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}}}}
42 \addto\extrasenglish{%
43 \renewcommand*{\equationautorefname}[1]{}
44 \renewcommand{\sectionautorefname}{sec.\negthinspace}
45 \renewcommand{\subsectionautorefname}{sec.\negthinspace}
46 \renewcommand{\subsubsectionautorefname}{sec.\negthinspace}
49 % don't load packages twice
50 % see first footnote in sec. 9.3
51 \@ifundefined{textcolor}{\usepackage{color}}{}
53 % the pages of the TOC are numbered roman
54 % and a PDF-bookmark for the TOC is added
56 \let\myTOC\tableofcontents
57 \renewcommand{\tableofcontents}{%
59 \pdfbookmark[1]{\contentsname}{}
62 \pagenumbering{arabic}}
64 % insert additional vertical space of 1.5 mm between footnotes,
66 \renewcommand{\footnote}[1]{\myFoot{#1\vspace{1.5mm}}}
68 % provides caption formatting
69 \setkomafont{captionlabel}{\bfseries}
72 \usepackage[samesize]{cancel}
74 % enables calculation of values
77 % for multiple columns used in sec. 24.7
83 % for the Fourier transformation symbol
86 % define a color, used in sec.9.3
87 \definecolor{darkgreen}{cmyk}{0.5, 0, 1, 0.5}
89 % declare operators (see sec. 10.4 and sec. 15.2)
90 \DeclareMathOperator*{\Lozenge}{\blacklozenge}
91 \DeclareMathOperator{\sgn}{sgn}
93 \newcommand{\spce}{\textvisiblespace}
95 % example definitions for sec. 20.1
96 \newcommand{\gr}{\Longrightarrow}
97 \newcommand{\us}[1]{\underline{#1}}
98 \newcommand{\fb}[3]{\framebox#1#2{$#3$}}
99 \newcommand{\cb}[3][white]{\fcolorbox{#2}{#1}{$#3$}}
100 \newcommand{\fracS}[3][]{\genfrac{}{}{#1}{}{#2}{#3}}
102 % example macro from sec. 19.4
103 %\def\tagform@#1{\maketag@@@{|#1|}}
105 % macro from sec. 10.2
106 \def\clap#1{\hbox to 0pt{\hss #1\hss}}
107 \def\mathclap {\mathpalette \mathclapinternal}
108 \def\mathclapinternal #1#2{\clap{$\mathsurround =0pt #1{#2}$}}
111 % ------------------------------------
112 % used to check for needed LaTeX packages
115 % check for package eurosym
116 % used for the Euro symbol
118 \IfFileExists{eurosym.sty}
119 {\usepackage[gennarrow]{eurosym}
120 \setboolean{eurosym}{true}}
121 {\setboolean{eurosym}{false}}
123 % check for package braket
124 % used for physical vectors
126 \IfFileExists{braket.sty}
128 \setboolean{braket}{true}}
129 {\setboolean{braket}{false}}
131 % check for package cancel
133 \IfFileExists{cancel.sty}
135 \setboolean{cancel}{true}}
136 {\setboolean{cancel}{false}}
138 % check for package upgreek
140 \IfFileExists{upgreek.sty}
141 {\usepackage{upgreek}
142 \setboolean{upgreek}{true}}
143 {\setboolean{upgreek}{false}}
145 \options bibliography=totoc,index=totoc,BCOR7.5mm,titlepage,captions=tableheading
146 \use_default_options false
147 \maintain_unincluded_children false
149 \language_package default
154 \font_typewriter default
155 \font_default_family default
156 \use_non_tex_fonts false
163 \default_output_format default
165 \bibtex_command default
166 \index_command default
170 \pdf_title "LyX's Math Manual"
171 \pdf_author "LyX Team, Uwe Stöhr"
172 \pdf_subject "LyX-documentation about math"
173 \pdf_keywords "LyX, Mathed"
175 \pdf_bookmarksnumbered true
176 \pdf_bookmarksopen true
177 \pdf_bookmarksopenlevel 1
178 \pdf_breaklinks false
182 \pdf_pdfusetitle false
183 \pdf_quoted_options "linkcolor=black, citecolor=black, urlcolor=blue, filecolor=blue, pdfpagelayout=OneColumn, pdfnewwindow=true, pdfstartview=XYZ, plainpages=false"
193 \paperorientation portrait
196 \notefontcolor #0000ff
203 \paragraph_separation skip
205 \quotes_language english
208 \paperpagestyle plain
212 \tracking_changes false
213 \output_changes false
216 \html_be_strict false
222 LyX's detailed Math manual
230 \begin_layout Plain Layout
232 If you have comments or error corrections, please send them to the LyX Documenta
236 \begin_inset CommandInset href
238 name "lyx-docs@lists.lyx.org"
239 target "lyx-docs@lists.lyx.org?subject=LyX's Math manual"
250 \begin_inset Note Note
253 \begin_layout Plain Layout
260 \begin_inset Newline newline
264 \begin_inset Newline newline
272 \begin_layout Standard
273 \begin_inset CommandInset toc
274 LatexCommand tableofcontents
281 \begin_layout Standard
282 \begin_inset Note Note
285 \begin_layout Plain Layout
286 To export this document to PDF, PS or DVI the LaTeX-packages
288 braket, cancel, eurosym, mathdots, mhchem
295 If they are not installed the document can be export anyway but the sections
296 where the packages are required will not appear in the output.
301 ; if it is not installed, this file cannot be exported.
304 \begin_layout Plain Layout
305 The latest PDF-version of this document can be found here:
306 \begin_inset Newline newline
311 http://wiki.lyx.org/LyX/DocumentationDevelopment#Math
319 \begin_layout Standard
320 \begin_inset Newpage newpage
326 \begin_layout Section
330 \begin_layout Standard
331 This document explains LyX's math features and is furthermore a collection
332 of LaTeX-commands used for mathematical characters and constructs.
333 The explanations are designed for the usage of commands.
334 It is therefore required that you have read the section
345 \begin_layout Standard
346 Most of the characters and many constructs explained in this manual are
347 also accessible via the menu
351 \SpecialChar \menuseparator
367 But everybody who has to write lots of formulas will notice that it is
368 much faster to use commands instead of the math toolbar.
369 Therefore this manual is focused on commands but also mentions the correspondin
370 g toolbar buttons when available.
373 \begin_layout Standard
374 If not specially mentioned the commands are only available within formulas.
375 To be able to use all commands explained in this document, the option
379 must be used in the document settings (menu
381 Document\SpecialChar \menuseparator
382 Settings\SpecialChar \menuseparator
393 \begin_layout Plain Layout
396 Use AMS math package automatically
402 \begin_layout Plain Layout
411 -math when math constructs are found that are supported by LyX.
419 \begin_layout Standard
420 This document doesn't list all
424 \begin_layout Plain Layout
437 \begin_layout Plain Layout
442 \begin_layout Plain Layout
451 -math commands is in the file
454 \begin_inset CommandInset href
457 target "ftp://ctan.tug.org/tex-archive/macros/amstex/doc/amsguide.ps"
463 , which is part of every LaTeX standard installation.
468 for lucidity reasons.
471 \begin_layout Section
475 \begin_layout Standard
476 To create an inline formula
477 \begin_inset Index idx
480 \begin_layout Plain Layout
486 that is embedded into a text line, use one of the shortcuts
492 or the toolbar button
493 \begin_inset Graphics
494 filename ../images/math-mode.png
500 \begin_inset Newline newline
503 To create a display style formula
504 \begin_inset Index idx
507 \begin_layout Plain Layout
508 Formula ! display style
513 that will appear bigger and in an own paragraph, use one of these shortcuts:
523 \begin_layout Standard
524 To change a display style formula to an inline formula, set the cursor into
525 the formula and use one of the shortcuts
533 Edit\SpecialChar \menuseparator
534 Math\SpecialChar \menuseparator
538 The same way is used to change an inline formula to a display style formula.
541 \begin_layout Standard
542 To display parts of an inline formula in the size of a display style formula,
550 \begin_inset Index idx
553 \begin_layout Plain Layout
562 Then a new blue box appears in which the desired formula part is inserted.
565 \begin_layout Standard
566 Only inline formulas are allowed inside tables.
569 \begin_layout Standard
574 can be turned on in the menu
576 View\SpecialChar \menuseparator
580 When you click there on
581 \begin_inset Quotes eld
585 \begin_inset Quotes erd
588 the toolbar will be shown permanently at the bottom; this state is visualized
593 menu with a checkmark.
594 When you click in this state again on
595 \begin_inset Quotes eld
599 \begin_inset Quotes erd
610 is only shown when the cursor is within a formula; this state is visualized
611 by the renaming of the menu entry from
612 \begin_inset Quotes eld
616 \begin_inset Quotes erd
620 \begin_inset Quotes eld
628 \begin_inset Quotes erd
634 \begin_layout Standard
636 \begin_inset Index idx
639 \begin_layout Plain Layout
645 is invoked by pressing the toolbar button
646 \begin_inset Graphics
647 filename ../images/ert-insert.png
654 Insert\SpecialChar \menuseparator
659 \begin_layout Plain Layout
675 \begin_inset Note Note
678 \begin_layout Plain Layout
679 In LyX there are three
680 \begin_inset Quotes eld
684 \begin_inset Quotes erd
687 that appear in the output with sub- and superscript letters: TeX, LaTeX
691 \begin_layout Plain Layout
692 To avoid that these names are recognized as proper names, a TeX-brace pair
701 \begin_layout Standard
702 To change the LaTeX-preamble
703 \begin_inset Index idx
706 \begin_layout Plain Layout
714 Document\SpecialChar \menuseparator
715 Settings\SpecialChar \menuseparator
720 \begin_layout Plain Layout
736 \begin_layout Standard
737 To edit matrices, case differentiations and multiline formulas subsequently,
740 Edit\SpecialChar \menuseparator
745 Edit\SpecialChar \menuseparator
747 \begin_inset space \thinspace{}
751 \begin_inset space \thinspace{}
761 When lines and columns are swapped via the menu, the column or line where
762 the cursor is in is exchanged with the column to the right or the line
764 Is the cursor in the last column or row, the exchange is done with the
765 column to the left or the line above.
768 \begin_layout Standard
769 To write text in formulas
773 \begin_layout Plain Layout
774 For multiline formulas the command
781 \begin_inset CommandInset ref
783 reference "sub:Text-in-multiline"
797 \begin_inset Index idx
800 \begin_layout Plain Layout
807 \begin_inset Index idx
810 \begin_layout Plain Layout
817 This mode is invoked with the shortcut
823 or by the insertion of the command
830 \begin_inset Index idx
833 \begin_layout Plain Layout
842 The text appears black in LyX and can therefore be distinguished from the
843 other formula parts that appear blue.
844 In the output mathematical text is set upright, in contrary to other formula
848 \begin_layout Subsection*
852 \begin_layout Standard
853 Most of the LaTeX-commands for math constructs have the following scheme:
856 \begin_layout Standard
872 \begin_layout Standard
873 A command starts always with a backslash
874 \begin_inset Quotes gld
884 \begin_inset Quotes grd
888 To omit optional arguments, also omit the associated brackets.
889 The braces around the required arguments are named in this document as
891 \begin_inset Index idx
894 \begin_layout Plain Layout
901 If you add in a formula a left brace to a command name, LyX creates automatical
903 In all other cases TeX-braces are created in formulas with the command
911 TeX-braces appear red in LyX, in contrary to normal braces that appear
913 In TeX-mode no command is needed to get TeX-braces.
914 TeX-braces don't appear in the output.
917 \begin_layout Standard
918 When commands without arguments, like commands for symbols are entered in
919 TeX-mode, a space character must
923 be behind the command to end it.
924 This space doesn't appear in the output.
925 When the space should appear in the output, the space must be followed
926 by a protected space in normal text.
929 \begin_layout Standard
930 A protected space is inserted with
933 arg "space-insert protected"
939 \begin_layout Subsection*
940 \begin_inset Newpage newpage
946 \begin_layout Itemize
951 \begin_layout Plain Layout
952 This visible space character can be created with the command
959 \begin_inset Index idx
962 \begin_layout Plain Layout
970 , inserted in TeX-mode.
979 \begin_layout Plain Layout
992 denotes a space character to be input.
995 \begin_layout Itemize
997 \begin_inset Formula $\to$
1000 denotes the usage of the corresponding arrow key on the keyboard.
1003 \begin_layout Subsection*
1007 \begin_layout Standard
1009 \begin_inset Float table
1015 \begin_layout Plain Layout
1017 \begin_inset Caption
1019 \begin_layout Plain Layout
1020 \begin_inset CommandInset label
1022 name "tab:Available-units"
1034 \begin_layout Plain Layout
1036 \begin_inset Tabular
1037 <lyxtabular version="3" rows="13" columns="2">
1038 <features tabularvalignment="middle">
1039 <column alignment="center" valignment="top" width="0">
1040 <column alignment="center" valignment="top" width="0">
1042 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
1045 \begin_layout Plain Layout
1051 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
1054 \begin_layout Plain Layout
1062 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
1065 \begin_layout Plain Layout
1071 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
1074 \begin_layout Plain Layout
1082 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
1085 \begin_layout Plain Layout
1091 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
1094 \begin_layout Plain Layout
1102 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
1105 \begin_layout Plain Layout
1111 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
1114 \begin_layout Plain Layout
1116 \begin_inset space \thinspace{}
1120 \begin_inset space \thinspace{}
1130 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
1133 \begin_layout Plain Layout
1139 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
1142 \begin_layout Plain Layout
1144 \begin_inset space \thinspace{}
1148 \begin_inset space \thinspace{}
1158 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
1161 \begin_layout Plain Layout
1167 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
1170 \begin_layout Plain Layout
1172 \begin_inset space \thinspace{}
1176 \begin_inset space \thinspace{}
1186 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
1189 \begin_layout Plain Layout
1195 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
1198 \begin_layout Plain Layout
1200 \begin_inset space \thinspace{}
1204 \begin_inset space \thinspace{}
1214 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
1217 \begin_layout Plain Layout
1223 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
1226 \begin_layout Plain Layout
1228 \begin_inset space \thinspace{}
1232 \begin_inset space \thinspace{}
1242 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
1245 \begin_layout Plain Layout
1251 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
1254 \begin_layout Plain Layout
1256 \begin_inset space \thinspace{}
1260 \begin_inset Formula $\approx$
1264 \begin_inset space \thinspace{}
1274 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
1277 \begin_layout Plain Layout
1283 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
1286 \begin_layout Plain Layout
1288 \begin_inset space \thinspace{}
1292 \begin_inset space \thinspace{}
1302 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
1305 \begin_layout Plain Layout
1311 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
1314 \begin_layout Plain Layout
1318 \begin_inset Quotes eld
1324 \begin_inset Quotes erd
1334 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
1337 \begin_layout Plain Layout
1343 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
1346 \begin_layout Plain Layout
1348 \begin_inset Quotes eld
1356 \begin_inset Quotes erd
1366 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
1369 \begin_layout Plain Layout
1375 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
1378 \begin_layout Plain Layout
1380 \begin_inset space \thinspace{}
1384 \begin_inset Formula $\nicefrac{1}{18}$
1388 \begin_inset space \thinspace{}
1409 \begin_layout Standard
1410 \begin_inset Newpage newpage
1416 \begin_layout Section
1420 \begin_layout Subsection
1422 \begin_inset Index idx
1425 \begin_layout Plain Layout
1432 \begin_inset Index idx
1435 \begin_layout Plain Layout
1442 \begin_inset Index idx
1445 \begin_layout Plain Layout
1450 \begin_layout Plain Layout
1461 \begin_layout Plain Layout
1474 \begin_inset Index idx
1477 \begin_layout Plain Layout
1482 \begin_layout Plain Layout
1493 \begin_layout Plain Layout
1508 \begin_layout Standard
1509 Indices are created with an underscore
1510 \begin_inset Quotes eld
1514 \begin_inset Quotes erd
1517 or via the math toolbar button
1518 \begin_inset Graphics
1519 filename ../images/math-subscript.png
1524 , exponents with a caret
1525 \begin_inset Quotes eld
1529 \begin_inset Quotes erd
1532 or via the math toolbar button
1533 \begin_inset Graphics
1534 filename ../images/math-superscript.png
1542 \begin_layout Standard
1544 \begin_inset Tabular
1545 <lyxtabular version="3" rows="4" columns="2">
1546 <features tabularvalignment="middle">
1547 <column alignment="center" valignment="top" width="0pt">
1548 <column alignment="center" valignment="top" width="0pt">
1550 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
1553 \begin_layout Plain Layout
1559 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
1562 \begin_layout Plain Layout
1564 \begin_inset Note Note
1567 \begin_layout Plain Layout
1574 is only used as spacer.
1586 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
1589 \begin_layout Plain Layout
1595 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
1598 \begin_layout Plain Layout
1599 \begin_inset Formula $B_{V}$
1609 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
1612 \begin_layout Plain Layout
1618 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
1621 \begin_layout Plain Layout
1622 \begin_inset Formula $\raisebox{5mm}{}B^{V}$
1632 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
1635 \begin_layout Plain Layout
1640 \begin_layout Plain Layout
1654 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
1657 \begin_layout Plain Layout
1658 \begin_inset Formula $\raisebox{5mm}{}B^{A}$
1674 \begin_layout Standard
1675 As the caret is in some languages an accent, vowels will be accentuated
1676 in this case and not set as exponents
1680 \begin_layout Plain Layout
1681 Depending on the used keyboard settings this can also happen for other character
1688 To get in this case exponents, press
1692 after the caret as in the last example.
1695 \begin_layout Subsection
1697 \begin_inset CommandInset label
1699 name "sub:Fractions"
1704 \begin_inset Index idx
1707 \begin_layout Plain Layout
1716 \begin_layout Standard
1717 Fractions are generated with the command
1724 \begin_inset Index idx
1727 \begin_layout Plain Layout
1735 or via the math toolbar button
1736 \begin_inset Graphics
1737 filename ../images/math/frac.png
1743 The font size is adjusted automatically, depending on whether the fraction
1744 is in an inline or display style formula.
1745 With the math toolbar button
1746 \begin_inset Graphics
1747 filename ../images/math/frac-square.png
1752 you can select different fraction types.
1755 \begin_layout Standard
1763 \begin_inset Index idx
1766 \begin_layout Plain Layout
1774 a fraction can be created that has in any case the size of a display style
1783 \begin_inset Index idx
1786 \begin_layout Plain Layout
1794 the fraction appears always with the size of an inline formula.
1798 \begin_layout Standard
1799 A line with the fraction
1800 \begin_inset Formula $\frac{1}{2}$
1803 that was created with the command
1812 \begin_layout Standard
1813 A line with the fraction
1814 \begin_inset Formula $\dfrac{1}{2}$
1817 that was created with the command
1826 \begin_layout Standard
1828 \begin_inset Tabular
1829 <lyxtabular version="3" rows="4" columns="2">
1830 <features tabularvalignment="middle">
1831 <column alignment="center" valignment="top" width="0pt">
1832 <column alignment="center" valignment="top" width="0pt">
1834 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
1837 \begin_layout Plain Layout
1843 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
1846 \begin_layout Plain Layout
1848 \begin_inset Note Note
1851 \begin_layout Plain Layout
1858 is only used as spacer.
1870 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
1873 \begin_layout Plain Layout
1880 \begin_layout Plain Layout
1890 \begin_inset Formula $\downarrow$
1898 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
1901 \begin_layout Plain Layout
1902 \begin_inset Formula $\raisebox{4.5mm}{}\frac{A}{B}\raisebox{-2.5mm}{}$
1912 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
1915 \begin_layout Plain Layout
1922 \begin_layout Plain Layout
1932 \begin_inset Formula $\downarrow$
1940 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
1943 \begin_layout Plain Layout
1944 \begin_inset Formula $\raisebox{7mm}{}\dfrac{A}{B}\raisebox{-4mm}{}$
1954 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
1957 \begin_layout Plain Layout
1964 \begin_layout Plain Layout
1977 \begin_layout Plain Layout
1992 \begin_layout Plain Layout
2002 \begin_inset Formula $\downarrow$
2006 \begin_inset Formula $\downarrow\downarrow$
2014 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
2017 \begin_layout Plain Layout
2018 \begin_inset Formula $\raisebox{8mm}{}\dfrac{e^{\frac{1}{2}}}{3}\raisebox{-4mm}{}$
2034 \begin_layout Standard
2035 \begin_inset VSpace bigskip
2039 \begin_inset Newpage newpage
2042 For nested fractions the command
2049 \begin_inset Index idx
2052 \begin_layout Plain Layout
2062 \begin_inset VSpace -3mm
2068 \begin_layout Standard
2069 \begin_inset Formula
2071 \textrm{created with \textbf{\textbackslash frac}} & & \textrm{created with \textbf{\textbackslash cfrac}}\\
2072 \frac{A}{B+\frac{C+\frac{E}{F}}{D}} & & \cfrac{A}{B+\cfrac{C+\cfrac{E}{F}}{D}}
2080 \begin_layout Standard
2081 The command for the example above is:
2084 \begin_layout Standard
2093 \begin_layout Plain Layout
2103 \begin_inset Formula $\downarrow$
2112 \begin_layout Plain Layout
2127 \begin_layout Plain Layout
2137 \begin_inset Formula $\downarrow$
2141 \begin_inset Formula $\downarrow$
2147 \begin_layout Standard
2148 \begin_inset VSpace medskip
2154 \begin_layout Standard
2161 sets the fraction always in the size of a displayed formula, also when
2162 it is part of another fraction.
2165 \begin_layout Standard
2166 It is possible to specify the alignment of the numerator.
2173 is used to left align it, the command
2186 centers the numerator.
2187 These fractions demonstrate the different alignments:
2190 \begin_layout Standard
2191 \begin_inset Formula $\cfrac[l]{A}{B+C}$
2195 \begin_inset Formula $\cfrac{A}{B+C}$
2199 \begin_inset Formula $\cfrac[r]{A}{B+C}$
2205 \begin_layout Standard
2206 \begin_inset Note Greyedout
2209 \begin_layout Plain Layout
2226 are no real LaTeX commands but represent the command
2230 cfrac[alignment]{numerator}{denominator}
2233 Therefore you cannot use them in TeX code.
2241 \begin_layout Standard
2242 \begin_inset VSpace medskip
2245 It is often advantageous to combine
2258 \begin_inset Formula
2260 \cfrac{A}{B+\cfrac{C+\frac{E}{F}}{D}}
2268 \begin_layout Standard
2269 For inline fractions with a sloped fraction stroke you can use the command
2277 \begin_inset Index idx
2280 \begin_layout Plain Layout
2289 \begin_inset Formula $\nicefrac{5}{31}$
2299 \begin_inset Index idx
2302 \begin_layout Plain Layout
2311 \begin_inset Formula $\unitfrac{5}{31}$
2314 There is furthermore the command
2320 that offers to write a fraction in combination with a number:
2321 \begin_inset Formula $\unitfrac[2]{1}{3}$
2327 \begin_layout Standard
2328 \begin_inset Note Greyedout
2331 \begin_layout Plain Layout
2342 is not a real LaTeX command but the command
2343 \begin_inset Newline newline
2350 unitfrac[number]{numerator}{denominator}
2353 Therefore you cannot use it in TeX code.
2361 \begin_layout Standard
2362 How to define own fractions where the fraction stroke can be changed, is
2364 \begin_inset CommandInset ref
2366 reference "sub:Self-defined-Fractions"
2373 \begin_layout Subsection
2375 \begin_inset Index idx
2378 \begin_layout Plain Layout
2387 \begin_layout Standard
2388 Square roots are created with
2395 \begin_inset Index idx
2398 \begin_layout Plain Layout
2406 or the math toolbar button
2407 \begin_inset Graphics
2408 filename ../images/math/sqrt.png
2413 , all other roots with the command
2420 \begin_inset Index idx
2423 \begin_layout Plain Layout
2431 or with the math toolbar button
2432 \begin_inset Graphics
2433 filename ../images/math/root.png
2441 \begin_layout Standard
2443 \begin_inset Tabular
2444 <lyxtabular version="3" rows="3" columns="2">
2445 <features tabularvalignment="middle">
2446 <column alignment="center" valignment="top" width="0pt">
2447 <column alignment="center" valignment="top" width="0pt">
2449 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
2452 \begin_layout Plain Layout
2458 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
2461 \begin_layout Plain Layout
2463 \begin_inset Note Note
2466 \begin_layout Plain Layout
2473 is only used as spacer.
2485 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
2488 \begin_layout Plain Layout
2495 \begin_layout Plain Layout
2509 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
2512 \begin_layout Plain Layout
2513 \begin_inset Formula $\raisebox{4.5mm}{}\sqrt{A-B}$
2523 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
2526 \begin_layout Plain Layout
2533 \begin_layout Plain Layout
2543 \begin_inset Formula $\downarrow$
2551 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
2554 \begin_layout Plain Layout
2555 \begin_inset Formula $\raisebox{4.5mm}{}\sqrt[3]{A-B}$
2571 \begin_layout Standard
2572 A square root can also be created with
2578 when the root index field is left empty.
2581 \begin_layout Standard
2582 With certain indices the distance to the root is too small, like in this
2584 \begin_inset Formula $\sqrt[\beta]{B}$
2588 \begin_inset Newline newline
2592 \begin_inset Formula $\beta$
2596 To avoid this, the commands
2603 \begin_inset Index idx
2606 \begin_layout Plain Layout
2621 \begin_inset Index idx
2624 \begin_layout Plain Layout
2632 are used with the following scheme:
2635 \begin_layout Standard
2649 \begin_layout Standard
2650 Distance is the number of Big Points (unit bp;
2651 \begin_inset Formula $\mathrm{72\, bp=1\, inch}$
2654 ), that the index should be moved to the left or top, resp..
2655 The commands are written to the index.
2656 This way the command
2657 \begin_inset Newline newline
2667 \begin_inset Formula $\to$
2673 \begin_inset Formula $\to$
2682 \begin_layout Plain Layout
2692 \begin_inset Formula $\to$
2696 \begin_inset Newline newline
2701 produces a correct typeset formula:
2702 \begin_inset Formula $\sqrt[\leftroot{-1}\uproot{2}\beta]{B}$
2708 \begin_layout Subsection
2709 Binomial Coefficients
2710 \begin_inset Index idx
2713 \begin_layout Plain Layout
2714 Binomial coefficients
2722 \begin_layout Standard
2723 Binomial coefficients are inserted with the command
2730 \begin_inset Index idx
2733 \begin_layout Plain Layout
2741 or with the submenu of the math toolbar button
2742 \begin_inset Graphics
2743 filename ../images/math/frac-square.png
2749 Analog to fractions (
2768 \begin_inset Index idx
2771 \begin_layout Plain Layout
2786 \begin_inset Index idx
2789 \begin_layout Plain Layout
2798 For other brackets around binomial coeficients there are the commands
2805 \begin_inset Index idx
2808 \begin_layout Plain Layout
2823 \begin_inset Index idx
2826 \begin_layout Plain Layout
2837 \begin_layout Standard
2839 \begin_inset Tabular
2840 <lyxtabular version="3" rows="6" columns="2">
2841 <features tabularvalignment="middle">
2842 <column alignment="center" valignment="top" width="0pt">
2843 <column alignment="center" valignment="top" width="0pt">
2845 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
2848 \begin_layout Plain Layout
2854 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
2857 \begin_layout Plain Layout
2859 \begin_inset Note Note
2862 \begin_layout Plain Layout
2869 is only used as spacer.
2881 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
2884 \begin_layout Plain Layout
2891 \begin_layout Plain Layout
2901 \begin_inset Formula $\downarrow$
2909 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
2912 \begin_layout Plain Layout
2913 \begin_inset Formula $\raisebox{5mm}{}\binom{A}{B}\raisebox{-2.5mm}{}$
2923 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
2926 \begin_layout Plain Layout
2933 \begin_layout Plain Layout
2943 \begin_inset Formula $\downarrow$
2951 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
2954 \begin_layout Plain Layout
2955 \begin_inset Formula $\raisebox{5mm}{}\dbinom{A}{B}\raisebox{-2.5mm}{}$
2965 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
2968 \begin_layout Plain Layout
2975 \begin_layout Plain Layout
2985 \begin_inset Formula $\downarrow$
2993 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
2996 \begin_layout Plain Layout
2997 \begin_inset Formula $\raisebox{5mm}{}\tbinom{A}{B}\raisebox{-2.5mm}{}$
3007 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
3010 \begin_layout Plain Layout
3017 \begin_layout Plain Layout
3027 \begin_inset Formula $\downarrow$
3035 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
3038 \begin_layout Plain Layout
3039 \begin_inset Formula $\raisebox{5mm}{}{A \brack B}\raisebox{-2.5mm}{}$
3049 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
3052 \begin_layout Plain Layout
3059 \begin_layout Plain Layout
3069 \begin_inset Formula $\downarrow$
3077 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
3080 \begin_layout Plain Layout
3081 \begin_inset Formula $\raisebox{5mm}{}{A \brace B}\raisebox{-2.5mm}{}$
3097 \begin_layout Subsection
3098 Case Differentiations
3099 \begin_inset Index idx
3102 \begin_layout Plain Layout
3103 Case differentiations
3111 \begin_layout Standard
3113 \begin_inset Tabular
3114 <lyxtabular version="3" rows="3" columns="2">
3115 <features tabularvalignment="middle">
3116 <column alignment="center" valignment="top" width="0pt">
3117 <column alignment="center" valignment="top" width="0pt">
3119 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
3122 \begin_layout Plain Layout
3128 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
3131 \begin_layout Plain Layout
3139 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
3142 \begin_layout Plain Layout
3149 \begin_layout Plain Layout
3159 \begin_inset Formula $\to$
3163 \begin_inset Index idx
3166 \begin_layout Plain Layout
3179 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
3182 \begin_layout Plain Layout
3183 \begin_inset Formula $\begin{cases}
3194 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
3197 \begin_layout Plain Layout
3204 \begin_layout Plain Layout
3216 arg "newline-insert newline"
3224 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
3227 \begin_layout Plain Layout
3228 \begin_inset Formula $\begin{cases}
3229 A & \textrm{for }x>0\\
3230 B & \textrm{for }x=0
3247 \begin_layout Standard
3254 or the usage of the math toolbar button
3255 \begin_inset Graphics
3256 filename ../images/math/cases.png
3261 you can create new lines with the shortcut
3264 arg "newline-insert newline"
3267 or the table toolbar button
3268 \begin_inset Graphics
3269 filename ../images/tabular-feature_append-row.png
3277 \begin_layout Standard
3284 is also available via the menu
3286 Insert\SpecialChar \menuseparator
3287 Math\SpecialChar \menuseparator
3293 \begin_layout Subsection
3295 \begin_inset Index idx
3298 \begin_layout Plain Layout
3307 \begin_layout Standard
3315 \begin_inset Index idx
3318 \begin_layout Plain Layout
3326 every character can be displayed canceled.
3327 The characters are quasi accentuated by a slash.
3330 \begin_layout Standard
3332 \begin_inset Tabular
3333 <lyxtabular version="3" rows="4" columns="2">
3334 <features tabularvalignment="middle">
3335 <column alignment="center" valignment="top" width="0pt">
3336 <column alignment="center" valignment="top" width="0pt">
3338 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
3341 \begin_layout Plain Layout
3347 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
3350 \begin_layout Plain Layout
3358 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
3361 \begin_layout Plain Layout
3369 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
3372 \begin_layout Plain Layout
3373 \begin_inset Formula $\not=$
3383 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
3386 \begin_layout Plain Layout
3396 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
3399 \begin_layout Plain Layout
3400 \begin_inset Formula $\not\le$
3410 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
3413 \begin_layout Plain Layout
3423 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
3426 \begin_layout Plain Layout
3427 \begin_inset Formula $\not\parallel$
3443 \begin_layout Standard
3444 The last example shows, that not all negations look good.
3445 Therefore there are for some negations special commands (see
3446 \begin_inset CommandInset ref
3448 reference "sub:Mathematical-Symbols"
3453 \begin_inset CommandInset ref
3455 reference "sec:Relations"
3462 \begin_layout Subsection
3464 \begin_inset CommandInset label
3466 name "sub:Placeholders"
3471 \begin_inset Index idx
3474 \begin_layout Plain Layout
3481 \begin_inset Index idx
3484 \begin_layout Plain Layout
3485 Chemical characters ! Isotopes
3491 \begin_inset Index idx
3494 \begin_layout Plain Layout
3499 \begin_layout Plain Layout
3510 \begin_layout Plain Layout
3525 \begin_layout Standard
3527 \begin_inset space \thinspace{}
3531 \begin_inset space \space{}
3538 \begin_layout Plain Layout
3539 Typesetting isotopes and chemical symbols is described in
3540 \begin_inset CommandInset ref
3542 reference "sub:Chemical-Symbols-and"
3551 the following problem occurs:
3554 \begin_layout Standard
3556 \begin_inset Tabular
3557 <lyxtabular version="3" rows="2" columns="2">
3558 <features tabularvalignment="middle">
3559 <column alignment="center" valignment="top" width="0pt">
3560 <column alignment="center" valignment="top" width="0pt">
3562 <cell alignment="center" valignment="top" usebox="none">
3565 \begin_layout Plain Layout
3566 Indices created with sub- and superscripts:
3571 <cell alignment="center" valignment="top" usebox="none">
3574 \begin_layout Plain Layout
3575 \begin_inset Formula $_{9}^{19}\mathrm{F}\raisebox{-3mm}{}$
3585 <cell alignment="center" valignment="top" usebox="none">
3588 \begin_layout Plain Layout
3594 <cell alignment="center" valignment="top" usebox="none">
3597 \begin_layout Plain Layout
3598 \begin_inset Formula $_{\phantom{1}9}^{19}\mathrm{F}$
3612 \begin_inset Note Note
3615 \begin_layout Plain Layout
3622 is only used as spacer.
3630 \begin_layout Standard
3631 The shorter index is by default placed below or above the first character
3632 of the longer index.
3633 To avoid this there is the command
3640 \begin_inset Index idx
3643 \begin_layout Plain Layout
3651 or the math toolbar button
3652 \begin_inset space \thinspace{}
3659 \begin_layout Plain Layout
3660 can be found in the submenu of the toolbar button
3661 \begin_inset Graphics
3662 filename ../images/math/space.png
3673 \begin_inset Graphics
3674 filename ../images/math/phantom.png
3679 that creates one or more phantom characters.
3686 a small blue box appears that is superposed with two red arrows.
3687 The arrows indicate that the complete width and height of the box content
3688 will be created as placeholder.
3689 Phantom characters are accordingly placeholders with the size of the characters.
3692 \begin_layout Standard
3694 \begin_inset Tabular
3695 <lyxtabular version="3" rows="4" columns="2">
3696 <features tabularvalignment="middle">
3697 <column alignment="center" valignment="top" width="0">
3698 <column alignment="center" valignment="top" width="0">
3700 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
3703 \begin_layout Plain Layout
3709 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
3712 \begin_layout Plain Layout
3714 \begin_inset Note Note
3717 \begin_layout Plain Layout
3724 is only used as spacer.
3736 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
3739 \begin_layout Plain Layout
3744 \begin_layout Plain Layout
3759 \begin_layout Plain Layout
3769 \begin_inset Formula $\to$
3776 \begin_layout Plain Layout
3790 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
3793 \begin_layout Plain Layout
3794 \begin_inset Formula $\raisebox{4.5mm}{}{}_{\phantom{1}9}^{19}\mathrm{F}\raisebox{-2.5mm}{}$
3804 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
3807 \begin_layout Plain Layout
3812 \begin_layout Plain Layout
3827 \begin_layout Plain Layout
3837 \begin_inset Formula $\to$
3844 \begin_layout Plain Layout
3858 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
3861 \begin_layout Plain Layout
3862 \begin_inset Formula $\raisebox{4.5mm}{}{}_{\phantom{23}9}^{235}\mathrm{F}\raisebox{-2.5mm}{}$
3872 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
3875 \begin_layout Plain Layout
3882 \begin_layout Plain Layout
3897 \begin_layout Plain Layout
3907 \begin_inset Formula $\to$
3914 \begin_layout Plain Layout
3928 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
3931 \begin_layout Plain Layout
3932 \begin_inset Formula $\raisebox{4.5mm}{}\Lambda_{MMt}^{\phantom{ii}t}\raisebox{-2.5mm}{}$
3948 \begin_layout Standard
3949 Furthermore there are the commands
3956 \begin_inset Index idx
3959 \begin_layout Plain Layout
3968 \begin_inset space ~
3972 \begin_inset Graphics
3973 filename ../images/math/vphantom.png
3985 \begin_inset Index idx
3988 \begin_layout Plain Layout
3997 \begin_inset space ~
4001 \begin_inset Graphics
4002 filename ../images/math/hphantom.png
4014 creates only space for the maximal height of the characters in the box
4015 but not for its width.
4022 creates only space for the width of the box content.
4023 Therefore the boxes of both commands have only one red arrow.
4026 \begin_layout Standard
4037 \begin_layout Plain Layout
4052 space for the height of the integral sign,
4056 \begin_layout Plain Layout
4063 creates an integral sign, see
4064 \begin_inset CommandInset ref
4066 reference "sub:Big-Operators"
4075 because this is the larger character.
4076 An example application is in
4077 \begin_inset CommandInset ref
4079 reference "sub:Multiline-Brackets"
4086 \begin_layout Standard
4087 Placeholders can also be used for text when it is inserted via the menu
4090 Insert\SpecialChar \menuseparator
4091 Formatting\SpecialChar \menuseparator
4097 \begin_layout Standard
4099 \begin_inset Newline newline
4103 \begin_inset Phantom Phantom
4106 \begin_layout Plain Layout
4115 \begin_layout Subsection
4117 \begin_inset Index idx
4120 \begin_layout Plain Layout
4127 \begin_inset Index idx
4130 \begin_layout Plain Layout
4131 Formula ! underlined
4139 \begin_layout Standard
4141 \begin_inset Tabular
4142 <lyxtabular version="3" rows="4" columns="2">
4143 <features tabularvalignment="middle">
4144 <column alignment="center" valignment="top" width="0pt">
4145 <column alignment="center" valignment="top" width="0pt">
4147 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
4150 \begin_layout Plain Layout
4156 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
4159 \begin_layout Plain Layout
4161 \begin_inset Note Note
4164 \begin_layout Plain Layout
4171 is only used as spacer.
4183 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
4186 \begin_layout Plain Layout
4193 \begin_layout Plain Layout
4203 \begin_inset Index idx
4206 \begin_layout Plain Layout
4219 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
4222 \begin_layout Plain Layout
4223 \begin_inset Formula $\raisebox{5mm}{}\overline{A+B}$
4233 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
4236 \begin_layout Plain Layout
4243 \begin_layout Plain Layout
4253 \begin_inset Index idx
4256 \begin_layout Plain Layout
4269 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
4272 \begin_layout Plain Layout
4273 \begin_inset Formula $\underline{A+B}\raisebox{-2.5mm}{}$
4283 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
4286 \begin_layout Plain Layout
4293 \begin_layout Plain Layout
4308 \begin_layout Plain Layout
4322 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
4325 \begin_layout Plain Layout
4326 \begin_inset Formula $\raisebox{5mm}{}\overline{\underline{A+B}}\raisebox{-2.5mm}{}$
4342 \begin_layout Standard
4343 In the last example it doesn't matter if first
4358 \begin_layout Standard
4359 To double underline e.
4360 \begin_inset space \thinspace{}
4364 \begin_inset space \space{}
4376 \begin_layout Standard
4377 It is possible to place up to 6 lines above or below characters.
4380 \begin_layout Standard
4381 \begin_inset VSpace bigskip
4384 Custom lines can be created using the command
4391 \begin_inset Index idx
4394 \begin_layout Plain Layout
4402 which has the following scheme:
4405 \begin_layout Standard
4410 rule[vertical offset]{length}{thickness}
4413 \begin_layout Standard
4414 The optional vertical offset shifts the line upwards (or downwards, when
4415 the value is negative).
4417 \begin_inset CommandInset ref
4419 reference "tab:Available-units"
4423 can be used for the values.
