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 exported 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 checked 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 which will appear bigger, has a different format, and will be in a separate
514 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 which 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 always starts 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 automatically
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 which 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 "command-alternatives space-insert protected ; math-space"
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.
1005 key can often be used instead of
1006 \begin_inset Formula $\to$
1010 \begin_inset Formula $\downarrow$
1018 \begin_inset Formula $\leftarrow$
1022 \begin_inset Formula $\uparrow$
1028 \begin_layout Subsection*
1032 \begin_layout Standard
1034 \begin_inset Float table
1040 \begin_layout Plain Layout
1042 \begin_inset Caption
1044 \begin_layout Plain Layout
1045 \begin_inset CommandInset label
1047 name "tab:Available-units"
1059 \begin_layout Plain Layout
1061 \begin_inset Tabular
1062 <lyxtabular version="3" rows="13" columns="2">
1063 <features tabularvalignment="middle">
1064 <column alignment="center" valignment="top" width="0">
1065 <column alignment="center" valignment="top" width="0">
1067 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
1070 \begin_layout Plain Layout
1076 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
1079 \begin_layout Plain Layout
1087 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
1090 \begin_layout Plain Layout
1096 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
1099 \begin_layout Plain Layout
1107 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
1110 \begin_layout Plain Layout
1116 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
1119 \begin_layout Plain Layout
1127 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
1130 \begin_layout Plain Layout
1136 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
1139 \begin_layout Plain Layout
1141 \begin_inset space \thinspace{}
1145 \begin_inset space \thinspace{}
1155 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
1158 \begin_layout Plain Layout
1164 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
1167 \begin_layout Plain Layout
1169 \begin_inset space \thinspace{}
1173 \begin_inset space \thinspace{}
1183 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
1186 \begin_layout Plain Layout
1192 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
1195 \begin_layout Plain Layout
1197 \begin_inset space \thinspace{}
1201 \begin_inset space \thinspace{}
1211 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
1214 \begin_layout Plain Layout
1220 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
1223 \begin_layout Plain Layout
1225 \begin_inset space \thinspace{}
1229 \begin_inset space \thinspace{}
1239 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
1242 \begin_layout Plain Layout
1248 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
1251 \begin_layout Plain Layout
1253 \begin_inset space \thinspace{}
1257 \begin_inset space \thinspace{}
1267 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
1270 \begin_layout Plain Layout
1276 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
1279 \begin_layout Plain Layout
1281 \begin_inset space \thinspace{}
1285 \begin_inset Formula $\approx$
1289 \begin_inset space \thinspace{}
1299 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
1302 \begin_layout Plain Layout
1308 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
1311 \begin_layout Plain Layout
1313 \begin_inset space \thinspace{}
1317 \begin_inset space \thinspace{}
1327 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
1330 \begin_layout Plain Layout
1336 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
1339 \begin_layout Plain Layout
1343 \begin_inset Quotes eld
1349 \begin_inset Quotes erd
1359 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
1362 \begin_layout Plain Layout
1368 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
1371 \begin_layout Plain Layout
1373 \begin_inset Quotes eld
1381 \begin_inset Quotes erd
1391 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
1394 \begin_layout Plain Layout
1400 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
1403 \begin_layout Plain Layout
1405 \begin_inset space \thinspace{}
1409 \begin_inset Formula $\nicefrac{1}{18}$
1413 \begin_inset space \thinspace{}
1434 \begin_layout Standard
1435 \begin_inset Newpage newpage
1441 \begin_layout Section
1445 \begin_layout Subsection
1447 \begin_inset Index idx
1450 \begin_layout Plain Layout
1457 \begin_inset Index idx
1460 \begin_layout Plain Layout
1467 \begin_inset Index idx
1470 \begin_layout Plain Layout
1475 \begin_layout Plain Layout
1486 \begin_layout Plain Layout
1499 \begin_inset Index idx
1502 \begin_layout Plain Layout
1507 \begin_layout Plain Layout
1518 \begin_layout Plain Layout
1533 \begin_layout Standard
1534 Indices are created with an underscore
1535 \begin_inset Quotes eld
1539 \begin_inset Quotes erd
1542 or via the math toolbar button
1543 \begin_inset Graphics
1544 filename ../images/math-subscript.png
1549 , exponents with a caret
1550 \begin_inset Quotes eld
1554 \begin_inset Quotes erd
1557 or via the math toolbar button
1558 \begin_inset Graphics
1559 filename ../images/math-superscript.png
1567 \begin_layout Standard
1569 \begin_inset Tabular
1570 <lyxtabular version="3" rows="4" columns="2">
1571 <features tabularvalignment="middle">
1572 <column alignment="center" valignment="top" width="0pt">
1573 <column alignment="center" valignment="top" width="0pt">
1575 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
1578 \begin_layout Plain Layout
1584 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
1587 \begin_layout Plain Layout
1589 \begin_inset Note Note
1592 \begin_layout Plain Layout
1599 is only used as spacer.
1611 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
1614 \begin_layout Plain Layout
1620 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
1623 \begin_layout Plain Layout
1624 \begin_inset Formula $B_{V}$
1634 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
1637 \begin_layout Plain Layout
1643 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
1646 \begin_layout Plain Layout
1647 \begin_inset Formula $\raisebox{5mm}{}B^{V}$
1657 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
1660 \begin_layout Plain Layout
1665 \begin_layout Plain Layout
1679 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
1682 \begin_layout Plain Layout
1683 \begin_inset Formula $\raisebox{5mm}{}B^{A}$
1699 \begin_layout Standard
1700 As the caret is in some languages an accent, vowels will be accentuated
1701 in this case and not set as exponents
1705 \begin_layout Plain Layout
1706 Depending on the used keyboard settings this can also happen for characters
1713 To get exponents in this case, press
1717 after the caret as in the last example.
1720 \begin_layout Subsection
1722 \begin_inset CommandInset label
1724 name "sub:Fractions"
1729 \begin_inset Index idx
1732 \begin_layout Plain Layout
1741 \begin_layout Standard
1742 Fractions are generated with the command
1749 \begin_inset Index idx
1752 \begin_layout Plain Layout
1760 or via the math toolbar button
1761 \begin_inset Graphics
1762 filename ../images/math/frac.png
1768 The font size is adjusted automatically, depending on whether the fraction
1769 is in an inline or display style formula.
1770 With the math toolbar button
1771 \begin_inset Graphics
1772 filename ../images/math/frac-square.png
1777 you can select different fraction types.
1780 \begin_layout Standard
1788 \begin_inset Index idx
1791 \begin_layout Plain Layout
1799 a fraction can be created that always has the size of a display style formula.
1807 \begin_inset Index idx
1810 \begin_layout Plain Layout
1818 the fraction appears always with the size of an inline formula.
1822 \begin_layout Standard
1823 A line with the fraction
1824 \begin_inset Formula $\frac{1}{2}$
1827 that was created with the command
1836 \begin_layout Standard
1837 A line with the fraction
1838 \begin_inset Formula $\dfrac{1}{2}$
1841 that was created with the command
1850 \begin_layout Standard
1852 \begin_inset Tabular
1853 <lyxtabular version="3" rows="4" columns="2">
1854 <features tabularvalignment="middle">
1855 <column alignment="center" valignment="top" width="0pt">
1856 <column alignment="center" valignment="top" width="0pt">
1858 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
1861 \begin_layout Plain Layout
1867 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
1870 \begin_layout Plain Layout
1872 \begin_inset Note Note
1875 \begin_layout Plain Layout
1882 is only used as spacer.
1894 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
1897 \begin_layout Plain Layout
1904 \begin_layout Plain Layout
1914 \begin_inset Formula $\downarrow$
1922 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
1925 \begin_layout Plain Layout
1926 \begin_inset Formula $\raisebox{4.5mm}{}\frac{A}{B}\raisebox{-2.5mm}{}$
1936 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
1939 \begin_layout Plain Layout
1946 \begin_layout Plain Layout
1956 \begin_inset Formula $\downarrow$
1964 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
1967 \begin_layout Plain Layout
1968 \begin_inset Formula $\raisebox{7mm}{}\dfrac{A}{B}\raisebox{-4mm}{}$
1978 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
1981 \begin_layout Plain Layout
1988 \begin_layout Plain Layout
2003 \begin_layout Plain Layout
2013 \begin_inset Formula $\downarrow$
2017 \begin_inset Formula $\downarrow\downarrow$
2025 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
2028 \begin_layout Plain Layout
2029 \begin_inset Formula $\raisebox{8mm}{}\dfrac{e^{\frac{1}{2}}}{3}\raisebox{-4mm}{}$
2045 \begin_layout Standard
2046 \begin_inset VSpace bigskip
2050 \begin_inset Newpage newpage
2053 For nested fractions the command
2060 \begin_inset Index idx
2063 \begin_layout Plain Layout
2073 \begin_inset VSpace -3mm
2079 \begin_layout Standard
2080 \begin_inset Formula
2082 \textrm{created with \textbf{\textbackslash frac}} & & \textrm{created with \textbf{\textbackslash cfrac}}\\
2083 \frac{A}{B+\frac{C+\frac{E}{F}}{D}} & & \cfrac{A}{B+\cfrac{C+\cfrac{E}{F}}{D}}
2091 \begin_layout Standard
2092 The command for the example above is:
2095 \begin_layout Standard
2104 \begin_layout Plain Layout
2114 \begin_inset Formula $\downarrow$
2123 \begin_layout Plain Layout
2138 \begin_layout Plain Layout
2148 \begin_inset Formula $\downarrow$
2152 \begin_inset Formula $\downarrow$
2158 \begin_layout Standard
2159 \begin_inset VSpace medskip
2165 \begin_layout Standard
2172 sets the fraction always in the size of a displayed formula, also when
2173 it is part of another fraction.
2176 \begin_layout Standard
2177 It is possible to specify the alignment of the numerator.
2184 is used to left align it, the command
2197 centers the numerator.
2198 These fractions demonstrate the different alignments:
2201 \begin_layout Standard
2204 \begin_inset Formula
2206 \cfrac[l]{A}{B+C}\,,\,\cfrac{A}{B+C}\,,\,\cfrac[r]{A}{B+C}
2214 \begin_layout Standard
2215 \begin_inset Note Greyedout
2218 \begin_layout Plain Layout
2235 are no real LaTeX commands but represent the command
2239 cfrac[alignment]{numerator}{denominator}
2242 Therefore you cannot use them in TeX code.
2250 \begin_layout Standard
2251 \begin_inset VSpace medskip
2254 It is often advantageous to combine
2267 \begin_inset Formula
2269 \cfrac{A}{B+\cfrac{C+\frac{E}{F}}{D}}
2277 \begin_layout Standard
2278 For inline fractions with a sloped fraction stroke you can use the command
2286 \begin_inset Index idx
2289 \begin_layout Plain Layout
2298 \begin_inset Formula $\nicefrac{5}{31}$
2308 \begin_inset Index idx
2311 \begin_layout Plain Layout
2320 \begin_inset Formula $\unitfrac{5}{31}$
2323 There is furthermore the command
2329 that offers to write a fraction in combination with a number:
2330 \begin_inset Formula $\unitfrac[2]{1}{3}$
2336 \begin_layout Standard
2337 \begin_inset Note Greyedout
2340 \begin_layout Plain Layout
2351 is not a real LaTeX command but the command
2352 \begin_inset Newline newline
2359 unitfrac[number]{numerator}{denominator}
2362 Therefore you cannot use it in TeX code.
2370 \begin_layout Standard
2371 How to define own fractions where the fraction stroke can be changed, is
2373 \begin_inset CommandInset ref
2375 reference "sub:Self-defined-Fractions"
2382 \begin_layout Standard
2383 \begin_inset Newpage newpage
2389 \begin_layout Subsection
2391 \begin_inset Index idx
2394 \begin_layout Plain Layout
2403 \begin_layout Standard
2404 Square roots are created with
2411 \begin_inset Index idx
2414 \begin_layout Plain Layout
2422 or the math toolbar button
2423 \begin_inset Graphics
2424 filename ../images/math/sqrt.png
2429 , all other roots with the command
2436 \begin_inset Index idx
2439 \begin_layout Plain Layout
2447 or with the math toolbar button
2448 \begin_inset Graphics
2449 filename ../images/math/root.png
2457 \begin_layout Standard
2459 \begin_inset Tabular
2460 <lyxtabular version="3" rows="3" columns="2">
2461 <features tabularvalignment="middle">
2462 <column alignment="center" valignment="top" width="0pt">
2463 <column alignment="center" valignment="top" width="0pt">
2465 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
2468 \begin_layout Plain Layout
2474 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
2477 \begin_layout Plain Layout
2479 \begin_inset Note Note
2482 \begin_layout Plain Layout
2489 is only used as spacer.
2501 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
2504 \begin_layout Plain Layout
2511 \begin_layout Plain Layout
2525 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
2528 \begin_layout Plain Layout
2529 \begin_inset Formula $\raisebox{4.5mm}{}\sqrt{A-B}$
2539 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
2542 \begin_layout Plain Layout
2549 \begin_layout Plain Layout
2559 \begin_inset Formula $\downarrow$
2567 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
2570 \begin_layout Plain Layout
2571 \begin_inset Formula $\raisebox{4.5mm}{}\sqrt[3]{A-B}$
2587 \begin_layout Standard
2588 A square root can also be created with
2594 when the root index field is left empty.
2597 \begin_layout Standard
2598 With certain indices the distance to the root is too small, like in this
2600 \begin_inset Formula $\sqrt[\beta]{B}$
2604 \begin_inset Newline newline
2608 \begin_inset Formula $\beta$
2612 To avoid this, the commands
2619 \begin_inset Index idx
2622 \begin_layout Plain Layout
2637 \begin_inset Index idx
2640 \begin_layout Plain Layout
2648 are used with the following scheme:
2651 \begin_layout Standard
2665 \begin_layout Standard
2666 Distance is the number of Big Points (unit bp;
2667 \begin_inset Formula $\mathrm{72\, bp=1\, inch}$
2670 ), that the index should be moved to the left or top, resp..
2671 The commands are written to the index.
2672 This way the command
2673 \begin_inset Newline newline
2683 \begin_inset Formula $\to$
2689 \begin_inset Formula $\to$
2698 \begin_layout Plain Layout
2708 \begin_inset Formula $\to$
2712 \begin_inset Newline newline
2717 produces a correct typeset formula:
2718 \begin_inset Formula $\sqrt[\leftroot{-1}\uproot{2}\beta]{B}$
2724 \begin_layout Subsection
2725 Binomial Coefficients
2726 \begin_inset Index idx
2729 \begin_layout Plain Layout
2730 Binomial coefficients
2738 \begin_layout Standard
2739 Binomial coefficients are inserted with the command
2746 \begin_inset Index idx
2749 \begin_layout Plain Layout
2757 or with the submenu of the math toolbar button
2758 \begin_inset Graphics
2759 filename ../images/math/frac-square.png
2777 there are the commands
2784 \begin_inset Index idx
2787 \begin_layout Plain Layout
2802 \begin_inset Index idx
2805 \begin_layout Plain Layout
2814 For other brackets around binomial coeficients there are the commands
2821 \begin_inset Index idx
2824 \begin_layout Plain Layout
2839 \begin_inset Index idx
2842 \begin_layout Plain Layout
2853 \begin_layout Standard
2855 \begin_inset Tabular
2856 <lyxtabular version="3" rows="6" columns="2">
2857 <features tabularvalignment="middle">
2858 <column alignment="center" valignment="top" width="0pt">
2859 <column alignment="center" valignment="top" width="0pt">
2861 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
2864 \begin_layout Plain Layout
2870 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
2873 \begin_layout Plain Layout
2875 \begin_inset Note Note
2878 \begin_layout Plain Layout
2885 is only used as spacer.
2897 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
2900 \begin_layout Plain Layout
2907 \begin_layout Plain Layout
2917 \begin_inset Formula $\downarrow$
2925 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
2928 \begin_layout Plain Layout
2929 \begin_inset Formula $\raisebox{5mm}{}\binom{A}{B}\raisebox{-2.5mm}{}$
2939 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
2942 \begin_layout Plain Layout
2949 \begin_layout Plain Layout
2959 \begin_inset Formula $\downarrow$
2967 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
2970 \begin_layout Plain Layout
2971 \begin_inset Formula $\raisebox{5mm}{}\dbinom{A}{B}\raisebox{-2.5mm}{}$
2981 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
2984 \begin_layout Plain Layout
2991 \begin_layout Plain Layout
3001 \begin_inset Formula $\downarrow$
3009 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
3012 \begin_layout Plain Layout
3013 \begin_inset Formula $\raisebox{5mm}{}\tbinom{A}{B}\raisebox{-2.5mm}{}$
3023 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
3026 \begin_layout Plain Layout
3033 \begin_layout Plain Layout
3043 \begin_inset Formula $\downarrow$
3051 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
3054 \begin_layout Plain Layout
3055 \begin_inset Formula $\raisebox{5mm}{}{A \brack B}\raisebox{-2.5mm}{}$
3065 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
3068 \begin_layout Plain Layout
3075 \begin_layout Plain Layout
3085 \begin_inset Formula $\downarrow$
3093 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
3096 \begin_layout Plain Layout
3097 \begin_inset Formula $\raisebox{5mm}{}{A \brace B}\raisebox{-2.5mm}{}$
3113 \begin_layout Subsection
3114 Case Differentiations
3115 \begin_inset Index idx
3118 \begin_layout Plain Layout
3119 Case differentiations
3127 \begin_layout Standard
3129 \begin_inset Tabular
3130 <lyxtabular version="3" rows="3" columns="2">
3131 <features tabularvalignment="middle">
3132 <column alignment="center" valignment="top" width="0pt">
3133 <column alignment="center" valignment="top" width="0pt">
3135 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
3138 \begin_layout Plain Layout
3144 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
3147 \begin_layout Plain Layout
3155 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
3158 \begin_layout Plain Layout
3165 \begin_layout Plain Layout
3175 \begin_inset Formula $\to$
3179 \begin_inset Index idx
3182 \begin_layout Plain Layout
3195 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
3198 \begin_layout Plain Layout
3199 \begin_inset Formula $\begin{cases}
3210 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
3213 \begin_layout Plain Layout
3220 \begin_layout Plain Layout
3232 arg "newline-insert newline"
3240 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
3243 \begin_layout Plain Layout
3244 \begin_inset Formula $\begin{cases}
3245 A & \textrm{for }x>0\\
3246 B & \textrm{for }x=0
3263 \begin_layout Standard
3270 or pressing the math toolbar button
3271 \begin_inset Graphics
3272 filename ../images/math/cases.png
3277 you can create new lines with the shortcut
3280 arg "newline-insert newline"
3283 or the table toolbar button
3284 \begin_inset Graphics
3285 filename ../images/tabular-feature_append-row.png
3293 \begin_layout Standard
3300 is also available via the menu
3302 Insert\SpecialChar \menuseparator
3303 Math\SpecialChar \menuseparator
3309 \begin_layout Subsection
3311 \begin_inset Index idx
3314 \begin_layout Plain Layout
3323 \begin_layout Standard
3331 \begin_inset Index idx
3334 \begin_layout Plain Layout
3342 every character can be displayed canceled.
3343 The characters are quasi accentuated by a slash.
3346 \begin_layout Standard
3348 \begin_inset Tabular
3349 <lyxtabular version="3" rows="4" columns="2">
3350 <features tabularvalignment="middle">
3351 <column alignment="center" valignment="top" width="0pt">
3352 <column alignment="center" valignment="top" width="0pt">
3354 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
3357 \begin_layout Plain Layout
3363 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
3366 \begin_layout Plain Layout
3374 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
3377 \begin_layout Plain Layout
3385 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
3388 \begin_layout Plain Layout
3389 \begin_inset Formula $\not=$
3399 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
3402 \begin_layout Plain Layout
3412 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
3415 \begin_layout Plain Layout
3416 \begin_inset Formula $\not\le$
3426 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
3429 \begin_layout Plain Layout
3439 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
3442 \begin_layout Plain Layout
3443 \begin_inset Formula $\not\parallel$
3459 \begin_layout Standard
3460 The last example shows that not all negations look good.
3461 Therefore there are special commands for some negations (see
3462 \begin_inset CommandInset ref
3464 reference "sub:Mathematical-Symbols"
3469 \begin_inset CommandInset ref
3471 reference "sec:Relations"
3478 \begin_layout Subsection
3480 \begin_inset CommandInset label
3482 name "sub:Placeholders"
3487 \begin_inset Index idx
3490 \begin_layout Plain Layout
3497 \begin_inset Index idx
3500 \begin_layout Plain Layout
3501 Chemical characters ! Isotopes
3507 \begin_inset Index idx
3510 \begin_layout Plain Layout
3515 \begin_layout Plain Layout
3526 \begin_layout Plain Layout
3541 \begin_layout Standard
3543 \begin_inset space \thinspace{}
3547 \begin_inset space \space{}
3554 \begin_layout Plain Layout
3555 Typesetting isotopes and chemical symbols is described in
3556 \begin_inset CommandInset ref
3558 reference "sub:Chemical-Symbols-and"
3567 the following problem occurs:
3570 \begin_layout Standard
3572 \begin_inset Tabular
3573 <lyxtabular version="3" rows="2" columns="2">
3574 <features tabularvalignment="middle">
3575 <column alignment="center" valignment="top" width="0pt">
3576 <column alignment="center" valignment="top" width="0pt">
3578 <cell alignment="center" valignment="top" usebox="none">
3581 \begin_layout Plain Layout
3582 Indices created with sub- and superscripts:
3587 <cell alignment="center" valignment="top" usebox="none">
3590 \begin_layout Plain Layout
3591 \begin_inset Formula $_{9}^{19}\mathrm{F}\raisebox{-3mm}{}$
3601 <cell alignment="center" valignment="top" usebox="none">
3604 \begin_layout Plain Layout
3610 <cell alignment="center" valignment="top" usebox="none">
3613 \begin_layout Plain Layout
3614 \begin_inset Formula $_{\phantom{1}9}^{19}\mathrm{F}$
3628 \begin_inset Note Note
3631 \begin_layout Plain Layout
3638 is only used as spacer.
3646 \begin_layout Standard
3647 The shorter index is by default placed below or above the first character
3648 of the longer index.
3649 To avoid this there is the command
3656 \begin_inset Index idx
3659 \begin_layout Plain Layout
3667 or the math toolbar button
3668 \begin_inset space \thinspace{}
3675 \begin_layout Plain Layout
3676 can be found in the submenu of the toolbar button
3677 \begin_inset Graphics
3678 filename ../images/math/space.png
3689 \begin_inset Graphics
3690 filename ../images/math/phantom.png
3695 that creates one or more phantom characters.
3702 a small blue box appears that is superposed with two red arrows.
3703 The arrows indicate that the complete width and height of the box content
3704 will be created as placeholder.
3705 Phantom characters are accordingly placeholders with the size of the characters.
3708 \begin_layout Standard
3710 \begin_inset Tabular
3711 <lyxtabular version="3" rows="4" columns="2">
3712 <features tabularvalignment="middle">
3713 <column alignment="center" valignment="top" width="0">
3714 <column alignment="center" valignment="top" width="0">
3716 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
3719 \begin_layout Plain Layout
3725 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
3728 \begin_layout Plain Layout
3730 \begin_inset Note Note
3733 \begin_layout Plain Layout
3740 is only used as spacer.
3752 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
3755 \begin_layout Plain Layout
3760 \begin_layout Plain Layout
3775 \begin_layout Plain Layout
3785 \begin_inset Formula $\to$
3792 \begin_layout Plain Layout
3806 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
3809 \begin_layout Plain Layout
3810 \begin_inset Formula $\raisebox{4.5mm}{}{}_{\phantom{1}9}^{19}\mathrm{F}\raisebox{-2.5mm}{}$
3820 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
3823 \begin_layout Plain Layout
3828 \begin_layout Plain Layout
3843 \begin_layout Plain Layout
3853 \begin_inset Formula $\to$
3860 \begin_layout Plain Layout
3874 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
3877 \begin_layout Plain Layout
3878 \begin_inset Formula $\raisebox{4.5mm}{}{}_{\phantom{23}9}^{235}\mathrm{F}\raisebox{-2.5mm}{}$
3888 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
3891 \begin_layout Plain Layout
3898 \begin_layout Plain Layout
3913 \begin_layout Plain Layout
3923 \begin_inset Formula $\to$
3930 \begin_layout Plain Layout
3944 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
3947 \begin_layout Plain Layout
3948 \begin_inset Formula $\raisebox{4.5mm}{}\Lambda_{MMt}^{\phantom{ii}t}\raisebox{-2.5mm}{}$
3964 \begin_layout Standard
3965 Furthermore there are the commands
3972 \begin_inset Index idx
3975 \begin_layout Plain Layout
3984 \begin_inset space ~
3988 \begin_inset Graphics
3989 filename ../images/math/vphantom.png
4001 \begin_inset Index idx
4004 \begin_layout Plain Layout
4013 \begin_inset space ~
4017 \begin_inset Graphics
4018 filename ../images/math/hphantom.png
4030 creates only space for the maximal height of the characters in the box
4031 but not for its width.
4038 creates only space for the width of the box content.
4039 Therefore the boxes of both commands have only one red arrow.
4042 \begin_layout Standard
4043 For example the command
4053 \begin_layout Plain Layout
4068 creates space for the height of the integral sign,
4072 \begin_layout Plain Layout
4079 creates an integral sign, see
4080 \begin_inset CommandInset ref
4082 reference "sub:Big-Operators"
4091 because this is the larger character.
4092 An example application is in
4093 \begin_inset CommandInset ref
4095 reference "sub:Multiline-Brackets"
4102 \begin_layout Standard
4103 Placeholders can also be used for text when they are inserted via the menu
4106 Insert\SpecialChar \menuseparator
4107 Formatting\SpecialChar \menuseparator
4113 \begin_layout Standard
4115 \begin_inset Newline newline
4119 \begin_inset Phantom Phantom
4122 \begin_layout Plain Layout
4131 \begin_layout Subsection
4133 \begin_inset Index idx
4136 \begin_layout Plain Layout
4143 \begin_inset Index idx
4146 \begin_layout Plain Layout
4147 Formula ! underlined
4155 \begin_layout Standard
4157 \begin_inset Tabular
4158 <lyxtabular version="3" rows="4" columns="2">
4159 <features tabularvalignment="middle">
4160 <column alignment="center" valignment="top" width="0pt">
4161 <column alignment="center" valignment="top" width="0pt">
4163 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
4166 \begin_layout Plain Layout
4172 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
4175 \begin_layout Plain Layout
4177 \begin_inset Note Note
4180 \begin_layout Plain Layout
4187 is only used as spacer.
4199 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
4202 \begin_layout Plain Layout
4209 \begin_layout Plain Layout
4219 \begin_inset Index idx
4222 \begin_layout Plain Layout
4235 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
4238 \begin_layout Plain Layout
4239 \begin_inset Formula $\raisebox{5mm}{}\overline{A+B}$
4249 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
4252 \begin_layout Plain Layout
4259 \begin_layout Plain Layout
4269 \begin_inset Index idx
4272 \begin_layout Plain Layout
4285 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
4288 \begin_layout Plain Layout
4289 \begin_inset Formula $\underline{A+B}\raisebox{-2.5mm}{}$
4299 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
4302 \begin_layout Plain Layout
4309 \begin_layout Plain Layout
4324 \begin_layout Plain Layout
4338 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
4341 \begin_layout Plain Layout
4342 \begin_inset Formula $\raisebox{5mm}{}\overline{\underline{A+B}}\raisebox{-2.5mm}{}$
4358 \begin_layout Standard
4359 In the last example it doesn't matter if first
4374 \begin_layout Standard
4375 To double underline use
4384 \begin_layout Standard
4385 It is possible to place up to 6 lines above or below characters.
4388 \begin_layout Standard
4389 \begin_inset VSpace bigskip
4392 Custom lines can be created using the command
4399 \begin_inset Index idx
4402 \begin_layout Plain Layout
4410 which has the following scheme:
4413 \begin_layout Standard
4418 rule[vertical offset]{length}{thickness}
4421 \begin_layout Standard
4422 The optional vertical offset shifts the line upwards (or downwards, when
4423 the value is negative).
4425 \begin_inset CommandInset ref
4427 reference "tab:Available-units"
4431 can be used for the values.
4432 Here are two example lines created with the commands
4433 \begin_inset Newline newline
4440 rule[-2ex]{3cm}{2pt}
4451 \begin_layout Standard
4453 \begin_inset Formula $\rule[-2ex]{3cm}{2pt}\rule{2cm}{1pt}$
4459 \begin_layout Standard
4466 can also be used for text when a line is inserted via the menu
4468 Insert\SpecialChar \menuseparator
4469 Formatting\SpecialChar \menuseparator
4471 \begin_inset space ~
4479 \begin_layout Standard
4481 \begin_inset CommandInset line
4492 \begin_layout Subsection
4494 \begin_inset CommandInset label
4501 \begin_inset Index idx
4504 \begin_layout Plain Layout
4513 \begin_layout Standard
4514 There are different types of ellipses available.
4518 \begin_layout Plain Layout
4519 In the math toolbar in the submenu of the button
4520 \begin_inset Graphics
4521 filename ../images/math/ldots.png
4531 For listings dots at the baseline are used (
4538 \begin_inset Index idx
4541 \begin_layout Plain Layout
4549 ), while for operations dots are needed that are on the same height as the
4557 \begin_inset Index idx
4560 \begin_layout Plain Layout
4569 When using the command
4576 \begin_inset Index idx
4579 \begin_layout Plain Layout
4587 , LaTeX decides on the basis of the next character what type is used.
4590 \begin_layout Standard
4592 \begin_inset Tabular
4593 <lyxtabular version="3" rows="9" columns="2">
4594 <features tabularvalignment="middle">
4595 <column alignment="center" valignment="top" width="0pt">
4596 <column alignment="center" valignment="top" width="0pt">
4598 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
4601 \begin_layout Plain Layout
4607 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
4610 \begin_layout Plain Layout
4618 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
4621 \begin_layout Plain Layout
4626 \begin_layout Plain Layout
4641 \begin_layout Plain Layout
4655 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
4658 \begin_layout Plain Layout
4659 \begin_inset Formula $A_{1},\dots,A_{n}$
4669 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
4672 \begin_layout Plain Layout
4677 \begin_layout Plain Layout
4692 \begin_layout Plain Layout
4706 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
4709 \begin_layout Plain Layout
4710 \begin_inset Formula $A_{1}+\dots+A_{n}$
4720 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
4723 \begin_layout Plain Layout
4728 \begin_layout Plain Layout
4743 \begin_layout Plain Layout
4757 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
4760 \begin_layout Plain Layout
4761 \begin_inset Formula $A_{1},\ldots,A_{n}$
4771 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
4774 \begin_layout Plain Layout
4779 \begin_layout Plain Layout
4794 \begin_layout Plain Layout
4808 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
4811 \begin_layout Plain Layout
4812 \begin_inset Formula $A_{1}+\cdots+A_{n}$
4822 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
4825 \begin_layout Plain Layout
4833 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
4836 \begin_layout Plain Layout
4837 \begin_inset Formula $\vdots$
4847 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
4850 \begin_layout Plain Layout
4858 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
4861 \begin_layout Plain Layout
4862 \begin_inset Formula $\ddots$
4872 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
4875 \begin_layout Plain Layout
4883 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
4886 \begin_layout Plain Layout
4887 \begin_inset Formula $\iddots$
4897 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
4900 \begin_layout Plain Layout
4902 \begin_inset space \thinspace{}
4905 matrix with the different dots
4910 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
4913 \begin_layout Plain Layout
4914 \begin_inset Formula $\begin{array}{ccc}
4915 A_{11} & \cdots & A_{1m}\\
4916 \vdots & \ddots & \vdots\\
4917 A_{n1} & \cdots & A_{nm}
4934 \begin_layout Standard
4935 The ellipses available in menu
4937 Insert\SpecialChar \menuseparator
4939 \begin_inset space ~
4953 \begin_layout Standard
4954 \begin_inset VSpace medskip
4963 , one of the options
4965 Use mathdots package (automatically)
4967 must be set in the document settings under
4970 \begin_inset space ~
4976 \begin_inset Newline newline
4981 Use mathdots package
4983 will improve the appearance of all dots in the documents if their font
4984 style or size is not the default.
4987 \begin_layout Standard
4988 \begin_inset VSpace medskip
4991 Specially for matrices there are ellipses that span over several columns.
4992 They are created with the command
4999 \begin_inset Index idx
5002 \begin_layout Plain Layout
5010 , that has the following scheme:
5013 \begin_layout Standard
5018 hdotsfor[distance]{number of columns}
5021 \begin_layout Standard
5022 The number of columns specifies how many columns should be spanned.
5023 Distance is a factor for the distance between the dots.
5026 \begin_layout Standard
5027 In the following matrix the command
5033 was inserted in the first box of the second line, to get an ellipsis with
5034 a dot distance twice as long as with the command
5041 \begin_inset Formula
5043 \left(\begin{array}{cccc}
5052 Note that the matrix fields that should be spanned must be empty, otherwise
5053 you get LaTeX-errors.
5056 \begin_layout Standard
5057 \begin_inset VSpace bigskip
5060 Furthermore you can fill with the command
5067 \begin_inset Index idx
5070 \begin_layout Plain Layout
5078 the rest of a line with dots.
5079 The effect of these commands is the same as with
5086 \begin_inset CommandInset ref
5088 reference "sub:Variable-Space"
5095 \begin_layout Standard
5096 For example the command
5104 \begin_layout Plain Layout
5118 \begin_layout Standard
5119 \begin_inset Formula $A\dotfill B$
5125 \begin_layout Standard
5132 there is for a line the command
5139 \begin_inset Index idx
5142 \begin_layout Plain Layout
5153 \begin_layout Standard
5154 \begin_inset Formula $A\hrulefill B$
5160 \begin_layout Standard
5161 To use the commands for text, they have to be inserted in TeX-mode.
5164 \begin_layout Section
5166 \begin_inset CommandInset label
5173 \begin_inset Index idx
5176 \begin_layout Plain Layout
5185 \begin_layout Standard
5186 Matrices can be inserted via the math toolbar button
5187 \begin_inset Graphics
5188 filename ../images/dialog-show_mathmatrix.png
5195 Insert\SpecialChar \menuseparator
5196 Math\SpecialChar \menuseparator
5200 In the matrix dialog you can specify the number of columns and rows, the
5201 alignment and the decoration.
5202 The vertical alignment is only of importance for matrices in inline formulas:
5205 \begin_layout Standard
5206 The first matrix is top
5207 \begin_inset Formula $\begin{array}[t]{cccc}
5215 \begin_inset Formula $\begin{array}{cccc}
5222 and the third bottom
5223 \begin_inset Formula $\begin{array}[b]{cccc}
5233 \begin_layout Standard
5234 The horizontal alignment specifies how the column entries should be aligned.
5235 It is set by entering a letter for every column.
5240 denotes left aligned,
5249 To create for example a 4
5254 \begin_inset space ~
5257 matrix where the first column is left aligned, the second and third are
5258 centered and the last one is right aligned, one enters for the horizontal
5264 Normally in a matrix all columns are centered, therefore the default for
5272 \begin_layout Standard
5273 Horizontal alignment:
5276 \begin_layout Standard
5282 \begin_inset Formula $\begin{array}{lll}
5294 \begin_inset Formula $\begin{array}{ccc}
5306 \begin_inset Formula $\begin{array}{rrr}
5316 \begin_layout Standard
5317 To add or delete rows and columns subsequently, the math toolbar buttons
5319 \begin_inset Graphics
5320 filename ../images/tabular-feature_append-row.png
5326 \begin_inset Graphics
5327 filename ../images/tabular-feature_delete-row.png
5333 \begin_inset space \thinspace{}
5338 Edit\SpecialChar \menuseparator
5342 New rows can also be created with
5345 arg "newline-insert newline"
5351 \begin_layout Standard
5352 \begin_inset VSpace bigskip
5359 adds parentheses in the selected style around the matrix.
5360 Alternatively, parentheses can can either be created with the commands
5368 \begin_inset Index idx
5371 \begin_layout Plain Layout
5386 \begin_inset Index idx
5389 \begin_layout Plain Layout
5400 \begin_inset space ~
5406 \begin_inset CommandInset ref
5408 reference "sub:Automatic-Bracket-Size"
5412 , or by using the following commands:
5413 \begin_inset VSpace medskip
5419 \begin_layout Standard
5420 \begin_inset space \hfill{}
5424 \begin_inset Tabular
5425 <lyxtabular version="3" rows="4" columns="2">
5426 <features tabularvalignment="middle">
5427 <column alignment="center" valignment="top" width="0">
5428 <column alignment="center" valignment="top" width="0">
5430 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
5433 \begin_layout Plain Layout
5439 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
5442 \begin_layout Plain Layout
5444 \begin_inset Note Note
5447 \begin_layout Plain Layout
5454 is only used as spacer.
