1 #LyX 2.1 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 % solves the following problem:
27 % If the dection number consits of too many numerals the section heading
28 % will be printed in the TOC without a space between it and the section number.
29 % As solution more space between the number and the heading is inserted:
30 \renewcommand{\l@subsection}{\@dottedtocline{2}{1.5em}{2.8em}}
31 \renewcommand{\l@subsubsection}{\@dottedtocline{3}{4.3em}{3.6em}}
33 % increase link area for cross-references and autoname them,
34 \AtBeginDocument{\renewcommand{\ref}[1]{\mbox{\autoref{#1}}}}
35 \@ifundefined{extrasenglish}{\usepackage[english]{babel}}{}
36 \addto\extrasenglish{%
37 \renewcommand*{\equationautorefname}[1]{}%
38 \renewcommand{\sectionautorefname}{sec.\negthinspace}%
39 \renewcommand{\subsectionautorefname}{sec.\negthinspace}%
40 \renewcommand{\subsubsectionautorefname}{sec.\negthinspace}%
43 % don't load packages twice
44 % see first footnote in sec. 9.3
45 \@ifundefined{textcolor}{\usepackage{color}}{}
47 % the pages of the TOC are numbered roman
48 % and a PDF-bookmark for the TOC is added
50 \let\myTOC\tableofcontents
51 \renewcommand{\tableofcontents}{%
53 \pdfbookmark[1]{\contentsname}{}
56 \pagenumbering{arabic}}
58 % insert additional vertical space of 1.5 mm between footnotes,
60 \renewcommand{\footnote}[1]{\myFoot{#1\vspace{1.5mm}}}
62 % provides caption formatting
63 \setkomafont{captionlabel}{\bfseries}
65 % enables calculation of values
68 % for multiple columns used in sec. 24.7
74 % for the Fourier transformation symbol
77 % define a color, used in sec.9.3
78 \definecolor{darkgreen}{cmyk}{0.5, 0, 1, 0.5}
80 % declare operators (see sec. 10.4 and sec. 15.2)
81 \DeclareMathOperator*{\Lozenge}{\blacklozenge}
82 \DeclareMathOperator{\sgn}{sgn}
84 % example definitions for sec. 20.1
85 \newcommand{\gr}{\Longrightarrow}
86 \newcommand{\us}[1]{\underline{#1}}
87 \newcommand{\fb}[3]{\framebox#1#2{$#3$}}
88 \newcommand{\cb}[3][white]{\fcolorbox{#2}{#1}{$#3$}}
89 \newcommand{\fracS}[3][]{\genfrac{}{}{#1}{}{#2}{#3}}
91 % example macro from sec. 19.4
92 %\def\tagform@#1{\maketag@@@{|#1|}}
94 % macro from sec. 10.2
95 \def\clap#1{\hbox to 0pt{\hss #1\hss}}
96 \def\mathclap {\mathpalette \mathclapinternal}
97 \def\mathclapinternal #1#2{\clap{$\mathsurround =0pt #1{#2}$}}
100 % ------------------------------------
101 % used to check for needed LaTeX packages
104 % check for package eurosym
105 % used for the Euro symbol
107 \IfFileExists{eurosym.sty}
108 {\usepackage[gennarrow]{eurosym}
109 \setboolean{eurosym}{true}}
110 {\setboolean{eurosym}{false}}
112 % check for package braket
113 % used for physical vectors
115 \IfFileExists{braket.sty}
117 \setboolean{braket}{true}}
118 {\setboolean{braket}{false}}
120 % check for package cancel
122 \IfFileExists{cancel.sty}
123 {\setboolean{cancel}{true}}
124 {\setboolean{cancel}{false}}
126 % check for package upgreek
128 \IfFileExists{upgreek.sty}
129 {\usepackage{upgreek}
130 \setboolean{upgreek}{true}}
131 {\setboolean{upgreek}{false}}
133 \options bibliography=totoc,index=totoc,BCOR7.5mm,titlepage,captions=tableheading
134 \use_default_options false
135 \maintain_unincluded_children false
137 \language_package default
142 \font_typewriter default
144 \font_default_family default
145 \use_non_tex_fonts false
151 \default_output_format default
153 \bibtex_command default
154 \index_command default
158 \pdf_title "LyX's Math Manual"
159 \pdf_author "LyX Team, Uwe Stöhr"
160 \pdf_subject "LyX-documentation about math"
161 \pdf_keywords "LyX, Mathed"
163 \pdf_bookmarksnumbered true
164 \pdf_bookmarksopen true
165 \pdf_bookmarksopenlevel 1
166 \pdf_breaklinks false
170 \pdf_pdfusetitle false
171 \pdf_quoted_options "linkcolor=black, citecolor=black, urlcolor=blue, filecolor=blue, pdfpagelayout=OneColumn, pdfnewwindow=true, pdfstartview=XYZ, plainpages=false"
174 \use_package amsmath 2
175 \use_package amssymb 2
176 \use_package cancel 1
178 \use_package mathdots 1
179 \use_package mathtools 0
180 \use_package mhchem 1
181 \use_package stackrel 0
182 \use_package stmaryrd 0
183 \use_package undertilde 0
185 \cite_engine_type default
189 \paperorientation portrait
193 \notefontcolor #0000ff
200 \paragraph_separation skip
202 \quotes_language english
205 \paperpagestyle plain
209 \tracking_changes false
210 \output_changes false
213 \html_be_strict false
219 LyX's detailed Math manual
227 \begin_layout Plain Layout
229 If you have comments or error corrections, please send them to the LyX Documenta
233 \begin_inset CommandInset href
235 name "lyx-docs@lists.lyx.org"
236 target "lyx-docs@lists.lyx.org?subject=LyX's Math manual"
247 \begin_inset Note Note
250 \begin_layout Plain Layout
257 \begin_inset Newline newline
261 \begin_inset Newline newline
269 \begin_layout Standard
270 \begin_inset CommandInset toc
271 LatexCommand tableofcontents
278 \begin_layout Standard
279 \begin_inset Note Note
282 \begin_layout Plain Layout
283 To export this document to PDF, PS or DVI the LaTeX-packages
285 braket, cancel, eurosym, mathdots, mhchem
292 If they are not installed the document can be exported anyway but the sections
293 where the packages are required will not appear in the output.
298 ; if it is not installed, this file cannot be exported.
301 \begin_layout Plain Layout
302 The latest PDF-version of this document can be found here:
303 \begin_inset Newline newline
308 http://wiki.lyx.org/LyX/DocumentationDevelopment#Math
316 \begin_layout Standard
317 \begin_inset Newpage newpage
323 \begin_layout Section
327 \begin_layout Standard
328 This document explains LyX's math features and is furthermore a collection
329 of LaTeX-commands used for mathematical characters and constructs.
330 The explanations are designed for the usage of commands.
331 It is therefore required that you have read the section
342 \begin_layout Standard
343 Most of the characters and many constructs explained in this manual are
344 also accessible via the menu
348 \SpecialChar \menuseparator
364 But everybody who has to write lots of formulas will notice that it is
365 much faster to use commands instead of the math toolbar.
366 Therefore this manual is focused on commands but also mentions the correspondin
367 g toolbar buttons when available.
370 \begin_layout Standard
371 If not specially mentioned the commands are only available within formulas.
372 To be able to use all commands explained in this document, the option
376 must be checked in the document settings (menu
378 Document\SpecialChar \menuseparator
379 Settings\SpecialChar \menuseparator
390 \begin_layout Plain Layout
393 Use AMS math package automatically
399 \begin_layout Plain Layout
408 -math when math constructs are found that are supported by LyX.
416 \begin_layout Standard
417 This document doesn't list all
421 \begin_layout Plain Layout
434 \begin_layout Plain Layout
439 \begin_layout Plain Layout
448 -math commands is in the file
451 \begin_inset CommandInset href
454 target "ftp://ftp.ams.org/pub/tex/doc/amstex/amsguide.pdf"
460 , which is part of every LaTeX standard installation.
465 for lucidity reasons.
468 \begin_layout Section
472 \begin_layout Standard
473 To create an inline formula
474 \begin_inset Index idx
477 \begin_layout Plain Layout
483 that is embedded into a text line, use one of the shortcuts
489 or the toolbar button
490 \begin_inset Graphics
491 filename ../images/math-mode.png
497 \begin_inset Newline newline
500 To create a display style formula
501 \begin_inset Index idx
504 \begin_layout Plain Layout
505 Formula ! display style
510 which will appear bigger, has a different format, and will be in a separate
511 paragraph, use one of these shortcuts:
520 \begin_layout Standard
521 To change a display style formula to an inline formula, set the cursor into
522 the formula and use one of the shortcuts
530 Edit\SpecialChar \menuseparator
531 Math\SpecialChar \menuseparator
535 The same way is used to change an inline formula to a display style formula.
538 \begin_layout Standard
539 To display parts of an inline formula in the size of a display style formula,
547 \begin_inset Index idx
550 \begin_layout Plain Layout
559 Then a new blue box appears in which the desired formula part is inserted.
562 \begin_layout Standard
563 Only inline formulas are allowed inside tables.
566 \begin_layout Standard
571 can be turned on in the menu
573 View\SpecialChar \menuseparator
577 When you click there on
578 \begin_inset Quotes eld
582 \begin_inset Quotes erd
585 the toolbar will be shown permanently at the bottom; this state is visualized
590 menu with a checkmark.
591 When you click in this state again on
592 \begin_inset Quotes eld
596 \begin_inset Quotes erd
607 is only shown when the cursor is within a formula; this state is visualized
608 by the renaming of the menu entry from
609 \begin_inset Quotes eld
613 \begin_inset Quotes erd
617 \begin_inset Quotes eld
625 \begin_inset Quotes erd
631 \begin_layout Standard
633 \begin_inset Index idx
636 \begin_layout Plain Layout
642 is invoked by pressing the toolbar button
643 \begin_inset Graphics
644 filename ../images/ert-insert.png
651 Insert\SpecialChar \menuseparator
656 \begin_layout Plain Layout
672 \begin_inset Note Note
675 \begin_layout Plain Layout
676 In LyX there are three
677 \begin_inset Quotes eld
681 \begin_inset Quotes erd
684 that appear in the output with sub- and superscript letters: TeX, LaTeX
688 \begin_layout Plain Layout
689 To avoid that these names are recognized as proper names, a TeX-brace pair
698 \begin_layout Standard
699 To change the LaTeX-preamble
700 \begin_inset Index idx
703 \begin_layout Plain Layout
711 Document\SpecialChar \menuseparator
712 Settings\SpecialChar \menuseparator
717 \begin_layout Plain Layout
733 \begin_layout Standard
734 To edit matrices, case differentiations and multiline formulas subsequently,
737 Edit\SpecialChar \menuseparator
742 Edit\SpecialChar \menuseparator
744 \begin_inset space \thinspace{}
748 \begin_inset space \thinspace{}
758 When lines and columns are swapped via the menu, the column or line where
759 the cursor is in is exchanged with the column to the right or the line
761 Is the cursor in the last column or row, the exchange is done with the
762 column to the left or the line above.
765 \begin_layout Standard
766 To write text in formulas
770 \begin_layout Plain Layout
771 For multiline formulas the command
778 \begin_inset CommandInset ref
780 reference "sub:Text-in-multiline"
794 \begin_inset Index idx
797 \begin_layout Plain Layout
804 \begin_inset Index idx
807 \begin_layout Plain Layout
814 This mode is invoked with the shortcut
820 or by the insertion of the command
827 \begin_inset Index idx
830 \begin_layout Plain Layout
839 The text appears black in LyX and can therefore be distinguished from the
840 other formula parts which appear blue.
841 In the output mathematical text is set upright, in contrary to other formula
845 \begin_layout Subsection*
849 \begin_layout Standard
850 Most of the LaTeX-commands for math constructs have the following scheme:
853 \begin_layout Standard
869 \begin_layout Standard
870 A command always starts with a backslash
871 \begin_inset Quotes gld
881 \begin_inset Quotes grd
885 To omit optional arguments, also omit the associated brackets.
886 The braces around the required arguments are named in this document as
888 \begin_inset Index idx
891 \begin_layout Plain Layout
898 If you add in a formula a left brace to a command name, LyX automatically
900 In all other cases TeX-braces are created in formulas with the command
908 TeX-braces appear red in LyX, in contrary to normal braces which appear
910 In TeX-mode no command is needed to get TeX-braces.
911 TeX-braces don't appear in the output.
914 \begin_layout Standard
915 When commands without arguments, like commands for symbols are entered in
916 TeX-mode, a space character must
920 be behind the command to end it.
921 This space doesn't appear in the output.
922 When the space should appear in the output, the space must be followed
923 by a protected space in normal text.
926 \begin_layout Standard
927 A protected space is inserted with
930 arg "command-alternatives space-insert protected ; math-space"
936 \begin_layout Subsection*
937 \begin_inset Newpage newpage
943 \begin_layout Itemize
945 \begin_inset space \textvisiblespace{}
948 denotes a space character to be input.
951 \begin_layout Itemize
953 \begin_inset Formula $\to$
956 denotes the usage of the corresponding arrow key on the keyboard.
961 key can often be used instead of
962 \begin_inset Formula $\to$
966 \begin_inset Formula $\downarrow$
974 \begin_inset Formula $\leftarrow$
978 \begin_inset Formula $\uparrow$
984 \begin_layout Subsection*
988 \begin_layout Standard
990 \begin_inset Float table
996 \begin_layout Plain Layout
998 \begin_inset Caption Standard
1000 \begin_layout Plain Layout
1001 \begin_inset CommandInset label
1003 name "tab:Available-units"
1015 \begin_layout Plain Layout
1017 \begin_inset Tabular
1018 <lyxtabular version="3" rows="13" columns="2">
1019 <features rotate="0" tabularvalignment="middle">
1020 <column alignment="center" valignment="top">
1021 <column alignment="center" valignment="top">
1023 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
1026 \begin_layout Plain Layout
1032 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
1035 \begin_layout Plain Layout
1043 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
1046 \begin_layout Plain Layout
1052 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
1055 \begin_layout Plain Layout
1063 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
1066 \begin_layout Plain Layout
1072 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
1075 \begin_layout Plain Layout
1083 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
1086 \begin_layout Plain Layout
1092 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
1095 \begin_layout Plain Layout
1097 \begin_inset space \thinspace{}
1101 \begin_inset space \thinspace{}
1111 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
1114 \begin_layout Plain Layout
1120 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
1123 \begin_layout Plain Layout
1125 \begin_inset space \thinspace{}
1129 \begin_inset space \thinspace{}
1139 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
1142 \begin_layout Plain Layout
1148 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
1151 \begin_layout Plain Layout
1153 \begin_inset space \thinspace{}
1157 \begin_inset space \thinspace{}
1167 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
1170 \begin_layout Plain Layout
1176 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
1179 \begin_layout Plain Layout
1181 \begin_inset space \thinspace{}
1185 \begin_inset space \thinspace{}
1195 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
1198 \begin_layout Plain Layout
1204 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
1207 \begin_layout Plain Layout
1209 \begin_inset space \thinspace{}
1213 \begin_inset space \thinspace{}
1223 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
1226 \begin_layout Plain Layout
1232 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
1235 \begin_layout Plain Layout
1237 \begin_inset space \thinspace{}
1241 \begin_inset Formula $\approx$
1245 \begin_inset space \thinspace{}
1255 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
1258 \begin_layout Plain Layout
1264 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
1267 \begin_layout Plain Layout
1269 \begin_inset space \thinspace{}
1273 \begin_inset space \thinspace{}
1283 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
1286 \begin_layout Plain Layout
1292 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
1295 \begin_layout Plain Layout
1299 \begin_inset Quotes eld
1305 \begin_inset Quotes erd
1315 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
1318 \begin_layout Plain Layout
1324 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
1327 \begin_layout Plain Layout
1329 \begin_inset Quotes eld
1337 \begin_inset Quotes erd
1347 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
1350 \begin_layout Plain Layout
1356 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
1359 \begin_layout Plain Layout
1361 \begin_inset space \thinspace{}
1365 \begin_inset Formula $\nicefrac{1}{18}$
1369 \begin_inset space \thinspace{}
1390 \begin_layout Standard
1391 \begin_inset Newpage newpage
1397 \begin_layout Section
1401 \begin_layout Subsection
1403 \begin_inset Index idx
1406 \begin_layout Plain Layout
1413 \begin_inset Index idx
1416 \begin_layout Plain Layout
1423 \begin_inset Index idx
1426 \begin_layout Plain Layout
1431 \begin_layout Plain Layout
1442 \begin_layout Plain Layout
1455 \begin_inset Index idx
1458 \begin_layout Plain Layout
1463 \begin_layout Plain Layout
1474 \begin_layout Plain Layout
1489 \begin_layout Standard
1490 Indices are created with an underscore
1491 \begin_inset Quotes eld
1495 \begin_inset Quotes erd
1498 or via the math toolbar button
1499 \begin_inset Graphics
1500 filename ../images/math-subscript.png
1505 , exponents with a caret
1506 \begin_inset Quotes eld
1510 \begin_inset Quotes erd
1513 or via the math toolbar button
1514 \begin_inset Graphics
1515 filename ../images/math-superscript.png
1523 \begin_layout Standard
1525 \begin_inset Tabular
1526 <lyxtabular version="3" rows="4" columns="2">
1527 <features rotate="0" tabularvalignment="middle">
1528 <column alignment="center" valignment="top" width="0pt">
1529 <column alignment="center" valignment="top" width="0pt">
1531 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
1534 \begin_layout Plain Layout
1540 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
1543 \begin_layout Plain Layout
1545 \begin_inset Note Note
1548 \begin_layout Plain Layout
1555 is only used as spacer.
1567 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
1570 \begin_layout Plain Layout
1576 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
1579 \begin_layout Plain Layout
1580 \begin_inset Formula $B_{V}$
1590 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
1593 \begin_layout Plain Layout
1599 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
1602 \begin_layout Plain Layout
1603 \begin_inset Formula $\raisebox{5mm}{}B^{V}$
1613 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
1616 \begin_layout Plain Layout
1618 \begin_inset space \textvisiblespace{}
1626 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
1629 \begin_layout Plain Layout
1630 \begin_inset Formula $\raisebox{5mm}{}B^{A}$
1646 \begin_layout Standard
1647 As the caret is in some languages an accent, vowels will be accentuated
1648 in this case and not set as exponents
1652 \begin_layout Plain Layout
1653 Depending on the used keyboard settings this can also happen for characters
1660 To get exponents in this case, press
1664 after the caret as in the last example.
1667 \begin_layout Subsection
1669 \begin_inset CommandInset label
1671 name "sub:Fractions"
1676 \begin_inset Index idx
1679 \begin_layout Plain Layout
1688 \begin_layout Standard
1689 Fractions are generated with the command
1696 \begin_inset Index idx
1699 \begin_layout Plain Layout
1707 or via the math toolbar button
1708 \begin_inset Graphics
1709 filename ../images/math/frac.png
1715 The font size is adjusted automatically, depending on whether the fraction
1716 is in an inline or display style formula.
1717 With the math toolbar button
1718 \begin_inset Graphics
1719 filename ../images/math/frac-square.png
1724 you can select different fraction types.
1727 \begin_layout Standard
1735 \begin_inset Index idx
1738 \begin_layout Plain Layout
1746 a fraction can be created that always has the size of a display style formula.
1754 \begin_inset Index idx
1757 \begin_layout Plain Layout
1765 the fraction appears always with the size of an inline formula.
1769 \begin_layout Standard
1770 A line with the fraction
1771 \begin_inset Formula $\frac{1}{2}$
1774 that was created with the command
1783 \begin_layout Standard
1784 A line with the fraction
1785 \begin_inset Formula $\dfrac{1}{2}$
1788 that was created with the command
1797 \begin_layout Standard
1799 \begin_inset Tabular
1800 <lyxtabular version="3" rows="4" columns="2">
1801 <features rotate="0" tabularvalignment="middle">
1802 <column alignment="center" valignment="top" width="0pt">
1803 <column alignment="center" valignment="top" width="0pt">
1805 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
1808 \begin_layout Plain Layout
1814 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
1817 \begin_layout Plain Layout
1819 \begin_inset Note Note
1822 \begin_layout Plain Layout
1829 is only used as spacer.
1841 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
1844 \begin_layout Plain Layout
1848 \begin_inset space \textvisiblespace{}
1852 \begin_inset Formula $\downarrow$
1860 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
1863 \begin_layout Plain Layout
1864 \begin_inset Formula $\raisebox{4.5mm}{}\frac{A}{B}\raisebox{-2.5mm}{}$
1874 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
1877 \begin_layout Plain Layout
1881 \begin_inset space \textvisiblespace{}
1885 \begin_inset Formula $\downarrow$
1893 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
1896 \begin_layout Plain Layout
1897 \begin_inset Formula $\raisebox{7mm}{}\dfrac{A}{B}\raisebox{-4mm}{}$
1907 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
1910 \begin_layout Plain Layout
1914 \begin_inset space \textvisiblespace{}
1920 \begin_inset space \textvisiblespace{}
1924 \begin_inset Formula $\downarrow$
1928 \begin_inset Formula $\downarrow\downarrow$
1936 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
1939 \begin_layout Plain Layout
1940 \begin_inset Formula $\raisebox{8mm}{}\dfrac{e^{\frac{1}{2}}}{3}\raisebox{-4mm}{}$
1956 \begin_layout Standard
1957 \begin_inset VSpace bigskip
1961 \begin_inset Newpage newpage
1964 For nested fractions the command
1971 \begin_inset Index idx
1974 \begin_layout Plain Layout
1984 \begin_inset VSpace -3mm
1990 \begin_layout Standard
1991 \begin_inset Formula
1993 \textrm{created with \textbf{\textbackslash frac}} & & \textrm{created with \textbf{\textbackslash cfrac}}\\
1994 \frac{A}{B+\frac{C+\frac{E}{F}}{D}} & & \cfrac{A}{B+\cfrac{C+\cfrac{E}{F}}{D}}
2002 \begin_layout Standard
2003 The command for the example above is:
2006 \begin_layout Standard
2012 \begin_inset space \textvisiblespace{}
2016 \begin_inset Formula $\downarrow$
2022 \begin_inset space \textvisiblespace{}
2028 \begin_inset space \textvisiblespace{}
2032 \begin_inset Formula $\downarrow$
2036 \begin_inset Formula $\downarrow$
2042 \begin_layout Standard
2043 \begin_inset VSpace medskip
2049 \begin_layout Standard
2056 sets the fraction always in the size of a displayed formula, also when
2057 it is part of another fraction.
2060 \begin_layout Standard
2061 It is possible to specify the alignment of the numerator.
2068 is used to left align it, the command
2081 centers the numerator.
2082 These fractions demonstrate the different alignments:
2085 \begin_layout Standard
2088 \begin_inset Formula
2090 \cfrac[l]{A}{B+C}\,,\,\cfrac{A}{B+C}\,,\,\cfrac[r]{A}{B+C}
2098 \begin_layout Standard
2099 \begin_inset Note Greyedout
2102 \begin_layout Plain Layout
2119 are no real LaTeX commands but represent the command
2123 cfrac[alignment]{numerator}{denominator}
2126 Therefore you cannot use them in TeX code.
2134 \begin_layout Standard
2135 \begin_inset VSpace medskip
2138 It is often advantageous to combine
2151 \begin_inset Formula
2153 \cfrac{A}{B+\cfrac{C+\frac{E}{F}}{D}}
2161 \begin_layout Standard
2162 For inline fractions with a sloped fraction stroke you can use the command
2170 \begin_inset Index idx
2173 \begin_layout Plain Layout
2182 \begin_inset Formula $\nicefrac{5}{31}$
2192 \begin_inset Index idx
2195 \begin_layout Plain Layout
2204 \begin_inset Formula $\unitfrac{5}{31}$
2207 There is furthermore the command
2213 that offers to write a fraction in combination with a number:
2214 \begin_inset Formula $\unitfrac[2]{1}{3}$
2220 \begin_layout Standard
2221 \begin_inset Note Greyedout
2224 \begin_layout Plain Layout
2235 is not a real LaTeX command but the command
2236 \begin_inset Newline newline
2243 unitfrac[number]{numerator}{denominator}
2246 Therefore you cannot use it in TeX code.
2254 \begin_layout Standard
2255 How to define own fractions where the fraction stroke can be changed, is
2257 \begin_inset CommandInset ref
2259 reference "sub:Self-defined-Fractions"
2266 \begin_layout Standard
2267 \begin_inset Newpage newpage
2273 \begin_layout Subsection
2275 \begin_inset Index idx
2278 \begin_layout Plain Layout
2287 \begin_layout Standard
2288 Square roots are created with
2295 \begin_inset Index idx
2298 \begin_layout Plain Layout
2306 or the math toolbar button
2307 \begin_inset Graphics
2308 filename ../images/math/sqrt.png
2313 , all other roots with the command
2320 \begin_inset Index idx
2323 \begin_layout Plain Layout
2331 or with the math toolbar button
2332 \begin_inset Graphics
2333 filename ../images/math/root.png
2341 \begin_layout Standard
2343 \begin_inset Tabular
2344 <lyxtabular version="3" rows="3" columns="2">
2345 <features rotate="0" tabularvalignment="middle">
2346 <column alignment="center" valignment="top" width="0pt">
2347 <column alignment="center" valignment="top" width="0pt">
2349 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
2352 \begin_layout Plain Layout
2358 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
2361 \begin_layout Plain Layout
2363 \begin_inset Note Note
2366 \begin_layout Plain Layout
2373 is only used as spacer.
2385 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
2388 \begin_layout Plain Layout
2392 \begin_inset space \textvisiblespace{}
2400 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
2403 \begin_layout Plain Layout
2404 \begin_inset Formula $\raisebox{4.5mm}{}\sqrt{A-B}$
2414 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
2417 \begin_layout Plain Layout
2421 \begin_inset space \textvisiblespace{}
2425 \begin_inset Formula $\downarrow$
2433 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
2436 \begin_layout Plain Layout
2437 \begin_inset Formula $\raisebox{4.5mm}{}\sqrt[3]{A-B}$
2453 \begin_layout Standard
2454 A square root can also be created with
2460 when the root index field is left empty.
2463 \begin_layout Standard
2464 With certain indices the distance to the root is too small, like in this
2466 \begin_inset Formula $\sqrt[\beta]{B}$
2470 \begin_inset Newline newline
2474 \begin_inset Formula $\beta$
2478 To avoid this, the commands
2485 \begin_inset Index idx
2488 \begin_layout Plain Layout
2503 \begin_inset Index idx
2506 \begin_layout Plain Layout
2514 are used with the following scheme:
2517 \begin_layout Standard
2531 \begin_layout Standard
2532 Distance is the number of Big Points (unit bp;
2533 \begin_inset Formula $\mathrm{72\, bp=1\, inch}$
2536 ), that the index should be moved to the left or top, resp..
2537 The commands are written to the index.
2538 This way the command
2539 \begin_inset Newline newline
2549 \begin_inset Formula $\to$
2555 \begin_inset Formula $\to$
2561 \begin_inset space \textvisiblespace{}
2565 \begin_inset Formula $\to$
2569 \begin_inset Newline newline
2574 produces a correct typeset formula:
2575 \begin_inset Formula $\sqrt[\leftroot{-1}\uproot{2}\beta]{B}$
2581 \begin_layout Subsection
2582 Binomial Coefficients
2583 \begin_inset Index idx
2586 \begin_layout Plain Layout
2587 Binomial coefficients
2595 \begin_layout Standard
2596 Binomial coefficients are inserted with the command
2603 \begin_inset Index idx
2606 \begin_layout Plain Layout
2614 or with the submenu of the math toolbar button
2615 \begin_inset Graphics
2616 filename ../images/math/frac-square.png
2634 there are the commands
2641 \begin_inset Index idx
2644 \begin_layout Plain Layout
2659 \begin_inset Index idx
2662 \begin_layout Plain Layout
2671 For other brackets around binomial coeficients there are the commands
2678 \begin_inset Index idx
2681 \begin_layout Plain Layout
2696 \begin_inset Index idx
2699 \begin_layout Plain Layout
2710 \begin_layout Standard
2712 \begin_inset Tabular
2713 <lyxtabular version="3" rows="6" columns="2">
2714 <features rotate="0" tabularvalignment="middle">
2715 <column alignment="center" valignment="top" width="0pt">
2716 <column alignment="center" valignment="top" width="0pt">
2718 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
2721 \begin_layout Plain Layout
2727 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
2730 \begin_layout Plain Layout
2732 \begin_inset Note Note
2735 \begin_layout Plain Layout
2742 is only used as spacer.
2754 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
2757 \begin_layout Plain Layout
2761 \begin_inset space \textvisiblespace{}
2765 \begin_inset Formula $\downarrow$
2773 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
2776 \begin_layout Plain Layout
2777 \begin_inset Formula $\raisebox{5mm}{}\binom{A}{B}\raisebox{-2.5mm}{}$
2787 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
2790 \begin_layout Plain Layout
2794 \begin_inset space \textvisiblespace{}
2798 \begin_inset Formula $\downarrow$
2806 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
2809 \begin_layout Plain Layout
2810 \begin_inset Formula $\raisebox{5mm}{}\dbinom{A}{B}\raisebox{-2.5mm}{}$
2820 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
2823 \begin_layout Plain Layout
2827 \begin_inset space \textvisiblespace{}
2831 \begin_inset Formula $\downarrow$
2839 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
2842 \begin_layout Plain Layout
2843 \begin_inset Formula $\raisebox{5mm}{}\tbinom{A}{B}\raisebox{-2.5mm}{}$
2853 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
2856 \begin_layout Plain Layout
2860 \begin_inset space \textvisiblespace{}
2864 \begin_inset Formula $\downarrow$
2872 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
2875 \begin_layout Plain Layout
2876 \begin_inset Formula $\raisebox{5mm}{}{A \brack B}\raisebox{-2.5mm}{}$
2886 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
2889 \begin_layout Plain Layout
2893 \begin_inset space \textvisiblespace{}
2897 \begin_inset Formula $\downarrow$
2905 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
2908 \begin_layout Plain Layout
2909 \begin_inset Formula $\raisebox{5mm}{}{A \brace B}\raisebox{-2.5mm}{}$
2925 \begin_layout Subsection
2926 Case Differentiations
2927 \begin_inset Index idx
2930 \begin_layout Plain Layout
2931 Case differentiations
2939 \begin_layout Standard
2941 \begin_inset Tabular
2942 <lyxtabular version="3" rows="3" columns="2">
2943 <features rotate="0" tabularvalignment="middle">
2944 <column alignment="center" valignment="top" width="0pt">
2945 <column alignment="center" valignment="top" width="0pt">
2947 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
2950 \begin_layout Plain Layout
2956 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
2959 \begin_layout Plain Layout
2967 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
2970 \begin_layout Plain Layout
2974 \begin_inset space \textvisiblespace{}
2978 \begin_inset Formula $\to$
2982 \begin_inset Index idx
2985 \begin_layout Plain Layout
2998 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
3001 \begin_layout Plain Layout
3002 \begin_inset Formula $\begin{cases}
3013 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
3016 \begin_layout Plain Layout
3020 \begin_inset space \textvisiblespace{}
3026 arg "newline-insert newline"
3034 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
3037 \begin_layout Plain Layout
3038 \begin_inset Formula $\begin{cases}
3039 A & \textrm{for }x>0\\
3040 B & \textrm{for }x=0
3057 \begin_layout Standard
3064 or pressing the math toolbar button
3065 \begin_inset Graphics
3066 filename ../images/math/cases.png
3071 you can create new lines with the shortcut
3074 arg "newline-insert newline"
3077 or the table toolbar button
3078 \begin_inset Graphics
3079 filename ../images/tabular-feature_append-row.png
3087 \begin_layout Standard
3094 is also available via the menu
3096 Insert\SpecialChar \menuseparator
3097 Math\SpecialChar \menuseparator
3103 \begin_layout Subsection
3105 \begin_inset Index idx
3108 \begin_layout Plain Layout
3117 \begin_layout Standard
3125 \begin_inset Index idx
3128 \begin_layout Plain Layout
3136 every character can be displayed canceled.
3137 The characters are quasi accentuated by a slash.
3140 \begin_layout Standard
3142 \begin_inset Tabular
3143 <lyxtabular version="3" rows="4" columns="2">
3144 <features rotate="0" tabularvalignment="middle">
3145 <column alignment="center" valignment="top" width="0pt">
3146 <column alignment="center" valignment="top" width="0pt">
3148 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
3151 \begin_layout Plain Layout
3157 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
3160 \begin_layout Plain Layout
3168 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
3171 \begin_layout Plain Layout
3179 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
3182 \begin_layout Plain Layout
3183 \begin_inset Formula $\not=$
3193 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
3196 \begin_layout Plain Layout
3206 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
3209 \begin_layout Plain Layout
3210 \begin_inset Formula $\not\le$
3220 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
3223 \begin_layout Plain Layout
3233 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
3236 \begin_layout Plain Layout
3237 \begin_inset Formula $\not\parallel$
3253 \begin_layout Standard
3254 The last example shows that not all negations look good.
3255 Therefore there are special commands for some negations (see
3256 \begin_inset CommandInset ref
3258 reference "sub:Mathematical-Symbols"
3263 \begin_inset CommandInset ref
3265 reference "sec:Relations"
3272 \begin_layout Subsection
3274 \begin_inset CommandInset label
3276 name "sub:Placeholders"
3281 \begin_inset Index idx
3284 \begin_layout Plain Layout
3291 \begin_inset Index idx
3294 \begin_layout Plain Layout
3295 Chemical characters ! Isotopes
3301 \begin_inset Index idx
3304 \begin_layout Plain Layout
3309 \begin_layout Plain Layout
3320 \begin_layout Plain Layout
3335 \begin_layout Standard
3337 \begin_inset space \thinspace{}
3341 \begin_inset space \space{}
3348 \begin_layout Plain Layout
3349 Typesetting isotopes and chemical symbols is described in
3350 \begin_inset CommandInset ref
3352 reference "sub:Chemical-Symbols-and"
3361 the following problem occurs:
3364 \begin_layout Standard
3366 \begin_inset Tabular
3367 <lyxtabular version="3" rows="2" columns="2">
3368 <features rotate="0" tabularvalignment="middle">
3369 <column alignment="center" valignment="top" width="0pt">
3370 <column alignment="center" valignment="top" width="0pt">
3372 <cell alignment="center" valignment="top" usebox="none">
3375 \begin_layout Plain Layout
3376 Indices created with sub- and superscripts:
3381 <cell alignment="center" valignment="top" usebox="none">
3384 \begin_layout Plain Layout
3385 \begin_inset Formula $_{9}^{19}\mathrm{F}\raisebox{-3mm}{}$
3395 <cell alignment="center" valignment="top" usebox="none">
3398 \begin_layout Plain Layout
3404 <cell alignment="center" valignment="top" usebox="none">
3407 \begin_layout Plain Layout
3408 \begin_inset Formula $_{\phantom{1}9}^{19}\mathrm{F}$
3422 \begin_inset Note Note
3425 \begin_layout Plain Layout
3432 is only used as spacer.
3440 \begin_layout Standard
3441 The shorter index is by default placed below or above the first character
3442 of the longer index.
3443 To avoid this there is the command
3450 \begin_inset Index idx
3453 \begin_layout Plain Layout
3461 or the math toolbar button
3462 \begin_inset space \thinspace{}
3469 \begin_layout Plain Layout
3470 can be found in the submenu of the toolbar button
3471 \begin_inset Graphics
3472 filename ../images/math/space.png
3483 \begin_inset Graphics
3484 filename ../images/math/phantom.png
3489 that creates one or more phantom characters.
3496 a small blue box appears that is superposed with two red arrows.
3497 The arrows indicate that the complete width and height of the box content
3498 will be created as placeholder.
3499 Phantom characters are accordingly placeholders with the size of the characters.
3502 \begin_layout Standard
3504 \begin_inset Tabular
3505 <lyxtabular version="3" rows="4" columns="2">
3506 <features rotate="0" tabularvalignment="middle">
3507 <column alignment="center" valignment="top">
3508 <column alignment="center" valignment="top">
3510 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
3513 \begin_layout Plain Layout
3519 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
3522 \begin_layout Plain Layout
3524 \begin_inset Note Note
3527 \begin_layout Plain Layout
3534 is only used as spacer.
3546 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
3549 \begin_layout Plain Layout
3551 \begin_inset space \textvisiblespace{}
3557 \begin_inset space \textvisiblespace{}
3561 \begin_inset Formula $\to$
3565 \begin_inset space \textvisiblespace{}
3573 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
3576 \begin_layout Plain Layout
3577 \begin_inset Formula $\raisebox{4.5mm}{}{}_{\phantom{1}9}^{19}\mathrm{F}\raisebox{-2.5mm}{}$
3587 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
3590 \begin_layout Plain Layout
3592 \begin_inset space \textvisiblespace{}
3598 \begin_inset space \textvisiblespace{}
3602 \begin_inset Formula $\to$
3606 \begin_inset space \textvisiblespace{}
3614 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
3617 \begin_layout Plain Layout
3618 \begin_inset Formula $\raisebox{4.5mm}{}{}_{\phantom{23}9}^{235}\mathrm{F}\raisebox{-2.5mm}{}$
3628 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
3631 \begin_layout Plain Layout
3635 \begin_inset space \textvisiblespace{}
3641 \begin_inset space \textvisiblespace{}
3645 \begin_inset Formula $\to$
3649 \begin_inset space \textvisiblespace{}
3657 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
3660 \begin_layout Plain Layout
3661 \begin_inset Formula $\raisebox{4.5mm}{}\Lambda_{MMt}^{\phantom{ii}t}\raisebox{-2.5mm}{}$
3677 \begin_layout Standard
3678 Furthermore there are the commands
3685 \begin_inset Index idx
3688 \begin_layout Plain Layout
3697 \begin_inset space ~
3701 \begin_inset Graphics
3702 filename ../images/math/vphantom.png
3714 \begin_inset Index idx
3717 \begin_layout Plain Layout
3726 \begin_inset space ~
3730 \begin_inset Graphics
3731 filename ../images/math/hphantom.png
3743 creates only space for the maximal height of the characters in the box
3744 but not for its width.
3751 creates only space for the width of the box content.
3752 Therefore the boxes of both commands have only one red arrow.
3755 \begin_layout Standard
3756 For example the command
3761 \begin_inset space \textvisiblespace{}
3768 creates space for the height of the integral sign,
3772 \begin_layout Plain Layout
3779 creates an integral sign, see
3780 \begin_inset CommandInset ref
3782 reference "sub:Big-Operators"
3791 because this is the larger character.
3792 An example application is in
3793 \begin_inset CommandInset ref
3795 reference "sub:Multiline-Brackets"
3802 \begin_layout Standard
3803 Placeholders can also be used for text when they are inserted via the menu
3806 Insert\SpecialChar \menuseparator
3807 Formatting\SpecialChar \menuseparator
3813 \begin_layout Standard
3815 \begin_inset Newline newline
3819 \begin_inset Phantom Phantom
3822 \begin_layout Plain Layout
3831 \begin_layout Subsection
3833 \begin_inset Index idx
3836 \begin_layout Plain Layout
3843 \begin_inset Index idx
3846 \begin_layout Plain Layout
3847 Formula ! underlined
3855 \begin_layout Standard
3857 \begin_inset Tabular
3858 <lyxtabular version="3" rows="4" columns="2">
3859 <features rotate="0" tabularvalignment="middle">
3860 <column alignment="center" valignment="top" width="0pt">
3861 <column alignment="center" valignment="top" width="0pt">
3863 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
3866 \begin_layout Plain Layout
3872 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
3875 \begin_layout Plain Layout
3877 \begin_inset Note Note
3880 \begin_layout Plain Layout
3887 is only used as spacer.