4424 Here are two example lines created with the commands
4425 \begin_inset Newline newline
4432 rule[-2ex]{3cm}{2pt}
4443 \begin_layout Standard
4445 \begin_inset Formula $\rule[-2ex]{3cm}{2pt}\rule{2cm}{1pt}$
4451 \begin_layout Standard
4458 can also be used for text when a line is inserted via the menu
4460 Insert\SpecialChar \menuseparator
4461 Formatting\SpecialChar \menuseparator
4463 \begin_inset space ~
4471 \begin_layout Standard
4473 \begin_inset CommandInset line
4484 \begin_layout Subsection
4486 \begin_inset CommandInset label
4493 \begin_inset Index idx
4496 \begin_layout Plain Layout
4505 \begin_layout Standard
4506 There are different types of ellipses available.
4510 \begin_layout Plain Layout
4511 In the math toolbar in the submenu of the button
4512 \begin_inset Graphics
4513 filename ../images/math/ldots.png
4523 For listings dots at the baseline are used (
4530 \begin_inset Index idx
4533 \begin_layout Plain Layout
4541 ), while for operations dots are needed that are on the same height as the
4549 \begin_inset Index idx
4552 \begin_layout Plain Layout
4561 When using the command
4568 \begin_inset Index idx
4571 \begin_layout Plain Layout
4579 , LaTeX decides on the basis of the next character what type is used.
4582 \begin_layout Standard
4584 \begin_inset Tabular
4585 <lyxtabular version="3" rows="9" columns="2">
4586 <features tabularvalignment="middle">
4587 <column alignment="center" valignment="top" width="0pt">
4588 <column alignment="center" valignment="top" width="0pt">
4590 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
4593 \begin_layout Plain Layout
4599 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
4602 \begin_layout Plain Layout
4610 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
4613 \begin_layout Plain Layout
4618 \begin_layout Plain Layout
4633 \begin_layout Plain Layout
4647 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
4650 \begin_layout Plain Layout
4651 \begin_inset Formula $A_{1},\dots,A_{n}$
4661 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
4664 \begin_layout Plain Layout
4669 \begin_layout Plain Layout
4684 \begin_layout Plain Layout
4698 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
4701 \begin_layout Plain Layout
4702 \begin_inset Formula $A_{1}+\dots+A_{n}$
4712 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
4715 \begin_layout Plain Layout
4720 \begin_layout Plain Layout
4735 \begin_layout Plain Layout
4749 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
4752 \begin_layout Plain Layout
4753 \begin_inset Formula $A_{1},\ldots,A_{n}$
4763 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
4766 \begin_layout Plain Layout
4771 \begin_layout Plain Layout
4786 \begin_layout Plain Layout
4800 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
4803 \begin_layout Plain Layout
4804 \begin_inset Formula $A_{1}+\cdots+A_{n}$
4814 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
4817 \begin_layout Plain Layout
4825 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
4828 \begin_layout Plain Layout
4829 \begin_inset Formula $\vdots$
4839 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
4842 \begin_layout Plain Layout
4850 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
4853 \begin_layout Plain Layout
4854 \begin_inset Formula $\ddots$
4864 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
4867 \begin_layout Plain Layout
4875 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
4878 \begin_layout Plain Layout
4879 \begin_inset Formula $\iddots$
4889 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
4892 \begin_layout Plain Layout
4894 \begin_inset space \thinspace{}
4897 matrix with the different dots
4902 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
4905 \begin_layout Plain Layout
4906 \begin_inset Formula $\begin{array}{ccc}
4907 A_{11} & \cdots & A_{1m}\\
4908 \vdots & \ddots & \vdots\\
4909 A_{n1} & \cdots & A_{nm}
4926 \begin_layout Standard
4927 The ellipses available in menu
4929 Insert\SpecialChar \menuseparator
4931 \begin_inset space ~
4945 \begin_layout Standard
4946 \begin_inset VSpace medskip
4955 , one of the options
4957 Use mathdots package (automatically)
4959 must be set in the document settings under
4962 \begin_inset space ~
4968 \begin_inset Newline newline
4973 Use mathdots package
4975 will improve the appearance of all dots in the documents if their font
4976 style or size is not the default.
4979 \begin_layout Standard
4980 \begin_inset VSpace medskip
4983 Specially for matrices there are ellipses that span over several columns.
4984 They are created with the command
4991 \begin_inset Index idx
4994 \begin_layout Plain Layout
5002 , that has the following scheme:
5005 \begin_layout Standard
5010 hdotsfor[distance]{number of columns}
5013 \begin_layout Standard
5014 The number of columns specifies how many columns should be spanned.
5015 Distance is a factor for the distance between the dots.
5018 \begin_layout Standard
5019 In the following matrix the command
5025 was inserted in the first box of the second line, to get an ellipsis with
5026 a dot distance twice as long as with the command
5033 \begin_inset Formula
5035 \left(\begin{array}{cccc}
5044 Note that the matrix fields that should be spanned must be empty, otherwise
5045 you get LaTeX-errors.
5048 \begin_layout Standard
5049 \begin_inset VSpace bigskip
5052 Furthermore you can fill with the command
5059 \begin_inset Index idx
5062 \begin_layout Plain Layout
5070 the rest of a line with dots.
5071 The effect of these commands is the same like with
5078 \begin_inset CommandInset ref
5080 reference "sub:Variable-Space"
5087 \begin_layout Standard
5088 For example the command
5096 \begin_layout Plain Layout
5110 \begin_layout Standard
5111 \begin_inset Formula $A\dotfill B$
5117 \begin_layout Standard
5124 there is for a line the command
5131 \begin_inset Index idx
5134 \begin_layout Plain Layout
5145 \begin_layout Standard
5146 \begin_inset Formula $A\hrulefill B$
5152 \begin_layout Standard
5153 To use the commands for text, they have to be inserted in TeX-mode.
5156 \begin_layout Section
5158 \begin_inset CommandInset label
5165 \begin_inset Index idx
5168 \begin_layout Plain Layout
5177 \begin_layout Standard
5178 Matrices can be inserted via the math toolbar button
5179 \begin_inset Graphics
5180 filename ../images/dialog-show_mathmatrix.png
5187 Insert\SpecialChar \menuseparator
5188 Math\SpecialChar \menuseparator
5192 In the matrix dialog you can specify the number of columns and rows, the
5193 alignment and the decoration.
5194 The vertical alignment is hereby only of importance for matrices in inline
5198 \begin_layout Standard
5199 The first matrix is top
5200 \begin_inset Formula $\begin{array}[t]{cccc}
5208 \begin_inset Formula $\begin{array}{cccc}
5215 and the third bottom
5216 \begin_inset Formula $\begin{array}[b]{cccc}
5226 \begin_layout Standard
5227 The horizontal alignment specifies how the column entries should be aligned.
5228 It is set by entering a letter for every column.
5233 denotes left aligned,
5242 To create for example a 4
5247 \begin_inset space ~
5250 matrix where the first column is left aligned, the second and third are
5251 centered and the last one is right aligned, one enters for the horizontal
5257 Normally are in a matrix all columns centered, therefore the default is
5258 for every column is a
5265 \begin_layout Standard
5266 Horizontal alignment:
5269 \begin_layout Standard
5275 \begin_inset Formula $\begin{array}{lll}
5287 \begin_inset Formula $\begin{array}{ccc}
5299 \begin_inset Formula $\begin{array}{rrr}
5309 \begin_layout Standard
5310 To add or delete rows and columns subsequently, the math toolbar buttons
5312 \begin_inset Graphics
5313 filename ../images/tabular-feature_append-row.png
5319 \begin_inset Graphics
5320 filename ../images/tabular-feature_delete-row.png
5326 \begin_inset space \thinspace{}
5331 Edit\SpecialChar \menuseparator
5335 New rows can also be created with
5338 arg "newline-insert newline"
5344 \begin_layout Standard
5345 \begin_inset VSpace bigskip
5352 adds parentheses in the selected style around the matrix.
5353 Alternatively, parentheses can can either be created with the commands
5361 \begin_inset Index idx
5364 \begin_layout Plain Layout
5379 \begin_inset Index idx
5382 \begin_layout Plain Layout
5393 \begin_inset space ~
5399 \begin_inset CommandInset ref
5401 reference "sub:Automatic-Bracket-Size"
5405 , or by using the following commands:
5406 \begin_inset VSpace medskip
5412 \begin_layout Standard
5413 \begin_inset space \hfill{}
5417 \begin_inset Tabular
5418 <lyxtabular version="3" rows="4" columns="2">
5419 <features tabularvalignment="middle">
5420 <column alignment="center" valignment="top" width="0">
5421 <column alignment="center" valignment="top" width="0">
5423 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
5426 \begin_layout Plain Layout
5432 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
5435 \begin_layout Plain Layout
5437 \begin_inset Note Note
5440 \begin_layout Plain Layout
5447 is only used as spacer.
5459 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
5462 \begin_layout Plain Layout
5469 \begin_layout Plain Layout
5483 \begin_inset space \thinspace{}
5491 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
5494 \begin_layout Plain Layout
5495 \begin_inset Formula $\raisebox{7.5mm}{}\begin{bmatrix}\begin{array}{cc}
5496 0 & \textrm{-}\mathrm{i}\\
5498 \end{array}\end{bmatrix}\raisebox{-5.3mm}{}$
5508 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
5511 \begin_layout Plain Layout
5518 \begin_layout Plain Layout
5532 \begin_inset space \thinspace{}
5540 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
5543 \begin_layout Plain Layout
5544 \begin_inset Formula $\raisebox{7.5mm}{}\begin{Bmatrix}\begin{array}{cc}
5545 0 & \textrm{-}\mathrm{i}\\
5547 \end{array}\end{Bmatrix}\raisebox{-5.3mm}{}$
5557 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
5560 \begin_layout Plain Layout
5567 \begin_layout Plain Layout
5581 \begin_inset space \thinspace{}
5589 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
5592 \begin_layout Plain Layout
5593 \begin_inset Formula $\raisebox{7.5mm}{}\begin{pmatrix}\begin{array}{cc}
5594 0 & \textrm{-}\mathrm{i}\\
5596 \end{array}\end{pmatrix}\raisebox{-5.3mm}{}$
5610 \begin_inset space \hfill{}
5614 \begin_inset Tabular
5615 <lyxtabular version="3" rows="4" columns="2">
5616 <features tabularvalignment="middle">
5617 <column alignment="center" valignment="top" width="0">
5618 <column alignment="center" valignment="top" width="0">
5620 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
5623 \begin_layout Plain Layout
5629 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
5632 \begin_layout Plain Layout
5640 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
5643 \begin_layout Plain Layout
5650 \begin_layout Plain Layout
5664 \begin_inset space \thinspace{}
5672 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
5675 \begin_layout Plain Layout
5676 \begin_inset Formula $\raisebox{7.5mm}{}\begin{vmatrix}\begin{array}{cc}
5677 0 & \textrm{-}\mathrm{i}\\
5679 \end{array}\end{vmatrix}\raisebox{-5.3mm}{}$
5689 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
5692 \begin_layout Plain Layout
5699 \begin_layout Plain Layout
5713 \begin_inset space \thinspace{}
5721 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
5724 \begin_layout Plain Layout
5725 \begin_inset Formula $\raisebox{7.5mm}{}\begin{Vmatrix}\begin{array}{cc}
5726 0 & \textrm{-}\mathrm{i}\\
5728 \end{array}\end{Vmatrix}\raisebox{-5.3mm}{}$
5738 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
5741 \begin_layout Plain Layout
5748 \begin_layout Plain Layout
5762 \begin_inset space \thinspace{}
5770 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
5773 \begin_layout Plain Layout
5774 \begin_inset Formula $\raisebox{7.5mm}{}\begin{matrix}\begin{array}{cc}
5775 0 & \textrm{-}\mathrm{i}\\
5777 \end{array}\end{matrix}\raisebox{-5.3mm}{}$
5791 \begin_inset space \hfill{}
5797 \begin_layout Standard
5798 \begin_inset VSpace medskip
5802 \begin_inset space \thinspace{}
5806 \begin_inset space \space{}
5815 is inserted, a blue box appears between two vertical lines where the matrix
5817 \begin_inset Newline newline
5820 Note that decorated matrices ignore the vertical alignment.
5823 \begin_layout Standard
5824 \begin_inset Note Greyedout
5827 \begin_layout Plain Layout
5832 LaTeX limits the number of matrix columns with decorations to 10.
5833 If you need more than 10
5834 \begin_inset space ~
5837 columns, you have to add this line to the document preamble:
5840 \begin_layout Plain Layout
5845 setcounter{MaxMatrixCols}{number}
5848 \begin_layout Plain Layout
5853 is the number of columns between 11 and 99.
5861 \begin_layout Standard
5862 \begin_inset VSpace bigskip
5865 As all multiline formulas are matrices, the length
5872 \begin_inset Index idx
5875 \begin_layout Plain Layout
5883 that is described in
5884 \begin_inset CommandInset ref
5886 reference "sub:Column-Separation"
5890 can also be used to change the column separation of matrices.
5893 \begin_layout Standard
5894 To change the row separation, the command
5901 \begin_inset Index idx
5904 \begin_layout Plain Layout
5913 It is used as follows:
5916 \begin_layout Standard
5923 arraystretch}{stretch factor}
5924 \begin_inset Index idx
5927 \begin_layout Plain Layout
5938 \begin_layout Standard
5945 assigns the stretch factor to the predefined command
5953 \begin_inset space \thinspace{}
5957 \begin_inset space \space{}
5960 the row separation, use the factor 2.
5961 This is then used for all following matrices.
5962 To go back to the original separation, assign the factor 1 to
5971 \begin_layout Standard
5972 To set matrices into a text line, the command
5979 \begin_inset Index idx
5982 \begin_layout Plain Layout
5991 When it is inserted a blue box with two dashed lines appears.
5992 In this box the matrix is inserted.
5995 \begin_layout Standard
5997 \begin_inset Formula $\left(\begin{smallmatrix}A & B\\
5999 \end{smallmatrix}\right)$
6005 \begin_layout Section
6006 Brackets and Delimiters
6007 \begin_inset Index idx
6010 \begin_layout Plain Layout
6017 \begin_inset Index idx
6020 \begin_layout Plain Layout
6029 \begin_layout Subsection
6030 Vertical Brackets and Delimiters
6031 \begin_inset Index idx
6034 \begin_layout Plain Layout
6043 \begin_layout Standard
6044 \begin_inset space \hfill{}
6048 \begin_inset Tabular
6049 <lyxtabular version="3" rows="9" columns="2">
6050 <features tabularvalignment="middle">
6051 <column alignment="center" valignment="top" width="0pt">
6052 <column alignment="center" valignment="top" width="0pt">
6054 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
6057 \begin_layout Plain Layout
6063 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
6066 \begin_layout Plain Layout
6074 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
6077 \begin_layout Plain Layout
6083 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
6086 \begin_layout Plain Layout
6087 \begin_inset Formula $($
6097 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
6100 \begin_layout Plain Layout
6106 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
6109 \begin_layout Plain Layout
6110 \begin_inset Formula $\{$
6120 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
6123 \begin_layout Plain Layout
6129 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
6132 \begin_layout Plain Layout
6133 \begin_inset Formula $[$
6143 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
6146 \begin_layout Plain Layout
6154 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
6157 \begin_layout Plain Layout
6158 \begin_inset Formula $\langle$
6168 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
6171 \begin_layout Plain Layout
6179 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
6182 \begin_layout Plain Layout
6183 \begin_inset Formula $\lceil$
6193 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
6196 \begin_layout Plain Layout
6204 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
6207 \begin_layout Plain Layout
6208 \begin_inset Formula $\lfloor$
6218 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
6221 \begin_layout Plain Layout
6227 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
6230 \begin_layout Plain Layout
6231 \begin_inset Formula $/$
6241 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
6244 \begin_layout Plain Layout
6250 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
6253 \begin_layout Plain Layout
6254 \begin_inset Formula $|$
6268 \begin_inset space \hfill{}
6272 \begin_inset Tabular
6273 <lyxtabular version="3" rows="9" columns="2">
6274 <features tabularvalignment="middle">
6275 <column alignment="center" valignment="top" width="0pt">
6276 <column alignment="center" valignment="top" width="0pt">
6278 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
6281 \begin_layout Plain Layout
6287 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
6290 \begin_layout Plain Layout
6298 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
6301 \begin_layout Plain Layout
6307 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
6310 \begin_layout Plain Layout
6311 \begin_inset Formula $)$
6321 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
6324 \begin_layout Plain Layout
6330 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
6333 \begin_layout Plain Layout
6334 \begin_inset Formula $\}$
6344 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
6347 \begin_layout Plain Layout
6353 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
6356 \begin_layout Plain Layout
6357 \begin_inset Formula $]$
6367 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
6370 \begin_layout Plain Layout
6378 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
6381 \begin_layout Plain Layout
6382 \begin_inset Formula $\rangle$
6392 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
6395 \begin_layout Plain Layout
6403 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
6406 \begin_layout Plain Layout
6407 \begin_inset Formula $\rceil$
6417 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
6420 \begin_layout Plain Layout
6428 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
6431 \begin_layout Plain Layout
6432 \begin_inset Formula $\rfloor$
6442 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
6445 \begin_layout Plain Layout
6455 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
6458 \begin_layout Plain Layout
6459 \begin_inset Formula $\backslash$
6469 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
6472 \begin_layout Plain Layout
6480 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
6483 \begin_layout Plain Layout
6484 \begin_inset Formula $\|$
6498 \begin_inset space \hfill{}
6504 \begin_layout Standard
6507 \begin_inset Note Greyedout
6510 \begin_layout Plain Layout
6515 In TeX-mode the command
6522 \begin_inset Index idx
6525 \begin_layout Plain Layout
6533 must be used for the backslash, because the command
6541 produces there a line break.
6549 \begin_layout Standard
6550 For all characters listed above the size can be adjusted with the commands
6551 described in the following two subsections.
6552 When using these commands, the characters < and > can directly be used
6553 instead of the commands
6568 \begin_layout Subsubsection
6570 \begin_inset CommandInset label
6572 name "sub:Manual-Bracket-Size"
6577 \begin_inset Index idx
6580 \begin_layout Plain Layout
6581 Bracket size ! manual
6589 \begin_layout Standard
6590 The bracket size can be specified manually by the LaTeX-commands
6597 \begin_inset Index idx
6600 \begin_layout Plain Layout
6633 denotes the smallest and
6639 the largest bracket size.
6642 \begin_layout Standard
6643 These commands are used to emphasize levels of brackets:
6646 \begin_layout Standard
6648 \begin_inset Tabular
6649 <lyxtabular version="3" rows="2" columns="2">
6650 <features tabularvalignment="middle">
6651 <column alignment="center" valignment="top" width="0pt">
6652 <column alignment="center" valignment="top" width="0pt">
6654 <cell alignment="center" valignment="top" usebox="none">
6657 \begin_layout Plain Layout
6658 all brackets in the same size:
6663 <cell alignment="center" valignment="top" usebox="none">
6666 \begin_layout Plain Layout
6667 \begin_inset Formula $((A+B)(A-B))^{C}\raisebox{-4mm}{}$
6677 <cell alignment="center" valignment="top" usebox="none">
6680 \begin_layout Plain Layout
6686 <cell alignment="center" valignment="top" usebox="none">
6689 \begin_layout Plain Layout
6690 \begin_inset Formula $\Big((A+B)(A-B)\Big)^{C}$
6704 \begin_inset Note Note
6707 \begin_layout Plain Layout
6714 is only used as spacer.
6722 \begin_layout Standard
6723 For the second formula the command
6733 \begin_layout Plain Layout
6747 \begin_layout Standard
6748 Here is an overview about all bracket sizes:
6751 \begin_layout Standard
6771 \begin_layout Plain Layout
6788 \begin_layout Plain Layout
6801 \begin_layout Plain Layout
6817 \begin_layout Standard
6819 \begin_inset Formula $\Bigg(\exp\bigg<\Big[\big\{\ln(3x)\big\}^{2}\sin(x)\Big]^{A}\bigg>\Bigg)^{0,5}$
6825 \begin_layout Standard
6832 -commands there is the variant
6839 \begin_inset Index idx
6842 \begin_layout Plain Layout
6850 that adds a bit more space between the bracket and its content, and the
6864 \begin_inset Index idx
6867 \begin_layout Plain Layout
6877 , that don't add additional space.
6882 at the end of the command
6888 is for a left bracket; for a right bracket this will be replaced by an
6894 A left or right bracket can each be an opening or closing bracket.
6897 \begin_layout Standard
6898 In the following table is a comparison of the variants:
6901 \begin_layout Standard
6903 \begin_inset Tabular
6904 <lyxtabular version="3" rows="5" columns="2">
6905 <features tabularvalignment="middle">
6906 <column alignment="center" valignment="middle" width="0">
6907 <column alignment="center" valignment="middle" width="0">
6909 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
6912 \begin_layout Plain Layout
6918 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
6921 \begin_layout Plain Layout
6923 \begin_inset Note Note
6926 \begin_layout Plain Layout
6933 is only used as spacer.
6945 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
6948 \begin_layout Plain Layout
6963 \begin_layout Plain Layout
6981 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
6984 \begin_layout Plain Layout
6985 \begin_inset Formula $\raisebox{5.5mm}{}\Bigm(\bigm(\ln(3x)\bigm)^{2}\Bigm)\raisebox{-3.25mm}{}$
6995 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
6998 \begin_layout Plain Layout
7013 \begin_layout Plain Layout
7031 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
7034 \begin_layout Plain Layout
7035 \begin_inset Formula $\raisebox{5.5mm}{}\Big(\big(\ln(3x)\big)^{2}\Big)\raisebox{-3.25mm}{}$
7045 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
7048 \begin_layout Plain Layout
7063 \begin_layout Plain Layout
7081 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
7084 \begin_layout Plain Layout
7085 \begin_inset Formula $\raisebox{5.5mm}{}\Bigl(\bigl(\ln(3x)\bigr)^{2}\Bigr)\raisebox{-3.25mm}{}$
7095 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
7098 \begin_layout Plain Layout
7110 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
7113 \begin_layout Plain Layout
7114 \begin_inset Formula $\raisebox{4.5mm}{}\bigl)\ln(3x)\bigr(\raisebox{-2mm}{}$
7130 \begin_layout Subsubsection
7131 Automatic Bracket Size
7132 \begin_inset CommandInset label
7134 name "sub:Automatic-Bracket-Size"
7139 \begin_inset Index idx
7142 \begin_layout Plain Layout
7143 Bracket size ! automatic
7151 \begin_layout Standard
7152 Brackets with variable size can be inserted with the commands
7159 \begin_inset Index idx
7162 \begin_layout Plain Layout
7177 \begin_inset Index idx
7180 \begin_layout Plain Layout
7188 or via the math toolbar button
7189 \begin_inset Graphics
7190 filename ../images/dialog-show_mathdelimiter.png
7208 the wanted bracket must be inserted.
7209 The bracket size will then automatically be calculated for the output.
7212 \begin_layout Standard
7214 normal bracket: The command
7224 \begin_layout Plain Layout
7234 \begin_inset Formula $\downarrow$
7241 \begin_layout Plain Layout
7253 \begin_inset Formula
7263 \begin_layout Standard
7265 multiline bracket: The command
7277 \begin_layout Plain Layout
7287 \begin_inset Formula $\downarrow$
7294 \begin_layout Plain Layout
7308 \begin_inset Formula
7310 \ln\left(\frac{A}{C}\right)
7318 \begin_layout Standard
7334 \begin_inset space ~
7340 This has the advantage that you can see in LyX immediately the real bracket
7341 size and that the matching right bracket will be created too.
7342 \begin_inset Newline newline
7345 The command for the last example would then be:
7359 \begin_layout Plain Layout
7369 \begin_inset Formula $\downarrow$
7375 \begin_layout Standard
7376 To omit a left or right bracket, a dot is inserted for the omitted bracket.
7377 For example the command
7387 \begin_layout Plain Layout
7397 \begin_inset Formula $\downarrow$
7404 \begin_layout Plain Layout
7420 \begin_inset Formula
7422 \left.\frac{A}{B}\right\}
7441 will be converted by LyX to brackets in the right size when the document
7442 is reloaded and an omitted bracket will appear as dashed line.
7445 \begin_layout Standard
7446 \begin_inset VSpace bigskip
7449 Because all popular LaTeX-Distributions use eTeX, an extension to LaTeX,
7457 \begin_inset Index idx
7460 \begin_layout Plain Layout
7468 is additionally available for all brackets and limits.
7469 With this command the height of the following character is adapted to the
7470 one of the surrounding brackets, what is e.
7471 \begin_inset space \thinspace{}
7475 \begin_inset space \space{}
7478 needed for physical vectors:
7479 \begin_inset Formula
7481 \left\langle \phi\:\middle|\: J=\frac{3}{2}\,,\, M_{J}\right\rangle
7486 For physical vectors there is a special LaTeX-package, described in
7487 \begin_inset CommandInset ref
7489 reference "sub:Physical-Vectors"
7496 \begin_layout Subsection
7498 \begin_inset Index idx
7501 \begin_layout Plain Layout
7502 Brackets ! horizontal
7510 \begin_layout Standard
7512 \begin_inset Tabular
7513 <lyxtabular version="3" rows="4" columns="2">
7514 <features tabularvalignment="middle">
7515 <column alignment="center" valignment="top" width="0pt">
7516 <column alignment="center" valignment="top" width="0pt">
7518 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
7521 \begin_layout Plain Layout
7523 \begin_inset Note Note
7526 \begin_layout Plain Layout
7533 is only used as spacer.
7543 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
7546 \begin_layout Plain Layout
7554 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
7557 \begin_layout Plain Layout
7561 \begin_layout Plain Layout
7576 \begin_layout Plain Layout
7589 \begin_layout Plain Layout
7602 \begin_layout Plain Layout
7615 \begin_layout Plain Layout
7623 \begin_inset Index idx
7626 \begin_layout Plain Layout
7639 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
7642 \begin_layout Plain Layout
7643 \begin_inset Formula $\overbrace{A+B}^{3}$
7653 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
7656 \begin_layout Plain Layout
7660 \begin_layout Plain Layout
7675 \begin_layout Plain Layout
7688 \begin_layout Plain Layout
7701 \begin_layout Plain Layout
7709 \begin_inset Index idx
7712 \begin_layout Plain Layout
7725 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
7728 \begin_layout Plain Layout
7729 \begin_inset Formula $\underbrace{A+B}_{5}$
7739 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
7742 \begin_layout Plain Layout
7749 \begin_layout Plain Layout
7764 \begin_layout Plain Layout
7777 \begin_layout Plain Layout
7790 \begin_layout Plain Layout
7803 \begin_layout Plain Layout
7816 \begin_layout Plain Layout
7829 \begin_layout Plain Layout
7843 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
7846 \begin_layout Plain Layout
7847 \begin_inset Formula $\overbrace{\underbrace{A+B_{w}}_{7}}^{C}$
7863 \begin_layout Standard
7864 In the last example it doesn't matter if
7876 is inserted at first.
7879 \begin_layout Standard
7880 \begin_inset VSpace bigskip
7883 When brackets are needed that overlap each other, multiline formulas, as
7885 \begin_inset CommandInset ref
7887 reference "sec:Multiline-Formulas"
7892 \begin_inset Formula
7894 A & = & \underbrace{gggg+bbqq}_{r}+\: dddd\\
7895 & & \hphantom{gggg+\:}\underbrace{\hphantom{bbqq+dddd}}_{s}
7900 In the first row the formula is inserted together with the first brace.
7901 It is hereby important that the space command
7905 \begin_layout Plain Layout
7906 Space commands are explained in
7907 \begin_inset CommandInset ref
7909 reference "sub:Predefined-Space"
7924 is inserted before the first
7925 \begin_inset Formula $d$
7928 , because the brace that ends behind the
7929 \begin_inset Formula $q$
7932 prevents that the following
7933 \begin_inset Quotes eld
7937 \begin_inset Quotes erd
7940 is surrounded by space.
7944 \begin_layout Plain Layout
7945 because a bracket is not handled as character, see
7946 \begin_inset CommandInset ref
7948 reference "sub:Binary-Operators"
7957 In the second row the second brace is inserted.
7958 As it should begin before the
7959 \begin_inset Formula $b$
7974 \begin_layout Plain Layout
7982 \begin_inset CommandInset ref
7984 reference "sub:Placeholders"
7993 This space is needed because the
7994 \begin_inset Quotes eld
7998 \begin_inset Quotes erd
8001 is also surrounded by space in the formula.
8002 The brace is placed under the command
8011 \begin_layout Standard
8012 It gets more complicated when brackets overlap each other, like in the following
8017 \begin_layout Plain Layout
8029 \begin_inset Formula
8031 & & \hphantom{gggg+\:}\overbrace{\hphantom{bbqq+dddd}}^{s}\\
8032 A & = & \underbrace{gggg+bbqq}_{r}+\: dddd
8041 \begin_layout Plain Layout
8052 The first formula row is the same as the second row of the previous example,
8053 with the difference that the brace is above.
8054 The second row contains the formula together with the second brace.
8055 To avoid that there is space between the upper brace in the first row and
8056 the formula, the row spacing need to be reduced.
8057 This is not easily possible due to a bug in LyX
8061 \begin_layout Plain Layout
8062 \begin_inset CommandInset href
8064 name "LyX-bug #1505"
8065 target "http://www.lyx.org/trac/ticket/1505"
8075 As solution for the problem, the global formula row separation
8082 \begin_inset Index idx
8085 \begin_layout Plain Layout
8093 must be changed to -6
8094 \begin_inset space \thinspace{}
8097 pt before the formula with the command
8112 is set back after the formula to the standard value of 3
8113 \begin_inset space \thinspace{}
8116 pt using the same command.
8117 More about the row separation in formulas is explained in
8118 \begin_inset CommandInset ref
8120 reference "sub:Line-Separation"
8127 \begin_layout Section
8129 \begin_inset Index idx
8132 \begin_layout Plain Layout
8141 \begin_layout Standard
8142 Arrows can be inserted via the math toolbar button
8143 \begin_inset Graphics
8144 filename ../images/math/leftarrow.png
8149 or the commands listed in the following subsections.
8152 \begin_layout Subsection
8154 \begin_inset Index idx
8157 \begin_layout Plain Layout
8166 \begin_layout Standard
8167 \begin_inset space \hfill{}
8171 \begin_inset Tabular
8172 <lyxtabular version="3" rows="8" columns="2">
8173 <features tabularvalignment="middle">
8174 <column alignment="center" valignment="top" width="0pt">
8175 <column alignment="center" valignment="top" width="0pt">
8177 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
8180 \begin_layout Plain Layout
8186 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
8189 \begin_layout Plain Layout
8197 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
8200 \begin_layout Plain Layout
8208 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
8211 \begin_layout Plain Layout
8212 \begin_inset Formula $\gets$
8222 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
8225 \begin_layout Plain Layout
8233 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
8236 \begin_layout Plain Layout
8237 \begin_inset Formula $\Leftarrow$
8247 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
8250 \begin_layout Plain Layout
8258 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
8261 \begin_layout Plain Layout
8262 \begin_inset Formula $\longleftarrow$
8272 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
8275 \begin_layout Plain Layout
8283 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
8286 \begin_layout Plain Layout
8287 \begin_inset Formula $\Longleftarrow$
8297 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
8300 \begin_layout Plain Layout
8308 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
8311 \begin_layout Plain Layout
8312 \begin_inset Formula $\leftharpoonup$
8322 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
8325 \begin_layout Plain Layout
8333 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
8336 \begin_layout Plain Layout
8337 \begin_inset Formula $\leftharpoondown$
8347 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
8350 \begin_layout Plain Layout
8358 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
8361 \begin_layout Plain Layout
8362 \begin_inset Formula $\hookleftarrow$
8376 \begin_inset space \hfill{}
8380 \begin_inset Tabular
8381 <lyxtabular version="3" rows="8" columns="2">
8382 <features tabularvalignment="middle">
8383 <column alignment="center" valignment="top" width="0pt">
8384 <column alignment="center" valignment="top" width="0pt">
8386 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
8389 \begin_layout Plain Layout
8395 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
8398 \begin_layout Plain Layout
8406 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
8409 \begin_layout Plain Layout
8417 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
8420 \begin_layout Plain Layout
8421 \begin_inset Formula $\to$
8431 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
8434 \begin_layout Plain Layout
8442 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
8445 \begin_layout Plain Layout
8446 \begin_inset Formula $\Rightarrow$
8456 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
8459 \begin_layout Plain Layout
8467 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
8470 \begin_layout Plain Layout
8471 \begin_inset Formula $\longrightarrow$
8481 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
8484 \begin_layout Plain Layout
8492 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
8495 \begin_layout Plain Layout
8496 \begin_inset Formula $\Longrightarrow$
8506 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
8509 \begin_layout Plain Layout
8517 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
8520 \begin_layout Plain Layout
8521 \begin_inset Formula $\rightharpoonup$
8531 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
8534 \begin_layout Plain Layout
8542 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
8545 \begin_layout Plain Layout
8546 \begin_inset Formula $\rightharpoondown$
8556 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
8559 \begin_layout Plain Layout
8567 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
8570 \begin_layout Plain Layout
8571 \begin_inset Formula $\hookrightarrow$
8585 \begin_inset space \hfill{}
8591 \begin_layout Standard
8592 \begin_inset space \hfill{}
8596 \begin_inset Tabular
8597 <lyxtabular version="3" rows="6" columns="2">
8598 <features tabularvalignment="middle">
8599 <column alignment="center" valignment="top" width="0pt">
8600 <column alignment="center" valignment="top" width="0pt">
8602 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
8605 \begin_layout Plain Layout
8611 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
8614 \begin_layout Plain Layout
8622 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
8625 \begin_layout Plain Layout
8633 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
8636 \begin_layout Plain Layout
8637 \begin_inset Formula $\leftrightarrow$
8647 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
8650 \begin_layout Plain Layout
8658 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
8661 \begin_layout Plain Layout
8662 \begin_inset Formula $\Leftrightarrow$
8672 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
8675 \begin_layout Plain Layout
8683 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
8686 \begin_layout Plain Layout
8687 \begin_inset Formula $\longleftrightarrow$
8697 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
8700 \begin_layout Plain Layout
8708 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
8711 \begin_layout Plain Layout
8712 \begin_inset Formula $\Longleftrightarrow$
8722 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
8725 \begin_layout Plain Layout
8733 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
8736 \begin_layout Plain Layout
8737 \begin_inset Formula $\rightleftharpoons$
8751 \begin_inset space \hspace{}
8756 \begin_inset space \hfill{}
8760 \begin_inset Tabular
8761 <lyxtabular version="3" rows="5" columns="2">
8762 <features tabularvalignment="middle">
8763 <column alignment="center" valignment="top" width="0pt">
8764 <column alignment="center" valignment="top" width="0pt">
8766 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
8769 \begin_layout Plain Layout
8775 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
8778 \begin_layout Plain Layout
8786 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
8789 \begin_layout Plain Layout
8797 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
8800 \begin_layout Plain Layout
8801 \begin_inset Formula $\mapsto$
8811 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
8814 \begin_layout Plain Layout
8822 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
8825 \begin_layout Plain Layout
8826 \begin_inset Formula $\longmapsto$
8836 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
8839 \begin_layout Plain Layout
8847 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
8850 \begin_layout Plain Layout
8851 \begin_inset Formula $\leadsto$
8861 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
8864 \begin_layout Plain Layout
8872 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
8875 \begin_layout Plain Layout
8876 \begin_inset Formula $\dasharrow$
8890 \begin_inset space \hfill{}
8896 \begin_layout Standard
8897 \begin_inset VSpace medskip
8900 Arrows used as accent like e.
8901 \begin_inset space \thinspace{}
8905 \begin_inset space \space{}
8908 vector arrows are listed in
8909 \begin_inset CommandInset ref
8911 reference "sec:Accents"
8918 \begin_layout Standard
8919 \begin_inset VSpace bigskip
8922 Furthermore there are the labeled arrows
8923 \begin_inset Index idx
8926 \begin_layout Plain Layout
8939 \begin_inset Index idx
8942 \begin_layout Plain Layout
8957 \begin_inset Index idx
8960 \begin_layout Plain Layout
8967 \begin_layout Plain Layout
8982 When inserting one of these commands in a formula, an arrow with two blue
8983 boxes appear where the label can be inserted.
8984 The length of the arrow adapts to the label width.
8987 \begin_layout Standard
8989 \begin_inset Tabular
8990 <lyxtabular version="3" rows="3" columns="2">
8991 <features tabularvalignment="middle">
8992 <column alignment="center" valignment="top" width="0pt">
8993 <column alignment="center" valignment="top" width="0pt">
8995 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
8998 \begin_layout Plain Layout
9004 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
9007 \begin_layout Plain Layout
9009 \begin_inset Note Note
9012 \begin_layout Plain Layout
9019 is only used as spacer.
9031 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
9034 \begin_layout Plain Layout
9041 \begin_layout Plain Layout
9051 \begin_inset Formula $\downarrow$
9055 \begin_inset Formula $\to$
9063 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
9066 \begin_layout Plain Layout
9067 \begin_inset Formula $\raisebox{5mm}{}F(a)\xleftarrow[x>0]{x=a}F(x)\raisebox{-4mm}{}$
9077 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
9080 \begin_layout Plain Layout
9087 \begin_layout Plain Layout
9097 \begin_inset Formula $\downarrow$
9101 \begin_inset Formula $\to$
9109 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
9112 \begin_layout Plain Layout
9113 \begin_inset Formula $\raisebox{5mm}{}F(x)\xrightarrow[x>0]{x=a}F(a)\raisebox{-4mm}{}$
9129 \begin_layout Subsection
9130 Vertical and diagonal Arrows
9131 \begin_inset Index idx
9134 \begin_layout Plain Layout
9141 \begin_inset Index idx
9144 \begin_layout Plain Layout
9153 \begin_layout Standard
9154 \begin_inset space \hfill{}
9158 \begin_inset Tabular
9159 <lyxtabular version="3" rows="7" columns="2">
9160 <features tabularvalignment="middle">
9161 <column alignment="center" valignment="top" width="0pt">
9162 <column alignment="center" valignment="top" width="0pt">
9164 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
9167 \begin_layout Plain Layout
9173 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
9176 \begin_layout Plain Layout
9184 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
9187 \begin_layout Plain Layout
9195 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
9198 \begin_layout Plain Layout
9199 \begin_inset Formula $\uparrow$
9209 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
9212 \begin_layout Plain Layout
9220 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
9223 \begin_layout Plain Layout
9224 \begin_inset Formula $\Uparrow$
9234 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
9237 \begin_layout Plain Layout
9245 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
9248 \begin_layout Plain Layout
9249 \begin_inset Formula $\updownarrow$
9259 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
9262 \begin_layout Plain Layout
9270 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
9273 \begin_layout Plain Layout
9274 \begin_inset Formula $\Updownarrow$
9284 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
9287 \begin_layout Plain Layout
9295 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
9298 \begin_layout Plain Layout
9299 \begin_inset Formula $\Downarrow$
9309 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
9312 \begin_layout Plain Layout
9320 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
9323 \begin_layout Plain Layout
9324 \begin_inset Formula $\downarrow$
9338 \begin_inset space \hfill{}
9342 \begin_inset Tabular
9343 <lyxtabular version="3" rows="5" columns="2">
9344 <features tabularvalignment="middle">
9345 <column alignment="center" valignment="top" width="0pt">
9346 <column alignment="center" valignment="top" width="0pt">
9348 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
9351 \begin_layout Plain Layout
9357 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
9360 \begin_layout Plain Layout
9368 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
9371 \begin_layout Plain Layout
9379 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
9382 \begin_layout Plain Layout
9383 \begin_inset Formula $\nearrow$
9393 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
9396 \begin_layout Plain Layout
9404 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
9407 \begin_layout Plain Layout
9408 \begin_inset Formula $\searrow$
9418 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
9421 \begin_layout Plain Layout
9429 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
9432 \begin_layout Plain Layout
9433 \begin_inset Formula $\swarrow$
9443 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
9446 \begin_layout Plain Layout
9454 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
9457 \begin_layout Plain Layout
9458 \begin_inset Formula $\nwarrow$
9472 \begin_inset space \hfill{}
9478 \begin_layout Standard
9479 \begin_inset VSpace medskip
9482 Vertical arrows can be used also as delimiter together with the commands
9484 \begin_inset CommandInset ref
9486 reference "sub:Manual-Bracket-Size"
9491 \begin_inset CommandInset ref
9493 reference "sub:Automatic-Bracket-Size"
9500 \begin_layout Section
9502 \begin_inset CommandInset label
9509 \begin_inset Index idx
9512 \begin_layout Plain Layout
9521 \begin_layout Standard
9522 Accents can be inserted via the math toolbar button
9523 \begin_inset Graphics
9524 filename ../images/math/hat.png
9529 or the commands listed in the following subsections.
