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}
66 \usepackage[samesize]{cancel}
68 % enables calculation of values
71 % for multiple columns used in sec. 24.7
77 % for the Fourier transformation symbol
80 % define a color, used in sec.9.3
81 \definecolor{darkgreen}{cmyk}{0.5, 0, 1, 0.5}
83 % declare operators (see sec. 10.4 and sec. 15.2)
84 \DeclareMathOperator*{\Lozenge}{\blacklozenge}
85 \DeclareMathOperator{\sgn}{sgn}
87 % example definitions for sec. 20.1
88 \newcommand{\gr}{\Longrightarrow}
89 \newcommand{\us}[1]{\underline{#1}}
90 \newcommand{\fb}[3]{\framebox#1#2{$#3$}}
91 \newcommand{\cb}[3][white]{\fcolorbox{#2}{#1}{$#3$}}
92 \newcommand{\fracS}[3][]{\genfrac{}{}{#1}{}{#2}{#3}}
94 % example macro from sec. 19.4
95 %\def\tagform@#1{\maketag@@@{|#1|}}
97 % macro from sec. 10.2
98 \def\clap#1{\hbox to 0pt{\hss #1\hss}}
99 \def\mathclap {\mathpalette \mathclapinternal}
100 \def\mathclapinternal #1#2{\clap{$\mathsurround =0pt #1{#2}$}}
103 % ------------------------------------
104 % used to check for needed LaTeX packages
107 % check for package eurosym
108 % used for the Euro symbol
110 \IfFileExists{eurosym.sty}
111 {\usepackage[gennarrow]{eurosym}
112 \setboolean{eurosym}{true}}
113 {\setboolean{eurosym}{false}}
115 % check for package braket
116 % used for physical vectors
118 \IfFileExists{braket.sty}
120 \setboolean{braket}{true}}
121 {\setboolean{braket}{false}}
123 % check for package cancel
125 \IfFileExists{cancel.sty}
127 \setboolean{cancel}{true}}
128 {\setboolean{cancel}{false}}
130 % check for package upgreek
132 \IfFileExists{upgreek.sty}
133 {\usepackage{upgreek}
134 \setboolean{upgreek}{true}}
135 {\setboolean{upgreek}{false}}
137 \options bibliography=totoc,index=totoc,BCOR7.5mm,titlepage,captions=tableheading
138 \use_default_options false
139 \maintain_unincluded_children false
141 \language_package default
146 \font_typewriter default
148 \font_default_family default
149 \use_non_tex_fonts false
155 \default_output_format default
157 \bibtex_command default
158 \index_command default
162 \pdf_title "LyX's Math Manual"
163 \pdf_author "LyX Team, Uwe Stöhr"
164 \pdf_subject "LyX-documentation about math"
165 \pdf_keywords "LyX, Mathed"
167 \pdf_bookmarksnumbered true
168 \pdf_bookmarksopen true
169 \pdf_bookmarksopenlevel 1
170 \pdf_breaklinks false
174 \pdf_pdfusetitle false
175 \pdf_quoted_options "linkcolor=black, citecolor=black, urlcolor=blue, filecolor=blue, pdfpagelayout=OneColumn, pdfnewwindow=true, pdfstartview=XYZ, plainpages=false"
178 \use_package amsmath 2
179 \use_package amssymb 2
180 \use_package cancel 0
182 \use_package mathdots 1
183 \use_package mathtools 0
184 \use_package mhchem 1
185 \use_package stackrel 0
186 \use_package stmaryrd 0
187 \use_package undertilde 0
189 \cite_engine_type default
193 \paperorientation portrait
197 \notefontcolor #0000ff
204 \paragraph_separation skip
206 \quotes_language english
209 \paperpagestyle plain
213 \tracking_changes false
214 \output_changes false
217 \html_be_strict false
223 LyX's detailed Math manual
231 \begin_layout Plain Layout
233 If you have comments or error corrections, please send them to the LyX Documenta
237 \begin_inset CommandInset href
239 name "lyx-docs@lists.lyx.org"
240 target "lyx-docs@lists.lyx.org?subject=LyX's Math manual"
251 \begin_inset Note Note
254 \begin_layout Plain Layout
261 \begin_inset Newline newline
265 \begin_inset Newline newline
273 \begin_layout Standard
274 \begin_inset CommandInset toc
275 LatexCommand tableofcontents
282 \begin_layout Standard
283 \begin_inset Note Note
286 \begin_layout Plain Layout
287 To export this document to PDF, PS or DVI the LaTeX-packages
289 braket, cancel, eurosym, mathdots, mhchem
296 If they are not installed the document can be exported anyway but the sections
297 where the packages are required will not appear in the output.