3899 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
3902 \begin_layout Plain Layout
3906 \begin_inset space \textvisiblespace{}
3910 \begin_inset Index idx
3913 \begin_layout Plain Layout
3926 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
3929 \begin_layout Plain Layout
3930 \begin_inset Formula $\raisebox{5mm}{}\overline{A+B}$
3940 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
3943 \begin_layout Plain Layout
3947 \begin_inset space \textvisiblespace{}
3951 \begin_inset Index idx
3954 \begin_layout Plain Layout
3967 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
3970 \begin_layout Plain Layout
3971 \begin_inset Formula $\underline{A+B}\raisebox{-2.5mm}{}$
3981 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
3984 \begin_layout Plain Layout
3988 \begin_inset space \textvisiblespace{}
3994 \begin_inset space \textvisiblespace{}
4002 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
4005 \begin_layout Plain Layout
4006 \begin_inset Formula $\raisebox{5mm}{}\overline{\underline{A+B}}\raisebox{-2.5mm}{}$
4022 \begin_layout Standard
4023 In the last example it doesn't matter if first
4038 \begin_layout Standard
4039 To double underline use
4048 \begin_layout Standard
4049 It is possible to place up to 6 lines above or below characters.
4052 \begin_layout Standard
4053 \begin_inset VSpace bigskip
4056 Custom lines can be created using the command
4063 \begin_inset Index idx
4066 \begin_layout Plain Layout
4074 which has the following scheme:
4077 \begin_layout Standard
4082 rule[vertical offset]{length}{thickness}
4085 \begin_layout Standard
4086 The optional vertical offset shifts the line upwards (or downwards, when
4087 the value is negative).
4089 \begin_inset CommandInset ref
4091 reference "tab:Available-units"
4095 can be used for the values.
4096 Here are two example lines created with the commands
4097 \begin_inset Newline newline
4104 rule[-2ex]{3cm}{2pt}
4115 \begin_layout Standard
4117 \begin_inset Formula $\rule[-2ex]{3cm}{2pt}\rule{2cm}{1pt}$
4123 \begin_layout Standard
4130 can also be used for text when a line is inserted via the menu
4132 Insert\SpecialChar \menuseparator
4133 Formatting\SpecialChar \menuseparator
4135 \begin_inset space ~
4143 \begin_layout Standard
4145 \begin_inset CommandInset line
4156 \begin_layout Subsection
4158 \begin_inset CommandInset label
4165 \begin_inset Index idx
4168 \begin_layout Plain Layout
4177 \begin_layout Standard
4178 There are different types of ellipses available.
4182 \begin_layout Plain Layout
4183 In the math toolbar in the submenu of the button
4184 \begin_inset Graphics
4185 filename ../images/math/ldots.png
4195 For listings dots at the baseline are used (
4202 \begin_inset Index idx
4205 \begin_layout Plain Layout
4213 ), while for operations dots are needed that are on the same height as the
4221 \begin_inset Index idx
4224 \begin_layout Plain Layout
4233 When using the command
4240 \begin_inset Index idx
4243 \begin_layout Plain Layout
4251 , LaTeX decides on the basis of the next character what type is used.
4254 \begin_layout Standard
4256 \begin_inset Tabular
4257 <lyxtabular version="3" rows="9" columns="2">
4258 <features rotate="0" tabularvalignment="middle">
4259 <column alignment="center" valignment="top" width="0pt">
4260 <column alignment="center" valignment="top" width="0pt">
4262 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
4265 \begin_layout Plain Layout
4271 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
4274 \begin_layout Plain Layout
4282 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
4285 \begin_layout Plain Layout
4287 \begin_inset space \textvisiblespace{}
4293 \begin_inset space \textvisiblespace{}
4301 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
4304 \begin_layout Plain Layout
4305 \begin_inset Formula $A_{1},\dots,A_{n}$
4315 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
4318 \begin_layout Plain Layout
4320 \begin_inset space \textvisiblespace{}
4326 \begin_inset space \textvisiblespace{}
4334 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
4337 \begin_layout Plain Layout
4338 \begin_inset Formula $A_{1}+\dots+A_{n}$
4348 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
4351 \begin_layout Plain Layout
4353 \begin_inset space \textvisiblespace{}
4359 \begin_inset space \textvisiblespace{}
4367 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
4370 \begin_layout Plain Layout
4371 \begin_inset Formula $A_{1},\ldots,A_{n}$
4381 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
4384 \begin_layout Plain Layout
4386 \begin_inset space \textvisiblespace{}
4392 \begin_inset space \textvisiblespace{}
4400 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
4403 \begin_layout Plain Layout
4404 \begin_inset Formula $A_{1}+\cdots+A_{n}$
4414 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
4417 \begin_layout Plain Layout
4425 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
4428 \begin_layout Plain Layout
4429 \begin_inset Formula $\vdots$
4439 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
4442 \begin_layout Plain Layout
4450 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
4453 \begin_layout Plain Layout
4454 \begin_inset Formula $\ddots$
4464 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
4467 \begin_layout Plain Layout
4475 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
4478 \begin_layout Plain Layout
4479 \begin_inset Formula $\iddots$
4489 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
4492 \begin_layout Plain Layout
4494 \begin_inset space \thinspace{}
4497 matrix with the different dots
4502 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
4505 \begin_layout Plain Layout
4506 \begin_inset Formula $\begin{array}{ccc}
4507 A_{11} & \cdots & A_{1m}\\
4508 \vdots & \ddots & \vdots\\
4509 A_{n1} & \cdots & A_{nm}
4526 \begin_layout Standard
4527 The ellipses available in menu
4529 Insert\SpecialChar \menuseparator
4531 \begin_inset space ~
4545 \begin_layout Standard
4546 \begin_inset VSpace medskip
4555 , one of the options
4557 Use mathdots package (automatically)
4559 must be set in the document settings under
4562 \begin_inset space ~
4568 \begin_inset Newline newline
4573 Use mathdots package
4575 will improve the appearance of all dots in the documents if their font
4576 style or size is not the default.
4579 \begin_layout Standard
4580 \begin_inset VSpace medskip
4583 Specially for matrices there are ellipses that span over several columns.
4584 They are created with the command
4591 \begin_inset Index idx
4594 \begin_layout Plain Layout
4602 , that has the following scheme:
4605 \begin_layout Standard
4610 hdotsfor[distance]{number of columns}
4613 \begin_layout Standard
4614 The number of columns specifies how many columns should be spanned.
4615 Distance is a factor for the distance between the dots.
4618 \begin_layout Standard
4619 In the following matrix the command
4625 was inserted in the first box of the second line, to get an ellipsis with
4626 a dot distance twice as long as with the command
4633 \begin_inset Formula
4635 \left(\begin{array}{cccc}
4644 Note that the matrix fields that should be spanned must be empty, otherwise
4645 you get LaTeX-errors.
4648 \begin_layout Standard
4649 \begin_inset VSpace bigskip
4652 Furthermore you can fill with the command
4659 \begin_inset Index idx
4662 \begin_layout Plain Layout
4670 the rest of a line with dots.
4671 The effect of these commands is the same as with
4678 \begin_inset CommandInset ref
4680 reference "sub:Variable-Space"
4687 \begin_layout Standard
4688 For example the command
4693 \begin_inset space \textvisiblespace{}
4701 \begin_layout Standard
4702 \begin_inset Formula $A\dotfill B$
4708 \begin_layout Standard
4715 there is for a line the command
4722 \begin_inset Index idx
4725 \begin_layout Plain Layout
4736 \begin_layout Standard
4737 \begin_inset Formula $A\hrulefill B$
4743 \begin_layout Standard
4744 To use the commands for text, they have to be inserted in TeX-mode.
4747 \begin_layout Section
4749 \begin_inset CommandInset label
4756 \begin_inset Index idx
4759 \begin_layout Plain Layout
4768 \begin_layout Standard
4769 Matrices can be inserted via the math toolbar button
4770 \begin_inset Graphics
4771 filename ../images/dialog-show_mathmatrix.png
4778 Insert\SpecialChar \menuseparator
4779 Math\SpecialChar \menuseparator
4783 In the matrix dialog you can specify the number of columns and rows, the
4784 alignment and the decoration.
4785 The vertical alignment is only of importance for matrices in inline formulas:
4788 \begin_layout Standard
4789 The first matrix is top
4790 \begin_inset Formula $\begin{array}[t]{cccc}
4798 \begin_inset Formula $\begin{array}{cccc}
4805 and the third bottom
4806 \begin_inset Formula $\begin{array}[b]{cccc}
4816 \begin_layout Standard
4817 The horizontal alignment specifies how the column entries should be aligned.
4818 It is set by entering a letter for every column.
4823 denotes left aligned,
4832 To create for example a 4
4837 \begin_inset space ~
4840 matrix where the first column is left aligned, the second and third are
4841 centered and the last one is right aligned, one enters for the horizontal
4847 Normally in a matrix all columns are centered, therefore the default for
4855 \begin_layout Standard
4856 Horizontal alignment:
4859 \begin_layout Standard
4865 \begin_inset Formula $\begin{array}{lll}
4877 \begin_inset Formula $\begin{array}{ccc}
4889 \begin_inset Formula $\begin{array}{rrr}
4899 \begin_layout Standard
4900 To add or delete rows and columns subsequently, the math toolbar buttons
4902 \begin_inset Graphics
4903 filename ../images/tabular-feature_append-row.png
4909 \begin_inset Graphics
4910 filename ../images/tabular-feature_delete-row.png
4916 \begin_inset space \thinspace{}
4921 Edit\SpecialChar \menuseparator
4925 New rows can also be created with
4928 arg "newline-insert newline"
4934 \begin_layout Standard
4935 \begin_inset VSpace bigskip
4942 adds parentheses in the selected style around the matrix.
4943 Alternatively, parentheses can can either be created with the commands
4951 \begin_inset Index idx
4954 \begin_layout Plain Layout
4969 \begin_inset Index idx
4972 \begin_layout Plain Layout
4983 \begin_inset space ~
4989 \begin_inset CommandInset ref
4991 reference "sub:Automatic-Bracket-Size"
4995 , or by using the following commands:
4996 \begin_inset VSpace medskip
5002 \begin_layout Standard
5003 \begin_inset space \hfill{}
5007 \begin_inset Tabular
5008 <lyxtabular version="3" rows="4" columns="2">
5009 <features rotate="0" tabularvalignment="middle">
5010 <column alignment="center" valignment="top">
5011 <column alignment="center" valignment="top">
5013 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
5016 \begin_layout Plain Layout
5022 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
5025 \begin_layout Plain Layout
5027 \begin_inset Note Note
5030 \begin_layout Plain Layout
5037 is only used as spacer.
5049 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
5052 \begin_layout Plain Layout
5056 \begin_inset space \textvisiblespace{}
5064 \begin_inset space \thinspace{}
5072 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
5075 \begin_layout Plain Layout
5076 \begin_inset Formula $\raisebox{7.5mm}{}\begin{bmatrix}\begin{array}{cc}
5077 0 & \textrm{-}\mathrm{i}\\
5079 \end{array}\end{bmatrix}\raisebox{-5.3mm}{}$
5089 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
5092 \begin_layout Plain Layout
5096 \begin_inset space \textvisiblespace{}
5104 \begin_inset space \thinspace{}
5112 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
5115 \begin_layout Plain Layout
5116 \begin_inset Formula $\raisebox{7.5mm}{}\begin{Bmatrix}\begin{array}{cc}
5117 0 & \textrm{-}\mathrm{i}\\
5119 \end{array}\end{Bmatrix}\raisebox{-5.3mm}{}$
5129 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
5132 \begin_layout Plain Layout
5136 \begin_inset space \textvisiblespace{}
5144 \begin_inset space \thinspace{}
5152 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
5155 \begin_layout Plain Layout
5156 \begin_inset Formula $\raisebox{7.5mm}{}\begin{pmatrix}\begin{array}{cc}
5157 0 & \textrm{-}\mathrm{i}\\
5159 \end{array}\end{pmatrix}\raisebox{-5.3mm}{}$
5173 \begin_inset space \hfill{}
5177 \begin_inset Tabular
5178 <lyxtabular version="3" rows="4" columns="2">
5179 <features rotate="0" tabularvalignment="middle">
5180 <column alignment="center" valignment="top">
5181 <column alignment="center" valignment="top">
5183 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
5186 \begin_layout Plain Layout
5192 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
5195 \begin_layout Plain Layout
5203 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
5206 \begin_layout Plain Layout
5210 \begin_inset space \textvisiblespace{}
5218 \begin_inset space \thinspace{}
5226 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
5229 \begin_layout Plain Layout
5230 \begin_inset Formula $\raisebox{7.5mm}{}\begin{vmatrix}\begin{array}{cc}
5231 0 & \textrm{-}\mathrm{i}\\
5233 \end{array}\end{vmatrix}\raisebox{-5.3mm}{}$
5243 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
5246 \begin_layout Plain Layout
5250 \begin_inset space \textvisiblespace{}
5258 \begin_inset space \thinspace{}
5266 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
5269 \begin_layout Plain Layout
5270 \begin_inset Formula $\raisebox{7.5mm}{}\begin{Vmatrix}\begin{array}{cc}
5271 0 & \textrm{-}\mathrm{i}\\
5273 \end{array}\end{Vmatrix}\raisebox{-5.3mm}{}$
5283 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
5286 \begin_layout Plain Layout
5290 \begin_inset space \textvisiblespace{}
5298 \begin_inset space \thinspace{}
5306 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
5309 \begin_layout Plain Layout
5310 \begin_inset Formula $\raisebox{7.5mm}{}\begin{matrix}\begin{array}{cc}
5311 0 & \textrm{-}\mathrm{i}\\
5313 \end{array}\end{matrix}\raisebox{-5.3mm}{}$
5327 \begin_inset space \hfill{}
5333 \begin_layout Standard
5334 \begin_inset VSpace medskip
5338 \begin_inset space \thinspace{}
5342 \begin_inset space \space{}
5351 is inserted, a blue box appears between two vertical lines where the matrix
5353 \begin_inset Newline newline
5356 Note that decorated matrices ignore the vertical alignment.
5359 \begin_layout Standard
5360 \begin_inset VSpace bigskip
5363 As all multiline formulas are matrices, the length
5370 \begin_inset Index idx
5373 \begin_layout Plain Layout
5381 that is described in
5382 \begin_inset CommandInset ref
5384 reference "sub:Column-Separation"
5388 can also be used to change the column separation of matrices.
5391 \begin_layout Standard
5392 To change the row separation, the command
5399 \begin_inset Index idx
5402 \begin_layout Plain Layout
5411 It is used as follows:
5414 \begin_layout Standard
5421 arraystretch}{stretch factor}
5422 \begin_inset Index idx
5425 \begin_layout Plain Layout
5436 \begin_layout Standard
5443 assigns the stretch factor to the predefined command
5451 \begin_inset space \thinspace{}
5455 \begin_inset space \space{}
5458 the row separation, use the factor 2.
5459 This is then used for all following matrices.
5460 To go back to the original separation, assign the factor 1 to
5469 \begin_layout Standard
5470 To set matrices into a text line, the command
5477 \begin_inset Index idx
5480 \begin_layout Plain Layout
5489 When it is inserted a blue box with two dashed lines appears.
5490 In this box the matrix is inserted.
5493 \begin_layout Standard
5495 \begin_inset Formula $\left(\begin{smallmatrix}A & B\\
5497 \end{smallmatrix}\right)$
5503 \begin_layout Section
5504 Brackets and Delimiters
5505 \begin_inset Index idx
5508 \begin_layout Plain Layout
5515 \begin_inset Index idx
5518 \begin_layout Plain Layout
5527 \begin_layout Subsection
5528 Vertical Brackets and Delimiters
5529 \begin_inset Index idx
5532 \begin_layout Plain Layout
5541 \begin_layout Standard
5542 \begin_inset space \hfill{}
5546 \begin_inset Tabular
5547 <lyxtabular version="3" rows="9" columns="2">
5548 <features rotate="0" tabularvalignment="middle">
5549 <column alignment="center" valignment="top" width="0pt">
5550 <column alignment="center" valignment="top" width="0pt">
5552 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
5555 \begin_layout Plain Layout
5561 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
5564 \begin_layout Plain Layout
5572 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
5575 \begin_layout Plain Layout
5581 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
5584 \begin_layout Plain Layout
5585 \begin_inset Formula $($
5595 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
5598 \begin_layout Plain Layout
5604 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
5607 \begin_layout Plain Layout
5608 \begin_inset Formula $\{$
5618 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
5621 \begin_layout Plain Layout
5627 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
5630 \begin_layout Plain Layout
5631 \begin_inset Formula $[$
5641 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
5644 \begin_layout Plain Layout
5652 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
5655 \begin_layout Plain Layout
5656 \begin_inset Formula $\langle$
5666 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
5669 \begin_layout Plain Layout
5677 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
5680 \begin_layout Plain Layout
5681 \begin_inset Formula $\lceil$
5691 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
5694 \begin_layout Plain Layout
5702 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
5705 \begin_layout Plain Layout
5706 \begin_inset Formula $\lfloor$
5716 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
5719 \begin_layout Plain Layout
5725 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
5728 \begin_layout Plain Layout
5729 \begin_inset Formula $/$
5739 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
5742 \begin_layout Plain Layout
5748 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
5751 \begin_layout Plain Layout
5752 \begin_inset Formula $|$
5766 \begin_inset space \hfill{}
5770 \begin_inset Tabular
5771 <lyxtabular version="3" rows="9" columns="2">
5772 <features rotate="0" tabularvalignment="middle">
5773 <column alignment="center" valignment="top" width="0pt">
5774 <column alignment="center" valignment="top" width="0pt">
5776 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
5779 \begin_layout Plain Layout
5785 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
5788 \begin_layout Plain Layout
5796 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
5799 \begin_layout Plain Layout
5805 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
5808 \begin_layout Plain Layout
5809 \begin_inset Formula $)$
5819 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
5822 \begin_layout Plain Layout
5828 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
5831 \begin_layout Plain Layout
5832 \begin_inset Formula $\}$
5842 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
5845 \begin_layout Plain Layout
5851 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
5854 \begin_layout Plain Layout
5855 \begin_inset Formula $]$
5865 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
5868 \begin_layout Plain Layout
5876 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
5879 \begin_layout Plain Layout
5880 \begin_inset Formula $\rangle$
5890 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
5893 \begin_layout Plain Layout
5901 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
5904 \begin_layout Plain Layout
5905 \begin_inset Formula $\rceil$
5915 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
5918 \begin_layout Plain Layout
5926 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
5929 \begin_layout Plain Layout
5930 \begin_inset Formula $\rfloor$
5940 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
5943 \begin_layout Plain Layout
5953 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
5956 \begin_layout Plain Layout
5957 \begin_inset Formula $\backslash$
5967 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
5970 \begin_layout Plain Layout
5978 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
5981 \begin_layout Plain Layout
5982 \begin_inset Formula $\|$
5996 \begin_inset space \hfill{}
6002 \begin_layout Standard
6005 \begin_inset Note Greyedout
6008 \begin_layout Plain Layout
6013 In TeX-mode the command
6020 \begin_inset Index idx
6023 \begin_layout Plain Layout
6031 must be used for the backslash, because the command
6039 produces a line break there.
6047 \begin_layout Standard
6048 For all characters listed above the size can be adjusted with the commands
6049 described in the following two subsections.
6050 When using these commands, the characters < and > can directly be used
6051 instead of the commands
6066 \begin_layout Subsubsection
6068 \begin_inset CommandInset label
6070 name "sub:Manual-Bracket-Size"
6075 \begin_inset Index idx
6078 \begin_layout Plain Layout
6079 Bracket size ! manual
6087 \begin_layout Standard
6088 The bracket size can be specified manually by the LaTeX-commands
6095 \begin_inset Index idx
6098 \begin_layout Plain Layout
6131 denotes the smallest and
6137 the largest bracket size.
6140 \begin_layout Standard
6141 These commands are used to emphasize levels of brackets:
6144 \begin_layout Standard
6146 \begin_inset Tabular
6147 <lyxtabular version="3" rows="2" columns="2">
6148 <features rotate="0" tabularvalignment="middle">
6149 <column alignment="center" valignment="top" width="0pt">
6150 <column alignment="center" valignment="top" width="0pt">
6152 <cell alignment="center" valignment="top" usebox="none">
6155 \begin_layout Plain Layout
6156 all brackets in the same size:
6161 <cell alignment="center" valignment="top" usebox="none">
6164 \begin_layout Plain Layout
6165 \begin_inset Formula $((A+B)(A-B))^{C}\raisebox{-4mm}{}$
6175 <cell alignment="center" valignment="top" usebox="none">
6178 \begin_layout Plain Layout
6184 <cell alignment="center" valignment="top" usebox="none">
6187 \begin_layout Plain Layout
6188 \begin_inset Formula $\Big((A+B)(A-B)\Big)^{C}$
6202 \begin_inset Note Note
6205 \begin_layout Plain Layout
6212 is only used as spacer.
6220 \begin_layout Standard
6221 For the second formula the command
6228 \begin_inset space \textvisiblespace{}
6236 \begin_layout Standard
6237 Here is an overview about all bracket sizes:
6240 \begin_layout Standard
6257 \begin_inset space \textvisiblespace{}
6265 \begin_inset space \textvisiblespace{}
6269 \begin_inset space \textvisiblespace{}
6279 \begin_layout Standard
6281 \begin_inset Formula $\Bigg(\exp\bigg<\Big[\big\{\ln(3x)\big\}^{2}\sin(x)\Big]^{A}\bigg>\Bigg)^{0,5}$
6287 \begin_layout Standard
6294 -commands there is the variant
6301 \begin_inset Index idx
6304 \begin_layout Plain Layout
6312 that adds a bit more space between the bracket and its content, and the
6326 \begin_inset Index idx
6329 \begin_layout Plain Layout
6339 , that don't add additional space.
6344 at the end of the command
6350 is for a left bracket; for a right bracket this will be replaced by an
6356 A left or right bracket can each be an opening or closing bracket.
6359 \begin_layout Standard
6360 In the following table is a comparison of the variants:
6363 \begin_layout Standard
6365 \begin_inset Tabular
6366 <lyxtabular version="3" rows="5" columns="2">
6367 <features rotate="0" tabularvalignment="middle">
6368 <column alignment="center" valignment="middle">
6369 <column alignment="center" valignment="middle">
6371 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
6374 \begin_layout Plain Layout
6380 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
6383 \begin_layout Plain Layout
6385 \begin_inset Note Note
6388 \begin_layout Plain Layout
6395 is only used as spacer.
6407 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
6410 \begin_layout Plain Layout
6420 \begin_inset space \textvisiblespace{}
6430 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
6433 \begin_layout Plain Layout
6434 \begin_inset Formula $\raisebox{5.5mm}{}\Bigm(\bigm(\ln(3x)\bigm)^{2}\Bigm)\raisebox{-3.25mm}{}$
6444 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
6447 \begin_layout Plain Layout
6457 \begin_inset space \textvisiblespace{}
6467 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
6470 \begin_layout Plain Layout
6471 \begin_inset Formula $\raisebox{5.5mm}{}\Big(\big(\ln(3x)\big)^{2}\Big)\raisebox{-3.25mm}{}$
6481 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
6484 \begin_layout Plain Layout
6494 \begin_inset space \textvisiblespace{}
6504 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
6507 \begin_layout Plain Layout
6508 \begin_inset Formula $\raisebox{5.5mm}{}\Bigl(\bigl(\ln(3x)\bigr)^{2}\Bigr)\raisebox{-3.25mm}{}$
6518 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
6521 \begin_layout Plain Layout
6533 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
6536 \begin_layout Plain Layout
6537 \begin_inset Formula $\raisebox{4.5mm}{}\bigl)\ln(3x)\bigr(\raisebox{-2mm}{}$
6553 \begin_layout Subsubsection
6554 Automatic Bracket Size
6555 \begin_inset CommandInset label
6557 name "sub:Automatic-Bracket-Size"
6562 \begin_inset Index idx
6565 \begin_layout Plain Layout
6566 Bracket size ! automatic
6574 \begin_layout Standard
6575 Brackets with variable size can be inserted with the commands
6582 \begin_inset Index idx
6585 \begin_layout Plain Layout
6600 \begin_inset Index idx
6603 \begin_layout Plain Layout
6611 or via the math toolbar button
6612 \begin_inset Graphics
6613 filename ../images/dialog-show_mathdelimiter.png
6631 the wanted bracket must be inserted.
6632 The bracket size will then automatically be calculated for the output.
6635 \begin_layout Standard
6637 normal bracket: The command
6644 \begin_inset space \textvisiblespace{}
6648 \begin_inset Formula $\downarrow$
6652 \begin_inset space \textvisiblespace{}
6658 \begin_inset Formula
6668 \begin_layout Standard
6670 multiline bracket: The command
6679 \begin_inset space \textvisiblespace{}
6683 \begin_inset Formula $\downarrow$
6687 \begin_inset space \textvisiblespace{}
6695 \begin_inset Formula
6697 \ln\left(\frac{A}{C}\right)
6705 \begin_layout Standard
6721 \begin_inset space ~
6727 This has the advantage that you can see in LyX immediately the real bracket
6728 size and that the matching right bracket will be created too.
6729 \begin_inset Newline newline
6732 The command for the last example would then be:
6743 \begin_inset space \textvisiblespace{}
6747 \begin_inset Formula $\downarrow$
6753 \begin_layout Standard
6754 To omit a left or right bracket, a dot is inserted for the omitted bracket.
6755 For example the command
6762 \begin_inset space \textvisiblespace{}
6766 \begin_inset Formula $\downarrow$
6770 \begin_inset space \textvisiblespace{}
6780 \begin_inset Formula
6782 \left.\frac{A}{B}\right\}
6801 will be converted by LyX to brackets in the right size when the document
6802 is reloaded and an omitted bracket will appear as dashed line.
6805 \begin_layout Standard
6806 \begin_inset VSpace bigskip
6809 Because all popular LaTeX-Distributions use eTeX, an extension to LaTeX,
6817 \begin_inset Index idx
6820 \begin_layout Plain Layout
6828 is additionally available for all brackets and limits.
6829 With this command the height of the following character is adapted to the
6830 one of the surrounding brackets, what is e.
6831 \begin_inset space \thinspace{}
6835 \begin_inset space \space{}
6838 needed for physical vectors:
6839 \begin_inset Formula
6841 \left\langle \phi\:\middle|\: J=\frac{3}{2}\,,\, M_{J}\right\rangle
6846 For physical vectors there is a special LaTeX-package, described in
6847 \begin_inset CommandInset ref
6849 reference "sub:Physical-Vectors"
6856 \begin_layout Subsection
6858 \begin_inset Index idx
6861 \begin_layout Plain Layout
6862 Brackets ! horizontal
6870 \begin_layout Standard
6872 \begin_inset Tabular
6873 <lyxtabular version="3" rows="4" columns="2">
6874 <features rotate="0" tabularvalignment="middle">
6875 <column alignment="center" valignment="top" width="0pt">
6876 <column alignment="center" valignment="top" width="0pt">
6878 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
6881 \begin_layout Plain Layout
6883 \begin_inset Note Note
6886 \begin_layout Plain Layout
6893 is only used as spacer.
6903 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
6906 \begin_layout Plain Layout
6914 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
6917 \begin_layout Plain Layout
6921 \begin_layout Plain Layout
6933 \begin_inset space \textvisiblespace{}
6937 \begin_inset space \textvisiblespace{}
6944 \begin_layout Plain Layout
6952 \begin_inset Index idx
6955 \begin_layout Plain Layout
6968 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
6971 \begin_layout Plain Layout
6972 \begin_inset Formula $\overbrace{A+B}^{3}$
6982 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
6985 \begin_layout Plain Layout
6989 \begin_layout Plain Layout
7001 \begin_inset space \textvisiblespace{}
7005 \begin_inset space \textvisiblespace{}
7012 \begin_layout Plain Layout
7020 \begin_inset Index idx
7023 \begin_layout Plain Layout
7036 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
7039 \begin_layout Plain Layout
7040 \begin_inset Formula $\underbrace{A+B}_{5}$
7050 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
7053 \begin_layout Plain Layout
7057 \begin_inset space \textvisiblespace{}
7063 \begin_inset space \textvisiblespace{}
7067 \begin_inset space \textvisiblespace{}
7071 \begin_inset space \textvisiblespace{}
7075 \begin_inset space \textvisiblespace{}
7079 \begin_inset space \textvisiblespace{}
7083 \begin_inset space \textvisiblespace{}
7091 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
7094 \begin_layout Plain Layout
7095 \begin_inset Formula $\overbrace{\underbrace{A+B_{w}}_{7}}^{C}$
7111 \begin_layout Standard
7112 In the last example it doesn't matter if
7124 is inserted at first.
7127 \begin_layout Standard
7128 \begin_inset VSpace bigskip
7131 When brackets are needed that overlap each other, multiline formulas, as
7133 \begin_inset CommandInset ref
7135 reference "sec:Multiline-Formulas"
7140 \begin_inset Formula
7142 A & = & \underbrace{gggg+bbqq}_{r}+\: dddd\\
7143 & & \hphantom{gggg+\:}\underbrace{\hphantom{bbqq+dddd}}_{s}
7148 In the first row the formula is inserted together with the first brace.
7149 It is hereby important that the space command
7153 \begin_layout Plain Layout
7154 Space commands are explained in
7155 \begin_inset CommandInset ref
7157 reference "sub:Predefined-Space"
7172 is inserted before the first
7173 \begin_inset Formula $d$
7176 , because the brace that ends behind the
7177 \begin_inset Formula $q$
7180 prevents that the following
7181 \begin_inset Quotes eld
7185 \begin_inset Quotes erd
7188 is surrounded by space.
7192 \begin_layout Plain Layout
7193 because a bracket is not handled as a character, see
7194 \begin_inset CommandInset ref
7196 reference "sub:Binary-Operators"
7205 In the second row the second brace is inserted.
7206 As it should begin before the
7207 \begin_inset Formula $b$
7222 \begin_layout Plain Layout
7230 \begin_inset CommandInset ref
7232 reference "sub:Placeholders"
7241 This space is needed because the
7242 \begin_inset Quotes eld
7246 \begin_inset Quotes erd
7249 is also surrounded by space in the formula.
7250 The brace is placed under the command
7259 \begin_layout Standard
7260 It gets more complicated when brackets overlap each other, like in the following
7265 \begin_layout Plain Layout
7277 \begin_inset Formula
7279 & & \hphantom{gggg+\:}\overbrace{\hphantom{bbqq+dddd}}^{s}\\
7280 A & = & \underbrace{gggg+bbqq}_{r}+\: dddd
7289 \begin_layout Plain Layout
7300 The first formula row is the same as the second row of the previous example,
7301 with the difference that the brace is above.
7302 The second row contains the formula together with the second brace.
7303 To avoid that there is space between the upper brace in the first row and
7304 the formula, the row spacing needs to be reduced.
7305 This is not easily possible due to a bug in LyX
7309 \begin_layout Plain Layout
7310 \begin_inset CommandInset href
7312 name "LyX-bug #1505"
7313 target "http://www.lyx.org/trac/ticket/1505"
7323 As a solution for the problem, the global formula row separation
7330 \begin_inset Index idx
7333 \begin_layout Plain Layout
7341 must be changed to -6
7342 \begin_inset space \thinspace{}
7345 pt before the formula with the command
7360 is set back after the formula to the standard value of 3
7361 \begin_inset space \thinspace{}
7364 pt using the same command.
7365 More about the row separation in formulas is explained in
7366 \begin_inset CommandInset ref
7368 reference "sub:Line-Separation"
7375 \begin_layout Section
7377 \begin_inset Index idx
7380 \begin_layout Plain Layout
7389 \begin_layout Standard
7390 Arrows can be inserted via the math toolbar button
7391 \begin_inset Graphics
7392 filename ../images/math/leftarrow.png
7397 or the commands listed in the following subsections.
7400 \begin_layout Subsection
7402 \begin_inset Index idx
7405 \begin_layout Plain Layout
7414 \begin_layout Standard
7415 \begin_inset space \hfill{}
7419 \begin_inset Tabular
7420 <lyxtabular version="3" rows="8" columns="2">
7421 <features rotate="0" tabularvalignment="middle">
7422 <column alignment="center" valignment="top" width="0pt">
7423 <column alignment="center" valignment="top" width="0pt">
7425 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
7428 \begin_layout Plain Layout
7434 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
7437 \begin_layout Plain Layout
7445 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
7448 \begin_layout Plain Layout
7456 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
7459 \begin_layout Plain Layout
7460 \begin_inset Formula $\gets$
7470 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
7473 \begin_layout Plain Layout
7481 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
7484 \begin_layout Plain Layout
7485 \begin_inset Formula $\Leftarrow$
7495 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
7498 \begin_layout Plain Layout
7506 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
7509 \begin_layout Plain Layout
7510 \begin_inset Formula $\longleftarrow$
7520 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
7523 \begin_layout Plain Layout
7531 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
7534 \begin_layout Plain Layout
7535 \begin_inset Formula $\Longleftarrow$
7545 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
7548 \begin_layout Plain Layout
7556 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
7559 \begin_layout Plain Layout
7560 \begin_inset Formula $\leftharpoonup$
7570 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
7573 \begin_layout Plain Layout
7581 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
7584 \begin_layout Plain Layout
7585 \begin_inset Formula $\leftharpoondown$
7595 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
7598 \begin_layout Plain Layout
7606 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
7609 \begin_layout Plain Layout
7610 \begin_inset Formula $\hookleftarrow$
7624 \begin_inset space \hfill{}
7628 \begin_inset Tabular
7629 <lyxtabular version="3" rows="8" columns="2">
7630 <features rotate="0" tabularvalignment="middle">
7631 <column alignment="center" valignment="top" width="0pt">
7632 <column alignment="center" valignment="top" width="0pt">
7634 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
7637 \begin_layout Plain Layout
7643 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
7646 \begin_layout Plain Layout
7654 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
7657 \begin_layout Plain Layout
7665 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
7668 \begin_layout Plain Layout
7669 \begin_inset Formula $\to$
7679 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
7682 \begin_layout Plain Layout
7690 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
7693 \begin_layout Plain Layout
7694 \begin_inset Formula $\Rightarrow$
7704 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
7707 \begin_layout Plain Layout
7715 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
7718 \begin_layout Plain Layout
7719 \begin_inset Formula $\longrightarrow$
7729 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
7732 \begin_layout Plain Layout
7740 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
7743 \begin_layout Plain Layout
7744 \begin_inset Formula $\Longrightarrow$
7754 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
7757 \begin_layout Plain Layout
7765 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
7768 \begin_layout Plain Layout
7769 \begin_inset Formula $\rightharpoonup$
7779 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
7782 \begin_layout Plain Layout
7790 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
7793 \begin_layout Plain Layout
7794 \begin_inset Formula $\rightharpoondown$
7804 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
7807 \begin_layout Plain Layout
7815 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
7818 \begin_layout Plain Layout
7819 \begin_inset Formula $\hookrightarrow$
7833 \begin_inset space \hfill{}
7839 \begin_layout Standard
7840 \begin_inset space \hfill{}
7844 \begin_inset Tabular
7845 <lyxtabular version="3" rows="6" columns="2">
7846 <features rotate="0" tabularvalignment="middle">
7847 <column alignment="center" valignment="top" width="0pt">
7848 <column alignment="center" valignment="top" width="0pt">
7850 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
7853 \begin_layout Plain Layout
7859 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
7862 \begin_layout Plain Layout
7870 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
7873 \begin_layout Plain Layout
7881 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
7884 \begin_layout Plain Layout
7885 \begin_inset Formula $\leftrightarrow$
7895 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
7898 \begin_layout Plain Layout
7906 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
7909 \begin_layout Plain Layout
7910 \begin_inset Formula $\Leftrightarrow$
7920 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
7923 \begin_layout Plain Layout
7931 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
7934 \begin_layout Plain Layout
7935 \begin_inset Formula $\longleftrightarrow$
7945 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
7948 \begin_layout Plain Layout
7956 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
7959 \begin_layout Plain Layout
7960 \begin_inset Formula $\Longleftrightarrow$
7970 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
7973 \begin_layout Plain Layout
7981 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
7984 \begin_layout Plain Layout
7985 \begin_inset Formula $\rightleftharpoons$
7999 \begin_inset space \hspace{}
8004 \begin_inset space \hfill{}
8008 \begin_inset Tabular
8009 <lyxtabular version="3" rows="5" columns="2">
8010 <features rotate="0" tabularvalignment="middle">
8011 <column alignment="center" valignment="top" width="0pt">
8012 <column alignment="center" valignment="top" width="0pt">
8014 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
8017 \begin_layout Plain Layout
8023 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
8026 \begin_layout Plain Layout
8034 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
8037 \begin_layout Plain Layout
8045 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
8048 \begin_layout Plain Layout
8049 \begin_inset Formula $\mapsto$
8059 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
8062 \begin_layout Plain Layout
8070 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
8073 \begin_layout Plain Layout
8074 \begin_inset Formula $\longmapsto$
8084 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
8087 \begin_layout Plain Layout
8095 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
8098 \begin_layout Plain Layout
8099 \begin_inset Formula $\leadsto$
8109 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
8112 \begin_layout Plain Layout
8120 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
8123 \begin_layout Plain Layout
8124 \begin_inset Formula $\dasharrow$
8138 \begin_inset space \hfill{}
8144 \begin_layout Standard
8145 \begin_inset VSpace medskip
8148 Arrows used as accents like e.
8149 \begin_inset space \thinspace{}
8153 \begin_inset space \space{}
8156 vector arrows are listed in
8157 \begin_inset CommandInset ref
8159 reference "sec:Accents"
8166 \begin_layout Standard
8167 \begin_inset VSpace bigskip
8170 Furthermore there are the labeled arrows
8171 \begin_inset Index idx
8174 \begin_layout Plain Layout
8187 \begin_inset Index idx
8190 \begin_layout Plain Layout
8205 \begin_inset Index idx
8208 \begin_layout Plain Layout
8215 \begin_layout Plain Layout
8230 When inserting one of these commands in a formula, an arrow with two blue
8231 boxes appear where the label can be inserted.
8232 The length of the arrow adapts to the label width.
8235 \begin_layout Standard
8237 \begin_inset Tabular
8238 <lyxtabular version="3" rows="3" columns="2">
8239 <features rotate="0" tabularvalignment="middle">
8240 <column alignment="center" valignment="top" width="0pt">
8241 <column alignment="center" valignment="top" width="0pt">
8243 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
8246 \begin_layout Plain Layout
8252 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
8255 \begin_layout Plain Layout
8257 \begin_inset Note Note
8260 \begin_layout Plain Layout
8267 is only used as spacer.
