
26148 \begin_inset Formula $\textrm{Œ}$
26158 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
26161 \begin_layout Plain Layout
26169 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
26172 \begin_layout Plain Layout
26173 \begin_inset Formula $\textrm{æ}$
26183 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
26186 \begin_layout Plain Layout
26194 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
26197 \begin_layout Plain Layout
26198 \begin_inset Formula $\textrm{Æ}$
26208 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
26211 \begin_layout Plain Layout
26219 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
26222 \begin_layout Plain Layout
26223 \begin_inset Formula $\textrm{\aa}$
26233 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
26236 \begin_layout Plain Layout
26240 \begin_inset Index idx
26243 \begin_layout Plain Layout
26250 \begin_layout Plain Layout
26271 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
26274 \begin_layout Plain Layout
26275 \begin_inset Formula $\textrm{Å}$
26285 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
26288 \begin_layout Plain Layout
26296 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
26299 \begin_layout Plain Layout
26300 \begin_inset Formula $\textrm{ı}$
26314 \begin_inset space \hfill{}
26318 \begin_inset Tabular
26319 <lyxtabular version="3" rows="8" columns="2">
26320 <features tabularvalignment="middle">
26321 <column alignment="block" valignment="top" width="0">
26322 <column alignment="center" valignment="top" width="0">
26324 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
26327 \begin_layout Plain Layout
26329 \begin_inset Note Note
26332 \begin_layout Plain Layout
26334 \begin_inset space \thinspace{}
26337 mm is used for separation, because otherwise the output will be ¡ and ¿
26348 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
26351 \begin_layout Plain Layout
26359 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
26362 \begin_layout Plain Layout
26370 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
26373 \begin_layout Plain Layout
26374 \begin_inset Formula $\textrm{ø}$
26384 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
26387 \begin_layout Plain Layout
26395 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
26398 \begin_layout Plain Layout
26399 \begin_inset Formula $\textrm{Ø}$
26409 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
26412 \begin_layout Plain Layout
26420 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
26423 \begin_layout Plain Layout
26424 \begin_inset Formula $\textrm{ł}$
26434 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
26437 \begin_layout Plain Layout
26445 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
26448 \begin_layout Plain Layout
26449 \begin_inset Formula $\textrm{Ł}$
26459 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
26462 \begin_layout Plain Layout
26464 \begin_inset space \hspace{}
26472 \begin_layout Plain Layout
26486 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
26489 \begin_layout Plain Layout
26490 \begin_inset Formula $\textrm{!`}$
26500 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
26503 \begin_layout Plain Layout
26505 \begin_inset space \hspace{}
26513 \begin_layout Plain Layout
26527 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
26530 \begin_layout Plain Layout
26531 \begin_inset Formula $\textrm{?`}$
26541 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
26544 \begin_layout Plain Layout
26552 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
26555 \begin_layout Plain Layout
26556 \begin_inset Formula $\textrm{ȷ}$
26570 \begin_inset space \hfill{}
26576 \begin_layout Standard
26578 \begin_inset Formula $\textrm{\textrm{Å}}$
26582 \begin_inset Formula $\textrm{\textrm{Ø}}$
26585 can also be inserted via the math toolbar button
26586 \begin_inset Graphics
26587 filename ../images/math/digamma.png
26595 \begin_layout Standard
26596 An exception are the commands
26599 \begin_inset space \hspace{}
26608 \begin_inset space \hspace{}
26614 , because they can be inserted in LyX directly to text.
26617 \begin_layout Subsection
26619 \begin_inset CommandInset label
26621 name "sub:Accents-in-Text"
26626 \begin_inset Index idx
26629 \begin_layout Plain Layout
26638 \begin_layout Standard
26639 With the following commands all letters can be accented.
26640 The commands must be inserted in TeX-mode.
26643 \begin_layout Standard
26644 \begin_inset space \hfill{}
26648 \begin_inset Tabular
26649 <lyxtabular version="3" rows="8" columns="2">
26650 <features tabularvalignment="middle">
26651 <column alignment="block" valignment="top" width="0">
26652 <column alignment="block" valignment="top" width="0">
26654 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
26657 \begin_layout Plain Layout
26663 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
26666 \begin_layout Plain Layout
26674 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
26677 \begin_layout Plain Layout
26681 \begin_inset Quotes grd
26689 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
26692 \begin_layout Plain Layout
26696 \begin_layout Plain Layout
26712 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
26715 \begin_layout Plain Layout
26723 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
26726 \begin_layout Plain Layout
26730 \begin_layout Plain Layout
26746 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
26749 \begin_layout Plain Layout
26756 \begin_layout Plain Layout
26770 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
26773 \begin_layout Plain Layout
26777 \begin_layout Plain Layout
26793 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
26796 \begin_layout Plain Layout
26804 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
26807 \begin_layout Plain Layout
26811 \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" bottomline="true" leftline="true" usebox="none">
26877 \begin_layout Plain Layout
26884 \begin_layout Plain Layout
26898 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
26901 \begin_layout Plain Layout
26905 \begin_layout Plain Layout
26921 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
26924 \begin_layout Plain Layout
26931 \begin_layout Plain Layout
26945 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
26948 \begin_layout Plain Layout
26952 \begin_layout Plain Layout
26972 \begin_inset space \hfill{}
26976 \begin_inset Tabular
26977 <lyxtabular version="3" rows="8" columns="2">
26978 <features tabularvalignment="middle">
26979 <column alignment="block" valignment="top" width="0">
26980 <column alignment="center" valignment="top" width="0">
26982 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
26985 \begin_layout Plain Layout
26991 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
26994 \begin_layout Plain Layout
27002 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
27005 \begin_layout Plain Layout
27012 \begin_layout Plain Layout
27026 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
27029 \begin_layout Plain Layout
27033 \begin_layout Plain Layout
27049 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
27052 \begin_layout Plain Layout
27060 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
27063 \begin_layout Plain Layout
27067 \begin_layout Plain Layout
27083 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
27086 \begin_layout Plain Layout
27090 \begin_inset Index idx
27093 \begin_layout Plain Layout
27104 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
27107 \begin_layout Plain Layout
27111 \begin_layout Plain Layout
27127 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
27130 \begin_layout Plain Layout
27138 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
27141 \begin_layout Plain Layout
27145 \begin_layout Plain Layout
27161 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
27164 \begin_layout Plain Layout
27171 \begin_layout Plain Layout
27185 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
27188 \begin_layout Plain Layout
27192 \begin_layout Plain Layout
27208 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
27211 \begin_layout Plain Layout
27218 \begin_layout Plain Layout
27232 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
27235 \begin_layout Plain Layout
27239 \begin_layout Plain Layout
27255 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
27258 \begin_layout Plain Layout
27265 \begin_layout Plain Layout
27279 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
27282 \begin_layout Plain Layout
27286 \begin_layout Plain Layout
27306 \begin_inset space \hfill{}
27312 \begin_layout Standard
27313 \begin_inset VSpace medskip
27322 also two different characters can be accented.
27331 \begin_layout Plain Layout
27346 \begin_layout Plain Layout
27358 \begin_layout Standard
27371 can in combination with vowels directly be inserted with the keyboard without
27373 The same applies for the tilde
27377 \begin_layout Plain Layout
27378 This only applies for keyboards where the tilde is defined as accent.
27387 in combination with
27402 \begin_layout Standard
27445 and accents that are inserted directly with the keyboard are also available
27446 in mathematical text.
27447 For the other accents there are special math commands to be used in formulas,
27449 \begin_inset CommandInset ref
27451 reference "sub:Accents-for-one"
27458 \begin_layout Standard
27459 \begin_inset VSpace bigskip
27462 Furthermore, with the command
27469 \begin_inset Index idx
27472 \begin_layout Plain Layout
27480 all numbers and letters can be set into a circle, quasi accented with a
27481 circle, similar to the copyright symbol.
27484 \begin_layout Standard
27486 \begin_inset Tabular
27487 <lyxtabular version="3" rows="3" columns="2">
27488 <features tabularvalignment="middle">
27489 <column alignment="center" valignment="top" width="0">
27490 <column alignment="center" valignment="top" width="0">
27492 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
27495 \begin_layout Plain Layout
27501 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
27504 \begin_layout Plain Layout
27506 \begin_inset Note Note
27509 \begin_layout Plain Layout
27516 is only used as spacer.
27528 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
27531 \begin_layout Plain Layout
27539 <cell multicolumn="1" alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
27542 \begin_layout Plain Layout
27546 \begin_layout Plain Layout
27562 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
27565 \begin_layout Plain Layout
27576 raisebox{-1.5pt}{W}}
27581 <cell multicolumn="1" alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
27584 \begin_layout Plain Layout
27585 \begin_inset Formula $\raisebox{4.5mm}{}$
27592 \begin_layout Plain Layout
27610 \begin_inset Formula $\raisebox{-2mm}{}$
27626 \begin_layout Standard
27627 One has to take care that the character fits in the circle.
27638 \begin_layout Plain Layout
27640 \begin_inset CommandInset ref
27642 reference "sub:Font-Sizes"
27651 specifies thereby the size of the circle.
27662 \begin_layout Plain Layout
27664 \begin_inset CommandInset ref
27666 reference "sub:Boxes-without-Frame"
27675 the character can be centered.
27678 \begin_layout Subsection
27680 \begin_inset Index idx
27683 \begin_layout Plain Layout
27692 \begin_layout Standard
27693 Minuscule numbers are created with the command
27700 \begin_inset Index idx
27703 \begin_layout Plain Layout
27712 The command can be used in formulas and in TeX-mode.
27713 The command scheme is:
27716 \begin_layout Standard
27721 oldstylenums{number}
27724 \begin_layout Standard
27729 oldstylenums{0123456789
27732 \begin_inset Formula $\oldstylenums{0123456789}$
27738 \begin_layout Subsection
27739 Miscellaneous special Characters
27740 \begin_inset CommandInset label
27742 name "sub:Miscellaneous-special-Characters"
27747 \begin_inset Index idx
27750 \begin_layout Plain Layout
27751 Special characters ! miscellaneous
27759 \begin_layout Standard
27760 The following characters can only be inserted to formulas by using commands:
27763 \begin_layout Standard
27765 \begin_inset Tabular
27766 <lyxtabular version="3" rows="4" columns="2">
27767 <features tabularvalignment="middle">
27768 <column alignment="center" valignment="top" width="0">
27769 <column alignment="center" valignment="top" width="0">
27771 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
27774 \begin_layout Plain Layout
27780 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
27783 \begin_layout Plain Layout
27791 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
27794 \begin_layout Plain Layout
27801 \begin_layout Plain Layout
27815 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
27818 \begin_layout Plain Layout
27819 \begin_inset Formula $\mathcircumflex$
27829 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
27832 \begin_layout Plain Layout
27840 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
27843 \begin_layout Plain Layout
27844 \begin_inset Formula $\_$
27854 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
27857 \begin_layout Plain Layout
27862 \begin_layout Plain Layout
27874 \begin_inset Index idx
27877 \begin_layout Plain Layout
27890 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
27893 \begin_layout Plain Layout
27894 \begin_inset Formula $^{\circ}$
27910 \begin_layout Standard
27911 The degree sign ° can nevertheless be directly inserted if the LaTeX-preamble
27912 contains the following line
27916 \begin_layout Plain Layout
27917 More about this is described in
27918 \begin_inset CommandInset ref
27920 reference "sub:Text-Characters-in"
27932 \begin_layout Standard
27937 DeclareInputtext{176}{
27950 \begin_layout Standard
27951 \begin_inset Newpage newpage
27957 \begin_layout Section
27959 \begin_inset CommandInset label
27961 name "sec:Formula-Styles"
27966 \begin_inset Index idx
27969 \begin_layout Plain Layout
27978 \begin_layout Itemize
27979 There are two different alignment styles:
27983 \begin_layout Description
27984 Centered is the predefined standard
27987 \begin_layout Description
27988 Indented for this the option
27992 must be inserted in the menu
27994 Document\SpecialChar \menuseparator
28000 \begin_inset space ~
28006 \begin_layout Standard
28011 is used, the indentation can be adjusted with the length
28018 \begin_inset Index idx
28021 \begin_layout Plain Layout
28030 Should the distance be 15
28031 \begin_inset space \thinspace{}
28034 mm, the following command line is inserted in the LaTeX-preamble
28037 \begin_layout Standard
28047 \begin_layout Standard
28048 When no length is specified, the predefined value of 30
28049 \begin_inset space \thinspace{}
28056 \begin_layout Itemize
28057 And two different numbering styles:
28061 \begin_layout Description
28062 Right is the predefined standard
28065 \begin_layout Description
28066 Left for this the option
28070 must be inserted in the menu
28072 Document\SpecialChar \menuseparator
28078 \begin_inset space ~
28085 \begin_layout Standard
28094 can also be used together.
28095 In this case both options are inserted, separated by a comma.
28098 \begin_layout Standard
28099 The chosen styles are used for all displayed formulas of the document.
28100 When both, centered and indented formulas should be created in a document,
28106 The indented formulas are then set in a flalign environment, see
28107 \begin_inset CommandInset ref
28109 reference "sub:Flalign-Environment"
28116 \begin_layout Section
28118 \begin_inset CommandInset label
28120 name "sec:Multiline-Formulas"
28125 \begin_inset Index idx
28128 \begin_layout Plain Layout
28129 Formula ! multiline
28137 \begin_layout Subsection
28141 \begin_layout Standard
28142 In LyX multiline formulas are created by pressing
28147 arg "newline-insert newline"
28153 This creates either an
28155 eqnarray environment
28157 that is described in
28158 \begin_inset CommandInset ref
28160 reference "sub:Eqnarray-Environment"
28164 or, when the option
28166 Use AMS math package
28168 in the document settings is selected, an
28172 that is described in
28173 \begin_inset CommandInset ref
28175 reference "sub:Standard-align-Environment"
28182 \begin_layout Standard
28183 There are other multiline formula environments that can be created via the
28186 Insert\SpecialChar \menuseparator
28190 These environments are described in the following sections.
28193 \begin_layout Standard
28194 In all multiline formula environments a new line is created by pressing
28198 arg "newline-insert newline"
28202 To add or delete lines, the math toolbar buttons
28203 \begin_inset Graphics
28204 filename ../images/tabular-feature_append-row.png
28210 \begin_inset Graphics
28211 filename ../images/tabular-feature_delete-row.png
28216 , respectively, or the menu
28218 Edit\SpecialChar \menuseparator
28224 \begin_layout Subsubsection
28226 \begin_inset CommandInset label
28228 name "sub:Line-Separation"
28233 \begin_inset Index idx
28236 \begin_layout Plain Layout
28237 Formula ! multiline ! Line separation
28245 \begin_layout Standard
28246 There is sometimes not enough space in multiline formulas between the lines:
28247 \begin_inset Formula
28249 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}\\
28250 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
28258 \begin_layout Standard
28259 In LaTeX additional line space is specified as optional argument of the
28261 This is not yet possible in LyX
28265 \begin_layout Plain Layout
28267 \begin_inset CommandInset href
28269 name "LyX-bug #1505"
28270 target "http://www.lyx.org/trac/ticket/1505"
28279 , therefore the whole formula must be inserted in TeX-mode.