9532 \begin_layout Subsection
9533 Accents for one Character
9537 \begin_layout Plain Layout
9550 \begin_layout Plain Layout
9552 \begin_inset CommandInset ref
9554 reference "sub:Accents-in-Text"
9567 \begin_layout Plain Layout
9575 \begin_inset Note Note
9578 \begin_layout Plain Layout
9585 is used to avoid that the footnote appears in the PDF-bookmark.
9588 \begin_layout Plain Layout
9596 \begin_inset CommandInset ref
9598 reference "sub:Formulas-in-Section"
9608 \begin_inset CommandInset label
9610 name "sub:Accents-for-one"
9615 \begin_inset Index idx
9618 \begin_layout Plain Layout
9619 Accents ! for one character
9627 \begin_layout Standard
9628 \begin_inset space \hfill{}
9632 \begin_inset Tabular
9633 <lyxtabular version="3" rows="8" columns="2">
9634 <features tabularvalignment="middle">
9635 <column alignment="center" valignment="top" width="0pt">
9636 <column alignment="center" valignment="top" width="0pt">
9638 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
9641 \begin_layout Plain Layout
9647 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
9650 \begin_layout Plain Layout
9652 \begin_inset Note Note
9655 \begin_layout Plain Layout
9662 is only used as spacer.
9674 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
9677 \begin_layout Plain Layout
9684 \begin_layout Plain Layout
9698 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
9701 \begin_layout Plain Layout
9702 \begin_inset Formula $\raisebox{5mm}{}\dot{A}$
9712 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
9715 \begin_layout Plain Layout
9722 \begin_layout Plain Layout
9736 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
9739 \begin_layout Plain Layout
9740 \begin_inset Formula $\raisebox{5mm}{}\ddot{A}$
9750 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
9753 \begin_layout Plain Layout
9760 \begin_layout Plain Layout
9774 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
9777 \begin_layout Plain Layout
9778 \begin_inset Formula $\raisebox{5mm}{}\dddot{A}$
9788 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
9791 \begin_layout Plain Layout
9798 \begin_layout Plain Layout
9812 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
9815 \begin_layout Plain Layout
9816 \begin_inset Formula $\raisebox{5mm}{}\ddddot{A}$
9826 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
9829 \begin_layout Plain Layout
9836 \begin_layout Plain Layout
9846 \begin_inset Index idx
9849 \begin_layout Plain Layout
9860 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
9863 \begin_layout Plain Layout
9864 \begin_inset Formula $\raisebox{5mm}{}\vec{A}$
9874 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
9877 \begin_layout Plain Layout
9884 \begin_layout Plain Layout
9898 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
9901 \begin_layout Plain Layout
9902 \begin_inset Formula $\raisebox{5mm}{}\bar{A}$
9912 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
9915 \begin_layout Plain Layout
9922 \begin_layout Plain Layout
9936 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
9939 \begin_layout Plain Layout
9940 \begin_inset Formula $\raisebox{5mm}{}\mathring{A}$
9954 \begin_inset space \hfill{}
9958 \begin_inset Tabular
9959 <lyxtabular version="3" rows="7" columns="2">
9960 <features tabularvalignment="middle">
9961 <column alignment="center" valignment="top" width="0pt">
9962 <column alignment="center" valignment="top" width="0pt">
9964 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
9967 \begin_layout Plain Layout
9973 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
9976 \begin_layout Plain Layout
9984 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
9987 \begin_layout Plain Layout
9994 \begin_layout Plain Layout
10008 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
10011 \begin_layout Plain Layout
10012 \begin_inset Formula $\raisebox{5mm}{}\tilde{A}$
10022 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
10025 \begin_layout Plain Layout
10032 \begin_layout Plain Layout
10046 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
10049 \begin_layout Plain Layout
10050 \begin_inset Formula $\raisebox{5mm}{}\hat{A}$
10060 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
10063 \begin_layout Plain Layout
10070 \begin_layout Plain Layout
10084 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
10087 \begin_layout Plain Layout
10088 \begin_inset Formula $\raisebox{5mm}{}\check{A}$
10098 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
10101 \begin_layout Plain Layout
10108 \begin_layout Plain Layout
10122 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
10125 \begin_layout Plain Layout
10126 \begin_inset Formula $\raisebox{5mm}{}\acute{A}$
10136 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
10139 \begin_layout Plain Layout
10146 \begin_layout Plain Layout
10160 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
10163 \begin_layout Plain Layout
10164 \begin_inset Formula $\raisebox{5mm}{}\grave{A}$
10174 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
10177 \begin_layout Plain Layout
10184 \begin_layout Plain Layout
10198 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
10201 \begin_layout Plain Layout
10202 \begin_inset Formula $\raisebox{5mm}{}\breve{A}$
10216 \begin_inset space \hfill{}
10222 \begin_layout Standard
10223 \begin_inset VSpace bigskip
10229 \begin_layout Standard
10230 You can directly insert accents like é to formulas.
10231 LyX will transform them to the corresponding accent command.
10233 \begin_inset Index idx
10236 \begin_layout Plain Layout
10242 it is better to insert a quotation mark before the vowel.
10243 These two characters are then treated by LaTeX as
10247 character when the formula part with the umlaut is marked as German.
10255 \begin_inset Quotes eld
10259 \begin_inset Quotes erd
10262 umlauts are created as demonstrated in the following example:
10265 \begin_layout Standard
10266 \begin_inset VSpace -2mm
10272 \begin_layout Standard
10274 \begin_inset Tabular
10275 <lyxtabular version="3" rows="3" columns="2">
10276 <features tabularvalignment="middle">
10277 <column alignment="center" valignment="top" width="0">
10278 <column alignment="center" valignment="top" width="0">
10280 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
10283 \begin_layout Plain Layout
10289 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
10292 \begin_layout Plain Layout
10294 \begin_inset Note Note
10297 \begin_layout Plain Layout
10305 \begin_inset space \thinspace{}
10308 pt space are only used as spacer.
10320 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
10323 \begin_layout Plain Layout
10326 \begin_inset Quotes grd
10334 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
10337 \begin_layout Plain Layout
10338 \begin_inset space \hspace{}
10345 \begin_inset Formula $"i$
10355 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
10358 \begin_layout Plain Layout
10365 \begin_layout Plain Layout
10379 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
10382 \begin_layout Plain Layout
10383 \begin_inset Formula $\raisebox{5mm}{}\ddot{i}$
10399 \begin_layout Standard
10400 Another advantage to
10406 is that umlauts can directly be converted to mathematical text because
10407 the accent commands above are
10413 in mathematical text
10416 To convert an accented character to mathematical text, only the character
10417 under the accent may be converted.
10418 This applies also for all other conversions, e.
10419 \begin_inset space \thinspace{}
10423 \begin_inset space \space{}
10429 \begin_layout Standard
10430 In mathematical text, umlauts and other accented characters can directly
10434 \begin_layout Subsection
10435 Accents for Operators
10436 \begin_inset Index idx
10439 \begin_layout Plain Layout
10440 Accents ! for operators
10448 \begin_layout Standard
10456 \begin_inset Index idx
10459 \begin_layout Plain Layout
10474 \begin_inset Index idx
10477 \begin_layout Plain Layout
10485 characters can be placed above or below an operator, respectively, to accent
10494 \begin_inset Index idx
10497 \begin_layout Plain Layout
10505 characters can be set before and behind an operator.
10506 The command scheme is:
10509 \begin_layout Standard
10525 \begin_layout Standard
10532 must always be before the operator that should be accented.
10533 You can accent with several characters and even with other operators and
10541 for example only characters behind an operator, write nothing between the
10542 first braces but don't omit the braces.
10545 \begin_layout Standard
10546 For example the command
10551 \begin_inset Formula $\to$
10561 \begin_inset Formula $\to$
10570 \begin_layout Plain Layout
10586 \begin_inset Formula
10588 \sideset{}{'}\sum_{k=1}^{n}
10596 \begin_layout Standard
10605 \begin_layout Plain Layout
10620 \begin_layout Plain Layout
10632 \begin_inset Formula $\uparrow$
10640 \begin_inset Formula
10642 \overset{a}{\maltese}
10647 As seen in the last example, with
10659 also symbols and characters can be accented; with
10665 this is not possible.
10668 \begin_layout Subsection
10669 Accents for several Characters
10670 \begin_inset Index idx
10673 \begin_layout Plain Layout
10674 Accents ! for several characters
10682 \begin_layout Standard
10683 \begin_inset space \hfill{}
10687 \begin_inset Tabular
10688 <lyxtabular version="3" rows="5" columns="2">
10689 <features tabularvalignment="middle">
10690 <column alignment="center" valignment="top" width="0pt">
10691 <column alignment="center" valignment="top" width="0pt">
10693 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
10696 \begin_layout Plain Layout
10702 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
10705 \begin_layout Plain Layout
10707 \begin_inset Note Note
10710 \begin_layout Plain Layout
10717 is only used as spacer.
10729 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
10732 \begin_layout Plain Layout
10739 \begin_layout Plain Layout
10753 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
10756 \begin_layout Plain Layout
10757 \begin_inset Formula $\raisebox{6mm}{}\overleftarrow{A=B}\raisebox{-2mm}{}$
10767 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
10770 \begin_layout Plain Layout
10777 \begin_layout Plain Layout
10791 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
10794 \begin_layout Plain Layout
10795 \begin_inset Formula $\raisebox{5mm}{}\underleftarrow{A=B}\raisebox{-3mm}{}$
10805 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
10808 \begin_layout Plain Layout
10815 \begin_layout Plain Layout
10829 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
10832 \begin_layout Plain Layout
10833 \begin_inset Formula $\raisebox{6mm}{}\overleftrightarrow{A=B}\raisebox{-2mm}{}$
10843 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
10846 \begin_layout Plain Layout
10849 underleftrightarrow
10853 \begin_layout Plain Layout
10867 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
10870 \begin_layout Plain Layout
10871 \begin_inset Formula $\raisebox{5mm}{}\underleftrightarrow{A=B}\raisebox{-3mm}{}$
10885 \begin_inset space \hfill{}
10889 \begin_inset Tabular
10890 <lyxtabular version="3" rows="5" columns="2">
10891 <features tabularvalignment="middle">
10892 <column alignment="center" valignment="top" width="0pt">
10893 <column alignment="center" valignment="top" width="0pt">
10895 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
10898 \begin_layout Plain Layout
10904 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
10907 \begin_layout Plain Layout
10915 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
10918 \begin_layout Plain Layout
10925 \begin_layout Plain Layout
10939 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
10942 \begin_layout Plain Layout
10943 \begin_inset Formula $\raisebox{6mm}{}\overrightarrow{A=B}\raisebox{-2mm}{}$
10953 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
10956 \begin_layout Plain Layout
10963 \begin_layout Plain Layout
10977 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
10980 \begin_layout Plain Layout
10981 \begin_inset Formula $\raisebox{5mm}{}\underrightarrow{A=B}\raisebox{-3mm}{}$
10991 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
10994 \begin_layout Plain Layout
11001 \begin_layout Plain Layout
11015 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
11018 \begin_layout Plain Layout
11019 \begin_inset Formula $\raisebox{6mm}{}\widetilde{A=B}\raisebox{-2mm}{}$
11029 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
11032 \begin_layout Plain Layout
11039 \begin_layout Plain Layout
11053 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
11056 \begin_layout Plain Layout
11057 \begin_inset Formula $\raisebox{6mm}{}\widehat{A=B}\raisebox{-2mm}{}$
11071 \begin_inset space \hfill{}
11077 \begin_layout Standard
11078 \begin_inset VSpace medskip
11081 With these commands as many characters as you like can be accented.
11094 will only be set in the output with a length of three characters, as shown
11095 in the following example:
11096 \begin_inset Formula
11098 \widetilde{A+B=C-D}
11106 \begin_layout Standard
11114 \begin_inset Index idx
11117 \begin_layout Plain Layout
11132 \begin_inset Index idx
11135 \begin_layout Plain Layout
11143 described in the previous subsection it is also possible to accent several
11153 \begin_layout Plain Layout
11163 \begin_inset Formula $\downarrow$
11169 \begin_inset Formula
11171 \underset{***}{A=B}
11179 \begin_layout Section
11181 \begin_inset CommandInset label
11188 \begin_inset Index idx
11191 \begin_layout Plain Layout
11200 \begin_layout Subsection
11202 \begin_inset CommandInset label
11204 name "sub:Predefined-Space"
11209 \begin_inset Index idx
11212 \begin_layout Plain Layout
11213 Space ! horizontal ! predefined
11221 \begin_layout Standard
11222 Sometimes it is necessary to insert horizontal space to a formula.
11223 This is done by inserting a protected space (shortcut
11226 arg "space-insert protected"
11231 \begin_inset Quotes eld
11240 \begin_layout Plain Layout
11252 \begin_inset Quotes erd
11255 appears and by pressing
11259 several times one can select one of eight different space sizes.
11260 The spaces can also be inserted using the math toolbar button
11261 \begin_inset Graphics
11262 filename ../images/math/space.png
11267 or special commands.
11268 Independent from the inserted command, one can select the size again by
11276 \begin_layout Standard
11279 \begin_inset VSpace -5mm
11283 \begin_inset Tabular
11284 <lyxtabular version="3" rows="3" columns="7">
11285 <features tabularvalignment="middle">
11286 <column alignment="center" valignment="middle" width="6.8cm">
11287 <column alignment="center" valignment="top" width="0">
11288 <column alignment="center" valignment="top" width="0">
11289 <column alignment="center" valignment="top" width="0">
11290 <column alignment="center" valignment="top" width="0">
11291 <column alignment="center" valignment="top" width="0">
11292 <column alignment="center" valignment="top" width="0">
11294 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
11297 \begin_layout Plain Layout
11303 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
11306 \begin_layout Plain Layout
11314 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
11317 \begin_layout Plain Layout
11325 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
11328 \begin_layout Plain Layout
11336 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
11339 \begin_layout Plain Layout
11347 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
11350 \begin_layout Plain Layout
11358 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
11361 \begin_layout Plain Layout
11371 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
11374 \begin_layout Plain Layout
11379 keystrokes after inserting the protected space
11384 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
11387 \begin_layout Plain Layout
11393 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
11396 \begin_layout Plain Layout
11402 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
11405 \begin_layout Plain Layout
11411 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
11414 \begin_layout Plain Layout
11420 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
11423 \begin_layout Plain Layout
11429 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
11432 \begin_layout Plain Layout
11440 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
11443 \begin_layout Plain Layout
11449 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
11452 \begin_layout Plain Layout
11453 \begin_inset Formula $A\, B$
11461 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
11464 \begin_layout Plain Layout
11465 \begin_inset Formula $A\: B$
11473 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
11476 \begin_layout Plain Layout
11477 \begin_inset Formula $A\; B$
11485 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
11488 \begin_layout Plain Layout
11489 \begin_inset Formula $A\quad B$
11497 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
11500 \begin_layout Plain Layout
11501 \begin_inset Formula $A\qquad B$
11509 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
11512 \begin_layout Plain Layout
11513 \begin_inset Formula $A\! B$
11529 \begin_layout Standard
11530 The last size seem to produce no space.
11531 It is displayed red in LyX contrary to the other sizes, because it is a
11533 There are two more negative spaces:
11536 \begin_layout Standard
11538 \begin_inset Tabular
11539 <lyxtabular version="3" rows="3" columns="3">
11540 <features tabularvalignment="middle">
11541 <column alignment="center" valignment="middle" width="6.8cm">
11542 <column alignment="center" valignment="top" width="0pt">
11543 <column alignment="center" valignment="top" width="0pt">
11545 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
11548 \begin_layout Plain Layout
11554 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
11557 \begin_layout Plain Layout
11565 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
11568 \begin_layout Plain Layout
11578 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
11581 \begin_layout Plain Layout
11586 keystrokes after inserting the protected space
11591 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
11594 \begin_layout Plain Layout
11600 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
11603 \begin_layout Plain Layout
11611 <cell multicolumn="1" alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
11614 \begin_layout Plain Layout
11620 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
11623 \begin_layout Plain Layout
11624 \begin_inset Formula $A\negmedspace B$
11632 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
11635 \begin_layout Plain Layout
11636 \begin_inset Formula $A\negthickspace B$
11652 \begin_layout Standard
11653 Negative spaces can lead to characters overlapping each other.
11654 Thus they can be used to enforce ligatures, what is e.
11655 \begin_inset space \thinspace{}
11659 \begin_inset space \space{}
11662 useful for summation operators:
11665 \begin_layout Standard
11667 \begin_inset Tabular
11668 <lyxtabular version="3" rows="3" columns="2">
11669 <features tabularvalignment="middle">
11670 <column alignment="center" valignment="top" width="0">
11671 <column alignment="center" valignment="top" width="0">
11673 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
11676 \begin_layout Plain Layout
11682 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
11685 \begin_layout Plain Layout
11687 \begin_inset Note Note
11690 \begin_layout Plain Layout
11697 is only used as spacer.
11709 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
11712 \begin_layout Plain Layout
11721 \begin_layout Plain Layout
11735 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
11738 \begin_layout Plain Layout
11739 \begin_inset Formula $\raisebox{4.5mm}{}\sum\sum f_{kl}\raisebox{-2.5mm}{}$
11749 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
11752 \begin_layout Plain Layout
11763 \begin_layout Plain Layout
11777 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
11780 \begin_layout Plain Layout
11781 \begin_inset Formula $\raisebox{4.5mm}{}\sum\negmedspace\sum f_{kl}\raisebox{-2.5mm}{}$
11797 \begin_layout Standard
11798 Relations like for example equal signs, are always surrounded by space.
11799 To suppress this, the equal sign is placed into a TeX-brace.
11800 The following example demonstrates this:
11803 \begin_layout Standard
11805 \begin_inset Tabular
11806 <lyxtabular version="3" rows="2" columns="2">
11807 <features tabularvalignment="middle">
11808 <column alignment="center" valignment="top" width="0pt">
11809 <column alignment="center" valignment="top" width="0pt">
11811 <cell alignment="center" valignment="top" usebox="none">
11814 \begin_layout Plain Layout
11820 <cell alignment="center" valignment="top" usebox="none">
11823 \begin_layout Plain Layout
11824 \begin_inset Formula $A=B$
11834 <cell alignment="center" valignment="top" usebox="none">
11837 \begin_layout Plain Layout
11838 \begin_inset Note Note
11841 \begin_layout Plain Layout
11848 is only used as spacer.
11854 \begin_inset Formula $\raisebox{5mm}{}$
11857 equation without space
11862 <cell multicolumn="1" alignment="center" valignment="top" usebox="none">
11865 \begin_layout Plain Layout
11866 \begin_inset Formula $A{=}B$
11882 \begin_layout Standard
11884 The command for the last formula is:
11889 \begin_inset Formula $\to$
11895 \begin_layout Standard
11896 \begin_inset VSpace bigskip
11899 Spaces are needed for physical units, because the space between the value
11900 and the unit is the smallest one and not a normal space.
11901 For units in text, the smallest space is inserted via the menu
11903 Insert\SpecialChar \menuseparator
11904 Formatting\SpecialChar \menuseparator
11906 \begin_inset space ~
11914 arg "space-insert thin"
11920 \begin_layout Standard
11921 An example to visualize the difference:
11924 \begin_layout Standard
11925 \begin_inset Tabular
11926 <lyxtabular version="3" rows="2" columns="2">
11927 <features tabularvalignment="middle">
11928 <column alignment="left" valignment="top" width="0">
11929 <column alignment="left" valignment="top" width="0">
11931 <cell alignment="center" valignment="top" usebox="none">
11934 \begin_layout Plain Layout
11936 \begin_inset Formula $\cdot$
11944 <cell alignment="center" valignment="top" usebox="none">
11947 \begin_layout Plain Layout
11948 space between value and unit
11955 <cell alignment="center" valignment="top" usebox="none">
11958 \begin_layout Plain Layout
11960 \begin_inset space \thinspace{}
11964 \begin_inset Formula $\cdot$
11972 <cell alignment="center" valignment="top" usebox="none">
11975 \begin_layout Plain Layout
11976 smallest space between value and unit
11989 \begin_layout Subsection
11994 \begin_layout Plain Layout
12007 \begin_layout Plain Layout
12008 for vertical space in formulas see
12009 \begin_inset CommandInset ref
12011 reference "sub:Line-Separation"
12024 \begin_layout Plain Layout
12032 \begin_inset Note Note
12035 \begin_layout Plain Layout
12038 texorpdfstring is used to avoid that the footnote appears in the PDF-bookmark.
12041 \begin_layout Plain Layout
12044 texorpdfstring is in section
12045 \begin_inset CommandInset ref
12047 reference "sub:Formulas-in-Section"
12057 \begin_inset CommandInset label
12059 name "sub:Variable-Space"
12064 \begin_inset Index idx
12067 \begin_layout Plain Layout
12068 Space ! horizontal ! variable
12076 \begin_layout Standard
12077 Space with a defined length can be inserted with the command
12084 \begin_inset Index idx
12087 \begin_layout Plain Layout
12097 \begin_inset Quotes eld
12106 \begin_layout Plain Layout
12118 \begin_inset Quotes erd
12122 The length can be specified by left-clicking on the
12123 \begin_inset Quotes eld
12132 \begin_layout Plain Layout
12144 \begin_inset Quotes erd
12148 The length may also be negative.
12149 To insert so many space that the formula uses all available space, the
12157 \begin_inset Index idx
12160 \begin_layout Plain Layout
12171 \begin_layout Standard
12172 \begin_inset VSpace -1mm
12178 \begin_layout Standard
12180 \begin_inset Tabular
12181 <lyxtabular version="3" rows="4" columns="2">
12182 <features tabularvalignment="middle">
12183 <column alignment="center" valignment="top" width="0">
12184 <column alignment="center" valignment="top" width="0">
12186 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
12189 \begin_layout Plain Layout
12197 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
12200 \begin_layout Plain Layout
12208 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
12211 \begin_layout Plain Layout
12218 \begin_layout Plain Layout
12228 \begin_inset Formula $\to$
12234 \begin_inset space \thinspace{}
12242 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
12245 \begin_layout Plain Layout
12246 \begin_inset Formula $A=B\hspace{3cm}A\not=C$
12256 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
12259 \begin_layout Plain Layout
12266 \begin_layout Plain Layout
12276 \begin_inset Formula $\to$
12282 \begin_inset space \thinspace{}
12290 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
12293 \begin_layout Plain Layout
12294 \begin_inset Formula $A\hspace{-1mm}A\not=A$
12304 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
12307 \begin_layout Plain Layout
12314 \begin_layout Plain Layout
12328 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
12331 \begin_layout Plain Layout
12332 \begin_inset Formula $A=A\hfill B=B$
12348 \begin_layout Standard
12349 In the last example the available space is given by the longest column entry
12351 In an inline formula the space depends on the length of the line in which
12359 Thus, when the line uses the full width, no space will be created.
12366 only has an effect on displayed formulas when the formula style
12371 (Formula styles are explained in
12372 \begin_inset CommandInset ref
12374 reference "sec:Formula-Styles"
12381 \begin_layout Standard
12388 , there are the commands
12400 that fill the space with a pattern, see
12401 \begin_inset CommandInset ref
12403 reference "sub:Ellipses"
12410 \begin_layout Standard
12411 For text, variable space can be inserted via the menu
12413 Insert\SpecialChar \menuseparator
12414 Formatting\SpecialChar \menuseparator
12416 \begin_inset space ~
12424 \begin_layout Standard
12425 This is a line with
12426 \begin_inset space \hspace{}
12431 \begin_inset space \thinspace{}
12437 \begin_layout Standard
12438 This is a line with
12439 \begin_inset space \hfill{}
12445 \begin_layout Subsection
12446 Space besides inline Formulas
12447 \begin_inset Index idx
12450 \begin_layout Plain Layout
12451 Space ! besides inline formulas
12459 \begin_layout Standard
12460 The space that surrounds inline formulas can be adjusted with the length
12468 \begin_inset Index idx
12471 \begin_layout Plain Layout
12480 The value of a length is set with the command
12487 \begin_inset Index idx
12490 \begin_layout Plain Layout
12498 that has the following scheme:
12501 \begin_layout Standard
12506 setlength{length name}{value}
12509 \begin_layout Standard
12517 \begin_inset space \thinspace{}
12523 \begin_layout Standard
12533 \begin_layout Standard
12534 is inserted in TeX-mode.
12536 \begin_inset space \thinspace{}
12539 mm space will now be set around all inline formulas:
12543 \begin_layout Plain Layout
12557 \begin_layout Standard
12558 This is a line with an inline formula
12559 \begin_inset Formula $A=B$
12563 \begin_inset space \thinspace{}
12566 mm surrounding space.
12570 \begin_layout Plain Layout
12584 \begin_layout Standard
12585 To return to the predefined value,
12591 is set to the value 0
12592 \begin_inset space \thinspace{}
12598 \begin_layout Section
12600 \begin_inset Index idx
12603 \begin_layout Plain Layout
12610 \begin_inset Index idx
12613 \begin_layout Plain Layout
12618 \begin_layout Plain Layout
12629 \begin_layout Plain Layout
12644 \begin_layout Standard
12645 Boxes for text are described in chapter
12652 \begin_inset space ~
12660 \begin_layout Subsection
12662 \begin_inset CommandInset label
12664 name "sub:Boxes-with-Frame"
12669 \begin_inset Index idx
12672 \begin_layout Plain Layout
12681 \begin_layout Standard
12682 It is possible to frame formulas or parts of it with the commands
12689 \begin_inset Index idx
12692 \begin_layout Plain Layout
12707 \begin_inset Index idx
12710 \begin_layout Plain Layout
12721 \begin_layout Standard
12722 When one of these commands is inserted to a formula, a blue box appears
12723 within a frame to enter formula parts.
12730 an additional formula has to be created by
12734 within this box, because the box content will otherwise be treated as mathemati
12742 is used, a new formula is automatically created inside the frame.
12745 \begin_layout Standard
12752 is not suitable to frame displayed formulas because the formula will always
12753 be set in the size of the text.
12760 is in contrary not suitable to frame inline formulas, because the formula
12761 will always be set in the size of a displayed formula.
12764 \begin_layout Standard
12771 there is the command
12778 \begin_inset Index idx
12781 \begin_layout Plain Layout
12789 where additionally the frame width and the alignment can be specified.
12796 is used in the following scheme:
12799 \begin_layout Standard
12804 framebox[frame width][position]{box content}
12807 \begin_layout Standard
12808 The position can either be
12825 right aligns the formula in the box.
12826 When no position is given, the formula will be centered.
12827 \begin_inset Newline newline
12830 Is no width given, also no position can be given.
12831 In this case the frame width is adjusted to the box content like for
12840 \begin_layout Standard
12847 is inserted, a box appears containing three blue boxes.
12848 The first two boxes are surrounded by brackets and denote the two optional
12850 The third box is for formula parts like for
12859 \begin_layout Standard
12861 \begin_inset Tabular
12862 <lyxtabular version="3" rows="5" columns="2">
12863 <features tabularvalignment="middle">
12864 <column alignment="center" valignment="top" width="0">
12865 <column alignment="center" valignment="top" width="0">
12867 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
12870 \begin_layout Plain Layout
12876 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
12879 \begin_layout Plain Layout
12881 \begin_inset Note Note
12884 \begin_layout Plain Layout
12891 is only used as spacer.
12903 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
12906 \begin_layout Plain Layout
12913 \begin_layout Plain Layout
12932 \begin_layout Plain Layout
12946 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
12949 \begin_layout Plain Layout
12950 \begin_inset Formula $\raisebox{6mm}{}\fbox{\ensuremath{\int A=B}}\raisebox{-4mm}{}$
12960 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
12963 \begin_layout Plain Layout
12970 \begin_layout Plain Layout
12985 \begin_layout Plain Layout
12999 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
13002 \begin_layout Plain Layout
13003 \begin_inset Formula $\raisebox{8.5mm}{}\boxed{\int A=B}\raisebox{-6.5mm}{}$
13013 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
13016 \begin_layout Plain Layout
13023 \begin_layout Plain Layout
13037 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
13040 \begin_layout Plain Layout
13041 \begin_inset Formula $\raisebox{6mm}{}A+\fbox{B}\raisebox{-3mm}{}$
13051 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
13054 \begin_layout Plain Layout
13061 \begin_layout Plain Layout
13071 \begin_inset Formula $\to$
13075 \begin_inset Formula $\to$
13088 \begin_layout Plain Layout
13098 \begin_inset Formula $\downarrow$
13106 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
13109 \begin_layout Plain Layout
13110 \begin_inset Formula $\raisebox{6mm}{}$
13114 \begin_inset Formula $\framebox[20mm][]{\ensuremath{\frac{A}{B}}}$
13118 \begin_inset Formula $\raisebox{-4mm}{}$
13134 \begin_layout Standard
13135 The frame thickness can also be adjusted.
13136 To do this the following commands have to be inserted in TeX-mode before
13140 \begin_layout Standard
13150 \begin_inset Quotes eld
13154 \begin_inset Quotes erd
13168 \begin_inset Quotes eld
13172 \begin_inset Quotes erd
13178 \begin_layout Standard
13179 \begin_inset Quotes eld
13183 \begin_inset Quotes erd
13186 specifies the minimal distance between the frame and the first character
13188 An example for this is the following framed formula:
13192 \begin_layout Plain Layout
13204 \begin_inset Formula
13211 Before this formula the commands
13214 \begin_layout Standard
13236 \begin_layout Standard
13237 were inserted in TeX-mode.
13238 The given values are used for all following boxes.
13241 \begin_layout Standard
13242 To return to the standard frame size, the command
13245 \begin_layout Standard
13270 \begin_layout Plain Layout
13284 \begin_layout Standard
13285 is inserted in TeX-mode before the next formula.
13288 \begin_layout Subsection
13289 Boxes without Frame
13290 \begin_inset CommandInset label
13292 name "sub:Boxes-without-Frame"
13297 \begin_inset Index idx
13300 \begin_layout Plain Layout
13301 Boxes ! without frame
13309 \begin_layout Standard
13310 For boxes without a frame there are the following box commands:
13317 \begin_inset Index idx
13320 \begin_layout Plain Layout
13335 \begin_inset Index idx
13338 \begin_layout Plain Layout
13353 \begin_inset Index idx
13356 \begin_layout Plain Layout
13367 \begin_layout Standard
13374 a box can be super- or subscripted.
13375 But in contrary to normal super- and subscripting, the characters in the
13376 box keep their font size.
13383 is used in the following scheme:
13386 \begin_layout Standard
13391 raisebox{height}{box content}
13394 \begin_layout Standard
13395 When the box should contain a formula, an extra formula is needed like for
13406 \begin_inset Note Greyedout
13409 \begin_layout Plain Layout
13420 this extra formula is created by pressing
13424 twice instead of once because LyX doesn't yet support
13438 \begin_layout Standard
13440 \begin_inset Tabular
13441 <lyxtabular version="3" rows="4" columns="2">
13442 <features tabularvalignment="middle">
13443 <column alignment="center" valignment="top" width="0">
13444 <column alignment="center" valignment="top" width="0">
13446 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
13449 \begin_layout Plain Layout
13455 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
13458 \begin_layout Plain Layout
13466 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
13469 \begin_layout Plain Layout
13473 \begin_inset Formula $\to$
13479 \begin_inset Formula $\to$
13487 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
13490 \begin_layout Plain Layout
13491 \begin_inset Formula $H\raisebox{2mm}{al}lo$
13501 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
13504 \begin_layout Plain Layout
13508 \begin_inset Formula $\to$
13514 \begin_inset Formula $\to$
13522 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
13525 \begin_layout Plain Layout
13526 \begin_inset Formula $H\raisebox{-2mm}{al}lo$
13536 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
13539 \begin_layout Plain Layout
13543 \begin_inset Formula $\to$
13562 \begin_layout Plain Layout
13576 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
13579 \begin_layout Plain Layout
13580 \begin_inset Formula $A=\raisebox{-2mm}{\mbox{\ensuremath{\sqrt{B}}}}$
13596 \begin_layout Standard
13621 , with the difference that there is no frame.
13624 \begin_layout Subsection
13626 \begin_inset CommandInset label
13628 name "sub:Colored-Boxes"
13633 \begin_inset Index idx
13636 \begin_layout Plain Layout
13645 \begin_layout Standard
13646 To be able to use all commands explained in this section, the LaTeX-package
13655 \begin_layout Plain Layout
13660 is part of every LaTeX standard installation.
13666 \begin_inset Index idx
13669 \begin_layout Plain Layout
13675 has to be loaded in the LaTeX-preamble with the line
13679 \begin_layout Plain Layout
13680 When text is colored somewhere in the document with a predefined color,
13681 LyX loads the LaTeX-package
13686 Thus it is possible that the package is loaded twice, but this doesn't
13693 \begin_inset Note Note
13696 \begin_layout Plain Layout
13697 To avoid that the package is loaded twice, a macro was inserted to the LaTeX-pre
13706 \begin_layout Standard
13714 \begin_layout Standard
13715 \begin_inset VSpace medskip
13718 To color boxes, the command
13725 \begin_inset Index idx
13728 \begin_layout Plain Layout
13736 is used in the following scheme:
13739 \begin_layout Standard
13744 colorbox{color}{box content}
13747 \begin_layout Standard
13748 The box content can also be a box and a
13754 can also be part of another box (see the 2nd and 3rd example).
13755 When the box should contain a formula, an extra formula has to be created,
13756 the same way as for
13766 \begin_layout Plain Layout
13767 This also applies for the command
13781 \begin_layout Standard
13782 One of the following predefined colors can be chosen:
13785 \begin_layout Standard
13819 \begin_layout Standard
13821 \begin_inset Tabular
13822 <lyxtabular version="3" rows="4" columns="2">
13823 <features tabularvalignment="middle">
13824 <column alignment="center" valignment="top" width="0">
13825 <column alignment="center" valignment="top" width="0">
13827 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
13830 \begin_layout Plain Layout
13836 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
13839 \begin_layout Plain Layout
13841 \begin_inset Note Note
13844 \begin_layout Plain Layout
13851 is only used as spacer.
13863 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
13866 \begin_layout Plain Layout
13870 \begin_inset Formula $\to$
13880 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
13883 \begin_layout Plain Layout
13884 \begin_inset Formula $\raisebox{6mm}{}\colorbox{yellow}{A=B}\raisebox{-3mm}{}$
13894 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
13897 \begin_layout Plain Layout
13901 \begin_inset Formula $\to$
13912 \begin_layout Plain Layout
13926 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
13929 \begin_layout Plain Layout
13930 \begin_inset Formula $\raisebox{6mm}{}\colorbox{green}{\fbox{A=B}}\raisebox{-3mm}{}$
13940 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
13943 \begin_layout Plain Layout
13950 \begin_layout Plain Layout
13962 \begin_inset Formula $\to$
13981 \begin_layout Plain Layout
13995 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
13998 \begin_layout Plain Layout
13999 \begin_inset Formula $\raisebox{7mm}{}\fbox{\colorbox{green}{\mbox{\ensuremath{\int C=D}}}}\raisebox{-5mm}{}$
14015 \begin_layout Standard
14022 only colors the box but not the characters in the box.
14023 To color all characters, the whole formula is highlighted and the wanted
14024 color is chosen in the
14027 \begin_inset space ~
14033 The dialog can be called with the toolbar button
14034 \begin_inset Graphics
14035 filename ../images/dialog-show_character.png
14042 Edit\SpecialChar \menuseparator
14044 \begin_inset space ~
14047 Style\SpecialChar \menuseparator
14051 The formula number has then the same color as the formula.
14052 When the formula number should get another color than the formula characters,
14053 the color must be changed within the formula.
14056 \begin_layout Standard
14060 \begin_layout Standard
14063 \begin_inset Formula
14065 \int A=B\label{eq:red}
14073 \begin_inset Formula
14075 \textcolor{red}{\int A=B}\label{eq:redgreen}
14083 \begin_layout Standard
14085 \begin_inset CommandInset ref
14091 is completely colored red.
14092 \begin_inset Newline newline
14096 \begin_inset CommandInset ref
14098 reference "eq:redgreen"
14102 was first completely colored green to set the color for the formula number.
14103 Subsequently the formula characters were colored red.
14106 \begin_layout Standard
14107 \begin_inset VSpace bigskip
14110 To color the frame different than the rest of the box, the command
14117 \begin_inset Index idx
14120 \begin_layout Plain Layout
14128 is used in the following scheme:
14131 \begin_layout Standard
14136 fcolorbox{frame color}{color}{box content}
14139 \begin_layout Standard
14146 is an extension of the command
14153 The frame width is set, like for
14176 \begin_layout Plain Layout
14188 \begin_inset Formula
14190 \fcolorbox{cyan}{magenta}{A=B}
14199 \begin_layout Plain Layout
14213 \begin_layout Standard
14214 This formula was created with the command
14215 \begin_inset Newline newline
14223 \begin_inset Formula $\to$
14229 \begin_inset Formula $\to$
14239 \begin_layout Standard
14240 \begin_inset VSpace bigskip
14243 To use other colors than the predefined ones, they have to be defined first.
14246 \begin_layout Standard
14247 One can for example define the color
14248 \begin_inset Quotes eld
14256 \begin_inset Quotes erd
14259 with the LaTeX-preamble line:
14262 \begin_layout Standard
14267 definecolor{darkgreen}{cmyk}{0.5,
14282 \begin_inset Index idx
14285 \begin_layout Plain Layout
14296 \begin_layout Standard
14301 is the color space that denotes the colors
14318 The four comma separated numbers are the portion factor for the corresponding
14319 colors of the color space.
14320 The factors can be in the range of 0
14321 \begin_inset space \thinspace{}
14325 \begin_inset space \thinspace{}
14333 also the color space
14337 can be used for definitions.
14354 , so that there are in this case three portion factors for the corresponding
14356 Furthermore there is the color space
14360 with one portion factor for the gray value.
14363 \begin_layout Standard
14364 As example a framed box with the new defined color
14368 where the characters have been colored
14373 \begin_inset Formula
14375 \colorbox{darkgreen}{\color{yellow}\boxed{\int A\,\mathrm{d}x=\frac{\sqrt[5]{B}}{\ln\left(\frac{1}{3}\right)}}}
14383 \begin_layout Standard
14384 Self-defined colors can also be used for text with the help of the command
14392 \begin_inset Index idx
14395 \begin_layout Plain Layout
14404 \begin_layout Standard
14408 \begin_layout Plain Layout
14412 textcolor{darkgreen}{
14418 \begin_inset Quotes eld
14422 \begin_inset Quotes erd
14429 \begin_layout Plain Layout
14439 \begin_layout Standard
14447 \begin_inset Index idx
14450 \begin_layout Plain Layout
14458 is used in the scheme
14462 textcolor{color}{characters to color}
14467 \begin_layout Subsection
14469 \begin_inset CommandInset label
14471 name "sub:Paragraph-Boxes"
14476 \begin_inset Index idx
14479 \begin_layout Plain Layout
14480 Boxes ! as paragraph
14488 \begin_layout Standard
14489 A box that can contain several lines and paragraphs, a so called paragraph
14490 box (parbox), can be created with the menu
14492 Insert\SpecialChar \menuseparator
14495 or the toolbar button
14496 \begin_inset Graphics
14497 filename ../images/box-insert.png
14505 \begin_layout Standard
14506 The following example shows a framed parbox in a line:
14509 \begin_layout Standard
14510 \begin_inset VSpace medskip
14514 \begin_inset Box Boxed
14524 height_special "totalheight"
14527 \begin_layout Plain Layout
14528 This is a paragraph box.
14530 \begin_inset space \thinspace{}
14533 cm long and can also contain formulas:
14534 \begin_inset Formula $\int A\,\mathrm{d}s=C$
14545 \begin_layout Standard
14546 \begin_inset VSpace medskip
14552 \begin_layout Standard
14553 Such a box is created by right-clicking on the gray box inset.
14554 A dialog pops up showing the box properties.
14568 \begin_inset space \thinspace{}
14573 Vertical Box Alignment
14578 \begin_layout Standard
14579 \begin_inset VSpace medskip
14582 In LaTeX a parbox is created with the command
14589 \begin_inset Index idx
14592 \begin_layout Plain Layout
14600 that has the following scheme:
14603 \begin_layout Standard
14608 parbox[position]{width}{box content}
14611 \begin_layout Standard
14625 for bottom means that the box is aligned within the surrounding text with
14631 for top this is done with the first line.