8279 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
8282 \begin_layout Plain Layout
8286 \begin_inset space \textvisiblespace{}
8290 \begin_inset Formula $\downarrow$
8294 \begin_inset Formula $\to$
8302 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
8305 \begin_layout Plain Layout
8306 \begin_inset Formula $\raisebox{5mm}{}F(a)\xleftarrow[x>0]{x=a}F(x)\raisebox{-4mm}{}$
8316 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
8319 \begin_layout Plain Layout
8323 \begin_inset space \textvisiblespace{}
8327 \begin_inset Formula $\downarrow$
8331 \begin_inset Formula $\to$
8339 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
8342 \begin_layout Plain Layout
8343 \begin_inset Formula $\raisebox{5mm}{}F(x)\xrightarrow[x>0]{x=a}F(a)\raisebox{-4mm}{}$
8359 \begin_layout Subsection
8360 Vertical and diagonal Arrows
8361 \begin_inset Index idx
8364 \begin_layout Plain Layout
8371 \begin_inset Index idx
8374 \begin_layout Plain Layout
8383 \begin_layout Standard
8384 \begin_inset space \hfill{}
8388 \begin_inset Tabular
8389 <lyxtabular version="3" rows="7" columns="2">
8390 <features rotate="0" tabularvalignment="middle">
8391 <column alignment="center" valignment="top" width="0pt">
8392 <column alignment="center" valignment="top" width="0pt">
8394 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
8397 \begin_layout Plain Layout
8403 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
8406 \begin_layout Plain Layout
8414 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
8417 \begin_layout Plain Layout
8425 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
8428 \begin_layout Plain Layout
8429 \begin_inset Formula $\uparrow$
8439 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
8442 \begin_layout Plain Layout
8450 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
8453 \begin_layout Plain Layout
8454 \begin_inset Formula $\Uparrow$
8464 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
8467 \begin_layout Plain Layout
8475 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
8478 \begin_layout Plain Layout
8479 \begin_inset Formula $\updownarrow$
8489 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
8492 \begin_layout Plain Layout
8500 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
8503 \begin_layout Plain Layout
8504 \begin_inset Formula $\Updownarrow$
8514 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
8517 \begin_layout Plain Layout
8525 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
8528 \begin_layout Plain Layout
8529 \begin_inset Formula $\Downarrow$
8539 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
8542 \begin_layout Plain Layout
8550 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
8553 \begin_layout Plain Layout
8554 \begin_inset Formula $\downarrow$
8568 \begin_inset space \hfill{}
8572 \begin_inset Tabular
8573 <lyxtabular version="3" rows="5" columns="2">
8574 <features rotate="0" tabularvalignment="middle">
8575 <column alignment="center" valignment="top" width="0pt">
8576 <column alignment="center" valignment="top" width="0pt">
8578 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
8581 \begin_layout Plain Layout
8587 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
8590 \begin_layout Plain Layout
8598 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
8601 \begin_layout Plain Layout
8609 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
8612 \begin_layout Plain Layout
8613 \begin_inset Formula $\nearrow$
8623 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
8626 \begin_layout Plain Layout
8634 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
8637 \begin_layout Plain Layout
8638 \begin_inset Formula $\searrow$
8648 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
8651 \begin_layout Plain Layout
8659 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
8662 \begin_layout Plain Layout
8663 \begin_inset Formula $\swarrow$
8673 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
8676 \begin_layout Plain Layout
8684 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
8687 \begin_layout Plain Layout
8688 \begin_inset Formula $\nwarrow$
8702 \begin_inset space \hfill{}
8708 \begin_layout Standard
8709 \begin_inset VSpace medskip
8712 Vertical arrows can be used also as delimiters together with the commands
8714 \begin_inset CommandInset ref
8716 reference "sub:Manual-Bracket-Size"
8721 \begin_inset CommandInset ref
8723 reference "sub:Automatic-Bracket-Size"
8730 \begin_layout Section
8732 \begin_inset CommandInset label
8739 \begin_inset Index idx
8742 \begin_layout Plain Layout
8751 \begin_layout Standard
8752 Accents can be inserted via the math toolbar button
8753 \begin_inset Graphics
8754 filename ../images/math/hat.png
8759 or the commands listed in the following subsections.
8762 \begin_layout Subsection
8763 Accents for one Character
8767 \begin_layout Plain Layout
8780 \begin_layout Plain Layout
8782 \begin_inset CommandInset ref
8784 reference "sub:Accents-in-Text"
8797 \begin_layout Plain Layout
8805 \begin_inset Note Note
8808 \begin_layout Plain Layout
8815 is used to avoid that the footnote appears in the PDF-bookmark.
8818 \begin_layout Plain Layout
8826 \begin_inset CommandInset ref
8828 reference "sub:Formulas-in-Section"
8838 \begin_inset CommandInset label
8840 name "sub:Accents-for-one"
8845 \begin_inset Index idx
8848 \begin_layout Plain Layout
8849 Accents ! for one character
8857 \begin_layout Standard
8858 \begin_inset space \hfill{}
8862 \begin_inset Tabular
8863 <lyxtabular version="3" rows="8" columns="2">
8864 <features rotate="0" tabularvalignment="middle">
8865 <column alignment="center" valignment="top" width="0pt">
8866 <column alignment="center" valignment="top" width="0pt">
8868 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
8871 \begin_layout Plain Layout
8877 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
8880 \begin_layout Plain Layout
8882 \begin_inset Note Note
8885 \begin_layout Plain Layout
8892 is only used as spacer.
8904 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
8907 \begin_layout Plain Layout
8911 \begin_inset space \textvisiblespace{}
8919 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
8922 \begin_layout Plain Layout
8923 \begin_inset Formula $\raisebox{5mm}{}\dot{A}$
8933 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
8936 \begin_layout Plain Layout
8940 \begin_inset space \textvisiblespace{}
8948 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
8951 \begin_layout Plain Layout
8952 \begin_inset Formula $\raisebox{5mm}{}\ddot{A}$
8962 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
8965 \begin_layout Plain Layout
8969 \begin_inset space \textvisiblespace{}
8977 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
8980 \begin_layout Plain Layout
8981 \begin_inset Formula $\raisebox{5mm}{}\dddot{A}$
8991 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
8994 \begin_layout Plain Layout
8998 \begin_inset space \textvisiblespace{}
9006 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
9009 \begin_layout Plain Layout
9010 \begin_inset Formula $\raisebox{5mm}{}\ddddot{A}$
9020 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
9023 \begin_layout Plain Layout
9027 \begin_inset space \textvisiblespace{}
9031 \begin_inset Index idx
9034 \begin_layout Plain Layout
9045 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
9048 \begin_layout Plain Layout
9049 \begin_inset Formula $\raisebox{5mm}{}\vec{A}$
9059 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
9062 \begin_layout Plain Layout
9066 \begin_inset space \textvisiblespace{}
9074 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
9077 \begin_layout Plain Layout
9078 \begin_inset Formula $\raisebox{5mm}{}\bar{A}$
9088 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
9091 \begin_layout Plain Layout
9095 \begin_inset space \textvisiblespace{}
9103 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
9106 \begin_layout Plain Layout
9107 \begin_inset Formula $\raisebox{5mm}{}\mathring{A}$
9121 \begin_inset space \hfill{}
9125 \begin_inset Tabular
9126 <lyxtabular version="3" rows="7" columns="2">
9127 <features rotate="0" tabularvalignment="middle">
9128 <column alignment="center" valignment="top" width="0pt">
9129 <column alignment="center" valignment="top" width="0pt">
9131 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
9134 \begin_layout Plain Layout
9140 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
9143 \begin_layout Plain Layout
9151 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
9154 \begin_layout Plain Layout
9158 \begin_inset space \textvisiblespace{}
9166 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
9169 \begin_layout Plain Layout
9170 \begin_inset Formula $\raisebox{5mm}{}\tilde{A}$
9180 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
9183 \begin_layout Plain Layout
9187 \begin_inset space \textvisiblespace{}
9195 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
9198 \begin_layout Plain Layout
9199 \begin_inset Formula $\raisebox{5mm}{}\hat{A}$
9209 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
9212 \begin_layout Plain Layout
9216 \begin_inset space \textvisiblespace{}
9224 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
9227 \begin_layout Plain Layout
9228 \begin_inset Formula $\raisebox{5mm}{}\check{A}$
9238 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
9241 \begin_layout Plain Layout
9245 \begin_inset space \textvisiblespace{}
9253 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
9256 \begin_layout Plain Layout
9257 \begin_inset Formula $\raisebox{5mm}{}\acute{A}$
9267 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
9270 \begin_layout Plain Layout
9274 \begin_inset space \textvisiblespace{}
9282 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
9285 \begin_layout Plain Layout
9286 \begin_inset Formula $\raisebox{5mm}{}\grave{A}$
9296 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
9299 \begin_layout Plain Layout
9303 \begin_inset space \textvisiblespace{}
9311 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
9314 \begin_layout Plain Layout
9315 \begin_inset Formula $\raisebox{5mm}{}\breve{A}$
9329 \begin_inset space \hfill{}
9335 \begin_layout Standard
9336 \begin_inset VSpace bigskip
9342 \begin_layout Standard
9343 You can directly insert accents like é to formulas.
9344 LyX will transform them to the corresponding accent command.
9346 \begin_inset Index idx
9349 \begin_layout Plain Layout
9355 it is better to insert a quotation mark before the vowel.
9356 These two characters are then treated by LaTeX as
9360 character when the formula part with the umlaut is marked as German.
9368 \begin_inset Quotes eld
9372 \begin_inset Quotes erd
9375 umlauts are created as demonstrated in the following example:
9378 \begin_layout Standard
9379 \begin_inset VSpace -2mm
9385 \begin_layout Standard
9387 \begin_inset Tabular
9388 <lyxtabular version="3" rows="3" columns="2">
9389 <features rotate="0" tabularvalignment="middle">
9390 <column alignment="center" valignment="top">
9391 <column alignment="center" valignment="top">
9393 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
9396 \begin_layout Plain Layout
9402 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
9405 \begin_layout Plain Layout
9407 \begin_inset Note Note
9410 \begin_layout Plain Layout
9418 \begin_inset space \thinspace{}
9421 pt space are only used as spacer.
9433 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
9436 \begin_layout Plain Layout
9439 \begin_inset Quotes grd
9447 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
9450 \begin_layout Plain Layout
9451 \begin_inset space \hspace{}
9458 \begin_inset Formula $"i$
9468 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
9471 \begin_layout Plain Layout
9475 \begin_inset space \textvisiblespace{}
9483 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
9486 \begin_layout Plain Layout
9487 \begin_inset Formula $\raisebox{5mm}{}\ddot{i}$
9503 \begin_layout Standard
9504 Another advantage to
9510 is that umlauts can directly be converted to mathematical text because
9511 the accent commands above are
9517 in mathematical text
9520 To convert an accented character to mathematical text, only the character
9521 under the accent may be converted.
9522 This applies also for all other conversions, e.
9523 \begin_inset space \thinspace{}
9527 \begin_inset space \space{}
9533 \begin_layout Standard
9534 In mathematical text, umlauts and other accented characters can directly
9538 \begin_layout Subsection
9539 Accents for several Characters
9540 \begin_inset Index idx
9543 \begin_layout Plain Layout
9544 Accents ! for several characters
9552 \begin_layout Standard
9553 \begin_inset space \hfill{}
9557 \begin_inset Tabular
9558 <lyxtabular version="3" rows="5" columns="2">
9559 <features rotate="0" tabularvalignment="middle">
9560 <column alignment="center" valignment="top" width="0pt">
9561 <column alignment="center" valignment="top" width="0pt">
9563 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
9566 \begin_layout Plain Layout
9572 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
9575 \begin_layout Plain Layout
9577 \begin_inset Note Note
9580 \begin_layout Plain Layout
9587 is only used as spacer.
9599 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
9602 \begin_layout Plain Layout
9606 \begin_inset space \textvisiblespace{}
9614 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
9617 \begin_layout Plain Layout
9618 \begin_inset Formula $\raisebox{6mm}{}\overleftarrow{A=B}\raisebox{-2mm}{}$
9628 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
9631 \begin_layout Plain Layout
9635 \begin_inset space \textvisiblespace{}
9643 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
9646 \begin_layout Plain Layout
9647 \begin_inset Formula $\raisebox{5mm}{}\underleftarrow{A=B}\raisebox{-3mm}{}$
9657 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
9660 \begin_layout Plain Layout
9664 \begin_inset space \textvisiblespace{}
9672 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
9675 \begin_layout Plain Layout
9676 \begin_inset Formula $\raisebox{6mm}{}\overleftrightarrow{A=B}\raisebox{-2mm}{}$
9686 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
9689 \begin_layout Plain Layout
9693 \begin_inset space \textvisiblespace{}
9701 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
9704 \begin_layout Plain Layout
9705 \begin_inset Formula $\raisebox{5mm}{}\underleftrightarrow{A=B}\raisebox{-3mm}{}$
9719 \begin_inset space \hfill{}
9723 \begin_inset Tabular
9724 <lyxtabular version="3" rows="5" columns="2">
9725 <features rotate="0" tabularvalignment="middle">
9726 <column alignment="center" valignment="top" width="0pt">
9727 <column alignment="center" valignment="top" width="0pt">
9729 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
9732 \begin_layout Plain Layout
9738 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
9741 \begin_layout Plain Layout
9749 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
9752 \begin_layout Plain Layout
9756 \begin_inset space \textvisiblespace{}
9764 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
9767 \begin_layout Plain Layout
9768 \begin_inset Formula $\raisebox{6mm}{}\overrightarrow{A=B}\raisebox{-2mm}{}$
9778 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
9781 \begin_layout Plain Layout
9785 \begin_inset space \textvisiblespace{}
9793 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
9796 \begin_layout Plain Layout
9797 \begin_inset Formula $\raisebox{5mm}{}\underrightarrow{A=B}\raisebox{-3mm}{}$
9807 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
9810 \begin_layout Plain Layout
9814 \begin_inset space \textvisiblespace{}
9822 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
9825 \begin_layout Plain Layout
9826 \begin_inset Formula $\raisebox{6mm}{}\widetilde{A=B}\raisebox{-2mm}{}$
9836 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
9839 \begin_layout Plain Layout
9843 \begin_inset space \textvisiblespace{}
9851 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
9854 \begin_layout Plain Layout
9855 \begin_inset Formula $\raisebox{6mm}{}\widehat{A=B}\raisebox{-2mm}{}$
9869 \begin_inset space \hfill{}
9875 \begin_layout Standard
9876 \begin_inset VSpace medskip
9879 With these commands as many characters as you like can be accented.
9892 will only be set in the output with a length of three characters, as shown
9893 in the following example:
9894 \begin_inset Formula
9904 \begin_layout Standard
9912 \begin_inset Index idx
9915 \begin_layout Plain Layout
9930 \begin_inset Index idx
9933 \begin_layout Plain Layout
9941 described in the previous subsection it is also possible to accent several
9948 \begin_inset space \textvisiblespace{}
9952 \begin_inset Formula $\downarrow$
9958 \begin_inset Formula
9968 \begin_layout Standard
9969 \begin_inset Newpage newpage
9975 \begin_layout Section
9977 \begin_inset CommandInset label
9984 \begin_inset Index idx
9987 \begin_layout Plain Layout
9996 \begin_layout Subsection
9998 \begin_inset CommandInset label
10000 name "sub:Predefined-Space"
10005 \begin_inset Index idx
10008 \begin_layout Plain Layout
10009 Space ! horizontal ! predefined
10017 \begin_layout Standard
10018 Sometimes it is necessary to insert horizontal space into a formula.
10019 This is done by inserting a protected space (shortcut
10022 arg "command-alternatives space-insert protected ; math-space"
10027 \begin_inset Quotes eld
10033 \begin_inset space \textvisiblespace{}
10039 \begin_inset Quotes erd
10042 appears and by pressing
10046 several times one can select one of eight different space sizes.
10047 The spaces can also be inserted using the math toolbar button
10048 \begin_inset Graphics
10049 filename ../images/math/space.png
10054 or special commands.
10055 Independent from the inserted command, one can select the size again by
10063 \begin_layout Standard
10066 \begin_inset VSpace -5mm
10070 \begin_inset Tabular
10071 <lyxtabular version="3" rows="3" columns="7">
10072 <features rotate="0" tabularvalignment="middle">
10073 <column alignment="center" valignment="middle" width="6.8cm">
10074 <column alignment="center" valignment="top">
10075 <column alignment="center" valignment="top">
10076 <column alignment="center" valignment="top">
10077 <column alignment="center" valignment="top">
10078 <column alignment="center" valignment="top">
10079 <column alignment="center" valignment="top">
10081 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
10084 \begin_layout Plain Layout
10090 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
10093 \begin_layout Plain Layout
10101 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
10104 \begin_layout Plain Layout
10112 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
10115 \begin_layout Plain Layout
10123 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
10126 \begin_layout Plain Layout
10134 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
10137 \begin_layout Plain Layout
10145 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
10148 \begin_layout Plain Layout
10158 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
10161 \begin_layout Plain Layout
10166 keystrokes after inserting the protected space
10171 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
10174 \begin_layout Plain Layout
10180 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
10183 \begin_layout Plain Layout
10189 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
10192 \begin_layout Plain Layout
10198 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
10201 \begin_layout Plain Layout
10207 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
10210 \begin_layout Plain Layout
10216 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
10219 \begin_layout Plain Layout
10227 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
10230 \begin_layout Plain Layout
10236 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
10239 \begin_layout Plain Layout
10240 \begin_inset Formula $A\, B$
10248 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
10251 \begin_layout Plain Layout
10252 \begin_inset Formula $A\: B$
10260 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
10263 \begin_layout Plain Layout
10264 \begin_inset Formula $A\; B$
10272 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
10275 \begin_layout Plain Layout
10276 \begin_inset Formula $A\quad B$
10284 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
10287 \begin_layout Plain Layout
10288 \begin_inset Formula $A\qquad B$
10296 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
10299 \begin_layout Plain Layout
10300 \begin_inset Formula $A\! B$
10316 \begin_layout Standard
10317 The last size seem to produce no space.
10318 It is displayed red in LyX contrary to the other sizes, because it is a
10320 There are two more negative spaces:
10323 \begin_layout Standard
10325 \begin_inset Tabular
10326 <lyxtabular version="3" rows="3" columns="3">
10327 <features rotate="0" tabularvalignment="middle">
10328 <column alignment="center" valignment="middle" width="6.8cm">
10329 <column alignment="center" valignment="top" width="0pt">
10330 <column alignment="center" valignment="top" width="0pt">
10332 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
10335 \begin_layout Plain Layout
10341 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
10344 \begin_layout Plain Layout
10352 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
10355 \begin_layout Plain Layout
10365 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
10368 \begin_layout Plain Layout
10373 keystrokes after inserting the protected space
10378 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
10381 \begin_layout Plain Layout
10387 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
10390 \begin_layout Plain Layout
10398 <cell multicolumn="1" alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
10401 \begin_layout Plain Layout
10407 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
10410 \begin_layout Plain Layout
10411 \begin_inset Formula $A\negmedspace B$
10419 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
10422 \begin_layout Plain Layout
10423 \begin_inset Formula $A\negthickspace B$
10439 \begin_layout Standard
10440 Negative spaces can lead to characters overlapping each other.
10441 Thus they can be used to enforce ligatures, which are e.
10442 \begin_inset space \thinspace{}
10446 \begin_inset space \space{}
10449 useful for summation operators:
10452 \begin_layout Standard
10454 \begin_inset Tabular
10455 <lyxtabular version="3" rows="3" columns="2">
10456 <features rotate="0" tabularvalignment="middle">
10457 <column alignment="center" valignment="top">
10458 <column alignment="center" valignment="top">
10460 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
10463 \begin_layout Plain Layout
10469 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
10472 \begin_layout Plain Layout
10474 \begin_inset Note Note
10477 \begin_layout Plain Layout
10484 is only used as spacer.
10496 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
10499 \begin_layout Plain Layout
10505 \begin_inset space \textvisiblespace{}
10513 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
10516 \begin_layout Plain Layout
10517 \begin_inset Formula $\raisebox{4.5mm}{}\sum\sum f_{kl}\raisebox{-2.5mm}{}$
10527 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
10530 \begin_layout Plain Layout
10538 \begin_inset space \textvisiblespace{}
10546 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
10549 \begin_layout Plain Layout
10550 \begin_inset Formula $\raisebox{4.5mm}{}\sum\negmedspace\sum f_{kl}\raisebox{-2.5mm}{}$
10566 \begin_layout Standard
10567 Relations like for example equal signs, are always surrounded by space.
10568 To suppress this, the equal sign is placed into a TeX-brace.
10569 The following example demonstrates this:
10572 \begin_layout Standard
10574 \begin_inset Tabular
10575 <lyxtabular version="3" rows="2" columns="2">
10576 <features rotate="0" tabularvalignment="middle">
10577 <column alignment="center" valignment="top" width="0pt">
10578 <column alignment="center" valignment="top" width="0pt">
10580 <cell alignment="center" valignment="top" usebox="none">
10583 \begin_layout Plain Layout
10589 <cell alignment="center" valignment="top" usebox="none">
10592 \begin_layout Plain Layout
10593 \begin_inset Formula $A=B$
10603 <cell alignment="center" valignment="top" usebox="none">
10606 \begin_layout Plain Layout
10607 \begin_inset Note Note
10610 \begin_layout Plain Layout
10617 is only used as spacer.
10623 \begin_inset Formula $\raisebox{5mm}{}$
10626 equation without space
10631 <cell multicolumn="1" alignment="center" valignment="top" usebox="none">
10634 \begin_layout Plain Layout
10635 \begin_inset Formula $A{=}B$
10651 \begin_layout Standard
10653 The command for the last formula is:
10658 \begin_inset Formula $\to$
10664 \begin_layout Standard
10665 \begin_inset VSpace bigskip
10668 Spaces are needed for physical units, because the space between the value
10669 and the unit is the smallest one and not a normal space.
10670 For units in text, the smallest space is inserted via the menu
10672 Insert\SpecialChar \menuseparator
10673 Formatting\SpecialChar \menuseparator
10675 \begin_inset space ~
10683 arg "space-insert thin"
10689 \begin_layout Standard
10690 An example to visualize the difference:
10693 \begin_layout Standard
10694 \begin_inset Tabular
10695 <lyxtabular version="3" rows="2" columns="2">
10696 <features rotate="0" tabularvalignment="middle">
10697 <column alignment="left" valignment="top">
10698 <column alignment="left" valignment="top">
10700 <cell alignment="center" valignment="top" usebox="none">
10703 \begin_layout Plain Layout
10705 \begin_inset Formula $\cdot$
10713 <cell alignment="center" valignment="top" usebox="none">
10716 \begin_layout Plain Layout
10717 space between value and unit
10724 <cell alignment="center" valignment="top" usebox="none">
10727 \begin_layout Plain Layout
10729 \begin_inset space \thinspace{}
10733 \begin_inset Formula $\cdot$
10741 <cell alignment="center" valignment="top" usebox="none">
10744 \begin_layout Plain Layout
10745 smallest space between value and unit
10758 \begin_layout Subsection
10763 \begin_layout Plain Layout
10776 \begin_layout Plain Layout
10777 for vertical space in formulas see
10778 \begin_inset CommandInset ref
10780 reference "sub:Line-Separation"
10793 \begin_layout Plain Layout
10801 \begin_inset Note Note
10804 \begin_layout Plain Layout
10807 texorpdfstring is used to avoid that the footnote appears in the PDF-bookmark.
10810 \begin_layout Plain Layout
10813 texorpdfstring is in section
10814 \begin_inset CommandInset ref
10816 reference "sub:Formulas-in-Section"
10826 \begin_inset CommandInset label
10828 name "sub:Variable-Space"
10833 \begin_inset Index idx
10836 \begin_layout Plain Layout
10837 Space ! horizontal ! variable
10845 \begin_layout Standard
10846 Space with a defined length can be inserted with the command
10853 \begin_inset Index idx
10856 \begin_layout Plain Layout
10866 \begin_inset Quotes eld
10872 \begin_inset space \textvisiblespace{}
10878 \begin_inset Quotes erd
10882 The length can be specified by left-clicking on the
10883 \begin_inset Quotes eld
10889 \begin_inset space \textvisiblespace{}
10895 \begin_inset Quotes erd
10899 The length may also be negative.
10900 To insert as much space as is available, the command
10907 \begin_inset Index idx
10910 \begin_layout Plain Layout
10921 \begin_layout Standard
10922 \begin_inset VSpace -1mm
10928 \begin_layout Standard
10930 \begin_inset Tabular
10931 <lyxtabular version="3" rows="4" columns="2">
10932 <features rotate="0" tabularvalignment="middle">
10933 <column alignment="center" valignment="top">
10934 <column alignment="center" valignment="top">
10936 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
10939 \begin_layout Plain Layout
10947 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
10950 \begin_layout Plain Layout
10958 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
10961 \begin_layout Plain Layout
10965 \begin_inset space \textvisiblespace{}
10969 \begin_inset Formula $\to$
10975 \begin_inset space \thinspace{}
10983 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
10986 \begin_layout Plain Layout
10987 \begin_inset Formula $A=B\hspace{3cm}A\not=C$
10997 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
11000 \begin_layout Plain Layout
11004 \begin_inset space \textvisiblespace{}
11008 \begin_inset Formula $\to$
11014 \begin_inset space \thinspace{}
11022 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
11025 \begin_layout Plain Layout
11026 \begin_inset Formula $A\hspace{-1mm}A\not=A$
11036 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
11039 \begin_layout Plain Layout
11043 \begin_inset space \textvisiblespace{}
11051 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
11054 \begin_layout Plain Layout
11055 \begin_inset Formula $A=A\hfill B=B$
11071 \begin_layout Standard
11072 In the last example the available space is given by the longest column entry
11074 In an inline formula the space depends on the length of the line in which
11082 Thus, when the line uses the full width, no space will be created.
11089 only has an effect on displayed formulas when the formula style
11094 (Formula styles are explained in
11095 \begin_inset CommandInset ref
11097 reference "sec:Formula-Styles"
11104 \begin_layout Standard
11111 , there are the commands
11123 that fill the space with a pattern, see
11124 \begin_inset CommandInset ref
11126 reference "sub:Ellipses"
11133 \begin_layout Standard
11134 For text, variable space can be inserted via the menu
11136 Insert\SpecialChar \menuseparator
11137 Formatting\SpecialChar \menuseparator
11139 \begin_inset space ~
11147 \begin_layout Standard
11148 This is a line with
11149 \begin_inset space \hspace{}
11154 \begin_inset space \thinspace{}
11160 \begin_layout Standard
11161 This is a line with
11162 \begin_inset space \hfill{}
11168 \begin_layout Subsection
11169 Space besides inline Formulas
11170 \begin_inset Index idx
11173 \begin_layout Plain Layout
11174 Space ! besides inline formulas
11182 \begin_layout Standard
11183 The space that surrounds inline formulas can be adjusted with the length
11191 \begin_inset Index idx
11194 \begin_layout Plain Layout
11203 The value of a length is set with the command
11210 \begin_inset Index idx
11213 \begin_layout Plain Layout
11221 which has the following scheme:
11224 \begin_layout Standard
11229 setlength{length name}{value}
11232 \begin_layout Standard
11240 \begin_inset space \thinspace{}
11246 \begin_layout Standard
11256 \begin_layout Standard
11257 is inserted in TeX-mode.
11259 \begin_inset space \thinspace{}
11262 mm space will now be set around all inline formulas:
11266 \begin_layout Plain Layout
11280 \begin_layout Standard
11281 This is a line with an inline formula
11282 \begin_inset Formula $A=B$
11286 \begin_inset space \thinspace{}
11289 mm surrounding space.
11293 \begin_layout Plain Layout
11307 \begin_layout Standard
11308 To return to the predefined value,
11314 is set to the value 0
11315 \begin_inset space \thinspace{}
11321 \begin_layout Section
11323 \begin_inset Index idx
11326 \begin_layout Plain Layout
11333 \begin_inset Index idx
11336 \begin_layout Plain Layout
11341 \begin_layout Plain Layout
11352 \begin_layout Plain Layout
11367 \begin_layout Standard
11368 Boxes for text are described in chapter
11375 \begin_inset space ~
11383 \begin_layout Subsection
11385 \begin_inset CommandInset label
11387 name "sub:Boxes-with-Frame"
11392 \begin_inset Index idx
11395 \begin_layout Plain Layout
11404 \begin_layout Standard
11405 It is possible to frame a formula or part of one with the commands
11412 \begin_inset Index idx
11415 \begin_layout Plain Layout
11430 \begin_inset Index idx
11433 \begin_layout Plain Layout
11444 \begin_layout Standard
11445 When one of these commands is inserted in a formula, a blue box appears
11446 within a frame to enter formula parts.
11453 an additional formula has to be created by
11457 within this box, because the box content will otherwise be treated as mathemati
11465 is used, a new formula is automatically created inside the frame.
11468 \begin_layout Standard
11475 is not suitable to frame displayed formulas because the formula will always
11476 be set in the size of the text.
11483 is in contrary not suitable to frame inline formulas, because the formula
11484 will always be set in the size of a displayed formula.
11487 \begin_layout Standard
11501 \begin_inset Index idx
11504 \begin_layout Plain Layout
11512 where additionally the frame width and the alignment can be specified.
11519 is used in the following scheme:
11522 \begin_layout Standard
11527 framebox[frame width][position]{box content}
11530 \begin_layout Standard
11531 The position can either be
11548 right aligns the formula in the box.
11549 When no position is given, the formula will be centered.
11550 \begin_inset Newline newline
11553 If no width is given, also no position can be given.
11554 In this case the frame width is adjusted to the box content like for
11563 \begin_layout Standard
11570 is inserted, a box appears containing three blue boxes.
11571 The first two boxes are surrounded by brackets and denote the two optional
11573 The third box is for formula parts like for
11582 \begin_layout Standard
11583 \begin_inset Newpage newpage
11589 \begin_layout Standard
11591 \begin_inset Tabular
11592 <lyxtabular version="3" rows="5" columns="2">
11593 <features rotate="0" tabularvalignment="middle">
11594 <column alignment="center" valignment="top">
11595 <column alignment="center" valignment="top">
11597 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
11600 \begin_layout Plain Layout
11606 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
11609 \begin_layout Plain Layout
11611 \begin_inset Note Note
11614 \begin_layout Plain Layout
11621 is only used as spacer.
11633 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
11636 \begin_layout Plain Layout
11640 \begin_inset space \textvisiblespace{}
11650 \begin_inset space \textvisiblespace{}
11658 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
11661 \begin_layout Plain Layout
11662 \begin_inset Formula $\raisebox{6mm}{}\fbox{\ensuremath{\int A=B}}\raisebox{-4mm}{}$
11672 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
11675 \begin_layout Plain Layout
11679 \begin_inset space \textvisiblespace{}
11685 \begin_inset space \textvisiblespace{}
11693 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
11696 \begin_layout Plain Layout
11697 \begin_inset Formula $\raisebox{8.5mm}{}\boxed{\int A=B}\raisebox{-6.5mm}{}$
11707 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
11710 \begin_layout Plain Layout
11714 \begin_inset space \textvisiblespace{}
11722 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
11725 \begin_layout Plain Layout
11726 \begin_inset Formula $\raisebox{6mm}{}A+\fbox{B}\raisebox{-3mm}{}$
11736 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
11739 \begin_layout Plain Layout
11743 \begin_inset space \textvisiblespace{}
11747 \begin_inset Formula $\to$
11751 \begin_inset Formula $\to$
11761 \begin_inset space \textvisiblespace{}
11765 \begin_inset Formula $\downarrow$
11773 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
11776 \begin_layout Plain Layout
11777 \begin_inset Formula $\raisebox{6mm}{}$
11781 \begin_inset Formula $\framebox[20mm][]{\ensuremath{\frac{A}{B}}}$
11785 \begin_inset Formula $\raisebox{-4mm}{}$
11801 \begin_layout Standard
11802 The frame thickness can also be adjusted.
11803 To do this the following commands have to be inserted in TeX-mode before
11807 \begin_layout Standard
11817 \begin_inset Quotes eld
11821 \begin_inset Quotes erd
11835 \begin_inset Quotes eld
11839 \begin_inset Quotes erd
11845 \begin_layout Standard
11846 \begin_inset Quotes eld
11850 \begin_inset Quotes erd
11853 specifies the minimal distance between the frame and the first character
11855 An example for this is the following framed formula:
11859 \begin_layout Plain Layout
11871 \begin_inset Formula
11878 Before this formula the commands
11881 \begin_layout Standard
11903 \begin_layout Standard
11904 were inserted in TeX-mode.
11905 The given values are used for all following boxes.
11908 \begin_layout Standard
11909 To return to the standard frame size, the command
11912 \begin_layout Standard
11937 \begin_layout Plain Layout
11951 \begin_layout Standard
11952 is inserted in TeX-mode before the next formula.
11955 \begin_layout Subsection
11956 Boxes without Frame
11957 \begin_inset CommandInset label
11959 name "sub:Boxes-without-Frame"
11964 \begin_inset Index idx
11967 \begin_layout Plain Layout
11968 Boxes ! without frame
11976 \begin_layout Standard
11977 For boxes without a frame there are the following box commands:
11984 \begin_inset Index idx
11987 \begin_layout Plain Layout
12002 \begin_inset Index idx
12005 \begin_layout Plain Layout
12020 \begin_inset Index idx
12023 \begin_layout Plain Layout
12034 \begin_layout Standard
12041 a box can be super- or subscripted.
12042 But in contrary to normal super- and subscripting, the characters in the
12043 box keep their font size.
12050 is used in the following scheme:
12053 \begin_layout Standard
12058 raisebox{height}{box content}
12061 \begin_layout Standard
12062 When the box should contain a formula, an extra formula is needed like for
12073 \begin_inset Note Greyedout
12076 \begin_layout Plain Layout
12087 this extra formula is created by pressing
12091 twice instead of once because LyX doesn't yet support
12105 \begin_layout Standard
12107 \begin_inset Tabular
12108 <lyxtabular version="3" rows="4" columns="2">
12109 <features rotate="0" tabularvalignment="middle">
12110 <column alignment="center" valignment="top">
12111 <column alignment="center" valignment="top">
12113 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
12116 \begin_layout Plain Layout
12122 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
12125 \begin_layout Plain Layout
12133 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
12136 \begin_layout Plain Layout
12140 \begin_inset Formula $\to$
12146 \begin_inset Formula $\to$
12154 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
12157 \begin_layout Plain Layout
12158 \begin_inset Formula $H\raisebox{2mm}{al}lo$
12168 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
12171 \begin_layout Plain Layout
12175 \begin_inset Formula $\to$
12181 \begin_inset Formula $\to$
12189 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
12192 \begin_layout Plain Layout
12193 \begin_inset Formula $H\raisebox{-2mm}{al}lo$
12203 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
12206 \begin_layout Plain Layout
12210 \begin_inset Formula $\to$
12226 \begin_inset space \textvisiblespace{}
12234 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
12237 \begin_layout Plain Layout
12238 \begin_inset Formula $A=\raisebox{-2mm}{\mbox{\ensuremath{\sqrt{B}}}}$
12254 \begin_layout Standard
12279 , with the difference that there is no frame.
12282 \begin_layout Subsection
12284 \begin_inset CommandInset label
12286 name "sub:Colored-Boxes"
12291 \begin_inset Index idx
12294 \begin_layout Plain Layout
12303 \begin_layout Standard
12304 To be able to use all commands explained in this section, the LaTeX-package
12313 \begin_layout Plain Layout
12318 is part of every LaTeX standard installation.
12324 \begin_inset Index idx
12327 \begin_layout Plain Layout
12333 has to be loaded in the LaTeX-preamble with the line
12337 \begin_layout Plain Layout
12338 When text is colored somewhere in the document with a predefined color,
12339 LyX loads the LaTeX-package
12344 Thus it is possible that the package is loaded twice, but this does not
12351 \begin_inset Note Note
12354 \begin_layout Plain Layout
12355 To avoid that the package is loaded twice, a macro was inserted to the LaTeX-pre
12364 \begin_layout Standard
12372 \begin_layout Standard
12373 \begin_inset VSpace medskip
12376 To color boxes, the command
12383 \begin_inset Index idx
12386 \begin_layout Plain Layout
12394 is used in the following scheme:
12397 \begin_layout Standard
12402 colorbox{color}{box content}
12405 \begin_layout Standard
12406 The box content can also be a box and a
12412 can also be part of another box (see the 2nd and 3rd example).
12413 When the box should contain a formula, an extra formula has to be created,
12414 the same way as for
12424 \begin_layout Plain Layout
12425 This also applies for the command
12439 \begin_layout Standard
12440 One of the following predefined colors can be chosen:
12443 \begin_layout Standard
12477 \begin_layout Standard
12479 \begin_inset Tabular
12480 <lyxtabular version="3" rows="4" columns="2">
12481 <features rotate="0" tabularvalignment="middle">
12482 <column alignment="center" valignment="top">
12483 <column alignment="center" valignment="top">
12485 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
12488 \begin_layout Plain Layout
12494 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
12497 \begin_layout Plain Layout
12499 \begin_inset Note Note
12502 \begin_layout Plain Layout
12509 is only used as spacer.
12521 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
12524 \begin_layout Plain Layout
12528 \begin_inset Formula $\to$
12538 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
12541 \begin_layout Plain Layout
12542 \begin_inset Formula $\raisebox{6mm}{}\colorbox{yellow}{A=B}\raisebox{-3mm}{}$
12552 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
12555 \begin_layout Plain Layout
12559 \begin_inset Formula $\to$
12567 \begin_inset space \textvisiblespace{}
12575 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
12578 \begin_layout Plain Layout
12579 \begin_inset Formula $\raisebox{6mm}{}\colorbox{green}{\fbox{A=B}}\raisebox{-3mm}{}$
12589 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
12592 \begin_layout Plain Layout
12596 \begin_inset space \textvisiblespace{}
12602 \begin_inset Formula $\to$
12618 \begin_inset space \textvisiblespace{}
12626 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
12629 \begin_layout Plain Layout
12630 \begin_inset Formula $\raisebox{7mm}{}\fbox{\colorbox{green}{\mbox{\ensuremath{\int C=D}}}}\raisebox{-5mm}{}$
12646 \begin_layout Standard
12653 only colors the box but not the characters in the box.
12654 To color all characters, the whole formula is highlighted and the desired
12655 color is chosen in the
12658 \begin_inset space ~
12664 The dialog can be called with the toolbar button
12665 \begin_inset Graphics
12666 filename ../images/dialog-show_character.png
12673 Edit\SpecialChar \menuseparator
12675 \begin_inset space ~
12678 Style\SpecialChar \menuseparator
12682 The formula number then has the same color as the formula.
12683 When the formula number should get another color than the formula characters,
12684 the color must be changed within the formula.
12687 \begin_layout Standard
12691 \begin_layout Standard
12694 \begin_inset Formula
12696 \int A=B\label{eq:red}
12704 \begin_inset Formula
12706 \textcolor{red}{\int A=B}\label{eq:redgreen}
12714 \begin_layout Standard
12716 \begin_inset CommandInset ref
12722 is completely colored red.
12723 \begin_inset Newline newline
12727 \begin_inset CommandInset ref
12729 reference "eq:redgreen"
12733 was first completely colored green to set the color for the formula number.
12734 Subsequently the formula characters were colored red.
12737 \begin_layout Standard
12738 \begin_inset VSpace bigskip
12741 To color the frame different than the rest of the box, the command
12748 \begin_inset Index idx
12751 \begin_layout Plain Layout
12759 is used in the following scheme:
12762 \begin_layout Standard
12767 fcolorbox{frame color}{color}{box content}
12770 \begin_layout Standard
12777 is an extension of the command
12784 The frame width is set, like for
12807 \begin_layout Plain Layout
12819 \begin_inset Formula
12821 \fcolorbox{cyan}{magenta}{A=B}
12830 \begin_layout Plain Layout
12844 \begin_layout Standard
12845 This formula was created with the command
12846 \begin_inset Newline newline
12854 \begin_inset Formula $\to$
12860 \begin_inset Formula $\to$
12870 \begin_layout Standard
12871 \begin_inset VSpace bigskip
12874 To use other colors than the predefined ones, they have to be defined first.
12877 \begin_layout Standard
12878 One can for example define the color
12879 \begin_inset Quotes eld
12887 \begin_inset Quotes erd
12890 with the LaTeX-preamble line:
12893 \begin_layout Standard
12898 definecolor{darkgreen}{cmyk}{0.5,
12913 \begin_inset Index idx
12916 \begin_layout Plain Layout
12927 \begin_layout Standard
12932 is the color space that denotes the colors
12949 The four comma separated numbers are the portion factor for the corresponding
12950 colors of the color space.
12951 The factors can be in the range of 0
12952 \begin_inset space \thinspace{}
12956 \begin_inset space \thinspace{}
12964 also the color space
12968 can be used for definitions.
12985 , so that there are in this case three portion factors for the corresponding
12987 Furthermore there is the color space
12991 with one portion factor for the gray value.