5466 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
5469 \begin_layout Plain Layout
5476 \begin_layout Plain Layout
5490 \begin_inset space \thinspace{}
5498 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
5501 \begin_layout Plain Layout
5502 \begin_inset Formula $\raisebox{7.5mm}{}\begin{bmatrix}\begin{array}{cc}
5503 0 & \textrm{-}\mathrm{i}\\
5505 \end{array}\end{bmatrix}\raisebox{-5.3mm}{}$
5515 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
5518 \begin_layout Plain Layout
5525 \begin_layout Plain Layout
5539 \begin_inset space \thinspace{}
5547 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
5550 \begin_layout Plain Layout
5551 \begin_inset Formula $\raisebox{7.5mm}{}\begin{Bmatrix}\begin{array}{cc}
5552 0 & \textrm{-}\mathrm{i}\\
5554 \end{array}\end{Bmatrix}\raisebox{-5.3mm}{}$
5564 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
5567 \begin_layout Plain Layout
5574 \begin_layout Plain Layout
5588 \begin_inset space \thinspace{}
5596 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
5599 \begin_layout Plain Layout
5600 \begin_inset Formula $\raisebox{7.5mm}{}\begin{pmatrix}\begin{array}{cc}
5601 0 & \textrm{-}\mathrm{i}\\
5603 \end{array}\end{pmatrix}\raisebox{-5.3mm}{}$
5617 \begin_inset space \hfill{}
5621 \begin_inset Tabular
5622 <lyxtabular version="3" rows="4" columns="2">
5623 <features tabularvalignment="middle">
5624 <column alignment="center" valignment="top" width="0">
5625 <column alignment="center" valignment="top" width="0">
5627 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
5630 \begin_layout Plain Layout
5636 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
5639 \begin_layout Plain Layout
5647 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
5650 \begin_layout Plain Layout
5657 \begin_layout Plain Layout
5671 \begin_inset space \thinspace{}
5679 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
5682 \begin_layout Plain Layout
5683 \begin_inset Formula $\raisebox{7.5mm}{}\begin{vmatrix}\begin{array}{cc}
5684 0 & \textrm{-}\mathrm{i}\\
5686 \end{array}\end{vmatrix}\raisebox{-5.3mm}{}$
5696 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
5699 \begin_layout Plain Layout
5706 \begin_layout Plain Layout
5720 \begin_inset space \thinspace{}
5728 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
5731 \begin_layout Plain Layout
5732 \begin_inset Formula $\raisebox{7.5mm}{}\begin{Vmatrix}\begin{array}{cc}
5733 0 & \textrm{-}\mathrm{i}\\
5735 \end{array}\end{Vmatrix}\raisebox{-5.3mm}{}$
5745 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
5748 \begin_layout Plain Layout
5755 \begin_layout Plain Layout
5769 \begin_inset space \thinspace{}
5777 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
5780 \begin_layout Plain Layout
5781 \begin_inset Formula $\raisebox{7.5mm}{}\begin{matrix}\begin{array}{cc}
5782 0 & \textrm{-}\mathrm{i}\\
5784 \end{array}\end{matrix}\raisebox{-5.3mm}{}$
5798 \begin_inset space \hfill{}
5804 \begin_layout Standard
5805 \begin_inset VSpace medskip
5809 \begin_inset space \thinspace{}
5813 \begin_inset space \space{}
5822 is inserted, a blue box appears between two vertical lines where the matrix
5824 \begin_inset Newline newline
5827 Note that decorated matrices ignore the vertical alignment.
5830 \begin_layout Standard
5831 \begin_inset Note Greyedout
5834 \begin_layout Plain Layout
5839 LaTeX limits the number of matrix columns with decorations to 10.
5840 If you need more than 10
5841 \begin_inset space ~
5844 columns, you have to add this line to the document preamble:
5847 \begin_layout Plain Layout
5852 setcounter{MaxMatrixCols}{number}
5855 \begin_layout Plain Layout
5860 is the number of columns between 11 and 99.
5868 \begin_layout Standard
5869 \begin_inset VSpace bigskip
5872 As all multiline formulas are matrices, the length
5879 \begin_inset Index idx
5882 \begin_layout Plain Layout
5890 that is described in
5891 \begin_inset CommandInset ref
5893 reference "sub:Column-Separation"
5897 can also be used to change the column separation of matrices.
5900 \begin_layout Standard
5901 To change the row separation, the command
5908 \begin_inset Index idx
5911 \begin_layout Plain Layout
5920 It is used as follows:
5923 \begin_layout Standard
5930 arraystretch}{stretch factor}
5931 \begin_inset Index idx
5934 \begin_layout Plain Layout
5945 \begin_layout Standard
5952 assigns the stretch factor to the predefined command
5960 \begin_inset space \thinspace{}
5964 \begin_inset space \space{}
5967 the row separation, use the factor 2.
5968 This is then used for all following matrices.
5969 To go back to the original separation, assign the factor 1 to
5978 \begin_layout Standard
5979 To set matrices into a text line, the command
5986 \begin_inset Index idx
5989 \begin_layout Plain Layout
5998 When it is inserted a blue box with two dashed lines appears.
5999 In this box the matrix is inserted.
6002 \begin_layout Standard
6004 \begin_inset Formula $\left(\begin{smallmatrix}A & B\\
6006 \end{smallmatrix}\right)$
6012 \begin_layout Section
6013 Brackets and Delimiters
6014 \begin_inset Index idx
6017 \begin_layout Plain Layout
6024 \begin_inset Index idx
6027 \begin_layout Plain Layout
6036 \begin_layout Subsection
6037 Vertical Brackets and Delimiters
6038 \begin_inset Index idx
6041 \begin_layout Plain Layout
6050 \begin_layout Standard
6051 \begin_inset space \hfill{}
6055 \begin_inset Tabular
6056 <lyxtabular version="3" rows="9" columns="2">
6057 <features tabularvalignment="middle">
6058 <column alignment="center" valignment="top" width="0pt">
6059 <column alignment="center" valignment="top" width="0pt">
6061 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
6064 \begin_layout Plain Layout
6070 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
6073 \begin_layout Plain Layout
6081 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
6084 \begin_layout Plain Layout
6090 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
6093 \begin_layout Plain Layout
6094 \begin_inset Formula $($
6104 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
6107 \begin_layout Plain Layout
6113 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
6116 \begin_layout Plain Layout
6117 \begin_inset Formula $\{$
6127 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
6130 \begin_layout Plain Layout
6136 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
6139 \begin_layout Plain Layout
6140 \begin_inset Formula $[$
6150 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
6153 \begin_layout Plain Layout
6161 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
6164 \begin_layout Plain Layout
6165 \begin_inset Formula $\langle$
6175 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
6178 \begin_layout Plain Layout
6186 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
6189 \begin_layout Plain Layout
6190 \begin_inset Formula $\lceil$
6200 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
6203 \begin_layout Plain Layout
6211 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
6214 \begin_layout Plain Layout
6215 \begin_inset Formula $\lfloor$
6225 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
6228 \begin_layout Plain Layout
6234 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
6237 \begin_layout Plain Layout
6238 \begin_inset Formula $/$
6248 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
6251 \begin_layout Plain Layout
6257 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
6260 \begin_layout Plain Layout
6261 \begin_inset Formula $|$
6275 \begin_inset space \hfill{}
6279 \begin_inset Tabular
6280 <lyxtabular version="3" rows="9" columns="2">
6281 <features tabularvalignment="middle">
6282 <column alignment="center" valignment="top" width="0pt">
6283 <column alignment="center" valignment="top" width="0pt">
6285 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
6288 \begin_layout Plain Layout
6294 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
6297 \begin_layout Plain Layout
6305 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
6308 \begin_layout Plain Layout
6314 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
6317 \begin_layout Plain Layout
6318 \begin_inset Formula $)$
6328 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
6331 \begin_layout Plain Layout
6337 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
6340 \begin_layout Plain Layout
6341 \begin_inset Formula $\}$
6351 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
6354 \begin_layout Plain Layout
6360 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
6363 \begin_layout Plain Layout
6364 \begin_inset Formula $]$
6374 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
6377 \begin_layout Plain Layout
6385 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
6388 \begin_layout Plain Layout
6389 \begin_inset Formula $\rangle$
6399 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
6402 \begin_layout Plain Layout
6410 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
6413 \begin_layout Plain Layout
6414 \begin_inset Formula $\rceil$
6424 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
6427 \begin_layout Plain Layout
6435 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
6438 \begin_layout Plain Layout
6439 \begin_inset Formula $\rfloor$
6449 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
6452 \begin_layout Plain Layout
6462 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
6465 \begin_layout Plain Layout
6466 \begin_inset Formula $\backslash$
6476 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
6479 \begin_layout Plain Layout
6487 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
6490 \begin_layout Plain Layout
6491 \begin_inset Formula $\|$
6505 \begin_inset space \hfill{}
6511 \begin_layout Standard
6514 \begin_inset Note Greyedout
6517 \begin_layout Plain Layout
6522 In TeX-mode the command
6529 \begin_inset Index idx
6532 \begin_layout Plain Layout
6540 must be used for the backslash, because the command
6548 produces a line break there.
6556 \begin_layout Standard
6557 For all characters listed above the size can be adjusted with the commands
6558 described in the following two subsections.
6559 When using these commands, the characters < and > can directly be used
6560 instead of the commands
6575 \begin_layout Subsubsection
6577 \begin_inset CommandInset label
6579 name "sub:Manual-Bracket-Size"
6584 \begin_inset Index idx
6587 \begin_layout Plain Layout
6588 Bracket size ! manual
6596 \begin_layout Standard
6597 The bracket size can be specified manually by the LaTeX-commands
6604 \begin_inset Index idx
6607 \begin_layout Plain Layout
6640 denotes the smallest and
6646 the largest bracket size.
6649 \begin_layout Standard
6650 These commands are used to emphasize levels of brackets:
6653 \begin_layout Standard
6655 \begin_inset Tabular
6656 <lyxtabular version="3" rows="2" columns="2">
6657 <features tabularvalignment="middle">
6658 <column alignment="center" valignment="top" width="0pt">
6659 <column alignment="center" valignment="top" width="0pt">
6661 <cell alignment="center" valignment="top" usebox="none">
6664 \begin_layout Plain Layout
6665 all brackets in the same size:
6670 <cell alignment="center" valignment="top" usebox="none">
6673 \begin_layout Plain Layout
6674 \begin_inset Formula $((A+B)(A-B))^{C}\raisebox{-4mm}{}$
6684 <cell alignment="center" valignment="top" usebox="none">
6687 \begin_layout Plain Layout
6693 <cell alignment="center" valignment="top" usebox="none">
6696 \begin_layout Plain Layout
6697 \begin_inset Formula $\Big((A+B)(A-B)\Big)^{C}$
6711 \begin_inset Note Note
6714 \begin_layout Plain Layout
6721 is only used as spacer.
6729 \begin_layout Standard
6730 For the second formula the command
6740 \begin_layout Plain Layout
6754 \begin_layout Standard
6755 Here is an overview about all bracket sizes:
6758 \begin_layout Standard
6778 \begin_layout Plain Layout
6795 \begin_layout Plain Layout
6808 \begin_layout Plain Layout
6824 \begin_layout Standard
6826 \begin_inset Formula $\Bigg(\exp\bigg<\Big[\big\{\ln(3x)\big\}^{2}\sin(x)\Big]^{A}\bigg>\Bigg)^{0,5}$
6832 \begin_layout Standard
6839 -commands there is the variant
6846 \begin_inset Index idx
6849 \begin_layout Plain Layout
6857 that adds a bit more space between the bracket and its content, and the
6871 \begin_inset Index idx
6874 \begin_layout Plain Layout
6884 , that don't add additional space.
6889 at the end of the command
6895 is for a left bracket; for a right bracket this will be replaced by an
6901 A left or right bracket can each be an opening or closing bracket.
6904 \begin_layout Standard
6905 In the following table is a comparison of the variants:
6908 \begin_layout Standard
6910 \begin_inset Tabular
6911 <lyxtabular version="3" rows="5" columns="2">
6912 <features tabularvalignment="middle">
6913 <column alignment="center" valignment="middle" width="0">
6914 <column alignment="center" valignment="middle" width="0">
6916 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
6919 \begin_layout Plain Layout
6925 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
6928 \begin_layout Plain Layout
6930 \begin_inset Note Note
6933 \begin_layout Plain Layout
6940 is only used as spacer.
6952 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
6955 \begin_layout Plain Layout
6970 \begin_layout Plain Layout
6988 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
6991 \begin_layout Plain Layout
6992 \begin_inset Formula $\raisebox{5.5mm}{}\Bigm(\bigm(\ln(3x)\bigm)^{2}\Bigm)\raisebox{-3.25mm}{}$
7002 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
7005 \begin_layout Plain Layout
7020 \begin_layout Plain Layout
7038 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
7041 \begin_layout Plain Layout
7042 \begin_inset Formula $\raisebox{5.5mm}{}\Big(\big(\ln(3x)\big)^{2}\Big)\raisebox{-3.25mm}{}$
7052 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
7055 \begin_layout Plain Layout
7070 \begin_layout Plain Layout
7088 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
7091 \begin_layout Plain Layout
7092 \begin_inset Formula $\raisebox{5.5mm}{}\Bigl(\bigl(\ln(3x)\bigr)^{2}\Bigr)\raisebox{-3.25mm}{}$
7102 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
7105 \begin_layout Plain Layout
7117 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
7120 \begin_layout Plain Layout
7121 \begin_inset Formula $\raisebox{4.5mm}{}\bigl)\ln(3x)\bigr(\raisebox{-2mm}{}$
7137 \begin_layout Subsubsection
7138 Automatic Bracket Size
7139 \begin_inset CommandInset label
7141 name "sub:Automatic-Bracket-Size"
7146 \begin_inset Index idx
7149 \begin_layout Plain Layout
7150 Bracket size ! automatic
7158 \begin_layout Standard
7159 Brackets with variable size can be inserted with the commands
7166 \begin_inset Index idx
7169 \begin_layout Plain Layout
7184 \begin_inset Index idx
7187 \begin_layout Plain Layout
7195 or via the math toolbar button
7196 \begin_inset Graphics
7197 filename ../images/dialog-show_mathdelimiter.png
7215 the wanted bracket must be inserted.
7216 The bracket size will then automatically be calculated for the output.
7219 \begin_layout Standard
7221 normal bracket: The command
7231 \begin_layout Plain Layout
7241 \begin_inset Formula $\downarrow$
7248 \begin_layout Plain Layout
7260 \begin_inset Formula
7270 \begin_layout Standard
7272 multiline bracket: The command
7284 \begin_layout Plain Layout
7294 \begin_inset Formula $\downarrow$
7301 \begin_layout Plain Layout
7315 \begin_inset Formula
7317 \ln\left(\frac{A}{C}\right)
7325 \begin_layout Standard
7341 \begin_inset space ~
7347 This has the advantage that you can see in LyX immediately the real bracket
7348 size and that the matching right bracket will be created too.
7349 \begin_inset Newline newline
7352 The command for the last example would then be:
7366 \begin_layout Plain Layout
7376 \begin_inset Formula $\downarrow$
7382 \begin_layout Standard
7383 To omit a left or right bracket, a dot is inserted for the omitted bracket.
7384 For example the command
7394 \begin_layout Plain Layout
7404 \begin_inset Formula $\downarrow$
7411 \begin_layout Plain Layout
7427 \begin_inset Formula
7429 \left.\frac{A}{B}\right\}
7448 will be converted by LyX to brackets in the right size when the document
7449 is reloaded and an omitted bracket will appear as dashed line.
7452 \begin_layout Standard
7453 \begin_inset VSpace bigskip
7456 Because all popular LaTeX-Distributions use eTeX, an extension to LaTeX,
7464 \begin_inset Index idx
7467 \begin_layout Plain Layout
7475 is additionally available for all brackets and limits.
7476 With this command the height of the following character is adapted to the
7477 one of the surrounding brackets, what is e.
7478 \begin_inset space \thinspace{}
7482 \begin_inset space \space{}
7485 needed for physical vectors:
7486 \begin_inset Formula
7488 \left\langle \phi\:\middle|\: J=\frac{3}{2}\,,\, M_{J}\right\rangle
7493 For physical vectors there is a special LaTeX-package, described in
7494 \begin_inset CommandInset ref
7496 reference "sub:Physical-Vectors"
7503 \begin_layout Subsection
7505 \begin_inset Index idx
7508 \begin_layout Plain Layout
7509 Brackets ! horizontal
7517 \begin_layout Standard
7519 \begin_inset Tabular
7520 <lyxtabular version="3" rows="4" columns="2">
7521 <features tabularvalignment="middle">
7522 <column alignment="center" valignment="top" width="0pt">
7523 <column alignment="center" valignment="top" width="0pt">
7525 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
7528 \begin_layout Plain Layout
7530 \begin_inset Note Note
7533 \begin_layout Plain Layout
7540 is only used as spacer.
7550 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
7553 \begin_layout Plain Layout
7561 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
7564 \begin_layout Plain Layout
7568 \begin_layout Plain Layout
7583 \begin_layout Plain Layout
7596 \begin_layout Plain Layout
7609 \begin_layout Plain Layout
7622 \begin_layout Plain Layout
7630 \begin_inset Index idx
7633 \begin_layout Plain Layout
7646 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
7649 \begin_layout Plain Layout
7650 \begin_inset Formula $\overbrace{A+B}^{3}$
7660 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
7663 \begin_layout Plain Layout
7667 \begin_layout Plain Layout
7682 \begin_layout Plain Layout
7695 \begin_layout Plain Layout
7708 \begin_layout Plain Layout
7716 \begin_inset Index idx
7719 \begin_layout Plain Layout
7732 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
7735 \begin_layout Plain Layout
7736 \begin_inset Formula $\underbrace{A+B}_{5}$
7746 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
7749 \begin_layout Plain Layout
7756 \begin_layout Plain Layout
7771 \begin_layout Plain Layout
7784 \begin_layout Plain Layout
7797 \begin_layout Plain Layout
7810 \begin_layout Plain Layout
7823 \begin_layout Plain Layout
7836 \begin_layout Plain Layout
7850 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
7853 \begin_layout Plain Layout
7854 \begin_inset Formula $\overbrace{\underbrace{A+B_{w}}_{7}}^{C}$
7870 \begin_layout Standard
7871 In the last example it doesn't matter if
7883 is inserted at first.
7886 \begin_layout Standard
7887 \begin_inset VSpace bigskip
7890 When brackets are needed that overlap each other, multiline formulas, as
7892 \begin_inset CommandInset ref
7894 reference "sec:Multiline-Formulas"
7899 \begin_inset Formula
7901 A & = & \underbrace{gggg+bbqq}_{r}+\: dddd\\
7902 & & \hphantom{gggg+\:}\underbrace{\hphantom{bbqq+dddd}}_{s}
7907 In the first row the formula is inserted together with the first brace.
7908 It is hereby important that the space command
7912 \begin_layout Plain Layout
7913 Space commands are explained in
7914 \begin_inset CommandInset ref
7916 reference "sub:Predefined-Space"
7931 is inserted before the first
7932 \begin_inset Formula $d$
7935 , because the brace that ends behind the
7936 \begin_inset Formula $q$
7939 prevents that the following
7940 \begin_inset Quotes eld
7944 \begin_inset Quotes erd
7947 is surrounded by space.
7951 \begin_layout Plain Layout
7952 because a bracket is not handled as a character, see
7953 \begin_inset CommandInset ref
7955 reference "sub:Binary-Operators"
7964 In the second row the second brace is inserted.
7965 As it should begin before the
7966 \begin_inset Formula $b$
7981 \begin_layout Plain Layout
7989 \begin_inset CommandInset ref
7991 reference "sub:Placeholders"
8000 This space is needed because the
8001 \begin_inset Quotes eld
8005 \begin_inset Quotes erd
8008 is also surrounded by space in the formula.
8009 The brace is placed under the command
8018 \begin_layout Standard
8019 It gets more complicated when brackets overlap each other, like in the following
8024 \begin_layout Plain Layout
8036 \begin_inset Formula
8038 & & \hphantom{gggg+\:}\overbrace{\hphantom{bbqq+dddd}}^{s}\\
8039 A & = & \underbrace{gggg+bbqq}_{r}+\: dddd
8048 \begin_layout Plain Layout
8059 The first formula row is the same as the second row of the previous example,
8060 with the difference that the brace is above.
8061 The second row contains the formula together with the second brace.
8062 To avoid that there is space between the upper brace in the first row and
8063 the formula, the row spacing needs to be reduced.
8064 This is not easily possible due to a bug in LyX
8068 \begin_layout Plain Layout
8069 \begin_inset CommandInset href
8071 name "LyX-bug #1505"
8072 target "http://www.lyx.org/trac/ticket/1505"
8082 As a solution for the problem, the global formula row separation
8089 \begin_inset Index idx
8092 \begin_layout Plain Layout
8100 must be changed to -6
8101 \begin_inset space \thinspace{}
8104 pt before the formula with the command
8119 is set back after the formula to the standard value of 3
8120 \begin_inset space \thinspace{}
8123 pt using the same command.
8124 More about the row separation in formulas is explained in
8125 \begin_inset CommandInset ref
8127 reference "sub:Line-Separation"
8134 \begin_layout Section
8136 \begin_inset Index idx
8139 \begin_layout Plain Layout
8148 \begin_layout Standard
8149 Arrows can be inserted via the math toolbar button
8150 \begin_inset Graphics
8151 filename ../images/math/leftarrow.png
8156 or the commands listed in the following subsections.
8159 \begin_layout Subsection
8161 \begin_inset Index idx
8164 \begin_layout Plain Layout
8173 \begin_layout Standard
8174 \begin_inset space \hfill{}
8178 \begin_inset Tabular
8179 <lyxtabular version="3" rows="8" columns="2">
8180 <features tabularvalignment="middle">
8181 <column alignment="center" valignment="top" width="0pt">
8182 <column alignment="center" valignment="top" width="0pt">
8184 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
8187 \begin_layout Plain Layout
8193 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
8196 \begin_layout Plain Layout
8204 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
8207 \begin_layout Plain Layout
8215 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
8218 \begin_layout Plain Layout
8219 \begin_inset Formula $\gets$
8229 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
8232 \begin_layout Plain Layout
8240 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
8243 \begin_layout Plain Layout
8244 \begin_inset Formula $\Leftarrow$
8254 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
8257 \begin_layout Plain Layout
8265 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
8268 \begin_layout Plain Layout
8269 \begin_inset Formula $\longleftarrow$
8279 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
8282 \begin_layout Plain Layout
8290 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
8293 \begin_layout Plain Layout
8294 \begin_inset Formula $\Longleftarrow$
8304 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
8307 \begin_layout Plain Layout
8315 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
8318 \begin_layout Plain Layout
8319 \begin_inset Formula $\leftharpoonup$
8329 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
8332 \begin_layout Plain Layout
8340 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
8343 \begin_layout Plain Layout
8344 \begin_inset Formula $\leftharpoondown$
8354 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
8357 \begin_layout Plain Layout
8365 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
8368 \begin_layout Plain Layout
8369 \begin_inset Formula $\hookleftarrow$
8383 \begin_inset space \hfill{}
8387 \begin_inset Tabular
8388 <lyxtabular version="3" rows="8" columns="2">
8389 <features tabularvalignment="middle">
8390 <column alignment="center" valignment="top" width="0pt">
8391 <column alignment="center" valignment="top" width="0pt">
8393 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
8396 \begin_layout Plain Layout
8402 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
8405 \begin_layout Plain Layout
8413 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
8416 \begin_layout Plain Layout
8424 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
8427 \begin_layout Plain Layout
8428 \begin_inset Formula $\to$
8438 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
8441 \begin_layout Plain Layout
8449 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
8452 \begin_layout Plain Layout
8453 \begin_inset Formula $\Rightarrow$
8463 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
8466 \begin_layout Plain Layout
8474 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
8477 \begin_layout Plain Layout
8478 \begin_inset Formula $\longrightarrow$
8488 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
8491 \begin_layout Plain Layout
8499 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
8502 \begin_layout Plain Layout
8503 \begin_inset Formula $\Longrightarrow$
8513 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
8516 \begin_layout Plain Layout
8524 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
8527 \begin_layout Plain Layout
8528 \begin_inset Formula $\rightharpoonup$
8538 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
8541 \begin_layout Plain Layout
8549 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
8552 \begin_layout Plain Layout
8553 \begin_inset Formula $\rightharpoondown$
8563 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
8566 \begin_layout Plain Layout
8574 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
8577 \begin_layout Plain Layout
8578 \begin_inset Formula $\hookrightarrow$
8592 \begin_inset space \hfill{}
8598 \begin_layout Standard
8599 \begin_inset space \hfill{}
8603 \begin_inset Tabular
8604 <lyxtabular version="3" rows="6" columns="2">
8605 <features tabularvalignment="middle">
8606 <column alignment="center" valignment="top" width="0pt">
8607 <column alignment="center" valignment="top" width="0pt">
8609 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
8612 \begin_layout Plain Layout
8618 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
8621 \begin_layout Plain Layout
8629 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
8632 \begin_layout Plain Layout
8640 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
8643 \begin_layout Plain Layout
8644 \begin_inset Formula $\leftrightarrow$
8654 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
8657 \begin_layout Plain Layout
8665 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
8668 \begin_layout Plain Layout
8669 \begin_inset Formula $\Leftrightarrow$
8679 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
8682 \begin_layout Plain Layout
8690 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
8693 \begin_layout Plain Layout
8694 \begin_inset Formula $\longleftrightarrow$
8704 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
8707 \begin_layout Plain Layout
8715 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
8718 \begin_layout Plain Layout
8719 \begin_inset Formula $\Longleftrightarrow$
8729 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
8732 \begin_layout Plain Layout
8740 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
8743 \begin_layout Plain Layout
8744 \begin_inset Formula $\rightleftharpoons$
8758 \begin_inset space \hspace{}
8763 \begin_inset space \hfill{}
8767 \begin_inset Tabular
8768 <lyxtabular version="3" rows="5" columns="2">
8769 <features tabularvalignment="middle">
8770 <column alignment="center" valignment="top" width="0pt">
8771 <column alignment="center" valignment="top" width="0pt">
8773 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
8776 \begin_layout Plain Layout
8782 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
8785 \begin_layout Plain Layout
8793 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
8796 \begin_layout Plain Layout
8804 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
8807 \begin_layout Plain Layout
8808 \begin_inset Formula $\mapsto$
8818 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
8821 \begin_layout Plain Layout
8829 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
8832 \begin_layout Plain Layout
8833 \begin_inset Formula $\longmapsto$
8843 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
8846 \begin_layout Plain Layout
8854 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
8857 \begin_layout Plain Layout
8858 \begin_inset Formula $\leadsto$
8868 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
8871 \begin_layout Plain Layout
8879 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
8882 \begin_layout Plain Layout
8883 \begin_inset Formula $\dasharrow$
8897 \begin_inset space \hfill{}
8903 \begin_layout Standard
8904 \begin_inset VSpace medskip
8907 Arrows used as accents like e.
8908 \begin_inset space \thinspace{}
8912 \begin_inset space \space{}
8915 vector arrows are listed in
8916 \begin_inset CommandInset ref
8918 reference "sec:Accents"
8925 \begin_layout Standard
8926 \begin_inset VSpace bigskip
8929 Furthermore there are the labeled arrows
8930 \begin_inset Index idx
8933 \begin_layout Plain Layout
8946 \begin_inset Index idx
8949 \begin_layout Plain Layout
8964 \begin_inset Index idx
8967 \begin_layout Plain Layout
8974 \begin_layout Plain Layout
8989 When inserting one of these commands in a formula, an arrow with two blue
8990 boxes appear where the label can be inserted.
8991 The length of the arrow adapts to the label width.
8994 \begin_layout Standard
8996 \begin_inset Tabular
8997 <lyxtabular version="3" rows="3" columns="2">
8998 <features tabularvalignment="middle">
8999 <column alignment="center" valignment="top" width="0pt">
9000 <column alignment="center" valignment="top" width="0pt">
9002 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
9005 \begin_layout Plain Layout
9011 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
9014 \begin_layout Plain Layout
9016 \begin_inset Note Note
9019 \begin_layout Plain Layout
9026 is only used as spacer.
9038 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
9041 \begin_layout Plain Layout
9048 \begin_layout Plain Layout
9058 \begin_inset Formula $\downarrow$
9062 \begin_inset Formula $\to$
9070 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
9073 \begin_layout Plain Layout
9074 \begin_inset Formula $\raisebox{5mm}{}F(a)\xleftarrow[x>0]{x=a}F(x)\raisebox{-4mm}{}$
9084 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
9087 \begin_layout Plain Layout
9094 \begin_layout Plain Layout
9104 \begin_inset Formula $\downarrow$
9108 \begin_inset Formula $\to$
9116 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
9119 \begin_layout Plain Layout
9120 \begin_inset Formula $\raisebox{5mm}{}F(x)\xrightarrow[x>0]{x=a}F(a)\raisebox{-4mm}{}$
9136 \begin_layout Subsection
9137 Vertical and diagonal Arrows
9138 \begin_inset Index idx
9141 \begin_layout Plain Layout
9148 \begin_inset Index idx
9151 \begin_layout Plain Layout
9160 \begin_layout Standard
9161 \begin_inset space \hfill{}
9165 \begin_inset Tabular
9166 <lyxtabular version="3" rows="7" columns="2">
9167 <features tabularvalignment="middle">
9168 <column alignment="center" valignment="top" width="0pt">
9169 <column alignment="center" valignment="top" width="0pt">
9171 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
9174 \begin_layout Plain Layout
9180 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
9183 \begin_layout Plain Layout
9191 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
9194 \begin_layout Plain Layout
9202 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
9205 \begin_layout Plain Layout
9206 \begin_inset Formula $\uparrow$
9216 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
9219 \begin_layout Plain Layout
9227 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
9230 \begin_layout Plain Layout
9231 \begin_inset Formula $\Uparrow$
9241 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
9244 \begin_layout Plain Layout
9252 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
9255 \begin_layout Plain Layout
9256 \begin_inset Formula $\updownarrow$
9266 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
9269 \begin_layout Plain Layout
9277 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
9280 \begin_layout Plain Layout
9281 \begin_inset Formula $\Updownarrow$
9291 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
9294 \begin_layout Plain Layout
9302 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
9305 \begin_layout Plain Layout
9306 \begin_inset Formula $\Downarrow$
9316 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
9319 \begin_layout Plain Layout
9327 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
9330 \begin_layout Plain Layout
9331 \begin_inset Formula $\downarrow$
9345 \begin_inset space \hfill{}
9349 \begin_inset Tabular
9350 <lyxtabular version="3" rows="5" columns="2">
9351 <features tabularvalignment="middle">
9352 <column alignment="center" valignment="top" width="0pt">
9353 <column alignment="center" valignment="top" width="0pt">
9355 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
9358 \begin_layout Plain Layout
9364 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
9367 \begin_layout Plain Layout
9375 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
9378 \begin_layout Plain Layout
9386 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
9389 \begin_layout Plain Layout
9390 \begin_inset Formula $\nearrow$
9400 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
9403 \begin_layout Plain Layout
9411 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
9414 \begin_layout Plain Layout
9415 \begin_inset Formula $\searrow$
9425 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
9428 \begin_layout Plain Layout
9436 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
9439 \begin_layout Plain Layout
9440 \begin_inset Formula $\swarrow$
9450 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
9453 \begin_layout Plain Layout
9461 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
9464 \begin_layout Plain Layout
9465 \begin_inset Formula $\nwarrow$
9479 \begin_inset space \hfill{}
9485 \begin_layout Standard
9486 \begin_inset VSpace medskip
9489 Vertical arrows can be used also as delimiters together with the commands
9491 \begin_inset CommandInset ref
9493 reference "sub:Manual-Bracket-Size"
9498 \begin_inset CommandInset ref
9500 reference "sub:Automatic-Bracket-Size"
9507 \begin_layout Section
9509 \begin_inset CommandInset label
9516 \begin_inset Index idx
9519 \begin_layout Plain Layout
9528 \begin_layout Standard
9529 Accents can be inserted via the math toolbar button
9530 \begin_inset Graphics
9531 filename ../images/math/hat.png
9536 or the commands listed in the following subsections.
9539 \begin_layout Subsection
9540 Accents for one Character
9544 \begin_layout Plain Layout
9557 \begin_layout Plain Layout
9559 \begin_inset CommandInset ref
9561 reference "sub:Accents-in-Text"
9574 \begin_layout Plain Layout
9582 \begin_inset Note Note
9585 \begin_layout Plain Layout
9592 is used to avoid that the footnote appears in the PDF-bookmark.
9595 \begin_layout Plain Layout
9603 \begin_inset CommandInset ref
9605 reference "sub:Formulas-in-Section"
9615 \begin_inset CommandInset label
9617 name "sub:Accents-for-one"
9622 \begin_inset Index idx
9625 \begin_layout Plain Layout
9626 Accents ! for one character
9634 \begin_layout Standard
9635 \begin_inset space \hfill{}
9639 \begin_inset Tabular
9640 <lyxtabular version="3" rows="8" columns="2">
9641 <features tabularvalignment="middle">
9642 <column alignment="center" valignment="top" width="0pt">
9643 <column alignment="center" valignment="top" width="0pt">
9645 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
9648 \begin_layout Plain Layout
9654 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
9657 \begin_layout Plain Layout
9659 \begin_inset Note Note
9662 \begin_layout Plain Layout
9669 is only used as spacer.
9681 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
9684 \begin_layout Plain Layout
9691 \begin_layout Plain Layout
9705 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
9708 \begin_layout Plain Layout
9709 \begin_inset Formula $\raisebox{5mm}{}\dot{A}$
9719 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
9722 \begin_layout Plain Layout
9729 \begin_layout Plain Layout
9743 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
9746 \begin_layout Plain Layout
9747 \begin_inset Formula $\raisebox{5mm}{}\ddot{A}$
9757 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
9760 \begin_layout Plain Layout
9767 \begin_layout Plain Layout
9781 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
9784 \begin_layout Plain Layout
9785 \begin_inset Formula $\raisebox{5mm}{}\dddot{A}$
9795 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
9798 \begin_layout Plain Layout
9805 \begin_layout Plain Layout
9819 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
9822 \begin_layout Plain Layout
9823 \begin_inset Formula $\raisebox{5mm}{}\ddddot{A}$
9833 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
9836 \begin_layout Plain Layout
9843 \begin_layout Plain Layout
9853 \begin_inset Index idx
9856 \begin_layout Plain Layout
9867 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
9870 \begin_layout Plain Layout
9871 \begin_inset Formula $\raisebox{5mm}{}\vec{A}$
9881 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
9884 \begin_layout Plain Layout
9891 \begin_layout Plain Layout
9905 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
9908 \begin_layout Plain Layout
9909 \begin_inset Formula $\raisebox{5mm}{}\bar{A}$
9919 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
9922 \begin_layout Plain Layout
9929 \begin_layout Plain Layout
9943 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
9946 \begin_layout Plain Layout
9947 \begin_inset Formula $\raisebox{5mm}{}\mathring{A}$
9961 \begin_inset space \hfill{}
9965 \begin_inset Tabular
9966 <lyxtabular version="3" rows="7" columns="2">
9967 <features tabularvalignment="middle">
9968 <column alignment="center" valignment="top" width="0pt">
9969 <column alignment="center" valignment="top" width="0pt">
9971 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
9974 \begin_layout Plain Layout
9980 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
9983 \begin_layout Plain Layout
9991 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
9994 \begin_layout Plain Layout
10001 \begin_layout Plain Layout
10015 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
10018 \begin_layout Plain Layout
10019 \begin_inset Formula $\raisebox{5mm}{}\tilde{A}$
10029 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
10032 \begin_layout Plain Layout
10039 \begin_layout Plain Layout
10053 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
10056 \begin_layout Plain Layout
10057 \begin_inset Formula $\raisebox{5mm}{}\hat{A}$
10067 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
10070 \begin_layout Plain Layout
10077 \begin_layout Plain Layout
10091 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
10094 \begin_layout Plain Layout
10095 \begin_inset Formula $\raisebox{5mm}{}\check{A}$
10105 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
10108 \begin_layout Plain Layout
10115 \begin_layout Plain Layout
10129 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
10132 \begin_layout Plain Layout
10133 \begin_inset Formula $\raisebox{5mm}{}\acute{A}$
10143 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
10146 \begin_layout Plain Layout
10153 \begin_layout Plain Layout
10167 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
10170 \begin_layout Plain Layout
10171 \begin_inset Formula $\raisebox{5mm}{}\grave{A}$
10181 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
10184 \begin_layout Plain Layout
10191 \begin_layout Plain Layout
10205 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
10208 \begin_layout Plain Layout
10209 \begin_inset Formula $\raisebox{5mm}{}\breve{A}$
10223 \begin_inset space \hfill{}
10229 \begin_layout Standard
10230 \begin_inset VSpace bigskip
10236 \begin_layout Standard
10237 You can directly insert accents like é to formulas.
10238 LyX will transform them to the corresponding accent command.
10240 \begin_inset Index idx
10243 \begin_layout Plain Layout
10249 it is better to insert a quotation mark before the vowel.
10250 These two characters are then treated by LaTeX as
10254 character when the formula part with the umlaut is marked as German.
10262 \begin_inset Quotes eld
10266 \begin_inset Quotes erd
10269 umlauts are created as demonstrated in the following example:
10272 \begin_layout Standard
10273 \begin_inset VSpace -2mm
10279 \begin_layout Standard
10281 \begin_inset Tabular
10282 <lyxtabular version="3" rows="3" columns="2">
10283 <features tabularvalignment="middle">
10284 <column alignment="center" valignment="top" width="0">
10285 <column alignment="center" valignment="top" width="0">
10287 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
10290 \begin_layout Plain Layout
10296 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
10299 \begin_layout Plain Layout
10301 \begin_inset Note Note
10304 \begin_layout Plain Layout
10312 \begin_inset space \thinspace{}
10315 pt space are only used as spacer.
10327 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
10330 \begin_layout Plain Layout
10333 \begin_inset Quotes grd
10341 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
10344 \begin_layout Plain Layout
10345 \begin_inset space \hspace{}
10352 \begin_inset Formula $"i$
10362 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
10365 \begin_layout Plain Layout
10372 \begin_layout Plain Layout
10386 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
10389 \begin_layout Plain Layout
10390 \begin_inset Formula $\raisebox{5mm}{}\ddot{i}$
10406 \begin_layout Standard
10407 Another advantage to
10413 is that umlauts can directly be converted to mathematical text because
10414 the accent commands above are
10420 in mathematical text
10423 To convert an accented character to mathematical text, only the character
10424 under the accent may be converted.
10425 This applies also for all other conversions, e.
10426 \begin_inset space \thinspace{}
10430 \begin_inset space \space{}
10436 \begin_layout Standard
10437 In mathematical text, umlauts and other accented characters can directly
10441 \begin_layout Subsection
10442 Accents for Operators
10443 \begin_inset Index idx
10446 \begin_layout Plain Layout
10447 Accents ! for operators
10455 \begin_layout Standard
10463 \begin_inset Index idx
10466 \begin_layout Plain Layout
10481 \begin_inset Index idx
10484 \begin_layout Plain Layout
10492 characters can be placed above or below an operator, respectively, to accent
10501 \begin_inset Index idx
10504 \begin_layout Plain Layout
10512 characters can be set before and behind an operator.
10513 The command scheme is:
10516 \begin_layout Standard
10532 \begin_layout Standard
10539 must always be before the operator that should be accented.
10540 You can accent with several characters and even with other operators and
10548 for example only characters behind an operator, write nothing between the
10549 first braces but don't omit the braces.