14632 When no position is given, the box will be vertically centered, see section
14640 \begin_inset space ~
14645 manual for examples.
14648 \begin_layout Standard
14649 \begin_inset VSpace bigskip
14652 To frame formulas completely, including the formula number, the formula
14653 must be set into a parbox.
14654 To do this, the command
14668 is inserted in TeX-mode before the formula.
14676 \begin_inset Index idx
14679 \begin_layout Plain Layout
14687 is hereby the line width set for the document.
14688 Because the frame is outside the parbox, 2
14689 \begin_inset space \thinspace{}
14692 times the frame separation and the frame thickness must be subtracted from
14694 As this is not automatically done by LyX due to a bug
14698 \begin_layout Plain Layout
14699 \begin_inset CommandInset href
14701 name "LyX-bug #4483"
14702 target "http://www.lyx.org/trac/ticket/4483"
14711 , TeX-mode has to be used.
14712 To be able to multiply and subtract in arguments, the LaTeX-package
14720 \begin_layout Plain Layout
14725 is part of every LaTeX standard installation.
14731 \begin_inset Index idx
14734 \begin_layout Plain Layout
14740 must be loaded in the LaTeX-preamble with the line
14743 \begin_layout Standard
14751 \begin_layout Standard
14752 Behind the formula both boxes are closed by entering
14757 Here is an example:
14761 \begin_layout Plain Layout
14775 \begin_layout Standard
14779 \begin_layout Plain Layout
14797 \begin_inset Formula
14799 \int A\,\mathrm{d}x=\frac{\sqrt[5]{B}}{\ln\left(\frac{1}{3}\right)}
14808 \begin_layout Plain Layout
14819 \begin_layout Plain Layout
14833 \begin_layout Standard
14834 \begin_inset VSpace medskip
14837 As a parbox is used as argument of
14843 , there is in this case no difference between
14858 \begin_layout Standard
14859 \begin_inset VSpace bigskip
14862 Paragraph boxes are very useful to comment formulas directly.
14869 is used in combination with the command
14883 \begin_inset CommandInset ref
14885 reference "sub:User-defined-Numbering"
14892 \begin_layout Standard
14893 An example of a formula commented with
14902 \begin_layout Standard
14906 \begin_layout Plain Layout
14919 This is a description.
14920 It is distinctly separated from the formula and multiline.
14924 \begin_layout Plain Layout
14936 \begin_layout Standard
14937 Such a formula must be inserted completely in TeX-mode because LyX does
14938 not yet support the command
14945 The formula is created with the following command sequence:
14948 \begin_layout Standard
14961 is inserted in TeX-mode.
14965 \begin_layout Plain Layout
14966 When the formula style
14978 can also be replaced by
14985 (formula styles see
14986 \begin_inset CommandInset ref
14988 reference "sec:Formula-Styles"
14997 Then the description follows as normal text and finally
15003 is inserted in TeX-mode.
15016 hereby create a displayed formula.
15019 \begin_layout Standard
15026 can be seen in this example that was
15027 \begin_inset Quotes eld
15031 \begin_inset Quotes erd
15034 using the mathematical textmode:
15035 \begin_inset Formula
15037 5x-7b=3b\textrm{This is a description. It is not separated from the formula ...}
15045 \begin_layout Section
15047 \begin_inset Index idx
15050 \begin_layout Plain Layout
15059 \begin_layout Subsection
15061 \begin_inset CommandInset label
15063 name "sub:Big-Operators"
15068 \begin_inset Index idx
15071 \begin_layout Plain Layout
15078 \begin_inset Index idx
15081 \begin_layout Plain Layout
15088 \begin_inset Index idx
15091 \begin_layout Plain Layout
15100 \begin_layout Standard
15101 To be able to use all integral operators listed here, the option
15103 Use esint package automatically
15105 must be set in the document settings under
15108 \begin_inset space ~
15116 \begin_layout Standard
15117 \begin_inset space \hfill{}
15121 \begin_inset Tabular
15122 <lyxtabular version="3" rows="11" columns="2">
15123 <features tabularvalignment="middle">
15124 <column alignment="center" valignment="top" width="0pt">
15125 <column alignment="center" valignment="top" width="0pt">
15127 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
15130 \begin_layout Plain Layout
15136 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
15139 \begin_layout Plain Layout
15147 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
15150 \begin_layout Plain Layout
15154 \begin_inset Index idx
15157 \begin_layout Plain Layout
15170 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
15173 \begin_layout Plain Layout
15174 \begin_inset Formula $\int$
15184 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
15187 \begin_layout Plain Layout
15195 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
15198 \begin_layout Plain Layout
15199 \begin_inset Formula $\oint$
15209 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
15212 \begin_layout Plain Layout
15220 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
15223 \begin_layout Plain Layout
15224 \begin_inset Formula $\ointctrclockwise$
15234 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
15237 \begin_layout Plain Layout
15245 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
15248 \begin_layout Plain Layout
15249 \begin_inset Formula $\ointclockwise$
15259 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
15262 \begin_layout Plain Layout
15270 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
15273 \begin_layout Plain Layout
15274 \begin_inset Formula $\sqint$
15284 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
15287 \begin_layout Plain Layout
15295 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
15298 \begin_layout Plain Layout
15300 \begin_inset Formula $\fint$
15310 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
15313 \begin_layout Plain Layout
15321 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
15324 \begin_layout Plain Layout
15326 \begin_inset Formula $\landupint$
15336 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
15339 \begin_layout Plain Layout
15347 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
15350 \begin_layout Plain Layout
15352 \begin_inset Formula $\landdownint$
15362 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
15365 \begin_layout Plain Layout
15373 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
15376 \begin_layout Plain Layout
15377 \begin_inset Formula $\bigcap$
15387 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
15390 \begin_layout Plain Layout
15398 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
15401 \begin_layout Plain Layout
15402 \begin_inset Formula $\bigcup$
15416 \begin_inset space \hfill{}
15420 \begin_inset Tabular
15421 <lyxtabular version="3" rows="11" columns="2">
15422 <features tabularvalignment="middle">
15423 <column alignment="center" valignment="top" width="0pt">
15424 <column alignment="center" valignment="top" width="0pt">
15426 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
15429 \begin_layout Plain Layout
15435 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
15438 \begin_layout Plain Layout
15446 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
15449 \begin_layout Plain Layout
15453 \begin_inset Index idx
15456 \begin_layout Plain Layout
15469 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
15472 \begin_layout Plain Layout
15473 \begin_inset Formula $\sum$
15483 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
15486 \begin_layout Plain Layout
15490 \begin_inset Index idx
15493 \begin_layout Plain Layout
15506 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
15509 \begin_layout Plain Layout
15510 \begin_inset Formula $\prod$
15520 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
15523 \begin_layout Plain Layout
15531 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
15534 \begin_layout Plain Layout
15535 \begin_inset Formula $\coprod$
15545 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
15548 \begin_layout Plain Layout
15556 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
15559 \begin_layout Plain Layout
15560 \begin_inset Formula $\bigodot$
15570 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
15573 \begin_layout Plain Layout
15581 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
15584 \begin_layout Plain Layout
15585 \begin_inset Formula $\bigotimes$
15595 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
15598 \begin_layout Plain Layout
15606 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
15609 \begin_layout Plain Layout
15610 \begin_inset Formula $\bigoplus$
15620 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
15623 \begin_layout Plain Layout
15631 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
15634 \begin_layout Plain Layout
15635 \begin_inset Formula $\bigwedge$
15645 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
15648 \begin_layout Plain Layout
15656 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
15659 \begin_layout Plain Layout
15660 \begin_inset Formula $\bigvee$
15670 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
15673 \begin_layout Plain Layout
15681 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
15684 \begin_layout Plain Layout
15685 \begin_inset Formula $\bigsqcup$
15695 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
15698 \begin_layout Plain Layout
15706 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
15709 \begin_layout Plain Layout
15710 \begin_inset Formula $\biguplus$
15724 \begin_inset space \hfill{}
15730 \begin_layout Standard
15731 All big operators can also be inserted via the math toolbar button
15732 \begin_inset Graphics
15733 filename ../images/math/intop.png
15741 \begin_layout Standard
15742 The operators are called big because they are bigger than the sometimes
15743 equal looking binary operators.
15744 All big operators can have limits as described in the next subsection.
15747 \begin_layout Standard
15748 For all integral operators there is a second version available, ending on
15766 These operators are different from
15773 \begin_inset space \space{}
15776 in the style the operator limits are displayed, see
15777 \begin_inset CommandInset ref
15779 reference "sub:Operator-Limits"
15787 \begin_layout Subsubsection*
15788 Advice for Integrals
15791 \begin_layout Standard
15796 in an integral is an operator, that therefore has to be set upright.
15797 This is done by highlighting the
15801 and using the keyboard shortcut
15811 \begin_layout Plain Layout
15817 \begin_inset CommandInset ref
15819 reference "sub:Font-Styles"
15829 Finally the smallest space is inserted before the
15833 , as this is usual for operators.
15837 \begin_layout Standard
15839 \begin_inset Formula $\int A(x)dx$
15843 \begin_inset Newline newline
15847 \begin_inset Phantom HPhantom
15850 \begin_layout Plain Layout
15857 \begin_inset Formula $\int A(x)\,\mathrm{d}x$
15863 \begin_layout Standard
15864 For multiple integrals there are the following commands:
15865 \begin_inset VSpace medskip
15871 \begin_layout Standard
15872 \begin_inset space \hfill{}
15876 \begin_inset Tabular
15877 <lyxtabular version="3" rows="4" columns="2">
15878 <features tabularvalignment="middle">
15879 <column alignment="center" valignment="top" width="0">
15880 <column alignment="center" valignment="top" width="0">
15882 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
15885 \begin_layout Plain Layout
15891 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
15894 \begin_layout Plain Layout
15896 \begin_inset Note Note
15899 \begin_layout Plain Layout
15906 is only used as spacer.
15918 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
15921 \begin_layout Plain Layout
15929 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
15932 \begin_layout Plain Layout
15933 \begin_inset Formula $\raisebox{4.5mm}{}\iint\raisebox{-2.5mm}{}$
15943 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
15946 \begin_layout Plain Layout
15954 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
15957 \begin_layout Plain Layout
15958 \begin_inset Formula $\raisebox{4.5mm}{}\oiint\raisebox{-2.5mm}{}$
15968 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
15971 \begin_layout Plain Layout
15979 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
15982 \begin_layout Plain Layout
15983 \begin_inset Formula $\raisebox{4.5mm}{}\sqiint\raisebox{-2.5mm}{}$
15997 \begin_inset space \hfill{}
16001 \begin_inset Tabular
16002 <lyxtabular version="3" rows="4" columns="2">
16003 <features tabularvalignment="middle">
16004 <column alignment="center" valignment="top" width="0">
16005 <column alignment="center" valignment="top" width="0">
16007 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
16010 \begin_layout Plain Layout
16016 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
16019 \begin_layout Plain Layout
16027 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
16030 \begin_layout Plain Layout
16038 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
16041 \begin_layout Plain Layout
16042 \begin_inset Formula $\raisebox{4.5mm}{}\iiint\raisebox{-2.5mm}{}$
16052 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
16055 \begin_layout Plain Layout
16063 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
16066 \begin_layout Plain Layout
16067 \begin_inset Formula $\raisebox{4.5mm}{}\iiiint\raisebox{-2.5mm}{}$
16077 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
16080 \begin_layout Plain Layout
16088 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
16091 \begin_layout Plain Layout
16092 \begin_inset Formula $\raisebox{4.5mm}{}\dotsint\raisebox{-2.5mm}{}$
16106 \begin_inset space \hfill{}
16112 \begin_layout Subsection
16114 \begin_inset CommandInset label
16116 name "sub:Operator-Limits"
16121 \begin_inset Index idx
16124 \begin_layout Plain Layout
16133 \begin_layout Standard
16134 Limits are created by super- and subscripts:
16137 \begin_layout Standard
16139 \begin_inset Tabular
16140 <lyxtabular version="3" rows="2" columns="2">
16141 <features tabularvalignment="middle">
16142 <column alignment="center" valignment="top" width="0pt">
16143 <column alignment="center" valignment="top" width="0pt">
16145 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
16148 \begin_layout Plain Layout
16154 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
16157 \begin_layout Plain Layout
16159 \begin_inset Note Note
16162 \begin_layout Plain Layout
16169 is only used as spacer.
16181 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
16184 \begin_layout Plain Layout
16193 \begin_layout Plain Layout
16203 \begin_inset Formula $\to$
16207 \begin_inset Formula $\to$
16215 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
16218 \begin_layout Plain Layout
16219 \begin_inset Formula $\raisebox{5mm}{}\prod_{0}^{\infty}A(x)\raisebox{-2.5mm}{}$
16235 \begin_layout Standard
16236 Limits of inline formulas are set right beside the operator.
16237 Limits in displayed formulas are set above or below the operator, except
16238 for integral limits.
16241 \begin_layout Standard
16242 To force that the limits are set beside the operator, the cursor is set
16243 directly behind the operator and the limits type is changed with the menu
16246 Edit\SpecialChar \menuseparator
16247 Math\SpecialChar \menuseparator
16266 \begin_layout Standard
16267 The default limits type is this:
16268 \begin_inset Formula
16270 \sum_{x=0}^{\infty}\frac{1}{x^{2}}
16275 This is how it looks when the limits type was changed to
16282 \begin_inset Formula
16284 \sum\nolimits _{x=0}^{\infty}\frac{1}{x^{2}}
16289 For integrals, except those ending with
16305 etc., the limits are by default set beside the operator.
16306 But for multiple integrals the limits are often set below the operator.
16307 In the following example the limits type was therefore set to
16311 and so set below the integrals:
16312 \begin_inset Formula
16314 \iiint\limits _{V}X\,\mathrm{d}V=U\label{eq:VolInt}
16322 \begin_layout Standard
16323 \begin_inset VSpace medskip
16326 To specify conditions for limits, the commands
16333 \begin_inset Index idx
16336 \begin_layout Plain Layout
16351 \begin_inset Index idx
16354 \begin_layout Plain Layout
16363 To create for example this expression
16364 \begin_inset Formula
16366 \sum_{\begin{subarray}{c}
16370 \end{subarray}}^{n}k^{-2}\label{eq:substack}
16378 \begin_layout Standard
16379 the following has to be done:
16380 \begin_inset Newline newline
16395 \begin_layout Plain Layout
16407 One is now in a blue box under the summation operator and insert there
16416 \begin_layout Plain Layout
16428 The blue box is now within a purple box and now several lines can be written
16430 A new line is created by inserting a line break (
16433 arg "newline-insert newline"
16438 \begin_inset Newline newline
16443 0<k<1000 Ctrl+Return
16444 \begin_inset Newline newline
16449 is typed in, a new box appears below for the new line.
16452 \begin_layout Standard
16453 The alignment of the lines can be changed to left aligned with the
16463 Edit\SpecialChar \menuseparator
16467 To get right alignment,
16475 \begin_layout Plain Layout
16486 is inserted at the beginning of the line.
16489 \begin_layout Standard
16502 with the difference that the lines are always centered.
16505 \begin_layout Standard
16506 \begin_inset VSpace bigskip
16510 \begin_inset CommandInset ref
16512 reference "eq:substack"
16516 there can be too much space beside an operator, because the characters
16517 following the operator are set beside the limits.
16520 \begin_layout Standard
16521 To avoid this, the following macro can be used in the LaTeX-preamble:
16524 \begin_layout Standard
16538 \begin_inset Newline newline
16550 \begin_inset Newline newline
16557 mathclapinternal #1#2{
16561 mathsurround =0pt #1{#2}$}}
16564 \begin_layout Standard
16565 This defines the command
16572 \begin_inset Index idx
16575 \begin_layout Plain Layout
16583 that sets the width of the limit to 0
16584 \begin_inset space \thinspace{}
16588 The command scheme is
16591 \begin_layout Standard
16599 \begin_layout Standard
16600 where the limit can consist of several conditions.
16603 \begin_layout Standard
16605 \begin_inset CommandInset ref
16607 reference "eq:substack"
16611 , one uses the command
16614 \begin_layout Standard
16627 \begin_layout Plain Layout
16636 0<k<1000 Ctrl+Return
16639 \begin_layout Standard
16640 to create the lower limit.
16641 The summand is now directly behind the summation operator:
16642 \begin_inset Formula
16644 \sum_{\mathclap{\substack{0<k<1000\\
16656 \begin_layout Standard
16657 \begin_inset VSpace bigskip
16660 How to use one limit for several operators is described in
16661 \begin_inset CommandInset ref
16663 reference "sub:Self-defined-Operators"
16670 \begin_layout Standard
16671 \begin_inset Newpage newpage
16677 \begin_layout Subsection
16679 \begin_inset CommandInset label
16681 name "sub:Binary-Operators"
16686 \begin_inset Index idx
16689 \begin_layout Plain Layout
16698 \begin_layout Standard
16699 Binary operators are surrounded by space when there is a character before
16701 \begin_inset VSpace medskip
16707 \begin_layout Standard
16708 \begin_inset space \hfill{}
16712 \begin_inset Tabular
16713 <lyxtabular version="3" rows="13" columns="2">
16714 <features tabularvalignment="middle">
16715 <column alignment="center" valignment="top" width="0pt">
16716 <column alignment="center" valignment="top" width="0pt">
16718 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
16721 \begin_layout Plain Layout
16723 \begin_inset Note Note
16726 \begin_layout Plain Layout
16733 is only used as spacer.
16743 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
16746 \begin_layout Plain Layout
16754 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
16757 \begin_layout Plain Layout
16763 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
16766 \begin_layout Plain Layout
16767 \begin_inset Formula $+$
16777 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
16780 \begin_layout Plain Layout
16786 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
16789 \begin_layout Plain Layout
16790 \begin_inset Formula $-$
16800 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
16803 \begin_layout Plain Layout
16811 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
16814 \begin_layout Plain Layout
16815 \begin_inset Formula $\pm$
16825 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
16828 \begin_layout Plain Layout
16836 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
16839 \begin_layout Plain Layout
16840 \begin_inset Formula $\mp$
16850 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
16853 \begin_layout Plain Layout
16861 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
16864 \begin_layout Plain Layout
16865 \begin_inset Formula $\cdot$
16875 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
16878 \begin_layout Plain Layout
16886 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
16889 \begin_layout Plain Layout
16890 \begin_inset Formula $\times$
16900 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
16903 \begin_layout Plain Layout
16911 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
16914 \begin_layout Plain Layout
16915 \begin_inset Formula $\div$
16925 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
16928 \begin_layout Plain Layout
16932 \begin_layout Plain Layout
16945 \begin_layout Plain Layout
16957 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
16960 \begin_layout Plain Layout
16961 \begin_inset Formula $*$
16971 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
16974 \begin_layout Plain Layout
16982 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
16985 \begin_layout Plain Layout
16986 \begin_inset Formula $\star$
16996 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
16999 \begin_layout Plain Layout
17007 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
17010 \begin_layout Plain Layout
17011 \begin_inset Formula $\circ$
17021 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
17024 \begin_layout Plain Layout
17032 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
17035 \begin_layout Plain Layout
17036 \begin_inset Formula $\diamond$
17046 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
17049 \begin_layout Plain Layout
17057 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
17060 \begin_layout Plain Layout
17061 \begin_inset Formula $\bullet$
17075 \begin_inset space \hfill{}
17079 \begin_inset Tabular
17080 <lyxtabular version="3" rows="13" columns="2">
17081 <features tabularvalignment="middle">
17082 <column alignment="center" valignment="top" width="0pt">
17083 <column alignment="center" valignment="top" width="0pt">
17085 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
17088 \begin_layout Plain Layout
17094 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
17097 \begin_layout Plain Layout
17105 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
17108 \begin_layout Plain Layout
17116 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
17119 \begin_layout Plain Layout
17120 \begin_inset Formula $\nabla$
17130 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
17133 \begin_layout Plain Layout
17141 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
17144 \begin_layout Plain Layout
17145 \begin_inset Formula $\bigtriangledown$
17155 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
17158 \begin_layout Plain Layout
17166 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
17169 \begin_layout Plain Layout
17170 \begin_inset Formula $\bigtriangleup$
17180 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
17183 \begin_layout Plain Layout
17191 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
17194 \begin_layout Plain Layout
17195 \begin_inset Formula $\Box$
17205 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
17208 \begin_layout Plain Layout
17216 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
17219 \begin_layout Plain Layout
17220 \begin_inset Formula $\cap$
17230 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
17233 \begin_layout Plain Layout
17241 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
17244 \begin_layout Plain Layout
17245 \begin_inset Formula $\cup$
17255 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
17258 \begin_layout Plain Layout
17266 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
17269 \begin_layout Plain Layout
17270 \begin_inset Formula $\dagger$
17280 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
17283 \begin_layout Plain Layout
17291 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
17294 \begin_layout Plain Layout
17295 \begin_inset Formula $\ddagger$
17305 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
17308 \begin_layout Plain Layout
17316 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
17319 \begin_layout Plain Layout
17320 \begin_inset Formula $\wr$
17330 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
17333 \begin_layout Plain Layout
17341 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
17344 \begin_layout Plain Layout
17345 \begin_inset Formula $\bigcirc$
17355 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
17358 \begin_layout Plain Layout
17366 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
17369 \begin_layout Plain Layout
17370 \begin_inset Formula $\wedge$
17380 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
17383 \begin_layout Plain Layout
17391 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
17394 \begin_layout Plain Layout
17395 \begin_inset Formula $\vee$
17409 \begin_inset space \hfill{}
17413 \begin_inset Tabular
17414 <lyxtabular version="3" rows="13" columns="2">
17415 <features tabularvalignment="middle">
17416 <column alignment="center" valignment="top" width="0pt">
17417 <column alignment="center" valignment="top" width="0pt">
17419 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
17422 \begin_layout Plain Layout
17428 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
17431 \begin_layout Plain Layout
17439 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
17442 \begin_layout Plain Layout
17450 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
17453 \begin_layout Plain Layout
17454 \begin_inset Formula $\oplus$
17464 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
17467 \begin_layout Plain Layout
17475 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
17478 \begin_layout Plain Layout
17479 \begin_inset Formula $\ominus$
17489 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
17492 \begin_layout Plain Layout
17500 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
17503 \begin_layout Plain Layout
17504 \begin_inset Formula $\otimes$
17514 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
17517 \begin_layout Plain Layout
17525 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
17528 \begin_layout Plain Layout
17529 \begin_inset Formula $\oslash$
17539 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
17542 \begin_layout Plain Layout
17550 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
17553 \begin_layout Plain Layout
17554 \begin_inset Formula $\odot$
17564 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
17567 \begin_layout Plain Layout
17575 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
17578 \begin_layout Plain Layout
17579 \begin_inset Formula $\amalg$
17589 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
17592 \begin_layout Plain Layout
17600 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
17603 \begin_layout Plain Layout
17604 \begin_inset Formula $\uplus$
17614 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
17617 \begin_layout Plain Layout
17625 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
17628 \begin_layout Plain Layout
17629 \begin_inset Formula $\setminus$
17639 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
17642 \begin_layout Plain Layout
17650 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
17653 \begin_layout Plain Layout
17654 \begin_inset Formula $\sqcap$
17664 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
17667 \begin_layout Plain Layout
17675 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
17678 \begin_layout Plain Layout
17679 \begin_inset Formula $\sqcup$
17689 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
17692 \begin_layout Plain Layout
17700 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
17703 \begin_layout Plain Layout
17704 \begin_inset Formula $\triangleleft$
17714 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
17717 \begin_layout Plain Layout
17725 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
17728 \begin_layout Plain Layout
17729 \begin_inset Formula $\triangleright$
17743 \begin_inset space \hfill{}
17749 \begin_layout Standard
17750 All binary operators can also be inserted via the math toolbar button
17751 \begin_inset Graphics
17752 filename ../images/math/pm.png
17760 \begin_layout Standard
17761 To typeset the Laplace operator also
17778 \begin_inset Formula $\nabla^{2}$
17781 ) can be used instead of
17790 \begin_layout Standard
17797 Insert\SpecialChar \menuseparator
17809 \begin_layout Subsection
17810 Self-defined Operators
17811 \begin_inset CommandInset label
17813 name "sub:Self-defined-Operators"
17818 \begin_inset Index idx
17821 \begin_layout Plain Layout
17822 Operators ! self-defined
17830 \begin_layout Standard
17831 With the help of the command
17835 DeclareMathOperator
17838 \begin_inset Index idx
17841 \begin_layout Plain Layout
17846 DeclareMathOperator
17851 custom operators can be defined in the LaTeX-preamble.
17852 Its command scheme is:
17855 \begin_layout Standard
17860 DeclareMathOperator{new command}{display}
17863 \begin_layout Standard
17864 Display can be characters or symbols that define how the operator looks
17866 To define a big operator a * is set behind the command.
17867 All self-defined big operators can have limits as described in
17868 \begin_inset CommandInset ref
17870 reference "sub:Operator-Limits"
17877 \begin_layout Standard
17878 For example the LaTeX-preamble line
17881 \begin_layout Standard
17886 DeclareMathOperator*{
17893 \begin_layout Standard
17894 defines the command
17900 , that inserts a big operator consisting of the lozenge symbol from
17901 \begin_inset CommandInset ref
17903 reference "sub:Miscellaneous-Symbols"
17908 \begin_inset Formula
17910 \Lozenge_{n=1}^{\infty}
17915 The command for this formula is:
17926 \begin_inset Formula $\to$
17932 \begin_layout Standard
17933 \begin_inset VSpace bigskip
17936 When self-defined operators are not used several times in the document,
17937 they can also be defined with the commands
17944 \begin_inset Index idx
17947 \begin_layout Plain Layout
17962 \begin_inset Index idx
17965 \begin_layout Plain Layout
17973 , which have the following scheme:
17976 \begin_layout Standard
17990 \begin_layout Standard
17997 defines big operators,
18006 \begin_layout Standard
18014 \begin_inset space \thinspace{}
18018 \begin_inset space \space{}
18021 be used to use one limit for several operators:
18024 \begin_layout Standard
18025 \begin_inset Formula
18027 \mathop{\sum\negmedspace\sum}_{i,j=1}^{N}
18035 \begin_layout Standard
18036 The command for the formula above is:
18037 \begin_inset Newline newline
18056 \begin_layout Plain Layout
18068 \begin_inset Formula $\to$
18077 \begin_layout Plain Layout
18091 \begin_layout Section
18093 \begin_inset Index idx
18096 \begin_layout Plain Layout
18105 \begin_layout Subsection
18107 \begin_inset CommandInset label
18109 name "sub:Font-Styles"
18114 \begin_inset Index idx
18117 \begin_layout Plain Layout
18126 \begin_layout Standard
18127 Latin letters in formulas can be set in one of the following font styles:
18128 \begin_inset VSpace -2mm
18134 \begin_layout Standard
18136 \begin_inset Tabular
18137 <lyxtabular version="3" rows="7" columns="3">
18138 <features tabularvalignment="middle">
18139 <column alignment="center" valignment="top" width="0">
18140 <column alignment="center" valignment="top" width="0">
18141 <column alignment="center" valignment="top" width="0">
18143 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
18146 \begin_layout Plain Layout
18152 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
18155 \begin_layout Plain Layout
18161 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
18164 \begin_layout Plain Layout
18172 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
18175 \begin_layout Plain Layout
18184 \begin_layout Plain Layout
18200 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
18203 \begin_layout Plain Layout
18204 \begin_inset Formula $\mathbb{ABC}$
18212 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
18215 \begin_layout Plain Layout
18228 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
18231 \begin_layout Plain Layout
18240 \begin_layout Plain Layout
18256 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
18259 \begin_layout Plain Layout
18260 \begin_inset Formula $\mathbf{AbC}$
18268 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
18271 \begin_layout Plain Layout
18284 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
18287 \begin_layout Plain Layout
18296 \begin_layout Plain Layout
18312 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
18315 \begin_layout Plain Layout
18316 \begin_inset Formula $\boldsymbol{AbC}$
18324 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
18327 \begin_layout Plain Layout
18330 arg "font-boldsymbol"
18340 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
18343 \begin_layout Plain Layout
18352 \begin_layout Plain Layout
18368 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
18371 \begin_layout Plain Layout
18372 \begin_inset Formula $\mathcal{ABC}$
18380 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
18383 \begin_layout Plain Layout
18396 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
18399 \begin_layout Plain Layout
18408 \begin_layout Plain Layout
18424 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
18427 \begin_layout Plain Layout
18428 \begin_inset Formula $\mathfrak{AbC}$
18436 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
18439 \begin_layout Plain Layout
18447 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
18450 \begin_layout Plain Layout
18459 \begin_layout Plain Layout
18475 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
18478 \begin_layout Plain Layout
18479 \begin_inset Formula $\mathscr{AbC}$
18487 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
18490 \begin_layout Plain Layout
18504 \begin_layout Standard
18506 \begin_inset Tabular
18507 <lyxtabular version="3" rows="5" columns="3">
18508 <features tabularvalignment="middle">
18509 <column alignment="center" valignment="top" width="0">
18510 <column alignment="center" valignment="top" width="0">
18511 <column alignment="center" valignment="top" width="0">
18513 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
18516 \begin_layout Plain Layout
18522 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
18525 \begin_layout Plain Layout
18531 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
18534 \begin_layout Plain Layout
18542 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
18545 \begin_layout Plain Layout
18554 \begin_layout Plain Layout
18570 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
18573 \begin_layout Plain Layout
18574 \begin_inset Formula $\mathit{AbC}$
18582 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
18585 \begin_layout Plain Layout
18593 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
18596 \begin_layout Plain Layout
18605 \begin_layout Plain Layout
18621 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
18624 \begin_layout Plain Layout
18625 \begin_inset Formula $\mathrm{AbC}$
18633 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
18636 \begin_layout Plain Layout
18649 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
18652 \begin_layout Plain Layout
18661 \begin_layout Plain Layout
18677 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
18680 \begin_layout Plain Layout
18681 \begin_inset Formula $\mathsf{AbC}$
18689 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
18692 \begin_layout Plain Layout
18705 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
18708 \begin_layout Plain Layout
18717 \begin_layout Plain Layout
18733 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
18736 \begin_layout Plain Layout
18737 \begin_inset Formula $\mathtt{AbC}$
18745 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
18748 \begin_layout Plain Layout
18751 arg "font-typewriter"
18767 \begin_layout Standard
18768 \begin_inset Note Greyedout
18771 \begin_layout Plain Layout
18788 can only be used for big letters.
18796 \begin_layout Standard
18797 Predefined is the style
18806 \begin_layout Standard
18807 The style commands work also for letters in mathematical constructs:
18808 \begin_inset Formula
18810 \mathfrak{A=\frac{b}{C}}
18818 \begin_layout Standard
18819 Characters in mathematical text don't appear in a math font style but in
18820 the text font style
18827 That their style can't be set correctly via the text style dialog is a
18832 \begin_layout Plain Layout
18833 \begin_inset CommandInset href
18835 name "LyX-bug #4629"
18836 target "http://www.lyx.org/trac/ticket/4629"
18848 \begin_layout Standard
18849 Instead of the style commands the dialog
18851 Edit\SpecialChar \menuseparator
18852 Math\SpecialChar \menuseparator
18855 or the toolbar button
18856 \begin_inset Graphics
18857 filename ../images/math/font.png
18865 \begin_layout Subsection
18867 \begin_inset CommandInset label
18869 name "sub:Bold-Formulas"
18874 \begin_inset Index idx
18877 \begin_layout Plain Layout
18886 \begin_layout Standard
18887 To make a complete formula bold, the command
18893 from the previous subsection cannot be used, because it doesn't work for
18894 small Greek letters.
18895 Furthermore it prints Latin letters always upright, like in the following
18899 \begin_layout Standard
18900 \begin_inset Formula
18902 \mathbf{\int_{n}^{2}f(\theta)=\Gamma}\qquad\textrm{equation with \textbackslash mathbf}
18910 \begin_layout Standard
18911 To display the formula correctly, the command
18918 \begin_inset Formula
18920 \boldsymbol{\int_{n}^{2}f(\theta)=\Gamma\qquad\textrm{equation with \textbackslash boldsymbol}}
18925 It is also possible to set the formula in a
18927 boldmath environment
18930 This environment is created by inserting the command
18937 \begin_inset Index idx
18940 \begin_layout Plain Layout
18949 To end the environment, the command
18956 \begin_inset Index idx
18959 \begin_layout Plain Layout
18967 is inserted in TeX-mode.
18971 \begin_layout Plain Layout
18981 \begin_inset Formula
18983 \int_{n}^{2}f(\theta)=\Gamma\qquad\textrm{equation in a boldmath environment}
18992 \begin_layout Plain Layout
19004 \begin_layout Subsection
19006 \begin_inset Index idx
19009 \begin_layout Plain Layout
19018 \begin_layout Standard
19019 Formulas can be colored like normal text: Highlight a formula or a formula
19025 Here is a formula in magenta:
19026 \begin_inset Formula
19028 {\color{magenta}\int A\,\mathrm{d}x=\frac{\sqrt[5]{B}}{\ln\left(\frac{1}{3}\right)}}
19036 \begin_layout Standard
19037 You can also define your own colors as described in
19038 \begin_inset CommandInset ref
19040 reference "sub:Colored-Boxes"
19045 They can be used with the TeX code command
19052 \begin_inset Index idx
19055 \begin_layout Plain Layout
19066 \begin_layout Standard
19071 textcolor{color}{characters or formula}
19074 \begin_layout Standard
19075 The following example was colored completely dark green and partly red:
19078 \begin_layout Standard
19082 \begin_layout Plain Layout
19086 textcolor{darkgreen}{
19092 \begin_inset Formula
19094 \int A\,\mathrm{d}x=\frac{{\color{red}\sqrt[5]{B}}}{\ln\left(\frac{1}{3}\right)}
19103 \begin_layout Plain Layout
19113 \begin_layout Standard
19114 Due to a bug in LyX only complete formulas can be colored with self-defined
19119 \begin_layout Plain Layout
19120 \begin_inset CommandInset href
19122 name "LyX-bug #5269"
19123 target "http://www.lyx.org/trac/ticket/5269"
19135 \begin_layout Subsection
19137 \begin_inset CommandInset label
19139 name "sub:Font-Sizes"
19144 \begin_inset Index idx
19147 \begin_layout Plain Layout
19156 \begin_layout Standard
19157 For characters in formulas there are, analog to characters in text, the
19158 following size commands:
19161 \begin_layout Standard
19205 \begin_inset Newline newline
19227 \begin_layout Standard
19228 The size produced by the commands depends on the document font size, that
19229 corresponds with the command
19236 The other commands produce smaller or larger sizes than
19243 The font size can however not exceed a certain value.
19244 Is for example the document font size 12
19245 \begin_inset space \thinspace{}
19254 switches to the same size as
19264 \begin_layout Standard
19265 A size command is inserted in TeX-mode before the formula and sets the size
19266 for all following formula and text characters.
19267 To switch back to the initial size, the command
19273 is inserted behind the formula in TeX-mode.
19276 \begin_layout Standard
19277 Within a formula the size can be changed using the following size commands:
19280 \begin_layout Standard
19283 \begin_inset Tabular
19284 <lyxtabular version="3" rows="5" columns="2">
19285 <features tabularvalignment="middle">
19286 <column alignment="center" valignment="top" width="0">
19287 <column alignment="center" valignment="top" width="0">
19289 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
19292 \begin_layout Plain Layout
19298 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
19301 \begin_layout Plain Layout
19303 \begin_inset Note Note
19306 \begin_layout Plain Layout
19313 is only used as spacer.
19325 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
19328 \begin_layout Plain Layout
19332 \begin_inset Index idx
19335 \begin_layout Plain Layout
19348 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
19351 \begin_layout Plain Layout
19352 \begin_inset Formula $\raisebox{6.5mm}{}{\displaystyle E_{\mathrm{pot_{1}}}=\frac{K}{l+\frac{m}{n_{2}}}}\raisebox{-5.5mm}{}$
19362 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
19365 \begin_layout Plain Layout
19373 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
19376 \begin_layout Plain Layout
19377 \begin_inset Formula $\raisebox{4.5mm}{}{\textstyle E_{\mathrm{pot_{1}}}=\frac{K}{l+\frac{m}{n_{2}}}}\raisebox{-4mm}{}$
19387 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
19390 \begin_layout Plain Layout
19398 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
19401 \begin_layout Plain Layout
19402 \begin_inset Formula $\raisebox{4.5mm}{}{\scriptstyle E_{\mathrm{pot_{1}}}=\frac{K}{l+\frac{m}{n_{2}}}}\raisebox{-3.5mm}{}$
19412 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
19415 \begin_layout Plain Layout
19423 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
19426 \begin_layout Plain Layout
19427 \begin_inset Formula $\raisebox{4.5mm}{}{\scriptscriptstyle E_{\mathrm{pot_{1}}}=\frac{K}{l+\frac{m}{n_{2}}}}\raisebox{-3.5mm}{}$
19443 \begin_layout Standard
19444 After entering these commands, a blue box appears in which the formula parts
19448 \begin_layout Standard
19449 There is a further method to change the font size, that though only works
19450 for symbols or letters in mathematical text.
19451 To use it, one of the above text size commands is inserted in mathematical
19453 All following characters until the end of the mathematical text or until
19454 another size command will have the selected size.
19456 \begin_inset VSpace -2mm
19462 \begin_layout Standard
19466 \begin_layout Plain Layout
19476 \begin_inset Formula
19478 A=\frac{B}{c}\cdot\maltese
19484 \begin_inset Formula
19486 \maltese A\textrm{\Large\maltese\textit{A}}\textrm{\tiny\maltese\textit{A}}
19495 \begin_layout Plain Layout
19507 \begin_layout Standard
19508 \begin_inset VSpace medskip
19511 Before both formulas the command
19518 The command for the second formula is:
19519 \begin_inset Newline newline
19530 \begin_layout Plain Layout
19545 \begin_layout Plain Layout
19560 \begin_layout Plain Layout
19575 \begin_layout Plain Layout
19585 \begin_inset Formula $\to$
19589 \begin_inset Formula $\to$
19593 \begin_inset Newline newline
19597 \begin_inset space \hspace*{}
19611 \begin_layout Plain Layout
19626 \begin_layout Plain Layout
19641 \begin_layout Plain Layout
19653 \begin_layout Standard
19654 If a symbol cannot be displayed in different sizes, it will always be displayed
19655 in the default size.
19658 \begin_layout Section
19660 \begin_inset Index idx
19663 \begin_layout Plain Layout
19672 \begin_layout Standard
19673 Greek letters can also be inserted via the toolbar button
19674 \begin_inset Graphics
19675 filename ../images/math/alpha.png
19681 All international typesetting norms purport that Greek letters in math
19682 have to be typeset italic/slanted.