302 ; if it is not installed, this file cannot be exported.
305 \begin_layout Plain Layout
306 The latest PDF-version of this document can be found here:
307 \begin_inset Newline newline
312 http://wiki.lyx.org/LyX/DocumentationDevelopment#Math
320 \begin_layout Standard
321 \begin_inset Newpage newpage
327 \begin_layout Section
331 \begin_layout Standard
332 This document explains LyX's math features and is furthermore a collection
333 of LaTeX-commands used for mathematical characters and constructs.
334 The explanations are designed for the usage of commands.
335 It is therefore required that you have read the section
346 \begin_layout Standard
347 Most of the characters and many constructs explained in this manual are
348 also accessible via the menu
352 \SpecialChar \menuseparator
368 But everybody who has to write lots of formulas will notice that it is
369 much faster to use commands instead of the math toolbar.
370 Therefore this manual is focused on commands but also mentions the correspondin
371 g toolbar buttons when available.
374 \begin_layout Standard
375 If not specially mentioned the commands are only available within formulas.
376 To be able to use all commands explained in this document, the option
380 must be checked in the document settings (menu
382 Document\SpecialChar \menuseparator
383 Settings\SpecialChar \menuseparator
394 \begin_layout Plain Layout
397 Use AMS math package automatically
403 \begin_layout Plain Layout
412 -math when math constructs are found that are supported by LyX.
420 \begin_layout Standard
421 This document doesn't list all
425 \begin_layout Plain Layout
438 \begin_layout Plain Layout
443 \begin_layout Plain Layout
452 -math commands is in the file
455 \begin_inset CommandInset href
458 target "ftp://ftp.ams.org/pub/tex/doc/amstex/amsguide.pdf"
464 , which is part of every LaTeX standard installation.
469 for lucidity reasons.
472 \begin_layout Section
476 \begin_layout Standard
477 To create an inline formula
478 \begin_inset Index idx
481 \begin_layout Plain Layout
487 that is embedded into a text line, use one of the shortcuts
493 or the toolbar button
494 \begin_inset Graphics
495 filename ../images/math-mode.png
501 \begin_inset Newline newline
504 To create a display style formula
505 \begin_inset Index idx
508 \begin_layout Plain Layout
509 Formula ! display style
514 which will appear bigger, has a different format, and will be in a separate
515 paragraph, use one of these shortcuts:
524 \begin_layout Standard
525 To change a display style formula to an inline formula, set the cursor into
526 the formula and use one of the shortcuts
534 Edit\SpecialChar \menuseparator
535 Math\SpecialChar \menuseparator
539 The same way is used to change an inline formula to a display style formula.
542 \begin_layout Standard
543 To display parts of an inline formula in the size of a display style formula,
551 \begin_inset Index idx
554 \begin_layout Plain Layout
563 Then a new blue box appears in which the desired formula part is inserted.
566 \begin_layout Standard
567 Only inline formulas are allowed inside tables.
570 \begin_layout Standard
575 can be turned on in the menu
577 View\SpecialChar \menuseparator
581 When you click there on
582 \begin_inset Quotes eld
586 \begin_inset Quotes erd
589 the toolbar will be shown permanently at the bottom; this state is visualized
594 menu with a checkmark.