10552 \begin_layout Standard
10553 For example the command
10558 \begin_inset Formula $\to$
10568 \begin_inset Formula $\to$
10577 \begin_layout Plain Layout
10593 \begin_inset Formula
10595 \sideset{}{'}\sum_{k=1}^{n}
10603 \begin_layout Standard
10612 \begin_layout Plain Layout
10627 \begin_layout Plain Layout
10639 \begin_inset Formula $\uparrow$
10647 \begin_inset Formula
10649 \overset{a}{\maltese}
10654 As seen in the last example, with
10666 symbols and characters can also be accented; with
10672 this is not possible.
10675 \begin_layout Subsection
10676 Accents for several Characters
10677 \begin_inset Index idx
10680 \begin_layout Plain Layout
10681 Accents ! for several characters
10689 \begin_layout Standard
10690 \begin_inset space \hfill{}
10694 \begin_inset Tabular
10695 <lyxtabular version="3" rows="5" columns="2">
10696 <features tabularvalignment="middle">
10697 <column alignment="center" valignment="top" width="0pt">
10698 <column alignment="center" valignment="top" width="0pt">
10700 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
10703 \begin_layout Plain Layout
10709 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
10712 \begin_layout Plain Layout
10714 \begin_inset Note Note
10717 \begin_layout Plain Layout
10724 is only used as spacer.
10736 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
10739 \begin_layout Plain Layout
10746 \begin_layout Plain Layout
10760 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
10763 \begin_layout Plain Layout
10764 \begin_inset Formula $\raisebox{6mm}{}\overleftarrow{A=B}\raisebox{-2mm}{}$
10774 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
10777 \begin_layout Plain Layout
10784 \begin_layout Plain Layout
10798 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
10801 \begin_layout Plain Layout
10802 \begin_inset Formula $\raisebox{5mm}{}\underleftarrow{A=B}\raisebox{-3mm}{}$
10812 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
10815 \begin_layout Plain Layout
10822 \begin_layout Plain Layout
10836 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
10839 \begin_layout Plain Layout
10840 \begin_inset Formula $\raisebox{6mm}{}\overleftrightarrow{A=B}\raisebox{-2mm}{}$
10850 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
10853 \begin_layout Plain Layout
10856 underleftrightarrow
10860 \begin_layout Plain Layout
10874 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
10877 \begin_layout Plain Layout
10878 \begin_inset Formula $\raisebox{5mm}{}\underleftrightarrow{A=B}\raisebox{-3mm}{}$
10892 \begin_inset space \hfill{}
10896 \begin_inset Tabular
10897 <lyxtabular version="3" rows="5" columns="2">
10898 <features tabularvalignment="middle">
10899 <column alignment="center" valignment="top" width="0pt">
10900 <column alignment="center" valignment="top" width="0pt">
10902 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
10905 \begin_layout Plain Layout
10911 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
10914 \begin_layout Plain Layout
10922 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
10925 \begin_layout Plain Layout
10932 \begin_layout Plain Layout
10946 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
10949 \begin_layout Plain Layout
10950 \begin_inset Formula $\raisebox{6mm}{}\overrightarrow{A=B}\raisebox{-2mm}{}$
10960 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
10963 \begin_layout Plain Layout
10970 \begin_layout Plain Layout
10984 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
10987 \begin_layout Plain Layout
10988 \begin_inset Formula $\raisebox{5mm}{}\underrightarrow{A=B}\raisebox{-3mm}{}$
10998 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
11001 \begin_layout Plain Layout
11008 \begin_layout Plain Layout
11022 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
11025 \begin_layout Plain Layout
11026 \begin_inset Formula $\raisebox{6mm}{}\widetilde{A=B}\raisebox{-2mm}{}$
11036 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
11039 \begin_layout Plain Layout
11046 \begin_layout Plain Layout
11060 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
11063 \begin_layout Plain Layout
11064 \begin_inset Formula $\raisebox{6mm}{}\widehat{A=B}\raisebox{-2mm}{}$
11078 \begin_inset space \hfill{}
11084 \begin_layout Standard
11085 \begin_inset VSpace medskip
11088 With these commands as many characters as you like can be accented.
11101 will only be set in the output with a length of three characters, as shown
11102 in the following example:
11103 \begin_inset Formula
11105 \widetilde{A+B=C-D}
11113 \begin_layout Standard
11121 \begin_inset Index idx
11124 \begin_layout Plain Layout
11139 \begin_inset Index idx
11142 \begin_layout Plain Layout
11150 described in the previous subsection it is also possible to accent several
11160 \begin_layout Plain Layout
11170 \begin_inset Formula $\downarrow$
11176 \begin_inset Formula
11178 \underset{***}{A=B}
11186 \begin_layout Section
11188 \begin_inset CommandInset label
11195 \begin_inset Index idx
11198 \begin_layout Plain Layout
11207 \begin_layout Subsection
11209 \begin_inset CommandInset label
11211 name "sub:Predefined-Space"
11216 \begin_inset Index idx
11219 \begin_layout Plain Layout
11220 Space ! horizontal ! predefined
11228 \begin_layout Standard
11229 Sometimes it is necessary to insert horizontal space into a formula.
11230 This is done by inserting a protected space (shortcut
11233 arg "command-alternatives space-insert protected ; math-space"
11238 \begin_inset Quotes eld
11247 \begin_layout Plain Layout
11259 \begin_inset Quotes erd
11262 appears and by pressing
11266 several times one can select one of eight different space sizes.
11267 The spaces can also be inserted using the math toolbar button
11268 \begin_inset Graphics
11269 filename ../images/math/space.png
11274 or special commands.
11275 Independent from the inserted command, one can select the size again by
11283 \begin_layout Standard
11286 \begin_inset VSpace -5mm
11290 \begin_inset Tabular
11291 <lyxtabular version="3" rows="3" columns="7">
11292 <features tabularvalignment="middle">
11293 <column alignment="center" valignment="middle" width="6.8cm">
11294 <column alignment="center" valignment="top" width="0">
11295 <column alignment="center" valignment="top" width="0">
11296 <column alignment="center" valignment="top" width="0">
11297 <column alignment="center" valignment="top" width="0">
11298 <column alignment="center" valignment="top" width="0">
11299 <column alignment="center" valignment="top" width="0">
11301 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
11304 \begin_layout Plain Layout
11310 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
11313 \begin_layout Plain Layout
11321 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
11324 \begin_layout Plain Layout
11332 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
11335 \begin_layout Plain Layout
11343 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
11346 \begin_layout Plain Layout
11354 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
11357 \begin_layout Plain Layout
11365 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
11368 \begin_layout Plain Layout
11378 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
11381 \begin_layout Plain Layout
11386 keystrokes after inserting the protected space
11391 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
11394 \begin_layout Plain Layout
11400 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
11403 \begin_layout Plain Layout
11409 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
11412 \begin_layout Plain Layout
11418 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
11421 \begin_layout Plain Layout
11427 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
11430 \begin_layout Plain Layout
11436 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
11439 \begin_layout Plain Layout
11447 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
11450 \begin_layout Plain Layout
11456 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
11459 \begin_layout Plain Layout
11460 \begin_inset Formula $A\, B$
11468 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
11471 \begin_layout Plain Layout
11472 \begin_inset Formula $A\: B$
11480 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
11483 \begin_layout Plain Layout
11484 \begin_inset Formula $A\; B$
11492 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
11495 \begin_layout Plain Layout
11496 \begin_inset Formula $A\quad B$
11504 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
11507 \begin_layout Plain Layout
11508 \begin_inset Formula $A\qquad B$
11516 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
11519 \begin_layout Plain Layout
11520 \begin_inset Formula $A\! B$
11536 \begin_layout Standard
11537 The last size seem to produce no space.
11538 It is displayed red in LyX contrary to the other sizes, because it is a
11540 There are two more negative spaces:
11543 \begin_layout Standard
11545 \begin_inset Tabular
11546 <lyxtabular version="3" rows="3" columns="3">
11547 <features tabularvalignment="middle">
11548 <column alignment="center" valignment="middle" width="6.8cm">
11549 <column alignment="center" valignment="top" width="0pt">
11550 <column alignment="center" valignment="top" width="0pt">
11552 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
11555 \begin_layout Plain Layout
11561 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
11564 \begin_layout Plain Layout
11572 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
11575 \begin_layout Plain Layout
11585 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
11588 \begin_layout Plain Layout
11593 keystrokes after inserting the protected space
11598 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
11601 \begin_layout Plain Layout
11607 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
11610 \begin_layout Plain Layout
11618 <cell multicolumn="1" alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
11621 \begin_layout Plain Layout
11627 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
11630 \begin_layout Plain Layout
11631 \begin_inset Formula $A\negmedspace B$
11639 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
11642 \begin_layout Plain Layout
11643 \begin_inset Formula $A\negthickspace B$
11659 \begin_layout Standard
11660 Negative spaces can lead to characters overlapping each other.
11661 Thus they can be used to enforce ligatures, which are e.
11662 \begin_inset space \thinspace{}
11666 \begin_inset space \space{}
11669 useful for summation operators:
11672 \begin_layout Standard
11674 \begin_inset Tabular
11675 <lyxtabular version="3" rows="3" columns="2">
11676 <features tabularvalignment="middle">
11677 <column alignment="center" valignment="top" width="0">
11678 <column alignment="center" valignment="top" width="0">
11680 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
11683 \begin_layout Plain Layout
11689 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
11692 \begin_layout Plain Layout
11694 \begin_inset Note Note
11697 \begin_layout Plain Layout
11704 is only used as spacer.
11716 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
11719 \begin_layout Plain Layout
11728 \begin_layout Plain Layout
11742 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
11745 \begin_layout Plain Layout
11746 \begin_inset Formula $\raisebox{4.5mm}{}\sum\sum f_{kl}\raisebox{-2.5mm}{}$
11756 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
11759 \begin_layout Plain Layout
11770 \begin_layout Plain Layout
11784 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
11787 \begin_layout Plain Layout
11788 \begin_inset Formula $\raisebox{4.5mm}{}\sum\negmedspace\sum f_{kl}\raisebox{-2.5mm}{}$
11804 \begin_layout Standard
11805 Relations like for example equal signs, are always surrounded by space.
11806 To suppress this, the equal sign is placed into a TeX-brace.
11807 The following example demonstrates this:
11810 \begin_layout Standard
11812 \begin_inset Tabular
11813 <lyxtabular version="3" rows="2" columns="2">
11814 <features tabularvalignment="middle">
11815 <column alignment="center" valignment="top" width="0pt">
11816 <column alignment="center" valignment="top" width="0pt">
11818 <cell alignment="center" valignment="top" usebox="none">
11821 \begin_layout Plain Layout
11827 <cell alignment="center" valignment="top" usebox="none">
11830 \begin_layout Plain Layout
11831 \begin_inset Formula $A=B$
11841 <cell alignment="center" valignment="top" usebox="none">
11844 \begin_layout Plain Layout
11845 \begin_inset Note Note
11848 \begin_layout Plain Layout
11855 is only used as spacer.
11861 \begin_inset Formula $\raisebox{5mm}{}$
11864 equation without space
11869 <cell multicolumn="1" alignment="center" valignment="top" usebox="none">
11872 \begin_layout Plain Layout
11873 \begin_inset Formula $A{=}B$
11889 \begin_layout Standard
11891 The command for the last formula is:
11896 \begin_inset Formula $\to$
11902 \begin_layout Standard
11903 \begin_inset VSpace bigskip
11906 Spaces are needed for physical units, because the space between the value
11907 and the unit is the smallest one and not a normal space.
11908 For units in text, the smallest space is inserted via the menu
11910 Insert\SpecialChar \menuseparator
11911 Formatting\SpecialChar \menuseparator
11913 \begin_inset space ~
11921 arg "space-insert thin"
11927 \begin_layout Standard
11928 An example to visualize the difference:
11931 \begin_layout Standard
11932 \begin_inset Tabular
11933 <lyxtabular version="3" rows="2" columns="2">
11934 <features tabularvalignment="middle">
11935 <column alignment="left" valignment="top" width="0">
11936 <column alignment="left" valignment="top" width="0">
11938 <cell alignment="center" valignment="top" usebox="none">
11941 \begin_layout Plain Layout
11943 \begin_inset Formula $\cdot$
11951 <cell alignment="center" valignment="top" usebox="none">
11954 \begin_layout Plain Layout
11955 space between value and unit
11962 <cell alignment="center" valignment="top" usebox="none">
11965 \begin_layout Plain Layout
11967 \begin_inset space \thinspace{}
11971 \begin_inset Formula $\cdot$
11979 <cell alignment="center" valignment="top" usebox="none">
11982 \begin_layout Plain Layout
11983 smallest space between value and unit
11996 \begin_layout Subsection
12001 \begin_layout Plain Layout
12014 \begin_layout Plain Layout
12015 for vertical space in formulas see
12016 \begin_inset CommandInset ref
12018 reference "sub:Line-Separation"
12031 \begin_layout Plain Layout
12039 \begin_inset Note Note
12042 \begin_layout Plain Layout
12045 texorpdfstring is used to avoid that the footnote appears in the PDF-bookmark.
12048 \begin_layout Plain Layout
12051 texorpdfstring is in section
12052 \begin_inset CommandInset ref
12054 reference "sub:Formulas-in-Section"
12064 \begin_inset CommandInset label
12066 name "sub:Variable-Space"
12071 \begin_inset Index idx
12074 \begin_layout Plain Layout
12075 Space ! horizontal ! variable
12083 \begin_layout Standard
12084 Space with a defined length can be inserted with the command
12091 \begin_inset Index idx
12094 \begin_layout Plain Layout
12104 \begin_inset Quotes eld
12113 \begin_layout Plain Layout
12125 \begin_inset Quotes erd
12129 The length can be specified by left-clicking on the
12130 \begin_inset Quotes eld
12139 \begin_layout Plain Layout
12151 \begin_inset Quotes erd
12155 The length may also be negative.
12156 To insert as much space as is available, the command
12163 \begin_inset Index idx
12166 \begin_layout Plain Layout
12177 \begin_layout Standard
12178 \begin_inset VSpace -1mm
12184 \begin_layout Standard
12186 \begin_inset Tabular
12187 <lyxtabular version="3" rows="4" columns="2">
12188 <features tabularvalignment="middle">
12189 <column alignment="center" valignment="top" width="0">
12190 <column alignment="center" valignment="top" width="0">
12192 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
12195 \begin_layout Plain Layout
12203 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
12206 \begin_layout Plain Layout
12214 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
12217 \begin_layout Plain Layout
12224 \begin_layout Plain Layout
12234 \begin_inset Formula $\to$
12240 \begin_inset space \thinspace{}
12248 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
12251 \begin_layout Plain Layout
12252 \begin_inset Formula $A=B\hspace{3cm}A\not=C$
12262 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
12265 \begin_layout Plain Layout
12272 \begin_layout Plain Layout
12282 \begin_inset Formula $\to$
12288 \begin_inset space \thinspace{}
12296 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
12299 \begin_layout Plain Layout
12300 \begin_inset Formula $A\hspace{-1mm}A\not=A$
12310 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
12313 \begin_layout Plain Layout
12320 \begin_layout Plain Layout
12334 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
12337 \begin_layout Plain Layout
12338 \begin_inset Formula $A=A\hfill B=B$
12354 \begin_layout Standard
12355 In the last example the available space is given by the longest column entry
12357 In an inline formula the space depends on the length of the line in which
12365 Thus, when the line uses the full width, no space will be created.
12372 only has an effect on displayed formulas when the formula style
12377 (Formula styles are explained in
12378 \begin_inset CommandInset ref
12380 reference "sec:Formula-Styles"
12387 \begin_layout Standard
12394 , there are the commands
12406 that fill the space with a pattern, see
12407 \begin_inset CommandInset ref
12409 reference "sub:Ellipses"
12416 \begin_layout Standard
12417 For text, variable space can be inserted via the menu
12419 Insert\SpecialChar \menuseparator
12420 Formatting\SpecialChar \menuseparator
12422 \begin_inset space ~
12430 \begin_layout Standard
12431 This is a line with
12432 \begin_inset space \hspace{}
12437 \begin_inset space \thinspace{}
12443 \begin_layout Standard
12444 This is a line with
12445 \begin_inset space \hfill{}
12451 \begin_layout Subsection
12452 Space besides inline Formulas
12453 \begin_inset Index idx
12456 \begin_layout Plain Layout
12457 Space ! besides inline formulas
12465 \begin_layout Standard
12466 The space that surrounds inline formulas can be adjusted with the length
12474 \begin_inset Index idx
12477 \begin_layout Plain Layout
12486 The value of a length is set with the command
12493 \begin_inset Index idx
12496 \begin_layout Plain Layout
12504 which has the following scheme:
12507 \begin_layout Standard
12512 setlength{length name}{value}
12515 \begin_layout Standard
12523 \begin_inset space \thinspace{}
12529 \begin_layout Standard
12539 \begin_layout Standard
12540 is inserted in TeX-mode.
12542 \begin_inset space \thinspace{}
12545 mm space will now be set around all inline formulas:
12549 \begin_layout Plain Layout
12563 \begin_layout Standard
12564 This is a line with an inline formula
12565 \begin_inset Formula $A=B$
12569 \begin_inset space \thinspace{}
12572 mm surrounding space.
12576 \begin_layout Plain Layout
12590 \begin_layout Standard
12591 To return to the predefined value,
12597 is set to the value 0
12598 \begin_inset space \thinspace{}
12604 \begin_layout Section
12606 \begin_inset Index idx
12609 \begin_layout Plain Layout
12616 \begin_inset Index idx
12619 \begin_layout Plain Layout
12624 \begin_layout Plain Layout
12635 \begin_layout Plain Layout
12650 \begin_layout Standard
12651 Boxes for text are described in chapter
12658 \begin_inset space ~
12666 \begin_layout Subsection
12668 \begin_inset CommandInset label
12670 name "sub:Boxes-with-Frame"
12675 \begin_inset Index idx
12678 \begin_layout Plain Layout
12687 \begin_layout Standard
12688 It is possible to frame a formula or part of one with the commands
12695 \begin_inset Index idx
12698 \begin_layout Plain Layout
12713 \begin_inset Index idx
12716 \begin_layout Plain Layout
12727 \begin_layout Standard
12728 When one of these commands is inserted in a formula, a blue box appears
12729 within a frame to enter formula parts.
12736 an additional formula has to be created by
12740 within this box, because the box content will otherwise be treated as mathemati
12748 is used, a new formula is automatically created inside the frame.
12751 \begin_layout Standard
12758 is not suitable to frame displayed formulas because the formula will always
12759 be set in the size of the text.
12766 is in contrary not suitable to frame inline formulas, because the formula
12767 will always be set in the size of a displayed formula.
12770 \begin_layout Standard
12784 \begin_inset Index idx
12787 \begin_layout Plain Layout
12795 where additionally the frame width and the alignment can be specified.
12802 is used in the following scheme:
12805 \begin_layout Standard
12810 framebox[frame width][position]{box content}
12813 \begin_layout Standard
12814 The position can either be
12831 right aligns the formula in the box.
12832 When no position is given, the formula will be centered.
12833 \begin_inset Newline newline
12836 If no width is given, also no position can be given.
12837 In this case the frame width is adjusted to the box content like for
12846 \begin_layout Standard
12853 is inserted, a box appears containing three blue boxes.
12854 The first two boxes are surrounded by brackets and denote the two optional
12856 The third box is for formula parts like for
12865 \begin_layout Standard
12867 \begin_inset Tabular
12868 <lyxtabular version="3" rows="5" columns="2">
12869 <features tabularvalignment="middle">
12870 <column alignment="center" valignment="top" width="0">
12871 <column alignment="center" valignment="top" width="0">
12873 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
12876 \begin_layout Plain Layout
12882 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
12885 \begin_layout Plain Layout
12887 \begin_inset Note Note
12890 \begin_layout Plain Layout
12897 is only used as spacer.
12909 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
12912 \begin_layout Plain Layout
12919 \begin_layout Plain Layout
12938 \begin_layout Plain Layout
12952 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
12955 \begin_layout Plain Layout
12956 \begin_inset Formula $\raisebox{6mm}{}\fbox{\ensuremath{\int A=B}}\raisebox{-4mm}{}$
12966 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
12969 \begin_layout Plain Layout
12976 \begin_layout Plain Layout
12991 \begin_layout Plain Layout
13005 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
13008 \begin_layout Plain Layout
13009 \begin_inset Formula $\raisebox{8.5mm}{}\boxed{\int A=B}\raisebox{-6.5mm}{}$
13019 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
13022 \begin_layout Plain Layout
13029 \begin_layout Plain Layout
13043 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
13046 \begin_layout Plain Layout
13047 \begin_inset Formula $\raisebox{6mm}{}A+\fbox{B}\raisebox{-3mm}{}$
13057 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
13060 \begin_layout Plain Layout
13067 \begin_layout Plain Layout
13077 \begin_inset Formula $\to$
13081 \begin_inset Formula $\to$
13094 \begin_layout Plain Layout
13104 \begin_inset Formula $\downarrow$
13112 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
13115 \begin_layout Plain Layout
13116 \begin_inset Formula $\raisebox{6mm}{}$
13120 \begin_inset Formula $\framebox[20mm][]{\ensuremath{\frac{A}{B}}}$
13124 \begin_inset Formula $\raisebox{-4mm}{}$
13140 \begin_layout Standard
13141 The frame thickness can also be adjusted.
13142 To do this the following commands have to be inserted in TeX-mode before
13146 \begin_layout Standard
13156 \begin_inset Quotes eld
13160 \begin_inset Quotes erd
13174 \begin_inset Quotes eld
13178 \begin_inset Quotes erd
13184 \begin_layout Standard
13185 \begin_inset Quotes eld
13189 \begin_inset Quotes erd
13192 specifies the minimal distance between the frame and the first character
13194 An example for this is the following framed formula:
13198 \begin_layout Plain Layout
13210 \begin_inset Formula
13217 Before this formula the commands
13220 \begin_layout Standard
13242 \begin_layout Standard
13243 were inserted in TeX-mode.
13244 The given values are used for all following boxes.
13247 \begin_layout Standard
13248 To return to the standard frame size, the command
13251 \begin_layout Standard
13276 \begin_layout Plain Layout
13290 \begin_layout Standard
13291 is inserted in TeX-mode before the next formula.
13294 \begin_layout Subsection
13295 Boxes without Frame
13296 \begin_inset CommandInset label
13298 name "sub:Boxes-without-Frame"
13303 \begin_inset Index idx
13306 \begin_layout Plain Layout
13307 Boxes ! without frame
13315 \begin_layout Standard
13316 For boxes without a frame there are the following box commands:
13323 \begin_inset Index idx
13326 \begin_layout Plain Layout
13341 \begin_inset Index idx
13344 \begin_layout Plain Layout
13359 \begin_inset Index idx
13362 \begin_layout Plain Layout
13373 \begin_layout Standard
13380 a box can be super- or subscripted.
13381 But in contrary to normal super- and subscripting, the characters in the
13382 box keep their font size.
13389 is used in the following scheme:
13392 \begin_layout Standard
13397 raisebox{height}{box content}
13400 \begin_layout Standard
13401 When the box should contain a formula, an extra formula is needed like for
13412 \begin_inset Note Greyedout
13415 \begin_layout Plain Layout
13426 this extra formula is created by pressing
13430 twice instead of once because LyX doesn't yet support
13444 \begin_layout Standard
13446 \begin_inset Tabular
13447 <lyxtabular version="3" rows="4" columns="2">
13448 <features tabularvalignment="middle">
13449 <column alignment="center" valignment="top" width="0">
13450 <column alignment="center" valignment="top" width="0">
13452 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
13455 \begin_layout Plain Layout
13461 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
13464 \begin_layout Plain Layout
13472 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
13475 \begin_layout Plain Layout
13479 \begin_inset Formula $\to$
13485 \begin_inset Formula $\to$
13493 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
13496 \begin_layout Plain Layout
13497 \begin_inset Formula $H\raisebox{2mm}{al}lo$
13507 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
13510 \begin_layout Plain Layout
13514 \begin_inset Formula $\to$
13520 \begin_inset Formula $\to$
13528 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
13531 \begin_layout Plain Layout
13532 \begin_inset Formula $H\raisebox{-2mm}{al}lo$
13542 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
13545 \begin_layout Plain Layout
13549 \begin_inset Formula $\to$
13568 \begin_layout Plain Layout
13582 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
13585 \begin_layout Plain Layout
13586 \begin_inset Formula $A=\raisebox{-2mm}{\mbox{\ensuremath{\sqrt{B}}}}$
13602 \begin_layout Standard
13627 , with the difference that there is no frame.
13630 \begin_layout Subsection
13632 \begin_inset CommandInset label
13634 name "sub:Colored-Boxes"
13639 \begin_inset Index idx
13642 \begin_layout Plain Layout
13651 \begin_layout Standard
13652 To be able to use all commands explained in this section, the LaTeX-package
13661 \begin_layout Plain Layout
13666 is part of every LaTeX standard installation.
13672 \begin_inset Index idx
13675 \begin_layout Plain Layout
13681 has to be loaded in the LaTeX-preamble with the line
13685 \begin_layout Plain Layout
13686 When text is colored somewhere in the document with a predefined color,
13687 LyX loads the LaTeX-package
13692 Thus it is possible that the package is loaded twice, but this does not
13699 \begin_inset Note Note
13702 \begin_layout Plain Layout
13703 To avoid that the package is loaded twice, a macro was inserted to the LaTeX-pre
13712 \begin_layout Standard
13720 \begin_layout Standard
13721 \begin_inset VSpace medskip
13724 To color boxes, the command
13731 \begin_inset Index idx
13734 \begin_layout Plain Layout
13742 is used in the following scheme:
13745 \begin_layout Standard
13750 colorbox{color}{box content}
13753 \begin_layout Standard
13754 The box content can also be a box and a
13760 can also be part of another box (see the 2nd and 3rd example).
13761 When the box should contain a formula, an extra formula has to be created,
13762 the same way as for
13772 \begin_layout Plain Layout
13773 This also applies for the command
13787 \begin_layout Standard
13788 One of the following predefined colors can be chosen:
13791 \begin_layout Standard
13825 \begin_layout Standard
13827 \begin_inset Tabular
13828 <lyxtabular version="3" rows="4" columns="2">
13829 <features tabularvalignment="middle">
13830 <column alignment="center" valignment="top" width="0">
13831 <column alignment="center" valignment="top" width="0">
13833 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
13836 \begin_layout Plain Layout
13842 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
13845 \begin_layout Plain Layout
13847 \begin_inset Note Note
13850 \begin_layout Plain Layout
13857 is only used as spacer.
13869 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
13872 \begin_layout Plain Layout
13876 \begin_inset Formula $\to$
13886 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
13889 \begin_layout Plain Layout
13890 \begin_inset Formula $\raisebox{6mm}{}\colorbox{yellow}{A=B}\raisebox{-3mm}{}$
13900 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
13903 \begin_layout Plain Layout
13907 \begin_inset Formula $\to$
13918 \begin_layout Plain Layout
13932 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
13935 \begin_layout Plain Layout
13936 \begin_inset Formula $\raisebox{6mm}{}\colorbox{green}{\fbox{A=B}}\raisebox{-3mm}{}$
13946 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
13949 \begin_layout Plain Layout
13956 \begin_layout Plain Layout
13968 \begin_inset Formula $\to$
13987 \begin_layout Plain Layout
14001 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
14004 \begin_layout Plain Layout
14005 \begin_inset Formula $\raisebox{7mm}{}\fbox{\colorbox{green}{\mbox{\ensuremath{\int C=D}}}}\raisebox{-5mm}{}$
14021 \begin_layout Standard
14028 only colors the box but not the characters in the box.
14029 To color all characters, the whole formula is highlighted and the desired
14030 color is chosen in the
14033 \begin_inset space ~
14039 The dialog can be called with the toolbar button
14040 \begin_inset Graphics
14041 filename ../images/dialog-show_character.png
14048 Edit\SpecialChar \menuseparator
14050 \begin_inset space ~
14053 Style\SpecialChar \menuseparator
14057 The formula number then has the same color as the formula.
14058 When the formula number should get another color than the formula characters,
14059 the color must be changed within the formula.
14062 \begin_layout Standard
14066 \begin_layout Standard
14069 \begin_inset Formula
14071 \int A=B\label{eq:red}
14079 \begin_inset Formula
14081 \textcolor{red}{\int A=B}\label{eq:redgreen}
14089 \begin_layout Standard
14091 \begin_inset CommandInset ref
14097 is completely colored red.
14098 \begin_inset Newline newline
14102 \begin_inset CommandInset ref
14104 reference "eq:redgreen"
14108 was first completely colored green to set the color for the formula number.
14109 Subsequently the formula characters were colored red.
14112 \begin_layout Standard
14113 \begin_inset VSpace bigskip
14116 To color the frame different than the rest of the box, the command
14123 \begin_inset Index idx
14126 \begin_layout Plain Layout
14134 is used in the following scheme:
14137 \begin_layout Standard
14142 fcolorbox{frame color}{color}{box content}
14145 \begin_layout Standard
14152 is an extension of the command
14159 The frame width is set, like for
14182 \begin_layout Plain Layout
14194 \begin_inset Formula
14196 \fcolorbox{cyan}{magenta}{A=B}
14205 \begin_layout Plain Layout
14219 \begin_layout Standard
14220 This formula was created with the command
14221 \begin_inset Newline newline
14229 \begin_inset Formula $\to$
14235 \begin_inset Formula $\to$
14245 \begin_layout Standard
14246 \begin_inset VSpace bigskip
14249 To use other colors than the predefined ones, they have to be defined first.
14252 \begin_layout Standard
14253 One can for example define the color
14254 \begin_inset Quotes eld
14262 \begin_inset Quotes erd
14265 with the LaTeX-preamble line:
14268 \begin_layout Standard
14273 definecolor{darkgreen}{cmyk}{0.5,
14288 \begin_inset Index idx
14291 \begin_layout Plain Layout
14302 \begin_layout Standard
14307 is the color space that denotes the colors
14324 The four comma separated numbers are the portion factor for the corresponding
14325 colors of the color space.
14326 The factors can be in the range of 0
14327 \begin_inset space \thinspace{}
14331 \begin_inset space \thinspace{}
14339 also the color space
14343 can be used for definitions.
14360 , so that there are in this case three portion factors for the corresponding
14362 Furthermore there is the color space
14366 with one portion factor for the gray value.
14369 \begin_layout Standard
14370 As example a framed box with the new defined color
14374 where the characters have been colored
14379 \begin_inset Formula
14381 \colorbox{darkgreen}{\color{yellow}\boxed{\int A\,\mathrm{d}x=\frac{\sqrt[5]{B}}{\ln\left(\frac{1}{3}\right)}}}
14389 \begin_layout Standard
14390 Self-defined colors can also be used for text with the help of the command
14398 \begin_inset Index idx
14401 \begin_layout Plain Layout
14410 \begin_layout Standard
14414 \begin_layout Plain Layout
14418 textcolor{darkgreen}{
14424 \begin_inset Quotes eld
14428 \begin_inset Quotes erd
14435 \begin_layout Plain Layout
14445 \begin_layout Standard
14453 \begin_inset Index idx
14456 \begin_layout Plain Layout
14464 is used in the scheme
14468 textcolor{color}{characters to color}
14473 \begin_layout Subsection
14475 \begin_inset CommandInset label
14477 name "sub:Paragraph-Boxes"
14482 \begin_inset Index idx
14485 \begin_layout Plain Layout
14486 Boxes ! as paragraph
14494 \begin_layout Standard
14495 A box that can contain several lines and paragraphs, a so-called paragraph
14496 box (parbox), can be created with the menu
14498 Insert\SpecialChar \menuseparator
14501 or the toolbar button
14502 \begin_inset Graphics
14503 filename ../images/box-insert.png
14511 \begin_layout Standard
14512 The following example shows a framed parbox in a line:
14515 \begin_layout Standard
14516 \begin_inset VSpace medskip
14520 \begin_inset Box Boxed
14530 height_special "totalheight"
14533 \begin_layout Plain Layout
14534 This is a paragraph box.
14536 \begin_inset space \thinspace{}
14539 cm long and can also contain formulas:
14540 \begin_inset Formula $\int A\,\mathrm{d}s=C$
14551 \begin_layout Standard
14552 \begin_inset VSpace medskip
14558 \begin_layout Standard
14559 Such a box is created by right-clicking on the gray box inset.
14560 A dialog pops up showing the box properties.
14574 \begin_inset space \thinspace{}
14579 Vertical Box Alignment
14584 \begin_layout Standard
14585 \begin_inset VSpace medskip
14588 In LaTeX a parbox is created with the command
14595 \begin_inset Index idx
14598 \begin_layout Plain Layout
14606 which has the following scheme:
14609 \begin_layout Standard
14614 parbox[position]{width}{box content}
14617 \begin_layout Standard
14632 \begin_inset Quotes eld
14636 \begin_inset Quotes erd
14639 means that the box is aligned within the surrounding text with its last
14646 \begin_inset Quotes eld
14650 \begin_inset Quotes erd
14653 this is done with the first line.
14654 When no position is given, the box will be vertically centered, see section
14662 \begin_inset space ~
14667 manual for examples.
14670 \begin_layout Standard
14671 \begin_inset VSpace bigskip
14674 To frame formulas completely, including the formula number, the formula
14675 must be set into a parbox.
14676 To do this, the command
14690 is inserted in TeX-mode before the formula.
14698 \begin_inset Index idx
14701 \begin_layout Plain Layout
14709 is hereby the line width set for the document.
14710 Because the frame is outside the parbox, 2
14711 \begin_inset space \thinspace{}
14714 times the frame separation and the frame thickness must be subtracted from
14716 As this is not automatically done by LyX due to a bug
14720 \begin_layout Plain Layout
14721 \begin_inset CommandInset href
14723 name "LyX-bug #4483"
14724 target "http://www.lyx.org/trac/ticket/4483"
14733 , TeX-mode has to be used.
14734 To be able to multiply and subtract in arguments, the LaTeX-package
14742 \begin_layout Plain Layout
14747 is part of every LaTeX standard installation.
14753 \begin_inset Index idx
14756 \begin_layout Plain Layout
14762 must be loaded in the LaTeX-preamble with the line
14765 \begin_layout Standard
14773 \begin_layout Standard
14774 Behind the formula both boxes are closed by entering
14779 Here is an example:
14783 \begin_layout Plain Layout
14797 \begin_layout Standard
14801 \begin_layout Plain Layout
14819 \begin_inset Formula
14821 \int A\,\mathrm{d}x=\frac{\sqrt[5]{B}}{\ln\left(\frac{1}{3}\right)}
14830 \begin_layout Plain Layout
14841 \begin_layout Plain Layout
14855 \begin_layout Standard
14856 \begin_inset VSpace medskip
14859 As a parbox is used as the argument of
14865 , there is in this case no difference between
14880 \begin_layout Standard
14881 \begin_inset VSpace bigskip
14884 Paragraph boxes are very useful to comment formulas directly.
14891 is used in combination with the command
14905 \begin_inset CommandInset ref
14907 reference "sub:User-defined-Numbering"
14914 \begin_layout Standard
14915 An example of a formula commented with
14924 \begin_layout Standard
14928 \begin_layout Plain Layout
14941 This is a description.
14942 It is distinctly separated from the formula and multiline.
14946 \begin_layout Plain Layout
14958 \begin_layout Standard
14959 Such a formula must be inserted completely in TeX-mode because LyX does
14960 not yet support the command
14967 The formula is created with the following command sequence:
14970 \begin_layout Standard
14983 is inserted in TeX-mode.
14987 \begin_layout Plain Layout
14988 When the formula style
15000 can also be replaced by
15007 (formula styles see
15008 \begin_inset CommandInset ref
15010 reference "sec:Formula-Styles"
15019 Then the description follows as normal text and finally
15025 is inserted in TeX-mode.
15038 hereby create a displayed formula.