19683 In some languages, like French or Russian, they are nevertheless sometimes
19687 \begin_layout Subsection
19689 \begin_inset Index idx
19692 \begin_layout Plain Layout
19693 Greek letters ! small
19701 \begin_layout Standard
19702 \begin_inset space \hfill{}
19706 \begin_inset Tabular
19707 <lyxtabular version="3" rows="11" columns="2">
19708 <features tabularvalignment="middle">
19709 <column alignment="center" valignment="top" width="0pt">
19710 <column alignment="center" valignment="top" width="0pt">
19712 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
19715 \begin_layout Plain Layout
19721 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
19724 \begin_layout Plain Layout
19732 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
19735 \begin_layout Plain Layout
19743 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
19746 \begin_layout Plain Layout
19747 \begin_inset Formula $\alpha$
19757 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
19760 \begin_layout Plain Layout
19768 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
19771 \begin_layout Plain Layout
19772 \begin_inset Formula $\beta$
19782 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
19785 \begin_layout Plain Layout
19793 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
19796 \begin_layout Plain Layout
19797 \begin_inset Formula $\gamma$
19807 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
19810 \begin_layout Plain Layout
19818 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
19821 \begin_layout Plain Layout
19822 \begin_inset Formula $\delta$
19832 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
19835 \begin_layout Plain Layout
19843 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
19846 \begin_layout Plain Layout
19847 \begin_inset Formula $\epsilon$
19857 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
19860 \begin_layout Plain Layout
19868 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
19871 \begin_layout Plain Layout
19872 \begin_inset Formula $\varepsilon$
19882 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
19885 \begin_layout Plain Layout
19893 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
19896 \begin_layout Plain Layout
19897 \begin_inset Formula $\zeta$
19907 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
19910 \begin_layout Plain Layout
19918 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
19921 \begin_layout Plain Layout
19922 \begin_inset Formula $\eta$
19932 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
19935 \begin_layout Plain Layout
19943 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
19946 \begin_layout Plain Layout
19947 \begin_inset Formula $\theta$
19957 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
19960 \begin_layout Plain Layout
19968 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
19971 \begin_layout Plain Layout
19972 \begin_inset Formula $\vartheta$
19986 \begin_inset space \hfill{}
19990 \begin_inset Tabular
19991 <lyxtabular version="3" rows="12" columns="2">
19992 <features tabularvalignment="middle">
19993 <column alignment="center" valignment="top" width="0pt">
19994 <column alignment="center" valignment="top" width="0pt">
19996 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
19999 \begin_layout Plain Layout
20005 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
20008 \begin_layout Plain Layout
20016 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
20019 \begin_layout Plain Layout
20027 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
20030 \begin_layout Plain Layout
20031 \begin_inset Formula $\iota$
20041 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
20044 \begin_layout Plain Layout
20052 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
20055 \begin_layout Plain Layout
20056 \begin_inset Formula $\kappa$
20066 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
20069 \begin_layout Plain Layout
20077 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
20080 \begin_layout Plain Layout
20081 \begin_inset Formula $\varkappa$
20091 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
20094 \begin_layout Plain Layout
20102 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
20105 \begin_layout Plain Layout
20106 \begin_inset Formula $\lambda$
20116 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
20119 \begin_layout Plain Layout
20127 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
20130 \begin_layout Plain Layout
20131 \begin_inset Formula $\mu$
20141 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
20144 \begin_layout Plain Layout
20152 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
20155 \begin_layout Plain Layout
20156 \begin_inset Formula $\nu$
20166 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
20169 \begin_layout Plain Layout
20177 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
20180 \begin_layout Plain Layout
20181 \begin_inset Formula $\xi$
20191 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
20194 \begin_layout Plain Layout
20200 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
20203 \begin_layout Plain Layout
20204 \begin_inset Formula $o$
20214 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
20217 \begin_layout Plain Layout
20225 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
20228 \begin_layout Plain Layout
20229 \begin_inset Formula $\pi$
20239 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
20242 \begin_layout Plain Layout
20250 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
20253 \begin_layout Plain Layout
20254 \begin_inset Formula $\varpi$
20264 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
20267 \begin_layout Plain Layout
20275 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
20278 \begin_layout Plain Layout
20279 \begin_inset Formula $\rho$
20293 \begin_inset space \hfill{}
20297 \begin_inset Tabular
20298 <lyxtabular version="3" rows="11" columns="2">
20299 <features tabularvalignment="middle">
20300 <column alignment="center" valignment="top" width="0pt">
20301 <column alignment="center" valignment="top" width="0pt">
20303 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
20306 \begin_layout Plain Layout
20312 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
20315 \begin_layout Plain Layout
20323 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
20326 \begin_layout Plain Layout
20334 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
20337 \begin_layout Plain Layout
20338 \begin_inset Formula $\varrho$
20348 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
20351 \begin_layout Plain Layout
20359 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
20362 \begin_layout Plain Layout
20363 \begin_inset Formula $\sigma$
20373 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
20376 \begin_layout Plain Layout
20384 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
20387 \begin_layout Plain Layout
20388 \begin_inset Formula $\varsigma$
20398 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
20401 \begin_layout Plain Layout
20409 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
20412 \begin_layout Plain Layout
20413 \begin_inset Formula $\tau$
20423 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
20426 \begin_layout Plain Layout
20434 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
20437 \begin_layout Plain Layout
20438 \begin_inset Formula $\upsilon$
20448 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
20451 \begin_layout Plain Layout
20459 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
20462 \begin_layout Plain Layout
20463 \begin_inset Formula $\phi$
20473 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
20476 \begin_layout Plain Layout
20484 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
20487 \begin_layout Plain Layout
20488 \begin_inset Formula $\varphi$
20498 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
20501 \begin_layout Plain Layout
20509 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
20512 \begin_layout Plain Layout
20513 \begin_inset Formula $\chi$
20523 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
20526 \begin_layout Plain Layout
20534 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
20537 \begin_layout Plain Layout
20538 \begin_inset Formula $\psi$
20548 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
20551 \begin_layout Plain Layout
20559 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
20562 \begin_layout Plain Layout
20563 \begin_inset Formula $\omega$
20577 \begin_inset space \hfill{}
20583 \begin_layout Standard
20584 \begin_inset VSpace medskip
20590 \begin_layout Standard
20591 How to create special upright Greek letters is explained in
20592 \begin_inset CommandInset ref
20594 reference "sub:Upright-small-Greek"
20601 \begin_layout Subsection
20603 \begin_inset Index idx
20606 \begin_layout Plain Layout
20607 Greek letters ! big
20615 \begin_layout Standard
20616 \begin_inset space \hfill{}
20620 \begin_inset Tabular
20621 <lyxtabular version="3" rows="7" columns="2">
20622 <features tabularvalignment="middle">
20623 <column alignment="center" valignment="top" width="0pt">
20624 <column alignment="center" valignment="top" width="0pt">
20626 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
20629 \begin_layout Plain Layout
20635 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
20638 \begin_layout Plain Layout
20646 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
20649 \begin_layout Plain Layout
20657 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
20660 \begin_layout Plain Layout
20661 \begin_inset Formula $\Gamma$
20671 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
20674 \begin_layout Plain Layout
20682 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
20685 \begin_layout Plain Layout
20686 \begin_inset Formula $\Delta$
20696 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
20699 \begin_layout Plain Layout
20707 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
20710 \begin_layout Plain Layout
20711 \begin_inset Formula $\Theta$
20721 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
20724 \begin_layout Plain Layout
20732 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
20735 \begin_layout Plain Layout
20736 \begin_inset Formula $\Lambda$
20746 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
20749 \begin_layout Plain Layout
20757 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
20760 \begin_layout Plain Layout
20761 \begin_inset Formula $\Xi$
20771 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
20774 \begin_layout Plain Layout
20782 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
20785 \begin_layout Plain Layout
20786 \begin_inset Formula $\Pi$
20800 \begin_inset space \hfill{}
20804 \begin_inset Tabular
20805 <lyxtabular version="3" rows="6" columns="2">
20806 <features tabularvalignment="middle">
20807 <column alignment="center" valignment="top" width="0pt">
20808 <column alignment="center" valignment="top" width="0pt">
20810 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
20813 \begin_layout Plain Layout
20819 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
20822 \begin_layout Plain Layout
20830 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
20833 \begin_layout Plain Layout
20841 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
20844 \begin_layout Plain Layout
20845 \begin_inset Formula $\Sigma$
20855 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
20858 \begin_layout Plain Layout
20866 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
20869 \begin_layout Plain Layout
20870 \begin_inset Formula $\Upsilon$
20880 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
20883 \begin_layout Plain Layout
20891 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
20894 \begin_layout Plain Layout
20895 \begin_inset Formula $\Phi$
20905 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
20908 \begin_layout Plain Layout
20916 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
20919 \begin_layout Plain Layout
20920 \begin_inset Formula $\Psi$
20930 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
20933 \begin_layout Plain Layout
20941 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
20944 \begin_layout Plain Layout
20945 \begin_inset Formula $\Omega$
20959 \begin_inset space \hfill{}
20965 \begin_layout Standard
20966 \begin_inset VSpace medskip
20969 That the big Greek letters appear upright is caused by a design bug when
20971 To get correct italic big letters, begin every command with
20976 For example the command
20983 \begin_inset Formula $\varGamma$
20987 Another way is to load the package
20995 \begin_layout Plain Layout
21000 is part of the LaTeX-package
21005 \begin_inset Index idx
21008 \begin_layout Plain Layout
21013 \begin_layout Plain Layout
21033 \begin_inset Index idx
21036 \begin_layout Plain Layout
21042 with the LaTeX-preamble line
21045 \begin_layout Standard
21050 usepackage{fixmath}
21053 \begin_layout Standard
21054 Then all big Greek letters in a document will automatically be typeset italic.
21057 \begin_layout Subsection
21059 \begin_inset Index idx
21062 \begin_layout Plain Layout
21063 Greek letters ! bold
21071 \begin_layout Standard
21072 Greek letters cannot be set with different font styles like Latin letters.
21073 They can only be made bold with the command
21080 \begin_inset Index idx
21083 \begin_layout Plain Layout
21094 \begin_layout Standard
21096 \begin_inset Tabular
21097 <lyxtabular version="3" rows="3" columns="2">
21098 <features tabularvalignment="middle">
21099 <column alignment="center" valignment="top" width="0">
21100 <column alignment="center" valignment="top" width="0">
21102 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
21105 \begin_layout Plain Layout
21111 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
21114 \begin_layout Plain Layout
21122 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
21125 \begin_layout Plain Layout
21137 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
21140 \begin_layout Plain Layout
21141 \begin_inset Formula $\Upsilon\boldsymbol{\Upsilon}$
21151 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
21154 \begin_layout Plain Layout
21166 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
21169 \begin_layout Plain Layout
21170 \begin_inset Formula $\theta\boldsymbol{\theta}$
21186 \begin_layout Standard
21187 \begin_inset Newpage newpage
21193 \begin_layout Section
21198 \begin_layout Plain Layout
21211 \begin_layout Plain Layout
21212 A list with all symbols of most of the LaTeX-packages can be found in
21213 \begin_inset CommandInset citation
21228 \begin_layout Plain Layout
21236 \begin_inset Note Note
21239 \begin_layout Plain Layout
21242 texorpdfstring is used to avoid that the footnote appears in the PDF-bookmark.
21245 \begin_layout Plain Layout
21248 texorpdfstring is in section
21249 \begin_inset CommandInset ref
21251 reference "sub:Formulas-in-Section"
21261 \begin_inset Index idx
21264 \begin_layout Plain Layout
21273 \begin_layout Standard
21274 Many of the symbols listed in this section can also be inserted via the
21276 \begin_inset Graphics
21277 filename ../images/math/nabla.png
21283 \begin_inset Graphics
21284 filename ../images/math/digamma.png
21292 \begin_layout Subsection
21293 Mathematical Symbols
21294 \begin_inset CommandInset label
21296 name "sub:Mathematical-Symbols"
21301 \begin_inset Index idx
21304 \begin_layout Plain Layout
21305 Symbols ! mathematical
21313 \begin_layout Standard
21314 \begin_inset space \hfill{}
21318 \begin_inset Tabular
21319 <lyxtabular version="3" rows="10" columns="2">
21320 <features tabularvalignment="middle">
21321 <column alignment="center" valignment="top" width="0pt">
21322 <column alignment="center" valignment="top" width="0pt">
21324 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
21327 \begin_layout Plain Layout
21333 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
21336 \begin_layout Plain Layout
21344 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
21347 \begin_layout Plain Layout
21355 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
21358 \begin_layout Plain Layout
21359 \begin_inset Formula $\neg$
21369 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
21372 \begin_layout Plain Layout
21380 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
21383 \begin_layout Plain Layout
21384 \begin_inset Formula $\Im$
21394 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
21397 \begin_layout Plain Layout
21405 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
21408 \begin_layout Plain Layout
21409 \begin_inset Formula $\Re$
21419 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
21422 \begin_layout Plain Layout
21430 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
21433 \begin_layout Plain Layout
21434 \begin_inset Formula $\aleph$
21444 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
21447 \begin_layout Plain Layout
21455 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
21458 \begin_layout Plain Layout
21459 \begin_inset Formula $\partial$
21469 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
21472 \begin_layout Plain Layout
21480 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
21483 \begin_layout Plain Layout
21484 \begin_inset Formula $\infty$
21494 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
21497 \begin_layout Plain Layout
21505 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
21508 \begin_layout Plain Layout
21509 \begin_inset Formula $\wp$
21519 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
21522 \begin_layout Plain Layout
21530 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
21533 \begin_layout Plain Layout
21534 \begin_inset Formula $\imath$
21544 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
21547 \begin_layout Plain Layout
21555 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
21558 \begin_layout Plain Layout
21559 \begin_inset Formula $\jmath$
21573 \begin_inset space \hfill{}
21577 \begin_inset Tabular
21578 <lyxtabular version="3" rows="10" columns="2">
21579 <features tabularvalignment="middle">
21580 <column alignment="center" valignment="top" width="0pt">
21581 <column alignment="center" valignment="top" width="0pt">
21583 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
21586 \begin_layout Plain Layout
21592 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
21595 \begin_layout Plain Layout
21597 \begin_inset Note Note
21600 \begin_layout Plain Layout
21607 is only used as spacer.
21619 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
21622 \begin_layout Plain Layout
21630 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
21633 \begin_layout Plain Layout
21634 \begin_inset Formula $\forall$
21644 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
21647 \begin_layout Plain Layout
21655 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
21658 \begin_layout Plain Layout
21659 \begin_inset Formula $\exists$
21669 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
21672 \begin_layout Plain Layout
21680 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
21683 \begin_layout Plain Layout
21684 \begin_inset Formula $\nexists$
21694 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
21697 \begin_layout Plain Layout
21705 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
21708 \begin_layout Plain Layout
21709 \begin_inset Formula $\emptyset$
21719 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
21722 \begin_layout Plain Layout
21730 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
21733 \begin_layout Plain Layout
21734 \begin_inset Formula $\varnothing$
21744 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
21747 \begin_layout Plain Layout
21755 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
21758 \begin_layout Plain Layout
21759 \begin_inset Formula $\dag$
21769 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
21772 \begin_layout Plain Layout
21780 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
21783 \begin_layout Plain Layout
21784 \begin_inset Formula $\ddag$
21794 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
21797 \begin_layout Plain Layout
21805 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
21808 \begin_layout Plain Layout
21812 \begin_layout Plain Layout
21822 \begin_inset Formula $\complement$
21829 \begin_layout Plain Layout
21843 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
21846 \begin_layout Plain Layout
21854 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
21857 \begin_layout Plain Layout
21858 \begin_inset Formula $\Bbbk$
21872 \begin_inset space \hfill{}
21876 \begin_inset Tabular
21877 <lyxtabular version="3" rows="10" columns="2">
21878 <features tabularvalignment="middle">
21879 <column alignment="center" valignment="top" width="0pt">
21880 <column alignment="center" valignment="top" width="0pt">
21882 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
21885 \begin_layout Plain Layout
21891 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
21894 \begin_layout Plain Layout
21902 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
21905 \begin_layout Plain Layout
21913 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
21916 \begin_layout Plain Layout
21917 \begin_inset Formula $\prime$
21927 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
21930 \begin_layout Plain Layout
21938 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
21941 \begin_layout Plain Layout
21942 \begin_inset Formula $\backprime$
21952 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
21955 \begin_layout Plain Layout
21963 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
21966 \begin_layout Plain Layout
21967 \begin_inset Formula $\mho$
21977 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
21980 \begin_layout Plain Layout
21988 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
21991 \begin_layout Plain Layout
21992 \begin_inset Formula $\triangle$
22002 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
22005 \begin_layout Plain Layout
22013 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
22016 \begin_layout Plain Layout
22017 \begin_inset Formula $\angle$
22027 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
22030 \begin_layout Plain Layout
22038 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
22041 \begin_layout Plain Layout
22042 \begin_inset Formula $\measuredangle$
22052 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
22055 \begin_layout Plain Layout
22063 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
22066 \begin_layout Plain Layout
22067 \begin_inset Formula $\sphericalangle$
22077 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
22080 \begin_layout Plain Layout
22088 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
22091 \begin_layout Plain Layout
22092 \begin_inset Formula $\top$
22102 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
22105 \begin_layout Plain Layout
22113 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
22116 \begin_layout Plain Layout
22117 \begin_inset Formula $\bot$
22131 \begin_inset space \hfill{}
22137 \begin_layout Subsection
22138 Miscellaneous Symbols
22139 \begin_inset CommandInset label
22141 name "sub:Miscellaneous-Symbols"
22146 \begin_inset Index idx
22149 \begin_layout Plain Layout
22150 Symbols ! miscellaneous
22158 \begin_layout Standard
22161 \begin_inset Tabular
22162 <lyxtabular version="3" rows="10" columns="2">
22163 <features tabularvalignment="middle">
22164 <column alignment="center" valignment="top" width="0pt">
22165 <column alignment="center" valignment="top" width="0pt">
22167 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
22170 \begin_layout Plain Layout
22176 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
22179 \begin_layout Plain Layout
22187 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
22190 \begin_layout Plain Layout
22198 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
22201 \begin_layout Plain Layout
22202 \begin_inset Formula $\flat$
22212 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
22215 \begin_layout Plain Layout
22223 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
22226 \begin_layout Plain Layout
22227 \begin_inset Formula $\natural$
22237 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
22240 \begin_layout Plain Layout
22248 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
22251 \begin_layout Plain Layout
22252 \begin_inset Formula $\sharp$
22262 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
22265 \begin_layout Plain Layout
22273 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
22276 \begin_layout Plain Layout
22277 \begin_inset Formula $\surd$
22287 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
22290 \begin_layout Plain Layout
22298 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
22301 \begin_layout Plain Layout
22302 \begin_inset Formula $\checkmark$
22312 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
22315 \begin_layout Plain Layout
22323 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
22326 \begin_layout Plain Layout
22327 \begin_inset Formula $\yen$
22337 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
22340 \begin_layout Plain Layout
22348 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
22351 \begin_layout Plain Layout
22352 \begin_inset Formula $\pounds$
22362 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
22365 \begin_layout Plain Layout
22371 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
22374 \begin_layout Plain Layout
22375 \begin_inset Formula $\$$
22385 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
22388 \begin_layout Plain Layout
22394 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
22397 \begin_layout Plain Layout
22398 \begin_inset Formula $§$
22412 \begin_inset Tabular
22413 <lyxtabular version="3" rows="10" columns="2">
22414 <features tabularvalignment="middle">
22415 <column alignment="center" valignment="top" width="0">
22416 <column alignment="center" valignment="top" width="0">
22418 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
22421 \begin_layout Plain Layout
22427 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
22430 \begin_layout Plain Layout
22438 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
22441 \begin_layout Plain Layout
22449 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
22452 \begin_layout Plain Layout
22453 \begin_inset Formula $\hbar$
22463 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
22466 \begin_layout Plain Layout
22474 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
22477 \begin_layout Plain Layout
22478 \begin_inset Formula $\hslash$
22488 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
22491 \begin_layout Plain Layout
22499 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
22502 \begin_layout Plain Layout
22503 \begin_inset Formula $\clubsuit$
22513 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
22516 \begin_layout Plain Layout
22524 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
22527 \begin_layout Plain Layout
22528 \begin_inset Formula $\spadesuit$
22538 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
22541 \begin_layout Plain Layout
22549 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
22552 \begin_layout Plain Layout
22553 \begin_inset Formula $\bigstar$
22563 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
22566 \begin_layout Plain Layout
22574 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
22577 \begin_layout Plain Layout
22578 \begin_inset Formula $\blacklozenge$
22588 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
22591 \begin_layout Plain Layout
22599 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
22602 \begin_layout Plain Layout
22603 \begin_inset Formula $\blacktriangle$
22613 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
22616 \begin_layout Plain Layout
22624 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
22627 \begin_layout Plain Layout
22628 \begin_inset Formula $\blacktriangledown$
22638 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
22641 \begin_layout Plain Layout
22649 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
22652 \begin_layout Plain Layout
22653 \begin_inset Formula $\bullet$
22667 \begin_inset Tabular
22668 <lyxtabular version="3" rows="10" columns="2">
22669 <features tabularvalignment="middle">
22670 <column alignment="center" valignment="top" width="0pt">
22671 <column alignment="center" valignment="top" width="0pt">
22673 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
22676 \begin_layout Plain Layout
22682 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
22685 \begin_layout Plain Layout
22693 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
22696 \begin_layout Plain Layout
22704 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
22707 \begin_layout Plain Layout
22708 \begin_inset Formula $\diamondsuit$
22718 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
22721 \begin_layout Plain Layout
22729 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
22732 \begin_layout Plain Layout
22733 \begin_inset Formula $\Diamond$
22743 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
22746 \begin_layout Plain Layout
22754 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
22757 \begin_layout Plain Layout
22758 \begin_inset Formula $\heartsuit$
22768 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
22771 \begin_layout Plain Layout
22779 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
22782 \begin_layout Plain Layout
22783 \begin_inset Formula $\P$
22793 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
22796 \begin_layout Plain Layout
22804 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
22807 \begin_layout Plain Layout
22808 \begin_inset Formula $\copyright$
22818 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
22821 \begin_layout Plain Layout
22829 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
22832 \begin_layout Plain Layout
22833 \begin_inset Formula $\circledR$
22843 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
22846 \begin_layout Plain Layout
22854 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
22857 \begin_layout Plain Layout
22858 \begin_inset Formula $\maltese$
22868 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
22871 \begin_layout Plain Layout
22879 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
22882 \begin_layout Plain Layout
22883 \begin_inset Formula $\diagup$
22893 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
22896 \begin_layout Plain Layout
22904 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
22907 \begin_layout Plain Layout
22908 \begin_inset Formula $\diagdown$
22924 \begin_layout Standard
22925 \begin_inset VSpace medskip
22928 More symbols are listed in
22929 \begin_inset CommandInset ref
22931 reference "sub:Miscellaneous-special-Characters"
22938 \begin_layout Standard
22939 Some symbols can be displayed in different sizes, see
22940 \begin_inset CommandInset ref
22942 reference "sub:Font-Sizes"
22949 \begin_layout Subsection
22951 \begin_inset Index idx
22954 \begin_layout Plain Layout
22955 Symbols ! Euro-symbol
22961 \begin_inset Index idx
22964 \begin_layout Plain Layout
22971 \begin_layout Plain Layout
22988 \begin_layout Standard
22989 To use the Euro symbol in formulas, the LaTeX-package
22994 \begin_inset Index idx
22997 \begin_layout Plain Layout
23003 must be installed and loaded with the LaTeX-preamble line
23006 \begin_layout Standard
23011 usepackage[gennarrow]{eurosym}
23014 \begin_layout Standard
23015 The Euro symbol can now be inserted with the command
23022 \begin_inset Index idx
23025 \begin_layout Plain Layout
23036 \begin_layout Standard
23037 The Euro symbol can directly be inserted with the € key in mathematical
23038 text, without having
23053 can also be inserted in TeX-mode.
23054 The official currency symbol can then be inserted with the command
23061 \begin_inset Index idx
23064 \begin_layout Plain Layout
23072 , that is only available in TeX-mode.
23075 \begin_layout Standard
23079 \begin_layout Plain Layout
23089 \begin_inset Note Note
23092 \begin_layout Plain Layout
23093 The following table will only be displayed when the LaTeX-package
23105 \begin_layout Standard
23106 An overview about the different Euro symbols:
23109 \begin_layout Standard
23111 \begin_inset Tabular
23112 <lyxtabular version="3" rows="4" columns="3">
23113 <features tabularvalignment="middle">
23114 <column alignment="center" valignment="top" width="0pt">
23115 <column alignment="center" valignment="top" width="0pt">
23116 <column alignment="center" valignment="top" width="0pt">
23118 <cell multicolumn="1" alignment="center" valignment="top" bottomline="true" usebox="none">
23121 \begin_layout Plain Layout
23127 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
23130 \begin_layout Plain Layout
23136 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
23139 \begin_layout Plain Layout
23147 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
23150 \begin_layout Plain Layout
23156 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
23159 \begin_layout Plain Layout
23167 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
23170 \begin_layout Plain Layout
23171 \begin_inset Formula $\euro$
23181 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
23184 \begin_layout Plain Layout
23190 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
23193 \begin_layout Plain Layout
23199 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
23202 \begin_layout Plain Layout
23203 \begin_inset Formula $\mbox{€}$
23213 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
23216 \begin_layout Plain Layout
23222 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
23225 \begin_layout Plain Layout
23233 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
23236 \begin_layout Plain Layout
23240 \begin_layout Plain Layout
23262 \begin_layout Standard
23266 \begin_layout Plain Layout
23276 \begin_inset Note Note
23279 \begin_layout Plain Layout
23280 The following will be displayed when the LaTeX-package
23292 \begin_layout Standard
23293 You need to install the LaTeX-package
23297 to see the rest of this subsection in the output.
23300 \begin_layout Standard
23304 \begin_layout Plain Layout
23316 \begin_layout Section
23318 \begin_inset CommandInset label
23320 name "sec:Relations"
23325 \begin_inset Index idx
23328 \begin_layout Plain Layout
23335 \begin_inset Index idx
23338 \begin_layout Plain Layout
23343 \begin_layout Plain Layout
23354 \begin_layout Plain Layout
23369 \begin_layout Standard
23370 All relations can also be inserted via the toolbar button
23371 \begin_inset Graphics
23372 filename ../images/math/leq.png
23380 \begin_layout Standard
23381 \begin_inset space \hfill{}
23385 \begin_inset Tabular
23386 <lyxtabular version="3" rows="17" columns="2">
23387 <features tabularvalignment="middle">
23388 <column alignment="center" valignment="top" width="0pt">
23389 <column alignment="center" valignment="top" width="0pt">
23391 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
23394 \begin_layout Plain Layout
23400 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
23403 \begin_layout Plain Layout
23411 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
23414 \begin_layout Plain Layout
23420 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
23423 \begin_layout Plain Layout
23424 \begin_inset Formula $<$
23434 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
23437 \begin_layout Plain Layout
23445 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
23448 \begin_layout Plain Layout
23449 \begin_inset Formula $\le$
23459 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
23462 \begin_layout Plain Layout
23470 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
23473 \begin_layout Plain Layout
23474 \begin_inset Formula $\ll$
23484 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
23487 \begin_layout Plain Layout
23495 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
23498 \begin_layout Plain Layout
23499 \begin_inset Formula $\prec$
23509 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
23512 \begin_layout Plain Layout
23520 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
23523 \begin_layout Plain Layout
23524 \begin_inset Formula $\preceq$
23534 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
23537 \begin_layout Plain Layout
23545 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
23548 \begin_layout Plain Layout
23549 \begin_inset Formula $\subset$
23559 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
23562 \begin_layout Plain Layout
23570 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
23573 \begin_layout Plain Layout
23574 \begin_inset Formula $\subseteq$
23584 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
23587 \begin_layout Plain Layout
23595 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
23598 \begin_layout Plain Layout
23599 \begin_inset Formula $\sqsubseteq$
23609 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
23612 \begin_layout Plain Layout
23620 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
23623 \begin_layout Plain Layout
23624 \begin_inset Formula $\in$
23634 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
23637 \begin_layout Plain Layout
23645 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
23648 \begin_layout Plain Layout
23649 \begin_inset Formula $\vdash$
23659 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
23662 \begin_layout Plain Layout
23670 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
23673 \begin_layout Plain Layout
23674 \begin_inset Formula $\smile$
23684 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
23687 \begin_layout Plain Layout
23695 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
23698 \begin_layout Plain Layout
23699 \begin_inset Formula $\lhd$
23709 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
23712 \begin_layout Plain Layout
23720 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
23723 \begin_layout Plain Layout
23724 \begin_inset Formula $\unlhd$
23734 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
23737 \begin_layout Plain Layout
23745 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
23748 \begin_layout Plain Layout
23749 \begin_inset Formula $\gtrless$
23759 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
23762 \begin_layout Plain Layout
23770 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
23773 \begin_layout Plain Layout
23774 \begin_inset Formula $\mid$
23784 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
23787 \begin_layout Plain Layout
23795 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
23798 \begin_layout Plain Layout
23799 \begin_inset Formula $\nmid$
23813 \begin_inset space \hfill{}
23817 \begin_inset Tabular
23818 <lyxtabular version="3" rows="17" columns="2">
23819 <features tabularvalignment="middle">
23820 <column alignment="center" valignment="top" width="0pt">
23821 <column alignment="center" valignment="top" width="0pt">
23823 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
23826 \begin_layout Plain Layout
23832 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
23835 \begin_layout Plain Layout
23843 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
23846 \begin_layout Plain Layout
23852 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
23855 \begin_layout Plain Layout
23856 \begin_inset Formula $=$
23866 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
23869 \begin_layout Plain Layout
23877 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
23880 \begin_layout Plain Layout
23881 \begin_inset Formula $\not=$
23891 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
23894 \begin_layout Plain Layout
23902 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
23905 \begin_layout Plain Layout
23906 \begin_inset Formula $\equiv$
23916 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
23919 \begin_layout Plain Layout
23927 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
23930 \begin_layout Plain Layout
23931 \begin_inset Formula $\sim$
23941 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
23944 \begin_layout Plain Layout
23952 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
23955 \begin_layout Plain Layout
23956 \begin_inset Formula $\simeq$
23966 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
23969 \begin_layout Plain Layout
23977 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
23980 \begin_layout Plain Layout
23981 \begin_inset Formula $\approx$
23991 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
23994 \begin_layout Plain Layout
24002 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
24005 \begin_layout Plain Layout
24006 \begin_inset Formula $\cong$
24016 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
24019 \begin_layout Plain Layout
24027 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
24030 \begin_layout Plain Layout
24031 \begin_inset Formula $\bowtie$
24041 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
24044 \begin_layout Plain Layout
24052 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
24055 \begin_layout Plain Layout
24056 \begin_inset Formula $\notin$
24066 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
24069 \begin_layout Plain Layout
24077 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
24080 \begin_layout Plain Layout
24081 \begin_inset Formula $\perp$
24091 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
24094 \begin_layout Plain Layout
24102 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
24105 \begin_layout Plain Layout
24106 \begin_inset Formula $\propto$
24116 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
24119 \begin_layout Plain Layout
24127 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
24130 \begin_layout Plain Layout
24131 \begin_inset Formula $\asymp$
24141 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
24144 \begin_layout Plain Layout
24152 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
24155 \begin_layout Plain Layout
24156 \begin_inset Formula $\doteq$
24166 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
24169 \begin_layout Plain Layout
24177 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
24180 \begin_layout Plain Layout
24181 \begin_inset Formula $\circeq$
24191 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
24194 \begin_layout Plain Layout
24202 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
24205 \begin_layout Plain Layout
24206 \begin_inset Formula $\models$
24216 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
24219 \begin_layout Plain Layout
24227 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
24230 \begin_layout Plain Layout
24231 \begin_inset Formula $\widehat{=}$
24245 \begin_inset space \hfill{}
24249 \begin_inset Tabular
24250 <lyxtabular version="3" rows="17" columns="2">
24251 <features tabularvalignment="middle">
24252 <column alignment="center" valignment="top" width="0pt">
24253 <column alignment="center" valignment="top" width="0pt">
24255 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
24258 \begin_layout Plain Layout
24264 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
24267 \begin_layout Plain Layout
24275 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
24278 \begin_layout Plain Layout
24284 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
24287 \begin_layout Plain Layout
24288 \begin_inset Formula $>$
24298 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
24301 \begin_layout Plain Layout
24309 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
24312 \begin_layout Plain Layout
24313 \begin_inset Formula $\ge$
24323 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
24326 \begin_layout Plain Layout
24334 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
24337 \begin_layout Plain Layout
24338 \begin_inset Formula $\gg$
24348 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
24351 \begin_layout Plain Layout
24359 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
24362 \begin_layout Plain Layout
24363 \begin_inset Formula $\succ$
24373 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
24376 \begin_layout Plain Layout
24384 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
24387 \begin_layout Plain Layout
24388 \begin_inset Formula $\succeq$
24398 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
24401 \begin_layout Plain Layout
24409 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
24412 \begin_layout Plain Layout
24413 \begin_inset Formula $\supset$
24423 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
24426 \begin_layout Plain Layout
24434 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
24437 \begin_layout Plain Layout
24438 \begin_inset Formula $\supseteq$
24448 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
24451 \begin_layout Plain Layout
24459 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
24462 \begin_layout Plain Layout
24463 \begin_inset Formula $\sqsupseteq$
24473 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
24476 \begin_layout Plain Layout
24484 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
24487 \begin_layout Plain Layout
24488 \begin_inset Formula $\ni$
24498 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
24501 \begin_layout Plain Layout
24509 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
24512 \begin_layout Plain Layout
24513 \begin_inset Formula $\dashv$
24523 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
24526 \begin_layout Plain Layout
24534 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
24537 \begin_layout Plain Layout
24538 \begin_inset Formula $\frown$
24548 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
24551 \begin_layout Plain Layout
24559 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
24562 \begin_layout Plain Layout
24563 \begin_inset Formula $\rhd$
24573 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
24576 \begin_layout Plain Layout
24584 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
24587 \begin_layout Plain Layout
24588 \begin_inset Formula $\unrhd$
24598 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
24601 \begin_layout Plain Layout
24609 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
24612 \begin_layout Plain Layout
24613 \begin_inset Formula $\lessgtr$
24623 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
24626 \begin_layout Plain Layout
24634 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
24637 \begin_layout Plain Layout
24638 \begin_inset Formula $\parallel$
24648 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
24651 \begin_layout Plain Layout
24659 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
24662 \begin_layout Plain Layout
24663 \begin_inset Formula $\nparallel$
24677 \begin_inset space \hfill{}
24683 \begin_layout Standard
24684 \begin_inset VSpace medskip
24699 are bigger than the equal looking operators
24714 \begin_layout Standard
24715 Relations are, in contrary to symbols, always surrounded by space.
24718 \begin_layout Standard
24719 Relations with labels can be created with the command
24726 \begin_inset Index idx
24729 \begin_layout Plain Layout
24740 \begin_layout Standard
24742 \begin_inset Tabular
24743 <lyxtabular version="3" rows="2" columns="2">
24744 <features tabularvalignment="middle">
24745 <column alignment="center" valignment="top" width="0">
24746 <column alignment="center" valignment="top" width="0">
24748 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
24751 \begin_layout Plain Layout
24757 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
24760 \begin_layout Plain Layout
24762 \begin_inset Note Note
24765 \begin_layout Plain Layout
24772 is only used as spacer.
24784 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
24787 \begin_layout Plain Layout
24794 \begin_layout Plain Layout
24811 \begin_layout Plain Layout
24821 \begin_inset Formula $\downarrow$
24830 \begin_layout Plain Layout
24843 \begin_layout Plain Layout
24857 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
24860 \begin_layout Plain Layout
24861 \begin_inset Formula $\raisebox{5mm}{}A(r)\stackrel{r\to\infty}{\approx}B$
24877 \begin_layout Section
24881 \begin_layout Subsection
24882 Predefined Functions
24883 \begin_inset CommandInset label
24885 name "sub:Predefined-Functions"
24890 \begin_inset Index idx
24893 \begin_layout Plain Layout
24894 Functions ! predefined
24902 \begin_layout Standard
24903 In general, variables are set
24907 in mathematical expressions, but not function names, because
24908 \begin_inset Formula $sin$
24911 could be misunderstood as
24912 \begin_inset Formula $s\cdot i\cdot n$
24916 Therefore there are predefined functions, that are additionally a bit separated
24918 They are inserted as commands starting with a backslash before their name.
24921 \begin_layout Standard
24923 \begin_inset Tabular
24924 <lyxtabular version="3" rows="2" columns="4">
24925 <features tabularvalignment="middle">
24926 <column alignment="center" valignment="top" width="0pt">
24927 <column alignment="center" valignment="top" width="0pt">
24928 <column alignment="center" valignment="top" width="0pt">
24929 <column alignment="center" valignment="top" width="0pt">
24931 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
24934 \begin_layout Plain Layout
24940 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
24943 \begin_layout Plain Layout
24949 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
24952 \begin_layout Plain Layout
24958 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
24961 \begin_layout Plain Layout
24969 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
24972 \begin_layout Plain Layout
24978 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
24981 \begin_layout Plain Layout
24982 \begin_inset Formula $Asin(x)+B$
24990 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
24993 \begin_layout Plain Layout
25001 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
25004 \begin_layout Plain Layout
25005 \begin_inset Formula $A\sin(x)+B$
25021 \begin_layout Standard
25022 The following functions are predefined:
25025 \begin_layout Standard
25026 \begin_inset VSpace -2mm
25032 \begin_layout Standard
25034 \begin_inset Tabular
25035 <lyxtabular version="3" rows="9" columns="4">
25036 <features tabularvalignment="middle">
25037 <column alignment="center" valignment="top" width="0pt">
25038 <column alignment="center" valignment="top" width="0pt">
25039 <column alignment="center" valignment="top" width="0pt">
25040 <column alignment="center" valignment="top" width="0pt">
25042 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
25045 \begin_layout Plain Layout
25051 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
25054 \begin_layout Plain Layout
25060 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
25063 \begin_layout Plain Layout
25069 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
25072 \begin_layout Plain Layout
25080 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
25083 \begin_layout Plain Layout
25091 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
25094 \begin_layout Plain Layout
25102 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
25105 \begin_layout Plain Layout
25113 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
25116 \begin_layout Plain Layout
25126 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
25129 \begin_layout Plain Layout
25137 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
25140 \begin_layout Plain Layout
25148 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
25151 \begin_layout Plain Layout
25159 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
25162 \begin_layout Plain Layout
25172 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
25175 \begin_layout Plain Layout
25183 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
25186 \begin_layout Plain Layout
25194 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
25197 \begin_layout Plain Layout
25205 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
25208 \begin_layout Plain Layout
25218 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
25221 \begin_layout Plain Layout
25229 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
25232 \begin_layout Plain Layout
25240 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
25243 \begin_layout Plain Layout
25251 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
25254 \begin_layout Plain Layout
25264 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
25267 \begin_layout Plain Layout
25275 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
25278 \begin_layout Plain Layout
25286 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
25289 \begin_layout Plain Layout
25297 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
25300 \begin_layout Plain Layout
25310 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
25313 \begin_layout Plain Layout
25321 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
25324 \begin_layout Plain Layout
25332 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
25335 \begin_layout Plain Layout
25343 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
25346 \begin_layout Plain Layout
25356 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
25359 \begin_layout Plain Layout
25367 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
25370 \begin_layout Plain Layout
25378 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
25381 \begin_layout Plain Layout
25389 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
25392 \begin_layout Plain Layout
25402 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
25405 \begin_layout Plain Layout
25413 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
25416 \begin_layout Plain Layout
25424 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
25427 \begin_layout Plain Layout
25435 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
25438 \begin_layout Plain Layout
25454 \begin_layout Standard
25455 They can also be inserted with the math toolbar button
25456 \begin_inset Graphics
25457 filename ../images/math/functions.png
25465 \begin_layout Subsection
25466 Self-defined Functions
25467 \begin_inset Index idx
25470 \begin_layout Plain Layout
25471 Functions ! self-defined
25479 \begin_layout Standard
25480 To use a function that is not predefined, like for example the sign function
25481 sgn(x), there are two possibilities:
25484 \begin_layout Itemize
25485 Define the function by inserting the following line to the LaTeX-preamble
25489 \begin_layout Plain Layout
25494 DeclareMathOperator
25497 \begin_inset CommandInset ref
25499 reference "sub:Self-defined-Operators"
25509 \begin_inset Newline newline
25513 \begin_inset VSpace -3mm
25517 \begin_inset Newline newline
25524 DeclareMathOperator{
25529 \begin_inset Index idx
25532 \begin_layout Plain Layout
25537 DeclareMathOperator
25543 \begin_inset Newline newline
25547 \begin_inset VSpace -2mm
25551 \begin_inset Newline newline
25554 Now the new defined function can be called with the command
25563 \begin_layout Itemize
25564 Write the formula as usual, mark the formula name, in our example the letters
25569 , and change it to mathematical text.