28280 To add in our example space, the command
28288 is inserted at the end of the first line.
28293 \begin_layout Plain Layout
28300 \begin_layout Plain Layout
28302 B^{2}(B^{2}-2r_{g}^{2}+2x_{0}^{2}-2r_{k}^{2})+4x_{0}^{2}x^{2}+4x_{0}xD &
28305 textrm{-}4x^{2}B^{2}+4x_{0}xB^{2}
28312 \begin_layout Plain Layout
28316 left(B^{2}+x_{0}^{2}
28324 left(B^{2}-2r_{g}^{2}+2x_{0}^{2}-2r_{k}^{2}
28329 \begin_layout Plain Layout
28341 \begin_layout Standard
28342 \begin_inset VSpace bigskip
28345 To set the line separation for all lines in a formula, the length
28352 \begin_inset Index idx
28355 \begin_layout Plain Layout
28365 \begin_inset Formula $\mbox{line separation}=\mathrm{6\, pt+\backslash jot}$
28376 \begin_inset space \thinspace{}
28381 \begin_inset space \thinspace{}
28384 mm additional line separation as in the previous example, the command
28387 \begin_layout Standard
28397 \begin_layout Standard
28398 is inserted in TeX-mode before the formula.
28399 This requires that the LaTeX-package
28407 \begin_layout Plain Layout
28412 is part of every LaTeX standard installation.
28418 \begin_inset Index idx
28421 \begin_layout Plain Layout
28427 was loaded in LaTeX-preamble with the line
28430 \begin_layout Standard
28438 \begin_layout Standard
28443 \begin_layout Plain Layout
28455 \begin_inset Formula
28457 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}\\
28458 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
28466 \begin_layout Standard
28470 \begin_layout Plain Layout
28481 To get back to the predefined distance,
28487 is set to the value 3
28488 \begin_inset space \thinspace{}
28494 \begin_layout Subsubsection
28496 \begin_inset CommandInset label
28498 name "sub:Column-Separation"
28503 \begin_inset Index idx
28506 \begin_layout Plain Layout
28507 Formula ! multiline ! Column separation
28515 \begin_layout Standard
28516 Multiline formulas form a matrix.
28517 A formula in the eqnarray environment is for example a matrix with three
28519 By changing the column separation in this environment, the space beside
28520 the relation sign can be changed.
28523 \begin_layout Standard
28524 The column separation is specified with the length
28531 \begin_inset Index idx
28534 \begin_layout Plain Layout
28543 \begin_inset Newline newline
28546 column separation = 2
28547 \begin_inset space \thinspace{}
28557 \begin_inset Newline newline
28563 \begin_layout Standard
28573 \begin_layout Standard
28574 inserted in TeX-mode, sets for all following formulas a column separation
28576 \begin_inset space \thinspace{}
28580 To get back to the predefined distance,
28587 \begin_inset space \thinspace{}
28593 \begin_layout Standard
28595 \begin_inset space \thinspace{}
28598 cm column separation:
28602 \begin_layout Plain Layout
28614 \begin_inset Formula
28622 A formula with the predefined column separation for matrices of 10
28623 \begin_inset space \thinspace{}
28630 \begin_layout Plain Layout
28642 \begin_inset Formula
28653 \begin_layout Subsubsection
28655 \begin_inset Index idx
28658 \begin_layout Plain Layout
28667 \begin_layout Standard
28668 Long formulas can be typeset using these methods:
28671 \begin_layout Itemize
28672 When one side of the equation is much shorther than the line width, this
28673 one is chosen for the left side and the right side is typeset over two
28675 \begin_inset Formula
28677 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 \\
28678 & & -\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}
28683 The minus sign at the beginning of the second line does normally not appear
28684 as operator because it is the first character of the line.
28685 Thus it would not be surrounded by space and could not be distinguished
28686 from the fraction bar.
28688 \begin_inset space \thinspace{}
28691 pt space was inserted behind the minus sign with the command
28701 \begin_layout Plain Layout
28709 \begin_inset CommandInset ref
28711 reference "sub:Variable-Space"
28721 \begin_inset Index idx
28724 \begin_layout Plain Layout
28735 \begin_layout Itemize
28736 When both sides of the equation are too long, the command
28743 \begin_inset Index idx
28746 \begin_layout Plain Layout
28755 It is inserted to the first column of the first line and effects that all
28756 further insertions overwrite the following columns:
28757 \begin_inset Formula
28759 \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 \\
28760 & & -\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 \\
28761 & & =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}
28766 After the insertion of
28772 , the cursor is in a purple box that is a bit shifted to the left from the
28774 In this the formula is inserted.
28775 \begin_inset Newline newline
28778 The content of the further lines is inserted to the second or another formula
28780 The greater the column number where it was inserted, the larger the indentation.
28781 \begin_inset VSpace medskip
28785 \begin_inset Newline newline
28789 \begin_inset Note Greyedout
28792 \begin_layout Plain Layout
28793 Note the following when using
28802 \begin_layout Itemize
28803 The formula doesn't use the full page width.
28805 \begin_inset space \thinspace{}
28809 \begin_inset space \space{}
28813 \begin_inset Formula $-B^{2}$
28816 is added to the first line in the above example, it would have been outside
28818 To better use the width, negative space can be inserted at the beginning
28822 \begin_layout Itemize
28823 Due to a bug in LyX the cursor cannot be set with the mouse into the first
28828 \begin_layout Plain Layout
28829 \begin_inset CommandInset href
28831 name "LyX-bug #1429"
28832 target "http://www.lyx.org/trac/ticket/1429"
28841 One can only set the cursor at the beginning of the line and move it with
28850 \begin_layout Itemize
28851 Other methods to set long formulas are offered by the environments described
28853 \begin_inset CommandInset ref
28855 reference "sub:Multline-Environment"
28860 \begin_inset CommandInset ref
28862 reference "sub:Multiline-Formula-Parts"
28869 \begin_layout Subsubsection
28871 \begin_inset CommandInset label
28873 name "sub:Multiline-Brackets"
28878 \begin_inset Index idx
28881 \begin_layout Plain Layout
28882 Brackets ! for multiline expressions
28890 \begin_layout Standard
28891 For brackets spanning multiple lines the following problem occurs:
28892 \begin_inset Formula
28894 A & = & \sin(x)\left[\prod_{R=1}^{\infty}\frac{1}{R}+\cdots\right.\\
28895 & & \left.\cdots+B-D\right]
28903 \begin_layout Standard
28904 The closing bracket is smaller than the opening bracket because brackets
28905 with variable size may not span multiple lines.
28908 \begin_layout Standard
28909 To set the bracket size for the second line correctly, the first line is
28917 \begin_inset Index idx
28920 \begin_layout Plain Layout
28928 and the second line with
28936 \begin_layout Plain Layout
28950 \begin_inset CommandInset ref
28952 reference "sub:Automatic-Bracket-Size"
28964 \begin_inset Index idx
28967 \begin_layout Plain Layout
28993 \begin_layout Plain Layout
29012 \begin_layout Plain Layout
29031 \begin_layout Plain Layout
29043 \begin_inset Formula $\downarrow$
29049 \begin_inset Index idx
29052 \begin_layout Plain Layout
29060 is inserted, because the multiplication operator with its limits is the
29061 largest symbol in the first line and this should be the size for the bracket
29062 in the second line.
29065 \begin_layout Standard
29066 The result is this:
29067 \begin_inset Formula
29069 A & = & \sin(x)\left[\prod_{R=1}^{\infty}\frac{1}{R}+\cdots\right.\\
29070 & & \left.\vphantom{\prod_{R=1}^{\infty}}\cdots+B-D\right]
29078 \begin_layout Subsection
29082 \begin_layout Standard
29083 Align environments can be used for every kind of multiline formulas.
29084 They are specially useful to set several formulas side by side.
29087 \begin_layout Standard
29088 Align environments consist of columns.
29089 The odd columns are right aligned, the even ones left aligned.
29090 Every line in an Align environment can be numbered.
29093 \begin_layout Standard
29094 Align environments are created via the menu
29096 Insert\SpecialChar \menuseparator
29102 Edit\SpecialChar \menuseparator
29103 Math\SpecialChar \menuseparator
29104 Change Formula Type
29106 already existing formulas can be converted to Align environments.
29109 \begin_layout Standard
29110 To add or delete columns, the math toolbar buttons
29111 \begin_inset Graphics
29112 filename ../images/tabular-feature_append-column.png
29118 \begin_inset Graphics
29119 filename ../images/tabular-feature_delete-column.png
29124 , respectively, or the menu
29126 Edit\SpecialChar \menuseparator
29132 \begin_layout Subsubsection
29133 Standard align Environment
29134 \begin_inset CommandInset label
29136 name "sub:Standard-align-Environment"
29141 \begin_inset Index idx
29144 \begin_layout Plain Layout
29145 Formula ! multiline ! align environment
29153 \begin_layout Standard
29154 This Align environment is created by presssing
29157 arg "newline-insert newline"
29160 in a formula or by the menu
29162 Insert\SpecialChar \menuseparator
29163 Math\SpecialChar \menuseparator
29164 AMS align Environment
29169 \begin_layout Standard
29170 An example for two formulas set side by side, that are created with a four
29171 column align environment:
29172 \begin_inset Formula
29174 A & =\sin(B) & C & =D\\
29175 C & \ne A & B & \ne D
29180 As it can be seen, the formulas in this environment are placed so as if
29189 \begin_layout Plain Layout
29197 \begin_inset CommandInset ref
29199 reference "sub:Variable-Space"
29210 before the first and after every even column.
29211 When the formula style
29217 \begin_layout Plain Layout
29219 \begin_inset CommandInset ref
29221 reference "sec:Formula-Styles"
29232 is used, the formula is set without the
29238 before the first column.
29241 \begin_layout Subsubsection
29242 Alignat Environment
29243 \begin_inset Index idx
29246 \begin_layout Plain Layout
29247 Formula ! multiline ! alignat environment
29255 \begin_layout Standard
29256 The alignat environment has no predefined column separation.
29257 It can be inserted manually with the spaces that are described
29258 \begin_inset CommandInset ref
29260 reference "sub:Space"
29267 \begin_layout Standard
29268 The above example in the alignat environment where 1
29269 \begin_inset space \thinspace{}
29272 cm space was inserted at the beginning of the second formula:
29273 \begin_inset Formula
29274 \begin{alignat*}{2}
29275 A & =\sin(B) & \hspace{1cm}C & =D\\
29276 C & \ne A & B & \ne D
29281 Because the column separation can be set separately for every column, this
29282 environment is especially suitable to set three and more formulas side
29286 \begin_layout Subsubsection
29287 Flalign Environment
29288 \begin_inset CommandInset label
29290 name "sub:Flalign-Environment"
29295 \begin_inset Index idx
29298 \begin_layout Plain Layout
29299 Formula ! multiline ! flalign environment
29307 \begin_layout Standard
29308 In this environment the first two columns are always set as much as possible
29309 to the left and the last two ones to the right.
29311 \begin_inset Formula
29313 A & =1 & B & =2 & C & =3\\
29314 X & =\textrm{-}1 & Y & =\textrm{-}2 & Z & =4
29322 \begin_layout Standard
29323 By creating a flalign environment with an odd number of columns where an
29324 empty TeX-brace is inserted to the last column, several formulas in a document
29325 can be set to the left, although the formula style
29330 As example the indented formula
29331 \begin_inset CommandInset ref
29333 reference "eq:VolInt"
29338 \begin_inset Formula
29340 \hspace{30pt}\iiint\limits _{V}X\,\mathrm{d}V & =U & {}
29345 The first two columns contain the formula.
29346 To indent it as with the formula style
29351 \begin_inset space \thinspace{}
29354 pt space was inserted at the beginning of the first column.
29357 \begin_layout Subsection
29358 Eqnarray Environment
29359 \begin_inset CommandInset label
29361 name "sub:Eqnarray-Environment"
29366 \begin_inset Index idx
29369 \begin_layout Plain Layout
29370 Formula ! multiline ! eqnarray environment
29378 \begin_layout Standard
29379 When this environment has been created, three blue boxes appear.
29380 The content of the first box is right aligned, the content of the last
29382 The content of the middle box appears centered and a bit smaller, because
29383 it is designed to insert there only relation characters.
29384 \begin_inset Formula
29386 \frac{ABC}{D} & \frac{ABC}{D} & \frac{ABC}{D}\\
29396 \begin_layout Subsection
29398 \begin_inset Index idx
29401 \begin_layout Plain Layout
29402 Formula ! multiline ! gather environment
29410 \begin_layout Standard
29411 This environment consists of only one centered column.
29412 Every line can be numbered.
29413 \begin_inset Formula
29424 \begin_layout Subsection
29425 Multline Environment
29426 \begin_inset CommandInset label
29428 name "sub:Multline-Environment"
29433 \begin_inset Index idx
29436 \begin_layout Plain Layout
29437 Formula ! multiline ! multline environment
29445 \begin_layout Standard
29446 The multline environment consists, like the gather environment, of only
29448 But the first line is left aligned, the last one right aligned.
29449 All other lines are centered.
29450 Therefore this environment is suitable for long formulas.
29452 \begin_inset CommandInset ref
29454 reference "eq:lefteqn"
29458 in the multline environment:
29459 \begin_inset Formula
29461 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}\\
29462 -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}\\
29463 =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}}
29471 \begin_layout Standard
29472 In the output only the last (first) line of a multline environment appears
29473 numbered when the document numbering is right (left).