15041 \begin_layout Standard
15048 can be seen in this example that was
15049 \begin_inset Quotes eld
15053 \begin_inset Quotes erd
15056 using the mathematical textmode:
15057 \begin_inset Formula
15059 5x-7b=3b\textrm{This is a description. It is not separated from the formula ...}
15067 \begin_layout Section
15069 \begin_inset Index idx
15072 \begin_layout Plain Layout
15081 \begin_layout Subsection
15083 \begin_inset CommandInset label
15085 name "sub:Big-Operators"
15090 \begin_inset Index idx
15093 \begin_layout Plain Layout
15100 \begin_inset Index idx
15103 \begin_layout Plain Layout
15110 \begin_inset Index idx
15113 \begin_layout Plain Layout
15122 \begin_layout Standard
15123 To be able to use all integral operators listed here, the option
15125 Use esint package automatically
15127 must be set in the document settings under
15130 \begin_inset space ~
15138 \begin_layout Standard
15139 \begin_inset space \hfill{}
15143 \begin_inset Tabular
15144 <lyxtabular version="3" rows="11" columns="2">
15145 <features tabularvalignment="middle">
15146 <column alignment="center" valignment="top" width="0pt">
15147 <column alignment="center" valignment="top" width="0pt">
15149 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
15152 \begin_layout Plain Layout
15158 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
15161 \begin_layout Plain Layout
15169 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
15172 \begin_layout Plain Layout
15176 \begin_inset Index idx
15179 \begin_layout Plain Layout
15192 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
15195 \begin_layout Plain Layout
15196 \begin_inset Formula $\int$
15206 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
15209 \begin_layout Plain Layout
15217 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
15220 \begin_layout Plain Layout
15221 \begin_inset Formula $\oint$
15231 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
15234 \begin_layout Plain Layout
15242 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
15245 \begin_layout Plain Layout
15246 \begin_inset Formula $\ointctrclockwise$
15256 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
15259 \begin_layout Plain Layout
15267 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
15270 \begin_layout Plain Layout
15271 \begin_inset Formula $\ointclockwise$
15281 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
15284 \begin_layout Plain Layout
15292 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
15295 \begin_layout Plain Layout
15296 \begin_inset Formula $\sqint$
15306 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
15309 \begin_layout Plain Layout
15317 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
15320 \begin_layout Plain Layout
15322 \begin_inset Formula $\fint$
15332 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
15335 \begin_layout Plain Layout
15343 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
15346 \begin_layout Plain Layout
15348 \begin_inset Formula $\landupint$
15358 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
15361 \begin_layout Plain Layout
15369 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
15372 \begin_layout Plain Layout
15374 \begin_inset Formula $\landdownint$
15384 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
15387 \begin_layout Plain Layout
15395 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
15398 \begin_layout Plain Layout
15399 \begin_inset Formula $\bigcap$
15409 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
15412 \begin_layout Plain Layout
15420 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
15423 \begin_layout Plain Layout
15424 \begin_inset Formula $\bigcup$
15438 \begin_inset space \hfill{}
15442 \begin_inset Tabular
15443 <lyxtabular version="3" rows="11" columns="2">
15444 <features tabularvalignment="middle">
15445 <column alignment="center" valignment="top" width="0pt">
15446 <column alignment="center" valignment="top" width="0pt">
15448 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
15451 \begin_layout Plain Layout
15457 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
15460 \begin_layout Plain Layout
15468 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
15471 \begin_layout Plain Layout
15475 \begin_inset Index idx
15478 \begin_layout Plain Layout
15491 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
15494 \begin_layout Plain Layout
15495 \begin_inset Formula $\sum$
15505 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
15508 \begin_layout Plain Layout
15512 \begin_inset Index idx
15515 \begin_layout Plain Layout
15528 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
15531 \begin_layout Plain Layout
15532 \begin_inset Formula $\prod$
15542 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
15545 \begin_layout Plain Layout
15553 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
15556 \begin_layout Plain Layout
15557 \begin_inset Formula $\coprod$
15567 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
15570 \begin_layout Plain Layout
15578 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
15581 \begin_layout Plain Layout
15582 \begin_inset Formula $\bigodot$
15592 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
15595 \begin_layout Plain Layout
15603 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
15606 \begin_layout Plain Layout
15607 \begin_inset Formula $\bigotimes$
15617 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
15620 \begin_layout Plain Layout
15628 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
15631 \begin_layout Plain Layout
15632 \begin_inset Formula $\bigoplus$
15642 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
15645 \begin_layout Plain Layout
15653 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
15656 \begin_layout Plain Layout
15657 \begin_inset Formula $\bigwedge$
15667 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
15670 \begin_layout Plain Layout
15678 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
15681 \begin_layout Plain Layout
15682 \begin_inset Formula $\bigvee$
15692 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
15695 \begin_layout Plain Layout
15703 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
15706 \begin_layout Plain Layout
15707 \begin_inset Formula $\bigsqcup$
15717 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
15720 \begin_layout Plain Layout
15728 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
15731 \begin_layout Plain Layout
15732 \begin_inset Formula $\biguplus$
15746 \begin_inset space \hfill{}
15752 \begin_layout Standard
15753 All big operators can also be inserted via the math toolbar button
15754 \begin_inset Graphics
15755 filename ../images/math/intop.png
15763 \begin_layout Standard
15764 The operators are called big because they are bigger than the sometimes
15765 equal looking binary operators.
15766 All big operators can have limits as described in the next subsection.
15769 \begin_layout Standard
15770 For all integral operators there is a second version available, ending in
15788 These operators are different from
15795 \begin_inset space \space{}
15798 in the style the operator limits are displayed, see
15799 \begin_inset CommandInset ref
15801 reference "sub:Operator-Limits"
15809 \begin_layout Subsubsection*
15810 Advice for Integrals
15813 \begin_layout Standard
15818 in an integral is an operator, that therefore has to be set upright.
15819 This is done by highlighting the
15823 and using the keyboard shortcut
15833 \begin_layout Plain Layout
15839 \begin_inset CommandInset ref
15841 reference "sub:Font-Styles"
15851 Finally the smallest space is inserted before the
15855 , as this is usual for operators.
15859 \begin_layout Standard
15861 \begin_inset Formula $\int A(x)dx$
15865 \begin_inset Newline newline
15869 \begin_inset Phantom HPhantom
15872 \begin_layout Plain Layout
15879 \begin_inset Formula $\int A(x)\,\mathrm{d}x$
15885 \begin_layout Standard
15886 For multiple integrals there are the following commands:
15887 \begin_inset VSpace medskip
15893 \begin_layout Standard
15894 \begin_inset space \hfill{}
15898 \begin_inset Tabular
15899 <lyxtabular version="3" rows="4" columns="2">
15900 <features tabularvalignment="middle">
15901 <column alignment="center" valignment="top" width="0">
15902 <column alignment="center" valignment="top" width="0">
15904 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
15907 \begin_layout Plain Layout
15913 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
15916 \begin_layout Plain Layout
15918 \begin_inset Note Note
15921 \begin_layout Plain Layout
15928 is only used as spacer.
15940 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
15943 \begin_layout Plain Layout
15951 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
15954 \begin_layout Plain Layout
15955 \begin_inset Formula $\raisebox{4.5mm}{}\iint\raisebox{-2.5mm}{}$
15965 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
15968 \begin_layout Plain Layout
15976 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
15979 \begin_layout Plain Layout
15980 \begin_inset Formula $\raisebox{4.5mm}{}\oiint\raisebox{-2.5mm}{}$
15990 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
15993 \begin_layout Plain Layout
16001 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
16004 \begin_layout Plain Layout
16005 \begin_inset Formula $\raisebox{4.5mm}{}\sqiint\raisebox{-2.5mm}{}$
16019 \begin_inset space \hfill{}
16023 \begin_inset Tabular
16024 <lyxtabular version="3" rows="4" columns="2">
16025 <features tabularvalignment="middle">
16026 <column alignment="center" valignment="top" width="0">
16027 <column alignment="center" valignment="top" width="0">
16029 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
16032 \begin_layout Plain Layout
16038 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
16041 \begin_layout Plain Layout
16049 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
16052 \begin_layout Plain Layout
16060 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
16063 \begin_layout Plain Layout
16064 \begin_inset Formula $\raisebox{4.5mm}{}\iiint\raisebox{-2.5mm}{}$
16074 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
16077 \begin_layout Plain Layout
16085 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
16088 \begin_layout Plain Layout
16089 \begin_inset Formula $\raisebox{4.5mm}{}\iiiint\raisebox{-2.5mm}{}$
16099 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
16102 \begin_layout Plain Layout
16110 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
16113 \begin_layout Plain Layout
16114 \begin_inset Formula $\raisebox{4.5mm}{}\dotsint\raisebox{-2.5mm}{}$
16128 \begin_inset space \hfill{}
16134 \begin_layout Subsection
16136 \begin_inset CommandInset label
16138 name "sub:Operator-Limits"
16143 \begin_inset Index idx
16146 \begin_layout Plain Layout
16155 \begin_layout Standard
16156 Limits are created by super- and subscripts:
16159 \begin_layout Standard
16161 \begin_inset Tabular
16162 <lyxtabular version="3" rows="2" columns="2">
16163 <features tabularvalignment="middle">
16164 <column alignment="center" valignment="top" width="0pt">
16165 <column alignment="center" valignment="top" width="0pt">
16167 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
16170 \begin_layout Plain Layout
16176 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
16179 \begin_layout Plain Layout
16181 \begin_inset Note Note
16184 \begin_layout Plain Layout
16191 is only used as spacer.
16203 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
16206 \begin_layout Plain Layout
16215 \begin_layout Plain Layout
16225 \begin_inset Formula $\to$
16229 \begin_inset Formula $\to$
16237 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
16240 \begin_layout Plain Layout
16241 \begin_inset Formula $\raisebox{5mm}{}\prod_{0}^{\infty}A(x)\raisebox{-2.5mm}{}$
16257 \begin_layout Standard
16258 Limits of inline formulas are set right beside the operator.
16259 Limits in displayed formulas are set above or below the operator, except
16260 for integral limits.
16263 \begin_layout Standard
16264 To force that the limits are set beside the operator, the cursor is set
16265 directly behind the operator and the limits type is changed with the menu
16268 Edit\SpecialChar \menuseparator
16269 Math\SpecialChar \menuseparator
16288 \begin_layout Standard
16289 The default limits type is this:
16290 \begin_inset Formula
16292 \sum_{x=0}^{\infty}\frac{1}{x^{2}}
16297 This is how it looks when the limits type was changed to
16304 \begin_inset Formula
16306 \sum\nolimits _{x=0}^{\infty}\frac{1}{x^{2}}
16311 For integrals, except those ending with
16327 etc., the limits are by default set beside the operator.
16328 But for multiple integrals the limits are often set below the operator.
16329 In the following example the limits type was therefore set to
16333 and so set below the integrals:
16334 \begin_inset Formula
16336 \iiint\limits _{V}X\,\mathrm{d}V=U\label{eq:VolInt}
16344 \begin_layout Standard
16345 \begin_inset VSpace medskip
16348 To specify conditions for limits, the commands
16355 \begin_inset Index idx
16358 \begin_layout Plain Layout
16373 \begin_inset Index idx
16376 \begin_layout Plain Layout
16385 To create for example this expression
16386 \begin_inset Formula
16388 \sum_{\begin{subarray}{c}
16392 \end{subarray}}^{n}k^{-2}\label{eq:substack}
16400 \begin_layout Standard
16401 the following has to be done:
16402 \begin_inset Newline newline
16417 \begin_layout Plain Layout
16429 One is now in a blue box under the summation operator and insert there
16438 \begin_layout Plain Layout
16450 The blue box is now within a purple box and now several lines can be written
16452 A new line is created by inserting a line break (
16455 arg "newline-insert newline"
16460 \begin_inset Newline newline
16465 0<k<1000 Ctrl+Return
16466 \begin_inset Newline newline
16471 is typed in, a new box appears below for the new line.
16474 \begin_layout Standard
16475 The alignment of the lines can be changed to left aligned with the
16485 Edit\SpecialChar \menuseparator
16489 To get right alignment,
16497 \begin_layout Plain Layout
16508 is inserted at the beginning of the line.
16511 \begin_layout Standard
16524 with the difference that the lines are always centered.
16527 \begin_layout Standard
16528 \begin_inset VSpace bigskip
16532 \begin_inset CommandInset ref
16534 reference "eq:substack"
16538 there can be too much space beside an operator, because the characters
16539 following the operator are set beside the limits.
16542 \begin_layout Standard
16543 To avoid this, the following macro can be used in the LaTeX-preamble:
16546 \begin_layout Standard
16560 \begin_inset Newline newline
16572 \begin_inset Newline newline
16579 mathclapinternal #1#2{
16583 mathsurround =0pt #1{#2}$}}
16586 \begin_layout Standard
16587 This defines the command
16594 \begin_inset Index idx
16597 \begin_layout Plain Layout
16605 that sets the width of the limit to 0
16606 \begin_inset space \thinspace{}
16610 The command scheme is
16613 \begin_layout Standard
16621 \begin_layout Standard
16622 where the limit can consist of several conditions.
16625 \begin_layout Standard
16627 \begin_inset CommandInset ref
16629 reference "eq:substack"
16633 , one uses the command
16636 \begin_layout Standard
16649 \begin_layout Plain Layout
16658 0<k<1000 Ctrl+Return
16661 \begin_layout Standard
16662 to create the lower limit.
16663 The summand is now directly behind the summation operator:
16664 \begin_inset Formula
16666 \sum_{\mathclap{\substack{0<k<1000\\
16678 \begin_layout Standard
16679 \begin_inset VSpace bigskip
16682 How to use one limit for several operators is described in
16683 \begin_inset CommandInset ref
16685 reference "sub:Self-defined-Operators"
16692 \begin_layout Standard
16693 \begin_inset Newpage newpage
16699 \begin_layout Subsection
16701 \begin_inset CommandInset label
16703 name "sub:Binary-Operators"
16708 \begin_inset Index idx
16711 \begin_layout Plain Layout
16720 \begin_layout Standard
16721 Binary operators are surrounded by space when there is a character before
16723 \begin_inset VSpace medskip
16729 \begin_layout Standard
16730 \begin_inset space \hfill{}
16734 \begin_inset Tabular
16735 <lyxtabular version="3" rows="13" columns="2">
16736 <features tabularvalignment="middle">
16737 <column alignment="center" valignment="top" width="0pt">
16738 <column alignment="center" valignment="top" width="0pt">
16740 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
16743 \begin_layout Plain Layout
16745 \begin_inset Note Note
16748 \begin_layout Plain Layout
16755 is only used as spacer.
16765 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
16768 \begin_layout Plain Layout
16776 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
16779 \begin_layout Plain Layout
16785 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
16788 \begin_layout Plain Layout
16789 \begin_inset Formula $+$
16799 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
16802 \begin_layout Plain Layout
16808 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
16811 \begin_layout Plain Layout
16812 \begin_inset Formula $-$
16822 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
16825 \begin_layout Plain Layout
16833 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
16836 \begin_layout Plain Layout
16837 \begin_inset Formula $\pm$
16847 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
16850 \begin_layout Plain Layout
16858 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
16861 \begin_layout Plain Layout
16862 \begin_inset Formula $\mp$
16872 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
16875 \begin_layout Plain Layout
16883 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
16886 \begin_layout Plain Layout
16887 \begin_inset Formula $\cdot$
16897 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
16900 \begin_layout Plain Layout
16908 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
16911 \begin_layout Plain Layout
16912 \begin_inset Formula $\times$
16922 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
16925 \begin_layout Plain Layout
16933 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
16936 \begin_layout Plain Layout
16937 \begin_inset Formula $\div$
16947 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
16950 \begin_layout Plain Layout
16954 \begin_layout Plain Layout
16967 \begin_layout Plain Layout
16979 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
16982 \begin_layout Plain Layout
16983 \begin_inset Formula $*$
16993 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
16996 \begin_layout Plain Layout
17004 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
17007 \begin_layout Plain Layout
17008 \begin_inset Formula $\star$
17018 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
17021 \begin_layout Plain Layout
17029 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
17032 \begin_layout Plain Layout
17033 \begin_inset Formula $\circ$
17043 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
17046 \begin_layout Plain Layout
17054 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
17057 \begin_layout Plain Layout
17058 \begin_inset Formula $\diamond$
17068 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
17071 \begin_layout Plain Layout
17079 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
17082 \begin_layout Plain Layout
17083 \begin_inset Formula $\bullet$
17097 \begin_inset space \hfill{}
17101 \begin_inset Tabular
17102 <lyxtabular version="3" rows="13" columns="2">
17103 <features tabularvalignment="middle">
17104 <column alignment="center" valignment="top" width="0pt">
17105 <column alignment="center" valignment="top" width="0pt">
17107 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
17110 \begin_layout Plain Layout
17116 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
17119 \begin_layout Plain Layout
17127 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
17130 \begin_layout Plain Layout
17138 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
17141 \begin_layout Plain Layout
17142 \begin_inset Formula $\nabla$
17152 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
17155 \begin_layout Plain Layout
17163 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
17166 \begin_layout Plain Layout
17167 \begin_inset Formula $\bigtriangledown$
17177 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
17180 \begin_layout Plain Layout
17188 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
17191 \begin_layout Plain Layout
17192 \begin_inset Formula $\bigtriangleup$
17202 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
17205 \begin_layout Plain Layout
17213 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
17216 \begin_layout Plain Layout
17217 \begin_inset Formula $\Box$
17227 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
17230 \begin_layout Plain Layout
17238 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
17241 \begin_layout Plain Layout
17242 \begin_inset Formula $\cap$
17252 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
17255 \begin_layout Plain Layout
17263 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
17266 \begin_layout Plain Layout
17267 \begin_inset Formula $\cup$
17277 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
17280 \begin_layout Plain Layout
17288 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
17291 \begin_layout Plain Layout
17292 \begin_inset Formula $\dagger$
17302 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
17305 \begin_layout Plain Layout
17313 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
17316 \begin_layout Plain Layout
17317 \begin_inset Formula $\ddagger$
17327 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
17330 \begin_layout Plain Layout
17338 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
17341 \begin_layout Plain Layout
17342 \begin_inset Formula $\wr$
17352 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
17355 \begin_layout Plain Layout
17363 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
17366 \begin_layout Plain Layout
17367 \begin_inset Formula $\bigcirc$
17377 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
17380 \begin_layout Plain Layout
17388 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
17391 \begin_layout Plain Layout
17392 \begin_inset Formula $\wedge$
17402 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
17405 \begin_layout Plain Layout
17413 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
17416 \begin_layout Plain Layout
17417 \begin_inset Formula $\vee$
17431 \begin_inset space \hfill{}
17435 \begin_inset Tabular
17436 <lyxtabular version="3" rows="13" columns="2">
17437 <features tabularvalignment="middle">
17438 <column alignment="center" valignment="top" width="0pt">
17439 <column alignment="center" valignment="top" width="0pt">
17441 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
17444 \begin_layout Plain Layout
17450 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
17453 \begin_layout Plain Layout
17461 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
17464 \begin_layout Plain Layout
17472 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
17475 \begin_layout Plain Layout
17476 \begin_inset Formula $\oplus$
17486 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
17489 \begin_layout Plain Layout
17497 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
17500 \begin_layout Plain Layout
17501 \begin_inset Formula $\ominus$
17511 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
17514 \begin_layout Plain Layout
17522 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
17525 \begin_layout Plain Layout
17526 \begin_inset Formula $\otimes$
17536 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
17539 \begin_layout Plain Layout
17547 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
17550 \begin_layout Plain Layout
17551 \begin_inset Formula $\oslash$
17561 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
17564 \begin_layout Plain Layout
17572 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
17575 \begin_layout Plain Layout
17576 \begin_inset Formula $\odot$
17586 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
17589 \begin_layout Plain Layout
17597 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
17600 \begin_layout Plain Layout
17601 \begin_inset Formula $\amalg$
17611 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
17614 \begin_layout Plain Layout
17622 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
17625 \begin_layout Plain Layout
17626 \begin_inset Formula $\uplus$
17636 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
17639 \begin_layout Plain Layout
17647 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
17650 \begin_layout Plain Layout
17651 \begin_inset Formula $\setminus$
17661 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
17664 \begin_layout Plain Layout
17672 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
17675 \begin_layout Plain Layout
17676 \begin_inset Formula $\sqcap$
17686 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
17689 \begin_layout Plain Layout
17697 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
17700 \begin_layout Plain Layout
17701 \begin_inset Formula $\sqcup$
17711 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
17714 \begin_layout Plain Layout
17722 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
17725 \begin_layout Plain Layout
17726 \begin_inset Formula $\triangleleft$
17736 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
17739 \begin_layout Plain Layout
17747 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
17750 \begin_layout Plain Layout
17751 \begin_inset Formula $\triangleright$
17765 \begin_inset space \hfill{}
17771 \begin_layout Standard
17772 All binary operators can also be inserted via the math toolbar button
17773 \begin_inset Graphics
17774 filename ../images/math/pm.png
17782 \begin_layout Standard
17783 To typeset the Laplace operator also
17800 \begin_inset Formula $\nabla^{2}$
17803 ) can be used instead of
17812 \begin_layout Standard
17819 Insert\SpecialChar \menuseparator
17831 \begin_layout Subsection
17832 Self-defined Operators
17833 \begin_inset CommandInset label
17835 name "sub:Self-defined-Operators"
17840 \begin_inset Index idx
17843 \begin_layout Plain Layout
17844 Operators ! self-defined
17852 \begin_layout Standard
17853 With the help of the command
17857 DeclareMathOperator
17860 \begin_inset Index idx
17863 \begin_layout Plain Layout
17868 DeclareMathOperator
17873 custom operators can be defined in the LaTeX-preamble.
17874 Its command scheme is:
17877 \begin_layout Standard
17882 DeclareMathOperator{new command}{display}
17885 \begin_layout Standard
17886 Display can be characters or symbols that define how the operator looks
17888 To define a big operator a * is set behind the command.
17889 All self-defined big operators can have limits as described in
17890 \begin_inset CommandInset ref
17892 reference "sub:Operator-Limits"
17899 \begin_layout Standard
17900 For example the LaTeX-preamble line
17903 \begin_layout Standard
17908 DeclareMathOperator*{
17915 \begin_layout Standard
17916 defines the command
17922 , that inserts a big operator consisting of the lozenge symbol from
17923 \begin_inset CommandInset ref
17925 reference "sub:Miscellaneous-Symbols"
17930 \begin_inset Formula
17932 \Lozenge_{n=1}^{\infty}
17937 The command for this formula is:
17948 \begin_inset Formula $\to$
17954 \begin_layout Standard
17955 \begin_inset VSpace bigskip
17958 When self-defined operators are not used several times in the document,
17959 they can also be defined with the commands
17966 \begin_inset Index idx
17969 \begin_layout Plain Layout
17984 \begin_inset Index idx
17987 \begin_layout Plain Layout
17995 , which have the following scheme:
17998 \begin_layout Standard
18012 \begin_layout Standard
18019 defines big operators,
18028 \begin_layout Standard
18036 \begin_inset space \thinspace{}
18040 \begin_inset space \space{}
18043 be used to use one limit for several operators:
18046 \begin_layout Standard
18047 \begin_inset Formula
18049 \mathop{\sum\negmedspace\sum}_{i,j=1}^{N}
18057 \begin_layout Standard
18058 The command for the formula above is:
18059 \begin_inset Newline newline
18078 \begin_layout Plain Layout
18090 \begin_inset Formula $\to$
18099 \begin_layout Plain Layout
18113 \begin_layout Section
18115 \begin_inset Index idx
18118 \begin_layout Plain Layout
18127 \begin_layout Subsection
18129 \begin_inset CommandInset label
18131 name "sub:Font-Styles"
18136 \begin_inset Index idx
18139 \begin_layout Plain Layout
18148 \begin_layout Standard
18149 Latin letters in formulas can be set in one of the following font styles:
18150 \begin_inset VSpace -2mm
18156 \begin_layout Standard
18158 \begin_inset Tabular
18159 <lyxtabular version="3" rows="7" columns="3">
18160 <features tabularvalignment="middle">
18161 <column alignment="center" valignment="top" width="0">
18162 <column alignment="center" valignment="top" width="0">
18163 <column alignment="center" valignment="top" width="0">
18165 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
18168 \begin_layout Plain Layout
18174 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
18177 \begin_layout Plain Layout
18183 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
18186 \begin_layout Plain Layout
18194 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
18197 \begin_layout Plain Layout
18206 \begin_layout Plain Layout
18222 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
18225 \begin_layout Plain Layout
18226 \begin_inset Formula $\mathbb{ABC}$
18234 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
18237 \begin_layout Plain Layout
18250 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
18253 \begin_layout Plain Layout
18262 \begin_layout Plain Layout
18278 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
18281 \begin_layout Plain Layout
18282 \begin_inset Formula $\mathbf{AbC}$
18290 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
18293 \begin_layout Plain Layout
18306 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
18309 \begin_layout Plain Layout
18318 \begin_layout Plain Layout
18334 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
18337 \begin_layout Plain Layout
18338 \begin_inset Formula $\boldsymbol{AbC}$
18346 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
18349 \begin_layout Plain Layout
18352 arg "font-boldsymbol"
18362 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
18365 \begin_layout Plain Layout
18374 \begin_layout Plain Layout
18390 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
18393 \begin_layout Plain Layout
18394 \begin_inset Formula $\mathcal{ABC}$
18402 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
18405 \begin_layout Plain Layout
18418 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
18421 \begin_layout Plain Layout
18430 \begin_layout Plain Layout
18446 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
18449 \begin_layout Plain Layout
18450 \begin_inset Formula $\mathfrak{AbC}$
18458 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
18461 \begin_layout Plain Layout
18469 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
18472 \begin_layout Plain Layout
18481 \begin_layout Plain Layout
18497 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
18500 \begin_layout Plain Layout
18501 \begin_inset Formula $\mathscr{AbC}$
18509 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
18512 \begin_layout Plain Layout
18526 \begin_layout Standard
18528 \begin_inset Tabular
18529 <lyxtabular version="3" rows="5" columns="3">
18530 <features tabularvalignment="middle">
18531 <column alignment="center" valignment="top" width="0">
18532 <column alignment="center" valignment="top" width="0">
18533 <column alignment="center" valignment="top" width="0">
18535 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
18538 \begin_layout Plain Layout
18544 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
18547 \begin_layout Plain Layout
18553 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
18556 \begin_layout Plain Layout
18564 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
18567 \begin_layout Plain Layout
18576 \begin_layout Plain Layout
18592 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
18595 \begin_layout Plain Layout
18596 \begin_inset Formula $\mathit{AbC}$
18604 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
18607 \begin_layout Plain Layout
18615 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
18618 \begin_layout Plain Layout
18627 \begin_layout Plain Layout
18643 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
18646 \begin_layout Plain Layout
18647 \begin_inset Formula $\mathrm{AbC}$
18655 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
18658 \begin_layout Plain Layout
18671 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
18674 \begin_layout Plain Layout
18683 \begin_layout Plain Layout
18699 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
18702 \begin_layout Plain Layout
18703 \begin_inset Formula $\mathsf{AbC}$
18711 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
18714 \begin_layout Plain Layout
18727 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
18730 \begin_layout Plain Layout
18739 \begin_layout Plain Layout
18755 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
18758 \begin_layout Plain Layout
18759 \begin_inset Formula $\mathtt{AbC}$
18767 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
18770 \begin_layout Plain Layout
18773 arg "font-typewriter"
18789 \begin_layout Standard
18790 \begin_inset Note Greyedout
18793 \begin_layout Plain Layout
18810 can only be used for big letters.
18818 \begin_layout Standard
18819 Predefined is the style
18828 \begin_layout Standard
18829 The style commands work also for letters in mathematical constructs:
18830 \begin_inset Formula
18832 \mathfrak{A=\frac{b}{C}}
18840 \begin_layout Standard
18841 Characters in mathematical text don't appear in a math font style but in
18842 the text font style
18849 That their style can't be set correctly via the text style dialog is a
18854 \begin_layout Plain Layout
18855 \begin_inset CommandInset href
18857 name "LyX-bug #4629"
18858 target "http://www.lyx.org/trac/ticket/4629"
18870 \begin_layout Standard
18871 Instead of the style commands the dialog
18873 Edit\SpecialChar \menuseparator
18874 Math\SpecialChar \menuseparator
18877 or the toolbar button
18878 \begin_inset Graphics
18879 filename ../images/math/font.png
18887 \begin_layout Subsection
18889 \begin_inset CommandInset label
18891 name "sub:Bold-Formulas"
18896 \begin_inset Index idx
18899 \begin_layout Plain Layout
18908 \begin_layout Standard
18909 To make a complete formula bold, the command
18915 from the previous subsection cannot be used, because it doesn't work for
18916 small Greek letters.
18917 Furthermore it prints Latin letters always upright, like in the following
18921 \begin_layout Standard
18922 \begin_inset Formula
18924 \mathbf{\int_{n}^{2}f(\theta)=\Gamma}\qquad\textrm{equation with \textbackslash mathbf}
18932 \begin_layout Standard
18933 To display the formula correctly, the command
18940 \begin_inset Formula
18942 \boldsymbol{\int_{n}^{2}f(\theta)=\Gamma\qquad\textrm{equation with \textbackslash boldsymbol}}
18947 It is also possible to set the formula in a
18949 boldmath environment
18952 This environment is created by inserting the command
18959 \begin_inset Index idx
18962 \begin_layout Plain Layout
18971 To end the environment, the command
18978 \begin_inset Index idx
18981 \begin_layout Plain Layout
18989 is inserted in TeX-mode.
18993 \begin_layout Plain Layout
19003 \begin_inset Formula
19005 \int_{n}^{2}f(\theta)=\Gamma\qquad\textrm{equation in a boldmath environment}
19014 \begin_layout Plain Layout
19026 \begin_layout Subsection
19028 \begin_inset Index idx
19031 \begin_layout Plain Layout
19040 \begin_layout Standard
19041 Formulas can be colored like normal text: Highlight a formula or a formula
19047 Here is a formula in magenta:
19048 \begin_inset Formula
19050 {\color{magenta}\int A\,\mathrm{d}x=\frac{\sqrt[5]{B}}{\ln\left(\frac{1}{3}\right)}}
19058 \begin_layout Standard
19059 You can also define your own colors as described in
19060 \begin_inset CommandInset ref
19062 reference "sub:Colored-Boxes"
19067 They can be used with the TeX code command
19074 \begin_inset Index idx
19077 \begin_layout Plain Layout
19088 \begin_layout Standard
19093 textcolor{color}{characters or formula}
19096 \begin_layout Standard
19097 The following example was colored completely dark green and partly red:
19100 \begin_layout Standard
19104 \begin_layout Plain Layout
19108 textcolor{darkgreen}{
19114 \begin_inset Formula
19116 \int A\,\mathrm{d}x=\frac{{\color{red}\sqrt[5]{B}}}{\ln\left(\frac{1}{3}\right)}
19125 \begin_layout Plain Layout
19135 \begin_layout Standard
19136 Due to a bug in LyX only complete formulas can be colored with self-defined
19141 \begin_layout Plain Layout
19142 \begin_inset CommandInset href
19144 name "LyX-bug #5269"
19145 target "http://www.lyx.org/trac/ticket/5269"
19157 \begin_layout Subsection
19159 \begin_inset CommandInset label
19161 name "sub:Font-Sizes"
19166 \begin_inset Index idx
19169 \begin_layout Plain Layout
19178 \begin_layout Standard
19179 For characters in formulas there are, analog to characters in text, the
19180 following size commands:
19183 \begin_layout Standard
19227 \begin_inset Newline newline
19249 \begin_layout Standard
19250 The size produced by the commands depends on the document font size, which
19251 corresponds to the command
19258 The other commands produce smaller or larger sizes than
19265 The font size can however not exceed a certain value.
19266 Is for example the document font size 12
19267 \begin_inset space \thinspace{}
19276 switches to the same size as
19286 \begin_layout Standard
19287 A size command is inserted in TeX-mode before the formula and sets the size
19288 for all following formula and text characters.
19289 To switch back to the initial size, the command
19295 is inserted behind the formula in TeX-mode.
19298 \begin_layout Standard
19299 Within a formula the size can be changed using the following size commands:
19302 \begin_layout Standard
19305 \begin_inset Tabular
19306 <lyxtabular version="3" rows="5" columns="2">
19307 <features tabularvalignment="middle">
19308 <column alignment="center" valignment="top" width="0">
19309 <column alignment="center" valignment="top" width="0">
19311 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
19314 \begin_layout Plain Layout
19320 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
19323 \begin_layout Plain Layout
19325 \begin_inset Note Note
19328 \begin_layout Plain Layout
19335 is only used as spacer.
19347 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
19350 \begin_layout Plain Layout
19354 \begin_inset Index idx
19357 \begin_layout Plain Layout
19370 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
19373 \begin_layout Plain Layout
19374 \begin_inset Formula $\raisebox{6.5mm}{}{\displaystyle E_{\mathrm{pot_{1}}}=\frac{K}{l+\frac{m}{n_{2}}}}\raisebox{-5.5mm}{}$
19384 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
19387 \begin_layout Plain Layout
19395 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
19398 \begin_layout Plain Layout
19399 \begin_inset Formula $\raisebox{4.5mm}{}{\textstyle E_{\mathrm{pot_{1}}}=\frac{K}{l+\frac{m}{n_{2}}}}\raisebox{-4mm}{}$
19409 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
19412 \begin_layout Plain Layout
19420 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
19423 \begin_layout Plain Layout
19424 \begin_inset Formula $\raisebox{4.5mm}{}{\scriptstyle E_{\mathrm{pot_{1}}}=\frac{K}{l+\frac{m}{n_{2}}}}\raisebox{-3.5mm}{}$
19434 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
19437 \begin_layout Plain Layout
19445 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
19448 \begin_layout Plain Layout
19449 \begin_inset Formula $\raisebox{4.5mm}{}{\scriptscriptstyle E_{\mathrm{pot_{1}}}=\frac{K}{l+\frac{m}{n_{2}}}}\raisebox{-3.5mm}{}$
19465 \begin_layout Standard
19466 After entering these commands, a blue box appears in which the formula parts
19470 \begin_layout Standard
19471 There is a further method to change the font size, that though only works
19472 for symbols or letters in mathematical text.
19473 To use it, one of the above text size commands is inserted in mathematical
19475 All following characters until the end of the mathematical text or until
19476 another size command will have the selected size.
19478 \begin_inset VSpace -2mm
19484 \begin_layout Standard
19488 \begin_layout Plain Layout
19498 \begin_inset Formula
19500 A=\frac{B}{c}\cdot\maltese
19506 \begin_inset Formula
19508 \maltese A\textrm{\Large\maltese\textit{A}}\textrm{\tiny\maltese\textit{A}}
19517 \begin_layout Plain Layout
19529 \begin_layout Standard
19530 \begin_inset VSpace medskip
19533 Before both formulas the command
19540 The command for the second formula is:
19541 \begin_inset Newline newline
19552 \begin_layout Plain Layout
19567 \begin_layout Plain Layout
19582 \begin_layout Plain Layout
19597 \begin_layout Plain Layout
19607 \begin_inset Formula $\to$
19611 \begin_inset Formula $\to$
19615 \begin_inset Newline newline
19619 \begin_inset space \hspace*{}
19633 \begin_layout Plain Layout
19648 \begin_layout Plain Layout
19663 \begin_layout Plain Layout
19675 \begin_layout Standard
19676 If a symbol cannot be displayed in different sizes, it will always be displayed
19677 in the default size.
19680 \begin_layout Section
19682 \begin_inset Index idx
19685 \begin_layout Plain Layout
19694 \begin_layout Standard
19695 Greek letters can also be inserted via the toolbar button
19696 \begin_inset Graphics
19697 filename ../images/math/alpha.png
19703 All international typesetting norms purport that Greek letters in math
19704 have to be typeset italic/slanted.