25570 At last a space is inserted between prefactor and function.
25573 \begin_layout Standard
25574 The result is the same with both methods as with a predefined function
25578 \begin_layout Plain Layout
25579 In LyX self-defined functions are displayed red, predefined ones black.
25587 \begin_layout Standard
25589 \begin_inset Tabular
25590 <lyxtabular version="3" rows="3" columns="2">
25591 <features tabularvalignment="middle">
25592 <column alignment="center" valignment="top" width="0pt">
25593 <column alignment="center" valignment="top" width="0pt">
25595 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
25598 \begin_layout Plain Layout
25604 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
25607 \begin_layout Plain Layout
25615 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
25618 \begin_layout Plain Layout
25626 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
25629 \begin_layout Plain Layout
25630 \begin_inset Formula $A\sgn(x)+B$
25640 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
25643 \begin_layout Plain Layout
25647 \begin_inset Formula $\underbrace{\textrm{sgn}}_{\textrm{Alt+M}\,\textrm{M}}$
25655 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
25658 \begin_layout Plain Layout
25659 \begin_inset Formula $A\,\textrm{sgn}(x)+B$
25675 \begin_layout Standard
25676 The first method is more suitable when the self-defined function should
25677 be used several times.
25680 \begin_layout Subsection
25682 \begin_inset Index idx
25685 \begin_layout Plain Layout
25694 \begin_layout Standard
25695 For limits there are defined besides
25702 \begin_inset Index idx
25705 \begin_layout Plain Layout
25725 furthermore the following functions:
25728 \begin_layout Standard
25730 \begin_inset Tabular
25731 <lyxtabular version="3" rows="5" columns="2">
25732 <features tabularvalignment="middle">
25733 <column alignment="center" valignment="top" width="0">
25734 <column alignment="center" valignment="top" width="0">
25736 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
25739 \begin_layout Plain Layout
25745 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
25748 \begin_layout Plain Layout
25750 \begin_inset Note Note
25753 \begin_layout Plain Layout
25760 is only used as spacer.
25772 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
25775 \begin_layout Plain Layout
25783 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
25786 \begin_layout Plain Layout
25787 \begin_inset Formula $\varliminf$
25797 <cell alignment="center" valignment="top" leftline="true" usebox="none">
25800 \begin_layout Plain Layout
25808 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
25811 \begin_layout Plain Layout
25812 \begin_inset Formula $\varlimsup$
25822 <cell alignment="center" valignment="top" leftline="true" usebox="none">
25825 \begin_layout Plain Layout
25833 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
25836 \begin_layout Plain Layout
25837 \begin_inset Formula $\varprojlim$
25847 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
25850 \begin_layout Plain Layout
25858 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
25861 \begin_layout Plain Layout
25862 \begin_inset Formula $\varinjlim$
25866 \begin_inset Formula $\raisebox{-2.5mm}{}$
25882 \begin_layout Standard
25883 \begin_inset VSpace medskip
25886 The limit is created by inserting a subscript.
25887 It is set right beside the function in an inline formula:
25890 \begin_layout Standard
25892 \begin_inset Tabular
25893 <lyxtabular version="3" rows="2" columns="2">
25894 <features tabularvalignment="middle">
25895 <column alignment="center" valignment="top" width="0pt">
25896 <column alignment="center" valignment="top" width="0pt">
25898 <cell alignment="center" valignment="top" usebox="none">
25901 \begin_layout Plain Layout
25907 <cell alignment="center" valignment="top" usebox="none">
25910 \begin_layout Plain Layout
25911 \begin_inset space \hspace{}
25916 \begin_inset Note Note
25919 \begin_layout Plain Layout
25926 are used here as spacer.
25938 <cell alignment="center" valignment="top" usebox="none">
25941 \begin_layout Plain Layout
25950 \begin_layout Plain Layout
25963 \begin_layout Plain Layout
25977 <cell alignment="center" valignment="top" usebox="none">
25980 \begin_layout Plain Layout
25981 \begin_inset Formula $\hspace{1cm}\raisebox{5mm}{}\lim_{x\to A}x=B$
25997 \begin_layout Standard
25998 In a displayed formula the limit is set below the formula, as usual:
25999 \begin_inset Formula
26009 \begin_layout Subsection
26011 \begin_inset Index idx
26014 \begin_layout Plain Layout
26015 Functions ! modulo-
26023 \begin_layout Standard
26024 The modulo-function is special, because it exists in four variants.
26025 The variants in a displayed formula are:
26026 \begin_inset Formula
26028 \underline{\textrm{Command}\raisebox{-0.9mm}{}} & & \underline{\textrm{Result}}\\
26029 \mathrm{a\backslash mod\textrm{\spce}b} & & a\mod b\\
26030 \mathrm{a\backslash pmod\textrm{\spce}b} & & a\pmod b\\
26031 \mathrm{a\backslash bmod\textrm{\spce}b} & & a\bmod b\\
26032 \mathrm{a\backslash pod\textrm{\spce}b} & & a\pod b
26040 \begin_layout Standard
26041 In an inline formula less space is set before the function names for all
26043 By default the modulo-functions take only the first following character
26045 To use more than one character, one has to put them into TeX-braces:
26046 \begin_inset Formula
26048 \underline{\textrm{Command}\raisebox{-0.9mm}{}} & & \underline{\textrm{Result}}\\
26049 \mathrm{a\backslash pod\textrm{\spce}bcd} & & a\pod bcd\\
26050 \mathrm{a\backslash pod\backslash\{bc\to d} & & a\pod{bc}d
26058 \begin_layout Section
26060 \begin_inset Index idx
26063 \begin_layout Plain Layout
26072 \begin_layout Subsection
26073 Special Characters in Mathematical Text
26076 \begin_layout Standard
26077 The following commands can only be used in mathematical text or in TeX-mode:
26080 \begin_layout Standard
26081 \begin_inset space \hfill{}
26085 \begin_inset Tabular
26086 <lyxtabular version="3" rows="8" columns="2">
26087 <features tabularvalignment="middle">
26088 <column alignment="block" valignment="top" width="0">
26089 <column alignment="block" valignment="top" width="0">
26091 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
26094 \begin_layout Plain Layout
26100 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
26103 \begin_layout Plain Layout
26111 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
26114 \begin_layout Plain Layout
26122 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
26125 \begin_layout Plain Layout
26126 \begin_inset Formula $\textrm{œ}$
26136 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
26139 \begin_layout Plain Layout
26147 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
26150 \begin_layout Plain Layout
26151 \begin_inset Formula $\textrm{Œ}$
26161 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
26164 \begin_layout Plain Layout
26172 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
26175 \begin_layout Plain Layout
26176 \begin_inset Formula $\textrm{æ}$
26186 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
26189 \begin_layout Plain Layout
26197 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
26200 \begin_layout Plain Layout
26201 \begin_inset Formula $\textrm{Æ}$
26211 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
26214 \begin_layout Plain Layout
26222 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
26225 \begin_layout Plain Layout
26226 \begin_inset Formula $\textrm{\aa}$
26236 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
26239 \begin_layout Plain Layout
26243 \begin_inset Index idx
26246 \begin_layout Plain Layout
26253 \begin_layout Plain Layout
26274 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
26277 \begin_layout Plain Layout
26278 \begin_inset Formula $\textrm{Å}$
26288 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
26291 \begin_layout Plain Layout
26299 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
26302 \begin_layout Plain Layout
26303 \begin_inset Formula $\textrm{ı}$
26317 \begin_inset space \hfill{}
26321 \begin_inset Tabular
26322 <lyxtabular version="3" rows="8" columns="2">
26323 <features tabularvalignment="middle">
26324 <column alignment="block" valignment="top" width="0">
26325 <column alignment="center" valignment="top" width="0">
26327 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
26330 \begin_layout Plain Layout
26332 \begin_inset Note Note
26335 \begin_layout Plain Layout
26337 \begin_inset space \thinspace{}
26340 mm is used for separation, because otherwise the output will be ¡ and ¿
26351 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
26354 \begin_layout Plain Layout
26362 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
26365 \begin_layout Plain Layout
26373 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
26376 \begin_layout Plain Layout
26377 \begin_inset Formula $\textrm{ø}$
26387 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
26390 \begin_layout Plain Layout
26398 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
26401 \begin_layout Plain Layout
26402 \begin_inset Formula $\textrm{Ø}$
26412 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
26415 \begin_layout Plain Layout
26423 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
26426 \begin_layout Plain Layout
26427 \begin_inset Formula $\textrm{ł}$
26437 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
26440 \begin_layout Plain Layout
26448 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
26451 \begin_layout Plain Layout
26452 \begin_inset Formula $\textrm{Ł}$
26462 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
26465 \begin_layout Plain Layout
26467 \begin_inset space \hspace{}
26475 \begin_layout Plain Layout
26489 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
26492 \begin_layout Plain Layout
26493 \begin_inset Formula $\textrm{!`}$
26503 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
26506 \begin_layout Plain Layout
26508 \begin_inset space \hspace{}
26516 \begin_layout Plain Layout
26530 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
26533 \begin_layout Plain Layout
26534 \begin_inset Formula $\textrm{?`}$
26544 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
26547 \begin_layout Plain Layout
26555 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
26558 \begin_layout Plain Layout
26559 \begin_inset Formula $\textrm{ȷ}$
26573 \begin_inset space \hfill{}
26579 \begin_layout Standard
26581 \begin_inset Formula $\textrm{\textrm{Å}}$
26585 \begin_inset Formula $\textrm{\textrm{Ø}}$
26588 can also be inserted via the math toolbar button
26589 \begin_inset Graphics
26590 filename ../images/math/digamma.png
26598 \begin_layout Standard
26599 An exception are the commands
26602 \begin_inset space \hspace{}
26611 \begin_inset space \hspace{}
26617 , because they can be inserted in LyX directly to text.
26620 \begin_layout Subsection
26622 \begin_inset CommandInset label
26624 name "sub:Accents-in-Text"
26629 \begin_inset Index idx
26632 \begin_layout Plain Layout
26641 \begin_layout Standard
26642 With the following commands all letters can be accented.
26643 The commands must be inserted in TeX-mode.
26646 \begin_layout Standard
26647 \begin_inset space \hfill{}
26651 \begin_inset Tabular
26652 <lyxtabular version="3" rows="8" columns="2">
26653 <features tabularvalignment="middle">
26654 <column alignment="block" valignment="top" width="0">
26655 <column alignment="block" valignment="top" width="0">
26657 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
26660 \begin_layout Plain Layout
26666 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
26669 \begin_layout Plain Layout
26677 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
26680 \begin_layout Plain Layout
26684 \begin_inset Quotes grd
26692 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
26695 \begin_layout Plain Layout
26699 \begin_layout Plain Layout
26715 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
26718 \begin_layout Plain Layout
26726 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
26729 \begin_layout Plain Layout
26733 \begin_layout Plain Layout
26749 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
26752 \begin_layout Plain Layout
26759 \begin_layout Plain Layout
26773 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
26776 \begin_layout Plain Layout
26780 \begin_layout Plain Layout
26796 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
26799 \begin_layout Plain Layout
26807 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
26810 \begin_layout Plain Layout
26814 \begin_layout Plain Layout
26830 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
26833 \begin_layout Plain Layout
26840 \begin_layout Plain Layout
26854 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
26857 \begin_layout Plain Layout
26861 \begin_layout Plain Layout
26877 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
26880 \begin_layout Plain Layout
26887 \begin_layout Plain Layout
26901 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
26904 \begin_layout Plain Layout
26908 \begin_layout Plain Layout
26924 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
26927 \begin_layout Plain Layout
26934 \begin_layout Plain Layout
26948 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
26951 \begin_layout Plain Layout
26955 \begin_layout Plain Layout
26975 \begin_inset space \hfill{}
26979 \begin_inset Tabular
26980 <lyxtabular version="3" rows="8" columns="2">
26981 <features tabularvalignment="middle">
26982 <column alignment="block" valignment="top" width="0">
26983 <column alignment="center" valignment="top" width="0">
26985 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
26988 \begin_layout Plain Layout
26994 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
26997 \begin_layout Plain Layout
27005 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
27008 \begin_layout Plain Layout
27015 \begin_layout Plain Layout
27029 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
27032 \begin_layout Plain Layout
27036 \begin_layout Plain Layout
27052 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
27055 \begin_layout Plain Layout
27063 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
27066 \begin_layout Plain Layout
27070 \begin_layout Plain Layout
27086 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
27089 \begin_layout Plain Layout
27093 \begin_inset Index idx
27096 \begin_layout Plain Layout
27107 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
27110 \begin_layout Plain Layout
27114 \begin_layout Plain Layout
27130 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
27133 \begin_layout Plain Layout
27141 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
27144 \begin_layout Plain Layout
27148 \begin_layout Plain Layout
27164 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
27167 \begin_layout Plain Layout
27174 \begin_layout Plain Layout
27188 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
27191 \begin_layout Plain Layout
27195 \begin_layout Plain Layout
27211 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
27214 \begin_layout Plain Layout
27221 \begin_layout Plain Layout
27235 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
27238 \begin_layout Plain Layout
27242 \begin_layout Plain Layout
27258 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
27261 \begin_layout Plain Layout
27268 \begin_layout Plain Layout
27282 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
27285 \begin_layout Plain Layout
27289 \begin_layout Plain Layout
27309 \begin_inset space \hfill{}
27315 \begin_layout Standard
27316 \begin_inset VSpace medskip
27325 also two different characters can be accented.
27334 \begin_layout Plain Layout
27349 \begin_layout Plain Layout
27361 \begin_layout Standard
27374 can in combination with vowels directly be inserted with the keyboard without
27376 The same applies for the tilde
27380 \begin_layout Plain Layout
27381 This only applies for keyboards where the tilde is defined as accent.
27390 in combination with
27405 \begin_layout Standard
27448 and accents that are inserted directly with the keyboard are also available
27449 in mathematical text.
27450 For the other accents there are special math commands to be used in formulas,
27452 \begin_inset CommandInset ref
27454 reference "sub:Accents-for-one"
27461 \begin_layout Standard
27462 \begin_inset VSpace bigskip
27465 Furthermore, with the command
27472 \begin_inset Index idx
27475 \begin_layout Plain Layout
27483 all numbers and letters can be set into a circle, quasi accented with a
27484 circle, similar to the copyright symbol.
27487 \begin_layout Standard
27489 \begin_inset Tabular
27490 <lyxtabular version="3" rows="3" columns="2">
27491 <features tabularvalignment="middle">
27492 <column alignment="center" valignment="top" width="0">
27493 <column alignment="center" valignment="top" width="0">
27495 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
27498 \begin_layout Plain Layout
27504 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
27507 \begin_layout Plain Layout
27509 \begin_inset Note Note
27512 \begin_layout Plain Layout
27519 is only used as spacer.
27531 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
27534 \begin_layout Plain Layout
27542 <cell multicolumn="1" alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
27545 \begin_layout Plain Layout
27549 \begin_layout Plain Layout
27565 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
27568 \begin_layout Plain Layout
27579 raisebox{-1.5pt}{W}}
27584 <cell multicolumn="1" alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
27587 \begin_layout Plain Layout
27588 \begin_inset Formula $\raisebox{4.5mm}{}$
27595 \begin_layout Plain Layout
27613 \begin_inset Formula $\raisebox{-2mm}{}$
27629 \begin_layout Standard
27630 One has to take care that the character fits in the circle.
27641 \begin_layout Plain Layout
27643 \begin_inset CommandInset ref
27645 reference "sub:Font-Sizes"
27654 specifies thereby the size of the circle.
27665 \begin_layout Plain Layout
27667 \begin_inset CommandInset ref
27669 reference "sub:Boxes-without-Frame"
27678 the character can be centered.
27681 \begin_layout Subsection
27683 \begin_inset Index idx
27686 \begin_layout Plain Layout
27695 \begin_layout Standard
27696 Old-style figures (also known as old-style numerals) are created with the
27704 \begin_inset Index idx
27707 \begin_layout Plain Layout
27716 The command can be used in formulas and in TeX-mode.
27717 The command scheme is:
27720 \begin_layout Standard
27725 oldstylenums{number}
27728 \begin_layout Standard
27733 oldstylenums{0123456789
27736 \begin_inset Formula $\oldstylenums{0123456789}$
27742 \begin_layout Subsection
27743 Miscellaneous special Characters
27744 \begin_inset CommandInset label
27746 name "sub:Miscellaneous-special-Characters"
27751 \begin_inset Index idx
27754 \begin_layout Plain Layout
27755 Special characters ! miscellaneous
27763 \begin_layout Standard
27764 The following characters can only be inserted to formulas by using commands:
27767 \begin_layout Standard
27769 \begin_inset Tabular
27770 <lyxtabular version="3" rows="4" columns="2">
27771 <features tabularvalignment="middle">
27772 <column alignment="center" valignment="top" width="0">
27773 <column alignment="center" valignment="top" width="0">
27775 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
27778 \begin_layout Plain Layout
27784 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
27787 \begin_layout Plain Layout
27795 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
27798 \begin_layout Plain Layout
27805 \begin_layout Plain Layout
27819 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
27822 \begin_layout Plain Layout
27823 \begin_inset Formula $\mathcircumflex$
27833 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
27836 \begin_layout Plain Layout
27844 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
27847 \begin_layout Plain Layout
27848 \begin_inset Formula $\_$
27858 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
27861 \begin_layout Plain Layout
27866 \begin_layout Plain Layout
27878 \begin_inset Index idx
27881 \begin_layout Plain Layout
27894 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
27897 \begin_layout Plain Layout
27898 \begin_inset Formula $^{\circ}$
27914 \begin_layout Standard
27915 The degree sign ° can nevertheless be directly inserted if the LaTeX-preamble
27916 contains the following line
27920 \begin_layout Plain Layout
27921 More about this is described in
27922 \begin_inset CommandInset ref
27924 reference "sub:Text-Characters-in"
27936 \begin_layout Standard
27941 DeclareInputtext{176}{
27954 \begin_layout Standard
27955 \begin_inset Newpage newpage
27961 \begin_layout Section
27963 \begin_inset CommandInset label
27965 name "sec:Formula-Styles"
27970 \begin_inset Index idx
27973 \begin_layout Plain Layout
27982 \begin_layout Itemize
27983 There are two different alignment styles:
27987 \begin_layout Description
27988 Centered is the predefined standard
27991 \begin_layout Description
27992 Indented for this the option
27996 must be inserted in the menu
27998 Document\SpecialChar \menuseparator
28004 \begin_inset space ~
28010 \begin_layout Standard
28015 is used, the indentation can be adjusted with the length
28022 \begin_inset Index idx
28025 \begin_layout Plain Layout
28034 Should the distance be 15
28035 \begin_inset space \thinspace{}
28038 mm, the following command line is inserted in the LaTeX-preamble
28041 \begin_layout Standard
28051 \begin_layout Standard
28052 When no length is specified, the predefined value of 30
28053 \begin_inset space \thinspace{}
28060 \begin_layout Itemize
28061 And two different numbering styles:
28065 \begin_layout Description
28066 Right is the predefined standard
28069 \begin_layout Description
28070 Left for this the option
28074 must be inserted in the menu
28076 Document\SpecialChar \menuseparator
28082 \begin_inset space ~
28089 \begin_layout Standard
28098 can also be used together.
28099 In this case both options are inserted, separated by a comma.
28102 \begin_layout Standard
28103 The chosen styles are used for all displayed formulas of the document.
28104 When both, centered and indented formulas should be created in a document,
28110 The indented formulas are then set in a flalign environment, see
28111 \begin_inset CommandInset ref
28113 reference "sub:Flalign-Environment"
28120 \begin_layout Section
28122 \begin_inset CommandInset label
28124 name "sec:Multiline-Formulas"
28129 \begin_inset Index idx
28132 \begin_layout Plain Layout
28133 Formula ! multiline
28141 \begin_layout Subsection
28145 \begin_layout Standard
28146 In LyX multiline formulas are created by pressing
28151 arg "newline-insert newline"
28157 This creates either an
28159 eqnarray environment
28161 that is described in
28162 \begin_inset CommandInset ref
28164 reference "sub:Eqnarray-Environment"
28168 or, when the option
28170 Use AMS math package
28172 in the document settings is selected, an
28176 that is described in
28177 \begin_inset CommandInset ref
28179 reference "sub:Standard-align-Environment"
28186 \begin_layout Standard
28187 There are other multiline formula environments that can be created via the
28190 Insert\SpecialChar \menuseparator
28194 These environments are described in the following sections.
28197 \begin_layout Standard
28198 In all multiline formula environments a new line is created by pressing
28202 arg "newline-insert newline"
28206 To add or delete lines, the math toolbar buttons
28207 \begin_inset Graphics
28208 filename ../images/tabular-feature_append-row.png
28214 \begin_inset Graphics
28215 filename ../images/tabular-feature_delete-row.png
28220 , respectively, or the menu
28222 Edit\SpecialChar \menuseparator
28228 \begin_layout Subsubsection
28230 \begin_inset CommandInset label
28232 name "sub:Line-Separation"
28237 \begin_inset Index idx
28240 \begin_layout Plain Layout
28241 Formula ! multiline ! Line separation
28249 \begin_layout Standard
28250 There is sometimes not enough space in multiline formulas between the lines:
28251 \begin_inset Formula
28253 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}\\
28254 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
28262 \begin_layout Standard
28263 In LaTeX additional line space is specified as optional argument of the
28265 This is not yet possible in LyX
28269 \begin_layout Plain Layout
28271 \begin_inset CommandInset href
28273 name "LyX-bug #1505"
28274 target "http://www.lyx.org/trac/ticket/1505"
28283 , therefore the whole formula must be inserted in TeX-mode.
28284 To add in our example space, the command
28292 is inserted at the end of the first line.
28297 \begin_layout Plain Layout
28304 \begin_layout Plain Layout
28306 B^{2}(B^{2}-2r_{g}^{2}+2x_{0}^{2}-2r_{k}^{2})+4x_{0}^{2}x^{2}+4x_{0}xD &
28309 textrm{-}4x^{2}B^{2}+4x_{0}xB^{2}
28316 \begin_layout Plain Layout
28320 left(B^{2}+x_{0}^{2}
28328 left(B^{2}-2r_{g}^{2}+2x_{0}^{2}-2r_{k}^{2}
28333 \begin_layout Plain Layout
28345 \begin_layout Standard
28346 \begin_inset VSpace bigskip
28349 To set the line separation for all lines in a formula, the length
28356 \begin_inset Index idx
28359 \begin_layout Plain Layout
28369 \begin_inset Formula $\mbox{line separation}=\mathrm{6\, pt+\backslash jot}$
28380 \begin_inset space \thinspace{}
28385 \begin_inset space \thinspace{}
28388 mm additional line separation as in the previous example, the command
28391 \begin_layout Standard
28401 \begin_layout Standard
28402 is inserted in TeX-mode before the formula.
28403 This requires that the LaTeX-package
28411 \begin_layout Plain Layout
28416 is part of every LaTeX standard installation.
28422 \begin_inset Index idx
28425 \begin_layout Plain Layout
28431 was loaded in LaTeX-preamble with the line
28434 \begin_layout Standard
28442 \begin_layout Standard
28447 \begin_layout Plain Layout
28459 \begin_inset Formula
28461 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}\\
28462 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
28470 \begin_layout Standard
28474 \begin_layout Plain Layout
28485 To get back to the predefined distance,
28491 is set to the value 3
28492 \begin_inset space \thinspace{}
28498 \begin_layout Subsubsection
28500 \begin_inset CommandInset label
28502 name "sub:Column-Separation"
28507 \begin_inset Index idx
28510 \begin_layout Plain Layout
28511 Formula ! multiline ! Column separation
28519 \begin_layout Standard
28520 Multiline formulas form a matrix.
28521 A formula in the eqnarray environment is for example a matrix with three
28523 By changing the column separation in this environment, the space beside
28524 the relation sign can be changed.
28527 \begin_layout Standard
28528 The column separation is specified with the length
28535 \begin_inset Index idx
28538 \begin_layout Plain Layout
28547 \begin_inset Newline newline
28550 column separation = 2
28551 \begin_inset space \thinspace{}
28561 \begin_inset Newline newline
28567 \begin_layout Standard
28577 \begin_layout Standard
28578 inserted in TeX-mode, sets for all following formulas a column separation
28580 \begin_inset space \thinspace{}
28584 To get back to the predefined distance,
28591 \begin_inset space \thinspace{}
28597 \begin_layout Standard
28599 \begin_inset space \thinspace{}
28602 cm column separation:
28606 \begin_layout Plain Layout
28618 \begin_inset Formula
28626 A formula with the predefined column separation for matrices of 10
28627 \begin_inset space \thinspace{}
28634 \begin_layout Plain Layout
28646 \begin_inset Formula
28657 \begin_layout Subsubsection
28659 \begin_inset Index idx
28662 \begin_layout Plain Layout
28671 \begin_layout Standard
28672 Long formulas can be typeset using these methods:
28675 \begin_layout Itemize
28676 When one side of the equation is much shorther than the line width, this
28677 one is chosen for the left side and the right side is typeset over two
28679 \begin_inset Formula
28681 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 \\
28682 & & -\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}
28687 The minus sign at the beginning of the second line does normally not appear
28688 as operator because it is the first character of the line.
28689 Thus it would not be surrounded by space and could not be distinguished
28690 from the fraction bar.
28692 \begin_inset space \thinspace{}
28695 pt space was inserted behind the minus sign with the command
28705 \begin_layout Plain Layout
28713 \begin_inset CommandInset ref
28715 reference "sub:Variable-Space"
28725 \begin_inset Index idx
28728 \begin_layout Plain Layout
28739 \begin_layout Itemize
28740 When both sides of the equation are too long, the command
28747 \begin_inset Index idx
28750 \begin_layout Plain Layout
28759 It is inserted to the first column of the first line and effects that all
28760 further insertions overwrite the following columns:
28761 \begin_inset Formula
28763 \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 \\
28764 & & -\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 \\
28765 & & =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}
28770 After the insertion of
28776 , the cursor is in a purple box that is a bit shifted to the left from the
28778 In this the formula is inserted.
28779 \begin_inset Newline newline
28782 The content of the further lines is inserted to the second or another formula
28784 The greater the column number where it was inserted, the larger the indentation.
28785 \begin_inset VSpace medskip
28789 \begin_inset Newline newline
28793 \begin_inset Note Greyedout
28796 \begin_layout Plain Layout
28797 Note the following when using
28806 \begin_layout Itemize
28807 The formula doesn't use the full page width.
28809 \begin_inset space \thinspace{}
28813 \begin_inset space \space{}
28817 \begin_inset Formula $-B^{2}$
28820 is added to the first line in the above example, it would have been outside
28822 To better use the width, negative space can be inserted at the beginning
28826 \begin_layout Itemize
28827 Due to a bug in LyX the cursor cannot be set with the mouse into the first
28832 \begin_layout Plain Layout
28833 \begin_inset CommandInset href
28835 name "LyX-bug #1429"
28836 target "http://www.lyx.org/trac/ticket/1429"
28845 One can only set the cursor at the beginning of the line and move it with
28854 \begin_layout Itemize
28855 Other methods to set long formulas are offered by the environments described
28857 \begin_inset CommandInset ref
28859 reference "sub:Multline-Environment"
28864 \begin_inset CommandInset ref
28866 reference "sub:Multiline-Formula-Parts"
28873 \begin_layout Subsubsection
28875 \begin_inset CommandInset label
28877 name "sub:Multiline-Brackets"
28882 \begin_inset Index idx
28885 \begin_layout Plain Layout
28886 Brackets ! for multiline expressions
28894 \begin_layout Standard
28895 For brackets spanning multiple lines the following problem occurs:
28896 \begin_inset Formula
28898 A & = & \sin(x)\left[\prod_{R=1}^{\infty}\frac{1}{R}+\cdots\right.\\
28899 & & \left.\cdots+B-D\right]
28907 \begin_layout Standard
28908 The closing bracket is smaller than the opening bracket because brackets
28909 with variable size may not span multiple lines.
28912 \begin_layout Standard
28913 To set the bracket size for the second line correctly, the first line is
28921 \begin_inset Index idx
28924 \begin_layout Plain Layout
28932 and the second line with
28940 \begin_layout Plain Layout
28954 \begin_inset CommandInset ref
28956 reference "sub:Automatic-Bracket-Size"
28968 \begin_inset Index idx
28971 \begin_layout Plain Layout
28997 \begin_layout Plain Layout
29016 \begin_layout Plain Layout
29035 \begin_layout Plain Layout
29047 \begin_inset Formula $\downarrow$
29053 \begin_inset Index idx
29056 \begin_layout Plain Layout
29064 is inserted, because the multiplication operator with its limits is the
29065 largest symbol in the first line and this should be the size for the bracket
29066 in the second line.
29069 \begin_layout Standard
29070 The result is this:
29071 \begin_inset Formula
29073 A & = & \sin(x)\left[\prod_{R=1}^{\infty}\frac{1}{R}+\cdots\right.\\
29074 & & \left.\vphantom{\prod_{R=1}^{\infty}}\cdots+B-D\right]
29082 \begin_layout Subsection
29086 \begin_layout Standard
29087 Align environments can be used for every kind of multiline formulas.
29088 They are specially useful to set several formulas side by side.
29091 \begin_layout Standard
29092 Align environments consist of columns.
29093 The odd columns are right aligned, the even ones left aligned.
29094 Every line in an Align environment can be numbered.
29097 \begin_layout Standard
29098 Align environments are created via the menu
29100 Insert\SpecialChar \menuseparator
29106 Edit\SpecialChar \menuseparator
29107 Math\SpecialChar \menuseparator
29108 Change Formula Type
29110 already existing formulas can be converted to Align environments.
29113 \begin_layout Standard
29114 To add or delete columns, the math toolbar buttons
29115 \begin_inset Graphics
29116 filename ../images/tabular-feature_append-column.png
29122 \begin_inset Graphics
29123 filename ../images/tabular-feature_delete-column.png
29128 , respectively, or the menu
29130 Edit\SpecialChar \menuseparator
29136 \begin_layout Subsubsection
29137 Standard align Environment
29138 \begin_inset CommandInset label
29140 name "sub:Standard-align-Environment"
29145 \begin_inset Index idx
29148 \begin_layout Plain Layout
29149 Formula ! multiline ! align environment
29157 \begin_layout Standard
29158 This Align environment is created by presssing
29161 arg "newline-insert newline"
29164 in a formula or by the menu
29166 Insert\SpecialChar \menuseparator
29167 Math\SpecialChar \menuseparator
29168 AMS align Environment
29173 \begin_layout Standard
29174 An example for two formulas set side by side, that are created with a four
29175 column align environment:
29176 \begin_inset Formula
29178 A & =\sin(B) & C & =D\\
29179 C & \ne A & B & \ne D
29184 As it can be seen, the formulas in this environment are placed so as if
29193 \begin_layout Plain Layout
29201 \begin_inset CommandInset ref
29203 reference "sub:Variable-Space"
29214 before the first and after every even column.
29215 When the formula style
29221 \begin_layout Plain Layout
29223 \begin_inset CommandInset ref
29225 reference "sec:Formula-Styles"
29236 is used, the formula is set without the
29242 before the first column.
29245 \begin_layout Subsubsection
29246 Alignat Environment
29247 \begin_inset Index idx
29250 \begin_layout Plain Layout
29251 Formula ! multiline ! alignat environment
29259 \begin_layout Standard
29260 The alignat environment has no predefined column separation.
29261 It can be inserted manually with the spaces that are described
29262 \begin_inset CommandInset ref
29264 reference "sub:Space"
29271 \begin_layout Standard
29272 The above example in the alignat environment where 1
29273 \begin_inset space \thinspace{}
29276 cm space was inserted at the beginning of the second formula:
29277 \begin_inset Formula
29278 \begin{alignat*}{2}
29279 A & =\sin(B) & \hspace{1cm}C & =D\\
29280 C & \ne A & B & \ne D
29285 Because the column separation can be set separately for every column, this
29286 environment is especially suitable to set three and more formulas side
29290 \begin_layout Subsubsection
29291 Flalign Environment
29292 \begin_inset CommandInset label
29294 name "sub:Flalign-Environment"
29299 \begin_inset Index idx
29302 \begin_layout Plain Layout
29303 Formula ! multiline ! flalign environment
29311 \begin_layout Standard
29312 In this environment the first two columns are always set as much as possible
29313 to the left and the last two ones to the right.
29315 \begin_inset Formula
29317 A & =1 & B & =2 & C & =3\\
29318 X & =\textrm{-}1 & Y & =\textrm{-}2 & Z & =4
29326 \begin_layout Standard
29327 By creating a flalign environment with an odd number of columns where an
29328 empty TeX-brace is inserted to the last column, several formulas in a document
29329 can be set to the left, although the formula style
29334 As example the indented formula
29335 \begin_inset CommandInset ref
29337 reference "eq:VolInt"
29342 \begin_inset Formula
29344 \hspace{30pt}\iiint\limits _{V}X\,\mathrm{d}V & =U & {}
29349 The first two columns contain the formula.
29350 To indent it as with the formula style
29355 \begin_inset space \thinspace{}
29358 pt space was inserted at the beginning of the first column.
29361 \begin_layout Subsection
29362 Eqnarray Environment
29363 \begin_inset CommandInset label
29365 name "sub:Eqnarray-Environment"
29370 \begin_inset Index idx
29373 \begin_layout Plain Layout
29374 Formula ! multiline ! eqnarray environment
29382 \begin_layout Standard
29383 When this environment has been created, three blue boxes appear.
29384 The content of the first box is right aligned, the content of the last
29386 The content of the middle box appears centered and a bit smaller, because
29387 it is designed to insert there only relation characters.
29388 \begin_inset Formula
29390 \frac{ABC}{D} & \frac{ABC}{D} & \frac{ABC}{D}\\
29400 \begin_layout Subsection
29402 \begin_inset Index idx
29405 \begin_layout Plain Layout
29406 Formula ! multiline ! gather environment
29414 \begin_layout Standard
29415 This environment consists of only one centered column.
29416 Every line can be numbered.
29417 \begin_inset Formula
29428 \begin_layout Subsection
29429 Multline Environment
29430 \begin_inset CommandInset label
29432 name "sub:Multline-Environment"
29437 \begin_inset Index idx
29440 \begin_layout Plain Layout
29441 Formula ! multiline ! multline environment
29449 \begin_layout Standard
29450 The multline environment consists, like the gather environment, of only
29452 But the first line is left aligned, the last one right aligned.
29453 All other lines are centered.
29454 Therefore this environment is suitable for long formulas.
29456 \begin_inset CommandInset ref
29458 reference "eq:lefteqn"
29462 in the multline environment:
29463 \begin_inset Formula
29465 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}\\
29466 -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}\\
29467 =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}}
29475 \begin_layout Standard
29476 In the output only the last (first) line of a multline environment appears
29477 numbered when the document numbering is right (left).
29481 \begin_layout Plain Layout
29482 numbering styles see
29483 \begin_inset CommandInset ref
29485 reference "sec:Formula-Styles"
29497 \begin_layout Standard
29505 \begin_inset Index idx
29508 \begin_layout Plain Layout
29523 \begin_inset Index idx
29526 \begin_layout Plain Layout
29534 a centered line can be right or left aligned, respectively.
29535 The commands are used as follows:
29538 \begin_layout Standard
29543 shoveright{line content}
29549 shoveleft{line content}
29552 \begin_layout Standard
29553 \begin_inset VSpace medskip
29563 \begin_inset Index idx
29566 \begin_layout Plain Layout
29574 specifies the distance of the first line from the left page margin.
29575 Predefined is the length 0
29576 \begin_inset space \thinspace{}
29582 \begin_layout Standard
29583 As example the above formula where the command
29586 \begin_layout Standard
29596 \begin_layout Standard
29597 was inserted in TeX-mode before:
29601 \begin_layout Plain Layout
29613 \begin_inset Formula
29615 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}\\
29616 \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}}\\
29617 =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}}
29626 \begin_layout Plain Layout
29637 The second line was left aligned using
29646 \begin_layout Subsection
29647 Multiline Formula Parts
29648 \begin_inset CommandInset label
29650 name "sub:Multiline-Formula-Parts"
29655 \begin_inset Index idx
29658 \begin_layout Plain Layout
29659 Formula ! multiline ! formula parts
29667 \begin_layout Standard
29668 To display only parts of a formula with multiple lines, one of the following
29669 environments are used:
29686 They can be inserted via the menu
29688 Insert\SpecialChar \menuseparator
29691 or by using the commands described in this section.
29694 \begin_layout Standard
29695 The first three have the same properties as the corresponding multiline
29696 formula environments, but it is possible to set further formula parts beside
29699 \begin_inset Formula
29701 \left.\begin{aligned}\Delta x\Delta p & \ge\frac{\hbar}{2}\\
29702 \Delta E\Delta t & \ge\frac{\hbar}{2}
29704 \right\} \textrm{Uncertainty relations}
29712 \begin_layout Standard
29713 To get this formula, a displayed formula is created where the command
29720 \begin_inset Index idx
29723 \begin_layout Plain Layout
29732 A purple box appears around the blue formula box where now columns and
29733 lines can be added.
29734 Outside the multiline environment other formula parts can be set, like
29738 \begin_layout Standard
29739 The aligned environment is also suitable for long formulas whose lines are
29740 horizontally aligned.
29741 Using aligned in a displayed formula has the advantage that the formula
29742 number is vertically centered behind the lines.
29744 \begin_inset CommandInset ref
29746 reference "eq:shortlong"
29750 in the aligned environment:
29751 \begin_inset Formula
29753 \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}|}\\
29754 & -\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}|}
29763 \begin_layout Standard
29764 To use the environments
29783 \begin_inset Index idx
29786 \begin_layout Plain Layout
29801 \begin_inset Index idx
29804 \begin_layout Plain Layout
29819 \begin_inset Index idx
29822 \begin_layout Plain Layout
29830 are inserted, respectively.
29831 The split environment has the same properties as the aligned environment
29832 but it can only have two columns.
29835 \begin_layout Subsection
29836 Text in multiline Formulas
29837 \begin_inset CommandInset label
29839 name "sub:Text-in-multiline"
29844 \begin_inset Index idx
29847 \begin_layout Plain Layout
29854 \begin_inset Index idx
29857 \begin_layout Plain Layout
29858 Formula ! multiline ! text
29866 \begin_layout Standard
29867 In the Align environments, and the multline and gather environment, text
29868 can be inserted that will appear in a separate line and doesn't affect
29869 the column alignment.
29870 To do this, the command
29877 \begin_inset Index idx
29880 \begin_layout Plain Layout
29888 is used in the following scheme:
29891 \begin_layout Standard
29899 \begin_layout Standard
29900 The text should not be longer than a line because it cannot be hyphenated.
29901 As LyX doesn't yet support
29907 directly, the text is written as mathematical text.