29477 \begin_layout Plain Layout
29478 numbering styles see
29479 \begin_inset CommandInset ref
29481 reference "sec:Formula-Styles"
29493 \begin_layout Standard
29501 \begin_inset Index idx
29504 \begin_layout Plain Layout
29519 \begin_inset Index idx
29522 \begin_layout Plain Layout
29530 a centered line can be right or left aligned, respectively.
29531 The commands are used as follows:
29534 \begin_layout Standard
29539 shoveright{line content}
29545 shoveleft{line content}
29548 \begin_layout Standard
29549 \begin_inset VSpace medskip
29559 \begin_inset Index idx
29562 \begin_layout Plain Layout
29570 specifies the distance of the first line from the left page margin.
29571 Predefined is the length 0
29572 \begin_inset space \thinspace{}
29578 \begin_layout Standard
29579 As example the above formula where the command
29582 \begin_layout Standard
29592 \begin_layout Standard
29593 was inserted in TeX-mode before:
29597 \begin_layout Plain Layout
29609 \begin_inset Formula
29611 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}\\
29612 \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}}\\
29613 =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}}
29622 \begin_layout Plain Layout
29633 The second line was left aligned using
29642 \begin_layout Subsection
29643 Multiline Formula Parts
29644 \begin_inset CommandInset label
29646 name "sub:Multiline-Formula-Parts"
29651 \begin_inset Index idx
29654 \begin_layout Plain Layout
29655 Formula ! multiline ! formula parts
29663 \begin_layout Standard
29664 To display only parts of a formula with multiple lines, one of the following
29665 environments are used:
29682 They can be inserted via the menu
29684 Insert\SpecialChar \menuseparator
29687 or by using the commands described in this section.
29690 \begin_layout Standard
29691 The first three have the same properties as the corresponding multiline
29692 formula environments, but it is possible to set further formula parts beside
29695 \begin_inset Formula
29697 \left.\begin{aligned}\Delta x\Delta p & \ge\frac{\hbar}{2}\\
29698 \Delta E\Delta t & \ge\frac{\hbar}{2}
29700 \right\} \textrm{Uncertainty relations}
29708 \begin_layout Standard
29709 To get this formula, a displayed formula is created where the command
29716 \begin_inset Index idx
29719 \begin_layout Plain Layout
29728 A purple box appears around the blue formula box where now columns and
29729 lines can be added.
29730 Outside the multiline environment other formula parts can be set, like
29734 \begin_layout Standard
29735 The aligned environment is also suitable for long formulas whose lines are
29736 horizontally aligned.
29737 Using aligned in a displayed formula has the advantage that the formula
29738 number is vertically centered behind the lines.
29740 \begin_inset CommandInset ref
29742 reference "eq:shortlong"
29746 in the aligned environment:
29747 \begin_inset Formula
29749 \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}|}\\
29750 & -\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}|}
29759 \begin_layout Standard
29760 To use the environments
29779 \begin_inset Index idx
29782 \begin_layout Plain Layout
29797 \begin_inset Index idx
29800 \begin_layout Plain Layout
29815 \begin_inset Index idx
29818 \begin_layout Plain Layout
29826 are inserted, respectively.
29827 The split environment has the same properties as the aligned environment
29828 but it can only have two columns.
29831 \begin_layout Subsection
29832 Text in multiline Formulas
29833 \begin_inset CommandInset label
29835 name "sub:Text-in-multiline"
29840 \begin_inset Index idx
29843 \begin_layout Plain Layout
29850 \begin_inset Index idx
29853 \begin_layout Plain Layout
29854 Formula ! multiline ! text
29862 \begin_layout Standard
29863 In the Align environments, and the multline and gather environment, text
29864 can be inserted that will appear in a separate line and doesn't affect
29865 the column alignment.
29866 To do this, the command
29873 \begin_inset Index idx
29876 \begin_layout Plain Layout
29884 is used in the following scheme:
29887 \begin_layout Standard
29895 \begin_layout Standard
29896 The text should not be longer than a line because it cannot be hyphenated.
29897 As LyX doesn't yet support
29903 directly, the text is written as mathematical text.
29910 must hereby be at the beginning of a line and appears in the output above
29912 An example where the text was inserted at the beginning of the second line:
29913 \begin_inset Formula
29915 I & =a\sqrt{2}\int_{0}^{2\pi}\sqrt{1+\cos(\phi)}\;\mathrm{d}\phi\\
29916 \intertext{\text{integrand is symmetric to \ensuremath{\phi=\pi}, therefore}} & =2a\sqrt{2}\int_{0}^{\pi}\sqrt{1+\cos(\phi)}\;\mathrm{d}\phi
29924 \begin_layout Standard
29925 \begin_inset Newpage newpage
29931 \begin_layout Section
29933 \begin_inset Index idx
29936 \begin_layout Plain Layout
29943 \begin_inset Index idx
29946 \begin_layout Plain Layout
29947 Formula ! numbering|see
29951 \begin_layout Plain Layout
29962 \begin_layout Plain Layout
29977 \begin_layout Subsection
29981 \begin_layout Standard
29982 Numbered formulas can be created with the menu
29984 Insert\SpecialChar \menuseparator
29985 Math\SpecialChar \menuseparator
29987 \begin_inset space ~
29995 \begin_inset space ~
30001 Existing formulas can be numbered with the menu
30003 Edit\SpecialChar \menuseparator
30004 Math\SpecialChar \menuseparator
30006 \begin_inset space ~
30014 arg "math-number-toggle"
30018 The formula number is displayed in LyX behind the formula as number sign
30020 The number sign is replaced in the output by the formula number.
30023 \begin_layout Standard
30024 When numbering is turned on in multiline formulas, all lines will be numbered.
30025 But the numbering can be controlled with the menu
30027 Edit\SpecialChar \menuseparator
30028 Math\SpecialChar \menuseparator
30030 \begin_inset space ~
30034 \begin_inset space ~
30038 \begin_inset space ~
30046 arg "math-number-line-toggle"
30052 \begin_layout Standard
30053 Except for inline formulas, all formulas can be numbered with two different
30055 \begin_inset CommandInset ref
30057 reference "sec:Formula-Styles"
30064 \begin_layout Subsection
30066 \begin_inset Index idx
30069 \begin_layout Plain Layout
30070 Cross-references ! to formulas
30078 \begin_layout Standard
30079 All labeled formulas can be cross-referenced.
30080 A label is added by the menu
30082 Insert\SpecialChar \menuseparator
30085 or the toolbar button
30086 \begin_inset Graphics
30087 filename ../images/label-insert.png
30093 The cursor must hereby be inside a displayed formula.
30094 A dialog pops up displaying the prefix
30099 The label is inserted there behind the prefix.
30100 The predefined prefix means
30101 \begin_inset Quotes eld
30105 \begin_inset Quotes erd
30108 and makes it easier to find labels in large documents because it marks
30109 it as formula label to divide it from e.
30110 \begin_inset space \thinspace{}
30114 \begin_inset space \space{}
30118 To change a label, the menu
30120 Insert\SpecialChar \menuseparator
30126 \begin_layout Standard
30127 The name of the label is displayed in LyX within two parentheses behind
30129 A formula with a label is always numbered.
30132 \begin_layout Standard
30133 Cross-references are inserted via the menu
30135 Insert\SpecialChar \menuseparator
30138 or with the toolbar button
30139 \begin_inset Graphics
30140 filename ../images/dialog-show-new-inset_ref.png
30146 A formula cross-reference appears in the output as formula number.
30147 When in the cross-reference dialog window the format
30151 is chosen, the cross-reference appears in the output as formula number
30153 \begin_inset Newline newline
30156 By right-clicking on a cross-reference in LyX, one jumps to the formula
30157 that is referenced.
30160 \begin_layout Standard
30161 Here are as examples cross-references to formulas of the following subsections:
30162 \begin_inset Note Note
30165 \begin_layout Plain Layout
30166 Note the different cross-reference types.
30174 \begin_layout Standard
30176 \begin_inset CommandInset ref
30183 \begin_inset CommandInset ref
30191 \begin_inset CommandInset ref
30197 ) big Latin letters are used for the numbering in contrary to (
30198 \begin_inset CommandInset ref
30207 \begin_layout Standard
30208 \begin_inset VSpace medskip
30211 When the argument of
30219 \begin_layout Plain Layout
30227 \begin_inset CommandInset ref
30229 reference "sub:User-defined-Numbering"
30240 contains a box like in
30241 \begin_inset CommandInset ref
30243 reference "sub:Paragraph-Boxes"
30247 , the formula cannot be referenced.
30250 \begin_layout Subsection
30252 \begin_inset Index idx
30255 \begin_layout Plain Layout
30256 Formula numbering ! subnumbering
30264 \begin_layout Standard
30265 With the help of the commands
30269 begin{subequations}
30277 formulas can be subnumbered.
30278 Both commands are inserted in TeX-mode.
30281 \begin_layout Standard
30283 \begin_inset Formula
30294 \begin_layout Plain Layout
30298 addtocounter{equation}{-1}
30307 \begin_layout Plain Layout
30311 begin{subequations}
30317 \begin_inset VSpace -5mm
30321 \begin_inset Formula
30329 \begin_inset Formula
30339 \begin_layout Standard
30343 \begin_layout Plain Layout
30355 \begin_layout Standard
30356 To create the example, the following is done:
30359 \begin_layout Enumerate
30360 first formula is inserted
30363 \begin_layout Enumerate
30368 addtocounter{equation}{-1}
30370 begin{subequations}
30371 \begin_inset Index idx
30374 \begin_layout Plain Layout
30383 \begin_inset Newline newline
30388 is inserted after the first formula
30391 \begin_layout Enumerate
30392 second formula is inserted
30395 \begin_layout Enumerate
30396 third formula is inserted
30399 \begin_layout Enumerate
30406 is inserted after the third formula
30409 \begin_layout Standard
30410 Every formula between the commands
30422 is subnumbered as a, b,
30423 \begin_inset Newline linebreak
30426 c, \SpecialChar \ldots{}
30427 For multiline formulas every line will be subnumbered.
30428 All subnumbered formulas are treated as
30433 But as every numbered formula increases the counter
30437 by one, the command
30443 is needed to decrease it.
30444 Otherwise the formulas
30445 \begin_inset CommandInset ref
30452 \begin_inset CommandInset ref
30459 \begin_inset CommandInset ref
30465 would be numbered as
30466 \begin_inset CommandInset ref
30473 \begin_inset CommandInset ref
30480 \begin_inset CommandInset ref
30489 \begin_layout Standard
30490 By inserting the commands in TeX-mode, a space is created between the first
30493 \begin_inset space \thinspace{}
30496 mm vertical space is inserted after the command
30500 begin{subequations}
30503 When the formula style
30509 \begin_layout Plain Layout
30511 \begin_inset CommandInset ref
30513 reference "sec:Formula-Styles"
30525 \begin_inset space \thinspace{}
30528 mm space is inserted instead.
30531 \begin_layout Standard
30532 Here is an example for a multiline formula where the numbering was turned
30533 off for the second line:
30537 \begin_layout Plain Layout
30541 begin{subequations}
30547 \begin_inset Formula
30549 A & = & (B-Z)^{2}=(B-Z)(B-Z)\label{eq:d}\\
30550 & = & B^{2}-ZB-BZ+Z^{2}\nonumber \\
30551 & = & B^{2}-2BZ+Z^{2}\label{eq:f}
30560 \begin_layout Plain Layout
30572 \begin_layout Subsection
30573 User-defined Numbering
30574 \begin_inset CommandInset label
30576 name "sub:User-defined-Numbering"
30581 \begin_inset Index idx
30584 \begin_layout Plain Layout
30585 Formula numbering ! user-defined
30593 \begin_layout Standard
30594 \begin_inset Index idx
30597 \begin_layout Plain Layout
30598 Formula numbering ! self-defined delimiters
30603 With the standard numbering parentheses are set around the formula number.
30604 To replace the parentheses for example by vertical bars, the following
30605 line is added to the LaTeX-preamble:
30608 \begin_layout Standard
30620 \begin_inset Note Note
30623 \begin_layout Plain Layout
30624 This macro is already declared in the LaTeX-preamble for testing.
30625 To activate it, remove the percent sign at the beginning.
30633 \begin_layout Standard
30634 To use other characters, the vertical bars besides the
30638 are replaced by one ore more characters.
30639 To get only the formula number the vertical bars are omitted.
30642 \begin_layout Standard
30643 \begin_inset VSpace bigskip
30646 When there should be an expression of your choice instead of the consecutive
30647 formula number in parentheses behind the formula, the command
30654 \begin_inset Index idx
30657 \begin_layout Plain Layout
30666 \begin_inset Formula
30668 A+B=C\tag{something}\label{eq:tag}
30673 In this example the command
30681 \begin_layout Plain Layout
30692 was inserted to the formula.
30695 \begin_layout Standard
30704 \begin_layout Plain Layout
30715 is inserted instead, the star prevents the parentheses around the expression:
30716 \begin_inset Formula
30718 A+B=C\tag*{something}
30726 \begin_layout Standard
30727 \begin_inset VSpace bigskip
30730 To restart the formula numbering with new document parts or sections, the
30731 following command is used:
30734 \begin_layout Standard
30739 @addtoreset{equation}{part}
30742 \begin_inset Index idx
30745 \begin_layout Plain Layout
30750 \begin_layout Plain Layout
30761 \begin_layout Plain Layout
30774 \begin_layout Plain Layout
30785 \begin_layout Plain Layout
30798 \begin_inset Newline newline
30802 \begin_inset Newline newline
30809 @addtoreset{equation}{section}
30812 \begin_layout Standard
30813 To be able to use these commands in TeX-mode, the
30814 \begin_inset Quotes eld
30818 \begin_inset Quotes erd
30821 character has to be made
30822 \begin_inset Quotes eld
30826 \begin_inset Quotes erd
30829 for LaTeX using the command
30843 So the command sequence in TeX-mode is:
30846 \begin_layout Standard
30852 \begin_inset Newline newline
30857 @addtoreset{equation}{section}
30858 \begin_inset Newline newline
30866 \begin_layout Standard
30867 In the LaTeX-preamble
30879 can be omitted as they are automatically internally inserted by LyX.