12994 \begin_layout Standard
12995 As example a framed box with the new defined color
12999 where the characters have been colored
13004 \begin_inset Formula
13006 \colorbox{darkgreen}{\color{yellow}\boxed{\int A\,\mathrm{d}x=\frac{\sqrt[5]{B}}{\ln\left(\frac{1}{3}\right)}}}
13014 \begin_layout Standard
13015 Self-defined colors can also be used for text with the help of the command
13023 \begin_inset Index idx
13026 \begin_layout Plain Layout
13035 \begin_layout Standard
13039 \begin_layout Plain Layout
13043 textcolor{darkgreen}{
13049 \begin_inset Quotes eld
13053 \begin_inset Quotes erd
13060 \begin_layout Plain Layout
13070 \begin_layout Standard
13078 \begin_inset Index idx
13081 \begin_layout Plain Layout
13089 is used in the scheme
13093 textcolor{color}{characters to color}
13098 \begin_layout Subsection
13100 \begin_inset CommandInset label
13102 name "sub:Paragraph-Boxes"
13107 \begin_inset Index idx
13110 \begin_layout Plain Layout
13111 Boxes ! as paragraph
13119 \begin_layout Standard
13120 A box that can contain several lines and paragraphs, a so-called paragraph
13121 box (parbox), can be created with the menu
13123 Insert\SpecialChar \menuseparator
13126 or the toolbar button
13127 \begin_inset Graphics
13128 filename ../images/box-insert.png
13136 \begin_layout Standard
13137 The following example shows a framed parbox in a line:
13140 \begin_layout Standard
13141 \begin_inset VSpace medskip
13145 \begin_inset Box Boxed
13155 height_special "totalheight"
13158 \begin_layout Plain Layout
13159 This is a paragraph box.
13161 \begin_inset space \thinspace{}
13164 cm long and can also contain formulas:
13165 \begin_inset Formula $\int A\,\mathrm{d}s=C$
13176 \begin_layout Standard
13177 \begin_inset VSpace medskip
13183 \begin_layout Standard
13184 Such a box is created by right-clicking on the gray box inset.
13185 A dialog pops up showing the box properties.
13199 \begin_inset space \thinspace{}
13204 Vertical Box Alignment
13209 \begin_layout Standard
13210 \begin_inset VSpace medskip
13213 In LaTeX a parbox is created with the command
13220 \begin_inset Index idx
13223 \begin_layout Plain Layout
13231 which has the following scheme:
13234 \begin_layout Standard
13239 parbox[position]{width}{box content}
13242 \begin_layout Standard
13257 \begin_inset Quotes eld
13261 \begin_inset Quotes erd
13264 means that the box is aligned within the surrounding text with its last
13271 \begin_inset Quotes eld
13275 \begin_inset Quotes erd
13278 this is done with the first line.
13279 When no position is given, the box will be vertically centered, see section
13287 \begin_inset space ~
13292 manual for examples.
13295 \begin_layout Standard
13296 \begin_inset VSpace bigskip
13299 To frame formulas completely, including the formula number, the formula
13300 must be set into a parbox.
13301 To do this, the command
13315 is inserted in TeX-mode before the formula.
13323 \begin_inset Index idx
13326 \begin_layout Plain Layout
13334 is hereby the line width set for the document.
13335 Because the frame is outside the parbox, 2
13336 \begin_inset space \thinspace{}
13339 times the frame separation and the frame thickness must be subtracted from
13341 As this is not automatically done by LyX due to a bug
13345 \begin_layout Plain Layout
13346 \begin_inset CommandInset href
13348 name "LyX-bug #4483"
13349 target "http://www.lyx.org/trac/ticket/4483"
13358 , TeX-mode has to be used.
13359 To be able to multiply and subtract in arguments, the LaTeX-package
13367 \begin_layout Plain Layout
13372 is part of every LaTeX standard installation.
13378 \begin_inset Index idx
13381 \begin_layout Plain Layout
13387 must be loaded in the LaTeX-preamble with the line
13390 \begin_layout Standard
13398 \begin_layout Standard
13399 Behind the formula both boxes are closed by entering
13404 Here is an example:
13408 \begin_layout Plain Layout
13422 \begin_layout Standard
13426 \begin_layout Plain Layout
13444 \begin_inset Formula
13446 \int A\,\mathrm{d}x=\frac{\sqrt[5]{B}}{\ln\left(\frac{1}{3}\right)}
13455 \begin_layout Plain Layout
13466 \begin_layout Plain Layout
13480 \begin_layout Standard
13481 \begin_inset VSpace medskip
13484 As a parbox is used as the argument of
13490 , there is in this case no difference between
13505 \begin_layout Standard
13506 \begin_inset VSpace bigskip
13509 Paragraph boxes are very useful to comment formulas directly.
13516 is used in combination with the command
13530 \begin_inset CommandInset ref
13532 reference "sub:User-defined-Numbering"
13539 \begin_layout Standard
13540 An example of a formula commented with
13549 \begin_layout Standard
13553 \begin_layout Plain Layout
13566 This is a description.
13567 It is distinctly separated from the formula and multiline.
13571 \begin_layout Plain Layout
13583 \begin_layout Standard
13584 Such a formula must be inserted completely in TeX-mode because LyX does
13585 not yet support the command
13592 The formula is created with the following command sequence:
13595 \begin_layout Standard
13608 is inserted in TeX-mode.
13612 \begin_layout Plain Layout
13613 When the formula style
13625 can also be replaced by
13632 (formula styles see
13633 \begin_inset CommandInset ref
13635 reference "sec:Formula-Styles"
13644 Then the description follows as normal text and finally
13650 is inserted in TeX-mode.
13663 hereby create a displayed formula.
13666 \begin_layout Standard
13673 can be seen in this example that was
13674 \begin_inset Quotes eld
13678 \begin_inset Quotes erd
13681 using the mathematical textmode:
13682 \begin_inset Formula
13684 5x-7b=3b\textrm{This is a description. It is not separated from the formula ...}
13692 \begin_layout Section
13694 \begin_inset Index idx
13697 \begin_layout Plain Layout
13706 \begin_layout Subsection
13708 \begin_inset CommandInset label
13710 name "sub:Big-Operators"
13715 \begin_inset Index idx
13718 \begin_layout Plain Layout
13725 \begin_inset Index idx
13728 \begin_layout Plain Layout
13735 \begin_inset Index idx
13738 \begin_layout Plain Layout
13747 \begin_layout Standard
13748 To be able to use all integral operators listed here, the option
13750 Use esint package automatically
13752 must be set in the document settings under
13755 \begin_inset space ~
13763 \begin_layout Standard
13764 \begin_inset space \hfill{}
13768 \begin_inset Tabular
13769 <lyxtabular version="3" rows="11" columns="2">
13770 <features rotate="0" tabularvalignment="middle">
13771 <column alignment="center" valignment="top" width="0pt">
13772 <column alignment="center" valignment="top" width="0pt">
13774 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
13777 \begin_layout Plain Layout
13783 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
13786 \begin_layout Plain Layout
13794 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
13797 \begin_layout Plain Layout
13801 \begin_inset Index idx
13804 \begin_layout Plain Layout
13817 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
13820 \begin_layout Plain Layout
13821 \begin_inset Formula $\int$
13831 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
13834 \begin_layout Plain Layout
13842 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
13845 \begin_layout Plain Layout
13846 \begin_inset Formula $\oint$
13856 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
13859 \begin_layout Plain Layout
13867 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
13870 \begin_layout Plain Layout
13871 \begin_inset Formula $\ointctrclockwise$
13881 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
13884 \begin_layout Plain Layout
13892 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
13895 \begin_layout Plain Layout
13896 \begin_inset Formula $\ointclockwise$
13906 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
13909 \begin_layout Plain Layout
13917 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
13920 \begin_layout Plain Layout
13921 \begin_inset Formula $\sqint$
13931 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
13934 \begin_layout Plain Layout
13942 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
13945 \begin_layout Plain Layout
13947 \begin_inset Formula $\fint$
13957 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
13960 \begin_layout Plain Layout
13968 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
13971 \begin_layout Plain Layout
13973 \begin_inset Formula $\landupint$
13983 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
13986 \begin_layout Plain Layout
13994 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
13997 \begin_layout Plain Layout
13999 \begin_inset Formula $\landdownint$
14009 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
14012 \begin_layout Plain Layout
14020 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
14023 \begin_layout Plain Layout
14024 \begin_inset Formula $\bigcap$
14034 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
14037 \begin_layout Plain Layout
14045 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
14048 \begin_layout Plain Layout
14049 \begin_inset Formula $\bigcup$
14063 \begin_inset space \hfill{}
14067 \begin_inset Tabular
14068 <lyxtabular version="3" rows="11" columns="2">
14069 <features rotate="0" tabularvalignment="middle">
14070 <column alignment="center" valignment="top" width="0pt">
14071 <column alignment="center" valignment="top" width="0pt">
14073 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
14076 \begin_layout Plain Layout
14082 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
14085 \begin_layout Plain Layout
14093 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
14096 \begin_layout Plain Layout
14100 \begin_inset Index idx
14103 \begin_layout Plain Layout
14116 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
14119 \begin_layout Plain Layout
14120 \begin_inset Formula $\sum$
14130 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
14133 \begin_layout Plain Layout
14137 \begin_inset Index idx
14140 \begin_layout Plain Layout
14147 \begin_layout Plain Layout
14166 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
14169 \begin_layout Plain Layout
14170 \begin_inset Formula $\prod$
14180 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
14183 \begin_layout Plain Layout
14191 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
14194 \begin_layout Plain Layout
14195 \begin_inset Formula $\coprod$
14205 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
14208 \begin_layout Plain Layout
14216 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
14219 \begin_layout Plain Layout
14220 \begin_inset Formula $\bigodot$
14230 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
14233 \begin_layout Plain Layout
14241 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
14244 \begin_layout Plain Layout
14245 \begin_inset Formula $\bigotimes$
14255 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
14258 \begin_layout Plain Layout
14266 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
14269 \begin_layout Plain Layout
14270 \begin_inset Formula $\bigoplus$
14280 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
14283 \begin_layout Plain Layout
14291 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
14294 \begin_layout Plain Layout
14295 \begin_inset Formula $\bigwedge$
14305 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
14308 \begin_layout Plain Layout
14316 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
14319 \begin_layout Plain Layout
14320 \begin_inset Formula $\bigvee$
14330 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
14333 \begin_layout Plain Layout
14341 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
14344 \begin_layout Plain Layout
14345 \begin_inset Formula $\bigsqcup$
14355 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
14358 \begin_layout Plain Layout
14366 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
14369 \begin_layout Plain Layout
14370 \begin_inset Formula $\biguplus$
14384 \begin_inset space \hfill{}
14390 \begin_layout Standard
14391 All big operators can also be inserted via the math toolbar button
14392 \begin_inset Graphics
14393 filename ../images/math/intop.png
14401 \begin_layout Standard
14402 The operators are called big because they are bigger than the sometimes
14403 equal looking binary operators.
14404 All big operators can have limits as described in the next subsection.
14407 \begin_layout Standard
14408 For all integral operators there is a second version available, ending in
14426 These operators are different from
14433 \begin_inset space \space{}
14436 in the style the operator limits are displayed, see
14437 \begin_inset CommandInset ref
14439 reference "sub:Operator-Limits"
14447 \begin_layout Subsubsection*
14448 Advice for Integrals
14451 \begin_layout Standard
14456 in an integral is an operator, that therefore has to be set upright.
14457 This is done by highlighting the
14461 and using the keyboard shortcut
14471 \begin_layout Plain Layout
14477 \begin_inset CommandInset ref
14479 reference "sub:Font-Styles"
14489 Finally the smallest space is inserted before the
14493 , as this is usual for operators.
14497 \begin_layout Standard
14499 \begin_inset Formula $\int A(x)dx$
14503 \begin_inset Newline newline
14507 \begin_inset Phantom HPhantom
14510 \begin_layout Plain Layout
14517 \begin_inset Formula $\int A(x)\,\mathrm{d}x$
14523 \begin_layout Standard
14524 For multiple integrals there are the following commands:
14525 \begin_inset VSpace medskip
14531 \begin_layout Standard
14532 \begin_inset space \hfill{}
14536 \begin_inset Tabular
14537 <lyxtabular version="3" rows="4" columns="2">
14538 <features rotate="0" tabularvalignment="middle">
14539 <column alignment="center" valignment="top">
14540 <column alignment="center" valignment="top">
14542 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
14545 \begin_layout Plain Layout
14551 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
14554 \begin_layout Plain Layout
14556 \begin_inset Note Note
14559 \begin_layout Plain Layout
14566 is only used as spacer.
14578 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
14581 \begin_layout Plain Layout
14589 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
14592 \begin_layout Plain Layout
14593 \begin_inset Formula $\raisebox{4.5mm}{}\iint\raisebox{-2.5mm}{}$
14603 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
14606 \begin_layout Plain Layout
14614 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
14617 \begin_layout Plain Layout
14618 \begin_inset Formula $\raisebox{4.5mm}{}\oiint\raisebox{-2.5mm}{}$
14628 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
14631 \begin_layout Plain Layout
14639 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
14642 \begin_layout Plain Layout
14643 \begin_inset Formula $\raisebox{4.5mm}{}\sqiint\raisebox{-2.5mm}{}$
14657 \begin_inset space \hfill{}
14661 \begin_inset Tabular
14662 <lyxtabular version="3" rows="4" columns="2">
14663 <features rotate="0" tabularvalignment="middle">
14664 <column alignment="center" valignment="top">
14665 <column alignment="center" valignment="top">
14667 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
14670 \begin_layout Plain Layout
14676 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
14679 \begin_layout Plain Layout
14687 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
14690 \begin_layout Plain Layout
14698 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
14701 \begin_layout Plain Layout
14702 \begin_inset Formula $\raisebox{4.5mm}{}\iiint\raisebox{-2.5mm}{}$
14712 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
14715 \begin_layout Plain Layout
14723 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
14726 \begin_layout Plain Layout
14727 \begin_inset Formula $\raisebox{4.5mm}{}\iiiint\raisebox{-2.5mm}{}$
14737 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
14740 \begin_layout Plain Layout
14748 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
14751 \begin_layout Plain Layout
14752 \begin_inset Formula $\raisebox{4.5mm}{}\dotsint\raisebox{-2.5mm}{}$
14766 \begin_inset space \hfill{}
14772 \begin_layout Standard
14773 \begin_inset Newpage newpage
14779 \begin_layout Subsection
14781 \begin_inset CommandInset label
14783 name "sub:Operator-Limits"
14788 \begin_inset Index idx
14791 \begin_layout Plain Layout
14800 \begin_layout Standard
14801 Limits are created by super- and subscripts:
14804 \begin_layout Standard
14806 \begin_inset Tabular
14807 <lyxtabular version="3" rows="2" columns="2">
14808 <features rotate="0" tabularvalignment="middle">
14809 <column alignment="center" valignment="top" width="0pt">
14810 <column alignment="center" valignment="top" width="0pt">
14812 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
14815 \begin_layout Plain Layout
14821 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
14824 \begin_layout Plain Layout
14826 \begin_inset Note Note
14829 \begin_layout Plain Layout
14836 is only used as spacer.
14848 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
14851 \begin_layout Plain Layout
14857 \begin_inset space \textvisiblespace{}
14861 \begin_inset Formula $\to$
14865 \begin_inset Formula $\to$
14873 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
14876 \begin_layout Plain Layout
14877 \begin_inset Formula $\raisebox{5mm}{}\prod_{0}^{\infty}A(x)\raisebox{-2.5mm}{}$
14893 \begin_layout Standard
14894 Limits of inline formulas are set right beside the operator.
14895 Limits in displayed formulas are set above or below the operator, except
14896 for integral limits.
14899 \begin_layout Standard
14900 To force that the limits are set beside the operator, the cursor is set
14901 directly behind the operator and the limits type is changed with the menu
14904 Edit\SpecialChar \menuseparator
14905 Math\SpecialChar \menuseparator
14924 \begin_layout Standard
14925 The default limits type is this:
14926 \begin_inset Formula
14928 \sum_{x=0}^{\infty}\frac{1}{x^{2}}
14933 This is how it looks when the limits type was changed to
14940 \begin_inset Formula
14942 \sum\nolimits _{x=0}^{\infty}\frac{1}{x^{2}}
14947 For integrals, except those ending with
14963 etc., the limits are by default set beside the operator.
14964 But for multiple integrals the limits are often set below the operator.
14965 In the following example the limits type was therefore set to
14969 and so set below the integrals:
14970 \begin_inset Formula
14972 \iiint\limits _{V}X\,\mathrm{d}V=U\label{eq:VolInt}
14980 \begin_layout Standard
14981 \begin_inset VSpace medskip
14984 To specify conditions for limits, the commands
14991 \begin_inset Index idx
14994 \begin_layout Plain Layout
15009 \begin_inset Index idx
15012 \begin_layout Plain Layout
15021 To create for example this expression
15022 \begin_inset Formula
15024 \sum_{\begin{subarray}{c}
15028 \end{subarray}}^{n}k^{-2}\label{eq:substack}
15036 \begin_layout Standard
15037 the following has to be done:
15038 \begin_inset Newline newline
15050 \begin_inset space \textvisiblespace{}
15056 One is now in a blue box under the summation operator and insert there
15062 \begin_inset space \textvisiblespace{}
15068 The blue box is now within a purple box and now several lines can be written
15070 A new line is created by inserting a line break (
15073 arg "newline-insert newline"
15078 \begin_inset Newline newline
15083 0<k<1000 Ctrl+Return
15084 \begin_inset Newline newline
15089 is typed in, a new box appears below for the new line.
15092 \begin_layout Standard
15093 The alignment of the lines can be changed to left aligned with the
15103 Edit\SpecialChar \menuseparator
15107 To get right alignment,
15112 \begin_inset space \textvisiblespace{}
15117 is inserted at the beginning of the line.
15120 \begin_layout Standard
15133 with the difference that the lines are always centered.
15136 \begin_layout Standard
15137 \begin_inset VSpace bigskip
15141 \begin_inset CommandInset ref
15143 reference "eq:substack"
15147 there can be too much space beside an operator, because the characters
15148 following the operator are set beside the limits.
15151 \begin_layout Standard
15152 To avoid this, the following macro can be used in the LaTeX-preamble:
15155 \begin_layout Standard
15169 \begin_inset Newline newline
15181 \begin_inset Newline newline
15188 mathclapinternal #1#2{
15192 mathsurround =0pt #1{#2}$}}
15195 \begin_layout Standard
15196 This defines the command
15203 \begin_inset Index idx
15206 \begin_layout Plain Layout
15214 that sets the width of the limit to 0
15215 \begin_inset space \thinspace{}
15219 The command scheme is
15222 \begin_layout Standard
15230 \begin_layout Standard
15231 where the limit can consist of several conditions.
15234 \begin_layout Standard
15236 \begin_inset CommandInset ref
15238 reference "eq:substack"
15242 , one uses the command
15245 \begin_layout Standard
15255 \begin_inset space \textvisiblespace{}
15258 0<k<1000 Ctrl+Return
15261 \begin_layout Standard
15262 to create the lower limit.
15263 The summand is now directly behind the summation operator:
15264 \begin_inset Formula
15266 \sum_{\mathclap{\substack{0<k<1000\\
15278 \begin_layout Standard
15279 \begin_inset VSpace bigskip
15282 How to use one limit for several operators is described in
15283 \begin_inset CommandInset ref
15285 reference "sub:Self-defined-Operators"
15292 \begin_layout Subsection
15293 Decoration for Operators
15294 \begin_inset Index idx
15297 \begin_layout Plain Layout
15298 Operators ! Decoration
15306 \begin_layout Standard
15314 \begin_inset Index idx
15317 \begin_layout Plain Layout
15332 \begin_inset Index idx
15335 \begin_layout Plain Layout
15343 characters can be placed above or below an operator, respectively.
15351 \begin_inset Index idx
15354 \begin_layout Plain Layout
15362 characters can be set before and behind a big operator.
15363 The command scheme is:
15366 \begin_layout Standard
15382 \begin_layout Standard
15389 must always be before the operator.
15390 You can decorate with several characters and even with other operators
15392 To place for example only characters behind a big operator, write nothing
15393 between the first braces but don't omit the braces.
15396 \begin_layout Standard
15397 For example the command
15402 \begin_inset Formula $\to$
15412 \begin_inset Formula $\to$
15418 \begin_inset space \textvisiblespace{}
15428 \begin_inset Formula
15430 \sideset{}{'}\sum_{k=1}^{n}
15438 \begin_layout Standard
15439 \begin_inset Note Greyedout
15442 \begin_layout Plain Layout
15449 can only be used to decorate big operators, binary operators are not allowed.
15457 \begin_layout Standard
15470 can also be used to decorate symbols and characters.
15471 For example, the command
15476 \begin_inset space \textvisiblespace{}
15482 \begin_inset space \textvisiblespace{}
15488 \begin_inset Formula $\uparrow$
15496 \begin_inset Formula
15498 \overset{a}{\maltese}
15506 \begin_layout Subsection
15508 \begin_inset CommandInset label
15510 name "sub:Binary-Operators"
15515 \begin_inset Index idx
15518 \begin_layout Plain Layout
15527 \begin_layout Standard
15528 Binary operators are surrounded by space when there is a character before
15530 \begin_inset VSpace medskip
15536 \begin_layout Standard
15537 \begin_inset space \hfill{}
15541 \begin_inset Tabular
15542 <lyxtabular version="3" rows="13" columns="2">
15543 <features rotate="0" tabularvalignment="middle">
15544 <column alignment="center" valignment="top" width="0pt">
15545 <column alignment="center" valignment="top" width="0pt">
15547 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
15550 \begin_layout Plain Layout
15552 \begin_inset Note Note
15555 \begin_layout Plain Layout
15562 is only used as spacer.
15572 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
15575 \begin_layout Plain Layout
15583 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
15586 \begin_layout Plain Layout
15592 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
15595 \begin_layout Plain Layout
15596 \begin_inset Formula $+$
15606 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
15609 \begin_layout Plain Layout
15615 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
15618 \begin_layout Plain Layout
15619 \begin_inset Formula $-$
15629 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
15632 \begin_layout Plain Layout
15640 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
15643 \begin_layout Plain Layout
15644 \begin_inset Formula $\pm$
15654 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
15657 \begin_layout Plain Layout
15665 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
15668 \begin_layout Plain Layout
15669 \begin_inset Formula $\mp$
15679 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
15682 \begin_layout Plain Layout
15690 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
15693 \begin_layout Plain Layout
15694 \begin_inset Formula $\cdot$
15704 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
15707 \begin_layout Plain Layout
15715 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
15718 \begin_layout Plain Layout
15719 \begin_inset Formula $\times$
15729 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
15732 \begin_layout Plain Layout
15740 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
15743 \begin_layout Plain Layout
15744 \begin_inset Formula $\div$
15754 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
15757 \begin_layout Plain Layout
15761 \begin_layout Plain Layout
15774 \begin_layout Plain Layout
15786 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
15789 \begin_layout Plain Layout
15790 \begin_inset Formula $*$
15800 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
15803 \begin_layout Plain Layout
15811 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
15814 \begin_layout Plain Layout
15815 \begin_inset Formula $\star$
15825 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
15828 \begin_layout Plain Layout
15836 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
15839 \begin_layout Plain Layout
15840 \begin_inset Formula $\circ$
15850 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
15853 \begin_layout Plain Layout
15861 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
15864 \begin_layout Plain Layout
15865 \begin_inset Formula $\diamond$
15875 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
15878 \begin_layout Plain Layout
15886 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
15889 \begin_layout Plain Layout
15890 \begin_inset Formula $\bullet$
15904 \begin_inset space \hfill{}
15908 \begin_inset Tabular
15909 <lyxtabular version="3" rows="13" columns="2">
15910 <features rotate="0" tabularvalignment="middle">
15911 <column alignment="center" valignment="top" width="0pt">
15912 <column alignment="center" valignment="top" width="0pt">
15914 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
15917 \begin_layout Plain Layout
15923 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
15926 \begin_layout Plain Layout
15934 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
15937 \begin_layout Plain Layout
15945 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
15948 \begin_layout Plain Layout
15949 \begin_inset Formula $\nabla$
15959 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
15962 \begin_layout Plain Layout
15970 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
15973 \begin_layout Plain Layout
15974 \begin_inset Formula $\bigtriangledown$
15984 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
15987 \begin_layout Plain Layout
15995 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
15998 \begin_layout Plain Layout
15999 \begin_inset Formula $\bigtriangleup$
16009 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
16012 \begin_layout Plain Layout
16020 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
16023 \begin_layout Plain Layout
16024 \begin_inset Formula $\Box$
16034 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
16037 \begin_layout Plain Layout
16045 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
16048 \begin_layout Plain Layout
16049 \begin_inset Formula $\cap$
16059 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
16062 \begin_layout Plain Layout
16070 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
16073 \begin_layout Plain Layout
16074 \begin_inset Formula $\cup$
16084 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
16087 \begin_layout Plain Layout
16095 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
16098 \begin_layout Plain Layout
16099 \begin_inset Formula $\dagger$
16109 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
16112 \begin_layout Plain Layout
16120 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
16123 \begin_layout Plain Layout
16124 \begin_inset Formula $\ddagger$
16134 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
16137 \begin_layout Plain Layout
16145 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
16148 \begin_layout Plain Layout
16149 \begin_inset Formula $\wr$
16159 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
16162 \begin_layout Plain Layout
16170 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
16173 \begin_layout Plain Layout
16174 \begin_inset Formula $\bigcirc$
16184 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
16187 \begin_layout Plain Layout
16195 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
16198 \begin_layout Plain Layout
16199 \begin_inset Formula $\wedge$
16209 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
16212 \begin_layout Plain Layout
16220 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
16223 \begin_layout Plain Layout
16224 \begin_inset Formula $\vee$
16238 \begin_inset space \hfill{}
16242 \begin_inset Tabular
16243 <lyxtabular version="3" rows="13" columns="2">
16244 <features rotate="0" tabularvalignment="middle">
16245 <column alignment="center" valignment="top" width="0pt">
16246 <column alignment="center" valignment="top" width="0pt">
16248 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
16251 \begin_layout Plain Layout
16257 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
16260 \begin_layout Plain Layout
16268 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
16271 \begin_layout Plain Layout
16279 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
16282 \begin_layout Plain Layout
16283 \begin_inset Formula $\oplus$
16293 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
16296 \begin_layout Plain Layout
16304 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
16307 \begin_layout Plain Layout
16308 \begin_inset Formula $\ominus$
16318 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
16321 \begin_layout Plain Layout
16329 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
16332 \begin_layout Plain Layout
16333 \begin_inset Formula $\otimes$
16343 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
16346 \begin_layout Plain Layout
16354 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
16357 \begin_layout Plain Layout
16358 \begin_inset Formula $\oslash$
16368 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
16371 \begin_layout Plain Layout
16379 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
16382 \begin_layout Plain Layout
16383 \begin_inset Formula $\odot$
16393 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
16396 \begin_layout Plain Layout
16404 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
16407 \begin_layout Plain Layout
16408 \begin_inset Formula $\amalg$
16418 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
16421 \begin_layout Plain Layout
16429 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
16432 \begin_layout Plain Layout
16433 \begin_inset Formula $\uplus$
16443 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
16446 \begin_layout Plain Layout
16454 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
16457 \begin_layout Plain Layout
16458 \begin_inset Formula $\setminus$
16468 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
16471 \begin_layout Plain Layout
16479 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
16482 \begin_layout Plain Layout
16483 \begin_inset Formula $\sqcap$
16493 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
16496 \begin_layout Plain Layout
16504 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
16507 \begin_layout Plain Layout
16508 \begin_inset Formula $\sqcup$
16518 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
16521 \begin_layout Plain Layout
16529 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
16532 \begin_layout Plain Layout
16533 \begin_inset Formula $\triangleleft$
16543 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
16546 \begin_layout Plain Layout
16554 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
16557 \begin_layout Plain Layout
16558 \begin_inset Formula $\triangleright$
16572 \begin_inset space \hfill{}
16578 \begin_layout Standard
16579 All binary operators can also be inserted via the math toolbar button
16580 \begin_inset Graphics
16581 filename ../images/math/pm.png
16589 \begin_layout Standard
16590 To typeset the Laplace operator also
16607 \begin_inset Formula $\nabla^{2}$
16610 ) can be used instead of
16619 \begin_layout Standard
16626 Insert\SpecialChar \menuseparator
16638 \begin_layout Subsection
16639 Self-defined Operators
16640 \begin_inset CommandInset label
16642 name "sub:Self-defined-Operators"
16647 \begin_inset Index idx
16650 \begin_layout Plain Layout
16651 Operators ! self-defined
16659 \begin_layout Standard
16660 With the help of the command
16664 DeclareMathOperator
16667 \begin_inset Index idx
16670 \begin_layout Plain Layout
16675 DeclareMathOperator
16680 custom operators can be defined in the LaTeX-preamble.
16681 Its command scheme is:
16684 \begin_layout Standard
16689 DeclareMathOperator{new command}{display}
16692 \begin_layout Standard
16693 Display can be characters or symbols that define how the operator looks
16695 To define a big operator a * is set behind the command.
16696 All self-defined big operators can have limits as described in
16697 \begin_inset CommandInset ref
16699 reference "sub:Operator-Limits"
16706 \begin_layout Standard
16707 For example the LaTeX-preamble line
16710 \begin_layout Standard
16715 DeclareMathOperator*{
16722 \begin_layout Standard
16723 defines the command
16729 , that inserts a big operator consisting of the lozenge symbol from
16730 \begin_inset CommandInset ref
16732 reference "sub:Miscellaneous-Symbols"
16737 \begin_inset Formula
16739 \Lozenge_{n=1}^{\infty}
16744 The command for this formula is:
16755 \begin_inset Formula $\to$
16761 \begin_layout Standard
16762 \begin_inset VSpace bigskip
16765 When self-defined operators are not used several times in the document,
16766 they can also be defined with the commands
16773 \begin_inset Index idx
16776 \begin_layout Plain Layout
16791 \begin_inset Index idx
16794 \begin_layout Plain Layout
16802 , which have the following scheme:
16805 \begin_layout Standard
16819 \begin_layout Standard
16826 defines big operators,
16835 \begin_layout Standard
16843 \begin_inset space \thinspace{}
16847 \begin_inset space \space{}
16850 be used to use one limit for several operators:
16853 \begin_layout Standard
16854 \begin_inset Formula
16856 \mathop{\sum\negmedspace\sum}_{i,j=1}^{N}
16864 \begin_layout Standard
16865 The command for the formula above is:
16866 \begin_inset Newline newline
16882 \begin_inset space \textvisiblespace{}
16888 \begin_inset Formula $\to$
16894 \begin_inset space \textvisiblespace{}
16902 \begin_layout Section
16904 \begin_inset Index idx
16907 \begin_layout Plain Layout
16916 \begin_layout Subsection
16918 \begin_inset CommandInset label
16920 name "sub:Font-Styles"
16925 \begin_inset Index idx
16928 \begin_layout Plain Layout
16937 \begin_layout Standard
16938 Latin letters in formulas can be set in one of the following font styles:
16939 \begin_inset VSpace -2mm
16945 \begin_layout Standard
16947 \begin_inset Tabular
16948 <lyxtabular version="3" rows="7" columns="3">
16949 <features rotate="0" tabularvalignment="middle">
16950 <column alignment="center" valignment="top">
16951 <column alignment="center" valignment="top">
16952 <column alignment="center" valignment="top">
16954 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
16957 \begin_layout Plain Layout
16963 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
16966 \begin_layout Plain Layout
16972 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
16975 \begin_layout Plain Layout
16983 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
16986 \begin_layout Plain Layout
16992 \begin_inset space \textvisiblespace{}
17002 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
17005 \begin_layout Plain Layout
17006 \begin_inset Formula $\mathbb{ABC}$
17014 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
17017 \begin_layout Plain Layout
17030 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
17033 \begin_layout Plain Layout
17039 \begin_inset space \textvisiblespace{}
17049 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
17052 \begin_layout Plain Layout
17053 \begin_inset Formula $\mathbf{AbC}$
17061 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
17064 \begin_layout Plain Layout
17077 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
17080 \begin_layout Plain Layout
17086 \begin_inset space \textvisiblespace{}
17096 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
17099 \begin_layout Plain Layout
17100 \begin_inset Formula $\boldsymbol{AbC}$
17108 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
17111 \begin_layout Plain Layout
17114 arg "font-boldsymbol"
17124 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
17127 \begin_layout Plain Layout
17133 \begin_inset space \textvisiblespace{}
17143 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
17146 \begin_layout Plain Layout
17147 \begin_inset Formula $\mathcal{ABC}$
17155 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
17158 \begin_layout Plain Layout
17171 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
17174 \begin_layout Plain Layout
17180 \begin_inset space \textvisiblespace{}
17190 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
17193 \begin_layout Plain Layout
17194 \begin_inset Formula $\mathfrak{AbC}$
17202 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
17205 \begin_layout Plain Layout
17213 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
17216 \begin_layout Plain Layout
17222 \begin_inset space \textvisiblespace{}
17232 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
17235 \begin_layout Plain Layout
17236 \begin_inset Formula $\mathscr{AbC}$
17244 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
17247 \begin_layout Plain Layout
17261 \begin_layout Standard
17263 \begin_inset Tabular
17264 <lyxtabular version="3" rows="5" columns="3">
17265 <features rotate="0" tabularvalignment="middle">
17266 <column alignment="center" valignment="top">
17267 <column alignment="center" valignment="top">
17268 <column alignment="center" valignment="top">
17270 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
17273 \begin_layout Plain Layout
17279 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
17282 \begin_layout Plain Layout
17288 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
17291 \begin_layout Plain Layout
17299 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
17302 \begin_layout Plain Layout
17308 \begin_inset space \textvisiblespace{}
17318 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
17321 \begin_layout Plain Layout
17322 \begin_inset Formula $\mathit{AbC}$
17330 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
17333 \begin_layout Plain Layout
17341 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
17344 \begin_layout Plain Layout
17350 \begin_inset space \textvisiblespace{}
17360 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
17363 \begin_layout Plain Layout
17364 \begin_inset Formula $\mathrm{AbC}$
17372 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
17375 \begin_layout Plain Layout
17388 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
17391 \begin_layout Plain Layout
17397 \begin_inset space \textvisiblespace{}
17407 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
17410 \begin_layout Plain Layout
17411 \begin_inset Formula $\mathsf{AbC}$
17419 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
17422 \begin_layout Plain Layout
17435 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
17438 \begin_layout Plain Layout
17444 \begin_inset space \textvisiblespace{}
17454 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
17457 \begin_layout Plain Layout
17458 \begin_inset Formula $\mathtt{AbC}$
17466 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
17469 \begin_layout Plain Layout
17472 arg "font-typewriter"
17488 \begin_layout Standard
17489 \begin_inset Note Greyedout
17492 \begin_layout Plain Layout
17509 can only be used for big letters.
17517 \begin_layout Standard
17518 Predefined is the style
17527 \begin_layout Standard
17528 The style commands work also for letters in mathematical constructs:
17529 \begin_inset Formula
17531 \mathfrak{A=\frac{b}{C}}
17539 \begin_layout Standard
17540 Characters in mathematical text don't appear in a math font style but in
17541 the text font style
17548 That their style can't be set correctly via the text style dialog is a
17553 \begin_layout Plain Layout
17554 \begin_inset CommandInset href
17556 name "LyX-bug #4629"
17557 target "http://www.lyx.org/trac/ticket/4629"
17569 \begin_layout Standard
17570 Instead of the style commands the dialog
17572 Edit\SpecialChar \menuseparator
17573 Math\SpecialChar \menuseparator
17576 or the toolbar button
17577 \begin_inset Graphics
17578 filename ../images/math/font.png
17586 \begin_layout Subsection
17588 \begin_inset CommandInset label
17590 name "sub:Bold-Formulas"
17595 \begin_inset Index idx
17598 \begin_layout Plain Layout
17607 \begin_layout Standard
17608 To make a complete formula bold, the command
17614 from the previous subsection cannot be used, because it doesn't work for
17615 small Greek letters.
17616 Furthermore it prints Latin letters always upright, like in the following
17620 \begin_layout Standard
17621 \begin_inset Formula
17623 \mathbf{\int_{n}^{2}f(\theta)=\Gamma}\qquad\textrm{equation with \textbackslash mathbf}
17631 \begin_layout Standard
17632 To display the formula correctly, the command
17639 \begin_inset Formula
17641 \boldsymbol{\int_{n}^{2}f(\theta)=\Gamma\qquad\textrm{equation with \textbackslash boldsymbol}}
17646 It is also possible to set the formula in a
17648 boldmath environment
17651 This environment is created by inserting the command
17658 \begin_inset Index idx
17661 \begin_layout Plain Layout
17670 To end the environment, the command
17677 \begin_inset Index idx
17680 \begin_layout Plain Layout
17688 is inserted in TeX-mode.
17692 \begin_layout Plain Layout
17702 \begin_inset Formula
17704 \int_{n}^{2}f(\theta)=\Gamma\qquad\textrm{equation in a boldmath environment}
17713 \begin_layout Plain Layout
17725 \begin_layout Subsection
17727 \begin_inset Index idx
17730 \begin_layout Plain Layout
17739 \begin_layout Standard
17740 Formulas can be colored like normal text: Highlight a formula or a formula
17746 Here is a formula in magenta:
17747 \begin_inset Formula
17749 {\color{magenta}\int A\,\mathrm{d}x=\frac{\sqrt[5]{B}}{\ln\left(\frac{1}{3}\right)}}
17757 \begin_layout Standard
17758 You can also define your own colors as described in
17759 \begin_inset CommandInset ref
17761 reference "sub:Colored-Boxes"
17766 They can be used with the TeX code command
17773 \begin_inset Index idx
17776 \begin_layout Plain Layout
17787 \begin_layout Standard
17792 textcolor{color}{characters or formula}
17795 \begin_layout Standard
17796 The following example was colored completely dark green and partly red:
17799 \begin_layout Standard
17803 \begin_layout Plain Layout
17807 textcolor{darkgreen}{
17813 \begin_inset Formula
17815 \int A\,\mathrm{d}x=\frac{{\color{red}\sqrt[5]{B}}}{\ln\left(\frac{1}{3}\right)}
17824 \begin_layout Plain Layout
17834 \begin_layout Standard
17835 Due to a bug in LyX only complete formulas can be colored with self-defined
17840 \begin_layout Plain Layout
17841 \begin_inset CommandInset href
17843 name "LyX-bug #5269"
17844 target "http://www.lyx.org/trac/ticket/5269"
17856 \begin_layout Subsection
17858 \begin_inset CommandInset label
17860 name "sub:Font-Sizes"
17865 \begin_inset Index idx
17868 \begin_layout Plain Layout
17877 \begin_layout Standard
17878 For characters in formulas there are, analog to characters in text, the
17879 following size commands:
17882 \begin_layout Standard
17926 \begin_inset Newline newline
17948 \begin_layout Standard
17949 The size produced by the commands depends on the document font size, which
17950 corresponds to the command
17957 The other commands produce smaller or larger sizes than
17964 The font size can however not exceed a certain value.
17965 Is for example the document font size 12
17966 \begin_inset space \thinspace{}
17975 switches to the same size as
17985 \begin_layout Standard
17986 A size command is inserted in TeX-mode before the formula and sets the size
17987 for all following formula and text characters.
17988 To switch back to the initial size, the command
17994 is inserted behind the formula in TeX-mode.
17997 \begin_layout Standard
17998 Within a formula the size can be changed using the following size commands:
18001 \begin_layout Standard
18004 \begin_inset Tabular
18005 <lyxtabular version="3" rows="5" columns="2">
18006 <features rotate="0" tabularvalignment="middle">
18007 <column alignment="center" valignment="top">
18008 <column alignment="center" valignment="top">
18010 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
18013 \begin_layout Plain Layout
18019 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
18022 \begin_layout Plain Layout
18024 \begin_inset Note Note
18027 \begin_layout Plain Layout
18034 is only used as spacer.
18046 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
18049 \begin_layout Plain Layout
18053 \begin_inset Index idx
18056 \begin_layout Plain Layout
18069 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
18072 \begin_layout Plain Layout
18073 \begin_inset Formula $\raisebox{6.5mm}{}{\displaystyle E_{\mathrm{pot_{1}}}=\frac{K}{l+\frac{m}{n_{2}}}}\raisebox{-5.5mm}{}$
18083 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
18086 \begin_layout Plain Layout
18094 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
18097 \begin_layout Plain Layout
18098 \begin_inset Formula $\raisebox{4.5mm}{}{\textstyle E_{\mathrm{pot_{1}}}=\frac{K}{l+\frac{m}{n_{2}}}}\raisebox{-4mm}{}$
18108 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
18111 \begin_layout Plain Layout
18119 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
18122 \begin_layout Plain Layout
18123 \begin_inset Formula $\raisebox{4.5mm}{}{\scriptstyle E_{\mathrm{pot_{1}}}=\frac{K}{l+\frac{m}{n_{2}}}}\raisebox{-3.5mm}{}$
18133 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
18136 \begin_layout Plain Layout
18144 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
18147 \begin_layout Plain Layout
18148 \begin_inset Formula $\raisebox{4.5mm}{}{\scriptscriptstyle E_{\mathrm{pot_{1}}}=\frac{K}{l+\frac{m}{n_{2}}}}\raisebox{-3.5mm}{}$
18164 \begin_layout Standard
18165 After entering these commands, a blue box appears in which the formula parts
18169 \begin_layout Standard
18170 There is a further method to change the font size, that though only works
18171 for symbols or letters in mathematical text.