19705 In some languages, like French or Russian, they are nevertheless sometimes
19709 \begin_layout Subsection
19711 \begin_inset Index idx
19714 \begin_layout Plain Layout
19715 Greek letters ! small
19723 \begin_layout Standard
19724 \begin_inset space \hfill{}
19728 \begin_inset Tabular
19729 <lyxtabular version="3" rows="11" columns="2">
19730 <features tabularvalignment="middle">
19731 <column alignment="center" valignment="top" width="0pt">
19732 <column alignment="center" valignment="top" width="0pt">
19734 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
19737 \begin_layout Plain Layout
19743 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
19746 \begin_layout Plain Layout
19754 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
19757 \begin_layout Plain Layout
19765 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
19768 \begin_layout Plain Layout
19769 \begin_inset Formula $\alpha$
19779 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
19782 \begin_layout Plain Layout
19790 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
19793 \begin_layout Plain Layout
19794 \begin_inset Formula $\beta$
19804 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
19807 \begin_layout Plain Layout
19815 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
19818 \begin_layout Plain Layout
19819 \begin_inset Formula $\gamma$
19829 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
19832 \begin_layout Plain Layout
19840 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
19843 \begin_layout Plain Layout
19844 \begin_inset Formula $\delta$
19854 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
19857 \begin_layout Plain Layout
19865 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
19868 \begin_layout Plain Layout
19869 \begin_inset Formula $\epsilon$
19879 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
19882 \begin_layout Plain Layout
19890 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
19893 \begin_layout Plain Layout
19894 \begin_inset Formula $\varepsilon$
19904 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
19907 \begin_layout Plain Layout
19915 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
19918 \begin_layout Plain Layout
19919 \begin_inset Formula $\zeta$
19929 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
19932 \begin_layout Plain Layout
19940 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
19943 \begin_layout Plain Layout
19944 \begin_inset Formula $\eta$
19954 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
19957 \begin_layout Plain Layout
19965 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
19968 \begin_layout Plain Layout
19969 \begin_inset Formula $\theta$
19979 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
19982 \begin_layout Plain Layout
19990 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
19993 \begin_layout Plain Layout
19994 \begin_inset Formula $\vartheta$
20008 \begin_inset space \hfill{}
20012 \begin_inset Tabular
20013 <lyxtabular version="3" rows="12" columns="2">
20014 <features tabularvalignment="middle">
20015 <column alignment="center" valignment="top" width="0pt">
20016 <column alignment="center" valignment="top" width="0pt">
20018 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
20021 \begin_layout Plain Layout
20027 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
20030 \begin_layout Plain Layout
20038 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
20041 \begin_layout Plain Layout
20049 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
20052 \begin_layout Plain Layout
20053 \begin_inset Formula $\iota$
20063 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
20066 \begin_layout Plain Layout
20074 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
20077 \begin_layout Plain Layout
20078 \begin_inset Formula $\kappa$
20088 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
20091 \begin_layout Plain Layout
20099 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
20102 \begin_layout Plain Layout
20103 \begin_inset Formula $\varkappa$
20113 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
20116 \begin_layout Plain Layout
20124 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
20127 \begin_layout Plain Layout
20128 \begin_inset Formula $\lambda$
20138 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
20141 \begin_layout Plain Layout
20149 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
20152 \begin_layout Plain Layout
20153 \begin_inset Formula $\mu$
20163 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
20166 \begin_layout Plain Layout
20174 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
20177 \begin_layout Plain Layout
20178 \begin_inset Formula $\nu$
20188 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
20191 \begin_layout Plain Layout
20199 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
20202 \begin_layout Plain Layout
20203 \begin_inset Formula $\xi$
20213 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
20216 \begin_layout Plain Layout
20222 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
20225 \begin_layout Plain Layout
20226 \begin_inset Formula $o$
20236 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
20239 \begin_layout Plain Layout
20247 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
20250 \begin_layout Plain Layout
20251 \begin_inset Formula $\pi$
20261 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
20264 \begin_layout Plain Layout
20272 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
20275 \begin_layout Plain Layout
20276 \begin_inset Formula $\varpi$
20286 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
20289 \begin_layout Plain Layout
20297 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
20300 \begin_layout Plain Layout
20301 \begin_inset Formula $\rho$
20315 \begin_inset space \hfill{}
20319 \begin_inset Tabular
20320 <lyxtabular version="3" rows="11" columns="2">
20321 <features tabularvalignment="middle">
20322 <column alignment="center" valignment="top" width="0pt">
20323 <column alignment="center" valignment="top" width="0pt">
20325 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
20328 \begin_layout Plain Layout
20334 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
20337 \begin_layout Plain Layout
20345 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
20348 \begin_layout Plain Layout
20356 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
20359 \begin_layout Plain Layout
20360 \begin_inset Formula $\varrho$
20370 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
20373 \begin_layout Plain Layout
20381 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
20384 \begin_layout Plain Layout
20385 \begin_inset Formula $\sigma$
20395 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
20398 \begin_layout Plain Layout
20406 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
20409 \begin_layout Plain Layout
20410 \begin_inset Formula $\varsigma$
20420 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
20423 \begin_layout Plain Layout
20431 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
20434 \begin_layout Plain Layout
20435 \begin_inset Formula $\tau$
20445 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
20448 \begin_layout Plain Layout
20456 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
20459 \begin_layout Plain Layout
20460 \begin_inset Formula $\upsilon$
20470 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
20473 \begin_layout Plain Layout
20481 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
20484 \begin_layout Plain Layout
20485 \begin_inset Formula $\phi$
20495 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
20498 \begin_layout Plain Layout
20506 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
20509 \begin_layout Plain Layout
20510 \begin_inset Formula $\varphi$
20520 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
20523 \begin_layout Plain Layout
20531 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
20534 \begin_layout Plain Layout
20535 \begin_inset Formula $\chi$
20545 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
20548 \begin_layout Plain Layout
20556 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
20559 \begin_layout Plain Layout
20560 \begin_inset Formula $\psi$
20570 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
20573 \begin_layout Plain Layout
20581 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
20584 \begin_layout Plain Layout
20585 \begin_inset Formula $\omega$
20599 \begin_inset space \hfill{}
20605 \begin_layout Standard
20606 \begin_inset VSpace medskip
20612 \begin_layout Standard
20613 How to create special upright Greek letters is explained in
20614 \begin_inset CommandInset ref
20616 reference "sub:Upright-small-Greek"
20623 \begin_layout Subsection
20625 \begin_inset Index idx
20628 \begin_layout Plain Layout
20629 Greek letters ! big
20637 \begin_layout Standard
20638 \begin_inset space \hfill{}
20642 \begin_inset Tabular
20643 <lyxtabular version="3" rows="7" columns="2">
20644 <features tabularvalignment="middle">
20645 <column alignment="center" valignment="top" width="0pt">
20646 <column alignment="center" valignment="top" width="0pt">
20648 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
20651 \begin_layout Plain Layout
20657 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
20660 \begin_layout Plain Layout
20668 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
20671 \begin_layout Plain Layout
20679 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
20682 \begin_layout Plain Layout
20683 \begin_inset Formula $\Gamma$
20693 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
20696 \begin_layout Plain Layout
20704 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
20707 \begin_layout Plain Layout
20708 \begin_inset Formula $\Delta$
20718 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
20721 \begin_layout Plain Layout
20729 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
20732 \begin_layout Plain Layout
20733 \begin_inset Formula $\Theta$
20743 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
20746 \begin_layout Plain Layout
20754 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
20757 \begin_layout Plain Layout
20758 \begin_inset Formula $\Lambda$
20768 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
20771 \begin_layout Plain Layout
20779 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
20782 \begin_layout Plain Layout
20783 \begin_inset Formula $\Xi$
20793 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
20796 \begin_layout Plain Layout
20804 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
20807 \begin_layout Plain Layout
20808 \begin_inset Formula $\Pi$
20822 \begin_inset space \hfill{}
20826 \begin_inset Tabular
20827 <lyxtabular version="3" rows="6" columns="2">
20828 <features tabularvalignment="middle">
20829 <column alignment="center" valignment="top" width="0pt">
20830 <column alignment="center" valignment="top" width="0pt">
20832 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
20835 \begin_layout Plain Layout
20841 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
20844 \begin_layout Plain Layout
20852 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
20855 \begin_layout Plain Layout
20863 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
20866 \begin_layout Plain Layout
20867 \begin_inset Formula $\Sigma$
20877 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
20880 \begin_layout Plain Layout
20888 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
20891 \begin_layout Plain Layout
20892 \begin_inset Formula $\Upsilon$
20902 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
20905 \begin_layout Plain Layout
20913 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
20916 \begin_layout Plain Layout
20917 \begin_inset Formula $\Phi$
20927 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
20930 \begin_layout Plain Layout
20938 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
20941 \begin_layout Plain Layout
20942 \begin_inset Formula $\Psi$
20952 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
20955 \begin_layout Plain Layout
20963 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
20966 \begin_layout Plain Layout
20967 \begin_inset Formula $\Omega$
20981 \begin_inset space \hfill{}
20987 \begin_layout Standard
20988 \begin_inset VSpace medskip
20991 That the big Greek letters appear upright is caused by a design bug when
20993 To get correct italic big letters, begin every command with
20998 For example the command
21005 \begin_inset Formula $\varGamma$
21009 Another way is to load the package
21017 \begin_layout Plain Layout
21022 is part of the LaTeX-package
21027 \begin_inset Index idx
21030 \begin_layout Plain Layout
21035 \begin_layout Plain Layout
21055 \begin_inset Index idx
21058 \begin_layout Plain Layout
21064 with the LaTeX-preamble line
21067 \begin_layout Standard
21072 usepackage{fixmath}
21075 \begin_layout Standard
21076 Then all big Greek letters in a document will automatically be typeset italic.
21079 \begin_layout Subsection
21081 \begin_inset Index idx
21084 \begin_layout Plain Layout
21085 Greek letters ! bold
21093 \begin_layout Standard
21094 Greek letters cannot be set with different font styles like Latin letters.
21095 They can only be made bold with the command
21102 \begin_inset Index idx
21105 \begin_layout Plain Layout
21116 \begin_layout Standard
21118 \begin_inset Tabular
21119 <lyxtabular version="3" rows="3" columns="2">
21120 <features tabularvalignment="middle">
21121 <column alignment="center" valignment="top" width="0">
21122 <column alignment="center" valignment="top" width="0">
21124 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
21127 \begin_layout Plain Layout
21133 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
21136 \begin_layout Plain Layout
21144 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
21147 \begin_layout Plain Layout
21159 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
21162 \begin_layout Plain Layout
21163 \begin_inset Formula $\Upsilon\boldsymbol{\Upsilon}$
21173 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
21176 \begin_layout Plain Layout
21188 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
21191 \begin_layout Plain Layout
21192 \begin_inset Formula $\theta\boldsymbol{\theta}$
21208 \begin_layout Standard
21209 \begin_inset Newpage newpage
21215 \begin_layout Section
21220 \begin_layout Plain Layout
21233 \begin_layout Plain Layout
21234 A list with all symbols of most of the LaTeX-packages can be found in
21235 \begin_inset CommandInset citation
21250 \begin_layout Plain Layout
21258 \begin_inset Note Note
21261 \begin_layout Plain Layout
21264 texorpdfstring is used to avoid that the footnote appears in the PDF-bookmark.
21267 \begin_layout Plain Layout
21270 texorpdfstring is in section
21271 \begin_inset CommandInset ref
21273 reference "sub:Formulas-in-Section"
21283 \begin_inset Index idx
21286 \begin_layout Plain Layout
21295 \begin_layout Standard
21296 Many of the symbols listed in this section can also be inserted via the
21298 \begin_inset Graphics
21299 filename ../images/math/nabla.png
21305 \begin_inset Graphics
21306 filename ../images/math/digamma.png
21314 \begin_layout Subsection
21315 Mathematical Symbols
21316 \begin_inset CommandInset label
21318 name "sub:Mathematical-Symbols"
21323 \begin_inset Index idx
21326 \begin_layout Plain Layout
21327 Symbols ! mathematical
21335 \begin_layout Standard
21336 \begin_inset space \hfill{}
21340 \begin_inset Tabular
21341 <lyxtabular version="3" rows="10" columns="2">
21342 <features tabularvalignment="middle">
21343 <column alignment="center" valignment="top" width="0pt">
21344 <column alignment="center" valignment="top" width="0pt">
21346 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
21349 \begin_layout Plain Layout
21355 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
21358 \begin_layout Plain Layout
21366 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
21369 \begin_layout Plain Layout
21377 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
21380 \begin_layout Plain Layout
21381 \begin_inset Formula $\neg$
21391 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
21394 \begin_layout Plain Layout
21402 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
21405 \begin_layout Plain Layout
21406 \begin_inset Formula $\Im$
21416 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
21419 \begin_layout Plain Layout
21427 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
21430 \begin_layout Plain Layout
21431 \begin_inset Formula $\Re$
21441 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
21444 \begin_layout Plain Layout
21452 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
21455 \begin_layout Plain Layout
21456 \begin_inset Formula $\aleph$
21466 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
21469 \begin_layout Plain Layout
21477 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
21480 \begin_layout Plain Layout
21481 \begin_inset Formula $\partial$
21491 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
21494 \begin_layout Plain Layout
21502 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
21505 \begin_layout Plain Layout
21506 \begin_inset Formula $\infty$
21516 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
21519 \begin_layout Plain Layout
21527 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
21530 \begin_layout Plain Layout
21531 \begin_inset Formula $\wp$
21541 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
21544 \begin_layout Plain Layout
21552 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
21555 \begin_layout Plain Layout
21556 \begin_inset Formula $\imath$
21566 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
21569 \begin_layout Plain Layout
21577 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
21580 \begin_layout Plain Layout
21581 \begin_inset Formula $\jmath$
21595 \begin_inset space \hfill{}
21599 \begin_inset Tabular
21600 <lyxtabular version="3" rows="10" columns="2">
21601 <features tabularvalignment="middle">
21602 <column alignment="center" valignment="top" width="0pt">
21603 <column alignment="center" valignment="top" width="0pt">
21605 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
21608 \begin_layout Plain Layout
21614 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
21617 \begin_layout Plain Layout
21619 \begin_inset Note Note
21622 \begin_layout Plain Layout
21629 is only used as spacer.
21641 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
21644 \begin_layout Plain Layout
21652 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
21655 \begin_layout Plain Layout
21656 \begin_inset Formula $\forall$
21666 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
21669 \begin_layout Plain Layout
21677 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
21680 \begin_layout Plain Layout
21681 \begin_inset Formula $\exists$
21691 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
21694 \begin_layout Plain Layout
21702 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
21705 \begin_layout Plain Layout
21706 \begin_inset Formula $\nexists$
21716 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
21719 \begin_layout Plain Layout
21727 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
21730 \begin_layout Plain Layout
21731 \begin_inset Formula $\emptyset$
21741 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
21744 \begin_layout Plain Layout
21752 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
21755 \begin_layout Plain Layout
21756 \begin_inset Formula $\varnothing$
21766 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
21769 \begin_layout Plain Layout
21777 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
21780 \begin_layout Plain Layout
21781 \begin_inset Formula $\dag$
21791 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
21794 \begin_layout Plain Layout
21802 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
21805 \begin_layout Plain Layout
21806 \begin_inset Formula $\ddag$
21816 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
21819 \begin_layout Plain Layout
21827 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
21830 \begin_layout Plain Layout
21834 \begin_layout Plain Layout
21844 \begin_inset Formula $\complement$
21851 \begin_layout Plain Layout
21865 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
21868 \begin_layout Plain Layout
21876 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
21879 \begin_layout Plain Layout
21880 \begin_inset Formula $\Bbbk$
21894 \begin_inset space \hfill{}
21898 \begin_inset Tabular
21899 <lyxtabular version="3" rows="10" columns="2">
21900 <features tabularvalignment="middle">
21901 <column alignment="center" valignment="top" width="0pt">
21902 <column alignment="center" valignment="top" width="0pt">
21904 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
21907 \begin_layout Plain Layout
21913 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
21916 \begin_layout Plain Layout
21924 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
21927 \begin_layout Plain Layout
21935 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
21938 \begin_layout Plain Layout
21939 \begin_inset Formula $\prime$
21949 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
21952 \begin_layout Plain Layout
21960 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
21963 \begin_layout Plain Layout
21964 \begin_inset Formula $\backprime$
21974 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
21977 \begin_layout Plain Layout
21985 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
21988 \begin_layout Plain Layout
21989 \begin_inset Formula $\mho$
21999 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
22002 \begin_layout Plain Layout
22010 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
22013 \begin_layout Plain Layout
22014 \begin_inset Formula $\triangle$
22024 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
22027 \begin_layout Plain Layout
22035 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
22038 \begin_layout Plain Layout
22039 \begin_inset Formula $\angle$
22049 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
22052 \begin_layout Plain Layout
22060 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
22063 \begin_layout Plain Layout
22064 \begin_inset Formula $\measuredangle$
22074 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
22077 \begin_layout Plain Layout
22085 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
22088 \begin_layout Plain Layout
22089 \begin_inset Formula $\sphericalangle$
22099 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
22102 \begin_layout Plain Layout
22110 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
22113 \begin_layout Plain Layout
22114 \begin_inset Formula $\top$
22124 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
22127 \begin_layout Plain Layout
22135 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
22138 \begin_layout Plain Layout
22139 \begin_inset Formula $\bot$
22153 \begin_inset space \hfill{}
22159 \begin_layout Subsection
22160 Miscellaneous Symbols
22161 \begin_inset CommandInset label
22163 name "sub:Miscellaneous-Symbols"
22168 \begin_inset Index idx
22171 \begin_layout Plain Layout
22172 Symbols ! miscellaneous
22180 \begin_layout Standard
22183 \begin_inset Tabular
22184 <lyxtabular version="3" rows="10" columns="2">
22185 <features tabularvalignment="middle">
22186 <column alignment="center" valignment="top" width="0pt">
22187 <column alignment="center" valignment="top" width="0pt">
22189 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
22192 \begin_layout Plain Layout
22198 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
22201 \begin_layout Plain Layout
22209 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
22212 \begin_layout Plain Layout
22220 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
22223 \begin_layout Plain Layout
22224 \begin_inset Formula $\flat$
22234 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
22237 \begin_layout Plain Layout
22245 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
22248 \begin_layout Plain Layout
22249 \begin_inset Formula $\natural$
22259 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
22262 \begin_layout Plain Layout
22270 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
22273 \begin_layout Plain Layout
22274 \begin_inset Formula $\sharp$
22284 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
22287 \begin_layout Plain Layout
22295 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
22298 \begin_layout Plain Layout
22299 \begin_inset Formula $\surd$
22309 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
22312 \begin_layout Plain Layout
22320 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
22323 \begin_layout Plain Layout
22324 \begin_inset Formula $\checkmark$
22334 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
22337 \begin_layout Plain Layout
22345 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
22348 \begin_layout Plain Layout
22349 \begin_inset Formula $\yen$
22359 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
22362 \begin_layout Plain Layout
22370 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
22373 \begin_layout Plain Layout
22374 \begin_inset Formula $\pounds$
22384 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
22387 \begin_layout Plain Layout
22393 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
22396 \begin_layout Plain Layout
22397 \begin_inset Formula $\$$
22407 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
22410 \begin_layout Plain Layout
22416 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
22419 \begin_layout Plain Layout
22420 \begin_inset Formula $§$
22434 \begin_inset Tabular
22435 <lyxtabular version="3" rows="10" columns="2">
22436 <features tabularvalignment="middle">
22437 <column alignment="center" valignment="top" width="0">
22438 <column alignment="center" valignment="top" width="0">
22440 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
22443 \begin_layout Plain Layout
22449 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
22452 \begin_layout Plain Layout
22460 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
22463 \begin_layout Plain Layout
22471 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
22474 \begin_layout Plain Layout
22475 \begin_inset Formula $\hbar$
22485 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
22488 \begin_layout Plain Layout
22496 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
22499 \begin_layout Plain Layout
22500 \begin_inset Formula $\hslash$
22510 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
22513 \begin_layout Plain Layout
22521 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
22524 \begin_layout Plain Layout
22525 \begin_inset Formula $\clubsuit$
22535 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
22538 \begin_layout Plain Layout
22546 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
22549 \begin_layout Plain Layout
22550 \begin_inset Formula $\spadesuit$
22560 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
22563 \begin_layout Plain Layout
22571 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
22574 \begin_layout Plain Layout
22575 \begin_inset Formula $\bigstar$
22585 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
22588 \begin_layout Plain Layout
22596 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
22599 \begin_layout Plain Layout
22600 \begin_inset Formula $\blacklozenge$
22610 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
22613 \begin_layout Plain Layout
22621 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
22624 \begin_layout Plain Layout
22625 \begin_inset Formula $\blacktriangle$
22635 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
22638 \begin_layout Plain Layout
22646 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
22649 \begin_layout Plain Layout
22650 \begin_inset Formula $\blacktriangledown$
22660 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
22663 \begin_layout Plain Layout
22671 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
22674 \begin_layout Plain Layout
22675 \begin_inset Formula $\bullet$
22689 \begin_inset Tabular
22690 <lyxtabular version="3" rows="10" columns="2">
22691 <features tabularvalignment="middle">
22692 <column alignment="center" valignment="top" width="0pt">
22693 <column alignment="center" valignment="top" width="0pt">
22695 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
22698 \begin_layout Plain Layout
22704 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
22707 \begin_layout Plain Layout
22715 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
22718 \begin_layout Plain Layout
22726 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
22729 \begin_layout Plain Layout
22730 \begin_inset Formula $\diamondsuit$
22740 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
22743 \begin_layout Plain Layout
22751 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
22754 \begin_layout Plain Layout
22755 \begin_inset Formula $\Diamond$
22765 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
22768 \begin_layout Plain Layout
22776 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
22779 \begin_layout Plain Layout
22780 \begin_inset Formula $\heartsuit$
22790 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
22793 \begin_layout Plain Layout
22801 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
22804 \begin_layout Plain Layout
22805 \begin_inset Formula $\P$
22815 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
22818 \begin_layout Plain Layout
22826 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
22829 \begin_layout Plain Layout
22830 \begin_inset Formula $\copyright$
22840 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
22843 \begin_layout Plain Layout
22851 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
22854 \begin_layout Plain Layout
22855 \begin_inset Formula $\circledR$
22865 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
22868 \begin_layout Plain Layout
22876 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
22879 \begin_layout Plain Layout
22880 \begin_inset Formula $\maltese$
22890 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
22893 \begin_layout Plain Layout
22901 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
22904 \begin_layout Plain Layout
22905 \begin_inset Formula $\diagup$
22915 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
22918 \begin_layout Plain Layout
22926 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
22929 \begin_layout Plain Layout
22930 \begin_inset Formula $\diagdown$
22946 \begin_layout Standard
22947 \begin_inset VSpace medskip
22950 More symbols are listed in
22951 \begin_inset CommandInset ref
22953 reference "sub:Miscellaneous-special-Characters"
22960 \begin_layout Standard
22961 Some symbols can be displayed in different sizes, see
22962 \begin_inset CommandInset ref
22964 reference "sub:Font-Sizes"
22971 \begin_layout Subsection
22973 \begin_inset Index idx
22976 \begin_layout Plain Layout
22977 Symbols ! Euro-symbol
22983 \begin_inset Index idx
22986 \begin_layout Plain Layout
22993 \begin_layout Plain Layout
23010 \begin_layout Standard
23011 To use the Euro symbol in formulas, the LaTeX-package
23016 \begin_inset Index idx
23019 \begin_layout Plain Layout
23025 must be installed and loaded with the LaTeX-preamble line
23028 \begin_layout Standard
23033 usepackage[gennarrow]{eurosym}
23036 \begin_layout Standard
23037 The Euro symbol can now be inserted with the command
23044 \begin_inset Index idx
23047 \begin_layout Plain Layout
23058 \begin_layout Standard
23059 The Euro symbol can directly be inserted with the € key in mathematical
23060 text, without having
23075 can also be inserted in TeX-mode.
23076 The official currency symbol can then be inserted with the command
23083 \begin_inset Index idx
23086 \begin_layout Plain Layout
23094 , that is only available in TeX-mode.
23097 \begin_layout Standard
23101 \begin_layout Plain Layout
23111 \begin_inset Note Note
23114 \begin_layout Plain Layout
23115 The following table will only be displayed when the LaTeX-package
23127 \begin_layout Standard
23128 An overview about the different Euro symbols:
23131 \begin_layout Standard
23133 \begin_inset Tabular
23134 <lyxtabular version="3" rows="4" columns="3">
23135 <features tabularvalignment="middle">
23136 <column alignment="center" valignment="top" width="0pt">
23137 <column alignment="center" valignment="top" width="0pt">
23138 <column alignment="center" valignment="top" width="0pt">
23140 <cell multicolumn="1" alignment="center" valignment="top" bottomline="true" usebox="none">
23143 \begin_layout Plain Layout
23149 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
23152 \begin_layout Plain Layout
23158 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
23161 \begin_layout Plain Layout
23169 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
23172 \begin_layout Plain Layout
23178 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
23181 \begin_layout Plain Layout
23189 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
23192 \begin_layout Plain Layout
23193 \begin_inset Formula $\euro$
23203 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
23206 \begin_layout Plain Layout
23212 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
23215 \begin_layout Plain Layout
23221 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
23224 \begin_layout Plain Layout
23225 \begin_inset Formula $\mbox{€}$
23235 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
23238 \begin_layout Plain Layout
23244 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
23247 \begin_layout Plain Layout
23255 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
23258 \begin_layout Plain Layout
23262 \begin_layout Plain Layout
23284 \begin_layout Standard
23288 \begin_layout Plain Layout
23298 \begin_inset Note Note
23301 \begin_layout Plain Layout
23302 The following will be displayed when the LaTeX-package
23314 \begin_layout Standard
23315 You need to install the LaTeX-package
23319 to see the rest of this subsection in the output.
23322 \begin_layout Standard
23326 \begin_layout Plain Layout
23338 \begin_layout Section
23340 \begin_inset CommandInset label
23342 name "sec:Relations"
23347 \begin_inset Index idx
23350 \begin_layout Plain Layout
23357 \begin_inset Index idx
23360 \begin_layout Plain Layout
23365 \begin_layout Plain Layout
23376 \begin_layout Plain Layout
23391 \begin_layout Standard
23392 All relations can also be inserted via the toolbar button
23393 \begin_inset Graphics
23394 filename ../images/math/leq.png
23402 \begin_layout Standard
23403 \begin_inset space \hfill{}
23407 \begin_inset Tabular
23408 <lyxtabular version="3" rows="17" columns="2">
23409 <features tabularvalignment="middle">
23410 <column alignment="center" valignment="top" width="0pt">
23411 <column alignment="center" valignment="top" width="0pt">
23413 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
23416 \begin_layout Plain Layout
23422 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
23425 \begin_layout Plain Layout
23433 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
23436 \begin_layout Plain Layout
23442 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
23445 \begin_layout Plain Layout
23446 \begin_inset Formula $<$
23456 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
23459 \begin_layout Plain Layout
23467 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
23470 \begin_layout Plain Layout
23471 \begin_inset Formula $\le$
23481 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
23484 \begin_layout Plain Layout
23492 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
23495 \begin_layout Plain Layout
23496 \begin_inset Formula $\ll$
23506 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
23509 \begin_layout Plain Layout
23517 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
23520 \begin_layout Plain Layout
23521 \begin_inset Formula $\prec$
23531 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
23534 \begin_layout Plain Layout
23542 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
23545 \begin_layout Plain Layout
23546 \begin_inset Formula $\preceq$
23556 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
23559 \begin_layout Plain Layout
23567 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
23570 \begin_layout Plain Layout
23571 \begin_inset Formula $\subset$
23581 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
23584 \begin_layout Plain Layout
23592 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
23595 \begin_layout Plain Layout
23596 \begin_inset Formula $\subseteq$
23606 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
23609 \begin_layout Plain Layout
23617 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
23620 \begin_layout Plain Layout
23621 \begin_inset Formula $\sqsubseteq$
23631 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
23634 \begin_layout Plain Layout
23642 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
23645 \begin_layout Plain Layout
23646 \begin_inset Formula $\in$
23656 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
23659 \begin_layout Plain Layout
23667 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
23670 \begin_layout Plain Layout
23671 \begin_inset Formula $\vdash$
23681 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
23684 \begin_layout Plain Layout
23692 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
23695 \begin_layout Plain Layout
23696 \begin_inset Formula $\smile$
23706 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
23709 \begin_layout Plain Layout
23717 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
23720 \begin_layout Plain Layout
23721 \begin_inset Formula $\lhd$
23731 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
23734 \begin_layout Plain Layout
23742 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
23745 \begin_layout Plain Layout
23746 \begin_inset Formula $\unlhd$
23756 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
23759 \begin_layout Plain Layout
23767 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
23770 \begin_layout Plain Layout
23771 \begin_inset Formula $\gtrless$
23781 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
23784 \begin_layout Plain Layout
23792 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
23795 \begin_layout Plain Layout
23796 \begin_inset Formula $\mid$
23806 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
23809 \begin_layout Plain Layout
23817 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
23820 \begin_layout Plain Layout
23821 \begin_inset Formula $\nmid$
23835 \begin_inset space \hfill{}
23839 \begin_inset Tabular
23840 <lyxtabular version="3" rows="17" columns="2">
23841 <features tabularvalignment="middle">
23842 <column alignment="center" valignment="top" width="0pt">
23843 <column alignment="center" valignment="top" width="0pt">
23845 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
23848 \begin_layout Plain Layout
23854 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
23857 \begin_layout Plain Layout
23865 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
23868 \begin_layout Plain Layout
23874 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
23877 \begin_layout Plain Layout
23878 \begin_inset Formula $=$
23888 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
23891 \begin_layout Plain Layout
23899 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
23902 \begin_layout Plain Layout
23903 \begin_inset Formula $\not=$
23913 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
23916 \begin_layout Plain Layout
23924 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
23927 \begin_layout Plain Layout
23928 \begin_inset Formula $\equiv$
23938 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
23941 \begin_layout Plain Layout
23949 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
23952 \begin_layout Plain Layout
23953 \begin_inset Formula $\sim$
23963 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
23966 \begin_layout Plain Layout
23974 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
23977 \begin_layout Plain Layout
23978 \begin_inset Formula $\simeq$
23988 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
23991 \begin_layout Plain Layout
23999 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
24002 \begin_layout Plain Layout
24003 \begin_inset Formula $\approx$
24013 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
24016 \begin_layout Plain Layout
24024 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
24027 \begin_layout Plain Layout
24028 \begin_inset Formula $\cong$
24038 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
24041 \begin_layout Plain Layout
24049 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
24052 \begin_layout Plain Layout
24053 \begin_inset Formula $\bowtie$
24063 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
24066 \begin_layout Plain Layout
24074 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
24077 \begin_layout Plain Layout
24078 \begin_inset Formula $\notin$
24088 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
24091 \begin_layout Plain Layout
24099 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
24102 \begin_layout Plain Layout
24103 \begin_inset Formula $\perp$
24113 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
24116 \begin_layout Plain Layout
24124 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
24127 \begin_layout Plain Layout
24128 \begin_inset Formula $\propto$
24138 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
24141 \begin_layout Plain Layout
24149 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
24152 \begin_layout Plain Layout
24153 \begin_inset Formula $\asymp$
24163 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
24166 \begin_layout Plain Layout
24174 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
24177 \begin_layout Plain Layout
24178 \begin_inset Formula $\doteq$
24188 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
24191 \begin_layout Plain Layout
24199 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
24202 \begin_layout Plain Layout
24203 \begin_inset Formula $\circeq$
24213 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
24216 \begin_layout Plain Layout
24224 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
24227 \begin_layout Plain Layout
24228 \begin_inset Formula $\models$
24238 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
24241 \begin_layout Plain Layout
24249 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
24252 \begin_layout Plain Layout
24253 \begin_inset Formula $\widehat{=}$
24267 \begin_inset space \hfill{}
24271 \begin_inset Tabular
24272 <lyxtabular version="3" rows="17" columns="2">
24273 <features tabularvalignment="middle">
24274 <column alignment="center" valignment="top" width="0pt">
24275 <column alignment="center" valignment="top" width="0pt">
24277 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
24280 \begin_layout Plain Layout
24286 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
24289 \begin_layout Plain Layout
24297 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
24300 \begin_layout Plain Layout
24306 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
24309 \begin_layout Plain Layout
24310 \begin_inset Formula $>$
24320 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
24323 \begin_layout Plain Layout
24331 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
24334 \begin_layout Plain Layout
24335 \begin_inset Formula $\ge$
24345 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
24348 \begin_layout Plain Layout
24356 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
24359 \begin_layout Plain Layout
24360 \begin_inset Formula $\gg$
24370 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
24373 \begin_layout Plain Layout
24381 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
24384 \begin_layout Plain Layout
24385 \begin_inset Formula $\succ$
24395 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
24398 \begin_layout Plain Layout
24406 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
24409 \begin_layout Plain Layout
24410 \begin_inset Formula $\succeq$
24420 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
24423 \begin_layout Plain Layout
24431 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
24434 \begin_layout Plain Layout
24435 \begin_inset Formula $\supset$
24445 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
24448 \begin_layout Plain Layout
24456 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
24459 \begin_layout Plain Layout
24460 \begin_inset Formula $\supseteq$
24470 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
24473 \begin_layout Plain Layout
24481 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
24484 \begin_layout Plain Layout
24485 \begin_inset Formula $\sqsupseteq$
24495 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
24498 \begin_layout Plain Layout
24506 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
24509 \begin_layout Plain Layout
24510 \begin_inset Formula $\ni$
24520 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
24523 \begin_layout Plain Layout
24531 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
24534 \begin_layout Plain Layout
24535 \begin_inset Formula $\dashv$
24545 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
24548 \begin_layout Plain Layout
24556 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
24559 \begin_layout Plain Layout
24560 \begin_inset Formula $\frown$
24570 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
24573 \begin_layout Plain Layout
24581 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
24584 \begin_layout Plain Layout
24585 \begin_inset Formula $\rhd$
24595 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
24598 \begin_layout Plain Layout
24606 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
24609 \begin_layout Plain Layout
24610 \begin_inset Formula $\unrhd$
24620 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
24623 \begin_layout Plain Layout
24631 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
24634 \begin_layout Plain Layout
24635 \begin_inset Formula $\lessgtr$
24645 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
24648 \begin_layout Plain Layout
24656 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
24659 \begin_layout Plain Layout
24660 \begin_inset Formula $\parallel$
24670 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
24673 \begin_layout Plain Layout
24681 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
24684 \begin_layout Plain Layout
24685 \begin_inset Formula $\nparallel$
24699 \begin_inset space \hfill{}
24705 \begin_layout Standard
24706 \begin_inset VSpace medskip
24721 are bigger than the equal looking operators
24736 \begin_layout Standard
24737 Relations are, in contrary to symbols, always surrounded by space.
24740 \begin_layout Standard
24741 Relations with labels can be created with the command
24748 \begin_inset Index idx
24751 \begin_layout Plain Layout
24762 \begin_layout Standard
24764 \begin_inset Tabular
24765 <lyxtabular version="3" rows="2" columns="2">
24766 <features tabularvalignment="middle">
24767 <column alignment="center" valignment="top" width="0">
24768 <column alignment="center" valignment="top" width="0">
24770 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
24773 \begin_layout Plain Layout
24779 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
24782 \begin_layout Plain Layout
24784 \begin_inset Note Note
24787 \begin_layout Plain Layout
24794 is only used as spacer.
24806 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
24809 \begin_layout Plain Layout
24816 \begin_layout Plain Layout
24833 \begin_layout Plain Layout
24843 \begin_inset Formula $\downarrow$
24852 \begin_layout Plain Layout
24865 \begin_layout Plain Layout
24879 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
24882 \begin_layout Plain Layout
24883 \begin_inset Formula $\raisebox{5mm}{}A(r)\stackrel{r\to\infty}{\approx}B$
24899 \begin_layout Section
24903 \begin_layout Subsection
24904 Predefined Functions
24905 \begin_inset CommandInset label
24907 name "sub:Predefined-Functions"
24912 \begin_inset Index idx
24915 \begin_layout Plain Layout
24916 Functions ! predefined
24924 \begin_layout Standard
24925 In general, variables are set
24929 in mathematical expressions, but not function names, because
24930 \begin_inset Formula $sin$
24933 could be misunderstood as
24934 \begin_inset Formula $s\cdot i\cdot n$
24938 Therefore there are predefined functionswhich are additionally a bit separated
24940 They are inserted as commands starting with a backslash before their name.
24943 \begin_layout Standard
24945 \begin_inset Tabular
24946 <lyxtabular version="3" rows="2" columns="4">
24947 <features tabularvalignment="middle">
24948 <column alignment="center" valignment="top" width="0pt">
24949 <column alignment="center" valignment="top" width="0pt">
24950 <column alignment="center" valignment="top" width="0pt">
24951 <column alignment="center" valignment="top" width="0pt">
24953 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
24956 \begin_layout Plain Layout
24962 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
24965 \begin_layout Plain Layout
24971 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
24974 \begin_layout Plain Layout
24980 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
24983 \begin_layout Plain Layout
24991 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
24994 \begin_layout Plain Layout
25000 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
25003 \begin_layout Plain Layout
25004 \begin_inset Formula $Asin(x)+B$
25012 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
25015 \begin_layout Plain Layout
25023 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
25026 \begin_layout Plain Layout
25027 \begin_inset Formula $A\sin(x)+B$
25043 \begin_layout Standard
25044 The following functions are predefined:
25047 \begin_layout Standard
25048 \begin_inset VSpace -2mm
25054 \begin_layout Standard
25056 \begin_inset Tabular
25057 <lyxtabular version="3" rows="9" columns="4">
25058 <features tabularvalignment="middle">
25059 <column alignment="center" valignment="top" width="0pt">
25060 <column alignment="center" valignment="top" width="0pt">
25061 <column alignment="center" valignment="top" width="0pt">
25062 <column alignment="center" valignment="top" width="0pt">
25064 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
25067 \begin_layout Plain Layout
25073 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
25076 \begin_layout Plain Layout
25082 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
25085 \begin_layout Plain Layout
25091 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="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" usebox="none">
25116 \begin_layout Plain Layout
25124 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
25127 \begin_layout Plain Layout
25135 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
25138 \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" usebox="none">
25162 \begin_layout Plain Layout
25170 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
25173 \begin_layout Plain Layout
25181 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
25184 \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" usebox="none">
25208 \begin_layout Plain Layout
25216 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
25219 \begin_layout Plain Layout
25227 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
25230 \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" usebox="none">
25254 \begin_layout Plain Layout
25262 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
25265 \begin_layout Plain Layout
25273 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
25276 \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" usebox="none">
25300 \begin_layout Plain Layout
25308 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
25311 \begin_layout Plain Layout
25319 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
25322 \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" usebox="none">
25346 \begin_layout Plain Layout
25354 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
25357 \begin_layout Plain Layout
25365 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
25368 \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" usebox="none">
25392 \begin_layout Plain Layout
25400 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
25403 \begin_layout Plain Layout
25411 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
25414 \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" usebox="none">
25438 \begin_layout Plain Layout
25446 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
25449 \begin_layout Plain Layout
25457 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
25460 \begin_layout Plain Layout
25476 \begin_layout Standard
25477 They can also be inserted with the math toolbar button
25478 \begin_inset Graphics
25479 filename ../images/math/functions.png
25487 \begin_layout Subsection
25488 Self-defined Functions
25489 \begin_inset Index idx
25492 \begin_layout Plain Layout
25493 Functions ! self-defined
25501 \begin_layout Standard
25502 To use a function that is not predefined, like for example the sign function
25503 sgn(x), there are two possibilities:
25506 \begin_layout Itemize
25507 Define the function by inserting the following line to the LaTeX-preamble
25511 \begin_layout Plain Layout
25516 DeclareMathOperator
25519 \begin_inset CommandInset ref
25521 reference "sub:Self-defined-Operators"
25531 \begin_inset Newline newline
25535 \begin_inset VSpace -3mm
25539 \begin_inset Newline newline
25546 DeclareMathOperator{
25551 \begin_inset Index idx
25554 \begin_layout Plain Layout
25559 DeclareMathOperator
25565 \begin_inset Newline newline
25569 \begin_inset VSpace -2mm
25573 \begin_inset Newline newline
25576 Now the new defined function can be called with the command
25585 \begin_layout Itemize
25586 Write the formula as usual, mark the formula name, in our example the letters
25591 , and change it to mathematical text.
25592 Finally, a space is inserted between prefactor and function.
25595 \begin_layout Standard
25596 The result is the same with both methods as with a predefined function
25600 \begin_layout Plain Layout
25601 In LyX self-defined functions are displayed red, predefined ones black.
25609 \begin_layout Standard
25611 \begin_inset Tabular
25612 <lyxtabular version="3" rows="3" columns="2">
25613 <features tabularvalignment="middle">
25614 <column alignment="center" valignment="top" width="0pt">
25615 <column alignment="center" valignment="top" width="0pt">
25617 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
25620 \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
25637 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
25640 \begin_layout Plain Layout
25648 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
25651 \begin_layout Plain Layout
25652 \begin_inset Formula $A\sgn(x)+B$
25662 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
25665 \begin_layout Plain Layout
25669 \begin_inset Formula $\underbrace{\textrm{sgn}}_{\textrm{Alt+M}\,\textrm{M}}$
25677 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
25680 \begin_layout Plain Layout
25681 \begin_inset Formula $A\,\textrm{sgn}(x)+B$
25697 \begin_layout Standard
25698 The first method is more suitable when the self-defined function should
25699 be used several times.
25702 \begin_layout Subsection
25704 \begin_inset Index idx
25707 \begin_layout Plain Layout
25716 \begin_layout Standard
25717 For limits, in addition to the commands
25724 \begin_inset Index idx
25727 \begin_layout Plain Layout
25747 the following functions are defined:
25750 \begin_layout Standard
25752 \begin_inset Tabular
25753 <lyxtabular version="3" rows="5" columns="2">
25754 <features tabularvalignment="middle">
25755 <column alignment="center" valignment="top" width="0">
25756 <column alignment="center" valignment="top" width="0">
25758 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
25761 \begin_layout Plain Layout
25767 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
25770 \begin_layout Plain Layout
25772 \begin_inset Note Note
25775 \begin_layout Plain Layout
25782 is only used as spacer.