30882 \begin_layout Standard
30897 \begin_layout Plain Layout
30902 is part of the LaTeX-package
30907 \begin_inset Index idx
30910 \begin_layout Plain Layout
30911 Packages ! carlisle
30916 that is part of every LaTeX standard installation.
30922 \begin_inset Index idx
30925 \begin_layout Plain Layout
30926 Packages ! remreset
30931 has to be loaded in the LaTeX-preamble with the line
30934 \begin_layout Standard
30939 usepackage{remreset}
30942 \begin_layout Standard
30950 \begin_inset Index idx
30953 \begin_layout Plain Layout
30958 \begin_layout Plain Layout
30969 \begin_layout Plain Layout
30982 \begin_layout Plain Layout
30993 \begin_layout Plain Layout
31005 can be used with the same scheme as
31014 \begin_layout Standard
31015 \begin_inset VSpace bigskip
31018 Sometimes formulas should be numbered in the following form:
31021 \begin_layout Standard
31024 (section number.formula number)
31027 \begin_layout Standard
31028 The formula number should start with every section with
31029 \begin_inset Quotes eld
31033 \begin_inset Quotes erd
31039 \begin_layout Standard
31040 For this case there is the command
31047 \begin_inset Index idx
31050 \begin_layout Plain Layout
31058 , which is used with the following scheme:
31061 \begin_layout Standard
31066 numberwithin{counter}{sectioning}
31069 \begin_layout Standard
31070 Counter denotes what kind of numbering is affected, sectioning denotes what
31071 number is before the dot.
31074 \begin_layout Standard
31075 Thus in our case the following LaTeX-preamble or TeX-Code line is used:
31078 \begin_layout Standard
31083 numberwithin{equation}{section}
31086 \begin_layout Standard
31087 This is the result:
31091 \begin_layout Plain Layout
31095 numberwithin{equation}{section}
31101 \begin_inset Formula
31111 \begin_layout Standard
31113 \begin_inset space \thinspace{}
31117 \begin_inset space \space{}
31120 tables so that the number of the part is the sectioning,
31121 \begin_inset Newline newline
31128 numberwithin{table}{part}
31133 \begin_layout Standard
31134 To go back to the standard numbering or to prevent this kind of numbering
31135 when it is defined by the document class, the following command is inserted
31136 as TeX-Code or to the LaTeX-preamble:
31139 \begin_layout Standard
31149 \begin_inset Index idx
31152 \begin_layout Plain Layout
31166 \begin_layout Plain Layout
31182 \begin_inset Newline newline
31190 \begin_inset Newline newline
31202 \begin_layout Standard
31209 uses internally the command
31215 , described above, that also needs to be reverted.
31219 \begin_layout Plain Layout
31226 \begin_layout Plain Layout
31230 @removefromreset{equation}{section}
31233 \begin_layout Plain Layout
31245 \begin_layout Subsection
31246 Numbering with Roman Numbers and Letters
31247 \begin_inset Index idx
31250 \begin_layout Plain Layout
31251 Formula numbering ! with letters
31257 \begin_inset Index idx
31260 \begin_layout Plain Layout
31261 Formula numbering ! with Roman numbers
31269 \begin_layout Standard
31270 Formulas can also be numbered with Roman numbers and Latin letters.
31271 To number for example with small Roman numbers, the command
31274 \begin_layout Standard
31286 \begin_layout Standard
31287 is inserted before the formula in TeX-mode.
31295 \begin_inset Index idx
31298 \begin_layout Plain Layout
31306 redefines the predefined command
31322 \begin_layout Plain Layout
31329 has the same scheme like the command
31335 that is described in
31336 \begin_inset CommandInset ref
31338 reference "sub:The-Command-newcommand"
31351 is the formula counter.
31358 is used as prefix for a counter, the value of the counter is output as
31360 When a formula is numbered, LaTeX sets internally the command
31366 behind the formula.
31372 \begin_inset Index idx
31375 \begin_layout Plain Layout
31385 outputs the counter as small Roman number.
31388 \begin_layout Standard
31389 All formulas behind the command
31399 are now numbered Roman.
31400 To switch to numbering with big Roman numbers, the command is inserted
31414 \begin_inset Index idx
31417 \begin_layout Plain Layout
31429 \begin_inset Quotes eld
31433 \begin_inset Quotes erd
31436 with small Latin letters there is the command
31443 \begin_inset Index idx
31446 \begin_layout Plain Layout
31454 , for big ones there is the command
31461 \begin_inset Index idx
31464 \begin_layout Plain Layout
31477 \begin_layout Standard
31478 \begin_inset Note Greyedout
31481 \begin_layout Plain Layout
31486 Only maximal 26 formulas can be numbered with Latin letters in one document.
31494 \begin_layout Standard
31498 \begin_layout Plain Layout
31514 \begin_layout Standard
31515 \begin_inset Formula
31517 A=\textrm{small roman}
31526 \begin_layout Plain Layout
31540 \begin_inset Formula
31542 B=\textrm{big Roman}\label{eq:Rom}
31551 \begin_layout Plain Layout
31565 \begin_inset Formula
31567 C=\textrm{small Latin}
31576 \begin_layout Plain Layout
31590 \begin_inset Formula
31592 D=\textrm{big Latin}\label{eq:Lat}
31600 \begin_layout Standard
31601 To switch back to the default numbering, insert the command:
31604 \begin_layout Standard
31614 \begin_inset Index idx
31617 \begin_layout Plain Layout
31628 \begin_layout Standard
31632 \begin_layout Plain Layout
31646 \begin_inset Formula
31656 \begin_layout Standard
31657 \begin_inset VSpace medskip
31660 As you see, formulas are numbered serially independent from the numbering
31662 When then numbering should start with
31663 \begin_inset Quotes eld
31667 \begin_inset Quotes erd
31670 when the style is changed, new equation counters have to be defined.
31671 A description about this can be found in the file
31672 \begin_inset CommandInset href
31674 name "Formula-numbering.lyx"
31675 target "run:Formula-numbering.lyx"
31682 \begin_layout Section
31683 Chemical Symbols and Equations
31684 \begin_inset CommandInset label
31686 name "sub:Chemical-Symbols-and"
31691 \begin_inset Index idx
31694 \begin_layout Plain Layout
31695 Chemical characters ! Symbols
31701 \begin_inset Index idx
31704 \begin_layout Plain Layout
31711 \begin_inset Index idx
31714 \begin_layout Plain Layout
31723 \begin_layout Standard
31724 An example text from chemistry:
31727 \begin_layout Quote
31729 \begin_inset Formula $\mathrm{SO_{4}^{2-}}$
31732 -ion reacts with two
31733 \begin_inset Formula $\mathrm{Na^{+}}$
31736 -ions to sodium sulfate
31737 \begin_inset Formula $\left(\mathrm{Na_{2}SO_{4}}\right)$
31741 The chemical equation for this is:
31742 \begin_inset Formula
31744 \mathrm{2\, Na^{+}+SO_{4}^{2-}\longrightarrow Na_{2}SO_{4}}\label{eq:chem-reaction}
31752 \begin_layout Standard
31753 This chemical equation can directly be created as formula.
31754 To avoid that the symbols appear italic, everything is highlighted and
31755 changed by the shortcut
31761 to the upright font style.
31765 \begin_layout Plain Layout
31771 \begin_inset CommandInset ref
31773 reference "sub:Font-Styles"
31785 \begin_layout Standard
31786 A more convenient way to typeset chemical formulas is to use the command
31794 \begin_inset Index idx
31797 \begin_layout Plain Layout
31805 that is available when the LaTeX-package
31810 \begin_inset Index idx
31813 \begin_layout Plain Layout
31826 to a formula a new blue box appears where chemical formulas can be inserted
31827 in an intuitive way.
31830 \begin_layout Standard
31832 \begin_inset Tabular
31833 <lyxtabular version="3" rows="9" columns="2">
31834 <features tabularvalignment="middle">
31835 <column alignment="center" valignment="top" width="0">
31836 <column alignment="center" valignment="top" width="0">
31838 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
31841 \begin_layout Plain Layout
31847 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
31850 \begin_layout Plain Layout
31852 \begin_inset Note Note
31855 \begin_layout Plain Layout
31862 is only used as spacer.
31874 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
31877 \begin_layout Plain Layout
31884 \begin_layout Plain Layout
31898 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
31901 \begin_layout Plain Layout
31902 \begin_inset Formula $\raisebox{4.5mm}{}\ce{H2CO3}\raisebox{-2mm}{}$
31912 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
31915 \begin_layout Plain Layout
31922 \begin_layout Plain Layout
31936 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
31939 \begin_layout Plain Layout
31940 \begin_inset Formula $\raisebox{5mm}{}\ce{SO4^{2-}}\raisebox{-2mm}{}$
31950 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
31953 \begin_layout Plain Layout
31960 \begin_layout Plain Layout
31974 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
31977 \begin_layout Plain Layout
31978 \begin_inset Formula $\raisebox{4.5mm}{}\ce{(NH4)2S}\raisebox{-2mm}{}$
31988 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
31991 \begin_layout Plain Layout
31998 \begin_layout Plain Layout
32012 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
32015 \begin_layout Plain Layout
32016 \begin_inset Formula $\raisebox{4.5mm}{}\ce{KCr(SO4)2.12H2O}\raisebox{-2mm}{}$
32026 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
32029 \begin_layout Plain Layout
32036 \begin_layout Plain Layout
32051 \begin_layout Plain Layout
32066 \begin_layout Plain Layout
32080 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
32083 \begin_layout Plain Layout
32084 \begin_inset Formula $\raisebox{4.5mm}{}\ce{A-B\dbond C\tbond D}\raisebox{-2mm}{}$
32094 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
32097 \begin_layout Plain Layout
32104 \begin_layout Plain Layout
32114 \begin_inset Formula $\downarrow$
32118 \begin_inset Formula $\to$
32126 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
32129 \begin_layout Plain Layout
32130 \begin_inset Formula $\raisebox{5mm}{}\ce{_{90}^{227}Th+}\raisebox{-2mm}{}$
32140 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
32143 \begin_layout Plain Layout
32150 \begin_layout Plain Layout
32163 \begin_layout Plain Layout
32176 \begin_layout Plain Layout
32189 \begin_layout Plain Layout
32202 \begin_layout Plain Layout
32216 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
32219 \begin_layout Plain Layout
32220 \begin_inset Formula $\raisebox{4.5mm}{}\ce{CO2 + C <=> 2CO}\raisebox{-2mm}{}$
32230 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
32233 \begin_layout Plain Layout
32240 \begin_layout Plain Layout
32253 \begin_layout Plain Layout
32266 \begin_layout Plain Layout
32279 \begin_layout Plain Layout
32296 \begin_layout Plain Layout
32310 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
32313 \begin_layout Plain Layout
32314 \begin_inset Formula $\raisebox{5mm}{}\ce{CO2 + C ->[\alpha][\beta] 2CO}\raisebox{-4mm}{}$
32330 \begin_layout Standard
32331 \begin_inset Note Greyedout
32334 \begin_layout Plain Layout
32339 Inserting a formula to a
32345 box will lead to LaTeX errors.
32346 In this case TeX code has to be used like for
32360 \begin_layout Plain Layout
32381 \begin_layout Standard
32388 the command for equation
32389 \begin_inset space ~
32393 \begin_inset CommandInset ref
32395 reference "eq:chem-reaction"
32400 \begin_inset Newline newline
32411 \begin_layout Plain Layout
32424 \begin_layout Plain Layout
32437 \begin_layout Plain Layout
32450 \begin_layout Plain Layout
32463 \begin_layout Plain Layout
32476 \begin_layout Plain Layout
32488 \begin_layout Standard
32489 To create multiline chemical equations first a multiline formula is created
32491 \begin_inset CommandInset ref
32493 reference "sec:Multiline-Formulas"
32498 Afterwards the command
32504 is used in every small blue box of the formula.
32506 \begin_inset CommandInset ref
32508 reference "eq:TEOS-reaction-1"
32513 \begin_inset CommandInset ref
32515 reference "eq:TEOS-reaction-2"
32519 are an example of a multi-stage chemical reaction where every equation
32520 has its own number.
32521 \begin_inset Formula
32523 \ce{TEOS + 4O} & \ce{->} & \ce{Si(OH)4 + 4C2H4O}\label{eq:TEOS-reaction-1}\\
32524 \ce{Si(OH)4} & \ce{->} & \ce{SiO2 + 2H2O}\label{eq:TEOS-reaction-2}
32532 \begin_layout Standard
32543 package provides the command
32550 \begin_inset Index idx
32553 \begin_layout Plain Layout
32561 that has to be used for special cases.
32562 For more information about
32568 and more examples have a look at the documentation of
32573 \begin_inset CommandInset citation
32582 \begin_layout Section
32586 \begin_layout Standard
32587 LyX supports two types of commutative diagrams:
32595 that are explained in the following.
32598 \begin_layout Subsection
32600 \begin_inset Index idx
32603 \begin_layout Plain Layout
32612 \begin_layout Standard
32613 Diagrams of this type visualize relations by vertical and horizontal lines
32615 \begin_inset Formula
32617 \begin{CD}A@>>>B@>>>C\\
32628 \begin_layout Standard
32629 To get them, the command
32634 \begin_inset Index idx
32637 \begin_layout Plain Layout
32647 is inserted to a formula.
32648 A blue box appears with two dashed lines where further commands can be
32653 arg "newline-insert newline"
32656 a new line is created.
32657 Horizontal relations are inserted in odd, vertical in even formula lines.
32660 \begin_layout Standard
32661 To create the relations there are the following commands:
32664 \begin_layout Itemize
32669 creates a left arrow,
32680 \begin_layout Itemize
32685 creates an up arrow,
32693 a vertical equal sign
32696 \begin_layout Itemize
32702 is a placeholder for non-existent relations
32705 \begin_layout Standard
32706 All arrows can be labeled as follows:
32709 \begin_layout Itemize
32710 Is text inserted between the first and second < or >, resp., it is placed
32712 When it is inserted between the second and third one, it appears under
32716 \begin_layout Itemize
32717 When text for vertical arrows is inserted between the first and second A
32718 or V, resp., it is placed left beside the arrow.