18172 To use it, one of the above text size commands is inserted in mathematical
18174 All following characters until the end of the mathematical text or until
18175 another size command will have the selected size.
18177 \begin_inset VSpace -2mm
18183 \begin_layout Standard
18187 \begin_layout Plain Layout
18197 \begin_inset Formula
18199 A=\frac{B}{c}\cdot\maltese
18205 \begin_inset Formula
18207 \maltese A\textrm{\Large\maltese\textit{A}}\textrm{\tiny\maltese\textit{A}}
18216 \begin_layout Plain Layout
18228 \begin_layout Standard
18229 \begin_inset VSpace medskip
18232 Before both formulas the command
18239 The command for the second formula is:
18240 \begin_inset Newline newline
18248 \begin_inset space \textvisiblespace{}
18254 \begin_inset space \textvisiblespace{}
18260 \begin_inset space \textvisiblespace{}
18266 \begin_inset space \textvisiblespace{}
18270 \begin_inset Formula $\to$
18274 \begin_inset Formula $\to$
18278 \begin_inset Newline newline
18282 \begin_inset space \hspace*{}
18293 \begin_inset space \textvisiblespace{}
18299 \begin_inset space \textvisiblespace{}
18305 \begin_inset space \textvisiblespace{}
18311 \begin_layout Standard
18312 If a symbol cannot be displayed in different sizes, it will always be displayed
18313 in the default size.
18316 \begin_layout Section
18318 \begin_inset Index idx
18321 \begin_layout Plain Layout
18330 \begin_layout Standard
18331 Greek letters can also be inserted via the toolbar button
18332 \begin_inset Graphics
18333 filename ../images/math/alpha.png
18339 All international typesetting norms purport that Greek letters in math
18340 have to be typeset italic/slanted.
18341 In some languages, like French or Russian, they are nevertheless sometimes
18345 \begin_layout Subsection
18347 \begin_inset Index idx
18350 \begin_layout Plain Layout
18351 Greek letters ! small
18359 \begin_layout Standard
18360 \begin_inset space \hfill{}
18364 \begin_inset Tabular
18365 <lyxtabular version="3" rows="11" columns="2">
18366 <features rotate="0" tabularvalignment="middle">
18367 <column alignment="center" valignment="top" width="0pt">
18368 <column alignment="center" valignment="top" width="0pt">
18370 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
18373 \begin_layout Plain Layout
18379 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
18382 \begin_layout Plain Layout
18390 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
18393 \begin_layout Plain Layout
18401 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
18404 \begin_layout Plain Layout
18405 \begin_inset Formula $\alpha$
18415 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
18418 \begin_layout Plain Layout
18426 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
18429 \begin_layout Plain Layout
18430 \begin_inset Formula $\beta$
18440 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
18443 \begin_layout Plain Layout
18451 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
18454 \begin_layout Plain Layout
18455 \begin_inset Formula $\gamma$
18465 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
18468 \begin_layout Plain Layout
18476 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
18479 \begin_layout Plain Layout
18480 \begin_inset Formula $\delta$
18490 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
18493 \begin_layout Plain Layout
18501 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
18504 \begin_layout Plain Layout
18505 \begin_inset Formula $\epsilon$
18515 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
18518 \begin_layout Plain Layout
18526 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
18529 \begin_layout Plain Layout
18530 \begin_inset Formula $\varepsilon$
18540 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
18543 \begin_layout Plain Layout
18551 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
18554 \begin_layout Plain Layout
18555 \begin_inset Formula $\zeta$
18565 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
18568 \begin_layout Plain Layout
18576 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
18579 \begin_layout Plain Layout
18580 \begin_inset Formula $\eta$
18590 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
18593 \begin_layout Plain Layout
18601 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
18604 \begin_layout Plain Layout
18605 \begin_inset Formula $\theta$
18615 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
18618 \begin_layout Plain Layout
18626 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
18629 \begin_layout Plain Layout
18630 \begin_inset Formula $\vartheta$
18644 \begin_inset space \hfill{}
18648 \begin_inset Tabular
18649 <lyxtabular version="3" rows="12" columns="2">
18650 <features rotate="0" tabularvalignment="middle">
18651 <column alignment="center" valignment="top" width="0pt">
18652 <column alignment="center" valignment="top" width="0pt">
18654 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
18657 \begin_layout Plain Layout
18663 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
18666 \begin_layout Plain Layout
18674 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
18677 \begin_layout Plain Layout
18685 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
18688 \begin_layout Plain Layout
18689 \begin_inset Formula $\iota$
18699 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
18702 \begin_layout Plain Layout
18710 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
18713 \begin_layout Plain Layout
18714 \begin_inset Formula $\kappa$
18724 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
18727 \begin_layout Plain Layout
18735 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
18738 \begin_layout Plain Layout
18739 \begin_inset Formula $\varkappa$
18749 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
18752 \begin_layout Plain Layout
18760 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
18763 \begin_layout Plain Layout
18764 \begin_inset Formula $\lambda$
18774 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
18777 \begin_layout Plain Layout
18785 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
18788 \begin_layout Plain Layout
18789 \begin_inset Formula $\mu$
18799 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
18802 \begin_layout Plain Layout
18810 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
18813 \begin_layout Plain Layout
18814 \begin_inset Formula $\nu$
18824 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
18827 \begin_layout Plain Layout
18835 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
18838 \begin_layout Plain Layout
18839 \begin_inset Formula $\xi$
18849 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
18852 \begin_layout Plain Layout
18858 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
18861 \begin_layout Plain Layout
18862 \begin_inset Formula $o$
18872 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
18875 \begin_layout Plain Layout
18883 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
18886 \begin_layout Plain Layout
18887 \begin_inset Formula $\pi$
18897 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
18900 \begin_layout Plain Layout
18908 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
18911 \begin_layout Plain Layout
18912 \begin_inset Formula $\varpi$
18922 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
18925 \begin_layout Plain Layout
18933 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
18936 \begin_layout Plain Layout
18937 \begin_inset Formula $\rho$
18951 \begin_inset space \hfill{}
18955 \begin_inset Tabular
18956 <lyxtabular version="3" rows="11" columns="2">
18957 <features rotate="0" tabularvalignment="middle">
18958 <column alignment="center" valignment="top" width="0pt">
18959 <column alignment="center" valignment="top" width="0pt">
18961 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
18964 \begin_layout Plain Layout
18970 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
18973 \begin_layout Plain Layout
18981 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
18984 \begin_layout Plain Layout
18992 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
18995 \begin_layout Plain Layout
18996 \begin_inset Formula $\varrho$
19006 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
19009 \begin_layout Plain Layout
19017 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
19020 \begin_layout Plain Layout
19021 \begin_inset Formula $\sigma$
19031 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
19034 \begin_layout Plain Layout
19042 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
19045 \begin_layout Plain Layout
19046 \begin_inset Formula $\varsigma$
19056 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
19059 \begin_layout Plain Layout
19067 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
19070 \begin_layout Plain Layout
19071 \begin_inset Formula $\tau$
19081 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
19084 \begin_layout Plain Layout
19092 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
19095 \begin_layout Plain Layout
19096 \begin_inset Formula $\upsilon$
19106 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
19109 \begin_layout Plain Layout
19117 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
19120 \begin_layout Plain Layout
19121 \begin_inset Formula $\phi$
19131 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
19134 \begin_layout Plain Layout
19142 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
19145 \begin_layout Plain Layout
19146 \begin_inset Formula $\varphi$
19156 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
19159 \begin_layout Plain Layout
19167 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
19170 \begin_layout Plain Layout
19171 \begin_inset Formula $\chi$
19181 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
19184 \begin_layout Plain Layout
19192 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
19195 \begin_layout Plain Layout
19196 \begin_inset Formula $\psi$
19206 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
19209 \begin_layout Plain Layout
19217 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
19220 \begin_layout Plain Layout
19221 \begin_inset Formula $\omega$
19235 \begin_inset space \hfill{}
19241 \begin_layout Standard
19242 \begin_inset VSpace medskip
19248 \begin_layout Standard
19249 How to create special upright Greek letters is explained in
19250 \begin_inset CommandInset ref
19252 reference "sub:Upright-small-Greek"
19259 \begin_layout Subsection
19261 \begin_inset Index idx
19264 \begin_layout Plain Layout
19265 Greek letters ! big
19273 \begin_layout Standard
19274 \begin_inset space \hfill{}
19278 \begin_inset Tabular
19279 <lyxtabular version="3" rows="7" columns="2">
19280 <features rotate="0" tabularvalignment="middle">
19281 <column alignment="center" valignment="top" width="0pt">
19282 <column alignment="center" valignment="top" width="0pt">
19284 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
19287 \begin_layout Plain Layout
19293 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
19296 \begin_layout Plain Layout
19304 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
19307 \begin_layout Plain Layout
19315 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
19318 \begin_layout Plain Layout
19319 \begin_inset Formula $\Gamma$
19329 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
19332 \begin_layout Plain Layout
19340 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
19343 \begin_layout Plain Layout
19344 \begin_inset Formula $\Delta$
19354 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
19357 \begin_layout Plain Layout
19365 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
19368 \begin_layout Plain Layout
19369 \begin_inset Formula $\Theta$
19379 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
19382 \begin_layout Plain Layout
19390 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
19393 \begin_layout Plain Layout
19394 \begin_inset Formula $\Lambda$
19404 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
19407 \begin_layout Plain Layout
19415 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
19418 \begin_layout Plain Layout
19419 \begin_inset Formula $\Xi$
19429 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
19432 \begin_layout Plain Layout
19440 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
19443 \begin_layout Plain Layout
19444 \begin_inset Formula $\Pi$
19458 \begin_inset space \hfill{}
19462 \begin_inset Tabular
19463 <lyxtabular version="3" rows="6" columns="2">
19464 <features rotate="0" tabularvalignment="middle">
19465 <column alignment="center" valignment="top" width="0pt">
19466 <column alignment="center" valignment="top" width="0pt">
19468 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
19471 \begin_layout Plain Layout
19477 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
19480 \begin_layout Plain Layout
19488 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
19491 \begin_layout Plain Layout
19499 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
19502 \begin_layout Plain Layout
19503 \begin_inset Formula $\Sigma$
19513 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
19516 \begin_layout Plain Layout
19524 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
19527 \begin_layout Plain Layout
19528 \begin_inset Formula $\Upsilon$
19538 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
19541 \begin_layout Plain Layout
19549 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
19552 \begin_layout Plain Layout
19553 \begin_inset Formula $\Phi$
19563 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
19566 \begin_layout Plain Layout
19574 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
19577 \begin_layout Plain Layout
19578 \begin_inset Formula $\Psi$
19588 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
19591 \begin_layout Plain Layout
19599 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
19602 \begin_layout Plain Layout
19603 \begin_inset Formula $\Omega$
19617 \begin_inset space \hfill{}
19623 \begin_layout Standard
19624 \begin_inset VSpace medskip
19627 That the big Greek letters appear upright is caused by a design bug when
19629 To get correct italic big letters, begin every command with
19634 For example the command
19641 \begin_inset Formula $\varGamma$
19645 Another way is to load the package
19653 \begin_layout Plain Layout
19658 is part of the LaTeX-package
19663 \begin_inset Index idx
19666 \begin_layout Plain Layout
19671 \begin_layout Plain Layout
19691 \begin_inset Index idx
19694 \begin_layout Plain Layout
19700 with the LaTeX-preamble line
19703 \begin_layout Standard
19708 usepackage{fixmath}
19711 \begin_layout Standard
19712 Then all big Greek letters in a document will automatically be typeset italic.
19715 \begin_layout Subsection
19717 \begin_inset Index idx
19720 \begin_layout Plain Layout
19721 Greek letters ! bold
19729 \begin_layout Standard
19730 Greek letters cannot be set with different font styles like Latin letters.
19731 They can only be made bold with the command
19738 \begin_inset Index idx
19741 \begin_layout Plain Layout
19752 \begin_layout Standard
19754 \begin_inset Tabular
19755 <lyxtabular version="3" rows="3" columns="2">
19756 <features rotate="0" tabularvalignment="middle">
19757 <column alignment="center" valignment="top">
19758 <column alignment="center" valignment="top">
19760 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
19763 \begin_layout Plain Layout
19769 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
19772 \begin_layout Plain Layout
19780 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
19783 \begin_layout Plain Layout
19795 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
19798 \begin_layout Plain Layout
19799 \begin_inset Formula $\Upsilon\boldsymbol{\Upsilon}$
19809 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
19812 \begin_layout Plain Layout
19824 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
19827 \begin_layout Plain Layout
19828 \begin_inset Formula $\theta\boldsymbol{\theta}$
19844 \begin_layout Section
19849 \begin_layout Plain Layout
19862 \begin_layout Plain Layout
19863 A list with all symbols of most of the LaTeX-packages can be found in
19864 \begin_inset CommandInset citation
19879 \begin_layout Plain Layout
19887 \begin_inset Note Note
19890 \begin_layout Plain Layout
19893 texorpdfstring is used to avoid that the footnote appears in the PDF-bookmark.
19896 \begin_layout Plain Layout
19899 texorpdfstring is in section
19900 \begin_inset CommandInset ref
19902 reference "sub:Formulas-in-Section"
19912 \begin_inset Index idx
19915 \begin_layout Plain Layout
19924 \begin_layout Standard
19925 Many of the symbols listed in this section can also be inserted via the
19927 \begin_inset Graphics
19928 filename ../images/math/nabla.png
19934 \begin_inset Graphics
19935 filename ../images/math/digamma.png
19943 \begin_layout Subsection
19944 Mathematical Symbols
19945 \begin_inset CommandInset label
19947 name "sub:Mathematical-Symbols"
19952 \begin_inset Index idx
19955 \begin_layout Plain Layout
19956 Symbols ! mathematical
19964 \begin_layout Standard
19965 \begin_inset space \hfill{}
19969 \begin_inset Tabular
19970 <lyxtabular version="3" rows="10" columns="2">
19971 <features rotate="0" tabularvalignment="middle">
19972 <column alignment="center" valignment="top" width="0pt">
19973 <column alignment="center" valignment="top" width="0pt">
19975 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
19978 \begin_layout Plain Layout
19984 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
19987 \begin_layout Plain Layout
19995 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
19998 \begin_layout Plain Layout
20006 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
20009 \begin_layout Plain Layout
20010 \begin_inset Formula $\neg$
20020 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
20023 \begin_layout Plain Layout
20031 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
20034 \begin_layout Plain Layout
20035 \begin_inset Formula $\Im$
20045 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
20048 \begin_layout Plain Layout
20056 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
20059 \begin_layout Plain Layout
20060 \begin_inset Formula $\Re$
20070 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
20073 \begin_layout Plain Layout
20081 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
20084 \begin_layout Plain Layout
20085 \begin_inset Formula $\aleph$
20095 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
20098 \begin_layout Plain Layout
20106 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
20109 \begin_layout Plain Layout
20110 \begin_inset Formula $\partial$
20120 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
20123 \begin_layout Plain Layout
20131 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
20134 \begin_layout Plain Layout
20135 \begin_inset Formula $\infty$
20145 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
20148 \begin_layout Plain Layout
20156 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
20159 \begin_layout Plain Layout
20160 \begin_inset Formula $\wp$
20170 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
20173 \begin_layout Plain Layout
20181 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
20184 \begin_layout Plain Layout
20185 \begin_inset Formula $\imath$
20195 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
20198 \begin_layout Plain Layout
20206 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
20209 \begin_layout Plain Layout
20210 \begin_inset Formula $\jmath$
20224 \begin_inset space \hfill{}
20228 \begin_inset Tabular
20229 <lyxtabular version="3" rows="10" columns="2">
20230 <features rotate="0" tabularvalignment="middle">
20231 <column alignment="center" valignment="top" width="0pt">
20232 <column alignment="center" valignment="top" width="0pt">
20234 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
20237 \begin_layout Plain Layout
20243 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
20246 \begin_layout Plain Layout
20248 \begin_inset Note Note
20251 \begin_layout Plain Layout
20258 is only used as spacer.
20270 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
20273 \begin_layout Plain Layout
20281 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
20284 \begin_layout Plain Layout
20285 \begin_inset Formula $\forall$
20295 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
20298 \begin_layout Plain Layout
20306 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
20309 \begin_layout Plain Layout
20310 \begin_inset Formula $\exists$
20320 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
20323 \begin_layout Plain Layout
20331 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
20334 \begin_layout Plain Layout
20335 \begin_inset Formula $\nexists$
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 $\emptyset$
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 $\varnothing$
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 $\dag$
20420 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
20423 \begin_layout Plain Layout
20431 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
20434 \begin_layout Plain Layout
20435 \begin_inset Formula $\ddag$
20445 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
20448 \begin_layout Plain Layout
20456 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
20459 \begin_layout Plain Layout
20463 \begin_layout Plain Layout
20473 \begin_inset Formula $\complement$
20480 \begin_layout Plain Layout
20494 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
20497 \begin_layout Plain Layout
20505 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
20508 \begin_layout Plain Layout
20509 \begin_inset Formula $\Bbbk$
20523 \begin_inset space \hfill{}
20527 \begin_inset Tabular
20528 <lyxtabular version="3" rows="10" columns="2">
20529 <features rotate="0" tabularvalignment="middle">
20530 <column alignment="center" valignment="top" width="0pt">
20531 <column alignment="center" valignment="top" width="0pt">
20533 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
20536 \begin_layout Plain Layout
20542 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
20545 \begin_layout Plain Layout
20553 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
20556 \begin_layout Plain Layout
20564 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
20567 \begin_layout Plain Layout
20568 \begin_inset Formula $\prime$
20578 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
20581 \begin_layout Plain Layout
20589 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
20592 \begin_layout Plain Layout
20593 \begin_inset Formula $\backprime$
20603 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
20606 \begin_layout Plain Layout
20614 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
20617 \begin_layout Plain Layout
20618 \begin_inset Formula $\mho$
20628 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
20631 \begin_layout Plain Layout
20639 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
20642 \begin_layout Plain Layout
20643 \begin_inset Formula $\triangle$
20653 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
20656 \begin_layout Plain Layout
20664 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
20667 \begin_layout Plain Layout
20668 \begin_inset Formula $\angle$
20678 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
20681 \begin_layout Plain Layout
20689 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
20692 \begin_layout Plain Layout
20693 \begin_inset Formula $\measuredangle$
20703 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
20706 \begin_layout Plain Layout
20714 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
20717 \begin_layout Plain Layout
20718 \begin_inset Formula $\sphericalangle$
20728 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
20731 \begin_layout Plain Layout
20739 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
20742 \begin_layout Plain Layout
20743 \begin_inset Formula $\top$
20753 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
20756 \begin_layout Plain Layout
20764 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
20767 \begin_layout Plain Layout
20768 \begin_inset Formula $\bot$
20782 \begin_inset space \hfill{}
20788 \begin_layout Subsection
20789 Miscellaneous Symbols
20790 \begin_inset CommandInset label
20792 name "sub:Miscellaneous-Symbols"
20797 \begin_inset Index idx
20800 \begin_layout Plain Layout
20801 Symbols ! miscellaneous
20809 \begin_layout Standard
20812 \begin_inset Tabular
20813 <lyxtabular version="3" rows="10" columns="2">
20814 <features rotate="0" tabularvalignment="middle">
20815 <column alignment="center" valignment="top" width="0pt">
20816 <column alignment="center" valignment="top" width="0pt">
20818 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
20821 \begin_layout Plain Layout
20827 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
20830 \begin_layout Plain Layout
20838 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
20841 \begin_layout Plain Layout
20849 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
20852 \begin_layout Plain Layout
20853 \begin_inset Formula $\flat$
20863 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
20866 \begin_layout Plain Layout
20874 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
20877 \begin_layout Plain Layout
20878 \begin_inset Formula $\natural$
20888 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
20891 \begin_layout Plain Layout
20899 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
20902 \begin_layout Plain Layout
20903 \begin_inset Formula $\sharp$
20913 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
20916 \begin_layout Plain Layout
20924 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
20927 \begin_layout Plain Layout
20928 \begin_inset Formula $\surd$
20938 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
20941 \begin_layout Plain Layout
20949 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
20952 \begin_layout Plain Layout
20953 \begin_inset Formula $\checkmark$
20963 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
20966 \begin_layout Plain Layout
20974 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
20977 \begin_layout Plain Layout
20978 \begin_inset Formula $\yen$
20988 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
20991 \begin_layout Plain Layout
20999 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
21002 \begin_layout Plain Layout
21003 \begin_inset Formula $\pounds$
21013 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
21016 \begin_layout Plain Layout
21022 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
21025 \begin_layout Plain Layout
21026 \begin_inset Formula $\$$
21036 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
21039 \begin_layout Plain Layout
21045 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
21048 \begin_layout Plain Layout
21049 \begin_inset Formula $§$
21063 \begin_inset Tabular
21064 <lyxtabular version="3" rows="10" columns="2">
21065 <features rotate="0" tabularvalignment="middle">
21066 <column alignment="center" valignment="top">
21067 <column alignment="center" valignment="top">
21069 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
21072 \begin_layout Plain Layout
21078 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
21081 \begin_layout Plain Layout
21089 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
21092 \begin_layout Plain Layout
21100 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
21103 \begin_layout Plain Layout
21104 \begin_inset Formula $\hbar$
21114 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
21117 \begin_layout Plain Layout
21125 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
21128 \begin_layout Plain Layout
21129 \begin_inset Formula $\hslash$
21139 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
21142 \begin_layout Plain Layout
21150 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
21153 \begin_layout Plain Layout
21154 \begin_inset Formula $\clubsuit$
21164 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
21167 \begin_layout Plain Layout
21175 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
21178 \begin_layout Plain Layout
21179 \begin_inset Formula $\spadesuit$
21189 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
21192 \begin_layout Plain Layout
21200 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
21203 \begin_layout Plain Layout
21204 \begin_inset Formula $\bigstar$
21214 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
21217 \begin_layout Plain Layout
21225 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
21228 \begin_layout Plain Layout
21229 \begin_inset Formula $\blacklozenge$
21239 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
21242 \begin_layout Plain Layout
21250 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
21253 \begin_layout Plain Layout
21254 \begin_inset Formula $\blacktriangle$
21264 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
21267 \begin_layout Plain Layout
21275 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
21278 \begin_layout Plain Layout
21279 \begin_inset Formula $\blacktriangledown$
21289 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
21292 \begin_layout Plain Layout
21300 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
21303 \begin_layout Plain Layout
21304 \begin_inset Formula $\bullet$
21318 \begin_inset Tabular
21319 <lyxtabular version="3" rows="10" columns="2">
21320 <features rotate="0" tabularvalignment="middle">
21321 <column alignment="center" valignment="top" width="0pt">
21322 <column alignment="center" valignment="top" width="0pt">
21324 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
21327 \begin_layout Plain Layout
21333 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
21336 \begin_layout Plain Layout
21344 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
21347 \begin_layout Plain Layout
21355 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
21358 \begin_layout Plain Layout
21359 \begin_inset Formula $\diamondsuit$
21369 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
21372 \begin_layout Plain Layout
21380 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
21383 \begin_layout Plain Layout
21384 \begin_inset Formula $\Diamond$
21394 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
21397 \begin_layout Plain Layout
21405 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
21408 \begin_layout Plain Layout
21409 \begin_inset Formula $\heartsuit$
21419 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
21422 \begin_layout Plain Layout
21430 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
21433 \begin_layout Plain Layout
21434 \begin_inset Formula $\P$
21444 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
21447 \begin_layout Plain Layout
21455 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
21458 \begin_layout Plain Layout
21459 \begin_inset Formula $\copyright$
21469 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
21472 \begin_layout Plain Layout
21480 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
21483 \begin_layout Plain Layout
21484 \begin_inset Formula $\circledR$
21494 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
21497 \begin_layout Plain Layout
21505 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
21508 \begin_layout Plain Layout
21509 \begin_inset Formula $\maltese$
21519 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
21522 \begin_layout Plain Layout
21530 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
21533 \begin_layout Plain Layout
21534 \begin_inset Formula $\diagup$
21544 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
21547 \begin_layout Plain Layout
21555 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
21558 \begin_layout Plain Layout
21559 \begin_inset Formula $\diagdown$
21575 \begin_layout Standard
21576 \begin_inset VSpace medskip
21582 \begin_layout Standard
21583 Some symbols can be displayed in different sizes, see
21584 \begin_inset CommandInset ref
21586 reference "sub:Font-Sizes"
21593 \begin_layout Subsection
21595 \begin_inset Index idx
21598 \begin_layout Plain Layout
21599 Symbols ! Euro-symbol
21605 \begin_inset Index idx
21608 \begin_layout Plain Layout
21615 \begin_layout Plain Layout
21632 \begin_layout Standard
21633 To use the Euro symbol in formulas, the LaTeX-package
21638 \begin_inset Index idx
21641 \begin_layout Plain Layout
21647 must be installed and loaded with the LaTeX-preamble line
21650 \begin_layout Standard
21655 usepackage[gennarrow]{eurosym}
21658 \begin_layout Standard
21659 The Euro symbol can now be inserted with the command
21666 \begin_inset Index idx
21669 \begin_layout Plain Layout
21680 \begin_layout Standard
21681 The Euro symbol can directly be inserted with the € key in mathematical
21682 text, without having
21697 can also be inserted in TeX-mode.
21698 The official currency symbol can then be inserted with the command
21705 \begin_inset Index idx
21708 \begin_layout Plain Layout
21716 , that is only available in TeX-mode.
21719 \begin_layout Standard
21723 \begin_layout Plain Layout
21733 \begin_inset Note Note
21736 \begin_layout Plain Layout
21737 The following table will only be displayed when the LaTeX-package
21749 \begin_layout Standard
21750 An overview about the different Euro symbols:
21753 \begin_layout Standard
21755 \begin_inset Tabular
21756 <lyxtabular version="3" rows="4" columns="3">
21757 <features rotate="0" tabularvalignment="middle">
21758 <column alignment="center" valignment="top" width="0pt">
21759 <column alignment="center" valignment="top" width="0pt">
21760 <column alignment="center" valignment="top" width="0pt">
21762 <cell multicolumn="1" alignment="center" valignment="top" bottomline="true" usebox="none">
21765 \begin_layout Plain Layout
21771 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
21774 \begin_layout Plain Layout
21780 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
21783 \begin_layout Plain Layout
21791 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
21794 \begin_layout Plain Layout
21800 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
21803 \begin_layout Plain Layout
21811 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
21814 \begin_layout Plain Layout
21815 \begin_inset Formula $\euro$
21825 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
21828 \begin_layout Plain Layout
21834 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
21837 \begin_layout Plain Layout
21843 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
21846 \begin_layout Plain Layout
21847 \begin_inset Formula $\mbox{€}$
21857 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
21860 \begin_layout Plain Layout
21866 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
21869 \begin_layout Plain Layout
21877 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
21880 \begin_layout Plain Layout
21884 \begin_layout Plain Layout
21906 \begin_layout Standard
21910 \begin_layout Plain Layout
21920 \begin_inset Note Note
21923 \begin_layout Plain Layout
21924 The following will be displayed when the LaTeX-package
21936 \begin_layout Standard
21937 You need to install the LaTeX-package
21941 to see the rest of this subsection in the output.
21944 \begin_layout Standard
21948 \begin_layout Plain Layout
21960 \begin_layout Section
21962 \begin_inset CommandInset label
21964 name "sec:Relations"
21969 \begin_inset Index idx
21972 \begin_layout Plain Layout
21979 \begin_inset Index idx
21982 \begin_layout Plain Layout
21987 \begin_layout Plain Layout
21998 \begin_layout Plain Layout
22013 \begin_layout Standard
22014 All relations can also be inserted via the toolbar button
22015 \begin_inset Graphics
22016 filename ../images/math/leq.png
22024 \begin_layout Standard
22025 \begin_inset space \hfill{}
22029 \begin_inset Tabular
22030 <lyxtabular version="3" rows="17" columns="2">
22031 <features rotate="0" tabularvalignment="middle">
22032 <column alignment="center" valignment="top" width="0pt">
22033 <column alignment="center" valignment="top" width="0pt">
22035 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
22038 \begin_layout Plain Layout
22044 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
22047 \begin_layout Plain Layout
22055 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
22058 \begin_layout Plain Layout
22064 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
22067 \begin_layout Plain Layout
22068 \begin_inset Formula $<$
22078 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
22081 \begin_layout Plain Layout
22089 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
22092 \begin_layout Plain Layout
22093 \begin_inset Formula $\le$
22103 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
22106 \begin_layout Plain Layout
22114 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
22117 \begin_layout Plain Layout
22118 \begin_inset Formula $\ll$
22128 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
22131 \begin_layout Plain Layout
22139 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
22142 \begin_layout Plain Layout
22143 \begin_inset Formula $\prec$
22153 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
22156 \begin_layout Plain Layout
22164 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
22167 \begin_layout Plain Layout
22168 \begin_inset Formula $\preceq$
22178 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
22181 \begin_layout Plain Layout
22189 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
22192 \begin_layout Plain Layout
22193 \begin_inset Formula $\subset$
22203 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
22206 \begin_layout Plain Layout
22214 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
22217 \begin_layout Plain Layout
22218 \begin_inset Formula $\subseteq$
22228 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
22231 \begin_layout Plain Layout
22239 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
22242 \begin_layout Plain Layout
22243 \begin_inset Formula $\sqsubseteq$
22253 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
22256 \begin_layout Plain Layout
22264 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
22267 \begin_layout Plain Layout
22268 \begin_inset Formula $\in$
22278 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
22281 \begin_layout Plain Layout
22289 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
22292 \begin_layout Plain Layout
22293 \begin_inset Formula $\vdash$
22303 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
22306 \begin_layout Plain Layout
22314 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
22317 \begin_layout Plain Layout
22318 \begin_inset Formula $\smile$
22328 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
22331 \begin_layout Plain Layout
22339 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
22342 \begin_layout Plain Layout
22343 \begin_inset Formula $\lhd$
22353 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
22356 \begin_layout Plain Layout
22364 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
22367 \begin_layout Plain Layout
22368 \begin_inset Formula $\unlhd$
22378 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
22381 \begin_layout Plain Layout
22389 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
22392 \begin_layout Plain Layout
22393 \begin_inset Formula $\gtrless$
22403 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
22406 \begin_layout Plain Layout
22414 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
22417 \begin_layout Plain Layout
22418 \begin_inset Formula $\mid$
22428 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
22431 \begin_layout Plain Layout
22439 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
22442 \begin_layout Plain Layout
22443 \begin_inset Formula $\nmid$
22457 \begin_inset space \hfill{}
22461 \begin_inset Tabular
22462 <lyxtabular version="3" rows="17" columns="2">
22463 <features rotate="0" tabularvalignment="middle">
22464 <column alignment="center" valignment="top" width="0pt">
22465 <column alignment="center" valignment="top" width="0pt">
22467 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
22470 \begin_layout Plain Layout
22476 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
22479 \begin_layout Plain Layout
22487 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
22490 \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 $=$
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 $\not=$
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 $\equiv$
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 $\sim$
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 $\simeq$
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 $\approx$
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 $\cong$
22660 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
22663 \begin_layout Plain Layout
22671 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
22674 \begin_layout Plain Layout
22675 \begin_inset Formula $\bowtie$
22685 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
22688 \begin_layout Plain Layout
22696 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
22699 \begin_layout Plain Layout
22700 \begin_inset Formula $\notin$
22710 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
22713 \begin_layout Plain Layout
22721 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
22724 \begin_layout Plain Layout
22725 \begin_inset Formula $\perp$
22735 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
22738 \begin_layout Plain Layout
22746 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
22749 \begin_layout Plain Layout
22750 \begin_inset Formula $\propto$
22760 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
22763 \begin_layout Plain Layout
22771 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
22774 \begin_layout Plain Layout
22775 \begin_inset Formula $\asymp$
22785 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
22788 \begin_layout Plain Layout
22796 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
22799 \begin_layout Plain Layout
22800 \begin_inset Formula $\doteq$
22810 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
22813 \begin_layout Plain Layout
22821 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
22824 \begin_layout Plain Layout
22825 \begin_inset Formula $\circeq$
22835 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
22838 \begin_layout Plain Layout
22846 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
22849 \begin_layout Plain Layout
22850 \begin_inset Formula $\models$
22860 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
22863 \begin_layout Plain Layout
22871 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
22874 \begin_layout Plain Layout
22875 \begin_inset Formula $\widehat{=}$
22889 \begin_inset space \hfill{}
22893 \begin_inset Tabular
22894 <lyxtabular version="3" rows="17" columns="2">
22895 <features rotate="0" tabularvalignment="middle">
22896 <column alignment="center" valignment="top" width="0pt">
22897 <column alignment="center" valignment="top" width="0pt">
22899 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
22902 \begin_layout Plain Layout
22908 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
22911 \begin_layout Plain Layout
22919 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
22922 \begin_layout Plain Layout
22928 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
22931 \begin_layout Plain Layout
22932 \begin_inset Formula $>$
22942 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
22945 \begin_layout Plain Layout
22953 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
22956 \begin_layout Plain Layout
22957 \begin_inset Formula $\ge$
22967 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
22970 \begin_layout Plain Layout
22978 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
22981 \begin_layout Plain Layout
22982 \begin_inset Formula $\gg$
22992 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
22995 \begin_layout Plain Layout
23003 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
23006 \begin_layout Plain Layout
23007 \begin_inset Formula $\succ$
23017 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
23020 \begin_layout Plain Layout
23028 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
23031 \begin_layout Plain Layout
23032 \begin_inset Formula $\succeq$
23042 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
23045 \begin_layout Plain Layout
23053 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
23056 \begin_layout Plain Layout
23057 \begin_inset Formula $\supset$
23067 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
23070 \begin_layout Plain Layout
23078 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
23081 \begin_layout Plain Layout
23082 \begin_inset Formula $\supseteq$
23092 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
23095 \begin_layout Plain Layout
23103 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
23106 \begin_layout Plain Layout
23107 \begin_inset Formula $\sqsupseteq$
23117 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
23120 \begin_layout Plain Layout
23128 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
23131 \begin_layout Plain Layout
23132 \begin_inset Formula $\ni$
23142 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
23145 \begin_layout Plain Layout
23153 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
23156 \begin_layout Plain Layout
23157 \begin_inset Formula $\dashv$
23167 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
23170 \begin_layout Plain Layout
23178 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
23181 \begin_layout Plain Layout
23182 \begin_inset Formula $\frown$
23192 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
23195 \begin_layout Plain Layout
23203 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
23206 \begin_layout Plain Layout
23207 \begin_inset Formula $\rhd$
23217 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
23220 \begin_layout Plain Layout
23228 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
23231 \begin_layout Plain Layout
23232 \begin_inset Formula $\unrhd$
23242 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
23245 \begin_layout Plain Layout
23253 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
23256 \begin_layout Plain Layout
23257 \begin_inset Formula $\lessgtr$
23267 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
23270 \begin_layout Plain Layout
23278 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
23281 \begin_layout Plain Layout
23282 \begin_inset Formula $\parallel$
23292 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
23295 \begin_layout Plain Layout
23303 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
23306 \begin_layout Plain Layout
23307 \begin_inset Formula $\nparallel$
23321 \begin_inset space \hfill{}
23327 \begin_layout Standard
23328 \begin_inset VSpace medskip
23343 are bigger than the equal looking operators
23358 \begin_layout Standard
23359 Relations are, in contrary to symbols, always surrounded by space.
23362 \begin_layout Standard
23363 Relations with labels can be created with the command
23370 \begin_inset Index idx
23373 \begin_layout Plain Layout
23384 \begin_layout Standard
23386 \begin_inset Tabular
23387 <lyxtabular version="3" rows="2" columns="2">
23388 <features rotate="0" tabularvalignment="middle">
23389 <column alignment="center" valignment="top">
23390 <column alignment="center" valignment="top">
23392 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
23395 \begin_layout Plain Layout
23401 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
23404 \begin_layout Plain Layout
23406 \begin_inset Note Note
23409 \begin_layout Plain Layout
23416 is only used as spacer.
23428 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
23431 \begin_layout Plain Layout
23435 \begin_inset space \textvisiblespace{}
23443 \begin_inset space \textvisiblespace{}
23447 \begin_inset Formula $\downarrow$
23453 \begin_inset space \textvisiblespace{}
23457 \begin_inset space \textvisiblespace{}
23465 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
23468 \begin_layout Plain Layout
23469 \begin_inset Formula $\raisebox{5mm}{}A(r)\stackrel{r\to\infty}{\approx}B$
23485 \begin_layout Section
23489 \begin_layout Subsection
23490 Predefined Functions
23491 \begin_inset CommandInset label
23493 name "sub:Predefined-Functions"
23498 \begin_inset Index idx
23501 \begin_layout Plain Layout
23502 Functions ! predefined
23510 \begin_layout Standard
23511 In general, variables are set
23515 in mathematical expressions, but not function names, because
23516 \begin_inset Formula $sin$
23519 could be misunderstood as
23520 \begin_inset Formula $s\cdot i\cdot n$
23524 Therefore there are predefined functionswhich are additionally a bit separated
23526 They are inserted as commands starting with a backslash before their name.
23529 \begin_layout Standard
23531 \begin_inset Tabular
23532 <lyxtabular version="3" rows="2" columns="4">
23533 <features rotate="0" tabularvalignment="middle">
23534 <column alignment="center" valignment="top" width="0pt">
23535 <column alignment="center" valignment="top" width="0pt">
23536 <column alignment="center" valignment="top" width="0pt">
23537 <column alignment="center" valignment="top" width="0pt">
23539 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
23542 \begin_layout Plain Layout
23548 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
23551 \begin_layout Plain Layout
23557 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
23560 \begin_layout Plain Layout
23566 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
23569 \begin_layout Plain Layout
23577 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
23580 \begin_layout Plain Layout
23586 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
23589 \begin_layout Plain Layout
23590 \begin_inset Formula $Asin(x)+B$
23598 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
23601 \begin_layout Plain Layout
23609 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
23612 \begin_layout Plain Layout
23613 \begin_inset Formula $A\sin(x)+B$
23629 \begin_layout Standard
23630 The following functions are predefined:
23633 \begin_layout Standard
23634 \begin_inset VSpace -2mm
23640 \begin_layout Standard
23642 \begin_inset Tabular
23643 <lyxtabular version="3" rows="9" columns="4">
23644 <features rotate="0" tabularvalignment="middle">
23645 <column alignment="center" valignment="top" width="0pt">
23646 <column alignment="center" valignment="top" width="0pt">
23647 <column alignment="center" valignment="top" width="0pt">
23648 <column alignment="center" valignment="top" width="0pt">
23650 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
23653 \begin_layout Plain Layout
23659 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
23662 \begin_layout Plain Layout
23668 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
23671 \begin_layout Plain Layout
23677 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
23680 \begin_layout Plain Layout
23688 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
23691 \begin_layout Plain Layout
23699 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
23702 \begin_layout Plain Layout
23710 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
23713 \begin_layout Plain Layout
23721 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
23724 \begin_layout Plain Layout
23734 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
23737 \begin_layout Plain Layout
23745 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
23748 \begin_layout Plain Layout
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
23780 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
23783 \begin_layout Plain Layout
23791 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
23794 \begin_layout Plain Layout
23802 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
23805 \begin_layout Plain Layout
23813 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
23816 \begin_layout Plain Layout
23826 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
23829 \begin_layout Plain Layout
23837 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
23840 \begin_layout Plain Layout
23848 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
23851 \begin_layout Plain Layout
23859 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
23862 \begin_layout Plain Layout
23872 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
23875 \begin_layout Plain Layout
23883 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
23886 \begin_layout Plain Layout
23894 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
23897 \begin_layout Plain Layout
23905 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
23908 \begin_layout Plain Layout
23918 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
23921 \begin_layout Plain Layout
23929 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
23932 \begin_layout Plain Layout
23940 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
23943 \begin_layout Plain Layout
23951 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
23954 \begin_layout Plain Layout
23964 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
23967 \begin_layout Plain Layout
23975 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
23978 \begin_layout Plain Layout
23986 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
23989 \begin_layout Plain Layout
23997 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
24000 \begin_layout Plain Layout
24010 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
24013 \begin_layout Plain Layout
24021 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
24024 \begin_layout Plain Layout
24032 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
24035 \begin_layout Plain Layout
24043 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
24046 \begin_layout Plain Layout
24062 \begin_layout Standard
24063 They can also be inserted with the math toolbar button
24064 \begin_inset Graphics
24065 filename ../images/math/functions.png
24073 \begin_layout Subsection
24074 Self-defined Functions
24075 \begin_inset Index idx
24078 \begin_layout Plain Layout
24079 Functions ! self-defined
24087 \begin_layout Standard
24088 To use a function that is not predefined, like for example the sign function
24089 sgn(x), there are two possibilities:
24092 \begin_layout Itemize
24093 Define the function by inserting the following line to the LaTeX-preamble
24097 \begin_layout Plain Layout
24102 DeclareMathOperator
24105 \begin_inset CommandInset ref
24107 reference "sub:Self-defined-Operators"
24117 \begin_inset Newline newline
24121 \begin_inset VSpace -3mm
24125 \begin_inset Newline newline
24132 DeclareMathOperator{
24137 \begin_inset Index idx
24140 \begin_layout Plain Layout
24145 DeclareMathOperator
24151 \begin_inset Newline newline
24155 \begin_inset VSpace -2mm
24159 \begin_inset Newline newline
24162 Now the new defined function can be called with the command
24171 \begin_layout Itemize
24172 Write the formula as usual, mark the formula name, in our example the letters
24177 , and change it to mathematical text.