595 When you click in this state again on
596 \begin_inset Quotes eld
600 \begin_inset Quotes erd
611 is only shown when the cursor is within a formula; this state is visualized
612 by the renaming of the menu entry from
613 \begin_inset Quotes eld
617 \begin_inset Quotes erd
621 \begin_inset Quotes eld
629 \begin_inset Quotes erd
635 \begin_layout Standard
637 \begin_inset Index idx
640 \begin_layout Plain Layout
646 is invoked by pressing the toolbar button
647 \begin_inset Graphics
648 filename ../images/ert-insert.png
655 Insert\SpecialChar \menuseparator
660 \begin_layout Plain Layout
676 \begin_inset Note Note
679 \begin_layout Plain Layout
680 In LyX there are three
681 \begin_inset Quotes eld
685 \begin_inset Quotes erd
688 that appear in the output with sub- and superscript letters: TeX, LaTeX
692 \begin_layout Plain Layout
693 To avoid that these names are recognized as proper names, a TeX-brace pair
702 \begin_layout Standard
703 To change the LaTeX-preamble
704 \begin_inset Index idx
707 \begin_layout Plain Layout
715 Document\SpecialChar \menuseparator
716 Settings\SpecialChar \menuseparator
721 \begin_layout Plain Layout
737 \begin_layout Standard
738 To edit matrices, case differentiations and multiline formulas subsequently,
741 Edit\SpecialChar \menuseparator
746 Edit\SpecialChar \menuseparator
748 \begin_inset space \thinspace{}
752 \begin_inset space \thinspace{}
762 When lines and columns are swapped via the menu, the column or line where
763 the cursor is in is exchanged with the column to the right or the line
765 Is the cursor in the last column or row, the exchange is done with the
766 column to the left or the line above.
769 \begin_layout Standard
770 To write text in formulas
774 \begin_layout Plain Layout
775 For multiline formulas the command
782 \begin_inset CommandInset ref
784 reference "sub:Text-in-multiline"
798 \begin_inset Index idx
801 \begin_layout Plain Layout
808 \begin_inset Index idx
811 \begin_layout Plain Layout
818 This mode is invoked with the shortcut
824 or by the insertion of the command
831 \begin_inset Index idx
834 \begin_layout Plain Layout
843 The text appears black in LyX and can therefore be distinguished from the
844 other formula parts which appear blue.
845 In the output mathematical text is set upright, in contrary to other formula
849 \begin_layout Subsection*
853 \begin_layout Standard
854 Most of the LaTeX-commands for math constructs have the following scheme:
857 \begin_layout Standard
873 \begin_layout Standard
874 A command always starts with a backslash
875 \begin_inset Quotes gld
885 \begin_inset Quotes grd
889 To omit optional arguments, also omit the associated brackets.
890 The braces around the required arguments are named in this document as
892 \begin_inset Index idx
895 \begin_layout Plain Layout
902 If you add in a formula a left brace to a command name, LyX automatically
904 In all other cases TeX-braces are created in formulas with the command
912 TeX-braces appear red in LyX, in contrary to normal braces which appear
914 In TeX-mode no command is needed to get TeX-braces.
915 TeX-braces don't appear in the output.
918 \begin_layout Standard
919 When commands without arguments, like commands for symbols are entered in
920 TeX-mode, a space character must
924 be behind the command to end it.
925 This space doesn't appear in the output.
926 When the space should appear in the output, the space must be followed
927 by a protected space in normal text.
930 \begin_layout Standard
931 A protected space is inserted with
934 arg "command-alternatives space-insert protected ; math-space"
940 \begin_layout Subsection*
941 \begin_inset Newpage newpage
947 \begin_layout Itemize
949 \begin_inset space \textvisiblespace{}
952 denotes a space character to be input.
955 \begin_layout Itemize
957 \begin_inset Formula $\to$
960 denotes the usage of the corresponding arrow key on the keyboard.