32719 When it is inserted between the second and third one, it appears right
32721 If the text contains an A or V, these letters must be set into a TeX-brace.
32724 \begin_layout Standard
32725 As example a diagram with all possible relations:
32728 \begin_layout Standard
32729 \begin_inset Formula
32731 \begin{CD}A@>j>>B@>>k>C@=F\\
32742 \begin_layout Standard
32743 The command for this is:
32744 \begin_inset Newline newline
32755 \begin_layout Plain Layout
32764 A@>j>>B@>>k>C@=F Ctrl+Return
32765 \begin_inset Newline newline
32769 \begin_inset Phantom HPhantom
32772 \begin_layout Plain Layout
32781 \begin_layout Plain Layout
32800 \begin_inset Formula $\to$
32806 \begin_inset Newline newline
32810 \begin_inset Phantom HPhantom
32813 \begin_layout Plain Layout
32822 \begin_layout Plain Layout
32839 \begin_layout Subsection
32841 \begin_inset Index idx
32844 \begin_layout Plain Layout
32845 Diagrams ! xymatrix
32853 \begin_layout Standard
32854 To be able to use xymatrices, the LaTeX-package
32859 A xymatrix is created by inserting the command
32866 Then you are able to add new matrix columns and rows like for normal matrices,
32868 \begin_inset CommandInset ref
32870 reference "sec:Matrices"
32877 \begin_layout Standard
32878 In contrary to amscd diagrams, xymatrices supports diagonal and curved arrows,
32880 All possibilities to create commutative diagrams and decorations are explained
32885 that you find in the menu
32887 Help\SpecialChar \menuseparator
32889 \begin_inset space ~
32897 \begin_layout Subsection
32903 \begin_inset Index idx
32906 \begin_layout Plain Layout
32915 \begin_layout Standard
32920 -diagrams, the LaTeX-package
32929 -diagram is created by inserting the command
32936 Then you are able to add new matrix columns and rows like for normal matrices,
32938 \begin_inset CommandInset ref
32940 reference "sec:Matrices"
32947 \begin_layout Standard
32948 Examples how to create
32952 diagrams in LyX is given in the
32954 Feynman-diagram manual
32956 that you find in the menu
32958 Help\SpecialChar \menuseparator
32960 \begin_inset space ~
32968 \begin_layout Section
32969 User-defined Commands
32970 \begin_inset Index idx
32973 \begin_layout Plain Layout
32974 User-defined commands
32982 \begin_layout Standard
32983 \begin_inset Note Greyedout
32986 \begin_layout Plain Layout
32991 The names of user-defined commands and macros may only consist of Latin
33000 \begin_layout Subsection
33004 \begin_inset CommandInset label
33006 name "sub:The-Command-newcommand"
33011 \begin_inset Index idx
33014 \begin_layout Plain Layout
33015 User-defined commands !
33023 \begin_inset Index idx
33026 \begin_layout Plain Layout
33037 \begin_layout Standard
33038 Many LaTeX-commands are too long to be used frequently.
33039 But it is possible to define with the command
33045 new shorter commands.
33048 \begin_layout Standard
33049 The command scheme of
33058 \begin_layout Standard
33063 newcommand{new command name}[number of arguments][optional
33068 \begin_inset Newline newline
33072 \begin_inset Phantom HPhantom
33075 \begin_layout Plain Layout
33085 {command definition}
33088 \begin_layout Standard
33089 \begin_inset Note Greyedout
33092 \begin_layout Plain Layout
33097 Assure that the name of the new command is not already used in your document
33098 or by LaTeX-packages that you use.
33099 When you for example define the command
33111 , you get an error message because
33117 is already defined as command for
33118 \begin_inset Quotes eld
33122 \begin_inset Formula $\le$
33126 \begin_inset Quotes erd
33137 \begin_layout Standard
33138 The number of arguments is an integer in the range 0
33139 \begin_inset space \thinspace{}
33143 \begin_inset space \thinspace{}
33146 9 and specifies how many arguments the new command should have.
33147 With the optional value a value for an optional argument can be predefined.
33148 When this is done, the
33156 rgument of the new command is automatically an optional one.
33159 \begin_layout Standard
33160 Here are some examples:
33163 \begin_layout Itemize
33164 To define the command
33176 , the LaTeX-preamble line is:
33177 \begin_inset VSpace medskip
33181 \begin_inset Newline newline
33195 \begin_layout Itemize
33196 To define the command
33208 , the argument (that should be underlined) must be taken into account.
33209 For this the preamble line is:
33210 \begin_inset VSpace medskip
33214 \begin_inset Newline newline
33228 \begin_inset VSpace medskip
33232 \begin_inset Newline newline
33239 acts as argument placeholder, the
33243 behind it denotes that it is the placeholder for the first argument.
33246 \begin_layout Itemize
33254 \begin_inset space \thinspace{}
33258 \begin_inset space \space{}
33268 \begin_inset VSpace medskip
33272 \begin_inset Newline newline
33283 framebox#1#2{$#3$}}
33286 \begin_inset VSpace medskip
33290 \begin_inset Newline newline
33293 The two Dollar signs creates the extra formula needed for
33300 \begin_inset CommandInset ref
33302 reference "sub:Boxes-with-Frame"
33309 \begin_layout Itemize
33310 To create a new command for
33316 where the color for the box needn't to be specified, the argument for the
33317 color is defined optional:
33318 \begin_inset VSpace medskip
33322 \begin_inset Newline newline
33333 fcolorbox{#2}{#1}{$#3$}}
33336 \begin_inset VSpace medskip
33340 \begin_inset Newline newline
33343 When the color is not specified when using
33349 , the predefined color
33356 \begin_layout Standard
33357 A test of the new defined commands:
33360 \begin_layout Standard
33362 \begin_inset Tabular
33363 <lyxtabular version="3" rows="6" columns="2">
33364 <features tabularvalignment="middle">
33365 <column alignment="center" valignment="top" width="0">
33366 <column alignment="center" valignment="top" width="0">
33368 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
33371 \begin_layout Plain Layout
33377 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
33380 \begin_layout Plain Layout
33382 \begin_inset Note Note
33385 \begin_layout Plain Layout
33392 is only used as spacer.
33404 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
33407 \begin_layout Plain Layout
33414 \begin_layout Plain Layout
33428 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
33431 \begin_layout Plain Layout
33432 \begin_inset Formula $A\gr B$
33442 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
33445 \begin_layout Plain Layout
33453 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
33456 \begin_layout Plain Layout
33457 \begin_inset Formula $\raisebox{4.5mm}{}\us{ABcd}\raisebox{-2mm}{}$
33467 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
33470 \begin_layout Plain Layout
33474 \begin_inset Formula $\to$
33480 \begin_inset Formula $\to$
33491 \begin_layout Plain Layout
33505 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
33508 \begin_layout Plain Layout
33509 \begin_inset Formula $\raisebox{6mm}{}\fb{[2cm]}{}{\int A=B}\raisebox{-4mm}{}$
33519 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
33522 \begin_layout Plain Layout
33526 \begin_inset Formula $\to$
33537 \begin_layout Plain Layout
33551 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
33554 \begin_layout Plain Layout
33555 \begin_inset Formula $\raisebox{6mm}{}\cb{red}{\int A=B}\raisebox{-4mm}{}$
33565 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
33568 \begin_layout Plain Layout
33574 \begin_inset Formula $\to$
33585 \begin_layout Plain Layout
33599 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
33602 \begin_layout Plain Layout
33603 \begin_inset Formula $\raisebox{6mm}{}\cb[green]{red}{\int A=B}\raisebox{-4mm}{}$
33619 \begin_layout Subsection
33621 \begin_inset Index idx
33624 \begin_layout Plain Layout
33625 User-defined commands! Math macros
33631 \begin_inset Index idx
33634 \begin_layout Plain Layout
33643 \begin_layout Standard
33644 User-defined commands are especially convenient for complex expressions.
33645 When you are for example dealing in a document with quadratic equations,
33646 the same solution type occurs several times.
33647 The general form of a quadratic equation is
33648 \begin_inset Formula
33650 0=\lambda^{2}+p\lambda+q
33655 The general form of the solution is
33656 \begin_inset Formula
33658 \lambda_{1,2}=-\frac{p}{2}\pm\sqrt{\frac{p²}{4}-q}
33666 \begin_layout Standard
33667 To define a command for the solution formula where only the three parameters
33669 \begin_inset Formula $\lambda$
33673 \begin_inset Formula $p$
33677 \begin_inset Formula $q$
33680 need to be specified and the index of
33681 \begin_inset Formula $\lambda$
33684 can be given optionally, the LaTeX-preamble line is
33685 \begin_inset Newline newline
33701 \begin_inset Newline newline
33705 \begin_inset Phantom HPhantom
33708 \begin_layout Plain Layout
33722 frac{#3^{2}}{4}-#4}}
33725 \begin_layout Standard
33726 To create with this the solution formula, the command
33727 \begin_inset Newline newline
33737 \begin_inset Formula $\to$
33743 \begin_inset Formula $\to$
33750 is inserted to a formula
33755 \begin_layout Standard
33756 The definition of the new command is unintuitive because one has to know
33757 the schemes of all used LaTeX commands, e.
33758 \begin_inset space \thinspace{}
33762 \begin_inset space \space{}
33765 that a fraction is inserted in LaTeX as
33769 frac{numerator}{denominator}
33772 Furthermore one can easily forget a brace in the definition and cannot
33773 see in LyX what the new command is doing.
33774 To avoid these problems LyX offers the possibility to use math macros instead
33784 \begin_layout Standard
33785 A math macro is created by using the menu
33787 Insert\SpecialChar \menuseparator
33788 Math\SpecialChar \menuseparator
33791 or the toolbar button
33792 \begin_inset Graphics
33793 filename ../images/math-macro_newmacroname_newcommand.png
33799 The math macro toolbar appears together with the following box where the
33801 \begin_inset Newline newline
33805 \begin_inset space \hspace*{\fill}
33809 \begin_inset Graphics
33810 filename clipart/macrobox.png
33815 \begin_inset space \hspace*{\fill}
33819 \begin_inset Newline newline
33823 \begin_inset FormulaMacro
33824 \newcommand{\qG}[4][1,\,2]{#2_{#1}=-\frac{#3}{2}\pm\sqrt{\frac{#3^{2}}{4}-#4}}
33829 newmacroname is the default name of the macro that should be changed to
33830 something sensible.
33831 The wanted formula is inserted in the first blue box.
33832 An argument placeholder is inserted with the command
33839 \begin_inset space \thinspace{}
33843 \begin_inset space \space{}
33852 or by using the macro toolbar button
33853 \begin_inset Graphics
33854 filename ../images/math-macro-add-param.png
33860 Argument placeholders are displayed red.
33861 Maximum 9 arguments are possible.
33862 Optional arguments are created with the toolbar button
33863 \begin_inset Graphics
33864 filename ../images/math-macro-add-optional-param.png
33870 The first non-optional argument can be transformed to an optional one with
33872 \begin_inset Graphics
33873 filename ../images/math-macro-make-optional.png
33879 In the second blue box the appearance of the macro in LyX can be defined.
33880 Normally you want to see it as it is defined, so the box is kept empty.
33881 But when you have created a macro that needs lot of space on the screen,
33882 you can insert in the box for example
33883 \begin_inset Newline newline
33913 \begin_inset Newline newline
33918 For the macro only the arguments with the macro name in front of them will
33919 then be displayed in LyX, leading to a better overview.
33920 The formula appears in the output as defined in the first box.
33921 \begin_inset Newline newline
33924 The appearance of macros in formulas can furthermore be changed for single
33925 macros by setting the cursor in the macro and using the menu
33927 View\SpecialChar \menuseparator
33929 \begin_inset space ~
33933 \begin_inset space ~
33941 \begin_layout Standard
33942 To use a macro, the macro name is inserted as command to a formula, in our
33950 Our macro looks in LyX like this:
33951 \begin_inset Newline newline
33955 \begin_inset space \hspace*{\fill}
33959 \begin_inset Graphics
33960 filename clipart/macrouse.png
33965 \begin_inset space \hspace*{\fill}
33969 \begin_inset Newline newline
33972 Here is our macro example with the arguments
33973 \begin_inset Formula $x$
33977 \begin_inset Formula $\ln(x)$
33981 \begin_inset Formula $B$
33987 \begin_layout Standard
33988 \begin_inset Formula
33998 \begin_layout Standard
33999 LyX offers in the menu
34001 Tools\SpecialChar \menuseparator
34002 Preferences\SpecialChar \menuseparator
34003 Editing\SpecialChar \menuseparator
34006 different styles to edit macros.
34007 To find the style that suits you the most, choose a style and set the cursor
34008 in a macro formula to see the difference.
34011 \begin_layout Standard
34012 A math macro is transformed internally to a
34018 command when exporting the document.
34025 command is not placed in the LaTeX-preamble, therefore macros can only
34026 be used in formulas that are in the document below the macro definition
34030 \begin_layout Standard
34031 Math macros can also be directly be created from a
34038 When writing for example the command
34041 \begin_inset Newline newline
34050 xleftarrow[#2]{#1}}
34051 \begin_inset Newline newline
34056 in LyX as normal text, highlighting it completely and using then the shortcut
34061 , the command will be transformed to a math macro.
34062 Using this method you need to be careful that the
34068 command is typed correctly, otherwise you get a faulty macro leading to
34072 \begin_layout Standard
34073 Math macros currently yet have the problem that further formulas in macro
34074 definitions are handled wrongly.
34075 Therefore the example
34082 \begin_inset CommandInset ref
34084 reference "sub:The-Command-newcommand"
34088 cannot be created as macro.