24178 Finally, a space is inserted between prefactor and function.
24181 \begin_layout Standard
24182 The result is the same with both methods as with a predefined function
24186 \begin_layout Plain Layout
24187 In LyX self-defined functions are displayed red, predefined ones black.
24195 \begin_layout Standard
24197 \begin_inset Tabular
24198 <lyxtabular version="3" rows="3" columns="2">
24199 <features rotate="0" tabularvalignment="middle">
24200 <column alignment="center" valignment="top" width="0pt">
24201 <column alignment="center" valignment="top" width="0pt">
24203 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
24206 \begin_layout Plain Layout
24212 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
24215 \begin_layout Plain Layout
24223 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
24226 \begin_layout Plain Layout
24234 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
24237 \begin_layout Plain Layout
24238 \begin_inset Formula $A\sgn(x)+B$
24248 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
24251 \begin_layout Plain Layout
24255 \begin_inset Formula $\underbrace{\textrm{sgn}}_{\textrm{Alt+M}\,\textrm{M}}$
24263 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
24266 \begin_layout Plain Layout
24267 \begin_inset Formula $A\,\textrm{sgn}(x)+B$
24283 \begin_layout Standard
24284 The first method is more suitable when the self-defined function should
24285 be used several times.
24288 \begin_layout Subsection
24290 \begin_inset Index idx
24293 \begin_layout Plain Layout
24302 \begin_layout Standard
24303 For limits, in addition to the commands
24310 \begin_inset Index idx
24313 \begin_layout Plain Layout
24333 the following functions are defined:
24336 \begin_layout Standard
24338 \begin_inset Tabular
24339 <lyxtabular version="3" rows="5" columns="2">
24340 <features rotate="0" tabularvalignment="middle">
24341 <column alignment="center" valignment="top">
24342 <column alignment="center" valignment="top">
24344 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
24347 \begin_layout Plain Layout
24353 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
24356 \begin_layout Plain Layout
24358 \begin_inset Note Note
24361 \begin_layout Plain Layout
24368 is only used as spacer.
24380 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
24383 \begin_layout Plain Layout
24391 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
24394 \begin_layout Plain Layout
24395 \begin_inset Formula $\varliminf$
24405 <cell alignment="center" valignment="top" leftline="true" usebox="none">
24408 \begin_layout Plain Layout
24416 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
24419 \begin_layout Plain Layout
24420 \begin_inset Formula $\varlimsup$
24430 <cell alignment="center" valignment="top" leftline="true" usebox="none">
24433 \begin_layout Plain Layout
24441 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
24444 \begin_layout Plain Layout
24445 \begin_inset Formula $\varprojlim$
24455 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
24458 \begin_layout Plain Layout
24466 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
24469 \begin_layout Plain Layout
24470 \begin_inset Formula $\varinjlim$
24474 \begin_inset Formula $\raisebox{-2.5mm}{}$
24490 \begin_layout Standard
24491 \begin_inset VSpace medskip
24494 The limit is created by inserting a subscript.
24495 It is set right beside the function in an inline formula:
24498 \begin_layout Standard
24500 \begin_inset Tabular
24501 <lyxtabular version="3" rows="2" columns="2">
24502 <features rotate="0" tabularvalignment="middle">
24503 <column alignment="center" valignment="top" width="0pt">
24504 <column alignment="center" valignment="top" width="0pt">
24506 <cell alignment="center" valignment="top" usebox="none">
24509 \begin_layout Plain Layout
24515 <cell alignment="center" valignment="top" usebox="none">
24518 \begin_layout Plain Layout
24519 \begin_inset space \hspace{}
24524 \begin_inset Note Note
24527 \begin_layout Plain Layout
24534 are used here as spacer.
24546 <cell alignment="center" valignment="top" usebox="none">
24549 \begin_layout Plain Layout
24555 \begin_inset space \textvisiblespace{}
24559 \begin_inset space \textvisiblespace{}
24567 <cell alignment="center" valignment="top" usebox="none">
24570 \begin_layout Plain Layout
24571 \begin_inset Formula $\hspace{1cm}\raisebox{5mm}{}\lim_{x\to A}x=B$
24587 \begin_layout Standard
24588 In a displayed formula the limit is set below the formula, as usual:
24589 \begin_inset Formula
24599 \begin_layout Subsection
24601 \begin_inset Index idx
24604 \begin_layout Plain Layout
24605 Functions ! modulo-
24613 \begin_layout Standard
24614 The modulo-function is special, because it exists in four variants.
24615 The variants in a displayed formula are:
24616 \begin_inset Formula
24618 \underline{\textrm{Command}\raisebox{-0.9mm}{}} & & \underline{\textrm{Result}}\\
24619 \mathrm{a\backslash mod\textrm{␣}b} & & a\mod b\\
24620 \mathrm{a\backslash pmod\textrm{␣}b} & & a\pmod b\\
24621 \mathrm{a\backslash bmod\textrm{␣}b} & & a\bmod b\\
24622 \mathrm{a\backslash pod\textrm{␣}b} & & a\pod b
24630 \begin_layout Standard
24631 In an inline formula less space is set before the function names for all
24633 By default the modulo-functions take only the first following character
24635 To use more than one character, one has to put them into TeX-braces:
24636 \begin_inset Formula
24638 \underline{\textrm{Command}\raisebox{-0.9mm}{}} & & \underline{\textrm{Result}}\\
24639 \mathrm{a\backslash pod\textrm{␣}bcd} & & a\pod bcd\\
24640 \mathrm{a\backslash pod\backslash\{bc\to d} & & a\pod{bc}d
24648 \begin_layout Section
24650 \begin_inset Index idx
24653 \begin_layout Plain Layout
24662 \begin_layout Subsection
24663 Special Characters in Mathematical Text
24666 \begin_layout Standard
24667 The following commands can only be used in mathematical text or in TeX-mode:
24670 \begin_layout Standard
24671 \begin_inset space \hfill{}
24675 \begin_inset Tabular
24676 <lyxtabular version="3" rows="8" columns="2">
24677 <features rotate="0" tabularvalignment="middle">
24678 <column alignment="block" valignment="top">
24679 <column alignment="block" valignment="top">
24681 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
24684 \begin_layout Plain Layout
24690 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
24693 \begin_layout Plain Layout
24701 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
24704 \begin_layout Plain Layout
24712 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
24715 \begin_layout Plain Layout
24716 \begin_inset Formula $\textrm{œ}$
24726 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
24729 \begin_layout Plain Layout
24737 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
24740 \begin_layout Plain Layout
24741 \begin_inset Formula $\textrm{Œ}$
24751 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
24754 \begin_layout Plain Layout
24762 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
24765 \begin_layout Plain Layout
24766 \begin_inset Formula $\textrm{æ}$
24776 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
24779 \begin_layout Plain Layout
24787 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
24790 \begin_layout Plain Layout
24791 \begin_inset Formula $\textrm{Æ}$
24801 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
24804 \begin_layout Plain Layout
24812 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
24815 \begin_layout Plain Layout
24816 \begin_inset Formula $\textrm{\aa}$
24826 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
24829 \begin_layout Plain Layout
24833 \begin_inset Index idx
24836 \begin_layout Plain Layout
24843 \begin_layout Plain Layout
24864 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
24867 \begin_layout Plain Layout
24868 \begin_inset Formula $\textrm{Å}$
24878 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
24881 \begin_layout Plain Layout
24889 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
24892 \begin_layout Plain Layout
24893 \begin_inset Formula $\textrm{ı}$
24907 \begin_inset space \hfill{}
24911 \begin_inset Tabular
24912 <lyxtabular version="3" rows="8" columns="2">
24913 <features rotate="0" tabularvalignment="middle">
24914 <column alignment="block" valignment="top">
24915 <column alignment="center" valignment="top">
24917 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
24920 \begin_layout Plain Layout
24922 \begin_inset Note Note
24925 \begin_layout Plain Layout
24927 \begin_inset space \thinspace{}
24930 mm is used for separation, because otherwise the output will be ¡ and ¿
24941 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
24944 \begin_layout Plain Layout
24952 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
24955 \begin_layout Plain Layout
24963 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
24966 \begin_layout Plain Layout
24967 \begin_inset Formula $\textrm{ø}$
24977 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
24980 \begin_layout Plain Layout
24988 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
24991 \begin_layout Plain Layout
24992 \begin_inset Formula $\textrm{Ø}$
25002 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
25005 \begin_layout Plain Layout
25013 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
25016 \begin_layout Plain Layout
25017 \begin_inset Formula $\textrm{ł}$
25027 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
25030 \begin_layout Plain Layout
25038 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
25041 \begin_layout Plain Layout
25042 \begin_inset Formula $\textrm{Ł}$
25052 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
25055 \begin_layout Plain Layout
25057 \begin_inset space \hspace{}
25062 \begin_inset space \textvisiblespace{}
25070 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
25073 \begin_layout Plain Layout
25074 \begin_inset Formula $\textrm{!`}$
25084 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
25087 \begin_layout Plain Layout
25089 \begin_inset space \hspace{}
25094 \begin_inset space \textvisiblespace{}
25102 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
25105 \begin_layout Plain Layout
25106 \begin_inset Formula $\textrm{?`}$
25116 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
25119 \begin_layout Plain Layout
25127 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
25130 \begin_layout Plain Layout
25131 \begin_inset Formula $\textrm{ȷ}$
25145 \begin_inset space \hfill{}
25151 \begin_layout Standard
25153 \begin_inset Formula $\textrm{\textrm{Å}}$
25157 \begin_inset Formula $\textrm{\textrm{Ø}}$
25160 can also be inserted via the math toolbar button
25161 \begin_inset Graphics
25162 filename ../images/math/digamma.png
25170 \begin_layout Standard
25171 An exception are the commands
25174 \begin_inset space \hspace{}
25183 \begin_inset space \hspace{}
25189 , because they can be inserted in LyX directly to text.
25192 \begin_layout Subsection
25194 \begin_inset CommandInset label
25196 name "sub:Accents-in-Text"
25201 \begin_inset Index idx
25204 \begin_layout Plain Layout
25213 \begin_layout Standard
25214 With the following commands all letters can be accented.
25215 The commands must be inserted in TeX-mode.
25218 \begin_layout Standard
25219 \begin_inset space \hfill{}
25223 \begin_inset Tabular
25224 <lyxtabular version="3" rows="8" columns="2">
25225 <features rotate="0" tabularvalignment="middle">
25226 <column alignment="block" valignment="top">
25227 <column alignment="block" valignment="top">
25229 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
25232 \begin_layout Plain Layout
25238 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
25241 \begin_layout Plain Layout
25249 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
25252 \begin_layout Plain Layout
25256 \begin_inset Quotes grd
25264 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
25267 \begin_layout Plain Layout
25271 \begin_layout Plain Layout
25287 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
25290 \begin_layout Plain Layout
25298 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
25301 \begin_layout Plain Layout
25305 \begin_layout Plain Layout
25321 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
25324 \begin_layout Plain Layout
25328 \begin_inset space \textvisiblespace{}
25336 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
25339 \begin_layout Plain Layout
25343 \begin_layout Plain Layout
25359 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
25362 \begin_layout Plain Layout
25370 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
25373 \begin_layout Plain Layout
25377 \begin_layout Plain Layout
25393 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
25396 \begin_layout Plain Layout
25400 \begin_inset space \textvisiblespace{}
25408 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
25411 \begin_layout Plain Layout
25415 \begin_layout Plain Layout
25431 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
25434 \begin_layout Plain Layout
25438 \begin_inset space \textvisiblespace{}
25446 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
25449 \begin_layout Plain Layout
25453 \begin_layout Plain Layout
25469 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
25472 \begin_layout Plain Layout
25476 \begin_inset space \textvisiblespace{}
25484 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
25487 \begin_layout Plain Layout
25491 \begin_layout Plain Layout
25511 \begin_inset space \hfill{}
25515 \begin_inset Tabular
25516 <lyxtabular version="3" rows="8" columns="2">
25517 <features rotate="0" tabularvalignment="middle">
25518 <column alignment="block" valignment="top">
25519 <column alignment="center" valignment="top">
25521 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
25524 \begin_layout Plain Layout
25530 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
25533 \begin_layout Plain Layout
25541 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
25544 \begin_layout Plain Layout
25548 \begin_inset space \textvisiblespace{}
25556 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
25559 \begin_layout Plain Layout
25563 \begin_layout Plain Layout
25579 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
25582 \begin_layout Plain Layout
25590 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
25593 \begin_layout Plain Layout
25597 \begin_layout Plain Layout
25613 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
25616 \begin_layout Plain Layout
25620 \begin_inset Index idx
25623 \begin_layout Plain Layout
25634 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
25637 \begin_layout Plain Layout
25641 \begin_layout Plain Layout
25657 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
25660 \begin_layout Plain Layout
25668 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
25671 \begin_layout Plain Layout
25675 \begin_layout Plain Layout
25691 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
25694 \begin_layout Plain Layout
25698 \begin_inset space \textvisiblespace{}
25706 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
25709 \begin_layout Plain Layout
25713 \begin_layout Plain Layout
25729 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
25732 \begin_layout Plain Layout
25736 \begin_inset space \textvisiblespace{}
25744 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
25747 \begin_layout Plain Layout
25751 \begin_layout Plain Layout
25767 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
25770 \begin_layout Plain Layout
25774 \begin_inset space \textvisiblespace{}
25782 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
25785 \begin_layout Plain Layout
25789 \begin_layout Plain Layout
25809 \begin_inset space \hfill{}
25815 \begin_layout Standard
25816 \begin_inset VSpace medskip
25825 also two different characters can be accented.
25831 \begin_inset space \textvisiblespace{}
25840 \begin_layout Plain Layout
25852 \begin_layout Standard
25865 can in combination with vowels directly be inserted with the keyboard without
25867 The same applies for the tilde
25871 \begin_layout Plain Layout
25872 This only applies for keyboards where the tilde is defined as accent.
25881 in combination with
25896 \begin_layout Standard
25939 and accents that are inserted directly with the keyboard are also available
25940 in mathematical text.
25941 For the other accents there are special math commands to be used in formulas,
25943 \begin_inset CommandInset ref
25945 reference "sub:Accents-for-one"
25952 \begin_layout Standard
25953 \begin_inset VSpace bigskip
25956 Furthermore, with the command
25963 \begin_inset Index idx
25966 \begin_layout Plain Layout
25974 all numbers and letters can be set into a circle, quasi accented with a
25975 circle, similar to the copyright symbol.
25978 \begin_layout Standard
25980 \begin_inset Tabular
25981 <lyxtabular version="3" rows="3" columns="2">
25982 <features rotate="0" tabularvalignment="middle">
25983 <column alignment="center" valignment="top">
25984 <column alignment="center" valignment="top">
25986 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
25989 \begin_layout Plain Layout
25995 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
25998 \begin_layout Plain Layout
26000 \begin_inset Note Note
26003 \begin_layout Plain Layout
26010 is only used as spacer.
26022 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
26025 \begin_layout Plain Layout
26033 <cell multicolumn="1" alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
26036 \begin_layout Plain Layout
26040 \begin_layout Plain Layout
26056 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
26059 \begin_layout Plain Layout
26070 raisebox{-1.5pt}{W}}
26075 <cell multicolumn="1" alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
26078 \begin_layout Plain Layout
26079 \begin_inset Formula $\raisebox{4.5mm}{}$
26086 \begin_layout Plain Layout
26104 \begin_inset Formula $\raisebox{-2mm}{}$
26120 \begin_layout Standard
26121 One has to take care that the character fits in the circle.
26132 \begin_layout Plain Layout
26134 \begin_inset CommandInset ref
26136 reference "sub:Font-Sizes"
26145 specifies thereby the size of the circle.
26156 \begin_layout Plain Layout
26158 \begin_inset CommandInset ref
26160 reference "sub:Boxes-without-Frame"
26169 the character can be centered.
26172 \begin_layout Subsection
26174 \begin_inset Index idx
26177 \begin_layout Plain Layout
26186 \begin_layout Standard
26187 Old-style figures (also known as old-style numerals) are created with the
26195 \begin_inset Index idx
26198 \begin_layout Plain Layout
26207 The command can be used in formulas and in TeX-mode.
26208 The command scheme is:
26211 \begin_layout Standard
26216 oldstylenums{number}
26219 \begin_layout Standard
26224 oldstylenums{0123456789
26227 \begin_inset Formula $\oldstylenums{0123456789}$
26233 \begin_layout Section
26235 \begin_inset CommandInset label
26237 name "sec:Formula-Styles"
26242 \begin_inset Index idx
26245 \begin_layout Plain Layout
26254 \begin_layout Itemize
26255 There are two different alignment styles:
26259 \begin_layout Description
26260 Centered is the predefined standard
26263 \begin_layout Description
26264 Indented for this the option
26268 must be inserted in the menu
26270 Document\SpecialChar \menuseparator
26276 \begin_inset space ~
26282 \begin_layout Standard
26287 is used, the indentation can be adjusted with the length
26294 \begin_inset Index idx
26297 \begin_layout Plain Layout
26306 Should the distance be 15
26307 \begin_inset space \thinspace{}
26310 mm, the following command line is inserted in the LaTeX-preamble
26313 \begin_layout Standard
26323 \begin_layout Standard
26324 When no length is specified, the predefined value of 30
26325 \begin_inset space \thinspace{}
26332 \begin_layout Itemize
26333 And two different numbering styles:
26337 \begin_layout Description
26338 Right is the predefined standard
26341 \begin_layout Description
26342 Left for this the option
26346 must be inserted in the menu
26348 Document\SpecialChar \menuseparator
26354 \begin_inset space ~
26361 \begin_layout Standard
26370 can also be used together.
26371 In this case both options are inserted, separated by a comma.
26374 \begin_layout Standard
26375 The chosen styles are used for all displayed formulas of the document.
26376 When both, centered and indented formulas should be created in a document,
26382 The indented formulas are then set in a flalign environment, see
26383 \begin_inset CommandInset ref
26385 reference "sub:Flalign-Environment"
26392 \begin_layout Section
26394 \begin_inset CommandInset label
26396 name "sec:Multiline-Formulas"
26401 \begin_inset Index idx
26404 \begin_layout Plain Layout
26405 Formula ! multiline
26413 \begin_layout Subsection
26417 \begin_layout Standard
26418 In LyX multiline formulas are created by pressing
26423 arg "newline-insert newline"
26429 This creates either an
26431 eqnarray environment
26433 that is described in
26434 \begin_inset CommandInset ref
26436 reference "sub:Eqnarray-Environment"
26440 or, when the option
26442 Use AMS math package
26444 in the document settings is selected, an
26448 that is described in
26449 \begin_inset CommandInset ref
26451 reference "sub:Standard-align-Environment"
26456 The align environment is recommended because it provides in any case a
26457 typographically correct output.
26460 \begin_layout Standard
26461 There are other multiline formula environments that can be created via the
26464 Insert\SpecialChar \menuseparator
26468 These environments are described in the following sections.
26471 \begin_layout Standard
26472 In all multiline formula environments a new line is created by pressing
26476 arg "newline-insert newline"
26480 To add or delete lines, the math toolbar buttons
26481 \begin_inset Graphics
26482 filename ../images/tabular-feature_append-row.png
26488 \begin_inset Graphics
26489 filename ../images/tabular-feature_delete-row.png
26494 , respectively, or the menu
26496 Edit\SpecialChar \menuseparator
26502 \begin_layout Subsubsection
26504 \begin_inset CommandInset label
26506 name "sub:Line-Separation"
26511 \begin_inset Index idx
26514 \begin_layout Plain Layout
26515 Formula ! multiline ! Line separation
26523 \begin_layout Standard
26524 There is sometimes not enough space in multiline formulas between the lines:
26525 \begin_inset Formula
26527 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}\\
26528 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
26536 \begin_layout Standard
26537 In LaTeX additional line space is specified as optional argument of the
26539 This is not yet possible in LyX
26543 \begin_layout Plain Layout
26545 \begin_inset CommandInset href
26547 name "LyX-bug #1505"
26548 target "http://www.lyx.org/trac/ticket/1505"
26557 , therefore the whole formula must be inserted in TeX-mode.
26558 To add in our example space, the command
26566 is inserted at the end of the first line.
26571 \begin_layout Plain Layout
26578 \begin_layout Plain Layout
26580 B^{2}(B^{2}-2r_{g}^{2}+2x_{0}^{2}-2r_{k}^{2})+4x_{0}^{2}x^{2}+4x_{0}xD &
26583 textrm{-}4x^{2}B^{2}+4x_{0}xB^{2}
26590 \begin_layout Plain Layout
26594 left(B^{2}+x_{0}^{2}
26602 left(B^{2}-2r_{g}^{2}+2x_{0}^{2}-2r_{k}^{2}
26607 \begin_layout Plain Layout
26619 \begin_layout Standard
26620 \begin_inset VSpace bigskip
26623 To set the line separation for all lines in a formula, the length
26630 \begin_inset Index idx
26633 \begin_layout Plain Layout
26643 \begin_inset Formula $\mbox{line separation}=\mathrm{6\, pt+\backslash jot}$
26654 \begin_inset space \thinspace{}
26659 \begin_inset space \thinspace{}
26662 mm additional line separation as in the previous example, the command
26665 \begin_layout Standard
26675 \begin_layout Standard
26676 is inserted in TeX-mode before the formula.
26677 This requires that the LaTeX-package
26685 \begin_layout Plain Layout
26690 is part of every LaTeX standard installation.
26696 \begin_inset Index idx
26699 \begin_layout Plain Layout
26705 was loaded in LaTeX-preamble with the line
26708 \begin_layout Standard
26716 \begin_layout Standard
26721 \begin_layout Plain Layout
26733 \begin_inset Formula
26735 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}\\
26736 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
26744 \begin_layout Standard
26748 \begin_layout Plain Layout
26759 To get back to the predefined distance,
26765 is set to the value 3
26766 \begin_inset space \thinspace{}
26772 \begin_layout Subsubsection
26774 \begin_inset CommandInset label
26776 name "sub:Column-Separation"
26781 \begin_inset Index idx
26784 \begin_layout Plain Layout
26785 Formula ! multiline ! Column separation
26793 \begin_layout Standard
26794 Multiline formulas form a matrix.
26795 A formula in the eqnarray environment is for example a matrix with three
26797 By changing the column separation in this environment, the space beside
26798 the relation sign can be changed.
26801 \begin_layout Standard
26802 The column separation is specified with the length
26809 \begin_inset Index idx
26812 \begin_layout Plain Layout
26821 \begin_inset Newline newline
26824 column separation = 2
26825 \begin_inset space \thinspace{}
26835 \begin_inset Newline newline
26841 \begin_layout Standard
26851 \begin_layout Standard
26852 inserted in TeX-mode, sets for all following formulas a column separation
26854 \begin_inset space \thinspace{}
26858 To get back to the predefined distance,
26865 \begin_inset space \thinspace{}
26871 \begin_layout Standard
26873 \begin_inset space \thinspace{}
26876 cm column separation:
26880 \begin_layout Plain Layout
26892 \begin_inset Formula
26900 A formula with the predefined column separation for matrices of 10
26901 \begin_inset space \thinspace{}
26908 \begin_layout Plain Layout
26920 \begin_inset Formula
26931 \begin_layout Subsubsection
26933 \begin_inset Index idx
26936 \begin_layout Plain Layout
26945 \begin_layout Standard
26946 Long formulas can be typeset using these methods:
26949 \begin_layout Itemize
26950 When one side of the equation is much shorter than the line width, this
26951 one is chosen for the left side and the right side is typeset over two
26953 \begin_inset Formula
26955 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 \\
26956 & & -\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}
26961 The minus sign at the beginning of the second line does normally not appear
26962 as an operator because it is the first character of the line.
26963 Thus it would not be surrounded by space and could not be distinguished
26964 from the fraction bar.
26966 \begin_inset space \thinspace{}
26969 pt space was inserted behind the minus sign with the command
26979 \begin_layout Plain Layout
26987 \begin_inset CommandInset ref
26989 reference "sub:Variable-Space"
26999 \begin_inset Index idx
27002 \begin_layout Plain Layout
27013 \begin_layout Itemize
27014 When both sides of the equation are too long, the command
27021 \begin_inset Index idx
27024 \begin_layout Plain Layout
27033 It is inserted in the first column of the first line and causes all further
27034 insertions to overwrite the following columns:
27035 \begin_inset Formula
27037 \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 \\
27038 & & -\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 \\
27039 & & =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}
27044 After the insertion of
27050 , the cursor is in a purple box that is a bit shifted to the left from the
27052 In this the formula is inserted.
27053 \begin_inset Newline newline
27056 The content of the further lines is inserted to the second or another formula
27058 The greater the column number where it was inserted, the larger the indentation.
27059 \begin_inset VSpace medskip
27063 \begin_inset Newline newline
27067 \begin_inset Note Greyedout
27070 \begin_layout Plain Layout
27071 Note the following when using
27080 \begin_layout Itemize
27081 The formula doesn't use the full page width.
27083 \begin_inset space \thinspace{}
27087 \begin_inset space \space{}
27091 \begin_inset Formula $-B^{2}$
27094 is added to the first line in the above example, it would have been outside
27096 To better use the width, negative space can be inserted at the beginning
27100 \begin_layout Itemize
27101 Due to a bug in LyX the cursor cannot be set with the mouse into the first
27106 \begin_layout Plain Layout
27107 \begin_inset CommandInset href
27109 name "LyX-bug #1429"
27110 target "http://www.lyx.org/trac/ticket/1429"
27119 One can only set the cursor at the beginning of the line and move it with
27128 \begin_layout Itemize
27129 Other methods to set long formulas are offered by the environments described
27131 \begin_inset CommandInset ref
27133 reference "sub:Multline-Environment"
27138 \begin_inset CommandInset ref
27140 reference "sub:Multiline-Formula-Parts"
27147 \begin_layout Subsubsection
27149 \begin_inset CommandInset label
27151 name "sub:Multiline-Brackets"
27156 \begin_inset Index idx
27159 \begin_layout Plain Layout
27160 Brackets ! for multiline expressions
27168 \begin_layout Standard
27169 For brackets spanning multiple lines the following problem occurs:
27170 \begin_inset Formula
27172 A & = & \sin(x)\left[\prod_{R=1}^{\infty}\frac{1}{R}+\cdots\right.\\
27173 & & \left.\cdots+B-D\right]
27181 \begin_layout Standard
27182 The closing bracket is smaller than the opening bracket because brackets
27183 with variable size may not span multiple lines.
27186 \begin_layout Standard
27187 To set the bracket size for the second line correctly, the first line is
27195 \begin_inset Index idx
27198 \begin_layout Plain Layout
27206 and the second line with
27214 \begin_layout Plain Layout
27228 \begin_inset CommandInset ref
27230 reference "sub:Automatic-Bracket-Size"
27242 \begin_inset Index idx
27245 \begin_layout Plain Layout
27268 \begin_inset space \textvisiblespace{}
27278 \begin_inset space \textvisiblespace{}
27288 \begin_inset space \textvisiblespace{}
27294 \begin_inset Formula $\downarrow$
27300 \begin_inset Index idx
27303 \begin_layout Plain Layout
27311 is inserted, because the multiplication operator with its limits is the
27312 largest symbol in the first line and this should be the size for the bracket
27313 in the second line.
27316 \begin_layout Standard
27317 The result is this:
27318 \begin_inset Formula
27320 A & = & \sin(x)\left[\prod_{R=1}^{\infty}\frac{1}{R}+\cdots\right.\\
27321 & & \left.\vphantom{\prod_{R=1}^{\infty}}\cdots+B-D\right]
27329 \begin_layout Subsection
27333 \begin_layout Standard
27334 Align environments can be used for every kind of multiline formulas.
27335 They are especially useful to set several formulas side by side.
27338 \begin_layout Standard
27339 Align environments consist of columns.
27340 The odd columns are right aligned, the even ones left aligned.
27341 Every line in an Align environment can be numbered.
27344 \begin_layout Standard
27345 Align environments are created via the menu
27347 Insert\SpecialChar \menuseparator
27353 Edit\SpecialChar \menuseparator
27354 Math\SpecialChar \menuseparator
27355 Change Formula Type
27357 already existing formulas can be converted to Align environments.
27360 \begin_layout Standard
27361 To add or delete columns, the math toolbar buttons
27362 \begin_inset Graphics
27363 filename ../images/tabular-feature_append-column.png
27369 \begin_inset Graphics
27370 filename ../images/tabular-feature_delete-column.png
27375 , respectively, or the menu
27377 Edit\SpecialChar \menuseparator
27383 \begin_layout Subsubsection
27384 Standard align Environment
27385 \begin_inset CommandInset label
27387 name "sub:Standard-align-Environment"
27392 \begin_inset Index idx
27395 \begin_layout Plain Layout
27396 Formula ! multiline ! align environment
27404 \begin_layout Standard
27405 This Align environment is created by pressing
27408 arg "newline-insert newline"
27411 in a formula or by the menu
27413 Insert\SpecialChar \menuseparator
27414 Math\SpecialChar \menuseparator
27415 AMS align Environment
27420 \begin_layout Standard
27421 An example for two formulas set side by side, that are created with a four
27422 column align environment:
27423 \begin_inset Formula
27425 A & =\sin(B) & C & =D\\
27426 C & \ne A & B & \ne D
27431 As it can be seen, the formulas in this environment are placed so as if
27440 \begin_layout Plain Layout
27448 \begin_inset CommandInset ref
27450 reference "sub:Variable-Space"
27461 before the first and after every even column.
27462 When the formula style
27468 \begin_layout Plain Layout
27470 \begin_inset CommandInset ref
27472 reference "sec:Formula-Styles"
27483 is used, the formula is set without the
27489 before the first column.
27492 \begin_layout Subsubsection
27493 Alignat Environment
27494 \begin_inset Index idx
27497 \begin_layout Plain Layout
27498 Formula ! multiline ! alignat environment
27506 \begin_layout Standard
27507 The alignat environment has no predefined column separation.
27508 It can be inserted manually with the spaces that are described
27509 \begin_inset CommandInset ref
27511 reference "sub:Space"
27518 \begin_layout Standard
27519 The above example in the alignat environment where 1
27520 \begin_inset space \thinspace{}
27523 cm space was inserted at the beginning of the second formula:
27524 \begin_inset Formula
27525 \begin{alignat*}{2}
27526 A & =\sin(B) & \hspace{1cm}C & =D\\
27527 C & \ne A & B & \ne D
27532 Because the column separation can be set separately for every column, this
27533 environment is especially suitable to set three and more formulas side
27537 \begin_layout Subsubsection
27538 Flalign Environment
27539 \begin_inset CommandInset label
27541 name "sub:Flalign-Environment"
27546 \begin_inset Index idx
27549 \begin_layout Plain Layout
27550 Formula ! multiline ! flalign environment
27558 \begin_layout Standard
27559 In this environment the first two columns are always set as much as possible
27560 to the left and the last two ones to the right.
27562 \begin_inset Formula
27564 A & =1 & B & =2 & C & =3\\
27565 X & =\textrm{-}1 & Y & =\textrm{-}2 & Z & =4
27573 \begin_layout Standard
27574 By creating a flalign environment with an odd number of columns where an
27575 empty TeX-brace is inserted to the last column, several formulas in a document
27576 can be set to the left, although the formula style
27581 As example the indented formula
27582 \begin_inset CommandInset ref
27584 reference "eq:VolInt"
27589 \begin_inset Formula
27591 \hspace{30pt}\iiint\limits _{V}X\,\mathrm{d}V & =U & {}
27596 The first two columns contain the formula.
27597 To indent it as with the formula style
27602 \begin_inset space \thinspace{}
27605 pt space was inserted at the beginning of the first column.
27608 \begin_layout Subsection
27609 Eqnarray Environment
27610 \begin_inset CommandInset label
27612 name "sub:Eqnarray-Environment"
27617 \begin_inset Index idx
27620 \begin_layout Plain Layout
27621 Formula ! multiline ! eqnarray environment
27629 \begin_layout Standard
27630 When this environment has been created, three blue boxes appear.
27631 The content of the first box is right aligned, the content of the last
27633 The content of the middle box appears centered and a bit smaller, because
27634 it is designed to insert there only relation characters.
27635 \begin_inset Formula
27637 \frac{ABC}{D} & \frac{ABC}{D} & \frac{ABC}{D}\\
27647 \begin_layout Subsection
27649 \begin_inset Index idx
27652 \begin_layout Plain Layout
27653 Formula ! multiline ! gather environment
27661 \begin_layout Standard
27662 This environment consists of only one centered column.
27663 Every line can be numbered.
27664 \begin_inset Formula
27675 \begin_layout Subsection
27676 Multline Environment
27677 \begin_inset CommandInset label
27679 name "sub:Multline-Environment"
27684 \begin_inset Index idx
27687 \begin_layout Plain Layout
27688 Formula ! multiline ! multline environment
27696 \begin_layout Standard
27697 The multline environment consists, like the gather environment, of only
27699 But the first line is left aligned, the last one right aligned.
27700 All other lines are centered.
27701 Therefore this environment is suitable for long formulas.
27703 \begin_inset CommandInset ref
27705 reference "eq:lefteqn"
27709 in the multline environment:
27710 \begin_inset Formula
27712 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}\\
27713 -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}\\
27714 =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}}
27722 \begin_layout Standard
27723 In the output only the last (first) line of a multline environment appears
27724 numbered when the document numbering is right (left).
27728 \begin_layout Plain Layout
27729 numbering styles see
27730 \begin_inset CommandInset ref
27732 reference "sec:Formula-Styles"
27744 \begin_layout Standard
27752 \begin_inset Index idx
27755 \begin_layout Plain Layout
27770 \begin_inset Index idx
27773 \begin_layout Plain Layout
27781 a centered line can be right or left aligned, respectively.
27782 The commands are used as follows:
27785 \begin_layout Standard
27790 shoveright{line content}
27796 shoveleft{line content}
27799 \begin_layout Standard
27800 \begin_inset VSpace medskip
27810 \begin_inset Index idx
27813 \begin_layout Plain Layout
27821 specifies the distance of the first line from the left page margin.
27822 Predefined is the length 0
27823 \begin_inset space \thinspace{}
27829 \begin_layout Standard
27830 As example the above formula where the command
27833 \begin_layout Standard
27843 \begin_layout Standard
27844 was inserted in TeX-mode before:
27848 \begin_layout Plain Layout
27860 \begin_inset Formula
27862 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}\\
27863 \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}}\\
27864 =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}}
27873 \begin_layout Plain Layout
27884 The second line was left aligned using
27893 \begin_layout Subsection
27894 Multiline Formula Parts
27895 \begin_inset CommandInset label
27897 name "sub:Multiline-Formula-Parts"
27902 \begin_inset Index idx
27905 \begin_layout Plain Layout
27906 Formula ! multiline ! formula parts
27914 \begin_layout Standard
27915 To display only parts of a formula with multiple lines, one of the following
27916 environments is used:
27933 They can be inserted via the menu
27935 Insert\SpecialChar \menuseparator
27938 or by using the commands described in this section.
27941 \begin_layout Standard
27942 The first three have the same properties as the corresponding multiline
27943 formula environments, but it is possible to set further formula parts beside
27946 \begin_inset Formula
27948 \left.\begin{aligned}\Delta x\Delta p & \ge\frac{\hbar}{2}\\
27949 \Delta E\Delta t & \ge\frac{\hbar}{2}
27951 \right\} \textrm{Uncertainty relations}
27959 \begin_layout Standard
27960 To get this formula, a displayed formula is created where the command
27967 \begin_inset Index idx
27970 \begin_layout Plain Layout
27979 A purple box appears around the blue formula box where now columns and
27980 lines can be added.
27981 Outside the multiline environment other formula parts can be set, like
27985 \begin_layout Standard
27986 The aligned environment is also suitable for long formulas whose lines are
27987 horizontally aligned.
27988 Using aligned in a displayed formula has the advantage that the formula
27989 number is vertically centered behind the lines.
27991 \begin_inset CommandInset ref
27993 reference "eq:shortlong"
27997 in the aligned environment:
27998 \begin_inset Formula
28000 \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}|}\\
28001 & -\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}|}
28010 \begin_layout Standard
28011 To use the environments
28030 \begin_inset Index idx
28033 \begin_layout Plain Layout
28048 \begin_inset Index idx
28051 \begin_layout Plain Layout
28066 \begin_inset Index idx
28069 \begin_layout Plain Layout
28077 are inserted, respectively.
28078 The split environment has the same properties as the aligned environment
28079 but it can only have two columns.
28082 \begin_layout Subsection
28083 Text in multiline Formulas
28084 \begin_inset CommandInset label
28086 name "sub:Text-in-multiline"
28091 \begin_inset Index idx
28094 \begin_layout Plain Layout
28101 \begin_inset Index idx
28104 \begin_layout Plain Layout
28105 Formula ! multiline ! text
28113 \begin_layout Standard
28114 In the Align environments, and the multline and gather environment, text
28115 can be inserted that will appear in a separate line and doesn't affect
28116 the column alignment.
28117 To do this, the command
28124 \begin_inset Index idx
28127 \begin_layout Plain Layout
28135 is used in the following scheme:
28138 \begin_layout Standard
28146 \begin_layout Standard
28147 The text should not be longer than a line because it cannot be hyphenated.
28148 As LyX doesn't yet support
28154 directly, the text is written as mathematical text.