29914 must hereby be at the beginning of a line and appears in the output above
29916 An example where the text was inserted at the beginning of the second line:
29917 \begin_inset Formula
29919 I & =a\sqrt{2}\int_{0}^{2\pi}\sqrt{1+\cos(\phi)}\;\mathrm{d}\phi\\
29920 \intertext{\text{integrand is symmetric to \ensuremath{\phi=\pi}, therefore}} & =2a\sqrt{2}\int_{0}^{\pi}\sqrt{1+\cos(\phi)}\;\mathrm{d}\phi
29928 \begin_layout Standard
29929 \begin_inset Newpage newpage
29935 \begin_layout Section
29937 \begin_inset Index idx
29940 \begin_layout Plain Layout
29947 \begin_inset Index idx
29950 \begin_layout Plain Layout
29951 Formula ! numbering|see
29955 \begin_layout Plain Layout
29966 \begin_layout Plain Layout
29981 \begin_layout Subsection
29985 \begin_layout Standard
29986 Numbered formulas can be created with the menu
29988 Insert\SpecialChar \menuseparator
29989 Math\SpecialChar \menuseparator
29991 \begin_inset space ~
29999 \begin_inset space ~
30005 Existing formulas can be numbered with the menu
30007 Edit\SpecialChar \menuseparator
30008 Math\SpecialChar \menuseparator
30010 \begin_inset space ~
30018 arg "math-number-toggle"
30022 The formula number is displayed in LyX behind the formula as number sign
30024 The number sign is replaced in the output by the formula number.
30027 \begin_layout Standard
30028 When numbering is turned on in multiline formulas, all lines will be numbered.
30029 But the numbering can be controlled with the menu
30031 Edit\SpecialChar \menuseparator
30032 Math\SpecialChar \menuseparator
30034 \begin_inset space ~
30038 \begin_inset space ~
30042 \begin_inset space ~
30050 arg "math-number-line-toggle"
30056 \begin_layout Standard
30057 Except for inline formulas, all formulas can be numbered with two different
30059 \begin_inset CommandInset ref
30061 reference "sec:Formula-Styles"
30068 \begin_layout Subsection
30070 \begin_inset Index idx
30073 \begin_layout Plain Layout
30074 Cross-references ! to formulas
30082 \begin_layout Standard
30083 All labeled formulas can be cross-referenced.
30084 A label is added by the menu
30086 Insert\SpecialChar \menuseparator
30089 or the toolbar button
30090 \begin_inset Graphics
30091 filename ../images/label-insert.png
30097 The cursor must hereby be inside a displayed formula.
30098 A dialog pops up displaying the prefix
30103 The label is inserted there behind the prefix.
30104 The predefined prefix means
30105 \begin_inset Quotes eld
30109 \begin_inset Quotes erd
30112 and makes it easier to find labels in large documents because it marks
30113 it as formula label to divide it from e.
30114 \begin_inset space \thinspace{}
30118 \begin_inset space \space{}
30122 To change a label, the menu
30124 Insert\SpecialChar \menuseparator
30130 \begin_layout Standard
30131 The name of the label is displayed in LyX within two parentheses behind
30133 A formula with a label is always numbered.
30136 \begin_layout Standard
30137 Cross-references are inserted via the menu
30139 Insert\SpecialChar \menuseparator
30142 or with the toolbar button
30143 \begin_inset Graphics
30144 filename ../images/dialog-show-new-inset_ref.png
30150 A formula cross-reference appears in the output as formula number.
30151 When in the cross-reference dialog window the format
30155 is chosen, the cross-reference appears in the output as formula number
30157 \begin_inset Newline newline
30160 By right-clicking on a cross-reference in LyX, one jumps to the formula
30161 that is referenced.
30164 \begin_layout Standard
30165 Here are as examples cross-references to formulas of the following subsections:
30166 \begin_inset Note Note
30169 \begin_layout Plain Layout
30170 Note the different cross-reference types.
30178 \begin_layout Standard
30180 \begin_inset CommandInset ref
30187 \begin_inset CommandInset ref
30195 \begin_inset CommandInset ref
30201 ) big Latin letters are used for the numbering in contrary to (
30202 \begin_inset CommandInset ref
30211 \begin_layout Standard
30212 \begin_inset VSpace medskip
30215 When the argument of
30223 \begin_layout Plain Layout
30231 \begin_inset CommandInset ref
30233 reference "sub:User-defined-Numbering"
30244 contains a box like in
30245 \begin_inset CommandInset ref
30247 reference "sub:Paragraph-Boxes"
30251 , the formula cannot be referenced.
30254 \begin_layout Subsection
30256 \begin_inset Index idx
30259 \begin_layout Plain Layout
30260 Formula numbering ! subnumbering
30268 \begin_layout Standard
30269 With the help of the commands
30273 begin{subequations}
30281 formulas can be subnumbered.
30282 Both commands are inserted in TeX-mode.
30285 \begin_layout Standard
30287 \begin_inset Formula
30298 \begin_layout Plain Layout
30302 addtocounter{equation}{-1}
30311 \begin_layout Plain Layout
30315 begin{subequations}
30321 \begin_inset VSpace -5mm
30325 \begin_inset Formula
30333 \begin_inset Formula
30343 \begin_layout Standard
30347 \begin_layout Plain Layout
30359 \begin_layout Standard
30360 To create the example, the following is done:
30363 \begin_layout Enumerate
30364 first formula is inserted
30367 \begin_layout Enumerate
30372 addtocounter{equation}{-1}
30374 begin{subequations}
30375 \begin_inset Index idx
30378 \begin_layout Plain Layout
30387 \begin_inset Newline newline
30392 is inserted after the first formula
30395 \begin_layout Enumerate
30396 second formula is inserted
30399 \begin_layout Enumerate
30400 third formula is inserted
30403 \begin_layout Enumerate
30410 is inserted after the third formula
30413 \begin_layout Standard
30414 Every formula between the commands
30426 is subnumbered as a, b,
30427 \begin_inset Newline linebreak
30430 c, \SpecialChar \ldots{}
30431 For multiline formulas every line will be subnumbered.
30432 All subnumbered formulas are treated as
30437 But as every numbered formula increases the counter
30441 by one, the command
30447 is needed to decrease it.
30448 Otherwise the formulas
30449 \begin_inset CommandInset ref
30456 \begin_inset CommandInset ref
30463 \begin_inset CommandInset ref
30469 would be numbered as
30470 \begin_inset CommandInset ref
30477 \begin_inset CommandInset ref
30484 \begin_inset CommandInset ref
30493 \begin_layout Standard
30494 By inserting the commands in TeX-mode, a space is created between the first
30497 \begin_inset space \thinspace{}
30500 mm vertical space is inserted after the command
30504 begin{subequations}
30507 When the formula style
30513 \begin_layout Plain Layout
30515 \begin_inset CommandInset ref
30517 reference "sec:Formula-Styles"
30529 \begin_inset space \thinspace{}
30532 mm space is inserted instead.
30535 \begin_layout Standard
30536 Here is an example for a multiline formula where the numbering was turned
30537 off for the second line:
30541 \begin_layout Plain Layout
30545 begin{subequations}
30551 \begin_inset Formula
30553 A & = & (B-Z)^{2}=(B-Z)(B-Z)\label{eq:d}\\
30554 & = & B^{2}-ZB-BZ+Z^{2}\nonumber \\
30555 & = & B^{2}-2BZ+Z^{2}\label{eq:f}
30564 \begin_layout Plain Layout
30576 \begin_layout Subsection
30577 User-defined Numbering
30578 \begin_inset CommandInset label
30580 name "sub:User-defined-Numbering"
30585 \begin_inset Index idx
30588 \begin_layout Plain Layout
30589 Formula numbering ! user-defined
30597 \begin_layout Standard
30598 \begin_inset Index idx
30601 \begin_layout Plain Layout
30602 Formula numbering ! self-defined delimiters
30607 With the standard numbering parentheses are set around the formula number.
30608 To replace the parentheses for example by vertical bars, the following
30609 line is added to the LaTeX-preamble:
30612 \begin_layout Standard
30624 \begin_inset Note Note
30627 \begin_layout Plain Layout
30628 This macro is already declared in the LaTeX-preamble for testing.
30629 To activate it, remove the percent sign at the beginning.
30637 \begin_layout Standard
30638 To use other characters, the vertical bars besides the
30642 are replaced by one ore more characters.
30643 To get only the formula number the vertical bars are omitted.
30646 \begin_layout Standard
30647 \begin_inset VSpace bigskip
30650 When there should be an expression of your choice instead of the consecutive
30651 formula number in parentheses behind the formula, the command
30658 \begin_inset Index idx
30661 \begin_layout Plain Layout
30670 \begin_inset Formula
30672 A+B=C\tag{something}\label{eq:tag}
30677 In this example the command
30685 \begin_layout Plain Layout
30696 was inserted to the formula.
30699 \begin_layout Standard
30708 \begin_layout Plain Layout
30719 is inserted instead, the star prevents the parentheses around the expression:
30720 \begin_inset Formula
30722 A+B=C\tag*{something}
30730 \begin_layout Standard
30731 \begin_inset VSpace bigskip
30734 To restart the formula numbering with new document parts or sections, the
30735 following command is used:
30738 \begin_layout Standard
30743 @addtoreset{equation}{part}
30746 \begin_inset Index idx
30749 \begin_layout Plain Layout
30754 \begin_layout Plain Layout
30765 \begin_layout Plain Layout
30778 \begin_layout Plain Layout
30789 \begin_layout Plain Layout
30802 \begin_inset Newline newline
30806 \begin_inset Newline newline
30813 @addtoreset{equation}{section}
30816 \begin_layout Standard
30817 To be able to use these commands in TeX-mode, the
30818 \begin_inset Quotes eld
30822 \begin_inset Quotes erd
30825 character has to be made
30826 \begin_inset Quotes eld
30830 \begin_inset Quotes erd
30833 for LaTeX using the command
30847 So the command sequence in TeX-mode is:
30850 \begin_layout Standard
30856 \begin_inset Newline newline
30861 @addtoreset{equation}{section}
30862 \begin_inset Newline newline
30870 \begin_layout Standard
30871 In the LaTeX-preamble
30883 can be omitted as they are automatically internally inserted by LyX.
30886 \begin_layout Standard
30901 \begin_layout Plain Layout
30906 is part of the LaTeX-package
30911 \begin_inset Index idx
30914 \begin_layout Plain Layout
30915 Packages ! carlisle
30920 that is part of every LaTeX standard installation.
30926 \begin_inset Index idx
30929 \begin_layout Plain Layout
30930 Packages ! remreset
30935 has to be loaded in the LaTeX-preamble with the line
30938 \begin_layout Standard
30943 usepackage{remreset}
30946 \begin_layout Standard
30954 \begin_inset Index idx
30957 \begin_layout Plain Layout
30962 \begin_layout Plain Layout
30973 \begin_layout Plain Layout
30986 \begin_layout Plain Layout
30997 \begin_layout Plain Layout
31009 can be used with the same scheme as
31018 \begin_layout Standard
31019 \begin_inset VSpace bigskip
31022 Sometimes formulas should be numbered in the following form:
31025 \begin_layout Standard
31028 (section number.formula number)
31031 \begin_layout Standard
31032 The formula number should start with every section with
31033 \begin_inset Quotes eld
31037 \begin_inset Quotes erd
31043 \begin_layout Standard
31044 For this case there is the command
31051 \begin_inset Index idx
31054 \begin_layout Plain Layout
31062 , which is used with the following scheme:
31065 \begin_layout Standard
31070 numberwithin{counter}{sectioning}
31073 \begin_layout Standard
31074 Counter denotes what kind of numbering is affected, sectioning denotes what
31075 number is before the dot.
31078 \begin_layout Standard
31079 Thus in our case the following LaTeX-preamble or TeX code line is used:
31082 \begin_layout Standard
31087 numberwithin{equation}{section}
31090 \begin_layout Standard
31091 This is the result:
31095 \begin_layout Plain Layout
31099 numberwithin{equation}{section}
31105 \begin_inset Formula
31115 \begin_layout Standard
31117 \begin_inset space \thinspace{}
31121 \begin_inset space \space{}
31124 tables so that the number of the part is the sectioning,
31125 \begin_inset Newline newline
31132 numberwithin{table}{part}
31137 \begin_layout Standard
31138 To go back to the standard numbering or to prevent this kind of numbering
31139 when it is defined by the document class, the following command is inserted
31140 as TeX code or to the LaTeX-preamble:
31143 \begin_layout Standard
31153 \begin_inset Index idx
31156 \begin_layout Plain Layout
31170 \begin_layout Plain Layout
31186 \begin_inset Newline newline
31194 \begin_inset Newline newline
31206 \begin_layout Standard
31213 uses internally the command
31219 , described above, that also needs to be reverted.
31223 \begin_layout Plain Layout
31230 \begin_layout Plain Layout
31234 @removefromreset{equation}{section}
31237 \begin_layout Plain Layout
31249 \begin_layout Subsection
31250 Numbering with Roman Numbers and Letters
31251 \begin_inset Index idx
31254 \begin_layout Plain Layout
31255 Formula numbering ! with letters
31261 \begin_inset Index idx
31264 \begin_layout Plain Layout
31265 Formula numbering ! with Roman numbers
31273 \begin_layout Standard
31274 Formulas can also be numbered with Roman numbers and Latin letters.
31275 To number for example with small Roman numbers, the command
31278 \begin_layout Standard
31290 \begin_layout Standard
31291 is inserted before the formula in TeX-mode.
31299 \begin_inset Index idx
31302 \begin_layout Plain Layout
31310 redefines the predefined command
31326 \begin_layout Plain Layout
31333 has the same scheme like the command
31339 that is described in
31340 \begin_inset CommandInset ref
31342 reference "sub:The-Command-newcommand"
31355 is the formula counter.
31362 is used as prefix for a counter, the value of the counter is output as
31364 When a formula is numbered, LaTeX sets internally the command
31370 behind the formula.
31376 \begin_inset Index idx
31379 \begin_layout Plain Layout
31389 outputs the counter as small Roman number.
31392 \begin_layout Standard
31393 All formulas behind the command
31403 are now numbered Roman.
31404 To switch to numbering with big Roman numbers, the command is inserted
31418 \begin_inset Index idx
31421 \begin_layout Plain Layout
31433 \begin_inset Quotes eld
31437 \begin_inset Quotes erd
31440 with small Latin letters there is the command
31447 \begin_inset Index idx
31450 \begin_layout Plain Layout
31458 , for big ones there is the command
31465 \begin_inset Index idx
31468 \begin_layout Plain Layout
31481 \begin_layout Standard
31482 \begin_inset Note Greyedout
31485 \begin_layout Plain Layout
31490 Only maximal 26 formulas can be numbered with Latin letters in one document.
31498 \begin_layout Standard
31502 \begin_layout Plain Layout
31518 \begin_layout Standard
31519 \begin_inset Formula
31521 A=\textrm{small roman}
31530 \begin_layout Plain Layout
31544 \begin_inset Formula
31546 B=\textrm{big Roman}\label{eq:Rom}
31555 \begin_layout Plain Layout
31569 \begin_inset Formula
31571 C=\textrm{small Latin}
31580 \begin_layout Plain Layout
31594 \begin_inset Formula
31596 D=\textrm{big Latin}\label{eq:Lat}
31604 \begin_layout Standard
31605 To switch back to the default numbering, insert the command:
31608 \begin_layout Standard
31618 \begin_inset Index idx
31621 \begin_layout Plain Layout
31632 \begin_layout Standard
31636 \begin_layout Plain Layout
31650 \begin_inset Formula
31660 \begin_layout Standard
31661 \begin_inset VSpace medskip
31664 As you see, formulas are numbered serially independent from the numbering
31666 When then numbering should start with
31667 \begin_inset Quotes eld
31671 \begin_inset Quotes erd
31674 when the style is changed, new equation counters have to be defined.
31675 A description about this can be found in the file
31676 \begin_inset CommandInset href
31678 name "Formula-numbering.lyx"
31679 target "run:Formula-numbering.lyx"
31686 \begin_layout Section
31687 Chemical Symbols and Equations
31688 \begin_inset CommandInset label
31690 name "sub:Chemical-Symbols-and"
31695 \begin_inset Index idx
31698 \begin_layout Plain Layout
31699 Chemical characters ! Symbols
31705 \begin_inset Index idx
31708 \begin_layout Plain Layout
31715 \begin_inset Index idx
31718 \begin_layout Plain Layout
31727 \begin_layout Standard
31728 An example text from chemistry:
31731 \begin_layout Quote
31733 \begin_inset Formula $\mathrm{SO_{4}^{2-}}$
31736 -ion reacts with two
31737 \begin_inset Formula $\mathrm{Na^{+}}$
31740 -ions to sodium sulfate
31741 \begin_inset Formula $\left(\mathrm{Na_{2}SO_{4}}\right)$
31745 The chemical equation for this is:
31746 \begin_inset Formula
31748 \mathrm{2\, Na^{+}+SO_{4}^{2-}\longrightarrow Na_{2}SO_{4}}\label{eq:chem-reaction}
31756 \begin_layout Standard
31757 This chemical equation can directly be created as formula.
31758 To avoid that the symbols appear italic, everything is highlighted and
31759 changed by the shortcut
31765 to the upright font style.
31769 \begin_layout Plain Layout
31775 \begin_inset CommandInset ref
31777 reference "sub:Font-Styles"
31789 \begin_layout Standard
31790 A more convenient way to typeset chemical formulas is to use the command
31798 \begin_inset Index idx
31801 \begin_layout Plain Layout
31809 that is available when the LaTeX-package
31814 \begin_inset Index idx
31817 \begin_layout Plain Layout
31830 to a formula a new blue box appears where chemical formulas can be inserted
31831 in an intuitive way.
31834 \begin_layout Standard
31836 \begin_inset Tabular
31837 <lyxtabular version="3" rows="9" columns="2">
31838 <features tabularvalignment="middle">
31839 <column alignment="center" valignment="top" width="0">
31840 <column alignment="center" valignment="top" width="0">
31842 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
31845 \begin_layout Plain Layout
31851 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
31854 \begin_layout Plain Layout
31856 \begin_inset Note Note
31859 \begin_layout Plain Layout
31866 is only used as spacer.
31878 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
31881 \begin_layout Plain Layout
31888 \begin_layout Plain Layout
31902 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
31905 \begin_layout Plain Layout
31906 \begin_inset Formula $\raisebox{4.5mm}{}\ce{H2CO3}\raisebox{-2mm}{}$
31916 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
31919 \begin_layout Plain Layout
31926 \begin_layout Plain Layout
31940 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
31943 \begin_layout Plain Layout
31944 \begin_inset Formula $\raisebox{5mm}{}\ce{SO4^{2-}}\raisebox{-2mm}{}$
31954 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
31957 \begin_layout Plain Layout
31964 \begin_layout Plain Layout
31978 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
31981 \begin_layout Plain Layout
31982 \begin_inset Formula $\raisebox{4.5mm}{}\ce{(NH4)2S}\raisebox{-2mm}{}$
31992 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
31995 \begin_layout Plain Layout
32002 \begin_layout Plain Layout
32016 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
32019 \begin_layout Plain Layout
32020 \begin_inset Formula $\raisebox{4.5mm}{}\ce{KCr(SO4)2.12H2O}\raisebox{-2mm}{}$
32030 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
32033 \begin_layout Plain Layout
32040 \begin_layout Plain Layout
32055 \begin_layout Plain Layout
32070 \begin_layout Plain Layout
32084 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
32087 \begin_layout Plain Layout
32088 \begin_inset Formula $\raisebox{4.5mm}{}\ce{A-B\dbond C\tbond D}\raisebox{-2mm}{}$
32098 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
32101 \begin_layout Plain Layout
32108 \begin_layout Plain Layout
32118 \begin_inset Formula $\downarrow$
32122 \begin_inset Formula $\to$
32130 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
32133 \begin_layout Plain Layout
32134 \begin_inset Formula $\raisebox{5mm}{}\ce{_{90}^{227}Th+}\raisebox{-2mm}{}$
32144 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
32147 \begin_layout Plain Layout
32154 \begin_layout Plain Layout
32167 \begin_layout Plain Layout
32180 \begin_layout Plain Layout
32193 \begin_layout Plain Layout
32206 \begin_layout Plain Layout
32220 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
32223 \begin_layout Plain Layout
32224 \begin_inset Formula $\raisebox{4.5mm}{}\ce{CO2 + C <=> 2CO}\raisebox{-2mm}{}$
32234 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
32237 \begin_layout Plain Layout
32244 \begin_layout Plain Layout
32257 \begin_layout Plain Layout
32270 \begin_layout Plain Layout
32283 \begin_layout Plain Layout
32300 \begin_layout Plain Layout
32314 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
32317 \begin_layout Plain Layout
32318 \begin_inset Formula $\raisebox{5mm}{}\ce{CO2 + C ->[\alpha][\beta] 2CO}\raisebox{-4mm}{}$
32334 \begin_layout Standard
32335 \begin_inset Note Greyedout
32338 \begin_layout Plain Layout
32343 Inserting a formula to a
32349 box will lead to LaTeX errors.
32350 In this case TeX code has to be used like for
32364 \begin_layout Plain Layout
32385 \begin_layout Standard
32392 the command for equation
32393 \begin_inset space ~
32397 \begin_inset CommandInset ref
32399 reference "eq:chem-reaction"
32404 \begin_inset Newline newline
32415 \begin_layout Plain Layout
32428 \begin_layout Plain Layout
32441 \begin_layout Plain Layout
32454 \begin_layout Plain Layout
32467 \begin_layout Plain Layout
32480 \begin_layout Plain Layout
32492 \begin_layout Standard
32493 To create multiline chemical equations first a multiline formula is created
32495 \begin_inset CommandInset ref
32497 reference "sec:Multiline-Formulas"
32502 Afterwards the command
32508 is used in every small blue box of the formula.
32510 \begin_inset CommandInset ref
32512 reference "eq:TEOS-reaction-1"
32517 \begin_inset CommandInset ref
32519 reference "eq:TEOS-reaction-2"
32523 are an example of a multi-stage chemical reaction where every equation
32524 has its own number.
32525 \begin_inset Formula
32527 \ce{TEOS + 4O} & \ce{->} & \ce{Si(OH)4 + 4C2H4O}\label{eq:TEOS-reaction-1}\\
32528 \ce{Si(OH)4} & \ce{->} & \ce{SiO2 + 2H2O}\label{eq:TEOS-reaction-2}
32536 \begin_layout Standard
32547 package provides the command
32554 \begin_inset Index idx
32557 \begin_layout Plain Layout
32565 that has to be used for special cases.
32566 For more information about
32572 and more examples have a look at the documentation of
32577 \begin_inset CommandInset citation
32586 \begin_layout Section
32590 \begin_layout Standard
32591 LyX supports two types of commutative diagrams:
32599 that are explained in the following.
32602 \begin_layout Subsection
32604 \begin_inset Index idx
32607 \begin_layout Plain Layout
32616 \begin_layout Standard
32617 Diagrams of this type visualize relations by vertical and horizontal lines
32619 \begin_inset Formula
32621 \begin{CD}A@>>>B@>>>C\\
32632 \begin_layout Standard
32633 To get them, the command
32638 \begin_inset Index idx
32641 \begin_layout Plain Layout
32651 is inserted to a formula.
32652 A blue box appears with two dashed lines where further commands can be
32657 arg "newline-insert newline"
32660 a new line is created.
32661 Horizontal relations are inserted in odd, vertical in even formula lines.
32664 \begin_layout Standard
32665 To create the relations there are the following commands:
32668 \begin_layout Itemize
32673 creates a left arrow,
32684 \begin_layout Itemize
32689 creates an up arrow,
32697 a vertical equal sign
32700 \begin_layout Itemize
32706 is a placeholder for non-existent relations
32709 \begin_layout Standard
32710 All arrows can be labeled as follows:
32713 \begin_layout Itemize
32714 Is text inserted between the first and second < or >, resp., it is placed
32716 When it is inserted between the second and third one, it appears under
32720 \begin_layout Itemize
32721 When text for vertical arrows is inserted between the first and second A
32722 or V, resp., it is placed left beside the arrow.
32723 When it is inserted between the second and third one, it appears right
32725 If the text contains an A or V, these letters must be set into a TeX-brace.
32728 \begin_layout Standard
32729 As example a diagram with all possible relations:
32732 \begin_layout Standard
32733 \begin_inset Formula
32735 \begin{CD}A@>j>>B@>>k>C@=F\\
32746 \begin_layout Standard
32747 The command for this is:
32748 \begin_inset Newline newline
32759 \begin_layout Plain Layout
32768 A@>j>>B@>>k>C@=F Ctrl+Return
32769 \begin_inset Newline newline
32773 \begin_inset Phantom HPhantom
32776 \begin_layout Plain Layout
32785 \begin_layout Plain Layout
32804 \begin_inset Formula $\to$
32810 \begin_inset Newline newline
32814 \begin_inset Phantom HPhantom
32817 \begin_layout Plain Layout
32826 \begin_layout Plain Layout
32843 \begin_layout Subsection
32845 \begin_inset Index idx
32848 \begin_layout Plain Layout
32849 Diagrams ! xymatrix
32857 \begin_layout Standard
32858 To be able to use xymatrices, the LaTeX-package
32863 A xymatrix is created by inserting the command
32870 Then you are able to add new matrix columns and rows like for normal matrices,
32872 \begin_inset CommandInset ref
32874 reference "sec:Matrices"
32881 \begin_layout Standard
32882 In contrary to amscd diagrams, xymatrices supports diagonal and curved arrows,
32884 All possibilities to create commutative diagrams and decorations are explained
32889 that you find in the menu
32891 Help\SpecialChar \menuseparator
32893 \begin_inset space ~
32901 \begin_layout Subsection
32907 \begin_inset Index idx
32910 \begin_layout Plain Layout
32919 \begin_layout Standard
32924 -diagrams, the LaTeX-package
32933 -diagram is created by inserting the command
32940 Then you are able to add new matrix columns and rows like for normal matrices,
32942 \begin_inset CommandInset ref
32944 reference "sec:Matrices"
32951 \begin_layout Standard
32952 Examples how to create
32956 diagrams in LyX is given in the
32958 Feynman-diagram manual
32960 that you find in the menu
32962 Help\SpecialChar \menuseparator
32964 \begin_inset space ~
32972 \begin_layout Section
32973 User-defined Commands
32974 \begin_inset Index idx
32977 \begin_layout Plain Layout
32978 User-defined commands
32986 \begin_layout Standard
32987 \begin_inset Note Greyedout
32990 \begin_layout Plain Layout
32995 The names of user-defined commands and macros may only consist of Latin
33004 \begin_layout Subsection
33008 \begin_inset CommandInset label
33010 name "sub:The-Command-newcommand"
33015 \begin_inset Index idx
33018 \begin_layout Plain Layout
33019 User-defined commands !
33027 \begin_inset Index idx
33030 \begin_layout Plain Layout
33041 \begin_layout Standard
33042 Many LaTeX-commands are too long to be used frequently.
33043 But it is possible to define with the command
33049 new shorter commands.
33052 \begin_layout Standard
33053 The command scheme of
33062 \begin_layout Standard
33067 newcommand{new command name}[number of arguments][optional
33072 \begin_inset Newline newline
33076 \begin_inset Phantom HPhantom
33079 \begin_layout Plain Layout
33089 {command definition}
33092 \begin_layout Standard
33093 \begin_inset Note Greyedout
33096 \begin_layout Plain Layout
33101 Assure that the name of the new command is not already used in your document
33102 or by LaTeX-packages that you use.
33103 When you for example define the command
33115 , you get an error message because
33121 is already defined as command for
33122 \begin_inset Quotes eld
33126 \begin_inset Formula $\le$
33130 \begin_inset Quotes erd
33141 \begin_layout Standard
33142 The number of arguments is an integer in the range 0
33143 \begin_inset space \thinspace{}
33147 \begin_inset space \thinspace{}
33150 9 and specifies how many arguments the new command should have.
33151 With the optional value a value for an optional argument can be predefined.
33152 When this is done, the
33160 rgument of the new command is automatically an optional one.
33163 \begin_layout Standard
33164 Here are some examples:
33167 \begin_layout Itemize
33168 To define the command
33180 , the LaTeX-preamble line is:
33181 \begin_inset VSpace medskip
33185 \begin_inset Newline newline
33199 \begin_layout Itemize
33200 To define the command
33212 , the argument (that should be underlined) must be taken into account.
33213 For this the preamble line is:
33214 \begin_inset VSpace medskip
33218 \begin_inset Newline newline
33232 \begin_inset VSpace medskip
33236 \begin_inset Newline newline
33243 acts as argument placeholder, the
33247 behind it denotes that it is the placeholder for the first argument.
33250 \begin_layout Itemize
33258 \begin_inset space \thinspace{}
33262 \begin_inset space \space{}
33272 \begin_inset VSpace medskip
33276 \begin_inset Newline newline
33287 framebox#1#2{$#3$}}
33290 \begin_inset VSpace medskip
33294 \begin_inset Newline newline
33297 The two Dollar signs creates the extra formula needed for
33304 \begin_inset CommandInset ref
33306 reference "sub:Boxes-with-Frame"
33313 \begin_layout Itemize
33314 To create a new command for
33320 where the color for the box needn't to be specified, the argument for the
33321 color is defined optional:
33322 \begin_inset VSpace medskip
33326 \begin_inset Newline newline
33337 fcolorbox{#2}{#1}{$#3$}}
33340 \begin_inset VSpace medskip
33344 \begin_inset Newline newline
33347 When the color is not specified when using
33353 , the predefined color
33360 \begin_layout Standard
33361 A test of the new defined commands:
33364 \begin_layout Standard
33366 \begin_inset Tabular
33367 <lyxtabular version="3" rows="6" columns="2">
33368 <features tabularvalignment="middle">
33369 <column alignment="center" valignment="top" width="0">
33370 <column alignment="center" valignment="top" width="0">
33372 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
33375 \begin_layout Plain Layout
33381 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
33384 \begin_layout Plain Layout
33386 \begin_inset Note Note
33389 \begin_layout Plain Layout
33396 is only used as spacer.
33408 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
33411 \begin_layout Plain Layout
33418 \begin_layout Plain Layout
33432 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
33435 \begin_layout Plain Layout
33436 \begin_inset Formula $A\gr B$
33446 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
33449 \begin_layout Plain Layout
33457 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
33460 \begin_layout Plain Layout
33461 \begin_inset Formula $\raisebox{4.5mm}{}\us{ABcd}\raisebox{-2mm}{}$
33471 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
33474 \begin_layout Plain Layout
33478 \begin_inset Formula $\to$
33484 \begin_inset Formula $\to$
33495 \begin_layout Plain Layout
33509 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
33512 \begin_layout Plain Layout
33513 \begin_inset Formula $\raisebox{6mm}{}\fb{[2cm]}{}{\int A=B}\raisebox{-4mm}{}$
33523 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
33526 \begin_layout Plain Layout
33530 \begin_inset Formula $\to$
33541 \begin_layout Plain Layout
33555 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
33558 \begin_layout Plain Layout
33559 \begin_inset Formula $\raisebox{6mm}{}\cb{red}{\int A=B}\raisebox{-4mm}{}$
33569 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
33572 \begin_layout Plain Layout
33578 \begin_inset Formula $\to$
33589 \begin_layout Plain Layout
33603 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
33606 \begin_layout Plain Layout
33607 \begin_inset Formula $\raisebox{6mm}{}\cb[green]{red}{\int A=B}\raisebox{-4mm}{}$
33623 \begin_layout Subsection
33625 \begin_inset Index idx
33628 \begin_layout Plain Layout
33629 User-defined commands! Math macros
33635 \begin_inset Index idx
33638 \begin_layout Plain Layout
33647 \begin_layout Standard
33648 User-defined commands are especially convenient for complex expressions.
33649 When you are for example dealing in a document with quadratic equations,
33650 the same solution type occurs several times.
33651 The general form of a quadratic equation is
33652 \begin_inset Formula
33654 0=\lambda^{2}+p\lambda+q
33659 The general form of the solution is
33660 \begin_inset Formula
33662 \lambda_{1,2}=-\frac{p}{2}\pm\sqrt{\frac{p²}{4}-q}
33670 \begin_layout Standard
33671 To define a command for the solution formula where only the three parameters
33673 \begin_inset Formula $\lambda$
33677 \begin_inset Formula $p$
33681 \begin_inset Formula $q$
33684 need to be specified and the index of
33685 \begin_inset Formula $\lambda$
33688 can be given optionally, the LaTeX-preamble line is
33689 \begin_inset Newline newline
33705 \begin_inset Newline newline
33709 \begin_inset Phantom HPhantom
33712 \begin_layout Plain Layout
33726 frac{#3^{2}}{4}-#4}}
33729 \begin_layout Standard
33730 To create with this the solution formula, the command
33731 \begin_inset Newline newline
33741 \begin_inset Formula $\to$
33747 \begin_inset Formula $\to$
33754 is inserted to a formula
33759 \begin_layout Standard
33760 The definition of the new command is unintuitive because one has to know
33761 the schemes of all used LaTeX commands, e.
33762 \begin_inset space \thinspace{}
33766 \begin_inset space \space{}
33769 that a fraction is inserted in LaTeX as
33773 frac{numerator}{denominator}
33776 Furthermore one can easily forget a brace in the definition and cannot
33777 see in LyX what the new command is doing.
33778 To avoid these problems LyX offers the possibility to use math macros instead
33788 \begin_layout Standard
33789 A math macro is created by using the menu
33791 Insert\SpecialChar \menuseparator
33792 Math\SpecialChar \menuseparator
33795 or the toolbar button
33796 \begin_inset Graphics
33797 filename ../images/math-macro_newmacroname_newcommand.png
33803 The math macro toolbar appears together with the following box where the
33805 \begin_inset Newline newline
33809 \begin_inset space \hspace*{\fill}
33813 \begin_inset Graphics
33814 filename clipart/macrobox.png
33819 \begin_inset space \hspace*{\fill}
33823 \begin_inset Newline newline
33827 \begin_inset FormulaMacro
33828 \newcommand{\qG}[4][1,\,2]{#2_{#1}=-\frac{#3}{2}\pm\sqrt{\frac{#3^{2}}{4}-#4}}
33833 newmacroname is the default name of the macro that should be changed to
33834 something sensible.
33835 The wanted formula is inserted in the first blue box.
33836 An argument placeholder is inserted with the command
33843 \begin_inset space \thinspace{}
33847 \begin_inset space \space{}
33856 or by using the macro toolbar button
33857 \begin_inset Graphics
33858 filename ../images/math-macro-add-param.png
33864 Argument placeholders are displayed red.
33865 Maximum 9 arguments are possible.
33866 Optional arguments are created with the toolbar button
33867 \begin_inset Graphics
33868 filename ../images/math-macro-add-optional-param.png
33874 The first non-optional argument can be transformed to an optional one with
33876 \begin_inset Graphics
33877 filename ../images/math-macro-make-optional.png
33883 In the second blue box the appearance of the macro in LyX can be defined.
33884 Normally you want to see it as it is defined, so the box is kept empty.
33885 But when you have created a macro that needs lot of space on the screen,
33886 you can insert in the box for example
33887 \begin_inset Newline newline
33917 \begin_inset Newline newline
33922 For the macro only the arguments with the macro name in front of them will
33923 then be displayed in LyX, leading to a better overview.
33924 The formula appears in the output as defined in the first box.
33925 \begin_inset Newline newline
33928 The appearance of macros in formulas can furthermore be changed for single
33929 macros by setting the cursor in the macro and using the menu
33931 View\SpecialChar \menuseparator
33933 \begin_inset space ~
33937 \begin_inset space ~
33945 \begin_layout Standard
33946 To use a macro, the macro name is inserted as command to a formula, in our
33954 Our macro looks in LyX like this:
33955 \begin_inset Newline newline
33959 \begin_inset space \hspace*{\fill}
33963 \begin_inset Graphics
33964 filename clipart/macrouse.png
33969 \begin_inset space \hspace*{\fill}
33973 \begin_inset Newline newline
33976 Here is our macro example with the arguments
33977 \begin_inset Formula $x$
33981 \begin_inset Formula $\ln(x)$
33985 \begin_inset Formula $B$
33991 \begin_layout Standard
33992 \begin_inset Formula
34002 \begin_layout Standard
34003 LyX offers in the menu
34005 Tools\SpecialChar \menuseparator
34006 Preferences\SpecialChar \menuseparator
34007 Editing\SpecialChar \menuseparator
34010 different styles to edit macros.
34011 To find the style that suits you the most, choose a style and set the cursor
34012 in a macro formula to see the difference.
34015 \begin_layout Standard
34016 A math macro is transformed internally to a
34022 command when exporting the document.
34029 command is not placed in the LaTeX-preamble, therefore macros can only
34030 be used in formulas that are in the document below the macro definition
34034 \begin_layout Standard
34035 Math macros can also be directly be created from a
34042 When writing for example the command
34045 \begin_inset Newline newline
34054 xleftarrow[#2]{#1}}
34055 \begin_inset Newline newline
34060 in LyX as normal text, highlighting it completely and using then the shortcut
34065 , the command will be transformed to a math macro.
34066 Using this method you need to be careful that the
34072 command is typed correctly, otherwise you get a faulty macro leading to
34076 \begin_layout Standard
34077 Math macros currently yet have the problem that further formulas in macro
34078 definitions are handled wrongly.
34079 Therefore the example
34086 \begin_inset CommandInset ref
34088 reference "sub:The-Command-newcommand"
34092 cannot be created as macro.
34095 \begin_layout Standard
34096 When the cursor is in a macro definition box, you will see the macro toolbar
34100 \begin_layout Standard
34101 \begin_inset VSpace defskip
34107 \begin_layout Standard
34108 \begin_inset Graphics
34109 filename clipart/MacroToolbar.png
34114 \begin_inset Index idx
34117 \begin_layout Plain Layout
34126 \begin_layout Standard
34127 \begin_inset VSpace defskip
34133 \begin_layout Standard
34134 The macro toolbar contains from left to right the following buttons:
34137 \begin_layout Standard
34138 \begin_inset VSpace defskip
34144 \begin_layout Standard
34145 \begin_inset Tabular
34146 <lyxtabular version="3" rows="9" columns="2">
34147 <features islongtable="true" longtabularalignment="center">
34148 <column alignment="left" valignment="top" width="0">
34149 <column alignment="left" valignment="top" width="85col%">
34150 <row interlinespace="2.5mm">
34151 <cell alignment="center" valignment="top" usebox="none">
34154 \begin_layout Plain Layout
34155 \begin_inset Graphics
34156 filename ../images/math-macro-remove-param.png
34157 rotateOrigin center
34166 <cell alignment="center" valignment="top" usebox="none">
34169 \begin_layout Plain Layout
34172 Edit\SpecialChar \menuseparator
34173 Math\SpecialChar \menuseparator
34175 \begin_inset space ~
34178 Definition\SpecialChar \menuseparator
34179 Remove Last Argument
34185 <row interlinespace="2.5mm">
34186 <cell alignment="center" valignment="top" usebox="none">
34189 \begin_layout Plain Layout
34190 \begin_inset Graphics
34191 filename ../images/math-macro-add-param.png
34192 rotateOrigin center
34201 <cell alignment="center" valignment="top" usebox="none">
34204 \begin_layout Plain Layout
34207 Edit\SpecialChar \menuseparator
34208 Math\SpecialChar \menuseparator
34210 \begin_inset space ~
34213 Definition\SpecialChar \menuseparator
34220 <row interlinespace="2.5mm">
34221 <cell alignment="center" valignment="top" usebox="none">
34224 \begin_layout Plain Layout
34225 \begin_inset Graphics
34226 filename ../images/math-macro-make-optional.png
34227 rotateOrigin center
34236 <cell alignment="center" valignment="top" usebox="none">
34239 \begin_layout Plain Layout
34242 Edit\SpecialChar \menuseparator
34243 Math\SpecialChar \menuseparator
34245 \begin_inset space ~
34248 Definition\SpecialChar \menuseparator
34249 Make First Non-Optional into
34250 \begin_inset Newline newline
34254 \begin_inset Phantom HPhantom
34257 \begin_layout Plain Layout
34260 Edit\SpecialChar \menuseparator
34261 Math\SpecialChar \menuseparator
34263 \begin_inset space ~
34266 Definition\SpecialChar \menuseparator
34278 <row interlinespace="2.5mm">
34279 <cell alignment="center" valignment="top" usebox="none">
34282 \begin_layout Plain Layout
34283 \begin_inset Graphics
34284 filename ../images/math-macro-make-nonoptional.png
34285 rotateOrigin center
34294 <cell alignment="center" valignment="top" usebox="none">
34297 \begin_layout Plain Layout
34300 Edit\SpecialChar \menuseparator
34301 Math\SpecialChar \menuseparator
34303 \begin_inset space ~
34306 Definition\SpecialChar \menuseparator
34307 Make Last Optional into
34308 \begin_inset Newline newline
34312 \begin_inset Phantom HPhantom
34315 \begin_layout Plain Layout
34318 Edit\SpecialChar \menuseparator
34319 Math\SpecialChar \menuseparator
34321 \begin_inset space ~
34324 Definition\SpecialChar \menuseparator
34330 Non-Optional Argument
34336 <row interlinespace="2.5mm">
34337 <cell alignment="center" valignment="top" usebox="none">
34340 \begin_layout Plain Layout
34341 \begin_inset Graphics
34342 filename ../images/math-macro-remove-optional-param.png
34343 rotateOrigin center
34352 <cell alignment="center" valignment="top" usebox="none">
34355 \begin_layout Plain Layout
34358 Edit\SpecialChar \menuseparator
34359 Math\SpecialChar \menuseparator
34361 \begin_inset space ~
34364 Definition\SpecialChar \menuseparator
34365 Remove Optional Argument
34371 <row interlinespace="2.5mm">
34372 <cell alignment="center" valignment="top" usebox="none">
34375 \begin_layout Plain Layout
34376 \begin_inset Graphics
34377 filename ../images/math-macro-add-optional-param.png
34378 rotateOrigin center
34387 <cell alignment="center" valignment="top" usebox="none">
34390 \begin_layout Plain Layout
34393 Edit\SpecialChar \menuseparator
34394 Math\SpecialChar \menuseparator
34396 \begin_inset space ~
34399 Definition\SpecialChar \menuseparator
34400 Insert Optional Argument
34406 <row interlinespace="2.5mm">
34407 <cell alignment="center" valignment="top" usebox="none">
34410 \begin_layout Plain Layout
34411 \begin_inset Graphics
34412 filename ../images/math-macro-remove-greedy-param.png
34413 rotateOrigin center
34422 <cell alignment="center" valignment="top" usebox="none">
34425 \begin_layout Plain Layout
34428 Edit\SpecialChar \menuseparator
34429 Math\SpecialChar \menuseparator
34431 \begin_inset space ~
34434 Definition\SpecialChar \menuseparator
34435 Remove Last Argument
34436 \begin_inset Newline newline
34440 \begin_inset Phantom HPhantom
34443 \begin_layout Plain Layout
34446 Edit\SpecialChar \menuseparator
34447 Math\SpecialChar \menuseparator
34449 \begin_inset space ~
34452 Definition\SpecialChar \menuseparator
34458 Spitting Out To The Right
34464 <row interlinespace="2.5mm">
34465 <cell alignment="center" valignment="top" usebox="none">
34468 \begin_layout Plain Layout
34469 \begin_inset Graphics
34470 filename ../images/math-macro-append-greedy-param.png
34471 rotateOrigin center
34480 <cell alignment="center" valignment="top" usebox="none">
34483 \begin_layout Plain Layout
34486 Edit\SpecialChar \menuseparator
34487 Math\SpecialChar \menuseparator
34489 \begin_inset space ~
34492 Definition\SpecialChar \menuseparator
34494 \begin_inset Newline newline
34498 \begin_inset Phantom HPhantom
34501 \begin_layout Plain Layout
34504 Edit\SpecialChar \menuseparator
34505 Math\SpecialChar \menuseparator
34507 \begin_inset space ~
34510 Definition\SpecialChar \menuseparator
34516 Eating From The Right
34522 <row interlinespace="2.5mm">
34523 <cell alignment="center" valignment="top" usebox="none">
34526 \begin_layout Plain Layout
34527 \begin_inset Graphics
34528 filename ../images/math-macro-add-greedy-optional-param.png
34529 rotateOrigin center
34538 <cell alignment="center" valignment="top" usebox="none">
34541 \begin_layout Plain Layout
34544 Edit\SpecialChar \menuseparator
34545 Math\SpecialChar \menuseparator
34547 \begin_inset space ~
34550 Definition\SpecialChar \menuseparator
34551 Append Optional Argument
34552 \begin_inset Newline newline
34556 \begin_inset Phantom HPhantom
34559 \begin_layout Plain Layout
34562 Edit\SpecialChar \menuseparator
34563 Math\SpecialChar \menuseparator
34565 \begin_inset space ~
34568 Definition\SpecialChar \menuseparator
34574 Eating From The Right
34587 \begin_layout Section
34588 Computer Algebra Systems
34591 \begin_layout Standard
34592 LyX offers the exchange between mathematical expressions written in LyX's
34593 math editor and external applications or user defined scripts.