34091 \begin_layout Standard
34092 When the cursor is in a macro definition box, you will see the macro toolbar
34096 \begin_layout Standard
34097 \begin_inset VSpace defskip
34103 \begin_layout Standard
34104 \begin_inset Graphics
34105 filename clipart/MacroToolbar.png
34110 \begin_inset Index idx
34113 \begin_layout Plain Layout
34122 \begin_layout Standard
34123 \begin_inset VSpace defskip
34129 \begin_layout Standard
34130 The macro toolbar contains from left to right the following buttons:
34133 \begin_layout Standard
34134 \begin_inset VSpace defskip
34140 \begin_layout Standard
34141 \begin_inset Tabular
34142 <lyxtabular version="3" rows="9" columns="2">
34143 <features islongtable="true" longtabularalignment="center">
34144 <column alignment="left" valignment="top" width="0">
34145 <column alignment="left" valignment="top" width="85col%">
34146 <row interlinespace="2.5mm">
34147 <cell alignment="center" valignment="top" usebox="none">
34150 \begin_layout Plain Layout
34151 \begin_inset Graphics
34152 filename ../images/math-macro-remove-param.png
34153 rotateOrigin center
34162 <cell alignment="center" valignment="top" usebox="none">
34165 \begin_layout Plain Layout
34168 Edit\SpecialChar \menuseparator
34169 Math\SpecialChar \menuseparator
34171 \begin_inset space ~
34174 Definition\SpecialChar \menuseparator
34175 Remove Last Argument
34181 <row interlinespace="2.5mm">
34182 <cell alignment="center" valignment="top" usebox="none">
34185 \begin_layout Plain Layout
34186 \begin_inset Graphics
34187 filename ../images/math-macro-add-param.png
34188 rotateOrigin center
34197 <cell alignment="center" valignment="top" usebox="none">
34200 \begin_layout Plain Layout
34203 Edit\SpecialChar \menuseparator
34204 Math\SpecialChar \menuseparator
34206 \begin_inset space ~
34209 Definition\SpecialChar \menuseparator
34216 <row interlinespace="2.5mm">
34217 <cell alignment="center" valignment="top" usebox="none">
34220 \begin_layout Plain Layout
34221 \begin_inset Graphics
34222 filename ../images/math-macro-make-optional.png
34223 rotateOrigin center
34232 <cell alignment="center" valignment="top" usebox="none">
34235 \begin_layout Plain Layout
34238 Edit\SpecialChar \menuseparator
34239 Math\SpecialChar \menuseparator
34241 \begin_inset space ~
34244 Definition\SpecialChar \menuseparator
34245 Make First Non-Optional into
34246 \begin_inset Newline newline
34250 \begin_inset Phantom HPhantom
34253 \begin_layout Plain Layout
34256 Edit\SpecialChar \menuseparator
34257 Math\SpecialChar \menuseparator
34259 \begin_inset space ~
34262 Definition\SpecialChar \menuseparator
34274 <row interlinespace="2.5mm">
34275 <cell alignment="center" valignment="top" usebox="none">
34278 \begin_layout Plain Layout
34279 \begin_inset Graphics
34280 filename ../images/math-macro-make-nonoptional.png
34281 rotateOrigin center
34290 <cell alignment="center" valignment="top" usebox="none">
34293 \begin_layout Plain Layout
34296 Edit\SpecialChar \menuseparator
34297 Math\SpecialChar \menuseparator
34299 \begin_inset space ~
34302 Definition\SpecialChar \menuseparator
34303 Make Last Optional into
34304 \begin_inset Newline newline
34308 \begin_inset Phantom HPhantom
34311 \begin_layout Plain Layout
34314 Edit\SpecialChar \menuseparator
34315 Math\SpecialChar \menuseparator
34317 \begin_inset space ~
34320 Definition\SpecialChar \menuseparator
34326 Non-Optional Argument
34332 <row interlinespace="2.5mm">
34333 <cell alignment="center" valignment="top" usebox="none">
34336 \begin_layout Plain Layout
34337 \begin_inset Graphics
34338 filename ../images/math-macro-remove-optional-param.png
34339 rotateOrigin center
34348 <cell alignment="center" valignment="top" usebox="none">
34351 \begin_layout Plain Layout
34354 Edit\SpecialChar \menuseparator
34355 Math\SpecialChar \menuseparator
34357 \begin_inset space ~
34360 Definition\SpecialChar \menuseparator
34361 Remove Optional Argument
34367 <row interlinespace="2.5mm">
34368 <cell alignment="center" valignment="top" usebox="none">
34371 \begin_layout Plain Layout
34372 \begin_inset Graphics
34373 filename ../images/math-macro-add-optional-param.png
34374 rotateOrigin center
34383 <cell alignment="center" valignment="top" usebox="none">
34386 \begin_layout Plain Layout
34389 Edit\SpecialChar \menuseparator
34390 Math\SpecialChar \menuseparator
34392 \begin_inset space ~
34395 Definition\SpecialChar \menuseparator
34396 Insert Optional Argument
34402 <row interlinespace="2.5mm">
34403 <cell alignment="center" valignment="top" usebox="none">
34406 \begin_layout Plain Layout
34407 \begin_inset Graphics
34408 filename ../images/math-macro-remove-greedy-param.png
34409 rotateOrigin center
34418 <cell alignment="center" valignment="top" usebox="none">
34421 \begin_layout Plain Layout
34424 Edit\SpecialChar \menuseparator
34425 Math\SpecialChar \menuseparator
34427 \begin_inset space ~
34430 Definition\SpecialChar \menuseparator
34431 Remove Last Argument
34432 \begin_inset Newline newline
34436 \begin_inset Phantom HPhantom
34439 \begin_layout Plain Layout
34442 Edit\SpecialChar \menuseparator
34443 Math\SpecialChar \menuseparator
34445 \begin_inset space ~
34448 Definition\SpecialChar \menuseparator
34454 Spitting Out To The Right
34460 <row interlinespace="2.5mm">
34461 <cell alignment="center" valignment="top" usebox="none">
34464 \begin_layout Plain Layout
34465 \begin_inset Graphics
34466 filename ../images/math-macro-append-greedy-param.png
34467 rotateOrigin center
34476 <cell alignment="center" valignment="top" usebox="none">
34479 \begin_layout Plain Layout
34482 Edit\SpecialChar \menuseparator
34483 Math\SpecialChar \menuseparator
34485 \begin_inset space ~
34488 Definition\SpecialChar \menuseparator
34490 \begin_inset Newline newline
34494 \begin_inset Phantom HPhantom
34497 \begin_layout Plain Layout
34500 Edit\SpecialChar \menuseparator
34501 Math\SpecialChar \menuseparator
34503 \begin_inset space ~
34506 Definition\SpecialChar \menuseparator
34512 Eating From The Right
34518 <row interlinespace="2.5mm">
34519 <cell alignment="center" valignment="top" usebox="none">
34522 \begin_layout Plain Layout
34523 \begin_inset Graphics
34524 filename ../images/math-macro-add-greedy-optional-param.png
34525 rotateOrigin center
34534 <cell alignment="center" valignment="top" usebox="none">
34537 \begin_layout Plain Layout
34540 Edit\SpecialChar \menuseparator
34541 Math\SpecialChar \menuseparator
34543 \begin_inset space ~
34546 Definition\SpecialChar \menuseparator
34547 Append Optional Argument
34548 \begin_inset Newline newline
34552 \begin_inset Phantom HPhantom
34555 \begin_layout Plain Layout
34558 Edit\SpecialChar \menuseparator
34559 Math\SpecialChar \menuseparator
34561 \begin_inset space ~
34564 Definition\SpecialChar \menuseparator
34570 Eating From The Right
34583 \begin_layout Section
34584 Computer Algebra Systems
34587 \begin_layout Standard
34588 LyX offers the exchange between mathematical expressions written in LyX's
34589 math editor and external applications or user defined scripts.
34590 Currently supported applications are
34607 Note that the set of supported mathematical constructs is limited only
34608 to very simple cases.
34611 \begin_layout Subsection
34615 \begin_layout Standard
34616 Write some expression in a formula, go to the
34618 Edit\SpecialChar \menuseparator
34619 Math\SpecialChar \menuseparator
34620 Use Computer Algebra System
34622 menu and choose the application you have installed on the computer.
34623 After that the result of computation should show on the right side of the
34624 expression together with the
34625 \begin_inset Quotes eld
34629 \begin_inset Quotes erd
34635 \begin_layout Standard
34636 Here are few simple examples (with results from
34640 ) to show what kind of computations can be performed:
34643 \begin_layout Itemize
34644 \begin_inset Formula $\frac{37}{3}*2-\sum_{i=1}^{3}i^{i}=-\frac{22}{3}$
34650 \begin_layout Itemize
34651 \begin_inset Formula $\frac{37.0}{3}=12.33333333333333$
34657 \begin_layout Itemize
34658 \begin_inset Formula $\int_{1}^{2}\sin(x)dx=\cos1-\cos2$
34664 \begin_layout Itemize
34665 \begin_inset Formula $\det\left[\begin{array}{ccc}
34669 \end{array}\right]=-56$
34675 \begin_layout Itemize
34676 \begin_inset Formula $\lim_{x\rightarrow0}\left(\frac{\sin(x)}{x}\right)=1$
34682 \begin_layout Subsection
34686 \begin_layout Standard
34687 Currently there is no keyboard shortcut for calling the algebra applications.
34688 One can easily bind a shortcut to the
34692 LyX function (see the
34700 \begin_inset space \thinspace{}
34704 \begin_inset space ~
34711 key inside the math editor.
34716 one would use this shortcut definition command:
34719 \begin_layout Standard
34722 command-alternatives break-paragraph;math-extern maxima
34725 \begin_layout Standard
34726 \begin_inset Newpage newpage
34732 \begin_layout Section
34734 \begin_inset Index idx
34737 \begin_layout Plain Layout
34746 \begin_layout Subsection
34748 \begin_inset Index idx
34751 \begin_layout Plain Layout
34760 \begin_layout Standard
34761 Negative numbers often look ugly in formulas because the minus sign before
34762 the number is set with the same length as the minus operator sign.
34763 When writing the negative number in normal text, the minus sign appears
34767 \begin_layout Standard
34768 Thus, the problem disappears when converting the minus sign to mathematical
34772 \begin_layout Standard
34773 An example to visualize the problem:
34776 \begin_layout Standard
34778 \begin_inset Tabular
34779 <lyxtabular version="3" rows="3" columns="2">
34780 <features tabularvalignment="middle">
34781 <column alignment="right" valignment="top" width="0">
34782 <column alignment="left" valignment="top" width="0">
34784 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
34787 \begin_layout Plain Layout
34793 <cell alignment="center" valignment="top" topline="true" rightline="true" usebox="none">
34796 \begin_layout Plain Layout
34804 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
34807 \begin_layout Plain Layout
34813 <cell alignment="center" valignment="top" topline="true" bottomline="true" rightline="true" usebox="none">
34816 \begin_layout Plain Layout
34817 \begin_inset Formula $x=-2$
34827 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
34830 \begin_layout Plain Layout
34836 <cell alignment="center" valignment="top" topline="true" bottomline="true" rightline="true" usebox="none">
34839 \begin_layout Plain Layout
34840 \begin_inset Formula $x=\textrm{-}2$
34856 \begin_layout Subsection
34857 Comma as decimal Separator
34858 \begin_inset Index idx
34861 \begin_layout Plain Layout
34870 \begin_layout Standard
34871 In LaTeX a comma inside a formula is used, according to the English convention,
34872 as number group separator.
34873 So there will be space added behind all commas in formulas.
34876 \begin_layout Standard
34877 To avoid this, the comma is highlighted and changed to mathematical text
34887 \begin_layout Standard
34888 To use all formula commas in the document as decimal separator, the file
34897 \begin_layout Plain Layout
34902 is part of the LaTeX-package
34907 \begin_inset Index idx
34910 \begin_layout Plain Layout
34915 \begin_layout Plain Layout
34935 \begin_inset Index idx
34938 \begin_layout Plain Layout
34944 is loaded with the LaTeX-preamble line
34947 \begin_layout Standard
34955 \begin_layout Subsection
34957 \begin_inset CommandInset label
34959 name "sub:Physical-Vectors"
34964 \begin_inset Index idx
34967 \begin_layout Plain Layout
34976 \begin_layout Standard
34977 Predefined vectors are offered by the LaTeX-package
34982 \begin_inset Index idx
34985 \begin_layout Plain Layout
34991 that is loaded with the LaTeX-preamble line
34994 \begin_layout Standard
35002 \begin_layout Standard
35006 \begin_layout Plain Layout
35016 \begin_inset Note Note
35019 \begin_layout Plain Layout
35020 The following table will only be displayed when the LaTeX-package
35032 \begin_layout Standard
35033 The following commands are defined:
35036 \begin_layout Standard
35038 \begin_inset Tabular
35039 <lyxtabular version="3" rows="4" columns="2">
35040 <features tabularvalignment="middle">
35041 <column alignment="center" valignment="top" width="0">
35042 <column alignment="center" valignment="top" width="0">
35044 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
35047 \begin_layout Plain Layout
35053 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
35056 \begin_layout Plain Layout
35064 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
35067 \begin_layout Plain Layout
35077 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
35080 \begin_layout Plain Layout
35081 \begin_inset Formula $\Bra{\psi}$
35091 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
35094 \begin_layout Plain Layout
35104 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
35107 \begin_layout Plain Layout
35108 \begin_inset Formula $\Ket{\psi}$
35118 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
35121 \begin_layout Plain Layout
35133 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
35136 \begin_layout Plain Layout
35137 \begin_inset Formula $\Braket{\psi|\phi}$
35153 \begin_layout Standard
35160 assures that all vertical bars are set in the size of the surrounding brackets:
35161 \begin_inset Formula
35163 \Braket{\phi|J=\frac{3}{2}\,,\, M_{J}}
35172 \begin_layout Plain Layout
35182 \begin_inset Note Note
35185 \begin_layout Plain Layout
35186 The following will be displayed when the LaTeX-package
35198 \begin_layout Standard
35199 You need to install the LaTeX-package
35203 to see the rest of this subsection in the output.