25794 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
25797 \begin_layout Plain Layout
25805 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
25808 \begin_layout Plain Layout
25809 \begin_inset Formula $\varliminf$
25819 <cell alignment="center" valignment="top" leftline="true" usebox="none">
25822 \begin_layout Plain Layout
25830 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
25833 \begin_layout Plain Layout
25834 \begin_inset Formula $\varlimsup$
25844 <cell alignment="center" valignment="top" leftline="true" usebox="none">
25847 \begin_layout Plain Layout
25855 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
25858 \begin_layout Plain Layout
25859 \begin_inset Formula $\varprojlim$
25869 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
25872 \begin_layout Plain Layout
25880 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
25883 \begin_layout Plain Layout
25884 \begin_inset Formula $\varinjlim$
25888 \begin_inset Formula $\raisebox{-2.5mm}{}$
25904 \begin_layout Standard
25905 \begin_inset VSpace medskip
25908 The limit is created by inserting a subscript.
25909 It is set right beside the function in an inline formula:
25912 \begin_layout Standard
25914 \begin_inset Tabular
25915 <lyxtabular version="3" rows="2" columns="2">
25916 <features tabularvalignment="middle">
25917 <column alignment="center" valignment="top" width="0pt">
25918 <column alignment="center" valignment="top" width="0pt">
25920 <cell alignment="center" valignment="top" usebox="none">
25923 \begin_layout Plain Layout
25929 <cell alignment="center" valignment="top" usebox="none">
25932 \begin_layout Plain Layout
25933 \begin_inset space \hspace{}
25938 \begin_inset Note Note
25941 \begin_layout Plain Layout
25948 are used here as spacer.
25960 <cell alignment="center" valignment="top" usebox="none">
25963 \begin_layout Plain Layout
25972 \begin_layout Plain Layout
25985 \begin_layout Plain Layout
25999 <cell alignment="center" valignment="top" usebox="none">
26002 \begin_layout Plain Layout
26003 \begin_inset Formula $\hspace{1cm}\raisebox{5mm}{}\lim_{x\to A}x=B$
26019 \begin_layout Standard
26020 In a displayed formula the limit is set below the formula, as usual:
26021 \begin_inset Formula
26031 \begin_layout Subsection
26033 \begin_inset Index idx
26036 \begin_layout Plain Layout
26037 Functions ! modulo-
26045 \begin_layout Standard
26046 The modulo-function is special, because it exists in four variants.
26047 The variants in a displayed formula are:
26048 \begin_inset Formula
26050 \underline{\textrm{Command}\raisebox{-0.9mm}{}} & & \underline{\textrm{Result}}\\
26051 \mathrm{a\backslash mod\textrm{\spce}b} & & a\mod b\\
26052 \mathrm{a\backslash pmod\textrm{\spce}b} & & a\pmod b\\
26053 \mathrm{a\backslash bmod\textrm{\spce}b} & & a\bmod b\\
26054 \mathrm{a\backslash pod\textrm{\spce}b} & & a\pod b
26062 \begin_layout Standard
26063 In an inline formula less space is set before the function names for all
26065 By default the modulo-functions take only the first following character
26067 To use more than one character, one has to put them into TeX-braces:
26068 \begin_inset Formula
26070 \underline{\textrm{Command}\raisebox{-0.9mm}{}} & & \underline{\textrm{Result}}\\
26071 \mathrm{a\backslash pod\textrm{\spce}bcd} & & a\pod bcd\\
26072 \mathrm{a\backslash pod\backslash\{bc\to d} & & a\pod{bc}d
26080 \begin_layout Section
26082 \begin_inset Index idx
26085 \begin_layout Plain Layout
26094 \begin_layout Subsection
26095 Special Characters in Mathematical Text
26098 \begin_layout Standard
26099 The following commands can only be used in mathematical text or in TeX-mode:
26102 \begin_layout Standard
26103 \begin_inset space \hfill{}
26107 \begin_inset Tabular
26108 <lyxtabular version="3" rows="8" columns="2">
26109 <features tabularvalignment="middle">
26110 <column alignment="block" valignment="top" width="0">
26111 <column alignment="block" valignment="top" width="0">
26113 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
26116 \begin_layout Plain Layout
26122 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
26125 \begin_layout Plain Layout
26133 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
26136 \begin_layout Plain Layout
26144 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
26147 \begin_layout Plain Layout
26148 \begin_inset Formula $\textrm{œ}$
26158 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
26161 \begin_layout Plain Layout
26169 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
26172 \begin_layout Plain Layout
26173 \begin_inset Formula $\textrm{Œ}$
26183 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
26186 \begin_layout Plain Layout
26194 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
26197 \begin_layout Plain Layout
26198 \begin_inset Formula $\textrm{æ}$
26208 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
26211 \begin_layout Plain Layout
26219 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
26222 \begin_layout Plain Layout
26223 \begin_inset Formula $\textrm{Æ}$
26233 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
26236 \begin_layout Plain Layout
26244 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
26247 \begin_layout Plain Layout
26248 \begin_inset Formula $\textrm{\aa}$
26258 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
26261 \begin_layout Plain Layout
26265 \begin_inset Index idx
26268 \begin_layout Plain Layout
26275 \begin_layout Plain Layout
26296 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
26299 \begin_layout Plain Layout
26300 \begin_inset Formula $\textrm{Å}$
26310 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
26313 \begin_layout Plain Layout
26321 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
26324 \begin_layout Plain Layout
26325 \begin_inset Formula $\textrm{ı}$
26339 \begin_inset space \hfill{}
26343 \begin_inset Tabular
26344 <lyxtabular version="3" rows="8" columns="2">
26345 <features tabularvalignment="middle">
26346 <column alignment="block" valignment="top" width="0">
26347 <column alignment="center" valignment="top" width="0">
26349 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
26352 \begin_layout Plain Layout
26354 \begin_inset Note Note
26357 \begin_layout Plain Layout
26359 \begin_inset space \thinspace{}
26362 mm is used for separation, because otherwise the output will be ¡ and ¿
26373 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
26376 \begin_layout Plain Layout
26384 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
26387 \begin_layout Plain Layout
26395 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
26398 \begin_layout Plain Layout
26399 \begin_inset Formula $\textrm{ø}$
26409 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
26412 \begin_layout Plain Layout
26420 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
26423 \begin_layout Plain Layout
26424 \begin_inset Formula $\textrm{Ø}$
26434 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
26437 \begin_layout Plain Layout
26445 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
26448 \begin_layout Plain Layout
26449 \begin_inset Formula $\textrm{ł}$
26459 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
26462 \begin_layout Plain Layout
26470 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
26473 \begin_layout Plain Layout
26474 \begin_inset Formula $\textrm{Ł}$
26484 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
26487 \begin_layout Plain Layout
26489 \begin_inset space \hspace{}
26497 \begin_layout Plain Layout
26511 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
26514 \begin_layout Plain Layout
26515 \begin_inset Formula $\textrm{!`}$
26525 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
26528 \begin_layout Plain Layout
26530 \begin_inset space \hspace{}
26538 \begin_layout Plain Layout
26552 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
26555 \begin_layout Plain Layout
26556 \begin_inset Formula $\textrm{?`}$
26566 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
26569 \begin_layout Plain Layout
26577 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
26580 \begin_layout Plain Layout
26581 \begin_inset Formula $\textrm{ȷ}$
26595 \begin_inset space \hfill{}
26601 \begin_layout Standard
26603 \begin_inset Formula $\textrm{\textrm{Å}}$
26607 \begin_inset Formula $\textrm{\textrm{Ø}}$
26610 can also be inserted via the math toolbar button
26611 \begin_inset Graphics
26612 filename ../images/math/digamma.png
26620 \begin_layout Standard
26621 An exception are the commands
26624 \begin_inset space \hspace{}
26633 \begin_inset space \hspace{}
26639 , because they can be inserted in LyX directly to text.
26642 \begin_layout Subsection
26644 \begin_inset CommandInset label
26646 name "sub:Accents-in-Text"
26651 \begin_inset Index idx
26654 \begin_layout Plain Layout
26663 \begin_layout Standard
26664 With the following commands all letters can be accented.
26665 The commands must be inserted in TeX-mode.
26668 \begin_layout Standard
26669 \begin_inset space \hfill{}
26673 \begin_inset Tabular
26674 <lyxtabular version="3" rows="8" columns="2">
26675 <features tabularvalignment="middle">
26676 <column alignment="block" valignment="top" width="0">
26677 <column alignment="block" valignment="top" width="0">
26679 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
26682 \begin_layout Plain Layout
26688 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
26691 \begin_layout Plain Layout
26699 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
26702 \begin_layout Plain Layout
26706 \begin_inset Quotes grd
26714 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
26717 \begin_layout Plain Layout
26721 \begin_layout Plain Layout
26737 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
26740 \begin_layout Plain Layout
26748 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
26751 \begin_layout Plain Layout
26755 \begin_layout Plain Layout
26771 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
26774 \begin_layout Plain Layout
26781 \begin_layout Plain Layout
26795 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
26798 \begin_layout Plain Layout
26802 \begin_layout Plain Layout
26818 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
26821 \begin_layout Plain Layout
26829 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
26832 \begin_layout Plain Layout
26836 \begin_layout Plain Layout
26852 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
26855 \begin_layout Plain Layout
26862 \begin_layout Plain Layout
26876 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
26879 \begin_layout Plain Layout
26883 \begin_layout Plain Layout
26899 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
26902 \begin_layout Plain Layout
26909 \begin_layout Plain Layout
26923 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
26926 \begin_layout Plain Layout
26930 \begin_layout Plain Layout
26946 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
26949 \begin_layout Plain Layout
26956 \begin_layout Plain Layout
26970 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
26973 \begin_layout Plain Layout
26977 \begin_layout Plain Layout
26997 \begin_inset space \hfill{}
27001 \begin_inset Tabular
27002 <lyxtabular version="3" rows="8" columns="2">
27003 <features tabularvalignment="middle">
27004 <column alignment="block" valignment="top" width="0">
27005 <column alignment="center" valignment="top" width="0">
27007 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
27010 \begin_layout Plain Layout
27016 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
27019 \begin_layout Plain Layout
27027 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
27030 \begin_layout Plain Layout
27037 \begin_layout Plain Layout
27051 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
27054 \begin_layout Plain Layout
27058 \begin_layout Plain Layout
27074 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
27077 \begin_layout Plain Layout
27085 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
27088 \begin_layout Plain Layout
27092 \begin_layout Plain Layout
27108 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
27111 \begin_layout Plain Layout
27115 \begin_inset Index idx
27118 \begin_layout Plain Layout
27129 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
27132 \begin_layout Plain Layout
27136 \begin_layout Plain Layout
27152 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
27155 \begin_layout Plain Layout
27163 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
27166 \begin_layout Plain Layout
27170 \begin_layout Plain Layout
27186 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
27189 \begin_layout Plain Layout
27196 \begin_layout Plain Layout
27210 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
27213 \begin_layout Plain Layout
27217 \begin_layout Plain Layout
27233 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
27236 \begin_layout Plain Layout
27243 \begin_layout Plain Layout
27257 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
27260 \begin_layout Plain Layout
27264 \begin_layout Plain Layout
27280 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
27283 \begin_layout Plain Layout
27290 \begin_layout Plain Layout
27304 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
27307 \begin_layout Plain Layout
27311 \begin_layout Plain Layout
27331 \begin_inset space \hfill{}
27337 \begin_layout Standard
27338 \begin_inset VSpace medskip
27347 also two different characters can be accented.
27356 \begin_layout Plain Layout
27371 \begin_layout Plain Layout
27383 \begin_layout Standard
27396 can in combination with vowels directly be inserted with the keyboard without
27398 The same applies for the tilde
27402 \begin_layout Plain Layout
27403 This only applies for keyboards where the tilde is defined as accent.
27412 in combination with
27427 \begin_layout Standard
27470 and accents that are inserted directly with the keyboard are also available
27471 in mathematical text.
27472 For the other accents there are special math commands to be used in formulas,
27474 \begin_inset CommandInset ref
27476 reference "sub:Accents-for-one"
27483 \begin_layout Standard
27484 \begin_inset VSpace bigskip
27487 Furthermore, with the command
27494 \begin_inset Index idx
27497 \begin_layout Plain Layout
27505 all numbers and letters can be set into a circle, quasi accented with a
27506 circle, similar to the copyright symbol.
27509 \begin_layout Standard
27511 \begin_inset Tabular
27512 <lyxtabular version="3" rows="3" columns="2">
27513 <features tabularvalignment="middle">
27514 <column alignment="center" valignment="top" width="0">
27515 <column alignment="center" valignment="top" width="0">
27517 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
27520 \begin_layout Plain Layout
27526 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
27529 \begin_layout Plain Layout
27531 \begin_inset Note Note
27534 \begin_layout Plain Layout
27541 is only used as spacer.
27553 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
27556 \begin_layout Plain Layout
27564 <cell multicolumn="1" alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
27567 \begin_layout Plain Layout
27571 \begin_layout Plain Layout
27587 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
27590 \begin_layout Plain Layout
27601 raisebox{-1.5pt}{W}}
27606 <cell multicolumn="1" alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
27609 \begin_layout Plain Layout
27610 \begin_inset Formula $\raisebox{4.5mm}{}$
27617 \begin_layout Plain Layout
27635 \begin_inset Formula $\raisebox{-2mm}{}$
27651 \begin_layout Standard
27652 One has to take care that the character fits in the circle.
27663 \begin_layout Plain Layout
27665 \begin_inset CommandInset ref
27667 reference "sub:Font-Sizes"
27676 specifies thereby the size of the circle.
27687 \begin_layout Plain Layout
27689 \begin_inset CommandInset ref
27691 reference "sub:Boxes-without-Frame"
27700 the character can be centered.
27703 \begin_layout Subsection
27705 \begin_inset Index idx
27708 \begin_layout Plain Layout
27717 \begin_layout Standard
27718 Old-style figures (also known as old-style numerals) are created with the
27726 \begin_inset Index idx
27729 \begin_layout Plain Layout
27738 The command can be used in formulas and in TeX-mode.
27739 The command scheme is:
27742 \begin_layout Standard
27747 oldstylenums{number}
27750 \begin_layout Standard
27755 oldstylenums{0123456789
27758 \begin_inset Formula $\oldstylenums{0123456789}$
27764 \begin_layout Subsection
27765 Miscellaneous special Characters
27766 \begin_inset CommandInset label
27768 name "sub:Miscellaneous-special-Characters"
27773 \begin_inset Index idx
27776 \begin_layout Plain Layout
27777 Special characters ! miscellaneous
27785 \begin_layout Standard
27786 The following characters can only be inserted to formulas by using commands:
27789 \begin_layout Standard
27791 \begin_inset Tabular
27792 <lyxtabular version="3" rows="4" columns="2">
27793 <features tabularvalignment="middle">
27794 <column alignment="center" valignment="top" width="0">
27795 <column alignment="center" valignment="top" width="0">
27797 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
27800 \begin_layout Plain Layout
27806 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
27809 \begin_layout Plain Layout
27817 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
27820 \begin_layout Plain Layout
27827 \begin_layout Plain Layout
27841 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
27844 \begin_layout Plain Layout
27845 \begin_inset Formula $\mathcircumflex$
27855 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
27858 \begin_layout Plain Layout
27866 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
27869 \begin_layout Plain Layout
27870 \begin_inset Formula $\_$
27880 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
27883 \begin_layout Plain Layout
27888 \begin_layout Plain Layout
27900 \begin_inset Index idx
27903 \begin_layout Plain Layout
27916 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
27919 \begin_layout Plain Layout
27920 \begin_inset Formula $^{\circ}$
27936 \begin_layout Standard
27937 The degree sign ° can nevertheless be directly inserted if the LaTeX-preamble
27938 contains the following line
27942 \begin_layout Plain Layout
27943 More about this is described in
27944 \begin_inset CommandInset ref
27946 reference "sub:Text-Characters-in"
27958 \begin_layout Standard
27963 DeclareInputtext{176}{
27976 \begin_layout Standard
27977 \begin_inset Newpage newpage
27983 \begin_layout Section
27985 \begin_inset CommandInset label
27987 name "sec:Formula-Styles"
27992 \begin_inset Index idx
27995 \begin_layout Plain Layout
28004 \begin_layout Itemize
28005 There are two different alignment styles:
28009 \begin_layout Description
28010 Centered is the predefined standard
28013 \begin_layout Description
28014 Indented for this the option
28018 must be inserted in the menu
28020 Document\SpecialChar \menuseparator
28026 \begin_inset space ~
28032 \begin_layout Standard
28037 is used, the indentation can be adjusted with the length
28044 \begin_inset Index idx
28047 \begin_layout Plain Layout
28056 Should the distance be 15
28057 \begin_inset space \thinspace{}
28060 mm, the following command line is inserted in the LaTeX-preamble
28063 \begin_layout Standard
28073 \begin_layout Standard
28074 When no length is specified, the predefined value of 30
28075 \begin_inset space \thinspace{}
28082 \begin_layout Itemize
28083 And two different numbering styles:
28087 \begin_layout Description
28088 Right is the predefined standard
28091 \begin_layout Description
28092 Left for this the option
28096 must be inserted in the menu
28098 Document\SpecialChar \menuseparator
28104 \begin_inset space ~
28111 \begin_layout Standard
28120 can also be used together.
28121 In this case both options are inserted, separated by a comma.
28124 \begin_layout Standard
28125 The chosen styles are used for all displayed formulas of the document.
28126 When both, centered and indented formulas should be created in a document,
28132 The indented formulas are then set in a flalign environment, see
28133 \begin_inset CommandInset ref
28135 reference "sub:Flalign-Environment"
28142 \begin_layout Section
28144 \begin_inset CommandInset label
28146 name "sec:Multiline-Formulas"
28151 \begin_inset Index idx
28154 \begin_layout Plain Layout
28155 Formula ! multiline
28163 \begin_layout Subsection
28167 \begin_layout Standard
28168 In LyX multiline formulas are created by pressing
28173 arg "newline-insert newline"
28179 This creates either an
28181 eqnarray environment
28183 that is described in
28184 \begin_inset CommandInset ref
28186 reference "sub:Eqnarray-Environment"
28190 or, when the option
28192 Use AMS math package
28194 in the document settings is selected, an
28198 that is described in
28199 \begin_inset CommandInset ref
28201 reference "sub:Standard-align-Environment"
28206 The align environment is recommended because it provides in any case a
28207 typographically correct output.
28210 \begin_layout Standard
28211 There are other multiline formula environments that can be created via the
28214 Insert\SpecialChar \menuseparator
28218 These environments are described in the following sections.
28221 \begin_layout Standard
28222 In all multiline formula environments a new line is created by pressing
28226 arg "newline-insert newline"
28230 To add or delete lines, the math toolbar buttons
28231 \begin_inset Graphics
28232 filename ../images/tabular-feature_append-row.png
28238 \begin_inset Graphics
28239 filename ../images/tabular-feature_delete-row.png
28244 , respectively, or the menu
28246 Edit\SpecialChar \menuseparator
28252 \begin_layout Subsubsection
28254 \begin_inset CommandInset label
28256 name "sub:Line-Separation"
28261 \begin_inset Index idx
28264 \begin_layout Plain Layout
28265 Formula ! multiline ! Line separation
28273 \begin_layout Standard
28274 There is sometimes not enough space in multiline formulas between the lines:
28275 \begin_inset Formula
28277 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}\\
28278 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
28286 \begin_layout Standard
28287 In LaTeX additional line space is specified as optional argument of the
28289 This is not yet possible in LyX
28293 \begin_layout Plain Layout
28295 \begin_inset CommandInset href
28297 name "LyX-bug #1505"
28298 target "http://www.lyx.org/trac/ticket/1505"
28307 , therefore the whole formula must be inserted in TeX-mode.
28308 To add in our example space, the command
28316 is inserted at the end of the first line.
28321 \begin_layout Plain Layout
28328 \begin_layout Plain Layout
28330 B^{2}(B^{2}-2r_{g}^{2}+2x_{0}^{2}-2r_{k}^{2})+4x_{0}^{2}x^{2}+4x_{0}xD &
28333 textrm{-}4x^{2}B^{2}+4x_{0}xB^{2}
28340 \begin_layout Plain Layout
28344 left(B^{2}+x_{0}^{2}
28352 left(B^{2}-2r_{g}^{2}+2x_{0}^{2}-2r_{k}^{2}
28357 \begin_layout Plain Layout
28369 \begin_layout Standard
28370 \begin_inset VSpace bigskip
28373 To set the line separation for all lines in a formula, the length
28380 \begin_inset Index idx
28383 \begin_layout Plain Layout
28393 \begin_inset Formula $\mbox{line separation}=\mathrm{6\, pt+\backslash jot}$
28404 \begin_inset space \thinspace{}
28409 \begin_inset space \thinspace{}
28412 mm additional line separation as in the previous example, the command
28415 \begin_layout Standard
28425 \begin_layout Standard
28426 is inserted in TeX-mode before the formula.
28427 This requires that the LaTeX-package
28435 \begin_layout Plain Layout
28440 is part of every LaTeX standard installation.
28446 \begin_inset Index idx
28449 \begin_layout Plain Layout
28455 was loaded in LaTeX-preamble with the line
28458 \begin_layout Standard
28466 \begin_layout Standard
28471 \begin_layout Plain Layout
28483 \begin_inset Formula
28485 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}\\
28486 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
28494 \begin_layout Standard
28498 \begin_layout Plain Layout
28509 To get back to the predefined distance,
28515 is set to the value 3
28516 \begin_inset space \thinspace{}
28522 \begin_layout Subsubsection
28524 \begin_inset CommandInset label
28526 name "sub:Column-Separation"
28531 \begin_inset Index idx
28534 \begin_layout Plain Layout
28535 Formula ! multiline ! Column separation
28543 \begin_layout Standard
28544 Multiline formulas form a matrix.
28545 A formula in the eqnarray environment is for example a matrix with three
28547 By changing the column separation in this environment, the space beside
28548 the relation sign can be changed.
28551 \begin_layout Standard
28552 The column separation is specified with the length
28559 \begin_inset Index idx
28562 \begin_layout Plain Layout
28571 \begin_inset Newline newline
28574 column separation = 2
28575 \begin_inset space \thinspace{}
28585 \begin_inset Newline newline
28591 \begin_layout Standard
28601 \begin_layout Standard
28602 inserted in TeX-mode, sets for all following formulas a column separation
28604 \begin_inset space \thinspace{}
28608 To get back to the predefined distance,
28615 \begin_inset space \thinspace{}
28621 \begin_layout Standard
28623 \begin_inset space \thinspace{}
28626 cm column separation:
28630 \begin_layout Plain Layout
28642 \begin_inset Formula
28650 A formula with the predefined column separation for matrices of 10
28651 \begin_inset space \thinspace{}
28658 \begin_layout Plain Layout
28670 \begin_inset Formula
28681 \begin_layout Subsubsection
28683 \begin_inset Index idx
28686 \begin_layout Plain Layout
28695 \begin_layout Standard
28696 Long formulas can be typeset using these methods:
28699 \begin_layout Itemize
28700 When one side of the equation is much shorter than the line width, this
28701 one is chosen for the left side and the right side is typeset over two
28703 \begin_inset Formula
28705 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 \\
28706 & & -\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}
28711 The minus sign at the beginning of the second line does normally not appear
28712 as an operator because it is the first character of the line.
28713 Thus it would not be surrounded by space and could not be distinguished
28714 from the fraction bar.
28716 \begin_inset space \thinspace{}
28719 pt space was inserted behind the minus sign with the command
28729 \begin_layout Plain Layout
28737 \begin_inset CommandInset ref
28739 reference "sub:Variable-Space"
28749 \begin_inset Index idx
28752 \begin_layout Plain Layout
28763 \begin_layout Itemize
28764 When both sides of the equation are too long, the command
28771 \begin_inset Index idx
28774 \begin_layout Plain Layout
28783 It is inserted in the first column of the first line and causes all further
28784 insertions to overwrite the following columns:
28785 \begin_inset Formula
28787 \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 \\
28788 & & -\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 \\
28789 & & =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}
28794 After the insertion of
28800 , the cursor is in a purple box that is a bit shifted to the left from the
28802 In this the formula is inserted.
28803 \begin_inset Newline newline
28806 The content of the further lines is inserted to the second or another formula
28808 The greater the column number where it was inserted, the larger the indentation.
28809 \begin_inset VSpace medskip
28813 \begin_inset Newline newline
28817 \begin_inset Note Greyedout
28820 \begin_layout Plain Layout
28821 Note the following when using
28830 \begin_layout Itemize
28831 The formula doesn't use the full page width.
28833 \begin_inset space \thinspace{}
28837 \begin_inset space \space{}
28841 \begin_inset Formula $-B^{2}$
28844 is added to the first line in the above example, it would have been outside
28846 To better use the width, negative space can be inserted at the beginning
28850 \begin_layout Itemize
28851 Due to a bug in LyX the cursor cannot be set with the mouse into the first
28856 \begin_layout Plain Layout
28857 \begin_inset CommandInset href
28859 name "LyX-bug #1429"
28860 target "http://www.lyx.org/trac/ticket/1429"
28869 One can only set the cursor at the beginning of the line and move it with
28878 \begin_layout Itemize
28879 Other methods to set long formulas are offered by the environments described
28881 \begin_inset CommandInset ref
28883 reference "sub:Multline-Environment"
28888 \begin_inset CommandInset ref
28890 reference "sub:Multiline-Formula-Parts"
28897 \begin_layout Subsubsection
28899 \begin_inset CommandInset label
28901 name "sub:Multiline-Brackets"
28906 \begin_inset Index idx
28909 \begin_layout Plain Layout
28910 Brackets ! for multiline expressions
28918 \begin_layout Standard
28919 For brackets spanning multiple lines the following problem occurs:
28920 \begin_inset Formula
28922 A & = & \sin(x)\left[\prod_{R=1}^{\infty}\frac{1}{R}+\cdots\right.\\
28923 & & \left.\cdots+B-D\right]
28931 \begin_layout Standard
28932 The closing bracket is smaller than the opening bracket because brackets
28933 with variable size may not span multiple lines.
28936 \begin_layout Standard
28937 To set the bracket size for the second line correctly, the first line is
28945 \begin_inset Index idx
28948 \begin_layout Plain Layout
28956 and the second line with
28964 \begin_layout Plain Layout
28978 \begin_inset CommandInset ref
28980 reference "sub:Automatic-Bracket-Size"
28992 \begin_inset Index idx
28995 \begin_layout Plain Layout
29021 \begin_layout Plain Layout
29040 \begin_layout Plain Layout
29059 \begin_layout Plain Layout
29071 \begin_inset Formula $\downarrow$
29077 \begin_inset Index idx
29080 \begin_layout Plain Layout
29088 is inserted, because the multiplication operator with its limits is the
29089 largest symbol in the first line and this should be the size for the bracket
29090 in the second line.
29093 \begin_layout Standard
29094 The result is this:
29095 \begin_inset Formula
29097 A & = & \sin(x)\left[\prod_{R=1}^{\infty}\frac{1}{R}+\cdots\right.\\
29098 & & \left.\vphantom{\prod_{R=1}^{\infty}}\cdots+B-D\right]
29106 \begin_layout Subsection
29110 \begin_layout Standard
29111 Align environments can be used for every kind of multiline formulas.
29112 They are especially useful to set several formulas side by side.
29115 \begin_layout Standard
29116 Align environments consist of columns.
29117 The odd columns are right aligned, the even ones left aligned.
29118 Every line in an Align environment can be numbered.
29121 \begin_layout Standard
29122 Align environments are created via the menu
29124 Insert\SpecialChar \menuseparator
29130 Edit\SpecialChar \menuseparator
29131 Math\SpecialChar \menuseparator
29132 Change Formula Type
29134 already existing formulas can be converted to Align environments.
29137 \begin_layout Standard
29138 To add or delete columns, the math toolbar buttons
29139 \begin_inset Graphics
29140 filename ../images/tabular-feature_append-column.png
29146 \begin_inset Graphics
29147 filename ../images/tabular-feature_delete-column.png
29152 , respectively, or the menu
29154 Edit\SpecialChar \menuseparator
29160 \begin_layout Subsubsection
29161 Standard align Environment
29162 \begin_inset CommandInset label
29164 name "sub:Standard-align-Environment"
29169 \begin_inset Index idx
29172 \begin_layout Plain Layout
29173 Formula ! multiline ! align environment
29181 \begin_layout Standard
29182 This Align environment is created by presssing
29185 arg "newline-insert newline"
29188 in a formula or by the menu
29190 Insert\SpecialChar \menuseparator
29191 Math\SpecialChar \menuseparator
29192 AMS align Environment
29197 \begin_layout Standard
29198 An example for two formulas set side by side, that are created with a four
29199 column align environment:
29200 \begin_inset Formula
29202 A & =\sin(B) & C & =D\\
29203 C & \ne A & B & \ne D
29208 As it can be seen, the formulas in this environment are placed so as if
29217 \begin_layout Plain Layout
29225 \begin_inset CommandInset ref
29227 reference "sub:Variable-Space"
29238 before the first and after every even column.
29239 When the formula style
29245 \begin_layout Plain Layout
29247 \begin_inset CommandInset ref
29249 reference "sec:Formula-Styles"
29260 is used, the formula is set without the
29266 before the first column.
29269 \begin_layout Subsubsection
29270 Alignat Environment
29271 \begin_inset Index idx
29274 \begin_layout Plain Layout
29275 Formula ! multiline ! alignat environment
29283 \begin_layout Standard
29284 The alignat environment has no predefined column separation.
29285 It can be inserted manually with the spaces that are described
29286 \begin_inset CommandInset ref
29288 reference "sub:Space"
29295 \begin_layout Standard
29296 The above example in the alignat environment where 1
29297 \begin_inset space \thinspace{}
29300 cm space was inserted at the beginning of the second formula:
29301 \begin_inset Formula
29302 \begin{alignat*}{2}
29303 A & =\sin(B) & \hspace{1cm}C & =D\\
29304 C & \ne A & B & \ne D
29309 Because the column separation can be set separately for every column, this
29310 environment is especially suitable to set three and more formulas side
29314 \begin_layout Subsubsection
29315 Flalign Environment
29316 \begin_inset CommandInset label
29318 name "sub:Flalign-Environment"
29323 \begin_inset Index idx
29326 \begin_layout Plain Layout
29327 Formula ! multiline ! flalign environment
29335 \begin_layout Standard
29336 In this environment the first two columns are always set as much as possible
29337 to the left and the last two ones to the right.
29339 \begin_inset Formula
29341 A & =1 & B & =2 & C & =3\\
29342 X & =\textrm{-}1 & Y & =\textrm{-}2 & Z & =4
29350 \begin_layout Standard
29351 By creating a flalign environment with an odd number of columns where an
29352 empty TeX-brace is inserted to the last column, several formulas in a document
29353 can be set to the left, although the formula style
29358 As example the indented formula
29359 \begin_inset CommandInset ref
29361 reference "eq:VolInt"
29366 \begin_inset Formula
29368 \hspace{30pt}\iiint\limits _{V}X\,\mathrm{d}V & =U & {}
29373 The first two columns contain the formula.
29374 To indent it as with the formula style
29379 \begin_inset space \thinspace{}
29382 pt space was inserted at the beginning of the first column.
29385 \begin_layout Subsection
29386 Eqnarray Environment
29387 \begin_inset CommandInset label
29389 name "sub:Eqnarray-Environment"
29394 \begin_inset Index idx
29397 \begin_layout Plain Layout
29398 Formula ! multiline ! eqnarray environment
29406 \begin_layout Standard
29407 When this environment has been created, three blue boxes appear.
29408 The content of the first box is right aligned, the content of the last
29410 The content of the middle box appears centered and a bit smaller, because
29411 it is designed to insert there only relation characters.
29412 \begin_inset Formula
29414 \frac{ABC}{D} & \frac{ABC}{D} & \frac{ABC}{D}\\
29424 \begin_layout Subsection
29426 \begin_inset Index idx
29429 \begin_layout Plain Layout
29430 Formula ! multiline ! gather environment
29438 \begin_layout Standard
29439 This environment consists of only one centered column.
29440 Every line can be numbered.
29441 \begin_inset Formula
29452 \begin_layout Subsection
29453 Multline Environment
29454 \begin_inset CommandInset label
29456 name "sub:Multline-Environment"
29461 \begin_inset Index idx
29464 \begin_layout Plain Layout
29465 Formula ! multiline ! multline environment
29473 \begin_layout Standard
29474 The multline environment consists, like the gather environment, of only
29476 But the first line is left aligned, the last one right aligned.
29477 All other lines are centered.
29478 Therefore this environment is suitable for long formulas.
29480 \begin_inset CommandInset ref
29482 reference "eq:lefteqn"
29486 in the multline environment:
29487 \begin_inset Formula
29489 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}\\
29490 -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}\\
29491 =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}}
29499 \begin_layout Standard
29500 In the output only the last (first) line of a multline environment appears
29501 numbered when the document numbering is right (left).
29505 \begin_layout Plain Layout
29506 numbering styles see
29507 \begin_inset CommandInset ref
29509 reference "sec:Formula-Styles"
29521 \begin_layout Standard
29529 \begin_inset Index idx
29532 \begin_layout Plain Layout
29547 \begin_inset Index idx
29550 \begin_layout Plain Layout
29558 a centered line can be right or left aligned, respectively.
29559 The commands are used as follows:
29562 \begin_layout Standard
29567 shoveright{line content}
29573 shoveleft{line content}
29576 \begin_layout Standard
29577 \begin_inset VSpace medskip
29587 \begin_inset Index idx
29590 \begin_layout Plain Layout
29598 specifies the distance of the first line from the left page margin.
29599 Predefined is the length 0
29600 \begin_inset space \thinspace{}
29606 \begin_layout Standard
29607 As example the above formula where the command
29610 \begin_layout Standard
29620 \begin_layout Standard
29621 was inserted in TeX-mode before:
29625 \begin_layout Plain Layout
29637 \begin_inset Formula
29639 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}\\
29640 \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}}\\
29641 =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}}
29650 \begin_layout Plain Layout
29661 The second line was left aligned using
29670 \begin_layout Subsection
29671 Multiline Formula Parts
29672 \begin_inset CommandInset label
29674 name "sub:Multiline-Formula-Parts"
29679 \begin_inset Index idx
29682 \begin_layout Plain Layout
29683 Formula ! multiline ! formula parts
29691 \begin_layout Standard
29692 To display only parts of a formula with multiple lines, one of the following
29693 environments is used:
29710 They can be inserted via the menu
29712 Insert\SpecialChar \menuseparator
29715 or by using the commands described in this section.
29718 \begin_layout Standard
29719 The first three have the same properties as the corresponding multiline
29720 formula environments, but it is possible to set further formula parts beside
29723 \begin_inset Formula
29725 \left.\begin{aligned}\Delta x\Delta p & \ge\frac{\hbar}{2}\\
29726 \Delta E\Delta t & \ge\frac{\hbar}{2}
29728 \right\} \textrm{Uncertainty relations}
29736 \begin_layout Standard
29737 To get this formula, a displayed formula is created where the command
29744 \begin_inset Index idx
29747 \begin_layout Plain Layout
29756 A purple box appears around the blue formula box where now columns and
29757 lines can be added.
29758 Outside the multiline environment other formula parts can be set, like
29762 \begin_layout Standard
29763 The aligned environment is also suitable for long formulas whose lines are
29764 horizontally aligned.
29765 Using aligned in a displayed formula has the advantage that the formula
29766 number is vertically centered behind the lines.
29768 \begin_inset CommandInset ref
29770 reference "eq:shortlong"
29774 in the aligned environment:
29775 \begin_inset Formula
29777 \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}|}\\
29778 & -\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}|}
29787 \begin_layout Standard
29788 To use the environments
29807 \begin_inset Index idx
29810 \begin_layout Plain Layout
29825 \begin_inset Index idx
29828 \begin_layout Plain Layout
29843 \begin_inset Index idx
29846 \begin_layout Plain Layout
29854 are inserted, respectively.
29855 The split environment has the same properties as the aligned environment
29856 but it can only have two columns.
29859 \begin_layout Subsection
29860 Text in multiline Formulas
29861 \begin_inset CommandInset label
29863 name "sub:Text-in-multiline"
29868 \begin_inset Index idx
29871 \begin_layout Plain Layout
29878 \begin_inset Index idx
29881 \begin_layout Plain Layout
29882 Formula ! multiline ! text
29890 \begin_layout Standard
29891 In the Align environments, and the multline and gather environment, text
29892 can be inserted that will appear in a separate line and doesn't affect
29893 the column alignment.
29894 To do this, the command
29901 \begin_inset Index idx
29904 \begin_layout Plain Layout
29912 is used in the following scheme:
29915 \begin_layout Standard
29923 \begin_layout Standard
29924 The text should not be longer than a line because it cannot be hyphenated.
29925 As LyX doesn't yet support
29931 directly, the text is written as mathematical text.
29938 must hereby be at the beginning of a line and appears in the output above
29940 An example where the text was inserted at the beginning of the second line:
29941 \begin_inset Formula
29943 I & =a\sqrt{2}\int_{0}^{2\pi}\sqrt{1+\cos(\phi)}\;\mathrm{d}\phi\\
29944 \intertext{\text{integrand is symmetric to \ensuremath{\phi=\pi}, therefore}} & =2a\sqrt{2}\int_{0}^{\pi}\sqrt{1+\cos(\phi)}\;\mathrm{d}\phi
29952 \begin_layout Standard
29953 \begin_inset Newpage newpage
29959 \begin_layout Section
29961 \begin_inset Index idx
29964 \begin_layout Plain Layout
29971 \begin_inset Index idx
29974 \begin_layout Plain Layout
29975 Formula ! numbering|see
29979 \begin_layout Plain Layout
29990 \begin_layout Plain Layout
30005 \begin_layout Subsection
30009 \begin_layout Standard
30010 Numbered formulas can be created with the menu
30012 Insert\SpecialChar \menuseparator
30013 Math\SpecialChar \menuseparator
30015 \begin_inset space ~
30023 \begin_inset space ~
30029 Existing formulas can be numbered with the menu
30031 Edit\SpecialChar \menuseparator
30032 Math\SpecialChar \menuseparator
30034 \begin_inset space ~
30042 arg "math-number-toggle"
30046 The formula number is displayed in LyX behind the formula as a number sign
30048 The number sign is replaced in the output by the formula number.
30051 \begin_layout Standard
30052 When numbering is turned on in multiline formulas, all lines will be numbered.
30053 But the numbering can be controlled with the menu
30055 Edit\SpecialChar \menuseparator
30056 Math\SpecialChar \menuseparator
30058 \begin_inset space ~
30062 \begin_inset space ~
30066 \begin_inset space ~
30074 arg "math-number-line-toggle"
30080 \begin_layout Standard
30081 Except for inline formulas, all formulas can be numbered with two different
30083 \begin_inset CommandInset ref
30085 reference "sec:Formula-Styles"
30092 \begin_layout Subsection
30094 \begin_inset Index idx
30097 \begin_layout Plain Layout
30098 Cross-references ! to formulas
30106 \begin_layout Standard
30107 All labeled formulas can be cross-referenced.
30108 A label is added by the menu
30110 Insert\SpecialChar \menuseparator
30113 or the toolbar button
30114 \begin_inset Graphics
30115 filename ../images/label-insert.png
30121 The cursor must hereby be inside a displayed formula.
30122 Alternatively you can right-click on the formula and choose
30127 A dialog pops up displaying the prefix
30132 The label is inserted there behind the prefix.
30133 The predefined prefix means
30134 \begin_inset Quotes eld
30138 \begin_inset Quotes erd
30141 and makes it easier to find labels in large documents because it marks
30142 it as formula label to divide it from e.