965 key can often be used instead of
966 \begin_inset Formula $\to$
970 \begin_inset Formula $\downarrow$
978 \begin_inset Formula $\leftarrow$
982 \begin_inset Formula $\uparrow$
988 \begin_layout Subsection*
992 \begin_layout Standard
994 \begin_inset Float table
1000 \begin_layout Plain Layout
1002 \begin_inset Caption Standard
1004 \begin_layout Plain Layout
1005 \begin_inset CommandInset label
1007 name "tab:Available-units"
1019 \begin_layout Plain Layout
1021 \begin_inset Tabular
1022 <lyxtabular version="3" rows="13" columns="2">
1023 <features rotate="0" tabularvalignment="middle">
1024 <column alignment="center" valignment="top">
1025 <column alignment="center" valignment="top">
1027 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
1030 \begin_layout Plain Layout
1036 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
1039 \begin_layout Plain Layout
1047 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
1050 \begin_layout Plain Layout
1056 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
1059 \begin_layout Plain Layout
1067 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
1070 \begin_layout Plain Layout
1076 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
1079 \begin_layout Plain Layout
1087 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
1090 \begin_layout Plain Layout
1096 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
1099 \begin_layout Plain Layout
1101 \begin_inset space \thinspace{}
1105 \begin_inset space \thinspace{}
1115 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
1118 \begin_layout Plain Layout
1124 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
1127 \begin_layout Plain Layout
1129 \begin_inset space \thinspace{}
1133 \begin_inset space \thinspace{}
1143 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
1146 \begin_layout Plain Layout
1152 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
1155 \begin_layout Plain Layout
1157 \begin_inset space \thinspace{}
1161 \begin_inset space \thinspace{}
1171 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
1174 \begin_layout Plain Layout
1180 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
1183 \begin_layout Plain Layout
1185 \begin_inset space \thinspace{}
1189 \begin_inset space \thinspace{}
1199 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
1202 \begin_layout Plain Layout
1208 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
1211 \begin_layout Plain Layout
1213 \begin_inset space \thinspace{}
1217 \begin_inset space \thinspace{}
1227 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
1230 \begin_layout Plain Layout
1236 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
1239 \begin_layout Plain Layout
1241 \begin_inset space \thinspace{}
1245 \begin_inset Formula $\approx$
1249 \begin_inset space \thinspace{}
1259 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
1262 \begin_layout Plain Layout
1268 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
1271 \begin_layout Plain Layout
1273 \begin_inset space \thinspace{}
1277 \begin_inset space \thinspace{}
1287 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
1290 \begin_layout Plain Layout
1296 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
1299 \begin_layout Plain Layout
1303 \begin_inset Quotes eld
1309 \begin_inset Quotes erd
1319 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
1322 \begin_layout Plain Layout
1328 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
1331 \begin_layout Plain Layout
1333 \begin_inset Quotes eld
1341 \begin_inset Quotes erd
1351 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
1354 \begin_layout Plain Layout
1360 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
1363 \begin_layout Plain Layout
1365 \begin_inset space \thinspace{}
1369 \begin_inset Formula $\nicefrac{1}{18}$
1373 \begin_inset space \thinspace{}
1394 \begin_layout Standard
1395 \begin_inset Newpage newpage
1401 \begin_layout Section
1405 \begin_layout Subsection
1407 \begin_inset Index idx
1410 \begin_layout Plain Layout
1417 \begin_inset Index idx
1420 \begin_layout Plain Layout
1427 \begin_inset Index idx
1430 \begin_layout Plain Layout
1435 \begin_layout Plain Layout
1446 \begin_layout Plain Layout
1459 \begin_inset Index idx
1462 \begin_layout Plain Layout
1467 \begin_layout Plain Layout
1478 \begin_layout Plain Layout
1493 \begin_layout Standard
1494 Indices are created with an underscore
1495 \begin_inset Quotes eld
1499 \begin_inset Quotes erd
1502 or via the math toolbar button
1503 \begin_inset Graphics
1504 filename ../images/math-subscript.png
1509 , exponents with a caret
1510 \begin_inset Quotes eld
1514 \begin_inset Quotes erd
1517 or via the math toolbar button
1518 \begin_inset Graphics
1519 filename ../images/math-superscript.png
1527 \begin_layout Standard
1529 \begin_inset Tabular
1530 <lyxtabular version="3" rows="4" columns="2">
1531 <features rotate="0" tabularvalignment="middle">
1532 <column alignment="center" valignment="top" width="0pt">
1533 <column alignment="center" valignment="top" width="0pt">
1535 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
1538 \begin_layout Plain Layout
1544 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
1547 \begin_layout Plain Layout
1549 \begin_inset Note Note
1552 \begin_layout Plain Layout
1559 is only used as spacer.