35206 \begin_layout Standard
35210 \begin_layout Plain Layout
35222 \begin_layout Standard
35229 can also be achieved using the command
35235 , that is described in
35236 \begin_inset CommandInset ref
35238 reference "sub:Automatic-Bracket-Size"
35245 \begin_layout Subsection
35246 Self-defined Fractions
35247 \begin_inset CommandInset label
35249 name "sub:Self-defined-Fractions"
35254 \begin_inset Index idx
35257 \begin_layout Plain Layout
35258 Fractions ! self-defined
35266 \begin_layout Standard
35267 To define custom commands for fractions, the command
35274 \begin_inset Index idx
35277 \begin_layout Plain Layout
35285 is used in the following scheme:
35288 \begin_layout Standard
35301 bracket}{fraction bar thickness}{style}
35302 \begin_inset Newline newline
35306 \begin_inset Phantom HPhantom
35309 \begin_layout Plain Layout
35319 {numerator}{denominator}
35322 \begin_layout Standard
35323 The style is a number in the range of 0
35324 \begin_inset space \thinspace{}
35328 \begin_inset space \thinspace{}
35334 \begin_layout Standard
35336 \begin_inset Tabular
35337 <lyxtabular version="3" rows="5" columns="2">
35338 <features tabularvalignment="middle">
35339 <column alignment="center" valignment="top" width="0">
35340 <column alignment="center" valignment="top" width="0">
35342 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
35345 \begin_layout Plain Layout
35351 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
35354 \begin_layout Plain Layout
35362 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
35365 \begin_layout Plain Layout
35371 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
35374 \begin_layout Plain Layout
35375 display style formula
35382 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
35385 \begin_layout Plain Layout
35391 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
35394 \begin_layout Plain Layout
35402 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
35405 \begin_layout Plain Layout
35411 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
35414 \begin_layout Plain Layout
35422 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
35425 \begin_layout Plain Layout
35431 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
35434 \begin_layout Plain Layout
35448 \begin_layout Standard
35449 When no style is given, the size is adjusted to the surrounding environment
35450 like for the command
35459 \begin_layout Standard
35460 When no fraction bar thickness is given, the predefined value of 0.4
35461 \begin_inset space \thinspace{}
35467 \begin_layout Standard
35468 \begin_inset VSpace medskip
35471 For example, the commands
35484 \begin_inset CommandInset ref
35486 reference "sub:Fractions"
35490 are defined with the commands
35493 \begin_layout Standard
35502 genfrac{}{}{}{0}{#1}{#2}}
35505 \begin_layout Standard
35509 \begin_layout Standard
35518 genfrac{(}{)}{0pt}{1}{#1}{#2}}
35521 \begin_layout Standard
35522 \begin_inset VSpace medskip
35525 To define a fraction where the fraction bar thickness can be given as optional
35526 argument, the following line is inserted to the LaTeX-preamble:
35529 \begin_layout Standard
35538 genfrac{}{}{#1}{}{#2}{#3}}
35541 \begin_layout Standard
35543 \begin_inset Formula
35545 \text{Command} & & \mathrm{\backslash fracS[1mm]\backslash\{A\to\backslash\{B} & & \mathrm{\backslash fracS[5mm]\backslash\{A\to\backslash\{B}\\
35546 \text{Result} & & \fracS[1mm]{A}{B} & & \fracS[5mm]{A}{B}
35551 As one can see, the distance of the numerator and the denominator to the
35552 fraction bar is round about three times the bar thickness.
35555 \begin_layout Subsection
35557 \begin_inset Index idx
35560 \begin_layout Plain Layout
35569 \begin_layout Standard
35570 To cancel formulas or formula parts, the LaTeX-package
35575 \begin_inset Index idx
35578 \begin_layout Plain Layout
35584 has to be loaded with the LaTeX-preamble line
35587 \begin_layout Standard
35592 usepackage[samesize]{cancel}
35595 \begin_layout Standard
35599 \begin_layout Plain Layout
35609 \begin_inset Note Note
35612 \begin_layout Plain Layout
35613 The following table will only be displayed when the LaTeX-package
35625 \begin_layout Standard
35626 There are four ways to cancel formulas:
35629 \begin_layout Standard
35631 \begin_inset Tabular
35632 <lyxtabular version="3" rows="5" columns="2">
35633 <features tabularvalignment="middle">
35634 <column alignment="center" valignment="top" width="0">
35635 <column alignment="center" valignment="top" width="0">
35637 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
35640 \begin_layout Plain Layout
35646 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
35649 \begin_layout Plain Layout
35651 \begin_inset Note Note
35654 \begin_layout Plain Layout
35661 are used here as spacer.
35673 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
35676 \begin_layout Plain Layout
35685 \begin_layout Plain Layout
35699 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
35702 \begin_layout Plain Layout
35703 \begin_inset Formula $\raisebox{4.5mm}{}\cancel{\int A=B}\raisebox{-2.5mm}{}$
35713 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
35716 \begin_layout Plain Layout
35725 \begin_layout Plain Layout
35739 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
35742 \begin_layout Plain Layout
35743 \begin_inset Formula $\raisebox{4.5mm}{}\bcancel{\int A=B}\raisebox{-2.5mm}{}$
35753 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
35756 \begin_layout Plain Layout
35765 \begin_layout Plain Layout
35779 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
35782 \begin_layout Plain Layout
35783 \begin_inset Formula $\raisebox{4.5mm}{}\xcancel{\int A=B}\raisebox{-2.5mm}{}$
35793 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
35796 \begin_layout Plain Layout
35800 \begin_inset Formula $\to$
35811 \begin_layout Plain Layout
35825 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
35828 \begin_layout Plain Layout
35829 \begin_inset Formula $\raisebox{7mm}{}\cancelto{1}{\int A=B}\raisebox{-2.5mm}{}\hspace{3mm}$
35845 \begin_layout Standard
35852 is especially suitable to visualize the reduction of fractions within formulas:
35853 \begin_inset Formula
35855 \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}}}
35863 \begin_layout Standard
35867 \begin_layout Plain Layout
35877 \begin_inset Note Note
35880 \begin_layout Plain Layout
35881 The following will be displayed when the LaTeX-package
35893 \begin_layout Standard
35894 You need to install the LaTeX-package
35898 to see the rest of this subsection in the output.
35901 \begin_layout Standard
35905 \begin_layout Plain Layout
35917 \begin_layout Subsection
35918 Formulas in Section Headings
35919 \begin_inset CommandInset label
35921 name "sub:Formulas-in-Section"
35926 \begin_inset Index idx
35929 \begin_layout Plain Layout
35930 Formula ! in section headings
35938 \begin_layout Standard
35939 When formulas are used in section headings, the following has to be taken
35943 \begin_layout Standard
35944 \begin_inset Note Greyedout
35947 \begin_layout Plain Layout
35953 \begin_inset Index idx
35956 \begin_layout Plain Layout
35957 Packages ! hyperref
35962 support is enabled in the document settings dialog under
35965 \begin_inset space ~
35970 , PDF-bookmarks are created for every section heading in the table of contents.
35971 If a section heading contains formulas, they are incorrectly displayed
35972 in the bookmark text, because formulas in bookmarks infringe the PDF convention
35981 \begin_layout Standard
35982 Both problems can be solved by inserting at the end of the section heading
35983 a short title with the menu
35985 Insert\SpecialChar \menuseparator
35987 \begin_inset space ~
35993 Short titles are used as alternative for multiline section headings to
35994 keep the table of contents clearly arranged.
35995 Only the short title appears in the table of contents and therefore also
35996 in the PDF-bookmark.
35999 \begin_layout Standard
36000 When formulas should be used in the table of contents but
36004 is used, one can use the following command in TeX-mode:
36007 \begin_layout Standard
36012 texorpdfstring{part}{alternative}
36013 \begin_inset Index idx
36016 \begin_layout Plain Layout
36027 \begin_layout Standard
36028 Part is the part of the heading that shouldn't appear in the PDF-bookmark.
36029 This can be characters, formulas, footnotes, but also cross-references.
36030 The alternative is used instead of the part for the bookmark.
36033 \begin_layout Standard
36034 Here are two example headings:
36035 \begin_inset VSpace -3mm
36042 \begin_layout Plain Layout
36054 \begin_layout Subsubsection
36055 Heading without formula in table of contents
36056 \begin_inset Formula $\sqrt{-1}=\mathrm{i}$
36060 \begin_inset Argument
36063 \begin_layout Plain Layout
36064 Heading without formula in table of contents
36072 \begin_layout Subsubsection
36073 Heading with formula in table of contents
36077 \begin_layout Plain Layout
36087 \begin_inset Formula $\sqrt{-1}=\mathrm{i}$
36094 \begin_layout Plain Layout
36104 \begin_layout Standard
36108 \begin_layout Plain Layout
36117 In the first heading a short title was used, in the second one
36126 \begin_layout Standard
36127 To get the same formatting as for the other headings, the complete heading
36136 \begin_layout Plain Layout
36138 \begin_inset CommandInset ref
36140 reference "sub:Bold-Formulas"
36152 \begin_layout Subsection
36153 Formulas in multi-column Text
36154 \begin_inset Index idx
36157 \begin_layout Plain Layout
36158 Formula ! in multi-column text
36166 \begin_layout Standard
36167 Formulas in multi-column text are often too wide to fit into a column and
36168 thus need to be set over the whole page width.
36169 This is done by using the LaTeX-package
36177 \begin_layout Plain Layout
36182 is part of every LaTeX standard installation.
36188 \begin_inset Index idx
36191 \begin_layout Plain Layout
36192 Packages ! multicol
36197 , that is loaded with the LaTeX-preamble line
36200 \begin_layout Standard
36205 usepackage{multicol}
36208 \begin_layout Standard
36209 \begin_inset Note Greyedout
36212 \begin_layout Plain Layout
36213 Note herby that the setting
36216 \begin_inset space ~
36223 Document\SpecialChar \menuseparator
36229 \begin_inset space ~
36249 \begin_layout Standard
36250 Before the multi-column text the command
36253 \begin_layout Standard
36258 begin{multicols}{column number}
36261 \begin_layout Standard
36262 is written in TeX-mode.
36263 The column number is a number in the range of 2
36264 \begin_inset space \thinspace{}
36268 \begin_inset space \thinspace{}
36272 Before the formula the multi-column text is ended by inserting the command
36275 \begin_layout Standard
36283 \begin_layout Standard
36287 \begin_layout Standard
36288 Due to the command some space is automatically added before the formula.
36290 \begin_inset space \thinspace{}
36293 mm vertical space is inserted before the formula.
36294 When the formula style
36300 \begin_layout Plain Layout
36302 \begin_inset CommandInset ref
36304 reference "sec:Formula-Styles"
36316 \begin_inset space \thinspace{}
36319 mm space is inserted instead.
36322 \begin_layout Standard
36323 As example a multi-column text with a displayed formula:
36326 \begin_layout Standard
36332 \begin_layout Plain Layout
36336 begin{multicols}{2}
36341 Das Spektrum wird fouriertransformiert.
36342 Die Fouriertransformation wird verwendet, um die überlagerten Signale (Netzwerk
36343 , Lösungsmittel) zu trennen.
36344 Nachdem wir die Phasenverschiebung bestimmen konnten, interessiert uns
36345 nun das Aussehen des Ausgangssignals.
36346 Im Experiment haben wir es mit sehr vielen Teilchen zu tun, so dass man
36347 über alle Phasen integrieren muss.
36349 \begin_inset Formula $S$
36352 unser normiertes Ausgangssignal und
36353 \begin_inset Formula $P$
36356 die Phasenverteilungsfunktion, so ergibt sich die Beziehung
36360 \begin_layout Plain Layout
36370 \begin_inset VSpace -6mm
36374 \begin_inset Formula
36376 S(t)=S_{0}(t)\int_{-\infty}^{\infty}P(\phi,t)\mathrm{e}^{\mathrm{i}\phi}\,\mathrm{d}\phi
36385 \begin_layout Plain Layout
36389 begin{multicols}{2}
36395 \begin_inset Formula $S_{0}$
36398 das Signal ohne Gradient ist und die Normierungsbedingung
36399 \begin_inset Formula $\int_{-\infty}^{\infty}P(\phi,t)\,\mathrm{d}\phi=1$
36403 Nun dürfen wir aber nicht den Relaxationsprozess außer Acht lassen.
36405 \begin_inset Formula $\nicefrac{\pi}{2}$
36409 \begin_inset space \thinspace{}
36412 -rf-Puls beginnt sich die Magnetisierung zu entfokussieren, wodurch sich
36413 das Signal zusätzlich abschwächt.
36414 Diese Abschwächung verläuft exponentiell in Abhängigkeit der so genannten
36416 \begin_inset Formula $T_{2}$
36422 \begin_layout Standard
36428 \begin_layout Plain Layout
36440 \begin_layout Subsection
36441 Formulas with Description of Variables
36442 \begin_inset Index idx
36445 \begin_layout Plain Layout
36446 Formula ! with description of variables
36454 \begin_layout Standard
36455 To describe variables within a formula, like in formula
36456 \begin_inset CommandInset ref
36458 reference "eq:within"
36467 \begin_inset Formula $n$
36471 \begin_inset space ~
36474 matrix is used with left aligned columns for the
36475 \begin_inset Formula $n$
36482 \begin_layout Plain Layout
36484 \begin_inset CommandInset ref
36486 reference "sec:Matrices"
36495 To set the description in a smaller size, before the matrix e.
36496 \begin_inset space \thinspace{}
36500 \begin_inset space \space{}
36513 \begin_layout Plain Layout
36515 \begin_inset CommandInset ref
36517 reference "sub:Font-Sizes"
36529 \begin_layout Standard
36530 When the formula style
36536 \begin_layout Plain Layout
36538 \begin_inset CommandInset ref
36540 reference "sec:Formula-Styles"
36561 \begin_layout Plain Layout
36568 only works in formulas with the style
36573 \begin_inset CommandInset ref
36575 reference "sub:Variable-Space"
36584 is inserted before and after the matrix to have the same separation of
36585 the matrix from the equation and the side margin.
36588 \begin_layout Standard
36589 When the formula style
36593 is used, the method described in
36594 \begin_inset CommandInset ref
36596 reference "sub:Flalign-Environment"
36600 is used to indent formulas.
36602 \begin_inset CommandInset ref
36604 reference "eq:within"
36608 consists of five columns whereas in the first two columns contain the equation,
36609 the third the matrix and the last one an empty TeX-brace.