28161 must hereby be at the beginning of a line and appears in the output above
28163 An example where the text was inserted at the beginning of the second line:
28164 \begin_inset Formula
28166 I & =a\sqrt{2}\int_{0}^{2\pi}\sqrt{1+\cos(\phi)}\;\mathrm{d}\phi\\
28167 \intertext{\text{integrand is symmetric to \ensuremath{\phi=\pi}, therefore}} & =2a\sqrt{2}\int_{0}^{\pi}\sqrt{1+\cos(\phi)}\;\mathrm{d}\phi
28175 \begin_layout Section
28177 \begin_inset Index idx
28180 \begin_layout Plain Layout
28187 \begin_inset Index idx
28190 \begin_layout Plain Layout
28191 Formula ! numbering|see
28195 \begin_layout Plain Layout
28206 \begin_layout Plain Layout
28221 \begin_layout Subsection
28225 \begin_layout Standard
28226 Numbered formulas can be created with the menu
28228 Insert\SpecialChar \menuseparator
28229 Math\SpecialChar \menuseparator
28231 \begin_inset space ~
28239 \begin_inset space ~
28245 Existing formulas can be numbered with the menu
28247 Edit\SpecialChar \menuseparator
28248 Math\SpecialChar \menuseparator
28250 \begin_inset space ~
28258 arg "math-number-toggle"
28262 The formula number is displayed in LyX behind the formula as a number sign
28264 The number sign is replaced in the output by the formula number.
28267 \begin_layout Standard
28268 When numbering is turned on in multiline formulas, all lines will be numbered.
28269 But the numbering can be controlled with the menu
28271 Edit\SpecialChar \menuseparator
28272 Math\SpecialChar \menuseparator
28274 \begin_inset space ~
28278 \begin_inset space ~
28282 \begin_inset space ~
28290 arg "math-number-line-toggle"
28296 \begin_layout Standard
28297 Except for inline formulas, all formulas can be numbered with two different
28299 \begin_inset CommandInset ref
28301 reference "sec:Formula-Styles"
28308 \begin_layout Subsection
28310 \begin_inset Index idx
28313 \begin_layout Plain Layout
28314 Cross-references ! to formulas
28322 \begin_layout Standard
28323 All labeled formulas can be cross-referenced.
28324 A label is added by the menu
28326 Insert\SpecialChar \menuseparator
28329 or the toolbar button
28330 \begin_inset Graphics
28331 filename ../images/label-insert.png
28337 The cursor must hereby be inside a displayed formula.
28338 Alternatively you can right-click on the formula and choose
28343 A dialog pops up displaying the prefix
28348 The label is inserted there behind the prefix.
28349 The predefined prefix means
28350 \begin_inset Quotes eld
28354 \begin_inset Quotes erd
28357 and makes it easier to find labels in large documents because it marks
28358 it as formula label to divide it from e.
28359 \begin_inset space \thinspace{}
28363 \begin_inset space \space{}
28367 To change a label, the menu
28369 Insert\SpecialChar \menuseparator
28372 is used again or you right-click on a formula and then on
28379 \begin_layout Standard
28380 The name of the label is displayed in LyX within two parentheses behind
28382 A formula with a label is always numbered.
28385 \begin_layout Standard
28386 Cross-references are inserted via the menu
28388 Insert\SpecialChar \menuseparator
28391 or with the toolbar button
28392 \begin_inset Graphics
28393 filename ../images/dialog-show-new-inset_ref.png
28399 A formula cross-reference appears in the output as formula number.
28400 When in the cross-reference dialog window the format
28404 is chosen, the cross-reference appears in the output as formula number
28406 \begin_inset Newline newline
28409 By right-clicking on a cross-reference in LyX, one jumps to the formula
28410 that is referenced.
28413 \begin_layout Standard
28414 Here are as examples cross-references to formulas of the following subsections:
28415 \begin_inset Note Note
28418 \begin_layout Plain Layout
28419 Note the different cross-reference types.
28427 \begin_layout Standard
28429 \begin_inset CommandInset ref
28436 \begin_inset CommandInset ref
28444 \begin_inset CommandInset ref
28450 ) big Latin letters are used for the numbering in contrary to (
28451 \begin_inset CommandInset ref
28460 \begin_layout Standard
28461 \begin_inset VSpace medskip
28464 When the argument of
28472 \begin_layout Plain Layout
28480 \begin_inset CommandInset ref
28482 reference "sub:User-defined-Numbering"
28493 contains a box like in
28494 \begin_inset CommandInset ref
28496 reference "sub:Paragraph-Boxes"
28500 , the formula cannot be referenced.
28503 \begin_layout Subsection
28505 \begin_inset Index idx
28508 \begin_layout Plain Layout
28509 Formula numbering ! subnumbering
28517 \begin_layout Standard
28518 With the help of the commands
28522 begin{subequations}
28530 formulas can be subnumbered.
28531 Both commands are inserted in TeX-mode.
28534 \begin_layout Standard
28536 \begin_inset Formula
28547 \begin_layout Plain Layout
28551 addtocounter{equation}{-1}
28560 \begin_layout Plain Layout
28564 begin{subequations}
28570 \begin_inset VSpace -5mm
28574 \begin_inset Formula
28582 \begin_inset Formula
28592 \begin_layout Standard
28596 \begin_layout Plain Layout
28608 \begin_layout Standard
28609 To create the example, the following is done:
28612 \begin_layout Enumerate
28613 first formula is inserted
28616 \begin_layout Enumerate
28621 addtocounter{equation}{-1}
28623 begin{subequations}
28624 \begin_inset Index idx
28627 \begin_layout Plain Layout
28636 \begin_inset Newline newline
28641 is inserted after the first formula
28644 \begin_layout Enumerate
28645 second formula is inserted
28648 \begin_layout Enumerate
28649 third formula is inserted
28652 \begin_layout Enumerate
28659 is inserted after the third formula
28662 \begin_layout Standard
28663 Every formula between the commands
28675 is subnumbered as a, b,
28676 \begin_inset Newline linebreak
28679 c, \SpecialChar \ldots{}
28680 For multiline formulas every line will be subnumbered.
28681 All subnumbered formulas are treated as
28686 But as every numbered formula increases the counter
28690 by one, the command
28696 is needed to decrease it.
28697 Otherwise the formulas
28698 \begin_inset CommandInset ref
28705 \begin_inset CommandInset ref
28712 \begin_inset CommandInset ref
28718 would be numbered as
28719 \begin_inset CommandInset ref
28726 \begin_inset CommandInset ref
28733 \begin_inset CommandInset ref
28742 \begin_layout Standard
28743 By inserting the commands in TeX-mode, a space is created between the first
28746 \begin_inset space \thinspace{}
28749 mm vertical space is inserted after the command
28753 begin{subequations}
28756 When the formula style
28762 \begin_layout Plain Layout
28764 \begin_inset CommandInset ref
28766 reference "sec:Formula-Styles"
28778 \begin_inset space \thinspace{}
28781 mm space is inserted instead.
28784 \begin_layout Standard
28785 Here is an example for a multiline formula where the numbering was turned
28786 off for the second line:
28790 \begin_layout Plain Layout
28794 begin{subequations}
28800 \begin_inset Formula
28802 A & = & (B-Z)^{2}=(B-Z)(B-Z)\label{eq:d}\\
28803 & = & B^{2}-ZB-BZ+Z^{2}\nonumber \\
28804 & = & B^{2}-2BZ+Z^{2}\label{eq:f}
28813 \begin_layout Plain Layout
28825 \begin_layout Subsection
28826 User-defined Numbering
28827 \begin_inset CommandInset label
28829 name "sub:User-defined-Numbering"
28834 \begin_inset Index idx
28837 \begin_layout Plain Layout
28838 Formula numbering ! user-defined
28846 \begin_layout Standard
28847 \begin_inset Index idx
28850 \begin_layout Plain Layout
28851 Formula numbering ! self-defined delimiters
28856 With the standard numbering parentheses are set around the formula number.
28857 To replace the parentheses for example by vertical bars, the following
28858 line is added to the LaTeX-preamble:
28861 \begin_layout Standard
28873 \begin_inset Note Note
28876 \begin_layout Plain Layout
28877 This macro is already declared in the LaTeX-preamble for testing.
28878 To activate it, remove the percent sign at the beginning.
28886 \begin_layout Standard
28887 To use other characters, the vertical bars besides the
28891 are replaced by one ore more characters.
28892 To get only the formula number the vertical bars are omitted.
28895 \begin_layout Standard
28896 \begin_inset VSpace bigskip
28899 When there should be an expression of your choice instead of the consecutive
28900 formula number in parentheses behind the formula, the command
28907 \begin_inset Index idx
28910 \begin_layout Plain Layout
28919 \begin_inset Formula
28921 A+B=C\tag{something}\label{eq:tag}
28926 In this example the command
28931 \begin_inset space \textvisiblespace{}
28936 was inserted in the formula.
28939 \begin_layout Standard
28945 \begin_inset space \textvisiblespace{}
28950 is inserted instead, the star prevents the parentheses around the expression:
28951 \begin_inset Formula
28953 A+B=C\tag*{something}
28961 \begin_layout Standard
28962 \begin_inset VSpace bigskip
28965 To restart the formula numbering with new document parts or sections, the
28966 following command is used:
28969 \begin_layout Standard
28974 @addtoreset{equation}{part}
28977 \begin_inset Index idx
28980 \begin_layout Plain Layout
28985 \begin_layout Plain Layout
28996 \begin_layout Plain Layout
29009 \begin_layout Plain Layout
29020 \begin_layout Plain Layout
29033 \begin_inset Newline newline
29037 \begin_inset Newline newline
29044 @addtoreset{equation}{section}
29047 \begin_layout Standard
29048 To be able to use these commands in TeX-mode, the
29049 \begin_inset Quotes eld
29053 \begin_inset Quotes erd
29056 character has to be made
29057 \begin_inset Quotes eld
29061 \begin_inset Quotes erd
29064 for LaTeX using the command
29078 So the command sequence in TeX-mode is:
29081 \begin_layout Standard
29087 \begin_inset Newline newline
29092 @addtoreset{equation}{section}
29093 \begin_inset Newline newline
29101 \begin_layout Standard
29102 In the LaTeX-preamble
29114 can be omitted as they are automatically internally inserted by LyX.
29117 \begin_layout Standard
29132 \begin_layout Plain Layout
29137 is part of the LaTeX-package
29142 \begin_inset Index idx
29145 \begin_layout Plain Layout
29146 Packages ! carlisle
29151 that is part of every LaTeX standard installation.
29157 \begin_inset Index idx
29160 \begin_layout Plain Layout
29161 Packages ! remreset
29166 has to be loaded in the LaTeX-preamble with the line
29169 \begin_layout Standard
29174 usepackage{remreset}
29177 \begin_layout Standard
29185 \begin_inset Index idx
29188 \begin_layout Plain Layout
29193 \begin_layout Plain Layout
29204 \begin_layout Plain Layout
29217 \begin_layout Plain Layout
29228 \begin_layout Plain Layout
29240 can be used with the same scheme as
29249 \begin_layout Standard
29250 \begin_inset VSpace bigskip
29253 Sometimes formulas should be numbered in the following form:
29256 \begin_layout Standard
29259 (section number.formula number)
29262 \begin_layout Standard
29263 The formula number should start with every section with
29264 \begin_inset Quotes eld
29268 \begin_inset Quotes erd
29274 \begin_layout Standard
29275 For this case there is the command
29282 \begin_inset Index idx
29285 \begin_layout Plain Layout
29293 , which is used with the following scheme:
29296 \begin_layout Standard
29301 numberwithin{counter}{sectioning}
29304 \begin_layout Standard
29305 Counter denotes what kind of numbering is affected, sectioning denotes what
29306 number is before the dot.
29309 \begin_layout Standard
29310 Thus in our case the following LaTeX-preamble or TeX code line is used:
29313 \begin_layout Standard
29318 numberwithin{equation}{section}
29321 \begin_layout Standard
29322 This is the result:
29326 \begin_layout Plain Layout
29330 numberwithin{equation}{section}
29336 \begin_inset Formula
29346 \begin_layout Standard
29348 \begin_inset space \thinspace{}
29352 \begin_inset space \space{}
29355 tables so that the number of the part is the sectioning,
29356 \begin_inset Newline newline
29363 numberwithin{table}{part}
29368 \begin_layout Standard
29369 To go back to the standard numbering or to prevent this kind of numbering
29370 when it is defined by the document class, the following command is inserted
29371 as TeX code or to the LaTeX-preamble:
29374 \begin_layout Standard
29384 \begin_inset Index idx
29387 \begin_layout Plain Layout
29401 \begin_layout Plain Layout
29417 \begin_inset Newline newline
29425 \begin_inset Newline newline
29437 \begin_layout Standard
29444 uses internally the command
29450 , described above, that also needs to be reverted.
29454 \begin_layout Plain Layout
29461 \begin_layout Plain Layout
29465 @removefromreset{equation}{section}
29468 \begin_layout Plain Layout
29480 \begin_layout Subsection
29481 Numbering with Roman Numbers and Letters
29482 \begin_inset Index idx
29485 \begin_layout Plain Layout
29486 Formula numbering ! with letters
29492 \begin_inset Index idx
29495 \begin_layout Plain Layout
29496 Formula numbering ! with Roman numbers
29504 \begin_layout Standard
29505 Formulas can also be numbered with Roman numbers and Latin letters.
29506 To number for example with small Roman numbers, the command
29509 \begin_layout Standard
29521 \begin_layout Standard
29522 is inserted before the formula in TeX-mode.
29530 \begin_inset Index idx
29533 \begin_layout Plain Layout
29541 redefines the predefined command
29557 \begin_layout Plain Layout
29564 has the same scheme like the command
29570 that is described in
29571 \begin_inset CommandInset ref
29573 reference "sub:The-Command-newcommand"
29586 is the formula counter.
29593 is used as prefix for a counter, the value of the counter is output as
29595 When a formula is numbered, LaTeX sets internally the command
29601 behind the formula.
29607 \begin_inset Index idx
29610 \begin_layout Plain Layout
29620 outputs the counter as small Roman number.
29623 \begin_layout Standard
29624 All formulas behind the command
29634 are now numbered Roman.
29635 To switch to numbering with big Roman numbers, the command is inserted
29649 \begin_inset Index idx
29652 \begin_layout Plain Layout
29664 \begin_inset Quotes eld
29668 \begin_inset Quotes erd
29671 with small Latin letters there is the command
29678 \begin_inset Index idx
29681 \begin_layout Plain Layout
29689 , for big ones there is the command
29696 \begin_inset Index idx
29699 \begin_layout Plain Layout
29712 \begin_layout Standard
29713 \begin_inset Note Greyedout
29716 \begin_layout Plain Layout
29723 \begin_inset space ~
29726 formulas can be numbered with Latin letters in one document.
29734 \begin_layout Standard
29738 \begin_layout Plain Layout
29754 \begin_layout Standard
29755 \begin_inset Formula
29757 A=\textrm{small roman}
29766 \begin_layout Plain Layout
29780 \begin_inset Formula
29782 B=\textrm{big Roman}\label{eq:Rom}
29791 \begin_layout Plain Layout
29805 \begin_inset Formula
29807 C=\textrm{small Latin}
29816 \begin_layout Plain Layout
29830 \begin_inset Formula
29832 D=\textrm{big Latin}\label{eq:Lat}
29840 \begin_layout Standard
29841 To switch back to the default numbering, insert the command:
29844 \begin_layout Standard
29854 \begin_inset Index idx
29857 \begin_layout Plain Layout
29868 \begin_layout Standard
29872 \begin_layout Plain Layout
29886 \begin_inset Formula
29896 \begin_layout Standard
29897 \begin_inset VSpace medskip
29900 As you see, formulas are numbered serially independent from the numbering
29902 When then numbering should start with
29903 \begin_inset Quotes eld
29907 \begin_inset Quotes erd
29910 when the style is changed, new equation counters have to be defined.
29911 A description about this can be found in the file
29912 \begin_inset CommandInset href
29914 name "Formula-numbering.lyx"
29915 target "run:Formula-numbering.lyx"
29922 \begin_layout Standard
29923 \begin_inset Newpage newpage
29929 \begin_layout Section
29930 Chemical Symbols and Equations
29931 \begin_inset CommandInset label
29933 name "sub:Chemical-Symbols-and"
29938 \begin_inset Index idx
29941 \begin_layout Plain Layout
29942 Chemical characters ! Symbols
29948 \begin_inset Index idx
29951 \begin_layout Plain Layout
29958 \begin_inset Index idx
29961 \begin_layout Plain Layout
29970 \begin_layout Standard
29971 An example text from chemistry:
29974 \begin_layout Quote
29976 \begin_inset Formula $\mathrm{SO_{4}^{2-}}$
29979 -ion reacts with two
29980 \begin_inset Formula $\mathrm{Na^{+}}$
29983 -ions to sodium sulfate
29984 \begin_inset Formula $\left(\mathrm{Na_{2}SO_{4}}\right)$
29988 The chemical equation for this is:
29989 \begin_inset Formula
29991 \mathrm{2\, Na^{+}+SO_{4}^{2-}\longrightarrow Na_{2}SO_{4}}\label{eq:chem-reaction}
29999 \begin_layout Standard
30000 This chemical equation can directly be created as formula.
30001 To avoid that the symbols appear italic, everything is highlighted and
30002 changed by the shortcut
30008 to the upright font style.
30012 \begin_layout Plain Layout
30018 \begin_inset CommandInset ref
30020 reference "sub:Font-Styles"
30032 \begin_layout Standard
30033 A more convenient way to typeset chemical formulas is to use the command
30041 \begin_inset Index idx
30044 \begin_layout Plain Layout
30052 that is available when the LaTeX-package
30057 \begin_inset Index idx
30060 \begin_layout Plain Layout
30073 to a formula a new blue box appears where chemical formulas can be inserted
30074 in an intuitive way.
30077 \begin_layout Standard
30079 \begin_inset Tabular
30080 <lyxtabular version="3" rows="9" columns="2">
30081 <features rotate="0" tabularvalignment="middle">
30082 <column alignment="center" valignment="top">
30083 <column alignment="center" valignment="top">
30085 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
30088 \begin_layout Plain Layout
30094 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
30097 \begin_layout Plain Layout
30099 \begin_inset Note Note
30102 \begin_layout Plain Layout
30109 is only used as spacer.
30121 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
30124 \begin_layout Plain Layout
30128 \begin_inset space \textvisiblespace{}
30136 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
30139 \begin_layout Plain Layout
30140 \begin_inset Formula $\raisebox{4.5mm}{}\ce{H2CO3}\raisebox{-2mm}{}$
30150 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
30153 \begin_layout Plain Layout
30157 \begin_inset space \textvisiblespace{}
30165 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
30168 \begin_layout Plain Layout
30169 \begin_inset Formula $\raisebox{5mm}{}\ce{SO4^{2-}}\raisebox{-2mm}{}$
30179 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
30182 \begin_layout Plain Layout
30186 \begin_inset space \textvisiblespace{}
30194 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
30197 \begin_layout Plain Layout
30198 \begin_inset Formula $\raisebox{4.5mm}{}\ce{(NH4)2S}\raisebox{-2mm}{}$
30208 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
30211 \begin_layout Plain Layout
30215 \begin_inset space \textvisiblespace{}
30223 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
30226 \begin_layout Plain Layout
30227 \begin_inset Formula $\raisebox{4.5mm}{}\ce{KCr(SO4)2.12H2O}\raisebox{-2mm}{}$
30237 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
30240 \begin_layout Plain Layout
30244 \begin_inset space \textvisiblespace{}
30250 \begin_inset space \textvisiblespace{}
30256 \begin_inset space \textvisiblespace{}
30264 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
30267 \begin_layout Plain Layout
30268 \begin_inset Formula $\raisebox{4.5mm}{}\ce{A-B\dbond C\tbond D}\raisebox{-2mm}{}$
30278 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
30281 \begin_layout Plain Layout
30285 \begin_inset space \textvisiblespace{}
30289 \begin_inset Formula $\downarrow$
30293 \begin_inset Formula $\to$
30301 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
30304 \begin_layout Plain Layout
30305 \begin_inset Formula $\raisebox{5mm}{}\ce{_{90}^{227}Th+}\raisebox{-2mm}{}$
30315 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
30318 \begin_layout Plain Layout
30322 \begin_inset space \textvisiblespace{}
30326 \begin_inset space \textvisiblespace{}
30330 \begin_inset space \textvisiblespace{}
30334 \begin_inset space \textvisiblespace{}
30338 \begin_inset space \textvisiblespace{}
30346 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
30349 \begin_layout Plain Layout
30350 \begin_inset Formula $\raisebox{4.5mm}{}\ce{CO2 + C <=> 2CO}\raisebox{-2mm}{}$
30360 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
30363 \begin_layout Plain Layout
30367 \begin_inset space \textvisiblespace{}
30371 \begin_inset space \textvisiblespace{}
30375 \begin_inset space \textvisiblespace{}
30379 \begin_inset space \textvisiblespace{}
30387 \begin_inset space \textvisiblespace{}
30395 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
30398 \begin_layout Plain Layout
30399 \begin_inset Formula $\raisebox{5mm}{}\ce{CO2 + C ->[\alpha][\beta] 2CO}\raisebox{-4mm}{}$
30415 \begin_layout Standard
30416 \begin_inset Note Greyedout
30419 \begin_layout Plain Layout
30425 Inserting a formula to a
30431 box will lead to LaTeX errors due to a LyX bug.
30437 \begin_layout Plain Layout
30438 \begin_inset CommandInset href
30440 name "LyX-bug #8566"
30441 target "http://www.lyx.org/trac/ticket/8566"
30452 In this case TeX code has to be used like for
30466 \begin_layout Plain Layout
30487 \begin_layout Standard
30488 \begin_inset Note Greyedout
30491 \begin_layout Plain Layout
30497 It is not possible in LyX to use the character ^ to get an up-arrow as
30503 One instead uses a negative thin space followed by the command
30510 \begin_inset Formula $\ce{Fe + 2H+ -> Fe^{2+} + H2\negthinspace\uparrow}$
30521 \begin_layout Standard
30528 the command for equation
30529 \begin_inset space ~
30533 \begin_inset CommandInset ref
30535 reference "eq:chem-reaction"
30540 \begin_inset Newline newline
30548 \begin_inset space \textvisiblespace{}
30552 \begin_inset space \textvisiblespace{}
30556 \begin_inset space \textvisiblespace{}
30560 \begin_inset space \textvisiblespace{}
30564 \begin_inset space \textvisiblespace{}
30568 \begin_inset space \textvisiblespace{}
30574 \begin_layout Standard
30575 To create multiline chemical equations first a multiline formula is created
30577 \begin_inset CommandInset ref
30579 reference "sec:Multiline-Formulas"
30584 Afterwards the command
30590 is used in every small blue box of the formula.
30592 \begin_inset CommandInset ref
30594 reference "eq:TEOS-reaction-1"
30599 \begin_inset CommandInset ref
30601 reference "eq:TEOS-reaction-2"
30605 are an example of a multi-stage chemical reaction where every equation
30606 has its own number.
30607 \begin_inset Formula
30609 \ce{TEOS + 4O} & \ce{->} & \ce{Si(OH)4 + 4C2H4O}\label{eq:TEOS-reaction-1}\\
30610 \ce{Si(OH)4} & \ce{->} & \ce{SiO2 + 2H2O}\label{eq:TEOS-reaction-2}
30618 \begin_layout Standard
30629 package provides the command
30636 \begin_inset Index idx
30639 \begin_layout Plain Layout
30647 that has to be used for special cases.
30648 For more information about
30654 and more examples have a look at the documentation of
30659 \begin_inset CommandInset citation
30668 \begin_layout Section
30672 \begin_layout Standard
30673 LyX supports two types of commutative diagrams:
30681 that are explained in the following.
30684 \begin_layout Subsection
30686 \begin_inset Index idx
30689 \begin_layout Plain Layout
30698 \begin_layout Standard
30699 Diagrams of this type visualize relations by vertical and horizontal lines
30701 \begin_inset Formula
30703 \begin{CD}A@>>>B@>>>C\\
30714 \begin_layout Standard
30715 To get them, the command
30720 \begin_inset Index idx
30723 \begin_layout Plain Layout
30733 is inserted to a formula.
30734 A blue box appears with two dashed lines where further commands can be
30739 arg "newline-insert newline"
30742 a new line is created.
30743 Horizontal relations are inserted in odd, vertical in even formula lines.
30746 \begin_layout Standard
30747 To create the relations there are the following commands:
30750 \begin_layout Itemize
30755 creates a left arrow,
30766 \begin_layout Itemize
30771 creates an up arrow,
30779 a vertical equal sign
30782 \begin_layout Itemize
30788 is a placeholder for non-existent relations
30791 \begin_layout Standard
30792 All arrows can be labeled as follows:
30795 \begin_layout Itemize
30796 If text inserted between the first and second < or >, resp., it is placed
30798 When it is inserted between the second and third one, it appears under
30802 \begin_layout Itemize
30803 When text for vertical arrows is inserted between the first and second A
30804 or V, resp., it is placed left beside the arrow.
30805 When it is inserted between the second and third one, it appears right
30807 If the text contains an A or V, these letters must be set into a TeX-brace.
30810 \begin_layout Standard
30811 As example a diagram with all possible relations:
30814 \begin_layout Standard
30815 \begin_inset Formula
30817 \begin{CD}A@>j>>B@>>k>C@=F\\
30828 \begin_layout Standard
30829 The command for this is:
30830 \begin_inset Newline newline
30838 \begin_inset space \textvisiblespace{}
30841 A@>j>>B@>>k>C@=F Ctrl+Return
30842 \begin_inset Newline newline
30846 \begin_inset Phantom HPhantom
30849 \begin_layout Plain Layout
30855 \begin_inset space \textvisiblespace{}
30868 \begin_inset Formula $\to$
30874 \begin_inset Newline newline
30878 \begin_inset Phantom HPhantom
30881 \begin_layout Plain Layout
30887 \begin_inset space \textvisiblespace{}
30898 \begin_layout Subsection
30900 \begin_inset Index idx
30903 \begin_layout Plain Layout
30904 Diagrams ! xymatrix
30912 \begin_layout Standard
30913 To be able to use xymatrices, the LaTeX-package
30918 A xymatrix is created by inserting the command
30925 Then you are able to add new matrix columns and rows like for normal matrices,
30927 \begin_inset CommandInset ref
30929 reference "sec:Matrices"
30936 \begin_layout Standard
30937 In contrary to amscd diagrams, xymatrices supports diagonal and curved arrows,
30939 All possibilities to create commutative diagrams and decorations are explained
30944 that you find in the menu
30946 Help\SpecialChar \menuseparator
30948 \begin_inset space ~
30956 \begin_layout Subsection
30962 \begin_inset Index idx
30965 \begin_layout Plain Layout
30974 \begin_layout Standard
30979 -diagrams, the LaTeX-package
30988 -diagram is created by inserting the command
30995 Then you are able to add new matrix columns and rows like for normal matrices,
30997 \begin_inset CommandInset ref
30999 reference "sec:Matrices"
31006 \begin_layout Standard
31007 Examples how to create
31011 diagrams in LyX is given in the
31013 Feynman-diagram manual
31015 that you find in the menu
31017 Help\SpecialChar \menuseparator
31019 \begin_inset space ~
31027 \begin_layout Standard
31028 \begin_inset Newpage newpage
31034 \begin_layout Section
31035 User-defined Commands
31036 \begin_inset Index idx
31039 \begin_layout Plain Layout
31040 User-defined commands
31048 \begin_layout Standard
31049 \begin_inset Note Greyedout
31052 \begin_layout Plain Layout
31057 The names of user-defined commands and macros may only consist of Latin
31066 \begin_layout Subsection
31070 \begin_inset CommandInset label
31072 name "sub:The-Command-newcommand"
31077 \begin_inset Index idx
31080 \begin_layout Plain Layout
31081 User-defined commands !
31089 \begin_inset Index idx
31092 \begin_layout Plain Layout
31103 \begin_layout Standard
31104 Many LaTeX-commands are too long to be used frequently.
31105 But it is possible to define with the command
31111 new shorter commands.
31114 \begin_layout Standard
31115 The command scheme of
31124 \begin_layout Standard
31129 newcommand{new command name}[number of arguments][optional
31134 \begin_inset Newline newline
31138 \begin_inset Phantom HPhantom
31141 \begin_layout Plain Layout
31151 {command definition}
31154 \begin_layout Standard
31155 \begin_inset Note Greyedout
31158 \begin_layout Plain Layout
31163 Assure that the name of the new command is not already used in your document
31164 or by LaTeX-packages that you use.
31165 When you for example define the command
31177 , you get an error message because
31183 is already defined as command for
31184 \begin_inset Quotes eld
31188 \begin_inset Formula $\le$
31192 \begin_inset Quotes erd
31203 \begin_layout Standard
31204 The number of arguments is an integer in the range 0
31205 \begin_inset space \thinspace{}
31209 \begin_inset space \thinspace{}
31212 9 and specifies how many arguments the new command should have.
31213 With the optional value a value for an optional argument can be predefined.
31214 When this is done, the
31222 rgument of the new command is automatically an optional one.
31225 \begin_layout Standard
31226 Here are some examples:
31229 \begin_layout Itemize
31230 To define the command
31242 , the LaTeX-preamble line is:
31243 \begin_inset VSpace medskip
31247 \begin_inset Newline newline
31261 \begin_layout Itemize
31262 To define the command
31274 , the argument (that should be underlined) must be taken into account.
31275 For this the preamble line is:
31276 \begin_inset VSpace medskip
31280 \begin_inset Newline newline
31294 \begin_inset VSpace medskip
31298 \begin_inset Newline newline
31305 acts as argument placeholder, the
31309 behind it denotes that it is the placeholder for the first argument.
31312 \begin_layout Itemize
31320 \begin_inset space \thinspace{}
31324 \begin_inset space \space{}
31334 \begin_inset VSpace medskip
31338 \begin_inset Newline newline
31349 framebox#1#2{$#3$}}
31352 \begin_inset VSpace medskip
31356 \begin_inset Newline newline
31359 The two Dollar signs creates the extra formula needed for
31366 \begin_inset CommandInset ref
31368 reference "sub:Boxes-with-Frame"
31375 \begin_layout Itemize
31376 To create a new command for
31382 where the color for the box need not be specified, the argument for the
31383 color is defined optional:
31384 \begin_inset VSpace medskip
31388 \begin_inset Newline newline
31399 fcolorbox{#2}{#1}{$#3$}}
31402 \begin_inset VSpace medskip
31406 \begin_inset Newline newline
31409 When the color is not specified when using
31415 , the predefined color
31422 \begin_layout Standard
31423 A test of the new defined commands:
31426 \begin_layout Standard
31428 \begin_inset Tabular
31429 <lyxtabular version="3" rows="6" columns="2">
31430 <features rotate="0" tabularvalignment="middle">
31431 <column alignment="center" valignment="top">
31432 <column alignment="center" valignment="top">
31434 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
31437 \begin_layout Plain Layout
31443 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
31446 \begin_layout Plain Layout
31448 \begin_inset Note Note
31451 \begin_layout Plain Layout
31458 is only used as spacer.
31470 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
31473 \begin_layout Plain Layout
31477 \begin_inset space \textvisiblespace{}
31485 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
31488 \begin_layout Plain Layout
31489 \begin_inset Formula $A\gr B$
31499 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
31502 \begin_layout Plain Layout
31510 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
31513 \begin_layout Plain Layout
31514 \begin_inset Formula $\raisebox{4.5mm}{}\us{ABcd}\raisebox{-2mm}{}$
31524 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
31527 \begin_layout Plain Layout
31531 \begin_inset Formula $\to$
31537 \begin_inset Formula $\to$
31545 \begin_inset space \textvisiblespace{}
31553 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
31556 \begin_layout Plain Layout
31557 \begin_inset Formula $\raisebox{6mm}{}\fb{[2cm]}{}{\int A=B}\raisebox{-4mm}{}$
31567 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
31570 \begin_layout Plain Layout
31574 \begin_inset Formula $\to$
31582 \begin_inset space \textvisiblespace{}
31590 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
31593 \begin_layout Plain Layout
31594 \begin_inset Formula $\raisebox{6mm}{}\cb{red}{\int A=B}\raisebox{-4mm}{}$
31604 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
31607 \begin_layout Plain Layout
31613 \begin_inset Formula $\to$
31621 \begin_inset space \textvisiblespace{}
31629 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
31632 \begin_layout Plain Layout
31633 \begin_inset Formula $\raisebox{6mm}{}\cb[green]{red}{\int A=B}\raisebox{-4mm}{}$
31649 \begin_layout Subsection
31651 \begin_inset Index idx
31654 \begin_layout Plain Layout
31655 User-defined commands! Math macros
31661 \begin_inset Index idx
31664 \begin_layout Plain Layout
31673 \begin_layout Standard
31674 User-defined commands are especially convenient for complex expressions.
31675 When you are for example dealing with a document that has quadratic equations,
31676 the same solution type occurs several times.
31677 The general form of a quadratic equation is
31678 \begin_inset Formula
31680 0=\lambda^{2}+p\lambda+q
31685 The general form of the solution is
31686 \begin_inset Formula
31688 \lambda_{1,2}=-\frac{p}{2}\pm\sqrt{\frac{p²}{4}-q}
31696 \begin_layout Standard
31697 To define a command for the solution formula where only the three parameters
31699 \begin_inset Formula $\lambda$
31703 \begin_inset Formula $p$
31707 \begin_inset Formula $q$
31710 need to be specified and the index of
31711 \begin_inset Formula $\lambda$
31714 can be given optionally, the LaTeX-preamble line is
31715 \begin_inset Newline newline
31731 \begin_inset Newline newline
31735 \begin_inset Phantom HPhantom
31738 \begin_layout Plain Layout
31752 frac{#3^{2}}{4}-#4}}
31755 \begin_layout Standard
31756 To create with this the solution formula, the command
31757 \begin_inset Newline newline
31767 \begin_inset Formula $\to$
31773 \begin_inset Formula $\to$
31780 is inserted to a formula
31785 \begin_layout Standard
31786 The definition of the new command is unintuitive because one has to know
31787 the schemes of all used LaTeX commands, e.
31788 \begin_inset space \thinspace{}
31792 \begin_inset space \space{}
31795 that a fraction is inserted in LaTeX as
31799 frac{numerator}{denominator}
31802 Furthermore one can easily forget a brace in the definition and cannot
31803 see in LyX what the new command is doing.
31804 To avoid these problems LyX offers the possibility to use math macros instead
31814 \begin_layout Standard
31815 A math macro is created by using the menu
31817 Insert\SpecialChar \menuseparator
31818 Math\SpecialChar \menuseparator
31821 or the toolbar button
31822 \begin_inset Graphics
31823 filename ../images/math-macro_newmacroname_newcommand.png
31829 The math macro toolbar appears together with the following box where the
31831 \begin_inset Newline newline
31835 \begin_inset space \hspace*{\fill}
31839 \begin_inset Graphics
31840 filename clipart/macrobox.png
31845 \begin_inset space \hspace*{\fill}
31849 \begin_inset Newline newline
31853 \begin_inset FormulaMacro
31854 \newcommand{\qG}[4][1,\,2]{#2_{#1}=-\frac{#3}{2}\pm\sqrt{\frac{#3^{2}}{4}-#4}}
31859 newmacroname is the default name of the macro that should be changed to
31860 something sensible.
31861 The wanted formula is inserted in the first blue box.
31862 An argument placeholder is inserted with the command
31869 \begin_inset space \thinspace{}
31873 \begin_inset space \space{}
31882 or by using the macro toolbar button
31883 \begin_inset Graphics
31884 filename ../images/math-macro-add-param.png
31890 Argument placeholders are displayed red.
31892 \begin_inset space ~
31895 arguments are possible.
31896 Optional arguments are created with the toolbar button
31897 \begin_inset Graphics
31898 filename ../images/math-macro-add-optional-param.png
31904 The first non-optional argument can be transformed to an optional one with
31906 \begin_inset Graphics
31907 filename ../images/math-macro-make-optional.png
31913 In the second blue box the appearance of the macro in LyX can be defined.
31914 Normally you want to see it as it is defined, so the box is kept empty.
31915 But when you have created a macro that needs lot of space on the screen,
31916 you can insert in the box for example
31917 \begin_inset Newline newline
31947 \begin_inset Newline newline
31952 For the macro only the arguments with the macro name in front of them will
31953 then be displayed in LyX, leading to a better overview.
31954 The formula appears in the output as defined in the first box.
31955 \begin_inset Newline newline
31958 The appearance of macros in formulas can furthermore be changed for single
31959 macros by setting the cursor in the macro and using the menu
31961 View\SpecialChar \menuseparator
31963 \begin_inset space ~
31967 \begin_inset space ~
31975 \begin_layout Standard
31976 To use a macro, the macro name is inserted as command to a formula, in our
31984 Our macro looks in LyX like this:
31985 \begin_inset Newline newline
31989 \begin_inset space \hspace*{\fill}
31993 \begin_inset Graphics
31994 filename clipart/macrouse.png
31999 \begin_inset space \hspace*{\fill}
32003 \begin_inset Newline newline
32006 Here is our macro example with the arguments
32007 \begin_inset Formula $x$
32011 \begin_inset Formula $\ln(x)$
32015 \begin_inset Formula $B$
32021 \begin_layout Standard
32022 \begin_inset Formula
32032 \begin_layout Standard
32033 LyX offers in the menu
32035 Tools\SpecialChar \menuseparator
32036 Preferences\SpecialChar \menuseparator
32037 Editing\SpecialChar \menuseparator
32040 different styles to edit macros.
32041 To find the style that suits you the most, choose a style and set the cursor
32042 in a macro formula to see the difference.
32045 \begin_layout Standard
32046 A math macro is transformed internally to a
32052 command when exporting the document.
32059 command is not placed in the LaTeX-preamble, therefore macros can only
32060 be used in formulas that are in the document below the macro definition
32064 \begin_layout Standard
32065 Math macros can also be directly created from a
32072 When writing for example the command
32075 \begin_inset Newline newline
32084 xleftarrow[#2]{#1}}
32085 \begin_inset Newline newline
32090 in LyX as normal text, highlighting it completely and using then the shortcut
32095 , the command will be transformed to a math macro.
32096 Using this method you need to be careful that the
32102 command is typed correctly, otherwise you get a faulty macro leading to
32106 \begin_layout Standard
32107 Math macros currently have the problem that further formulas in macro definition
32108 s are handled wrongly.
32109 Therefore the example
32116 \begin_inset CommandInset ref
32118 reference "sub:The-Command-newcommand"
32122 cannot be created as macro.