1571 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
1574 \begin_layout Plain Layout
1580 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
1583 \begin_layout Plain Layout
1584 \begin_inset Formula $B_{V}$
1594 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
1597 \begin_layout Plain Layout
1603 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
1606 \begin_layout Plain Layout
1607 \begin_inset Formula $\raisebox{5mm}{}B^{V}$
1617 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
1620 \begin_layout Plain Layout
1622 \begin_inset space \textvisiblespace{}
1630 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
1633 \begin_layout Plain Layout
1634 \begin_inset Formula $\raisebox{5mm}{}B^{A}$
1650 \begin_layout Standard
1651 As the caret is in some languages an accent, vowels will be accentuated
1652 in this case and not set as exponents
1656 \begin_layout Plain Layout
1657 Depending on the used keyboard settings this can also happen for characters
1664 To get exponents in this case, press
1668 after the caret as in the last example.
1671 \begin_layout Subsection
1673 \begin_inset CommandInset label
1675 name "sub:Fractions"
1680 \begin_inset Index idx
1683 \begin_layout Plain Layout
1692 \begin_layout Standard
1693 Fractions are generated with the command
1700 \begin_inset Index idx
1703 \begin_layout Plain Layout
1711 or via the math toolbar button
1712 \begin_inset Graphics
1713 filename ../images/math/frac.png
1719 The font size is adjusted automatically, depending on whether the fraction
1720 is in an inline or display style formula.
1721 With the math toolbar button
1722 \begin_inset Graphics
1723 filename ../images/math/frac-square.png
1728 you can select different fraction types.
1731 \begin_layout Standard
1739 \begin_inset Index idx
1742 \begin_layout Plain Layout
1750 a fraction can be created that always has the size of a display style formula.
1758 \begin_inset Index idx
1761 \begin_layout Plain Layout
1769 the fraction appears always with the size of an inline formula.
1773 \begin_layout Standard
1774 A line with the fraction
1775 \begin_inset Formula $\frac{1}{2}$
1778 that was created with the command
1787 \begin_layout Standard
1788 A line with the fraction
1789 \begin_inset Formula $\dfrac{1}{2}$
1792 that was created with the command
1801 \begin_layout Standard
1803 \begin_inset Tabular
1804 <lyxtabular version="3" rows="4" columns="2">
1805 <features rotate="0" tabularvalignment="middle">
1806 <column alignment="center" valignment="top" width="0pt">
1807 <column alignment="center" valignment="top" width="0pt">
1809 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
1812 \begin_layout Plain Layout
1818 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
1821 \begin_layout Plain Layout
1823 \begin_inset Note Note
1826 \begin_layout Plain Layout
1833 is only used as spacer.