30143 \begin_inset space \thinspace{}
30147 \begin_inset space \space{}
30151 To change a label, the menu
30153 Insert\SpecialChar \menuseparator
30156 is used again or you right-click on a formula and then on
30163 \begin_layout Standard
30164 The name of the label is displayed in LyX within two parentheses behind
30166 A formula with a label is always numbered.
30169 \begin_layout Standard
30170 Cross-references are inserted via the menu
30172 Insert\SpecialChar \menuseparator
30175 or with the toolbar button
30176 \begin_inset Graphics
30177 filename ../images/dialog-show-new-inset_ref.png
30183 A formula cross-reference appears in the output as formula number.
30184 When in the cross-reference dialog window the format
30188 is chosen, the cross-reference appears in the output as formula number
30190 \begin_inset Newline newline
30193 By right-clicking on a cross-reference in LyX, one jumps to the formula
30194 that is referenced.
30197 \begin_layout Standard
30198 Here are as examples cross-references to formulas of the following subsections:
30199 \begin_inset Note Note
30202 \begin_layout Plain Layout
30203 Note the different cross-reference types.
30211 \begin_layout Standard
30213 \begin_inset CommandInset ref
30220 \begin_inset CommandInset ref
30228 \begin_inset CommandInset ref
30234 ) big Latin letters are used for the numbering in contrary to (
30235 \begin_inset CommandInset ref
30244 \begin_layout Standard
30245 \begin_inset VSpace medskip
30248 When the argument of
30256 \begin_layout Plain Layout
30264 \begin_inset CommandInset ref
30266 reference "sub:User-defined-Numbering"
30277 contains a box like in
30278 \begin_inset CommandInset ref
30280 reference "sub:Paragraph-Boxes"
30284 , the formula cannot be referenced.
30287 \begin_layout Subsection
30289 \begin_inset Index idx
30292 \begin_layout Plain Layout
30293 Formula numbering ! subnumbering
30301 \begin_layout Standard
30302 With the help of the commands
30306 begin{subequations}
30314 formulas can be subnumbered.
30315 Both commands are inserted in TeX-mode.
30318 \begin_layout Standard
30320 \begin_inset Formula
30331 \begin_layout Plain Layout
30335 addtocounter{equation}{-1}
30344 \begin_layout Plain Layout
30348 begin{subequations}
30354 \begin_inset VSpace -5mm
30358 \begin_inset Formula
30366 \begin_inset Formula
30376 \begin_layout Standard
30380 \begin_layout Plain Layout
30392 \begin_layout Standard
30393 To create the example, the following is done:
30396 \begin_layout Enumerate
30397 first formula is inserted
30400 \begin_layout Enumerate
30405 addtocounter{equation}{-1}
30407 begin{subequations}
30408 \begin_inset Index idx
30411 \begin_layout Plain Layout
30420 \begin_inset Newline newline
30425 is inserted after the first formula
30428 \begin_layout Enumerate
30429 second formula is inserted
30432 \begin_layout Enumerate
30433 third formula is inserted
30436 \begin_layout Enumerate
30443 is inserted after the third formula
30446 \begin_layout Standard
30447 Every formula between the commands
30459 is subnumbered as a, b,
30460 \begin_inset Newline linebreak
30463 c, \SpecialChar \ldots{}
30464 For multiline formulas every line will be subnumbered.
30465 All subnumbered formulas are treated as
30470 But as every numbered formula increases the counter
30474 by one, the command
30480 is needed to decrease it.
30481 Otherwise the formulas
30482 \begin_inset CommandInset ref
30489 \begin_inset CommandInset ref
30496 \begin_inset CommandInset ref
30502 would be numbered as
30503 \begin_inset CommandInset ref
30510 \begin_inset CommandInset ref
30517 \begin_inset CommandInset ref
30526 \begin_layout Standard
30527 By inserting the commands in TeX-mode, a space is created between the first
30530 \begin_inset space \thinspace{}
30533 mm vertical space is inserted after the command
30537 begin{subequations}
30540 When the formula style
30546 \begin_layout Plain Layout
30548 \begin_inset CommandInset ref
30550 reference "sec:Formula-Styles"
30562 \begin_inset space \thinspace{}
30565 mm space is inserted instead.
30568 \begin_layout Standard
30569 Here is an example for a multiline formula where the numbering was turned
30570 off for the second line:
30574 \begin_layout Plain Layout
30578 begin{subequations}
30584 \begin_inset Formula
30586 A & = & (B-Z)^{2}=(B-Z)(B-Z)\label{eq:d}\\
30587 & = & B^{2}-ZB-BZ+Z^{2}\nonumber \\
30588 & = & B^{2}-2BZ+Z^{2}\label{eq:f}
30597 \begin_layout Plain Layout
30609 \begin_layout Subsection
30610 User-defined Numbering
30611 \begin_inset CommandInset label
30613 name "sub:User-defined-Numbering"
30618 \begin_inset Index idx
30621 \begin_layout Plain Layout
30622 Formula numbering ! user-defined
30630 \begin_layout Standard
30631 \begin_inset Index idx
30634 \begin_layout Plain Layout
30635 Formula numbering ! self-defined delimiters
30640 With the standard numbering parentheses are set around the formula number.
30641 To replace the parentheses for example by vertical bars, the following
30642 line is added to the LaTeX-preamble:
30645 \begin_layout Standard
30657 \begin_inset Note Note
30660 \begin_layout Plain Layout
30661 This macro is already declared in the LaTeX-preamble for testing.
30662 To activate it, remove the percent sign at the beginning.
30670 \begin_layout Standard
30671 To use other characters, the vertical bars besides the
30675 are replaced by one ore more characters.
30676 To get only the formula number the vertical bars are omitted.
30679 \begin_layout Standard
30680 \begin_inset VSpace bigskip
30683 When there should be an expression of your choice instead of the consecutive
30684 formula number in parentheses behind the formula, the command
30691 \begin_inset Index idx
30694 \begin_layout Plain Layout
30703 \begin_inset Formula
30705 A+B=C\tag{something}\label{eq:tag}
30710 In this example the command
30718 \begin_layout Plain Layout
30729 was inserted in the formula.
30732 \begin_layout Standard
30741 \begin_layout Plain Layout
30752 is inserted instead, the star prevents the parentheses around the expression:
30753 \begin_inset Formula
30755 A+B=C\tag*{something}
30763 \begin_layout Standard
30764 \begin_inset VSpace bigskip
30767 To restart the formula numbering with new document parts or sections, the
30768 following command is used:
30771 \begin_layout Standard
30776 @addtoreset{equation}{part}
30779 \begin_inset Index idx
30782 \begin_layout Plain Layout
30787 \begin_layout Plain Layout
30798 \begin_layout Plain Layout
30811 \begin_layout Plain Layout
30822 \begin_layout Plain Layout
30835 \begin_inset Newline newline
30839 \begin_inset Newline newline
30846 @addtoreset{equation}{section}
30849 \begin_layout Standard
30850 To be able to use these commands in TeX-mode, the
30851 \begin_inset Quotes eld
30855 \begin_inset Quotes erd
30858 character has to be made
30859 \begin_inset Quotes eld
30863 \begin_inset Quotes erd
30866 for LaTeX using the command
30880 So the command sequence in TeX-mode is:
30883 \begin_layout Standard
30889 \begin_inset Newline newline
30894 @addtoreset{equation}{section}
30895 \begin_inset Newline newline
30903 \begin_layout Standard
30904 In the LaTeX-preamble
30916 can be omitted as they are automatically internally inserted by LyX.
30919 \begin_layout Standard
30934 \begin_layout Plain Layout
30939 is part of the LaTeX-package
30944 \begin_inset Index idx
30947 \begin_layout Plain Layout
30948 Packages ! carlisle
30953 that is part of every LaTeX standard installation.
30959 \begin_inset Index idx
30962 \begin_layout Plain Layout
30963 Packages ! remreset
30968 has to be loaded in the LaTeX-preamble with the line
30971 \begin_layout Standard
30976 usepackage{remreset}
30979 \begin_layout Standard
30987 \begin_inset Index idx
30990 \begin_layout Plain Layout
30995 \begin_layout Plain Layout
31006 \begin_layout Plain Layout
31019 \begin_layout Plain Layout
31030 \begin_layout Plain Layout
31042 can be used with the same scheme as
31051 \begin_layout Standard
31052 \begin_inset VSpace bigskip
31055 Sometimes formulas should be numbered in the following form:
31058 \begin_layout Standard
31061 (section number.formula number)
31064 \begin_layout Standard
31065 The formula number should start with every section with
31066 \begin_inset Quotes eld
31070 \begin_inset Quotes erd
31076 \begin_layout Standard
31077 For this case there is the command
31084 \begin_inset Index idx
31087 \begin_layout Plain Layout
31095 , which is used with the following scheme:
31098 \begin_layout Standard
31103 numberwithin{counter}{sectioning}
31106 \begin_layout Standard
31107 Counter denotes what kind of numbering is affected, sectioning denotes what
31108 number is before the dot.
31111 \begin_layout Standard
31112 Thus in our case the following LaTeX-preamble or TeX code line is used:
31115 \begin_layout Standard
31120 numberwithin{equation}{section}
31123 \begin_layout Standard
31124 This is the result:
31128 \begin_layout Plain Layout
31132 numberwithin{equation}{section}
31138 \begin_inset Formula
31148 \begin_layout Standard
31150 \begin_inset space \thinspace{}
31154 \begin_inset space \space{}
31157 tables so that the number of the part is the sectioning,
31158 \begin_inset Newline newline
31165 numberwithin{table}{part}
31170 \begin_layout Standard
31171 To go back to the standard numbering or to prevent this kind of numbering
31172 when it is defined by the document class, the following command is inserted
31173 as TeX code or to the LaTeX-preamble:
31176 \begin_layout Standard
31186 \begin_inset Index idx
31189 \begin_layout Plain Layout
31203 \begin_layout Plain Layout
31219 \begin_inset Newline newline
31227 \begin_inset Newline newline
31239 \begin_layout Standard
31246 uses internally the command
31252 , described above, that also needs to be reverted.
31256 \begin_layout Plain Layout
31263 \begin_layout Plain Layout
31267 @removefromreset{equation}{section}
31270 \begin_layout Plain Layout
31282 \begin_layout Subsection
31283 Numbering with Roman Numbers and Letters
31284 \begin_inset Index idx
31287 \begin_layout Plain Layout
31288 Formula numbering ! with letters
31294 \begin_inset Index idx
31297 \begin_layout Plain Layout
31298 Formula numbering ! with Roman numbers
31306 \begin_layout Standard
31307 Formulas can also be numbered with Roman numbers and Latin letters.
31308 To number for example with small Roman numbers, the command
31311 \begin_layout Standard
31323 \begin_layout Standard
31324 is inserted before the formula in TeX-mode.
31332 \begin_inset Index idx
31335 \begin_layout Plain Layout
31343 redefines the predefined command
31359 \begin_layout Plain Layout
31366 has the same scheme like the command
31372 that is described in
31373 \begin_inset CommandInset ref
31375 reference "sub:The-Command-newcommand"
31388 is the formula counter.
31395 is used as prefix for a counter, the value of the counter is output as
31397 When a formula is numbered, LaTeX sets internally the command
31403 behind the formula.
31409 \begin_inset Index idx
31412 \begin_layout Plain Layout
31422 outputs the counter as small Roman number.
31425 \begin_layout Standard
31426 All formulas behind the command
31436 are now numbered Roman.
31437 To switch to numbering with big Roman numbers, the command is inserted
31451 \begin_inset Index idx
31454 \begin_layout Plain Layout
31466 \begin_inset Quotes eld
31470 \begin_inset Quotes erd
31473 with small Latin letters there is the command
31480 \begin_inset Index idx
31483 \begin_layout Plain Layout
31491 , for big ones there is the command
31498 \begin_inset Index idx
31501 \begin_layout Plain Layout
31514 \begin_layout Standard
31515 \begin_inset Note Greyedout
31518 \begin_layout Plain Layout
31525 \begin_inset space ~
31528 formulas can be numbered with Latin letters in one document.
31536 \begin_layout Standard
31540 \begin_layout Plain Layout
31556 \begin_layout Standard
31557 \begin_inset Formula
31559 A=\textrm{small roman}
31568 \begin_layout Plain Layout
31582 \begin_inset Formula
31584 B=\textrm{big Roman}\label{eq:Rom}
31593 \begin_layout Plain Layout
31607 \begin_inset Formula
31609 C=\textrm{small Latin}
31618 \begin_layout Plain Layout
31632 \begin_inset Formula
31634 D=\textrm{big Latin}\label{eq:Lat}
31642 \begin_layout Standard
31643 To switch back to the default numbering, insert the command:
31646 \begin_layout Standard
31656 \begin_inset Index idx
31659 \begin_layout Plain Layout
31670 \begin_layout Standard
31674 \begin_layout Plain Layout
31688 \begin_inset Formula
31698 \begin_layout Standard
31699 \begin_inset VSpace medskip
31702 As you see, formulas are numbered serially independent from the numbering
31704 When then numbering should start with
31705 \begin_inset Quotes eld
31709 \begin_inset Quotes erd
31712 when the style is changed, new equation counters have to be defined.
31713 A description about this can be found in the file
31714 \begin_inset CommandInset href
31716 name "Formula-numbering.lyx"
31717 target "run:Formula-numbering.lyx"
31724 \begin_layout Section
31725 Chemical Symbols and Equations
31726 \begin_inset CommandInset label
31728 name "sub:Chemical-Symbols-and"
31733 \begin_inset Index idx
31736 \begin_layout Plain Layout
31737 Chemical characters ! Symbols
31743 \begin_inset Index idx
31746 \begin_layout Plain Layout
31753 \begin_inset Index idx
31756 \begin_layout Plain Layout
31765 \begin_layout Standard
31766 An example text from chemistry:
31769 \begin_layout Quote
31771 \begin_inset Formula $\mathrm{SO_{4}^{2-}}$
31774 -ion reacts with two
31775 \begin_inset Formula $\mathrm{Na^{+}}$
31778 -ions to sodium sulfate
31779 \begin_inset Formula $\left(\mathrm{Na_{2}SO_{4}}\right)$
31783 The chemical equation for this is:
31784 \begin_inset Formula
31786 \mathrm{2\, Na^{+}+SO_{4}^{2-}\longrightarrow Na_{2}SO_{4}}\label{eq:chem-reaction}
31794 \begin_layout Standard
31795 This chemical equation can directly be created as formula.
31796 To avoid that the symbols appear italic, everything is highlighted and
31797 changed by the shortcut
31803 to the upright font style.
31807 \begin_layout Plain Layout
31813 \begin_inset CommandInset ref
31815 reference "sub:Font-Styles"
31827 \begin_layout Standard
31828 A more convenient way to typeset chemical formulas is to use the command
31836 \begin_inset Index idx
31839 \begin_layout Plain Layout
31847 that is available when the LaTeX-package
31852 \begin_inset Index idx
31855 \begin_layout Plain Layout
31868 to a formula a new blue box appears where chemical formulas can be inserted
31869 in an intuitive way.
31872 \begin_layout Standard
31874 \begin_inset Tabular
31875 <lyxtabular version="3" rows="9" columns="2">
31876 <features tabularvalignment="middle">
31877 <column alignment="center" valignment="top" width="0">
31878 <column alignment="center" valignment="top" width="0">
31880 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
31883 \begin_layout Plain Layout
31889 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
31892 \begin_layout Plain Layout
31894 \begin_inset Note Note
31897 \begin_layout Plain Layout
31904 is only used as spacer.
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 $\raisebox{4.5mm}{}\ce{H2CO3}\raisebox{-2mm}{}$
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 $\raisebox{5mm}{}\ce{SO4^{2-}}\raisebox{-2mm}{}$
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 $\raisebox{4.5mm}{}\ce{(NH4)2S}\raisebox{-2mm}{}$
32030 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
32033 \begin_layout Plain Layout
32040 \begin_layout Plain Layout
32054 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
32057 \begin_layout Plain Layout
32058 \begin_inset Formula $\raisebox{4.5mm}{}\ce{KCr(SO4)2.12H2O}\raisebox{-2mm}{}$
32068 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
32071 \begin_layout Plain Layout
32078 \begin_layout Plain Layout
32093 \begin_layout Plain Layout
32108 \begin_layout Plain Layout
32122 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
32125 \begin_layout Plain Layout
32126 \begin_inset Formula $\raisebox{4.5mm}{}\ce{A-B\dbond C\tbond D}\raisebox{-2mm}{}$
32136 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
32139 \begin_layout Plain Layout
32146 \begin_layout Plain Layout
32156 \begin_inset Formula $\downarrow$
32160 \begin_inset Formula $\to$
32168 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
32171 \begin_layout Plain Layout
32172 \begin_inset Formula $\raisebox{5mm}{}\ce{_{90}^{227}Th+}\raisebox{-2mm}{}$
32182 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
32185 \begin_layout Plain Layout
32192 \begin_layout Plain Layout
32205 \begin_layout Plain Layout
32218 \begin_layout Plain Layout
32231 \begin_layout Plain Layout
32244 \begin_layout Plain Layout
32258 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
32261 \begin_layout Plain Layout
32262 \begin_inset Formula $\raisebox{4.5mm}{}\ce{CO2 + C <=> 2CO}\raisebox{-2mm}{}$
32272 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
32275 \begin_layout Plain Layout
32282 \begin_layout Plain Layout
32295 \begin_layout Plain Layout
32308 \begin_layout Plain Layout
32321 \begin_layout Plain Layout
32338 \begin_layout Plain Layout
32352 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
32355 \begin_layout Plain Layout
32356 \begin_inset Formula $\raisebox{5mm}{}\ce{CO2 + C ->[\alpha][\beta] 2CO}\raisebox{-4mm}{}$
32372 \begin_layout Standard
32373 \begin_inset Note Greyedout
32376 \begin_layout Plain Layout
32382 Inserting a formula to a
32388 box will lead to LaTeX errors.
32389 In this case TeX code has to be used like for
32403 \begin_layout Plain Layout
32424 \begin_layout Standard
32425 \begin_inset Note Greyedout
32428 \begin_layout Plain Layout
32434 It is not possible in LyX to use the character ^ to get an up-arrow as
32440 One instead uses a negative thin space followed by the command
32447 \begin_inset Formula $\ce{Fe + 2H+ -> Fe^{2+} + H2\negthinspace\uparrow}$
32458 \begin_layout Standard
32465 the command for equation
32466 \begin_inset space ~
32470 \begin_inset CommandInset ref
32472 reference "eq:chem-reaction"
32477 \begin_inset Newline newline
32488 \begin_layout Plain Layout
32501 \begin_layout Plain Layout
32514 \begin_layout Plain Layout
32527 \begin_layout Plain Layout
32540 \begin_layout Plain Layout
32553 \begin_layout Plain Layout
32565 \begin_layout Standard
32566 To create multiline chemical equations first a multiline formula is created
32568 \begin_inset CommandInset ref
32570 reference "sec:Multiline-Formulas"
32575 Afterwards the command
32581 is used in every small blue box of the formula.
32583 \begin_inset CommandInset ref
32585 reference "eq:TEOS-reaction-1"
32590 \begin_inset CommandInset ref
32592 reference "eq:TEOS-reaction-2"
32596 are an example of a multi-stage chemical reaction where every equation
32597 has its own number.
32598 \begin_inset Formula
32600 \ce{TEOS + 4O} & \ce{->} & \ce{Si(OH)4 + 4C2H4O}\label{eq:TEOS-reaction-1}\\
32601 \ce{Si(OH)4} & \ce{->} & \ce{SiO2 + 2H2O}\label{eq:TEOS-reaction-2}
32609 \begin_layout Standard
32620 package provides the command
32627 \begin_inset Index idx
32630 \begin_layout Plain Layout
32638 that has to be used for special cases.
32639 For more information about
32645 and more examples have a look at the documentation of
32650 \begin_inset CommandInset citation
32659 \begin_layout Section
32663 \begin_layout Standard
32664 LyX supports two types of commutative diagrams:
32672 that are explained in the following.
32675 \begin_layout Subsection
32677 \begin_inset Index idx
32680 \begin_layout Plain Layout
32689 \begin_layout Standard
32690 Diagrams of this type visualize relations by vertical and horizontal lines
32692 \begin_inset Formula
32694 \begin{CD}A@>>>B@>>>C\\
32705 \begin_layout Standard
32706 To get them, the command
32711 \begin_inset Index idx
32714 \begin_layout Plain Layout
32724 is inserted to a formula.
32725 A blue box appears with two dashed lines where further commands can be
32730 arg "newline-insert newline"
32733 a new line is created.
32734 Horizontal relations are inserted in odd, vertical in even formula lines.
32737 \begin_layout Standard
32738 To create the relations there are the following commands:
32741 \begin_layout Itemize
32746 creates a left arrow,
32757 \begin_layout Itemize
32762 creates an up arrow,
32770 a vertical equal sign
32773 \begin_layout Itemize
32779 is a placeholder for non-existent relations
32782 \begin_layout Standard
32783 All arrows can be labeled as follows:
32786 \begin_layout Itemize
32787 If text inserted between the first and second < or >, resp., it is placed
32789 When it is inserted between the second and third one, it appears under
32793 \begin_layout Itemize
32794 When text for vertical arrows is inserted between the first and second A
32795 or V, resp., it is placed left beside the arrow.
32796 When it is inserted between the second and third one, it appears right
32798 If the text contains an A or V, these letters must be set into a TeX-brace.
32801 \begin_layout Standard
32802 As example a diagram with all possible relations:
32805 \begin_layout Standard
32806 \begin_inset Formula
32808 \begin{CD}A@>j>>B@>>k>C@=F\\
32819 \begin_layout Standard
32820 The command for this is:
32821 \begin_inset Newline newline
32832 \begin_layout Plain Layout
32841 A@>j>>B@>>k>C@=F Ctrl+Return
32842 \begin_inset Newline newline
32846 \begin_inset Phantom HPhantom
32849 \begin_layout Plain Layout
32858 \begin_layout Plain Layout
32877 \begin_inset Formula $\to$
32883 \begin_inset Newline newline
32887 \begin_inset Phantom HPhantom
32890 \begin_layout Plain Layout
32899 \begin_layout Plain Layout
32916 \begin_layout Subsection
32918 \begin_inset Index idx
32921 \begin_layout Plain Layout
32922 Diagrams ! xymatrix
32930 \begin_layout Standard
32931 To be able to use xymatrices, the LaTeX-package
32936 A xymatrix is created by inserting the command
32943 Then you are able to add new matrix columns and rows like for normal matrices,
32945 \begin_inset CommandInset ref
32947 reference "sec:Matrices"
32954 \begin_layout Standard
32955 In contrary to amscd diagrams, xymatrices supports diagonal and curved arrows,
32957 All possibilities to create commutative diagrams and decorations are explained
32962 that you find in the menu
32964 Help\SpecialChar \menuseparator
32966 \begin_inset space ~
32974 \begin_layout Subsection
32980 \begin_inset Index idx
32983 \begin_layout Plain Layout
32992 \begin_layout Standard
32997 -diagrams, the LaTeX-package
33006 -diagram is created by inserting the command
33013 Then you are able to add new matrix columns and rows like for normal matrices,
33015 \begin_inset CommandInset ref
33017 reference "sec:Matrices"
33024 \begin_layout Standard
33025 Examples how to create
33029 diagrams in LyX is given in the
33031 Feynman-diagram manual
33033 that you find in the menu
33035 Help\SpecialChar \menuseparator
33037 \begin_inset space ~
33045 \begin_layout Section
33046 User-defined Commands
33047 \begin_inset Index idx
33050 \begin_layout Plain Layout
33051 User-defined commands
33059 \begin_layout Standard
33060 \begin_inset Note Greyedout
33063 \begin_layout Plain Layout
33068 The names of user-defined commands and macros may only consist of Latin
33077 \begin_layout Subsection
33081 \begin_inset CommandInset label
33083 name "sub:The-Command-newcommand"
33088 \begin_inset Index idx
33091 \begin_layout Plain Layout
33092 User-defined commands !
33100 \begin_inset Index idx
33103 \begin_layout Plain Layout
33114 \begin_layout Standard
33115 Many LaTeX-commands are too long to be used frequently.
33116 But it is possible to define with the command
33122 new shorter commands.
33125 \begin_layout Standard
33126 The command scheme of
33135 \begin_layout Standard
33140 newcommand{new command name}[number of arguments][optional
33145 \begin_inset Newline newline
33149 \begin_inset Phantom HPhantom
33152 \begin_layout Plain Layout
33162 {command definition}
33165 \begin_layout Standard
33166 \begin_inset Note Greyedout
33169 \begin_layout Plain Layout
33174 Assure that the name of the new command is not already used in your document
33175 or by LaTeX-packages that you use.
33176 When you for example define the command
33188 , you get an error message because
33194 is already defined as command for
33195 \begin_inset Quotes eld
33199 \begin_inset Formula $\le$
33203 \begin_inset Quotes erd
33214 \begin_layout Standard
33215 The number of arguments is an integer in the range 0
33216 \begin_inset space \thinspace{}
33220 \begin_inset space \thinspace{}
33223 9 and specifies how many arguments the new command should have.
33224 With the optional value a value for an optional argument can be predefined.
33225 When this is done, the
33233 rgument of the new command is automatically an optional one.
33236 \begin_layout Standard
33237 Here are some examples:
33240 \begin_layout Itemize
33241 To define the command
33253 , the LaTeX-preamble line is:
33254 \begin_inset VSpace medskip
33258 \begin_inset Newline newline
33272 \begin_layout Itemize
33273 To define the command
33285 , the argument (that should be underlined) must be taken into account.
33286 For this the preamble line is:
33287 \begin_inset VSpace medskip
33291 \begin_inset Newline newline
33305 \begin_inset VSpace medskip
33309 \begin_inset Newline newline
33316 acts as argument placeholder, the
33320 behind it denotes that it is the placeholder for the first argument.
33323 \begin_layout Itemize
33331 \begin_inset space \thinspace{}
33335 \begin_inset space \space{}
33345 \begin_inset VSpace medskip
33349 \begin_inset Newline newline
33360 framebox#1#2{$#3$}}
33363 \begin_inset VSpace medskip
33367 \begin_inset Newline newline
33370 The two Dollar signs creates the extra formula needed for
33377 \begin_inset CommandInset ref
33379 reference "sub:Boxes-with-Frame"
33386 \begin_layout Itemize
33387 To create a new command for
33393 where the color for the box need not be specified, the argument for the
33394 color is defined optional:
33395 \begin_inset VSpace medskip
33399 \begin_inset Newline newline
33410 fcolorbox{#2}{#1}{$#3$}}
33413 \begin_inset VSpace medskip
33417 \begin_inset Newline newline
33420 When the color is not specified when using
33426 , the predefined color
33433 \begin_layout Standard
33434 A test of the new defined commands:
33437 \begin_layout Standard
33439 \begin_inset Tabular
33440 <lyxtabular version="3" rows="6" columns="2">
33441 <features tabularvalignment="middle">
33442 <column alignment="center" valignment="top" width="0">
33443 <column alignment="center" valignment="top" width="0">
33445 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
33448 \begin_layout Plain Layout
33454 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
33457 \begin_layout Plain Layout
33459 \begin_inset Note Note
33462 \begin_layout Plain Layout
33469 is only used as spacer.
33481 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
33484 \begin_layout Plain Layout
33491 \begin_layout Plain Layout
33505 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
33508 \begin_layout Plain Layout
33509 \begin_inset Formula $A\gr B$
33519 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
33522 \begin_layout Plain Layout
33530 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
33533 \begin_layout Plain Layout
33534 \begin_inset Formula $\raisebox{4.5mm}{}\us{ABcd}\raisebox{-2mm}{}$
33544 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
33547 \begin_layout Plain Layout
33551 \begin_inset Formula $\to$
33557 \begin_inset Formula $\to$
33568 \begin_layout Plain Layout
33582 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
33585 \begin_layout Plain Layout
33586 \begin_inset Formula $\raisebox{6mm}{}\fb{[2cm]}{}{\int A=B}\raisebox{-4mm}{}$
33596 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
33599 \begin_layout Plain Layout
33603 \begin_inset Formula $\to$
33614 \begin_layout Plain Layout
33628 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
33631 \begin_layout Plain Layout
33632 \begin_inset Formula $\raisebox{6mm}{}\cb{red}{\int A=B}\raisebox{-4mm}{}$
33642 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
33645 \begin_layout Plain Layout
33651 \begin_inset Formula $\to$
33662 \begin_layout Plain Layout
33676 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
33679 \begin_layout Plain Layout
33680 \begin_inset Formula $\raisebox{6mm}{}\cb[green]{red}{\int A=B}\raisebox{-4mm}{}$
33696 \begin_layout Subsection
33698 \begin_inset Index idx
33701 \begin_layout Plain Layout
33702 User-defined commands! Math macros
33708 \begin_inset Index idx
33711 \begin_layout Plain Layout
33720 \begin_layout Standard
33721 User-defined commands are especially convenient for complex expressions.
33722 When you are for example dealing with a document that has quadratic equations,
33723 the same solution type occurs several times.
33724 The general form of a quadratic equation is
33725 \begin_inset Formula
33727 0=\lambda^{2}+p\lambda+q
33732 The general form of the solution is
33733 \begin_inset Formula
33735 \lambda_{1,2}=-\frac{p}{2}\pm\sqrt{\frac{p²}{4}-q}
33743 \begin_layout Standard
33744 To define a command for the solution formula where only the three parameters
33746 \begin_inset Formula $\lambda$
33750 \begin_inset Formula $p$
33754 \begin_inset Formula $q$
33757 need to be specified and the index of
33758 \begin_inset Formula $\lambda$
33761 can be given optionally, the LaTeX-preamble line is
33762 \begin_inset Newline newline
33778 \begin_inset Newline newline
33782 \begin_inset Phantom HPhantom
33785 \begin_layout Plain Layout
33799 frac{#3^{2}}{4}-#4}}
33802 \begin_layout Standard
33803 To create with this the solution formula, the command
33804 \begin_inset Newline newline
33814 \begin_inset Formula $\to$
33820 \begin_inset Formula $\to$
33827 is inserted to a formula
33832 \begin_layout Standard
33833 The definition of the new command is unintuitive because one has to know
33834 the schemes of all used LaTeX commands, e.
33835 \begin_inset space \thinspace{}
33839 \begin_inset space \space{}
33842 that a fraction is inserted in LaTeX as
33846 frac{numerator}{denominator}
33849 Furthermore one can easily forget a brace in the definition and cannot
33850 see in LyX what the new command is doing.
33851 To avoid these problems LyX offers the possibility to use math macros instead
33861 \begin_layout Standard
33862 A math macro is created by using the menu
33864 Insert\SpecialChar \menuseparator
33865 Math\SpecialChar \menuseparator
33868 or the toolbar button
33869 \begin_inset Graphics
33870 filename ../images/math-macro_newmacroname_newcommand.png
33876 The math macro toolbar appears together with the following box where the
33878 \begin_inset Newline newline
33882 \begin_inset space \hspace*{\fill}
33886 \begin_inset Graphics
33887 filename clipart/macrobox.png
33892 \begin_inset space \hspace*{\fill}
33896 \begin_inset Newline newline
33900 \begin_inset FormulaMacro
33901 \newcommand{\qG}[4][1,\,2]{#2_{#1}=-\frac{#3}{2}\pm\sqrt{\frac{#3^{2}}{4}-#4}}
33906 newmacroname is the default name of the macro that should be changed to
33907 something sensible.
33908 The wanted formula is inserted in the first blue box.
33909 An argument placeholder is inserted with the command
33916 \begin_inset space \thinspace{}
33920 \begin_inset space \space{}
33929 or by using the macro toolbar button
33930 \begin_inset Graphics
33931 filename ../images/math-macro-add-param.png
33937 Argument placeholders are displayed red.
33939 \begin_inset space ~
33942 arguments are possible.
33943 Optional arguments are created with the toolbar button
33944 \begin_inset Graphics
33945 filename ../images/math-macro-add-optional-param.png
33951 The first non-optional argument can be transformed to an optional one with
33953 \begin_inset Graphics
33954 filename ../images/math-macro-make-optional.png
33960 In the second blue box the appearance of the macro in LyX can be defined.
33961 Normally you want to see it as it is defined, so the box is kept empty.
33962 But when you have created a macro that needs lot of space on the screen,
33963 you can insert in the box for example
33964 \begin_inset Newline newline
33994 \begin_inset Newline newline
33999 For the macro only the arguments with the macro name in front of them will
34000 then be displayed in LyX, leading to a better overview.
34001 The formula appears in the output as defined in the first box.
34002 \begin_inset Newline newline
34005 The appearance of macros in formulas can furthermore be changed for single
34006 macros by setting the cursor in the macro and using the menu
34008 View\SpecialChar \menuseparator
34010 \begin_inset space ~
34014 \begin_inset space ~
34022 \begin_layout Standard
34023 To use a macro, the macro name is inserted as command to a formula, in our
34031 Our macro looks in LyX like this:
34032 \begin_inset Newline newline
34036 \begin_inset space \hspace*{\fill}
34040 \begin_inset Graphics
34041 filename clipart/macrouse.png
34046 \begin_inset space \hspace*{\fill}
34050 \begin_inset Newline newline
34053 Here is our macro example with the arguments
34054 \begin_inset Formula $x$
34058 \begin_inset Formula $\ln(x)$
34062 \begin_inset Formula $B$
34068 \begin_layout Standard
34069 \begin_inset Formula
34079 \begin_layout Standard
34080 LyX offers in the menu
34082 Tools\SpecialChar \menuseparator
34083 Preferences\SpecialChar \menuseparator
34084 Editing\SpecialChar \menuseparator
34087 different styles to edit macros.
34088 To find the style that suits you the most, choose a style and set the cursor
34089 in a macro formula to see the difference.
34092 \begin_layout Standard
34093 A math macro is transformed internally to a
34099 command when exporting the document.
34106 command is not placed in the LaTeX-preamble, therefore macros can only
34107 be used in formulas that are in the document below the macro definition
34111 \begin_layout Standard
34112 Math macros can also be directly created from a
34119 When writing for example the command
34122 \begin_inset Newline newline
34131 xleftarrow[#2]{#1}}
34132 \begin_inset Newline newline
34137 in LyX as normal text, highlighting it completely and using then the shortcut
34142 , the command will be transformed to a math macro.
34143 Using this method you need to be careful that the
34149 command is typed correctly, otherwise you get a faulty macro leading to
34153 \begin_layout Standard
34154 Math macros currently have the problem that further formulas in macro definition
34155 s are handled wrongly.
34156 Therefore the example
34163 \begin_inset CommandInset ref
34165 reference "sub:The-Command-newcommand"
34169 cannot be created as macro.