32125 \begin_layout Standard
32126 When the cursor is in a macro definition box, you will see the macro toolbar
32130 \begin_layout Standard
32131 \begin_inset VSpace defskip
32137 \begin_layout Standard
32138 \begin_inset Graphics
32139 filename clipart/MacroToolbar.png
32144 \begin_inset Index idx
32147 \begin_layout Plain Layout
32156 \begin_layout Standard
32157 \begin_inset VSpace defskip
32163 \begin_layout Standard
32164 The macro toolbar contains from left to right the following buttons:
32167 \begin_layout Standard
32168 \begin_inset VSpace defskip
32174 \begin_layout Standard
32175 \begin_inset Tabular
32176 <lyxtabular version="3" rows="9" columns="2">
32177 <features rotate="0" islongtable="true" longtabularalignment="center">
32178 <column alignment="left" valignment="top">
32179 <column alignment="left" valignment="top" width="85col%">
32180 <row interlinespace="2.5mm">
32181 <cell alignment="center" valignment="top" usebox="none">
32184 \begin_layout Plain Layout
32185 \begin_inset Graphics
32186 filename ../images/math-macro-remove-param.png
32187 rotateOrigin center
32196 <cell alignment="center" valignment="top" usebox="none">
32199 \begin_layout Plain Layout
32202 Edit\SpecialChar \menuseparator
32203 Math\SpecialChar \menuseparator
32205 \begin_inset space ~
32208 Definition\SpecialChar \menuseparator
32209 Remove Last Argument
32215 <row interlinespace="2.5mm">
32216 <cell alignment="center" valignment="top" usebox="none">
32219 \begin_layout Plain Layout
32220 \begin_inset Graphics
32221 filename ../images/math-macro-add-param.png
32222 rotateOrigin center
32231 <cell alignment="center" valignment="top" usebox="none">
32234 \begin_layout Plain Layout
32237 Edit\SpecialChar \menuseparator
32238 Math\SpecialChar \menuseparator
32240 \begin_inset space ~
32243 Definition\SpecialChar \menuseparator
32250 <row interlinespace="2.5mm">
32251 <cell alignment="center" valignment="top" usebox="none">
32254 \begin_layout Plain Layout
32255 \begin_inset Graphics
32256 filename ../images/math-macro-make-optional.png
32257 rotateOrigin center
32266 <cell alignment="center" valignment="top" usebox="none">
32269 \begin_layout Plain Layout
32272 Edit\SpecialChar \menuseparator
32273 Math\SpecialChar \menuseparator
32275 \begin_inset space ~
32278 Definition\SpecialChar \menuseparator
32279 Make First Non-Optional into
32280 \begin_inset Newline newline
32284 \begin_inset Phantom HPhantom
32287 \begin_layout Plain Layout
32290 Edit\SpecialChar \menuseparator
32291 Math\SpecialChar \menuseparator
32293 \begin_inset space ~
32296 Definition\SpecialChar \menuseparator
32308 <row interlinespace="2.5mm">
32309 <cell alignment="center" valignment="top" usebox="none">
32312 \begin_layout Plain Layout
32313 \begin_inset Graphics
32314 filename ../images/math-macro-make-nonoptional.png
32315 rotateOrigin center
32324 <cell alignment="center" valignment="top" usebox="none">
32327 \begin_layout Plain Layout
32330 Edit\SpecialChar \menuseparator
32331 Math\SpecialChar \menuseparator
32333 \begin_inset space ~
32336 Definition\SpecialChar \menuseparator
32337 Make Last Optional into
32338 \begin_inset Newline newline
32342 \begin_inset Phantom HPhantom
32345 \begin_layout Plain Layout
32348 Edit\SpecialChar \menuseparator
32349 Math\SpecialChar \menuseparator
32351 \begin_inset space ~
32354 Definition\SpecialChar \menuseparator
32360 Non-Optional Argument
32366 <row interlinespace="2.5mm">
32367 <cell alignment="center" valignment="top" usebox="none">
32370 \begin_layout Plain Layout
32371 \begin_inset Graphics
32372 filename ../images/math-macro-remove-optional-param.png
32373 rotateOrigin center
32382 <cell alignment="center" valignment="top" usebox="none">
32385 \begin_layout Plain Layout
32388 Edit\SpecialChar \menuseparator
32389 Math\SpecialChar \menuseparator
32391 \begin_inset space ~
32394 Definition\SpecialChar \menuseparator
32395 Remove Optional Argument
32401 <row interlinespace="2.5mm">
32402 <cell alignment="center" valignment="top" usebox="none">
32405 \begin_layout Plain Layout
32406 \begin_inset Graphics
32407 filename ../images/math-macro-add-optional-param.png
32408 rotateOrigin center
32417 <cell alignment="center" valignment="top" usebox="none">
32420 \begin_layout Plain Layout
32423 Edit\SpecialChar \menuseparator
32424 Math\SpecialChar \menuseparator
32426 \begin_inset space ~
32429 Definition\SpecialChar \menuseparator
32430 Insert Optional Argument
32436 <row interlinespace="2.5mm">
32437 <cell alignment="center" valignment="top" usebox="none">
32440 \begin_layout Plain Layout
32441 \begin_inset Graphics
32442 filename ../images/math-macro-remove-greedy-param.png
32443 rotateOrigin center
32452 <cell alignment="center" valignment="top" usebox="none">
32455 \begin_layout Plain Layout
32458 Edit\SpecialChar \menuseparator
32459 Math\SpecialChar \menuseparator
32461 \begin_inset space ~
32464 Definition\SpecialChar \menuseparator
32465 Remove Last Argument
32466 \begin_inset Newline newline
32470 \begin_inset Phantom HPhantom
32473 \begin_layout Plain Layout
32476 Edit\SpecialChar \menuseparator
32477 Math\SpecialChar \menuseparator
32479 \begin_inset space ~
32482 Definition\SpecialChar \menuseparator
32488 Spitting Out To The Right
32494 <row interlinespace="2.5mm">
32495 <cell alignment="center" valignment="top" usebox="none">
32498 \begin_layout Plain Layout
32499 \begin_inset Graphics
32500 filename ../images/math-macro-append-greedy-param.png
32501 rotateOrigin center
32510 <cell alignment="center" valignment="top" usebox="none">
32513 \begin_layout Plain Layout
32516 Edit\SpecialChar \menuseparator
32517 Math\SpecialChar \menuseparator
32519 \begin_inset space ~
32522 Definition\SpecialChar \menuseparator
32524 \begin_inset Newline newline
32528 \begin_inset Phantom HPhantom
32531 \begin_layout Plain Layout
32534 Edit\SpecialChar \menuseparator
32535 Math\SpecialChar \menuseparator
32537 \begin_inset space ~
32540 Definition\SpecialChar \menuseparator
32546 Eating From The Right
32552 <row interlinespace="2.5mm">
32553 <cell alignment="center" valignment="top" usebox="none">
32556 \begin_layout Plain Layout
32557 \begin_inset Graphics
32558 filename ../images/math-macro-add-greedy-optional-param.png
32559 rotateOrigin center
32568 <cell alignment="center" valignment="top" usebox="none">
32571 \begin_layout Plain Layout
32574 Edit\SpecialChar \menuseparator
32575 Math\SpecialChar \menuseparator
32577 \begin_inset space ~
32580 Definition\SpecialChar \menuseparator
32581 Append Optional Argument
32582 \begin_inset Newline newline
32586 \begin_inset Phantom HPhantom
32589 \begin_layout Plain Layout
32592 Edit\SpecialChar \menuseparator
32593 Math\SpecialChar \menuseparator
32595 \begin_inset space ~
32598 Definition\SpecialChar \menuseparator
32604 Eating From The Right
32617 \begin_layout Section
32618 Computer Algebra Systems
32621 \begin_layout Standard
32622 LyX offers the exchange between mathematical expressions written in LyX's
32623 math editor and external applications or user defined scripts.
32624 Currently supported applications are
32641 Note that the set of supported mathematical constructs is limited only
32642 to very simple cases.
32645 \begin_layout Subsection
32649 \begin_layout Standard
32650 Write some expression in a formula, go to the
32652 Edit\SpecialChar \menuseparator
32653 Math\SpecialChar \menuseparator
32654 Use Computer Algebra System
32656 menu and choose the application you have installed on the computer.
32657 After that the result of computation should show on the right side of the
32658 expression together with the
32659 \begin_inset Quotes eld
32663 \begin_inset Quotes erd
32669 \begin_layout Standard
32670 Here are few simple examples (with results from
32674 ) to show what kind of computations can be performed:
32677 \begin_layout Itemize
32678 \begin_inset Formula $\frac{37}{3}*2-\sum_{i=1}^{3}i^{i}=-\frac{22}{3}$
32684 \begin_layout Itemize
32685 \begin_inset Formula $\frac{37.0}{3}=12.33333333333333$
32691 \begin_layout Itemize
32692 \begin_inset Formula $\int_{1}^{2}\sin(x)dx=\cos1-\cos2$
32698 \begin_layout Itemize
32699 \begin_inset Formula $\det\left[\begin{array}{ccc}
32703 \end{array}\right]=-56$
32709 \begin_layout Itemize
32710 \begin_inset Formula $\lim_{x\rightarrow0}\left(\frac{\sin(x)}{x}\right)=1$
32716 \begin_layout Subsection
32720 \begin_layout Standard
32721 Currently there is no keyboard shortcut for calling the algebra applications.
32722 One can easily bind a shortcut to the
32726 LyX function (see the
32734 \begin_inset space \thinspace{}
32738 \begin_inset space \space{}
32745 key inside the math editor.
32750 one would use this shortcut definition command:
32753 \begin_layout Standard
32756 command-alternatives break-paragraph;math-extern maxima
32759 \begin_layout Section
32761 \begin_inset Index idx
32764 \begin_layout Plain Layout
32773 \begin_layout Subsection
32775 \begin_inset Index idx
32778 \begin_layout Plain Layout
32787 \begin_layout Standard
32788 Negative numbers often look ugly in formulas because the minus sign before
32789 the number is set with the same length as the minus operator sign.
32790 When writing the negative number in normal text, the minus sign appears
32794 \begin_layout Standard
32795 Thus, the problem disappears when converting the minus sign to mathematical
32799 \begin_layout Standard
32800 An example to visualize the problem:
32803 \begin_layout Standard
32805 \begin_inset Tabular
32806 <lyxtabular version="3" rows="3" columns="2">
32807 <features rotate="0" tabularvalignment="middle">
32808 <column alignment="right" valignment="top">
32809 <column alignment="left" valignment="top">
32811 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
32814 \begin_layout Plain Layout
32820 <cell alignment="center" valignment="top" topline="true" rightline="true" usebox="none">
32823 \begin_layout Plain Layout
32831 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
32834 \begin_layout Plain Layout
32840 <cell alignment="center" valignment="top" topline="true" bottomline="true" rightline="true" usebox="none">
32843 \begin_layout Plain Layout
32844 \begin_inset Formula $x=-2$
32854 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
32857 \begin_layout Plain Layout
32863 <cell alignment="center" valignment="top" topline="true" bottomline="true" rightline="true" usebox="none">
32866 \begin_layout Plain Layout
32867 \begin_inset Formula $x=\textrm{-}2$
32883 \begin_layout Subsection
32884 Comma as decimal Separator
32885 \begin_inset Index idx
32888 \begin_layout Plain Layout
32897 \begin_layout Standard
32898 In LaTeX a comma inside a formula is used, according to the English convention,
32899 as number group separator.
32900 So there will be space added behind all commas in formulas.
32903 \begin_layout Standard
32904 To avoid this, the comma is highlighted and changed to mathematical text
32914 \begin_layout Standard
32915 To use all formula commas in the document as decimal separator, the file
32924 \begin_layout Plain Layout
32929 is part of the LaTeX-package
32934 \begin_inset Index idx
32937 \begin_layout Plain Layout
32942 \begin_layout Plain Layout
32962 \begin_inset Index idx
32965 \begin_layout Plain Layout
32971 is loaded with the LaTeX-preamble line
32974 \begin_layout Standard
32982 \begin_layout Subsection
32984 \begin_inset CommandInset label
32986 name "sub:Physical-Vectors"
32991 \begin_inset Index idx
32994 \begin_layout Plain Layout
33003 \begin_layout Standard
33004 Predefined vectors are offered by the LaTeX-package
33009 \begin_inset Index idx
33012 \begin_layout Plain Layout
33018 that is loaded with the LaTeX-preamble line
33021 \begin_layout Standard
33029 \begin_layout Standard
33033 \begin_layout Plain Layout
33043 \begin_inset Note Note
33046 \begin_layout Plain Layout
33047 The following table will only be displayed when the LaTeX-package
33059 \begin_layout Standard
33060 The following commands are defined:
33063 \begin_layout Standard
33065 \begin_inset Tabular
33066 <lyxtabular version="3" rows="4" columns="2">
33067 <features rotate="0" tabularvalignment="middle">
33068 <column alignment="center" valignment="top">
33069 <column alignment="center" valignment="top">
33071 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
33074 \begin_layout Plain Layout
33080 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
33083 \begin_layout Plain Layout
33091 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
33094 \begin_layout Plain Layout
33104 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
33107 \begin_layout Plain Layout
33108 \begin_inset Formula $\Bra{\psi}$
33118 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
33121 \begin_layout Plain Layout
33131 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
33134 \begin_layout Plain Layout
33135 \begin_inset Formula $\Ket{\psi}$
33145 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
33148 \begin_layout Plain Layout
33160 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
33163 \begin_layout Plain Layout
33164 \begin_inset Formula $\Braket{\psi|\phi}$
33180 \begin_layout Standard
33187 assures that all vertical bars are set in the size of the surrounding brackets:
33188 \begin_inset Formula
33190 \Braket{\phi|J=\frac{3}{2}\,,\, M_{J}}
33199 \begin_layout Plain Layout
33209 \begin_inset Note Note
33212 \begin_layout Plain Layout
33213 The following will be displayed when the LaTeX-package
33225 \begin_layout Standard
33226 You need to install the LaTeX-package
33230 to see the rest of this subsection in the output.
33233 \begin_layout Standard
33237 \begin_layout Plain Layout
33249 \begin_layout Standard
33256 can also be achieved using the command
33262 , that is described in
33263 \begin_inset CommandInset ref
33265 reference "sub:Automatic-Bracket-Size"
33272 \begin_layout Subsection
33273 Self-defined Fractions
33274 \begin_inset CommandInset label
33276 name "sub:Self-defined-Fractions"
33281 \begin_inset Index idx
33284 \begin_layout Plain Layout
33285 Fractions ! self-defined
33293 \begin_layout Standard
33294 To define custom commands for fractions, the command
33301 \begin_inset Index idx
33304 \begin_layout Plain Layout
33311 \begin_layout Plain Layout
33325 is used in the following scheme:
33328 \begin_layout Standard
33341 bracket}{fraction bar thickness}{style}
33342 \begin_inset Newline newline
33346 \begin_inset Phantom HPhantom
33349 \begin_layout Plain Layout
33359 {numerator}{denominator}
33362 \begin_layout Standard
33363 The style is a number in the range of 0
33364 \begin_inset space \thinspace{}
33368 \begin_inset space \thinspace{}
33374 \begin_layout Standard
33376 \begin_inset Tabular
33377 <lyxtabular version="3" rows="5" columns="2">
33378 <features rotate="0" tabularvalignment="middle">
33379 <column alignment="center" valignment="top">
33380 <column alignment="center" valignment="top">
33382 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
33385 \begin_layout Plain Layout
33391 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
33394 \begin_layout Plain Layout
33402 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
33405 \begin_layout Plain Layout
33411 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
33414 \begin_layout Plain Layout
33415 display style formula
33422 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
33425 \begin_layout Plain Layout
33431 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
33434 \begin_layout Plain Layout
33442 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
33445 \begin_layout Plain Layout
33451 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
33454 \begin_layout Plain Layout
33462 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
33465 \begin_layout Plain Layout
33471 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
33474 \begin_layout Plain Layout
33488 \begin_layout Standard
33489 When no style is given, the size is adjusted to the surrounding environment
33490 like for the command
33499 \begin_layout Standard
33500 When no fraction bar thickness is given, the predefined value of 0.4
33501 \begin_inset space \thinspace{}
33507 \begin_layout Standard
33508 \begin_inset VSpace medskip
33511 For example, the commands
33524 \begin_inset CommandInset ref
33526 reference "sub:Fractions"
33530 are defined with the commands
33533 \begin_layout Standard
33542 genfrac{}{}{}{0}{#1}{#2}}
33545 \begin_layout Standard
33549 \begin_layout Standard
33558 genfrac{(}{)}{0pt}{1}{#1}{#2}}
33561 \begin_layout Standard
33562 \begin_inset VSpace medskip
33565 To define a fraction where the fraction bar thickness can be given as optional
33566 argument, the following line is inserted to the LaTeX-preamble:
33569 \begin_layout Standard
33578 genfrac{}{}{#1}{}{#2}{#3}}
33581 \begin_layout Standard
33583 \begin_inset Formula
33585 \text{Command} & & \mathrm{\backslash fracS[1mm]\backslash\{A\to\backslash\{B} & & \mathrm{\backslash fracS[5mm]\backslash\{A\to\backslash\{B}\\
33586 \text{Result} & & \fracS[1mm]{A}{B} & & \fracS[5mm]{A}{B}
33591 As one can see, the distance of the numerator and the denominator to the
33592 fraction bar is round about three times the bar thickness.
33595 \begin_layout Subsection
33597 \begin_inset Index idx
33600 \begin_layout Plain Layout
33609 \begin_layout Standard
33610 There are four ways to cancel formulas or parts of formulas:
33613 \begin_layout Standard
33617 \begin_layout Plain Layout
33627 \begin_inset Note Note
33630 \begin_layout Plain Layout
33631 The following table will only be displayed when the LaTeX-package
33643 \begin_layout Standard
33645 \begin_inset Tabular
33646 <lyxtabular version="3" rows="5" columns="2">
33647 <features rotate="0" tabularvalignment="middle">
33648 <column alignment="center" valignment="top">
33649 <column alignment="center" valignment="top">
33651 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
33654 \begin_layout Plain Layout
33660 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
33663 \begin_layout Plain Layout
33665 \begin_inset Note Note
33668 \begin_layout Plain Layout
33675 are used here as spacer.
33687 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
33690 \begin_layout Plain Layout
33694 \begin_inset space \textvisiblespace{}
33700 \begin_inset space \textvisiblespace{}
33708 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
33711 \begin_layout Plain Layout
33712 \begin_inset Formula $\raisebox{4.5mm}{}\cancel{\int A=B}\raisebox{-2.5mm}{}$
33722 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
33725 \begin_layout Plain Layout
33729 \begin_inset space \textvisiblespace{}
33735 \begin_inset space \textvisiblespace{}
33743 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
33746 \begin_layout Plain Layout
33747 \begin_inset Formula $\raisebox{4.5mm}{}\bcancel{\int A=B}\raisebox{-2.5mm}{}$
33757 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
33760 \begin_layout Plain Layout
33764 \begin_inset space \textvisiblespace{}
33770 \begin_inset space \textvisiblespace{}
33778 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
33781 \begin_layout Plain Layout
33782 \begin_inset Formula $\raisebox{4.5mm}{}\xcancel{\int A=B}\raisebox{-2.5mm}{}$
33792 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
33795 \begin_layout Plain Layout
33799 \begin_inset space \textvisiblespace{}
33805 \begin_inset space \textvisiblespace{}
33809 \begin_inset Formula $\to$
33817 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
33820 \begin_layout Plain Layout
33821 \begin_inset Formula $\raisebox{7mm}{}\cancelto{1}{\int A=B}\raisebox{-2.5mm}{}\hspace{3mm}$
33837 \begin_layout Standard
33844 is especially suitable to visualize the reduction of fractions within formulas:
33845 \begin_inset Formula
33847 \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}}}
33855 \begin_layout Standard
33856 To change the size of
33863 \begin_inset Quotes eld
33867 \begin_inset Quotes erd
33870 value one can add the LaTeX-preamble line
33873 \begin_layout Standard
33878 PassOptionsToPackage{option}{cancel}
33881 \begin_layout Standard
33890 which leads to the same size as for the canceled value, or
33894 which makes is it a bit smaller than normal.
33897 \begin_layout Standard
33898 To color the cancellation bar one adds this command as TeX code:
33901 \begin_layout Standard
33913 \begin_layout Standard
33918 can be replaced by a color of your choice.
33921 \begin_layout Standard
33925 \begin_layout Plain Layout
33941 \begin_layout Standard
33942 \begin_inset Formula
33944 \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}}}
33952 \begin_layout Standard
33956 \begin_layout Plain Layout
33970 \begin_inset Note Note
33973 \begin_layout Plain Layout
33982 \begin_layout Standard
33983 For further customizations, see the documentation of the package
33988 \begin_inset CommandInset citation
33995 \begin_inset Index idx
33998 \begin_layout Plain Layout
34007 \begin_layout Standard
34011 \begin_layout Plain Layout
34021 \begin_inset Note Note
34024 \begin_layout Plain Layout
34025 The following will be displayed when the LaTeX-package
34037 \begin_layout Standard
34038 You need to install the LaTeX-package
34042 to see the rest of this subsection in the output.
34045 \begin_layout Standard
34049 \begin_layout Plain Layout
34061 \begin_layout Standard
34062 \begin_inset Newpage newpage
34068 \begin_layout Subsection
34069 Formulas in Section Headings
34070 \begin_inset CommandInset label
34072 name "sub:Formulas-in-Section"
34077 \begin_inset Index idx
34080 \begin_layout Plain Layout
34081 Formula ! in section headings
34089 \begin_layout Standard
34090 When formulas are used in section headings, the following has to be taken
34094 \begin_layout Standard
34095 \begin_inset Note Greyedout
34098 \begin_layout Plain Layout
34104 \begin_inset Index idx
34107 \begin_layout Plain Layout
34108 Packages ! hyperref
34113 support is enabled in the document settings dialog under
34116 \begin_inset space ~
34121 , PDF-bookmarks are created for every section heading in the table of contents.
34122 If a section heading contains formulas, they are incorrectly displayed
34123 in the bookmark text, because formulas in bookmarks infringe the PDF convention
34132 \begin_layout Standard
34133 Both problems can be solved by inserting at the end of the section heading
34134 a short title with the menu
34136 Insert\SpecialChar \menuseparator
34138 \begin_inset space ~
34144 Short titles are used as alternative for multiline section headings to
34145 keep the table of contents clearly arranged.
34146 Only the short title appears in the table of contents and therefore also
34147 in the PDF-bookmark.
34150 \begin_layout Standard
34151 When formulas should be used in the table of contents but
34155 is used, one can use the following command in TeX-mode:
34158 \begin_layout Standard
34163 texorpdfstring{part}{alternative}
34164 \begin_inset Index idx
34167 \begin_layout Plain Layout
34178 \begin_layout Standard
34179 Part is the part of the heading that shouldn't appear in the PDF-bookmark.
34180 This can be characters, formulas, footnotes, but also cross-references.
34181 The alternative is used instead of the part for the bookmark.
34184 \begin_layout Standard
34185 Here are two example headings:
34186 \begin_inset VSpace -3mm
34193 \begin_layout Plain Layout
34205 \begin_layout Subsubsection
34206 Heading without formula in table of contents
34207 \begin_inset Formula $\sqrt{-1}=\mathrm{i}$
34211 \begin_inset Argument 1
34214 \begin_layout Plain Layout
34215 Heading without formula in table of contents
34223 \begin_layout Subsubsection
34224 Heading with formula in table of contents
34228 \begin_layout Plain Layout
34238 \begin_inset Formula $\sqrt{-1}=\mathrm{i}$
34245 \begin_layout Plain Layout
34255 \begin_layout Standard
34259 \begin_layout Plain Layout
34268 In the first heading a short title was used, in the second one
34277 \begin_layout Standard
34278 To get the same formatting as for the other headings, the complete heading
34287 \begin_layout Plain Layout
34289 \begin_inset CommandInset ref
34291 reference "sub:Bold-Formulas"
34303 \begin_layout Subsection
34304 Formulas in multi-column Text
34305 \begin_inset Index idx
34308 \begin_layout Plain Layout
34309 Formula ! in multi-column text
34317 \begin_layout Standard
34318 Formulas in multi-column text are often too wide to fit into a column and
34319 thus need to be set over the whole page width.
34320 This is done by using the LaTeX-package
34328 \begin_layout Plain Layout
34333 is part of every LaTeX standard installation.
34339 \begin_inset Index idx
34342 \begin_layout Plain Layout
34343 Packages ! multicol
34348 , that is loaded with the LaTeX-preamble line
34351 \begin_layout Standard
34356 usepackage{multicol}
34359 \begin_layout Standard
34360 \begin_inset Note Greyedout
34363 \begin_layout Plain Layout
34364 Note that in this case the setting
34367 \begin_inset space ~
34374 Document\SpecialChar \menuseparator
34380 \begin_inset space ~
34400 \begin_layout Standard
34401 Before the multi-column text the command
34404 \begin_layout Standard
34409 begin{multicols}{column number}
34412 \begin_layout Standard
34413 is written in TeX-mode.
34414 The column number is a number in the range of 2
34415 \begin_inset space \thinspace{}
34419 \begin_inset space \thinspace{}
34423 Before the formula the multi-column text is ended by inserting the command
34426 \begin_layout Standard
34434 \begin_layout Standard
34438 \begin_layout Standard
34439 Due to the command some space is automatically added before the formula.
34441 \begin_inset space \thinspace{}
34444 mm vertical space is inserted before the formula.
34445 When the formula style
34451 \begin_layout Plain Layout
34453 \begin_inset CommandInset ref
34455 reference "sec:Formula-Styles"
34467 \begin_inset space \thinspace{}
34470 mm space is inserted instead.
34473 \begin_layout Standard
34474 As example a multi-column text with a displayed formula:
34477 \begin_layout Standard
34483 \begin_layout Plain Layout
34487 begin{multicols}{2}
34492 Das Spektrum wird fouriertransformiert.
34493 Die Fouriertransformation wird verwendet, um die überlagerten Signale (Netzwerk
34494 , Lösungsmittel) zu trennen.
34495 Nachdem wir die Phasenverschiebung bestimmen konnten, interessiert uns
34496 nun das Aussehen des Ausgangssignals.
34497 Im Experiment haben wir es mit sehr vielen Teilchen zu tun, so dass man
34498 über alle Phasen integrieren muss.
34500 \begin_inset Formula $S$
34503 unser normiertes Ausgangssignal und
34504 \begin_inset Formula $P$
34507 die Phasenverteilungsfunktion, so ergibt sich die Beziehung
34511 \begin_layout Plain Layout
34521 \begin_inset VSpace -6mm
34525 \begin_inset Formula
34527 S(t)=S_{0}(t)\int_{-\infty}^{\infty}P(\phi,t)\mathrm{e}^{\mathrm{i}\phi}\,\mathrm{d}\phi
34536 \begin_layout Plain Layout
34540 begin{multicols}{2}
34546 \begin_inset Formula $S_{0}$
34549 das Signal ohne Gradient ist und die Normierungsbedingung
34550 \begin_inset Formula $\int_{-\infty}^{\infty}P(\phi,t)\,\mathrm{d}\phi=1$
34554 Nun dürfen wir aber nicht den Relaxationsprozess außer Acht lassen.
34556 \begin_inset Formula $\nicefrac{\pi}{2}$
34560 \begin_inset space \thinspace{}
34563 -rf-Puls beginnt sich die Magnetisierung zu entfokussieren, wodurch sich
34564 das Signal zusätzlich abschwächt.
34565 Diese Abschwächung verläuft exponentiell in Abhängigkeit der so genannten
34567 \begin_inset Formula $T_{2}$
34573 \begin_layout Standard
34579 \begin_layout Plain Layout
34591 \begin_layout Subsection
34592 Formulas with Description of Variables
34593 \begin_inset Index idx
34596 \begin_layout Plain Layout
34597 Formula ! with description of variables
34605 \begin_layout Standard
34606 To describe variables within a formula, like in formula
34607 \begin_inset CommandInset ref
34609 reference "eq:within"
34618 \begin_inset Formula $n$
34622 \begin_inset space ~
34625 matrix is used with left aligned columns for the
34626 \begin_inset Formula $n$
34633 \begin_layout Plain Layout
34635 \begin_inset CommandInset ref
34637 reference "sec:Matrices"
34646 To set the description in a smaller size, before the matrix e.
34647 \begin_inset space \thinspace{}
34651 \begin_inset space \space{}
34664 \begin_layout Plain Layout
34666 \begin_inset CommandInset ref
34668 reference "sub:Font-Sizes"
34680 \begin_layout Standard
34681 When the formula style
34687 \begin_layout Plain Layout
34689 \begin_inset CommandInset ref
34691 reference "sec:Formula-Styles"
34712 \begin_layout Plain Layout
34719 only works in formulas with the style
34724 \begin_inset CommandInset ref
34726 reference "sub:Variable-Space"
34735 is inserted before and after the matrix to have the same separation of
34736 the matrix from the equation and the side margin.
34739 \begin_layout Standard
34740 When the formula style
34744 is used, the method described in
34745 \begin_inset CommandInset ref
34747 reference "sub:Flalign-Environment"
34751 is used to indent formulas.
34753 \begin_inset CommandInset ref
34755 reference "eq:within"
34759 consists of five columns where in the first two columns contain the equation,
34760 the third the matrix and the last one an empty TeX-brace.
34761 \begin_inset Formula
34763 \hspace{30pt}F_{A} & =\rho·V·g & \footnotesize\begin{array}{ll}
34764 \rho & \textrm{density}\\
34765 V & \textrm{volume}\\
34766 g & \textrm{gravitational acceleration}
34767 \end{array} & & {}\label{eq:within}
34775 \begin_layout Subsection
34776 Upright small Greek Letters
34777 \begin_inset CommandInset label
34779 name "sub:Upright-small-Greek"
34784 \begin_inset Index idx
34787 \begin_layout Plain Layout
34788 Greek letters ! upright
34796 \begin_layout Standard
34797 Most of the math fonts only provide italic small Greek letters.
34798 But for symbols of elementary particles like pions and neutrinos, upright
34799 Greek letters are needed.
34808 \begin_layout Plain Layout
34813 is part of the LaTeX-package
34818 \begin_inset Index idx
34821 \begin_layout Plain Layout
34826 \begin_layout Plain Layout
34846 \begin_inset Index idx
34849 \begin_layout Plain Layout
34855 that is loaded with the LaTeX-preamble line
34858 \begin_layout Standard
34863 usepackage{upgreek}
34866 \begin_layout Standard
34872 \begin_layout Plain Layout
34882 \begin_inset Note Note
34885 \begin_layout Plain Layout
34886 The following table will only be displayed when the LaTeX-package
34895 They are created when the command for a small Greek letter is started with
34901 For example the command
34908 \begin_inset Formula $\uptau$
34914 \begin_layout Standard
34915 With these commands reactions of elementary particles can be typeset:
34916 \begin_inset Formula
34918 \uppi^{+}\to\upmu^{+}+\upnu_{\upmu}
34926 \begin_layout Standard
34927 The upright letters are more bold and wider than the italic ones.
34928 They should therefore not be used for units like
34929 \begin_inset Quotes eld
34933 \begin_inset Quotes erd
34939 \begin_layout Standard
34943 \begin_layout Plain Layout
34953 \begin_inset Note Note
34956 \begin_layout Plain Layout
34957 The following will be displayed when the LaTeX-package
34969 \begin_layout Standard
34970 You need to install the LaTeX-package
34974 to see the rest of this subsection in the output.
34977 \begin_layout Standard
34981 \begin_layout Plain Layout
34993 \begin_layout Subsection
34994 Text Characters in Formulas
34995 \begin_inset CommandInset label
34997 name "sub:Text-Characters-in"
35002 \begin_inset Index idx
35005 \begin_layout Plain Layout
35014 \begin_layout Standard
35015 In some cases you might want to insert text characters directly into formulas.
35016 When for example the centered dot · is often used in formulas like
35017 \begin_inset Formula $\nu=5·10^{5}\,\mathrm{Hz}$
35020 , one would have to insert the command
35030 \begin_layout Plain Layout
35032 \begin_inset CommandInset ref
35034 reference "sub:Binary-Operators"
35043 all the time, because this character is defined in all encodings as text
35045 But the encoding can be changed by this LaTeX-preamble line:
35048 \begin_layout Standard
35053 Declare Inputtext{183}{
35063 f\SpecialChar \textcompwordmark{}
35067 \begin_layout Standard
35068 The character encoding (menu
35070 Document\SpecialChar \menuseparator
35071 Settings\SpecialChar \menuseparator
35074 ) specifies what character appears when a keyboard key is pressed.
35075 When the key for the character '·' is pressed, internally the command
35082 But this command is not available in a formula so that you would get LaTeX-erro
35084 With the changed encoding the right command is chosen automatically, depending
35085 on if the character was inserted into a formula or not.
35088 \begin_layout Standard
35089 The encoding of several characters is saved in definition files.
35090 For example the encoding
35094 is defined in the file
35098 which is in the installation folder of LaTeX.
35099 Encodings should only be changed via the LaTeX-preamble and not in the
35101 Otherwise documents could not be edited by other LyX users working on other
35105 \begin_layout Standard
35106 \begin_inset VSpace medskip
35109 Besides the centered dot, in this document the degree sign ° is defined
35110 with the following LaTeX-preamble line so that it can be directly inserted
35114 \begin_layout Standard
35119 DeclareInputtext{176}{
35129 f\SpecialChar \textcompwordmark{}
35133 \begin_layout Standard
35134 \begin_inset Newpage newpage
35140 \begin_layout Section
35143 \begin_inset Index idx
35146 \begin_layout Plain Layout
35155 \begin_layout Standard
35156 This section is a summary of the most important typographic rules, listed
35161 \begin_layout Plain Layout
35162 This collection was partly taken from the German semi-official dictionary
35164 \begin_inset Quotes eld
35168 \begin_inset Quotes erd
35172 \begin_inset CommandInset citation
35178 that lists some of the ISO rules.
35179 More rules are listed in
35180 \begin_inset CommandInset citation
35194 \begin_layout Itemize
35203 \begin_layout Plain Layout
35204 done with font styles, see
35205 \begin_inset CommandInset ref
35207 reference "sub:Font-Styles"
35216 , no matter if they appear in italic text: 30
35217 \begin_inset space \thinspace{}
35221 \begin_inset Newline newline
35224 Between the value and the unit is the smallest space, see
35225 \begin_inset CommandInset ref
35227 reference "sub:Predefined-Space"
35232 \begin_inset Newline newline
35235 This convention is automatically fulfilled when the command
35242 When it is entered to a formula, two boxes appear.
35243 In the first one the value is inserted, in the second one the unit, and
35245 \begin_inset Formula $\unit[30]{km/h}$
35249 \begin_inset space \thinspace{}
35259 is not a real LaTeX command but the command
35265 , therefore you cannot use it in TeX code.
35268 \begin_layout Itemize
35269 Percent and perthousand signs are set like physical units:
35270 \begin_inset Newline newline
35274 \begin_inset space \thinspace{}
35280 \begin_layout Itemize
35281 The degree sign follows directly on the value: 15°, but not when it is used
35283 \begin_inset space \thinspace{}
35289 \begin_layout Itemize
35290 In numbers with more than four digits the smallest space is inserted before
35291 every third digit to group them:
35301 \begin_inset space \thinspace{}
35305 \begin_inset space \thinspace{}
35311 \begin_layout Itemize
35312 For dimensions like 120×90×40
35313 \begin_inset space \thinspace{}
35316 cm the multiplication sign
35317 \begin_inset Quotes eld
35321 \begin_inset Quotes erd
35325 It is available either via the command
35333 Insert\SpecialChar \menuseparator
35334 Special Character\SpecialChar \menuseparator
35340 \begin_layout Itemize
35341 Functions with names consisting of several letters are set upright to avoid
35343 \begin_inset CommandInset ref
35345 reference "sub:Predefined-Functions"
35352 \begin_layout Itemize
35353 Indices consisting of several letters, are set upright:
35354 \begin_inset Formula $E_{\mathrm{kin}}$
35358 \begin_inset Newline newline
35361 Components of matrices are set italic:
35362 \begin_inset Formula $\hat{H}_{kl}$
35368 \begin_layout Itemize
35369 The differentiation/integration operator 'd', the Euler's number 'e' and
35370 the imaginary unit 'i' should be set upright, to avoid mixing them up with
35374 \begin_layout Itemize
35375 The character that denotes a
35379 transformation is inserted either by the command
35384 \begin_inset space \textvisiblespace{}
35391 Insert\SpecialChar \menuseparator
35392 Special Character\SpecialChar \menuseparator
35393 Symbols\SpecialChar \menuseparator
35395 \begin_inset space ~
35401 \begin_inset Formula $\mathscr{F}$
35407 \begin_layout Standard
35408 \begin_inset Newpage newpage
35414 \begin_layout Section
35416 \begin_inset Index idx
35419 \begin_layout Plain Layout
35428 \begin_layout Standard
35429 Some characters and symbols can be created with several commands.
35430 Here is a list of the synonym commands:
35433 \begin_layout Standard
35434 \begin_inset VSpace bigskip
35438 \begin_inset space \hfill{}
35442 \begin_inset Tabular
35443 <lyxtabular version="3" rows="12" columns="2">
35444 <features rotate="0" tabularvalignment="middle">
35445 <column alignment="center" valignment="top" width="0pt">
35446 <column alignment="center" valignment="top" width="0pt">
35448 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
35451 \begin_layout Plain Layout
35457 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
35460 \begin_layout Plain Layout
35462 \begin_inset Note Note
35465 \begin_layout Plain Layout
35472 is only used as spacer.
35484 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
35487 \begin_layout Plain Layout
35495 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
35498 \begin_layout Plain Layout
35502 \begin_layout Plain Layout
35515 \begin_layout Plain Layout
35529 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
35532 \begin_layout Plain Layout
35540 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
35543 \begin_layout Plain Layout
35553 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
35556 \begin_layout Plain Layout
35564 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
35567 \begin_layout Plain Layout
35577 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
35580 \begin_layout Plain Layout
35588 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
35591 \begin_layout Plain Layout
35599 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
35602 \begin_layout Plain Layout
35610 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
35613 \begin_layout Plain Layout
35621 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
35624 \begin_layout Plain Layout
35632 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
35635 \begin_layout Plain Layout
35645 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
35648 \begin_layout Plain Layout
35656 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
35659 \begin_layout Plain Layout
35669 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
35672 \begin_layout Plain Layout
35680 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
35683 \begin_layout Plain Layout
35693 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
35696 \begin_layout Plain Layout
35704 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
35707 \begin_layout Plain Layout
35717 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
35720 \begin_layout Plain Layout
35728 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
35731 \begin_layout Plain Layout
35739 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
35742 \begin_layout Plain Layout
35750 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
35753 \begin_layout Plain Layout
35765 \begin_inset space \hfill{}
35769 \begin_inset Tabular
35770 <lyxtabular version="3" rows="12" columns="2">
35771 <features rotate="0" tabularvalignment="middle">
35772 <column alignment="center" valignment="top" width="0pt">
35773 <column alignment="center" valignment="top" width="0pt">
35775 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
35778 \begin_layout Plain Layout
35784 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
35787 \begin_layout Plain Layout
35795 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
35798 \begin_layout Plain Layout
35806 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
35809 \begin_layout Plain Layout
35821 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
35824 \begin_layout Plain Layout
35832 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
35835 \begin_layout Plain Layout
35845 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
35848 \begin_layout Plain Layout
35856 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
35859 \begin_layout Plain Layout
35869 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
35872 \begin_layout Plain Layout
35880 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
35883 \begin_layout Plain Layout
35891 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
35894 \begin_layout Plain Layout
35902 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
35905 \begin_layout Plain Layout
35913 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
35916 \begin_layout Plain Layout
35924 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
35927 \begin_layout Plain Layout
35937 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
35940 \begin_layout Plain Layout
35948 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
35951 \begin_layout Plain Layout
35961 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
35964 \begin_layout Plain Layout
35972 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
35975 \begin_layout Plain Layout
35985 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
35988 \begin_layout Plain Layout
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36023 \begin_layout Plain Layout
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36036 \begin_layout Plain Layout
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36047 \begin_layout Plain Layout
36061 \begin_inset space \hfill{}
36067 \begin_layout Standard
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36076 LatexCommand bibitem
36088 The LaTeX Companion
36091 Addison Wesley, 2004
36094 \begin_layout Bibliography
36095 \begin_inset CommandInset bibitem
36096 LatexCommand bibitem
36102 \begin_inset CommandInset href
36105 target "ftp://ftp.dante.de/tex-archive/info/math/voss/mathmode/Mathmode.pdf"
36109 of LaTeX's math abilities
36112 \begin_layout Bibliography
36113 \begin_inset CommandInset bibitem
36114 LatexCommand bibitem
36120 \begin_inset CommandInset href
36123 target "http://mirrors.ctan.org/macros/latex/required/amslatex/math/amsldoc.pdf"
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36143 \begin_layout Bibliography
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36145 LatexCommand bibitem
36151 \begin_inset CommandInset href
36154 target "ftp://ftp.dante.de/tex-archive/info/symbols/comprehensive/symbols-a4.pdf"
36158 of all symbols available with LaTeX-packages
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36163 LatexCommand bibitem
36169 \begin_inset CommandInset href
36171 name "Documentation"
36172 target "http://mirrors.ctan.org/macros/latex/contrib/cancel/cancel.pdf"
36176 of the LaTeX-package
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36195 LatexCommand bibitem
36201 \begin_inset CommandInset href
36203 name "Documentation"
36204 target "http://www.tug.org/applications/hyperref/ftp/doc/manual.pdf"
36208 of the LaTeX-package
36213 \begin_inset Index idx
36216 \begin_layout Plain Layout
36217 Packages ! hyperref
36225 \begin_layout Bibliography
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36227 LatexCommand bibitem
36233 \begin_inset CommandInset href
36235 name "Documentation"
36236 target "http://www.ctan.org/tex-archive/macros/latex/contrib/mhchem/mhchem.pdf"
36240 of the LaTeX-package
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36248 \begin_layout Plain Layout
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36258 \begin_inset CommandInset bibitem
36259 LatexCommand bibitem
36265 \begin_inset CommandInset href
36268 target "http://www.tug.org/TUGboat/Articles/tb22-4/tb72perlS.pdf"
36279 \begin_inset CommandInset ref
36281 reference "sub:Operator-Limits"
36286 \begin_inset Index idx
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36302 LatexCommand bibitem
36313 Auflage, Duden 2001
36316 \begin_layout Bibliography
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36318 LatexCommand bibitem
36324 \begin_inset CommandInset href
36327 target "http://physics.nist.gov/Document/checklist.pdf"
36331 for reviewing manuscripts
36334 \begin_layout Standard
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36336 LatexCommand printindex