34594 Currently supported applications are
34611 Note that the set of supported mathematical constructs is limited only
34612 to very simple cases.
34615 \begin_layout Subsection
34619 \begin_layout Standard
34620 Write some expression in a formula, go to the
34622 Edit\SpecialChar \menuseparator
34623 Math\SpecialChar \menuseparator
34624 Use Computer Algebra System
34626 menu and choose the application you have installed on the computer.
34627 After that the result of computation should show on the right side of the
34628 expression together with the
34629 \begin_inset Quotes eld
34633 \begin_inset Quotes erd
34639 \begin_layout Standard
34640 Here are few simple examples (with results from
34644 ) to show what kind of computations can be performed:
34647 \begin_layout Itemize
34648 \begin_inset Formula $\frac{37}{3}*2-\sum_{i=1}^{3}i^{i}=-\frac{22}{3}$
34654 \begin_layout Itemize
34655 \begin_inset Formula $\frac{37.0}{3}=12.33333333333333$
34661 \begin_layout Itemize
34662 \begin_inset Formula $\int_{1}^{2}\sin(x)dx=\cos1-\cos2$
34668 \begin_layout Itemize
34669 \begin_inset Formula $\det\left[\begin{array}{ccc}
34673 \end{array}\right]=-56$
34679 \begin_layout Itemize
34680 \begin_inset Formula $\lim_{x\rightarrow0}\left(\frac{\sin(x)}{x}\right)=1$
34686 \begin_layout Subsection
34690 \begin_layout Standard
34691 Currently there is no keyboard shortcut for calling the algebra applications.
34692 One can easily bind a shortcut to the
34696 LyX function (see the
34704 \begin_inset space \thinspace{}
34708 \begin_inset space ~
34715 key inside the math editor.
34720 one would use this shortcut definition command:
34723 \begin_layout Standard
34726 command-alternatives break-paragraph;math-extern maxima
34729 \begin_layout Standard
34730 \begin_inset Newpage newpage
34736 \begin_layout Section
34738 \begin_inset Index idx
34741 \begin_layout Plain Layout
34750 \begin_layout Subsection
34752 \begin_inset Index idx
34755 \begin_layout Plain Layout
34764 \begin_layout Standard
34765 Negative numbers often look ugly in formulas because the minus sign before
34766 the number is set with the same length as the minus operator sign.
34767 When writing the negative number in normal text, the minus sign appears
34771 \begin_layout Standard
34772 Thus, the problem disappears when converting the minus sign to mathematical
34776 \begin_layout Standard
34777 An example to visualize the problem:
34780 \begin_layout Standard
34782 \begin_inset Tabular
34783 <lyxtabular version="3" rows="3" columns="2">
34784 <features tabularvalignment="middle">
34785 <column alignment="right" valignment="top" width="0">
34786 <column alignment="left" valignment="top" width="0">
34788 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
34791 \begin_layout Plain Layout
34797 <cell alignment="center" valignment="top" topline="true" rightline="true" usebox="none">
34800 \begin_layout Plain Layout
34808 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
34811 \begin_layout Plain Layout
34817 <cell alignment="center" valignment="top" topline="true" bottomline="true" rightline="true" usebox="none">
34820 \begin_layout Plain Layout
34821 \begin_inset Formula $x=-2$
34831 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
34834 \begin_layout Plain Layout
34840 <cell alignment="center" valignment="top" topline="true" bottomline="true" rightline="true" usebox="none">
34843 \begin_layout Plain Layout
34844 \begin_inset Formula $x=\textrm{-}2$
34860 \begin_layout Subsection
34861 Comma as decimal Separator
34862 \begin_inset Index idx
34865 \begin_layout Plain Layout
34874 \begin_layout Standard
34875 In LaTeX a comma inside a formula is used, according to the English convention,
34876 as number group separator.
34877 So there will be space added behind all commas in formulas.
34880 \begin_layout Standard
34881 To avoid this, the comma is highlighted and changed to mathematical text
34891 \begin_layout Standard
34892 To use all formula commas in the document as decimal separator, the file
34901 \begin_layout Plain Layout
34906 is part of the LaTeX-package
34911 \begin_inset Index idx
34914 \begin_layout Plain Layout
34919 \begin_layout Plain Layout
34939 \begin_inset Index idx
34942 \begin_layout Plain Layout
34948 is loaded with the LaTeX-preamble line
34951 \begin_layout Standard
34959 \begin_layout Subsection
34961 \begin_inset CommandInset label
34963 name "sub:Physical-Vectors"
34968 \begin_inset Index idx
34971 \begin_layout Plain Layout
34980 \begin_layout Standard
34981 Predefined vectors are offered by the LaTeX-package
34986 \begin_inset Index idx
34989 \begin_layout Plain Layout
34995 that is loaded with the LaTeX-preamble line
34998 \begin_layout Standard
35006 \begin_layout Standard
35010 \begin_layout Plain Layout
35020 \begin_inset Note Note
35023 \begin_layout Plain Layout
35024 The following table will only be displayed when the LaTeX-package
35036 \begin_layout Standard
35037 The following commands are defined:
35040 \begin_layout Standard
35042 \begin_inset Tabular
35043 <lyxtabular version="3" rows="4" columns="2">
35044 <features tabularvalignment="middle">
35045 <column alignment="center" valignment="top" width="0">
35046 <column alignment="center" valignment="top" width="0">
35048 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
35051 \begin_layout Plain Layout
35057 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
35060 \begin_layout Plain Layout
35068 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
35071 \begin_layout Plain Layout
35081 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
35084 \begin_layout Plain Layout
35085 \begin_inset Formula $\Bra{\psi}$
35095 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
35098 \begin_layout Plain Layout
35108 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
35111 \begin_layout Plain Layout
35112 \begin_inset Formula $\Ket{\psi}$
35122 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
35125 \begin_layout Plain Layout
35137 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
35140 \begin_layout Plain Layout
35141 \begin_inset Formula $\Braket{\psi|\phi}$
35157 \begin_layout Standard
35164 assures that all vertical bars are set in the size of the surrounding brackets:
35165 \begin_inset Formula
35167 \Braket{\phi|J=\frac{3}{2}\,,\, M_{J}}
35176 \begin_layout Plain Layout
35186 \begin_inset Note Note
35189 \begin_layout Plain Layout
35190 The following will be displayed when the LaTeX-package
35202 \begin_layout Standard
35203 You need to install the LaTeX-package
35207 to see the rest of this subsection in the output.
35210 \begin_layout Standard
35214 \begin_layout Plain Layout
35226 \begin_layout Standard
35233 can also be achieved using the command
35239 , that is described in
35240 \begin_inset CommandInset ref
35242 reference "sub:Automatic-Bracket-Size"
35249 \begin_layout Subsection
35250 Self-defined Fractions
35251 \begin_inset CommandInset label
35253 name "sub:Self-defined-Fractions"
35258 \begin_inset Index idx
35261 \begin_layout Plain Layout
35262 Fractions ! self-defined
35270 \begin_layout Standard
35271 To define custom commands for fractions, the command
35278 \begin_inset Index idx
35281 \begin_layout Plain Layout
35289 is used in the following scheme:
35292 \begin_layout Standard
35305 bracket}{fraction bar thickness}{style}
35306 \begin_inset Newline newline
35310 \begin_inset Phantom HPhantom
35313 \begin_layout Plain Layout
35323 {numerator}{denominator}
35326 \begin_layout Standard
35327 The style is a number in the range of 0
35328 \begin_inset space \thinspace{}
35332 \begin_inset space \thinspace{}
35338 \begin_layout Standard
35340 \begin_inset Tabular
35341 <lyxtabular version="3" rows="5" columns="2">
35342 <features tabularvalignment="middle">
35343 <column alignment="center" valignment="top" width="0">
35344 <column alignment="center" valignment="top" width="0">
35346 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
35349 \begin_layout Plain Layout
35355 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
35358 \begin_layout Plain Layout
35366 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
35369 \begin_layout Plain Layout
35375 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
35378 \begin_layout Plain Layout
35379 display style formula
35386 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
35389 \begin_layout Plain Layout
35395 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
35398 \begin_layout Plain Layout
35406 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
35409 \begin_layout Plain Layout
35415 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
35418 \begin_layout Plain Layout
35426 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
35429 \begin_layout Plain Layout
35435 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
35438 \begin_layout Plain Layout
35452 \begin_layout Standard
35453 When no style is given, the size is adjusted to the surrounding environment
35454 like for the command
35463 \begin_layout Standard
35464 When no fraction bar thickness is given, the predefined value of 0.4
35465 \begin_inset space \thinspace{}
35471 \begin_layout Standard
35472 \begin_inset VSpace medskip
35475 For example, the commands
35488 \begin_inset CommandInset ref
35490 reference "sub:Fractions"
35494 are defined with the commands
35497 \begin_layout Standard
35506 genfrac{}{}{}{0}{#1}{#2}}
35509 \begin_layout Standard
35513 \begin_layout Standard
35522 genfrac{(}{)}{0pt}{1}{#1}{#2}}
35525 \begin_layout Standard
35526 \begin_inset VSpace medskip
35529 To define a fraction where the fraction bar thickness can be given as optional
35530 argument, the following line is inserted to the LaTeX-preamble:
35533 \begin_layout Standard
35542 genfrac{}{}{#1}{}{#2}{#3}}
35545 \begin_layout Standard
35546 \begin_inset Newpage newpage
35552 \begin_layout Standard
35554 \begin_inset Formula
35556 \text{Command} & & \mathrm{\backslash fracS[1mm]\backslash\{A\to\backslash\{B} & & \mathrm{\backslash fracS[5mm]\backslash\{A\to\backslash\{B}\\
35557 \text{Result} & & \fracS[1mm]{A}{B} & & \fracS[5mm]{A}{B}
35562 As one can see, the distance of the numerator and the denominator to the
35563 fraction bar is round about three times the bar thickness.
35566 \begin_layout Subsection
35568 \begin_inset Index idx
35571 \begin_layout Plain Layout
35580 \begin_layout Standard
35581 To cancel formulas or formula parts, the LaTeX-package
35586 \begin_inset Index idx
35589 \begin_layout Plain Layout
35595 has to be loaded with the LaTeX-preamble line
35598 \begin_layout Standard
35606 \begin_layout Standard
35610 \begin_layout Plain Layout
35620 \begin_inset Note Note
35623 \begin_layout Plain Layout
35624 The following table will only be displayed when the LaTeX-package
35636 \begin_layout Standard
35637 There are four ways to cancel formulas:
35640 \begin_layout Standard
35642 \begin_inset Tabular
35643 <lyxtabular version="3" rows="5" columns="2">
35644 <features tabularvalignment="middle">
35645 <column alignment="center" valignment="top" width="0">
35646 <column alignment="center" valignment="top" width="0">
35648 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
35651 \begin_layout Plain Layout
35657 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
35660 \begin_layout Plain Layout
35662 \begin_inset Note Note
35665 \begin_layout Plain Layout
35672 are used here as spacer.
35684 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
35687 \begin_layout Plain Layout
35696 \begin_layout Plain Layout
35710 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
35713 \begin_layout Plain Layout
35714 \begin_inset Formula $\raisebox{4.5mm}{}\cancel{\int A=B}\raisebox{-2.5mm}{}$
35724 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
35727 \begin_layout Plain Layout
35736 \begin_layout Plain Layout
35750 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
35753 \begin_layout Plain Layout
35754 \begin_inset Formula $\raisebox{4.5mm}{}\bcancel{\int A=B}\raisebox{-2.5mm}{}$
35764 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
35767 \begin_layout Plain Layout
35776 \begin_layout Plain Layout
35790 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
35793 \begin_layout Plain Layout
35794 \begin_inset Formula $\raisebox{4.5mm}{}\xcancel{\int A=B}\raisebox{-2.5mm}{}$
35804 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
35807 \begin_layout Plain Layout
35811 \begin_inset Formula $\to$
35822 \begin_layout Plain Layout
35836 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
35839 \begin_layout Plain Layout
35840 \begin_inset Formula $\raisebox{7mm}{}\cancelto{1}{\int A=B}\raisebox{-2.5mm}{}\hspace{3mm}$
35856 \begin_layout Standard
35863 is especially suitable to visualize the reduction of fractions within formulas:
35864 \begin_inset Formula
35866 \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}}}
35874 \begin_layout Standard
35875 To change the size of
35882 \begin_inset Quotes eld
35886 \begin_inset Quotes erd
35889 value one can load the package
35893 with either the option
35897 which leads to the same size as for the canceled value or with the option
35902 which makes is it a bit smaller than the size one gets without using a
35908 was loaded with this line:
35911 \begin_layout Standard
35916 usepackage[samesize]{cancel}
35919 \begin_layout Standard
35920 To color the cancellation bar one adds this command as TeX code:
35923 \begin_layout Standard
35935 \begin_layout Standard
35940 can be replaced by a color of your choice.
35943 \begin_layout Standard
35947 \begin_layout Plain Layout
35963 \begin_layout Standard
35964 \begin_inset Formula
35966 \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}}}
35974 \begin_layout Standard
35978 \begin_layout Plain Layout
35992 \begin_inset Note Note
35995 \begin_layout Plain Layout
36004 \begin_layout Standard
36005 For further customizations, see the documentation of the package
36010 \begin_inset CommandInset citation
36019 \begin_layout Standard
36023 \begin_layout Plain Layout
36033 \begin_inset Note Note
36036 \begin_layout Plain Layout
36037 The following will be displayed when the LaTeX-package
36049 \begin_layout Standard
36050 You need to install the LaTeX-package
36054 to see the rest of this subsection in the output.
36057 \begin_layout Standard
36061 \begin_layout Plain Layout
36073 \begin_layout Subsection
36074 Formulas in Section Headings
36075 \begin_inset CommandInset label
36077 name "sub:Formulas-in-Section"
36082 \begin_inset Index idx
36085 \begin_layout Plain Layout
36086 Formula ! in section headings
36094 \begin_layout Standard
36095 When formulas are used in section headings, the following has to be taken
36099 \begin_layout Standard
36100 \begin_inset Note Greyedout
36103 \begin_layout Plain Layout
36109 \begin_inset Index idx
36112 \begin_layout Plain Layout
36113 Packages ! hyperref
36118 support is enabled in the document settings dialog under
36121 \begin_inset space ~
36126 , PDF-bookmarks are created for every section heading in the table of contents.
36127 If a section heading contains formulas, they are incorrectly displayed
36128 in the bookmark text, because formulas in bookmarks infringe the PDF convention
36137 \begin_layout Standard
36138 Both problems can be solved by inserting at the end of the section heading
36139 a short title with the menu
36141 Insert\SpecialChar \menuseparator
36143 \begin_inset space ~
36149 Short titles are used as alternative for multiline section headings to
36150 keep the table of contents clearly arranged.
36151 Only the short title appears in the table of contents and therefore also
36152 in the PDF-bookmark.
36155 \begin_layout Standard
36156 When formulas should be used in the table of contents but
36160 is used, one can use the following command in TeX-mode:
36163 \begin_layout Standard
36168 texorpdfstring{part}{alternative}
36169 \begin_inset Index idx
36172 \begin_layout Plain Layout
36183 \begin_layout Standard
36184 Part is the part of the heading that shouldn't appear in the PDF-bookmark.
36185 This can be characters, formulas, footnotes, but also cross-references.
36186 The alternative is used instead of the part for the bookmark.
36189 \begin_layout Standard
36190 Here are two example headings:
36191 \begin_inset VSpace -3mm
36198 \begin_layout Plain Layout
36210 \begin_layout Subsubsection
36211 Heading without formula in table of contents
36212 \begin_inset Formula $\sqrt{-1}=\mathrm{i}$
36216 \begin_inset Argument
36219 \begin_layout Plain Layout
36220 Heading without formula in table of contents
36228 \begin_layout Subsubsection
36229 Heading with formula in table of contents
36233 \begin_layout Plain Layout
36243 \begin_inset Formula $\sqrt{-1}=\mathrm{i}$
36250 \begin_layout Plain Layout
36260 \begin_layout Standard
36264 \begin_layout Plain Layout
36273 In the first heading a short title was used, in the second one
36282 \begin_layout Standard
36283 To get the same formatting as for the other headings, the complete heading
36292 \begin_layout Plain Layout
36294 \begin_inset CommandInset ref
36296 reference "sub:Bold-Formulas"
36308 \begin_layout Subsection
36309 Formulas in multi-column Text
36310 \begin_inset Index idx
36313 \begin_layout Plain Layout
36314 Formula ! in multi-column text
36322 \begin_layout Standard
36323 Formulas in multi-column text are often too wide to fit into a column and
36324 thus need to be set over the whole page width.
36325 This is done by using the LaTeX-package
36333 \begin_layout Plain Layout
36338 is part of every LaTeX standard installation.
36344 \begin_inset Index idx
36347 \begin_layout Plain Layout
36348 Packages ! multicol
36353 , that is loaded with the LaTeX-preamble line
36356 \begin_layout Standard
36361 usepackage{multicol}
36364 \begin_layout Standard
36365 \begin_inset Note Greyedout
36368 \begin_layout Plain Layout
36369 Note herby that the setting
36372 \begin_inset space ~
36379 Document\SpecialChar \menuseparator
36385 \begin_inset space ~
36405 \begin_layout Standard
36406 Before the multi-column text the command
36409 \begin_layout Standard
36414 begin{multicols}{column number}
36417 \begin_layout Standard
36418 is written in TeX-mode.
36419 The column number is a number in the range of 2
36420 \begin_inset space \thinspace{}
36424 \begin_inset space \thinspace{}
36428 Before the formula the multi-column text is ended by inserting the command
36431 \begin_layout Standard
36439 \begin_layout Standard
36443 \begin_layout Standard
36444 Due to the command some space is automatically added before the formula.
36446 \begin_inset space \thinspace{}
36449 mm vertical space is inserted before the formula.
36450 When the formula style
36456 \begin_layout Plain Layout
36458 \begin_inset CommandInset ref
36460 reference "sec:Formula-Styles"
36472 \begin_inset space \thinspace{}
36475 mm space is inserted instead.
36478 \begin_layout Standard
36479 As example a multi-column text with a displayed formula:
36482 \begin_layout Standard
36488 \begin_layout Plain Layout
36492 begin{multicols}{2}
36497 Das Spektrum wird fouriertransformiert.
36498 Die Fouriertransformation wird verwendet, um die überlagerten Signale (Netzwerk
36499 , Lösungsmittel) zu trennen.
36500 Nachdem wir die Phasenverschiebung bestimmen konnten, interessiert uns
36501 nun das Aussehen des Ausgangssignals.
36502 Im Experiment haben wir es mit sehr vielen Teilchen zu tun, so dass man
36503 über alle Phasen integrieren muss.
36505 \begin_inset Formula $S$
36508 unser normiertes Ausgangssignal und
36509 \begin_inset Formula $P$
36512 die Phasenverteilungsfunktion, so ergibt sich die Beziehung
36516 \begin_layout Plain Layout
36526 \begin_inset VSpace -6mm
36530 \begin_inset Formula
36532 S(t)=S_{0}(t)\int_{-\infty}^{\infty}P(\phi,t)\mathrm{e}^{\mathrm{i}\phi}\,\mathrm{d}\phi
36541 \begin_layout Plain Layout
36545 begin{multicols}{2}
36551 \begin_inset Formula $S_{0}$
36554 das Signal ohne Gradient ist und die Normierungsbedingung
36555 \begin_inset Formula $\int_{-\infty}^{\infty}P(\phi,t)\,\mathrm{d}\phi=1$
36559 Nun dürfen wir aber nicht den Relaxationsprozess außer Acht lassen.
36561 \begin_inset Formula $\nicefrac{\pi}{2}$
36565 \begin_inset space \thinspace{}
36568 -rf-Puls beginnt sich die Magnetisierung zu entfokussieren, wodurch sich
36569 das Signal zusätzlich abschwächt.
36570 Diese Abschwächung verläuft exponentiell in Abhängigkeit der so genannten
36572 \begin_inset Formula $T_{2}$
36578 \begin_layout Standard
36584 \begin_layout Plain Layout
36596 \begin_layout Subsection
36597 Formulas with Description of Variables
36598 \begin_inset Index idx
36601 \begin_layout Plain Layout
36602 Formula ! with description of variables
36610 \begin_layout Standard
36611 To describe variables within a formula, like in formula
36612 \begin_inset CommandInset ref
36614 reference "eq:within"
36623 \begin_inset Formula $n$
36627 \begin_inset space ~
36630 matrix is used with left aligned columns for the
36631 \begin_inset Formula $n$
36638 \begin_layout Plain Layout
36640 \begin_inset CommandInset ref
36642 reference "sec:Matrices"
36651 To set the description in a smaller size, before the matrix e.
36652 \begin_inset space \thinspace{}
36656 \begin_inset space \space{}
36669 \begin_layout Plain Layout
36671 \begin_inset CommandInset ref
36673 reference "sub:Font-Sizes"
36685 \begin_layout Standard
36686 When the formula style
36692 \begin_layout Plain Layout
36694 \begin_inset CommandInset ref
36696 reference "sec:Formula-Styles"
36717 \begin_layout Plain Layout
36724 only works in formulas with the style
36729 \begin_inset CommandInset ref
36731 reference "sub:Variable-Space"
36740 is inserted before and after the matrix to have the same separation of
36741 the matrix from the equation and the side margin.
36744 \begin_layout Standard
36745 When the formula style
36749 is used, the method described in
36750 \begin_inset CommandInset ref
36752 reference "sub:Flalign-Environment"
36756 is used to indent formulas.
36758 \begin_inset CommandInset ref
36760 reference "eq:within"
36764 consists of five columns whereas in the first two columns contain the equation,
36765 the third the matrix and the last one an empty TeX-brace.
36766 \begin_inset Formula
36768 \hspace{30pt}F_{A} & =\rho·V·g & \footnotesize\begin{array}{ll}
36769 \rho & \textrm{density}\\
36770 V & \textrm{volume}\\
36771 g & \textrm{gravitational acceleration}
36772 \end{array} & & {}\label{eq:within}
36780 \begin_layout Subsection
36781 Upright small Greek Letters
36782 \begin_inset CommandInset label
36784 name "sub:Upright-small-Greek"
36789 \begin_inset Index idx
36792 \begin_layout Plain Layout
36793 Greek letters ! upright
36801 \begin_layout Standard
36802 Most of the math fonts only provide italic small Greek letters.
36803 But for symbols of elementary particles like pions and neutrinos, upright
36804 Greek letters are needed.
36813 \begin_layout Plain Layout
36818 is part of the LaTeX-package
36823 \begin_inset Index idx
36826 \begin_layout Plain Layout
36831 \begin_layout Plain Layout
36851 \begin_inset Index idx
36854 \begin_layout Plain Layout
36860 that is loaded with the LaTeX-preamble line
36863 \begin_layout Standard
36868 usepackage{upgreek}
36871 \begin_layout Standard
36877 \begin_layout Plain Layout
36887 \begin_inset Note Note
36890 \begin_layout Plain Layout
36891 The following table will only be displayed when the LaTeX-package
36900 They are created when the command for a small Greek letters is started
36906 For example the command
36913 \begin_inset Formula $\uptau$
36919 \begin_layout Standard
36920 With these commands reactions of elementary particles can be typeset:
36921 \begin_inset Formula
36923 \uppi^{+}\to\upmu^{+}+\upnu_{\upmu}
36931 \begin_layout Standard
36932 The upright letters are more bold and wider than the italic ones.
36933 They should therefore not be used for units like
36934 \begin_inset Quotes eld
36938 \begin_inset Quotes erd
36944 \begin_layout Standard
36948 \begin_layout Plain Layout
36958 \begin_inset Note Note
36961 \begin_layout Plain Layout
36962 The following will be displayed when the LaTeX-package
36974 \begin_layout Standard
36975 You need to install the LaTeX-package
36979 to see the rest of this subsection in the output.
36982 \begin_layout Standard
36986 \begin_layout Plain Layout
36998 \begin_layout Standard
36999 \begin_inset Newpage newpage
37005 \begin_layout Subsection
37006 Text Characters in Formulas
37007 \begin_inset CommandInset label
37009 name "sub:Text-Characters-in"
37014 \begin_inset Index idx
37017 \begin_layout Plain Layout
37026 \begin_layout Standard
37027 In some cases you might want to insert text characters directly into formulas.
37028 When for example the centered dot · is often used in formulas like
37029 \begin_inset Formula $\nu=5·10^{5}\,\mathrm{Hz}$
37032 , one would have to insert the command
37042 \begin_layout Plain Layout
37044 \begin_inset CommandInset ref
37046 reference "sub:Binary-Operators"
37055 all the time, because this character is defined in all encodings as text
37057 But the encoding can be changed by this LaTeX-preamble line:
37060 \begin_layout Standard
37065 Declare Inputtext{183}{
37075 f\SpecialChar \textcompwordmark{}
37079 \begin_layout Standard
37080 The character encoding (menu
37082 Document\SpecialChar \menuseparator
37083 Settings\SpecialChar \menuseparator
37086 ) specifies what character appears when a keyboard key is pressed.
37087 When the key for the character '·' is pressed, internally the command
37094 But this command is not available in a formula so that you would get LaTeX-erro
37096 With the changed encoding the right command is chosen automatically, depending
37097 on if the character was inserted into a formula or not.
37100 \begin_layout Standard
37101 The encoding of several characters is saved in definition files.
37102 Fore example the encoding
37106 is defined in the file
37110 that is in the installation folder of LaTeX.
37111 Encodings should only be changed via the LaTeX-preamble and not in the
37113 Otherwise own documents could not be edited by other LyX users working
37114 on other computers.
37117 \begin_layout Standard
37118 \begin_inset VSpace medskip
37121 Besides the centered dot, in this document the degree sign ° is defined
37122 with the following LaTeX-preamble line so that it can directly be inserted
37126 \begin_layout Standard
37131 DeclareInputtext{176}{
37141 f\SpecialChar \textcompwordmark{}
37145 \begin_layout Standard
37146 \begin_inset Newpage newpage
37152 \begin_layout Section
37155 \begin_inset Index idx
37158 \begin_layout Plain Layout
37167 \begin_layout Standard
37168 This section is a summary of the most important typographic rules, listed
37173 \begin_layout Plain Layout
37174 This collection was partly taken from the German semi-official dictionary
37176 \begin_inset Quotes eld
37180 \begin_inset Quotes erd
37184 \begin_inset CommandInset citation
37190 that lists some of the ISO rules.
37191 More rules are listed in
37192 \begin_inset CommandInset citation
37206 \begin_layout Itemize
37215 \begin_layout Plain Layout
37216 done with font styles, see
37217 \begin_inset CommandInset ref
37219 reference "sub:Font-Styles"
37228 , no matter if they appear in italic text: 30
37229 \begin_inset space \thinspace{}
37233 \begin_inset Newline newline
37236 Between the value and the unit is the smallest space, see
37237 \begin_inset CommandInset ref
37239 reference "sub:Predefined-Space"
37244 \begin_inset Newline newline
37247 This convention is automatically fulfilled when the command
37254 When it is entered to a formula, two boxes appear.
37255 In the first one the value is inserted, in the second one the unit, and
37257 \begin_inset Formula $\unit[30]{km/h}$
37261 \begin_inset space \thinspace{}
37271 is not a real LaTeX command but the command
37277 , therefore you cannot use it in TeX code.
37280 \begin_layout Itemize
37281 Percent and perthousand signs are set like physical units:
37282 \begin_inset Newline newline
37286 \begin_inset space \thinspace{}
37292 \begin_layout Itemize
37293 The degree sign follows directly on the value: 15°, but not when it is used
37295 \begin_inset space \thinspace{}
37301 \begin_layout Itemize
37302 In numbers with more than four digits the smallest space is inserted before
37303 every third digit to group them:
37313 \begin_inset space \thinspace{}
37317 \begin_inset space \thinspace{}
37323 \begin_layout Itemize
37324 For dimensions like 120×90×40
37325 \begin_inset space \thinspace{}
37328 cm the multiplication sign
37329 \begin_inset Quotes eld
37333 \begin_inset Quotes erd
37337 It is available either via the command
37345 Insert\SpecialChar \menuseparator
37346 Special Character\SpecialChar \menuseparator
37352 \begin_layout Itemize
37353 Functions with names consisting of several letters are set upright to avoid
37355 \begin_inset CommandInset ref
37357 reference "sub:Predefined-Functions"
37364 \begin_layout Itemize
37365 Indices consisting of several letters, are set upright:
37366 \begin_inset Formula $E_{\mathrm{kin}}$
37370 \begin_inset Newline newline
37373 Components of matrices are set italic:
37374 \begin_inset Formula $\hat{H}_{kl}$
37380 \begin_layout Itemize
37381 The differentiation/integration operator 'd', the Euler's number 'e' and
37382 the imaginary unit 'i' should be set upright, to avoid mixing them up with
37386 \begin_layout Itemize
37387 The character that denotes a
37391 transformation is inserted either by the command
37399 \begin_layout Plain Layout
37412 Insert\SpecialChar \menuseparator
37413 Special Character\SpecialChar \menuseparator
37414 Symbols\SpecialChar \menuseparator
37416 \begin_inset space ~
37422 \begin_inset Formula $\mathscr{F}$
37428 \begin_layout Standard
37429 \begin_inset Newpage newpage
37435 \begin_layout Section
37437 \begin_inset Index idx
37440 \begin_layout Plain Layout
37449 \begin_layout Standard
37450 Some characters and symbols can be created with several commands.
37451 Here is a list of the synonym commands:
37454 \begin_layout Standard
37455 \begin_inset VSpace bigskip
37459 \begin_inset space \hfill{}
37463 \begin_inset Tabular
37464 <lyxtabular version="3" rows="12" columns="2">
37465 <features tabularvalignment="middle">
37466 <column alignment="center" valignment="top" width="0pt">
37467 <column alignment="center" valignment="top" width="0pt">
37469 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
37472 \begin_layout Plain Layout
37478 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
37481 \begin_layout Plain Layout
37483 \begin_inset Note Note
37486 \begin_layout Plain Layout
37493 is only used as spacer.
37505 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
37508 \begin_layout Plain Layout
37516 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
37519 \begin_layout Plain Layout
37523 \begin_layout Plain Layout
37536 \begin_layout Plain Layout
37550 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
37553 \begin_layout Plain Layout
37561 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
37564 \begin_layout Plain Layout
37574 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
37577 \begin_layout Plain Layout
37585 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
37588 \begin_layout Plain Layout
37598 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
37601 \begin_layout Plain Layout
37609 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
37612 \begin_layout Plain Layout
37620 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
37623 \begin_layout Plain Layout
37631 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
37634 \begin_layout Plain Layout
37642 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
37645 \begin_layout Plain Layout
37653 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
37656 \begin_layout Plain Layout
37666 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
37669 \begin_layout Plain Layout
37677 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
37680 \begin_layout Plain Layout
37690 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
37693 \begin_layout Plain Layout
37701 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
37704 \begin_layout Plain Layout
37714 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
37717 \begin_layout Plain Layout
37725 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
37728 \begin_layout Plain Layout
37738 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
37741 \begin_layout Plain Layout
37749 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
37752 \begin_layout Plain Layout
37760 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
37763 \begin_layout Plain Layout
37771 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
37774 \begin_layout Plain Layout
37786 \begin_inset space \hfill{}
37790 \begin_inset Tabular
37791 <lyxtabular version="3" rows="12" columns="2">
37792 <features tabularvalignment="middle">
37793 <column alignment="center" valignment="top" width="0pt">
37794 <column alignment="center" valignment="top" width="0pt">
37796 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
37799 \begin_layout Plain Layout
37805 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
37808 \begin_layout Plain Layout
37816 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
37819 \begin_layout Plain Layout
37827 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
37830 \begin_layout Plain Layout
37842 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
37845 \begin_layout Plain Layout
37853 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
37856 \begin_layout Plain Layout
37866 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
37869 \begin_layout Plain Layout
37877 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
37880 \begin_layout Plain Layout
37890 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
37893 \begin_layout Plain Layout
37901 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
37904 \begin_layout Plain Layout
37912 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
37915 \begin_layout Plain Layout
37923 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
37926 \begin_layout Plain Layout
37934 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
37937 \begin_layout Plain Layout
37945 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
37948 \begin_layout Plain Layout
37958 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
37961 \begin_layout Plain Layout
37969 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
37972 \begin_layout Plain Layout
37982 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
37985 \begin_layout Plain Layout
37993 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
37996 \begin_layout Plain Layout
38006 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
38009 \begin_layout Plain Layout
38017 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
38020 \begin_layout Plain Layout
38030 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
38033 \begin_layout Plain Layout
38041 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
38044 \begin_layout Plain Layout
38054 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
38057 \begin_layout Plain Layout
38065 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
38068 \begin_layout Plain Layout
38082 \begin_inset space \hfill{}
38088 \begin_layout Standard
38089 \begin_inset Newpage newpage
38095 \begin_layout Bibliography
38096 \labelwidthstring References
38097 \begin_inset CommandInset bibitem
38098 LatexCommand bibitem
38110 The LaTeX Companion
38113 Addison Wesley, 2004
38116 \begin_layout Bibliography
38117 \labelwidthstring References
38118 \begin_inset CommandInset bibitem
38119 LatexCommand bibitem
38125 \begin_inset CommandInset href
38128 target "ftp://ftp.dante.de/tex-archive/info/math/voss/mathmode/Mathmode.pdf"
38132 of LaTeX's math abilities
38135 \begin_layout Bibliography
38136 \labelwidthstring References
38137 \begin_inset CommandInset bibitem
38138 LatexCommand bibitem
38144 \begin_inset CommandInset href
38147 target "ftp://ftp.ams.org/pub/tex/doc/amsmath/amsldoc.pdf"
38155 \begin_layout Plain Layout
38167 \begin_layout Bibliography
38168 \labelwidthstring References
38169 \begin_inset CommandInset bibitem
38170 LatexCommand bibitem
38176 \begin_inset CommandInset href
38179 target "ftp://ftp.dante.de/tex-archive/info/symbols/comprehensive/symbols-a4.pdf"
38183 of all symbols available with LaTeX-packages
38186 \begin_layout Bibliography
38187 \labelwidthstring References
38188 \begin_inset CommandInset bibitem
38189 LatexCommand bibitem
38195 \begin_inset CommandInset href
38197 name "Documentation"
38198 target "http://mirrors.ctan.org/macros/latex/contrib/cancel/cancel.pdf"
38202 of the LaTeX-package
38207 \begin_inset Index idx
38210 \begin_layout Plain Layout
38219 \begin_layout Bibliography
38220 \labelwidthstring References
38221 \begin_inset CommandInset bibitem
38222 LatexCommand bibitem
38228 \begin_inset CommandInset href
38230 name "Documentation"
38231 target "http://www.tug.org/applications/hyperref/ftp/doc/manual.pdf"
38235 of the LaTeX-package
38240 \begin_inset Index idx
38243 \begin_layout Plain Layout
38244 Packages ! hyperref
38252 \begin_layout Bibliography
38253 \labelwidthstring References
38254 \begin_inset CommandInset bibitem
38255 LatexCommand bibitem
38261 \begin_inset CommandInset href
38263 name "Documentation"
38264 target "http://www.ctan.org/tex-archive/macros/latex/contrib/mhchem/mhchem.pdf"
38268 of the LaTeX-package
38273 \begin_inset Index idx
38276 \begin_layout Plain Layout
38285 \begin_layout Bibliography
38286 \labelwidthstring References
38287 \begin_inset CommandInset bibitem
38288 LatexCommand bibitem
38294 \begin_inset CommandInset href
38297 target "http://www.tug.org/TUGboat/Articles/tb22-4/tb72perlS.pdf"
38308 \begin_inset CommandInset ref
38310 reference "sub:Operator-Limits"
38315 \begin_inset Index idx
38318 \begin_layout Plain Layout
38329 \begin_layout Bibliography
38330 \labelwidthstring References
38331 \begin_inset CommandInset bibitem
38332 LatexCommand bibitem
38343 Auflage, Duden 2001
38346 \begin_layout Bibliography
38347 \labelwidthstring References
38348 \begin_inset CommandInset bibitem
38349 LatexCommand bibitem
38355 \begin_inset CommandInset href
38358 target "http://physics.nist.gov/Document/checklist.pdf"
38362 for reviewing manuscripts
38365 \begin_layout Standard
38366 \begin_inset CommandInset index_print
38367 LatexCommand printindex