36610 \begin_inset Formula
36612 \hspace{30pt}F_{A} & =\rho·V·g & \footnotesize\begin{array}{ll}
36613 \rho & \textrm{density}\\
36614 V & \textrm{volume}\\
36615 g & \textrm{gravitational acceleration}
36616 \end{array} & & {}\label{eq:within}
36624 \begin_layout Subsection
36625 Upright small Greek Letters
36626 \begin_inset CommandInset label
36628 name "sub:Upright-small-Greek"
36633 \begin_inset Index idx
36636 \begin_layout Plain Layout
36637 Greek letters ! upright
36645 \begin_layout Standard
36646 Most of the math fonts only provide italic small Greek letters.
36647 But for symbols of elementary particles like pions and neutrinos, upright
36648 Greek letters are needed.
36657 \begin_layout Plain Layout
36662 is part of the LaTeX-package
36667 \begin_inset Index idx
36670 \begin_layout Plain Layout
36675 \begin_layout Plain Layout
36695 \begin_inset Index idx
36698 \begin_layout Plain Layout
36704 that is loaded with the LaTeX-preamble line
36707 \begin_layout Standard
36712 usepackage{upgreek}
36715 \begin_layout Standard
36721 \begin_layout Plain Layout
36731 \begin_inset Note Note
36734 \begin_layout Plain Layout
36735 The following table will only be displayed when the LaTeX-package
36744 They are created when the command for a small Greek letters is started
36750 For example the command
36757 \begin_inset Formula $\uptau$
36763 \begin_layout Standard
36764 With these commands reactions of elementary particles can be typeset:
36765 \begin_inset Formula
36767 \uppi^{+}\to\upmu^{+}+\upnu_{\upmu}
36775 \begin_layout Standard
36776 The upright letters are more bold and wider than the italic ones.
36777 They should therefore not be used for units like
36778 \begin_inset Quotes eld
36782 \begin_inset Quotes erd
36788 \begin_layout Standard
36792 \begin_layout Plain Layout
36802 \begin_inset Note Note
36805 \begin_layout Plain Layout
36806 The following will be displayed when the LaTeX-package
36818 \begin_layout Standard
36819 You need to install the LaTeX-package
36823 to see the rest of this subsection in the output.
36826 \begin_layout Standard
36830 \begin_layout Plain Layout
36842 \begin_layout Subsection
36843 Text Characters in Formulas
36844 \begin_inset CommandInset label
36846 name "sub:Text-Characters-in"
36851 \begin_inset Index idx
36854 \begin_layout Plain Layout
36863 \begin_layout Standard
36864 In some cases you might want to insert text characters directly into formulas.
36865 When for example the centered dot · is often used in formulas like
36866 \begin_inset Formula $\nu=5·10^{5}\,\mathrm{Hz}$
36869 , one would have to insert the command
36879 \begin_layout Plain Layout
36881 \begin_inset CommandInset ref
36883 reference "sub:Binary-Operators"
36892 all the time, because this character is defined in all encodings as text
36894 But the encoding can be changed by this LaTeX-preamble line:
36897 \begin_layout Standard
36902 Declare Inputtext{183}{
36912 f\SpecialChar \textcompwordmark{}
36916 \begin_layout Standard
36917 The character encoding (menu
36919 Document\SpecialChar \menuseparator
36920 Settings\SpecialChar \menuseparator
36923 ) specifies what character appears when a keyboard key is pressed.
36924 When the key for the character '·' is pressed, internally the command
36931 But this command is not available in a formula so that you would get LaTeX-erro
36933 With the changed encoding the right command is chosen automatically, depending
36934 on if the character was inserted into a formula or not.
36937 \begin_layout Standard
36938 The encoding of several characters is saved in definition files.
36939 Fore example the encoding
36943 is defined in the file
36947 that is in the installation folder of LaTeX.
36948 Encodings should only be changed via the LaTeX-preamble and not in the
36950 Otherwise own documents could not be edited by other LyX users working
36951 on other computers.
36954 \begin_layout Standard
36955 \begin_inset VSpace medskip
36958 Besides the centered dot, in this document the degree sign ° is defined
36959 with the following LaTeX-preamble line so that it can directly be inserted
36963 \begin_layout Standard
36968 DeclareInputtext{176}{
36978 f\SpecialChar \textcompwordmark{}
36982 \begin_layout Standard
36983 \begin_inset Newpage newpage
36989 \begin_layout Section
36992 \begin_inset Index idx
36995 \begin_layout Plain Layout
37004 \begin_layout Standard
37005 This section is a summary of the most important typographic rules, listed
37010 \begin_layout Plain Layout
37011 This collection was partly taken from the German semi-official dictionary
37013 \begin_inset Quotes eld
37017 \begin_inset Quotes erd
37021 \begin_inset CommandInset citation
37027 that lists some of the ISO rules.
37028 More rules are listed in
37029 \begin_inset CommandInset citation
37043 \begin_layout Itemize
37052 \begin_layout Plain Layout
37053 done with font styles, see
37054 \begin_inset CommandInset ref
37056 reference "sub:Font-Styles"
37065 , no matter if they appear in italic text: 30
37066 \begin_inset space \thinspace{}
37070 \begin_inset Newline newline
37073 Between the value and the unit is the smallest space, see
37074 \begin_inset CommandInset ref
37076 reference "sub:Predefined-Space"
37081 \begin_inset Newline newline
37084 This convention is automatically fulfilled when the command
37091 When it is entered to a formula, two boxes appear.
37092 In the first one the value is inserted, in the second one the unit, and
37094 \begin_inset Formula $\unit[30]{km/h}$
37098 \begin_inset space \thinspace{}
37108 is not a real LaTeX command but the command
37114 , therefore you cannot use it in TeX code.
37117 \begin_layout Itemize
37118 Percent and perthousand signs are set like physical units:
37119 \begin_inset Newline newline
37123 \begin_inset space \thinspace{}
37129 \begin_layout Itemize
37130 The degree sign follows directly on the value: 15°, but not when it is used
37132 \begin_inset space \thinspace{}
37138 \begin_layout Itemize
37139 In numbers with more than four digits the smallest space is inserted before
37140 every third digit to group them:
37150 \begin_inset space \thinspace{}
37154 \begin_inset space \thinspace{}
37160 \begin_layout Itemize
37161 For dimensions like 120×90×40
37162 \begin_inset space \thinspace{}
37165 cm the multiplication sign
37166 \begin_inset Quotes eld
37170 \begin_inset Quotes erd
37174 It is available either via the command
37182 Insert\SpecialChar \menuseparator
37183 Special Character\SpecialChar \menuseparator
37189 \begin_layout Itemize
37190 Functions with names consisting of several letters are set upright to avoid
37192 \begin_inset CommandInset ref
37194 reference "sub:Predefined-Functions"
37201 \begin_layout Itemize
37202 Indices consisting of several letters, are set upright:
37203 \begin_inset Formula $E_{\mathrm{kin}}$
37207 \begin_inset Newline newline
37210 Components of matrices are set italic:
37211 \begin_inset Formula $\hat{H}_{kl}$
37217 \begin_layout Itemize
37218 The differentiation/integration operator 'd', the Euler's number 'e' and
37219 the imaginary unit 'i' should be set upright, to avoid mixing them up with
37223 \begin_layout Itemize
37224 The character that denotes a
37228 transformation is inserted either by the command
37236 \begin_layout Plain Layout
37249 Insert\SpecialChar \menuseparator
37250 Special Character\SpecialChar \menuseparator
37251 Symbols\SpecialChar \menuseparator
37253 \begin_inset space ~
37259 \begin_inset Formula $\mathscr{F}$
37265 \begin_layout Standard
37266 \begin_inset Newpage newpage
37272 \begin_layout Section
37274 \begin_inset Index idx
37277 \begin_layout Plain Layout
37286 \begin_layout Standard
37287 Some characters and symbols can be created with several commands.
37288 Here is a list of the synonym commands:
37291 \begin_layout Standard
37292 \begin_inset VSpace bigskip
37296 \begin_inset space \hfill{}
37300 \begin_inset Tabular
37301 <lyxtabular version="3" rows="12" columns="2">
37302 <features tabularvalignment="middle">
37303 <column alignment="center" valignment="top" width="0pt">
37304 <column alignment="center" valignment="top" width="0pt">
37306 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
37309 \begin_layout Plain Layout
37315 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
37318 \begin_layout Plain Layout
37320 \begin_inset Note Note
37323 \begin_layout Plain Layout
37330 is only used as spacer.
37342 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
37345 \begin_layout Plain Layout
37353 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
37356 \begin_layout Plain Layout
37360 \begin_layout Plain Layout
37373 \begin_layout Plain Layout
37387 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
37390 \begin_layout Plain Layout
37398 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
37401 \begin_layout Plain Layout
37411 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
37414 \begin_layout Plain Layout
37422 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
37425 \begin_layout Plain Layout
37435 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
37438 \begin_layout Plain Layout
37446 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
37449 \begin_layout Plain Layout
37457 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
37460 \begin_layout Plain Layout
37468 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
37471 \begin_layout Plain Layout
37479 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
37482 \begin_layout Plain Layout
37490 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
37493 \begin_layout Plain Layout
37503 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
37506 \begin_layout Plain Layout
37514 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
37517 \begin_layout Plain Layout
37527 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
37530 \begin_layout Plain Layout
37538 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
37541 \begin_layout Plain Layout
37551 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
37554 \begin_layout Plain Layout
37562 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
37565 \begin_layout Plain Layout
37575 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
37578 \begin_layout Plain Layout
37586 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
37589 \begin_layout Plain Layout
37597 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
37600 \begin_layout Plain Layout
37608 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
37611 \begin_layout Plain Layout
37623 \begin_inset space \hfill{}
37627 \begin_inset Tabular
37628 <lyxtabular version="3" rows="12" columns="2">
37629 <features tabularvalignment="middle">
37630 <column alignment="center" valignment="top" width="0pt">
37631 <column alignment="center" valignment="top" width="0pt">
37633 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
37636 \begin_layout Plain Layout
37642 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
37645 \begin_layout Plain Layout
37653 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
37656 \begin_layout Plain Layout
37664 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
37667 \begin_layout Plain Layout
37679 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
37682 \begin_layout Plain Layout
37690 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
37693 \begin_layout Plain Layout
37703 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
37706 \begin_layout Plain Layout
37714 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
37717 \begin_layout Plain Layout
37727 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
37730 \begin_layout Plain Layout
37738 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
37741 \begin_layout Plain Layout
37749 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
37752 \begin_layout Plain Layout
37760 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
37763 \begin_layout Plain Layout
37771 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
37774 \begin_layout Plain Layout
37782 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
37785 \begin_layout Plain Layout
37795 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
37798 \begin_layout Plain Layout
37806 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
37809 \begin_layout Plain Layout
37819 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
37822 \begin_layout Plain Layout
37830 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
37833 \begin_layout Plain Layout
37843 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
37846 \begin_layout Plain Layout
37854 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
37857 \begin_layout Plain Layout
37867 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
37870 \begin_layout Plain Layout
37878 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
37881 \begin_layout Plain Layout
37891 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
37894 \begin_layout Plain Layout
37902 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
37905 \begin_layout Plain Layout
37919 \begin_inset space \hfill{}
37925 \begin_layout Standard
37926 \begin_inset Newpage newpage
37932 \begin_layout Bibliography
37933 \labelwidthstring References
37934 \begin_inset CommandInset bibitem
37935 LatexCommand bibitem
37947 The LaTeX Companion
37950 Addison Wesley, 2004
37953 \begin_layout Bibliography
37954 \labelwidthstring References
37955 \begin_inset CommandInset bibitem
37956 LatexCommand bibitem
37962 \begin_inset CommandInset href
37965 target "ftp://ftp.dante.de/tex-archive/info/math/voss/mathmode/Mathmode.pdf"
37969 of LaTeX's math abilities
37972 \begin_layout Bibliography
37973 \labelwidthstring References
37974 \begin_inset CommandInset bibitem
37975 LatexCommand bibitem
37981 \begin_inset CommandInset href
37984 target "ftp://ftp.ams.org/pub/tex/doc/amsmath/amsldoc.pdf"
37992 \begin_layout Plain Layout
38004 \begin_layout Bibliography
38005 \labelwidthstring References
38006 \begin_inset CommandInset bibitem
38007 LatexCommand bibitem
38013 \begin_inset CommandInset href
38016 target "ftp://ftp.dante.de/tex-archive/info/symbols/comprehensive/symbols-a4.pdf"
38020 of all symbols available with LaTeX-packages
38023 \begin_layout Bibliography
38024 \labelwidthstring References
38025 \begin_inset CommandInset bibitem
38026 LatexCommand bibitem
38032 \begin_inset CommandInset href
38034 name "Documentation"
38035 target "http://www.tug.org/applications/hyperref/ftp/doc/manual.pdf"
38039 of the LaTeX-package
38044 \begin_inset Index idx
38047 \begin_layout Plain Layout
38048 Packages ! hyperref
38056 \begin_layout Bibliography
38057 \labelwidthstring References
38058 \begin_inset CommandInset bibitem
38059 LatexCommand bibitem
38065 \begin_inset CommandInset href
38067 name "Documentation"
38068 target "http://www.ctan.org/tex-archive/macros/latex/contrib/mhchem/mhchem.pdf"
38072 of the LaTeX-package
38077 \begin_inset Index idx
38080 \begin_layout Plain Layout
38089 \begin_layout Bibliography
38090 \labelwidthstring References
38091 \begin_inset CommandInset bibitem
38092 LatexCommand bibitem
38098 \begin_inset CommandInset href
38101 target "http://www.tug.org/TUGboat/Articles/tb22-4/tb72perlS.pdf"
38112 \begin_inset CommandInset ref
38114 reference "sub:Operator-Limits"
38119 \begin_inset Index idx
38122 \begin_layout Plain Layout
38133 \begin_layout Bibliography
38134 \labelwidthstring References
38135 \begin_inset CommandInset bibitem
38136 LatexCommand bibitem
38147 Auflage, Duden 2001
38150 \begin_layout Bibliography
38151 \labelwidthstring References
38152 \begin_inset CommandInset bibitem
38153 LatexCommand bibitem
38159 \begin_inset CommandInset href
38162 target "http://physics.nist.gov/Document/checklist.pdf"
38166 for reviewing manuscripts
38169 \begin_layout Standard
38170 \begin_inset CommandInset index_print
38171 LatexCommand printindex