34172 \begin_layout Standard
34173 When the cursor is in a macro definition box, you will see the macro toolbar
34177 \begin_layout Standard
34178 \begin_inset VSpace defskip
34184 \begin_layout Standard
34185 \begin_inset Graphics
34186 filename clipart/MacroToolbar.png
34191 \begin_inset Index idx
34194 \begin_layout Plain Layout
34203 \begin_layout Standard
34204 \begin_inset VSpace defskip
34210 \begin_layout Standard
34211 The macro toolbar contains from left to right the following buttons:
34214 \begin_layout Standard
34215 \begin_inset VSpace defskip
34221 \begin_layout Standard
34222 \begin_inset Tabular
34223 <lyxtabular version="3" rows="9" columns="2">
34224 <features islongtable="true" longtabularalignment="center">
34225 <column alignment="left" valignment="top" width="0">
34226 <column alignment="left" valignment="top" width="85col%">
34227 <row interlinespace="2.5mm">
34228 <cell alignment="center" valignment="top" usebox="none">
34231 \begin_layout Plain Layout
34232 \begin_inset Graphics
34233 filename ../images/math-macro-remove-param.png
34234 rotateOrigin center
34243 <cell alignment="center" valignment="top" usebox="none">
34246 \begin_layout Plain Layout
34249 Edit\SpecialChar \menuseparator
34250 Math\SpecialChar \menuseparator
34252 \begin_inset space ~
34255 Definition\SpecialChar \menuseparator
34256 Remove Last Argument
34262 <row interlinespace="2.5mm">
34263 <cell alignment="center" valignment="top" usebox="none">
34266 \begin_layout Plain Layout
34267 \begin_inset Graphics
34268 filename ../images/math-macro-add-param.png
34269 rotateOrigin center
34278 <cell alignment="center" valignment="top" usebox="none">
34281 \begin_layout Plain Layout
34284 Edit\SpecialChar \menuseparator
34285 Math\SpecialChar \menuseparator
34287 \begin_inset space ~
34290 Definition\SpecialChar \menuseparator
34297 <row interlinespace="2.5mm">
34298 <cell alignment="center" valignment="top" usebox="none">
34301 \begin_layout Plain Layout
34302 \begin_inset Graphics
34303 filename ../images/math-macro-make-optional.png
34304 rotateOrigin center
34313 <cell alignment="center" valignment="top" usebox="none">
34316 \begin_layout Plain Layout
34319 Edit\SpecialChar \menuseparator
34320 Math\SpecialChar \menuseparator
34322 \begin_inset space ~
34325 Definition\SpecialChar \menuseparator
34326 Make First Non-Optional into
34327 \begin_inset Newline newline
34331 \begin_inset Phantom HPhantom
34334 \begin_layout Plain Layout
34337 Edit\SpecialChar \menuseparator
34338 Math\SpecialChar \menuseparator
34340 \begin_inset space ~
34343 Definition\SpecialChar \menuseparator
34355 <row interlinespace="2.5mm">
34356 <cell alignment="center" valignment="top" usebox="none">
34359 \begin_layout Plain Layout
34360 \begin_inset Graphics
34361 filename ../images/math-macro-make-nonoptional.png
34362 rotateOrigin center
34371 <cell alignment="center" valignment="top" usebox="none">
34374 \begin_layout Plain Layout
34377 Edit\SpecialChar \menuseparator
34378 Math\SpecialChar \menuseparator
34380 \begin_inset space ~
34383 Definition\SpecialChar \menuseparator
34384 Make Last Optional into
34385 \begin_inset Newline newline
34389 \begin_inset Phantom HPhantom
34392 \begin_layout Plain Layout
34395 Edit\SpecialChar \menuseparator
34396 Math\SpecialChar \menuseparator
34398 \begin_inset space ~
34401 Definition\SpecialChar \menuseparator
34407 Non-Optional Argument
34413 <row interlinespace="2.5mm">
34414 <cell alignment="center" valignment="top" usebox="none">
34417 \begin_layout Plain Layout
34418 \begin_inset Graphics
34419 filename ../images/math-macro-remove-optional-param.png
34420 rotateOrigin center
34429 <cell alignment="center" valignment="top" usebox="none">
34432 \begin_layout Plain Layout
34435 Edit\SpecialChar \menuseparator
34436 Math\SpecialChar \menuseparator
34438 \begin_inset space ~
34441 Definition\SpecialChar \menuseparator
34442 Remove Optional Argument
34448 <row interlinespace="2.5mm">
34449 <cell alignment="center" valignment="top" usebox="none">
34452 \begin_layout Plain Layout
34453 \begin_inset Graphics
34454 filename ../images/math-macro-add-optional-param.png
34455 rotateOrigin center
34464 <cell alignment="center" valignment="top" usebox="none">
34467 \begin_layout Plain Layout
34470 Edit\SpecialChar \menuseparator
34471 Math\SpecialChar \menuseparator
34473 \begin_inset space ~
34476 Definition\SpecialChar \menuseparator
34477 Insert Optional Argument
34483 <row interlinespace="2.5mm">
34484 <cell alignment="center" valignment="top" usebox="none">
34487 \begin_layout Plain Layout
34488 \begin_inset Graphics
34489 filename ../images/math-macro-remove-greedy-param.png
34490 rotateOrigin center
34499 <cell alignment="center" valignment="top" usebox="none">
34502 \begin_layout Plain Layout
34505 Edit\SpecialChar \menuseparator
34506 Math\SpecialChar \menuseparator
34508 \begin_inset space ~
34511 Definition\SpecialChar \menuseparator
34512 Remove Last Argument
34513 \begin_inset Newline newline
34517 \begin_inset Phantom HPhantom
34520 \begin_layout Plain Layout
34523 Edit\SpecialChar \menuseparator
34524 Math\SpecialChar \menuseparator
34526 \begin_inset space ~
34529 Definition\SpecialChar \menuseparator
34535 Spitting Out To The Right
34541 <row interlinespace="2.5mm">
34542 <cell alignment="center" valignment="top" usebox="none">
34545 \begin_layout Plain Layout
34546 \begin_inset Graphics
34547 filename ../images/math-macro-append-greedy-param.png
34548 rotateOrigin center
34557 <cell alignment="center" valignment="top" usebox="none">
34560 \begin_layout Plain Layout
34563 Edit\SpecialChar \menuseparator
34564 Math\SpecialChar \menuseparator
34566 \begin_inset space ~
34569 Definition\SpecialChar \menuseparator
34571 \begin_inset Newline newline
34575 \begin_inset Phantom HPhantom
34578 \begin_layout Plain Layout
34581 Edit\SpecialChar \menuseparator
34582 Math\SpecialChar \menuseparator
34584 \begin_inset space ~
34587 Definition\SpecialChar \menuseparator
34593 Eating From The Right
34599 <row interlinespace="2.5mm">
34600 <cell alignment="center" valignment="top" usebox="none">
34603 \begin_layout Plain Layout
34604 \begin_inset Graphics
34605 filename ../images/math-macro-add-greedy-optional-param.png
34606 rotateOrigin center
34615 <cell alignment="center" valignment="top" usebox="none">
34618 \begin_layout Plain Layout
34621 Edit\SpecialChar \menuseparator
34622 Math\SpecialChar \menuseparator
34624 \begin_inset space ~
34627 Definition\SpecialChar \menuseparator
34628 Append Optional Argument
34629 \begin_inset Newline newline
34633 \begin_inset Phantom HPhantom
34636 \begin_layout Plain Layout
34639 Edit\SpecialChar \menuseparator
34640 Math\SpecialChar \menuseparator
34642 \begin_inset space ~
34645 Definition\SpecialChar \menuseparator
34651 Eating From The Right
34664 \begin_layout Section
34665 Computer Algebra Systems
34668 \begin_layout Standard
34669 LyX offers the exchange between mathematical expressions written in LyX's
34670 math editor and external applications or user defined scripts.
34671 Currently supported applications are
34688 Note that the set of supported mathematical constructs is limited only
34689 to very simple cases.
34692 \begin_layout Subsection
34696 \begin_layout Standard
34697 Write some expression in a formula, go to the
34699 Edit\SpecialChar \menuseparator
34700 Math\SpecialChar \menuseparator
34701 Use Computer Algebra System
34703 menu and choose the application you have installed on the computer.
34704 After that the result of computation should show on the right side of the
34705 expression together with the
34706 \begin_inset Quotes eld
34710 \begin_inset Quotes erd
34716 \begin_layout Standard
34717 Here are few simple examples (with results from
34721 ) to show what kind of computations can be performed:
34724 \begin_layout Itemize
34725 \begin_inset Formula $\frac{37}{3}*2-\sum_{i=1}^{3}i^{i}=-\frac{22}{3}$
34731 \begin_layout Itemize
34732 \begin_inset Formula $\frac{37.0}{3}=12.33333333333333$
34738 \begin_layout Itemize
34739 \begin_inset Formula $\int_{1}^{2}\sin(x)dx=\cos1-\cos2$
34745 \begin_layout Itemize
34746 \begin_inset Formula $\det\left[\begin{array}{ccc}
34750 \end{array}\right]=-56$
34756 \begin_layout Itemize
34757 \begin_inset Formula $\lim_{x\rightarrow0}\left(\frac{\sin(x)}{x}\right)=1$
34763 \begin_layout Subsection
34767 \begin_layout Standard
34768 Currently there is no keyboard shortcut for calling the algebra applications.
34769 One can easily bind a shortcut to the
34773 LyX function (see the
34781 \begin_inset space \thinspace{}
34785 \begin_inset space ~
34792 key inside the math editor.
34797 one would use this shortcut definition command:
34800 \begin_layout Standard
34803 command-alternatives break-paragraph;math-extern maxima
34806 \begin_layout Standard
34807 \begin_inset Newpage newpage
34813 \begin_layout Section
34815 \begin_inset Index idx
34818 \begin_layout Plain Layout
34827 \begin_layout Subsection
34829 \begin_inset Index idx
34832 \begin_layout Plain Layout
34841 \begin_layout Standard
34842 Negative numbers often look ugly in formulas because the minus sign before
34843 the number is set with the same length as the minus operator sign.
34844 When writing the negative number in normal text, the minus sign appears
34848 \begin_layout Standard
34849 Thus, the problem disappears when converting the minus sign to mathematical
34853 \begin_layout Standard
34854 An example to visualize the problem:
34857 \begin_layout Standard
34859 \begin_inset Tabular
34860 <lyxtabular version="3" rows="3" columns="2">
34861 <features tabularvalignment="middle">
34862 <column alignment="right" valignment="top" width="0">
34863 <column alignment="left" valignment="top" width="0">
34865 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
34868 \begin_layout Plain Layout
34874 <cell alignment="center" valignment="top" topline="true" rightline="true" usebox="none">
34877 \begin_layout Plain Layout
34885 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
34888 \begin_layout Plain Layout
34894 <cell alignment="center" valignment="top" topline="true" bottomline="true" rightline="true" usebox="none">
34897 \begin_layout Plain Layout
34898 \begin_inset Formula $x=-2$
34908 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
34911 \begin_layout Plain Layout
34917 <cell alignment="center" valignment="top" topline="true" bottomline="true" rightline="true" usebox="none">
34920 \begin_layout Plain Layout
34921 \begin_inset Formula $x=\textrm{-}2$
34937 \begin_layout Subsection
34938 Comma as decimal Separator
34939 \begin_inset Index idx
34942 \begin_layout Plain Layout
34951 \begin_layout Standard
34952 In LaTeX a comma inside a formula is used, according to the English convention,
34953 as number group separator.
34954 So there will be space added behind all commas in formulas.
34957 \begin_layout Standard
34958 To avoid this, the comma is highlighted and changed to mathematical text
34968 \begin_layout Standard
34969 To use all formula commas in the document as decimal separator, the file
34978 \begin_layout Plain Layout
34983 is part of the LaTeX-package
34988 \begin_inset Index idx
34991 \begin_layout Plain Layout
34996 \begin_layout Plain Layout
35016 \begin_inset Index idx
35019 \begin_layout Plain Layout
35025 is loaded with the LaTeX-preamble line
35028 \begin_layout Standard
35036 \begin_layout Subsection
35038 \begin_inset CommandInset label
35040 name "sub:Physical-Vectors"
35045 \begin_inset Index idx
35048 \begin_layout Plain Layout
35057 \begin_layout Standard
35058 Predefined vectors are offered by the LaTeX-package
35063 \begin_inset Index idx
35066 \begin_layout Plain Layout
35072 that is loaded with the LaTeX-preamble line
35075 \begin_layout Standard
35083 \begin_layout Standard
35087 \begin_layout Plain Layout
35097 \begin_inset Note Note
35100 \begin_layout Plain Layout
35101 The following table will only be displayed when the LaTeX-package
35113 \begin_layout Standard
35114 The following commands are defined:
35117 \begin_layout Standard
35119 \begin_inset Tabular
35120 <lyxtabular version="3" rows="4" columns="2">
35121 <features tabularvalignment="middle">
35122 <column alignment="center" valignment="top" width="0">
35123 <column alignment="center" valignment="top" width="0">
35125 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
35128 \begin_layout Plain Layout
35134 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
35137 \begin_layout Plain Layout
35145 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
35148 \begin_layout Plain Layout
35158 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
35161 \begin_layout Plain Layout
35162 \begin_inset Formula $\Bra{\psi}$
35172 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
35175 \begin_layout Plain Layout
35185 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
35188 \begin_layout Plain Layout
35189 \begin_inset Formula $\Ket{\psi}$
35199 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
35202 \begin_layout Plain Layout
35214 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
35217 \begin_layout Plain Layout
35218 \begin_inset Formula $\Braket{\psi|\phi}$
35234 \begin_layout Standard
35241 assures that all vertical bars are set in the size of the surrounding brackets:
35242 \begin_inset Formula
35244 \Braket{\phi|J=\frac{3}{2}\,,\, M_{J}}
35253 \begin_layout Plain Layout
35263 \begin_inset Note Note
35266 \begin_layout Plain Layout
35267 The following will be displayed when the LaTeX-package
35279 \begin_layout Standard
35280 You need to install the LaTeX-package
35284 to see the rest of this subsection in the output.
35287 \begin_layout Standard
35291 \begin_layout Plain Layout
35303 \begin_layout Standard
35310 can also be achieved using the command
35316 , that is described in
35317 \begin_inset CommandInset ref
35319 reference "sub:Automatic-Bracket-Size"
35326 \begin_layout Subsection
35327 Self-defined Fractions
35328 \begin_inset CommandInset label
35330 name "sub:Self-defined-Fractions"
35335 \begin_inset Index idx
35338 \begin_layout Plain Layout
35339 Fractions ! self-defined
35347 \begin_layout Standard
35348 To define custom commands for fractions, the command
35355 \begin_inset Index idx
35358 \begin_layout Plain Layout
35366 is used in the following scheme:
35369 \begin_layout Standard
35382 bracket}{fraction bar thickness}{style}
35383 \begin_inset Newline newline
35387 \begin_inset Phantom HPhantom
35390 \begin_layout Plain Layout
35400 {numerator}{denominator}
35403 \begin_layout Standard
35404 The style is a number in the range of 0
35405 \begin_inset space \thinspace{}
35409 \begin_inset space \thinspace{}
35415 \begin_layout Standard
35417 \begin_inset Tabular
35418 <lyxtabular version="3" rows="5" columns="2">
35419 <features tabularvalignment="middle">
35420 <column alignment="center" valignment="top" width="0">
35421 <column alignment="center" valignment="top" width="0">
35423 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
35426 \begin_layout Plain Layout
35432 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
35435 \begin_layout Plain Layout
35443 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
35446 \begin_layout Plain Layout
35452 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
35455 \begin_layout Plain Layout
35456 display style formula
35463 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
35466 \begin_layout Plain Layout
35472 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
35475 \begin_layout Plain Layout
35483 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
35486 \begin_layout Plain Layout
35492 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
35495 \begin_layout Plain Layout
35503 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
35506 \begin_layout Plain Layout
35512 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
35515 \begin_layout Plain Layout
35529 \begin_layout Standard
35530 When no style is given, the size is adjusted to the surrounding environment
35531 like for the command
35540 \begin_layout Standard
35541 When no fraction bar thickness is given, the predefined value of 0.4
35542 \begin_inset space \thinspace{}
35548 \begin_layout Standard
35549 \begin_inset VSpace medskip
35552 For example, the commands
35565 \begin_inset CommandInset ref
35567 reference "sub:Fractions"
35571 are defined with the commands
35574 \begin_layout Standard
35583 genfrac{}{}{}{0}{#1}{#2}}
35586 \begin_layout Standard
35590 \begin_layout Standard
35599 genfrac{(}{)}{0pt}{1}{#1}{#2}}
35602 \begin_layout Standard
35603 \begin_inset VSpace medskip
35606 To define a fraction where the fraction bar thickness can be given as optional
35607 argument, the following line is inserted to the LaTeX-preamble:
35610 \begin_layout Standard
35619 genfrac{}{}{#1}{}{#2}{#3}}
35622 \begin_layout Standard
35623 \begin_inset Newpage newpage
35629 \begin_layout Standard
35631 \begin_inset Formula
35633 \text{Command} & & \mathrm{\backslash fracS[1mm]\backslash\{A\to\backslash\{B} & & \mathrm{\backslash fracS[5mm]\backslash\{A\to\backslash\{B}\\
35634 \text{Result} & & \fracS[1mm]{A}{B} & & \fracS[5mm]{A}{B}
35639 As one can see, the distance of the numerator and the denominator to the
35640 fraction bar is round about three times the bar thickness.
35643 \begin_layout Subsection
35645 \begin_inset Index idx
35648 \begin_layout Plain Layout
35657 \begin_layout Standard
35658 To cancel formulas or formula parts, the LaTeX-package
35663 \begin_inset Index idx
35666 \begin_layout Plain Layout
35672 has to be loaded with the LaTeX-preamble line
35675 \begin_layout Standard
35683 \begin_layout Standard
35687 \begin_layout Plain Layout
35697 \begin_inset Note Note
35700 \begin_layout Plain Layout
35701 The following table will only be displayed when the LaTeX-package
35713 \begin_layout Standard
35714 There are four ways to cancel formulas:
35717 \begin_layout Standard
35719 \begin_inset Tabular
35720 <lyxtabular version="3" rows="5" columns="2">
35721 <features tabularvalignment="middle">
35722 <column alignment="center" valignment="top" width="0">
35723 <column alignment="center" valignment="top" width="0">
35725 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
35728 \begin_layout Plain Layout
35734 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
35737 \begin_layout Plain Layout
35739 \begin_inset Note Note
35742 \begin_layout Plain Layout
35749 are used here as spacer.
35761 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
35764 \begin_layout Plain Layout
35773 \begin_layout Plain Layout
35787 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
35790 \begin_layout Plain Layout
35791 \begin_inset Formula $\raisebox{4.5mm}{}\cancel{\int A=B}\raisebox{-2.5mm}{}$
35801 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
35804 \begin_layout Plain Layout
35813 \begin_layout Plain Layout
35827 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
35830 \begin_layout Plain Layout
35831 \begin_inset Formula $\raisebox{4.5mm}{}\bcancel{\int A=B}\raisebox{-2.5mm}{}$
35841 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
35844 \begin_layout Plain Layout
35853 \begin_layout Plain Layout
35867 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
35870 \begin_layout Plain Layout
35871 \begin_inset Formula $\raisebox{4.5mm}{}\xcancel{\int A=B}\raisebox{-2.5mm}{}$
35881 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
35884 \begin_layout Plain Layout
35888 \begin_inset Formula $\to$
35899 \begin_layout Plain Layout
35913 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
35916 \begin_layout Plain Layout
35917 \begin_inset Formula $\raisebox{7mm}{}\cancelto{1}{\int A=B}\raisebox{-2.5mm}{}\hspace{3mm}$
35933 \begin_layout Standard
35940 is especially suitable to visualize the reduction of fractions within formulas:
35941 \begin_inset Formula
35943 \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}}}
35951 \begin_layout Standard
35952 To change the size of
35959 \begin_inset Quotes eld
35963 \begin_inset Quotes erd
35966 value one can load the package
35970 with either the option
35974 which leads to the same size as for the canceled value or with the option
35979 which makes is it a bit smaller than the size one gets without using a
35985 was loaded with this line:
35988 \begin_layout Standard
35993 usepackage[samesize]{cancel}
35996 \begin_layout Standard
35997 To color the cancellation bar one adds this command as TeX code:
36000 \begin_layout Standard
36012 \begin_layout Standard
36017 can be replaced by a color of your choice.
36020 \begin_layout Standard
36024 \begin_layout Plain Layout
36040 \begin_layout Standard
36041 \begin_inset Formula
36043 \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}}}
36051 \begin_layout Standard
36055 \begin_layout Plain Layout
36069 \begin_inset Note Note
36072 \begin_layout Plain Layout
36081 \begin_layout Standard
36082 For further customizations, see the documentation of the package
36087 \begin_inset CommandInset citation
36096 \begin_layout Standard
36100 \begin_layout Plain Layout
36110 \begin_inset Note Note
36113 \begin_layout Plain Layout
36114 The following will be displayed when the LaTeX-package
36126 \begin_layout Standard
36127 You need to install the LaTeX-package
36131 to see the rest of this subsection in the output.
36134 \begin_layout Standard
36138 \begin_layout Plain Layout
36150 \begin_layout Subsection
36151 Formulas in Section Headings
36152 \begin_inset CommandInset label
36154 name "sub:Formulas-in-Section"
36159 \begin_inset Index idx
36162 \begin_layout Plain Layout
36163 Formula ! in section headings
36171 \begin_layout Standard
36172 When formulas are used in section headings, the following has to be taken
36176 \begin_layout Standard
36177 \begin_inset Note Greyedout
36180 \begin_layout Plain Layout
36186 \begin_inset Index idx
36189 \begin_layout Plain Layout
36190 Packages ! hyperref
36195 support is enabled in the document settings dialog under
36198 \begin_inset space ~
36203 , PDF-bookmarks are created for every section heading in the table of contents.
36204 If a section heading contains formulas, they are incorrectly displayed
36205 in the bookmark text, because formulas in bookmarks infringe the PDF convention
36214 \begin_layout Standard
36215 Both problems can be solved by inserting at the end of the section heading
36216 a short title with the menu
36218 Insert\SpecialChar \menuseparator
36220 \begin_inset space ~
36226 Short titles are used as alternative for multiline section headings to
36227 keep the table of contents clearly arranged.
36228 Only the short title appears in the table of contents and therefore also
36229 in the PDF-bookmark.
36232 \begin_layout Standard
36233 When formulas should be used in the table of contents but
36237 is used, one can use the following command in TeX-mode:
36240 \begin_layout Standard
36245 texorpdfstring{part}{alternative}
36246 \begin_inset Index idx
36249 \begin_layout Plain Layout
36260 \begin_layout Standard
36261 Part is the part of the heading that shouldn't appear in the PDF-bookmark.
36262 This can be characters, formulas, footnotes, but also cross-references.
36263 The alternative is used instead of the part for the bookmark.
36266 \begin_layout Standard
36267 Here are two example headings:
36268 \begin_inset VSpace -3mm
36275 \begin_layout Plain Layout
36287 \begin_layout Subsubsection
36288 Heading without formula in table of contents
36289 \begin_inset Formula $\sqrt{-1}=\mathrm{i}$
36293 \begin_inset Argument
36296 \begin_layout Plain Layout
36297 Heading without formula in table of contents
36305 \begin_layout Subsubsection
36306 Heading with formula in table of contents
36310 \begin_layout Plain Layout
36320 \begin_inset Formula $\sqrt{-1}=\mathrm{i}$
36327 \begin_layout Plain Layout
36337 \begin_layout Standard
36341 \begin_layout Plain Layout
36350 In the first heading a short title was used, in the second one
36359 \begin_layout Standard
36360 To get the same formatting as for the other headings, the complete heading
36369 \begin_layout Plain Layout
36371 \begin_inset CommandInset ref
36373 reference "sub:Bold-Formulas"
36385 \begin_layout Subsection
36386 Formulas in multi-column Text
36387 \begin_inset Index idx
36390 \begin_layout Plain Layout
36391 Formula ! in multi-column text
36399 \begin_layout Standard
36400 Formulas in multi-column text are often too wide to fit into a column and
36401 thus need to be set over the whole page width.
36402 This is done by using the LaTeX-package
36410 \begin_layout Plain Layout
36415 is part of every LaTeX standard installation.
36421 \begin_inset Index idx
36424 \begin_layout Plain Layout
36425 Packages ! multicol
36430 , that is loaded with the LaTeX-preamble line
36433 \begin_layout Standard
36438 usepackage{multicol}
36441 \begin_layout Standard
36442 \begin_inset Note Greyedout
36445 \begin_layout Plain Layout
36446 Note that in this case the setting
36449 \begin_inset space ~
36456 Document\SpecialChar \menuseparator
36462 \begin_inset space ~
36482 \begin_layout Standard
36483 Before the multi-column text the command
36486 \begin_layout Standard
36491 begin{multicols}{column number}
36494 \begin_layout Standard
36495 is written in TeX-mode.
36496 The column number is a number in the range of 2
36497 \begin_inset space \thinspace{}
36501 \begin_inset space \thinspace{}
36505 Before the formula the multi-column text is ended by inserting the command
36508 \begin_layout Standard
36516 \begin_layout Standard
36520 \begin_layout Standard
36521 Due to the command some space is automatically added before the formula.
36523 \begin_inset space \thinspace{}
36526 mm vertical space is inserted before the formula.
36527 When the formula style
36533 \begin_layout Plain Layout
36535 \begin_inset CommandInset ref
36537 reference "sec:Formula-Styles"
36549 \begin_inset space \thinspace{}
36552 mm space is inserted instead.
36555 \begin_layout Standard
36556 As example a multi-column text with a displayed formula:
36559 \begin_layout Standard
36565 \begin_layout Plain Layout
36569 begin{multicols}{2}
36574 Das Spektrum wird fouriertransformiert.
36575 Die Fouriertransformation wird verwendet, um die überlagerten Signale (Netzwerk
36576 , Lösungsmittel) zu trennen.
36577 Nachdem wir die Phasenverschiebung bestimmen konnten, interessiert uns
36578 nun das Aussehen des Ausgangssignals.
36579 Im Experiment haben wir es mit sehr vielen Teilchen zu tun, so dass man
36580 über alle Phasen integrieren muss.
36582 \begin_inset Formula $S$
36585 unser normiertes Ausgangssignal und
36586 \begin_inset Formula $P$
36589 die Phasenverteilungsfunktion, so ergibt sich die Beziehung
36593 \begin_layout Plain Layout
36603 \begin_inset VSpace -6mm
36607 \begin_inset Formula
36609 S(t)=S_{0}(t)\int_{-\infty}^{\infty}P(\phi,t)\mathrm{e}^{\mathrm{i}\phi}\,\mathrm{d}\phi
36618 \begin_layout Plain Layout
36622 begin{multicols}{2}
36628 \begin_inset Formula $S_{0}$
36631 das Signal ohne Gradient ist und die Normierungsbedingung
36632 \begin_inset Formula $\int_{-\infty}^{\infty}P(\phi,t)\,\mathrm{d}\phi=1$
36636 Nun dürfen wir aber nicht den Relaxationsprozess außer Acht lassen.
36638 \begin_inset Formula $\nicefrac{\pi}{2}$
36642 \begin_inset space \thinspace{}
36645 -rf-Puls beginnt sich die Magnetisierung zu entfokussieren, wodurch sich
36646 das Signal zusätzlich abschwächt.
36647 Diese Abschwächung verläuft exponentiell in Abhängigkeit der so genannten
36649 \begin_inset Formula $T_{2}$
36655 \begin_layout Standard
36661 \begin_layout Plain Layout
36673 \begin_layout Subsection
36674 Formulas with Description of Variables
36675 \begin_inset Index idx
36678 \begin_layout Plain Layout
36679 Formula ! with description of variables
36687 \begin_layout Standard
36688 To describe variables within a formula, like in formula
36689 \begin_inset CommandInset ref
36691 reference "eq:within"
36700 \begin_inset Formula $n$
36704 \begin_inset space ~
36707 matrix is used with left aligned columns for the
36708 \begin_inset Formula $n$
36715 \begin_layout Plain Layout
36717 \begin_inset CommandInset ref
36719 reference "sec:Matrices"
36728 To set the description in a smaller size, before the matrix e.
36729 \begin_inset space \thinspace{}
36733 \begin_inset space \space{}
36746 \begin_layout Plain Layout
36748 \begin_inset CommandInset ref
36750 reference "sub:Font-Sizes"
36762 \begin_layout Standard
36763 When the formula style
36769 \begin_layout Plain Layout
36771 \begin_inset CommandInset ref
36773 reference "sec:Formula-Styles"
36794 \begin_layout Plain Layout
36801 only works in formulas with the style
36806 \begin_inset CommandInset ref
36808 reference "sub:Variable-Space"
36817 is inserted before and after the matrix to have the same separation of
36818 the matrix from the equation and the side margin.
36821 \begin_layout Standard
36822 When the formula style
36826 is used, the method described in
36827 \begin_inset CommandInset ref
36829 reference "sub:Flalign-Environment"
36833 is used to indent formulas.
36835 \begin_inset CommandInset ref
36837 reference "eq:within"
36841 consists of five columns where in the first two columns contain the equation,
36842 the third the matrix and the last one an empty TeX-brace.
36843 \begin_inset Formula
36845 \hspace{30pt}F_{A} & =\rho·V·g & \footnotesize\begin{array}{ll}
36846 \rho & \textrm{density}\\
36847 V & \textrm{volume}\\
36848 g & \textrm{gravitational acceleration}
36849 \end{array} & & {}\label{eq:within}
36857 \begin_layout Subsection
36858 Upright small Greek Letters
36859 \begin_inset CommandInset label
36861 name "sub:Upright-small-Greek"
36866 \begin_inset Index idx
36869 \begin_layout Plain Layout
36870 Greek letters ! upright
36878 \begin_layout Standard
36879 Most of the math fonts only provide italic small Greek letters.
36880 But for symbols of elementary particles like pions and neutrinos, upright
36881 Greek letters are needed.
36890 \begin_layout Plain Layout
36895 is part of the LaTeX-package
36900 \begin_inset Index idx
36903 \begin_layout Plain Layout
36908 \begin_layout Plain Layout
36928 \begin_inset Index idx
36931 \begin_layout Plain Layout
36937 that is loaded with the LaTeX-preamble line
36940 \begin_layout Standard
36945 usepackage{upgreek}
36948 \begin_layout Standard
36954 \begin_layout Plain Layout
36964 \begin_inset Note Note
36967 \begin_layout Plain Layout
36968 The following table will only be displayed when the LaTeX-package
36977 They are created when the command for a small Greek letter is started with
36983 For example the command
36990 \begin_inset Formula $\uptau$
36996 \begin_layout Standard
36997 With these commands reactions of elementary particles can be typeset:
36998 \begin_inset Formula
37000 \uppi^{+}\to\upmu^{+}+\upnu_{\upmu}
37008 \begin_layout Standard
37009 The upright letters are more bold and wider than the italic ones.
37010 They should therefore not be used for units like
37011 \begin_inset Quotes eld
37015 \begin_inset Quotes erd
37021 \begin_layout Standard
37025 \begin_layout Plain Layout
37035 \begin_inset Note Note
37038 \begin_layout Plain Layout
37039 The following will be displayed when the LaTeX-package
37051 \begin_layout Standard
37052 You need to install the LaTeX-package
37056 to see the rest of this subsection in the output.
37059 \begin_layout Standard
37063 \begin_layout Plain Layout
37075 \begin_layout Standard
37076 \begin_inset Newpage newpage
37082 \begin_layout Subsection
37083 Text Characters in Formulas
37084 \begin_inset CommandInset label
37086 name "sub:Text-Characters-in"
37091 \begin_inset Index idx
37094 \begin_layout Plain Layout
37103 \begin_layout Standard
37104 In some cases you might want to insert text characters directly into formulas.
37105 When for example the centered dot · is often used in formulas like
37106 \begin_inset Formula $\nu=5·10^{5}\,\mathrm{Hz}$
37109 , one would have to insert the command
37119 \begin_layout Plain Layout
37121 \begin_inset CommandInset ref
37123 reference "sub:Binary-Operators"
37132 all the time, because this character is defined in all encodings as text
37134 But the encoding can be changed by this LaTeX-preamble line:
37137 \begin_layout Standard
37142 Declare Inputtext{183}{
37152 f\SpecialChar \textcompwordmark{}
37156 \begin_layout Standard
37157 The character encoding (menu
37159 Document\SpecialChar \menuseparator
37160 Settings\SpecialChar \menuseparator
37163 ) specifies what character appears when a keyboard key is pressed.
37164 When the key for the character '·' is pressed, internally the command
37171 But this command is not available in a formula so that you would get LaTeX-erro
37173 With the changed encoding the right command is chosen automatically, depending
37174 on if the character was inserted into a formula or not.
37177 \begin_layout Standard
37178 The encoding of several characters is saved in definition files.
37179 For example the encoding
37183 is defined in the file
37187 which is in the installation folder of LaTeX.
37188 Encodings should only be changed via the LaTeX-preamble and not in the
37190 Otherwise documents could not be edited by other LyX users working on other
37194 \begin_layout Standard
37195 \begin_inset VSpace medskip
37198 Besides the centered dot, in this document the degree sign ° is defined
37199 with the following LaTeX-preamble line so that it can be directly inserted
37203 \begin_layout Standard
37208 DeclareInputtext{176}{
37218 f\SpecialChar \textcompwordmark{}
37222 \begin_layout Standard
37223 \begin_inset Newpage newpage
37229 \begin_layout Section
37232 \begin_inset Index idx
37235 \begin_layout Plain Layout
37244 \begin_layout Standard
37245 This section is a summary of the most important typographic rules, listed
37250 \begin_layout Plain Layout
37251 This collection was partly taken from the German semi-official dictionary
37253 \begin_inset Quotes eld
37257 \begin_inset Quotes erd
37261 \begin_inset CommandInset citation
37267 that lists some of the ISO rules.
37268 More rules are listed in
37269 \begin_inset CommandInset citation
37283 \begin_layout Itemize
37292 \begin_layout Plain Layout
37293 done with font styles, see
37294 \begin_inset CommandInset ref
37296 reference "sub:Font-Styles"
37305 , no matter if they appear in italic text: 30
37306 \begin_inset space \thinspace{}
37310 \begin_inset Newline newline
37313 Between the value and the unit is the smallest space, see
37314 \begin_inset CommandInset ref
37316 reference "sub:Predefined-Space"
37321 \begin_inset Newline newline
37324 This convention is automatically fulfilled when the command
37331 When it is entered to a formula, two boxes appear.
37332 In the first one the value is inserted, in the second one the unit, and
37334 \begin_inset Formula $\unit[30]{km/h}$
37338 \begin_inset space \thinspace{}
37348 is not a real LaTeX command but the command
37354 , therefore you cannot use it in TeX code.
37357 \begin_layout Itemize
37358 Percent and perthousand signs are set like physical units:
37359 \begin_inset Newline newline
37363 \begin_inset space \thinspace{}
37369 \begin_layout Itemize
37370 The degree sign follows directly on the value: 15°, but not when it is used
37372 \begin_inset space \thinspace{}
37378 \begin_layout Itemize
37379 In numbers with more than four digits the smallest space is inserted before
37380 every third digit to group them:
37390 \begin_inset space \thinspace{}
37394 \begin_inset space \thinspace{}
37400 \begin_layout Itemize
37401 For dimensions like 120×90×40
37402 \begin_inset space \thinspace{}
37405 cm the multiplication sign
37406 \begin_inset Quotes eld
37410 \begin_inset Quotes erd
37414 It is available either via the command
37422 Insert\SpecialChar \menuseparator
37423 Special Character\SpecialChar \menuseparator
37429 \begin_layout Itemize
37430 Functions with names consisting of several letters are set upright to avoid
37432 \begin_inset CommandInset ref
37434 reference "sub:Predefined-Functions"
37441 \begin_layout Itemize
37442 Indices consisting of several letters, are set upright:
37443 \begin_inset Formula $E_{\mathrm{kin}}$
37447 \begin_inset Newline newline
37450 Components of matrices are set italic:
37451 \begin_inset Formula $\hat{H}_{kl}$
37457 \begin_layout Itemize
37458 The differentiation/integration operator 'd', the Euler's number 'e' and
37459 the imaginary unit 'i' should be set upright, to avoid mixing them up with
37463 \begin_layout Itemize
37464 The character that denotes a
37468 transformation is inserted either by the command
37476 \begin_layout Plain Layout
37489 Insert\SpecialChar \menuseparator
37490 Special Character\SpecialChar \menuseparator
37491 Symbols\SpecialChar \menuseparator
37493 \begin_inset space ~
37499 \begin_inset Formula $\mathscr{F}$
37505 \begin_layout Standard
37506 \begin_inset Newpage newpage
37512 \begin_layout Section
37514 \begin_inset Index idx
37517 \begin_layout Plain Layout
37526 \begin_layout Standard
37527 Some characters and symbols can be created with several commands.
37528 Here is a list of the synonym commands:
37531 \begin_layout Standard
37532 \begin_inset VSpace bigskip
37536 \begin_inset space \hfill{}
37540 \begin_inset Tabular
37541 <lyxtabular version="3" rows="12" columns="2">
37542 <features tabularvalignment="middle">
37543 <column alignment="center" valignment="top" width="0pt">
37544 <column alignment="center" valignment="top" width="0pt">
37546 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
37549 \begin_layout Plain Layout
37555 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
37558 \begin_layout Plain Layout
37560 \begin_inset Note Note
37563 \begin_layout Plain Layout
37570 is only used as spacer.
37582 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
37585 \begin_layout Plain Layout
37593 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
37596 \begin_layout Plain Layout
37600 \begin_layout Plain Layout
37613 \begin_layout Plain Layout
37627 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
37630 \begin_layout Plain Layout
37638 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
37641 \begin_layout Plain Layout
37651 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
37654 \begin_layout Plain Layout
37662 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
37665 \begin_layout Plain Layout
37675 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
37678 \begin_layout Plain Layout
37686 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
37689 \begin_layout Plain Layout
37697 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
37700 \begin_layout Plain Layout
37708 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
37711 \begin_layout Plain Layout
37719 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
37722 \begin_layout Plain Layout
37730 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
37733 \begin_layout Plain Layout
37743 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
37746 \begin_layout Plain Layout
37754 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
37757 \begin_layout Plain Layout
37767 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
37770 \begin_layout Plain Layout
37778 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
37781 \begin_layout Plain Layout
37791 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
37794 \begin_layout Plain Layout
37802 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
37805 \begin_layout Plain Layout
37815 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
37818 \begin_layout Plain Layout
37826 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
37829 \begin_layout Plain Layout
37837 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
37840 \begin_layout Plain Layout
37848 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
37851 \begin_layout Plain Layout
37863 \begin_inset space \hfill{}
37867 \begin_inset Tabular
37868 <lyxtabular version="3" rows="12" columns="2">
37869 <features tabularvalignment="middle">
37870 <column alignment="center" valignment="top" width="0pt">
37871 <column alignment="center" valignment="top" width="0pt">
37873 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
37876 \begin_layout Plain Layout
37882 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
37885 \begin_layout Plain Layout
37893 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
37896 \begin_layout Plain Layout
37904 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
37907 \begin_layout Plain Layout
37919 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
37922 \begin_layout Plain Layout
37930 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
37933 \begin_layout Plain Layout
37943 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
37946 \begin_layout Plain Layout
37954 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
37957 \begin_layout Plain Layout
37967 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
37970 \begin_layout Plain Layout
37978 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
37981 \begin_layout Plain Layout
37989 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
37992 \begin_layout Plain Layout
38000 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
38003 \begin_layout Plain Layout
38011 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
38014 \begin_layout Plain Layout
38022 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
38025 \begin_layout Plain Layout
38035 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
38038 \begin_layout Plain Layout
38046 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
38049 \begin_layout Plain Layout
38059 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
38062 \begin_layout Plain Layout
38070 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
38073 \begin_layout Plain Layout
38083 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
38086 \begin_layout Plain Layout
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38187 The LaTeX Companion
38190 Addison Wesley, 2004
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38196 LatexCommand bibitem
38202 \begin_inset CommandInset href
38205 target "ftp://ftp.dante.de/tex-archive/info/math/voss/mathmode/Mathmode.pdf"
38209 of LaTeX's math abilities
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38253 \begin_inset CommandInset href
38256 target "ftp://ftp.dante.de/tex-archive/info/symbols/comprehensive/symbols-a4.pdf"
38260 of all symbols available with LaTeX-packages
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38274 name "Documentation"
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38279 of the LaTeX-package
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38308 target "http://www.tug.org/applications/hyperref/ftp/doc/manual.pdf"
38312 of the LaTeX-package
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38321 Packages ! hyperref
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38341 target "http://www.ctan.org/tex-archive/macros/latex/contrib/mhchem/mhchem.pdf"
38345 of the LaTeX-package
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38420 Auflage, Duden 2001
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38432 \begin_inset CommandInset href
38435 target "http://physics.nist.gov/Document/checklist.pdf"
38439 for reviewing manuscripts
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