1845 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
1848 \begin_layout Plain Layout
1852 \begin_inset space \textvisiblespace{}
1856 \begin_inset Formula $\downarrow$
1864 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
1867 \begin_layout Plain Layout
1868 \begin_inset Formula $\raisebox{4.5mm}{}\frac{A}{B}\raisebox{-2.5mm}{}$
1878 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
1881 \begin_layout Plain Layout
1885 \begin_inset space \textvisiblespace{}
1889 \begin_inset Formula $\downarrow$
1897 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
1900 \begin_layout Plain Layout
1901 \begin_inset Formula $\raisebox{7mm}{}\dfrac{A}{B}\raisebox{-4mm}{}$
1911 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
1914 \begin_layout Plain Layout
1918 \begin_inset space \textvisiblespace{}
1924 \begin_inset space \textvisiblespace{}
1928 \begin_inset Formula $\downarrow$
1932 \begin_inset Formula $\downarrow\downarrow$
1940 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
1943 \begin_layout Plain Layout
1944 \begin_inset Formula $\raisebox{8mm}{}\dfrac{e^{\frac{1}{2}}}{3}\raisebox{-4mm}{}$
1960 \begin_layout Standard
1961 \begin_inset VSpace bigskip
1965 \begin_inset Newpage newpage
1968 For nested fractions the command
1975 \begin_inset Index idx
1978 \begin_layout Plain Layout
1988 \begin_inset VSpace -3mm
1994 \begin_layout Standard
1995 \begin_inset Formula
1997 \textrm{created with \textbf{\textbackslash frac}} & & \textrm{created with \textbf{\textbackslash cfrac}}\\
1998 \frac{A}{B+\frac{C+\frac{E}{F}}{D}} & & \cfrac{A}{B+\cfrac{C+\cfrac{E}{F}}{D}}
2006 \begin_layout Standard
2007 The command for the example above is:
2010 \begin_layout Standard
2016 \begin_inset space \textvisiblespace{}
2020 \begin_inset Formula $\downarrow$
2026 \begin_inset space \textvisiblespace{}
2032 \begin_inset space \textvisiblespace{}
2036 \begin_inset Formula $\downarrow$
2040 \begin_inset Formula $\downarrow$
2046 \begin_layout Standard
2047 \begin_inset VSpace medskip
2053 \begin_layout Standard
2060 sets the fraction always in the size of a displayed formula, also when
2061 it is part of another fraction.
2064 \begin_layout Standard
2065 It is possible to specify the alignment of the numerator.
2072 is used to left align it, the command
2085 centers the numerator.
2086 These fractions demonstrate the different alignments:
2089 \begin_layout Standard
2092 \begin_inset Formula
2094 \cfrac[l]{A}{B+C}\,,\,\cfrac{A}{B+C}\,,\,\cfrac[r]{A}{B+C}
2102 \begin_layout Standard
2103 \begin_inset Note Greyedout
2106 \begin_layout Plain Layout
2123 are no real LaTeX commands but represent the command
2127 cfrac[alignment]{numerator}{denominator}
2130 Therefore you cannot use them in TeX code.
2138 \begin_layout Standard
2139 \begin_inset VSpace medskip
2142 It is often advantageous to combine
2155 \begin_inset Formula
2157 \cfrac{A}{B+\cfrac{C+\frac{E}{F}}{D}}
2165 \begin_layout Standard
2166 For inline fractions with a sloped fraction stroke you can use the command
2174 \begin_inset Index idx
2177 \begin_layout Plain Layout
2186 \begin_inset Formula $\nicefrac{5}{31}$
2196 \begin_inset Index idx
2199 \begin_layout Plain Layout
2208 \begin_inset Formula $\unitfrac{5}{31}$
2211 There is furthermore the command
2217 that offers to write a fraction in combination with a number:
2218 \begin_inset Formula $\unitfrac[2]{1}{3}$
2224 \begin_layout Standard
2225 \begin_inset Note Greyedout
2228 \begin_layout Plain Layout
2239 is not a real LaTeX command but the command
2240 \begin_inset Newline newline
2247 unitfrac[number]{numerator}{denominator}
2250 Therefore you cannot use it in TeX code.
2258 \begin_layout Standard
2259 How to define own fractions where the fraction stroke can be changed, is
2261 \begin_inset CommandInset ref
2263 reference "sub:Self-defined-Fractions"
2270 \begin_layout Standard
2271 \begin_inset Newpage newpage
2277 \begin_layout Subsection
2279 \begin_inset Index idx
2282 \begin_layout Plain Layout
2291 \begin_layout Standard
2292 Square roots are created with
2299 \begin_inset Index idx
2302 \begin_layout Plain Layout
2310 or the math toolbar button
2311 \begin_inset Graphics
2312 filename ../images/math/sqrt.png
2317 , all other roots with the command
2324 \begin_inset Index idx
2327 \begin_layout Plain Layout
2335 or with the math toolbar button
2336 \begin_inset Graphics
2337 filename ../images/math/root.png
2345 \begin_layout Standard
2347 \begin_inset Tabular
2348 <lyxtabular version="3" rows="3" columns="2">
2349 <features rotate="0" tabularvalignment="middle">
2350 <column alignment="center" valignment="top" width="0pt">
2351 <column alignment="center" valignment="top" width="0pt">
2353 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
2356 \begin_layout Plain Layout
2362 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
2365 \begin_layout Plain Layout
2367 \begin_inset Note Note
2370 \begin_layout Plain Layout
2377 is only used as spacer.
2389 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
2392 \begin_layout Plain Layout
2396 \begin_inset space \textvisiblespace{}
2404 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
2407 \begin_layout Plain Layout
2408 \begin_inset Formula $\raisebox{4.5mm}{}\sqrt{A-B}$
2418 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
2421 \begin_layout Plain Layout
2425 \begin_inset space \textvisiblespace{}
2429 \begin_inset Formula $\downarrow$
2437 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
2440 \begin_layout Plain Layout
2441 \begin_inset Formula $\raisebox{4.5mm}{}\sqrt[3]{A-B}$
2457 \begin_layout Standard
2458 A square root can also be created with
2464 when the root index field is left empty.
2467 \begin_layout Standard
2468 With certain indices the distance to the root is too small, like in this
2470 \begin_inset Formula $\sqrt[\beta]{B}$
2474 \begin_inset Newline newline
2478 \begin_inset Formula $\beta$
2482 To avoid this, the commands
2489 \begin_inset Index idx
2492 \begin_layout Plain Layout
2507 \begin_inset Index idx
2510 \begin_layout Plain Layout
2518 are used with the following scheme:
2521 \begin_layout Standard
2535 \begin_layout Standard
2536 Distance is the number of Big Points (unit bp;
2537 \begin_inset Formula $\mathrm{72\, bp=1\, inch}$
2540 ), that the index should be moved to the left or top, resp..
2541 The commands are written to the index.
2542 This way the command
2543 \begin_inset Newline newline
2553 \begin_inset Formula $\to$
2559 \begin_inset Formula $\to$
2565 \begin_inset space \textvisiblespace{}
2569 \begin_inset Formula $\to$
2573 \begin_inset Newline newline
2578 produces a correct typeset formula:
2579 \begin_inset Formula $\sqrt[\leftroot{-1}\uproot{2}\beta]{B}$
2585 \begin_layout Subsection
2586 Binomial Coefficients
2587 \begin_inset Index idx
2590 \begin_layout Plain Layout
2591 Binomial coefficients
2599 \begin_layout Standard
2600 Binomial coefficients are inserted with the command
2607 \begin_inset Index idx
2610 \begin_layout Plain Layout
2618 or with the submenu of the math toolbar button
2619 \begin_inset Graphics
2620 filename ../images/math/frac-square.png
2638 there are the commands
2645 \begin_inset Index idx
2648 \begin_layout Plain Layout
2663 \begin_inset Index idx
2666 \begin_layout Plain Layout
2675 For other brackets around binomial coeficients there are the commands
2682 \begin_inset Index idx
2685 \begin_layout Plain Layout
2700 \begin_inset Index idx
2703 \begin_layout Plain Layout
2714 \begin_layout Standard
2716 \begin_inset Tabular
2717 <lyxtabular version="3" rows="6" columns="2">
2718 <features rotate="0" tabularvalignment="middle">
2719 <column alignment="center" valignment="top" width="0pt">
2720 <column alignment="center" valignment="top" width="0pt">
2722 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
2725 \begin_layout Plain Layout
2731 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
2734 \begin_layout Plain Layout
2736 \begin_inset Note Note
2739 \begin_layout Plain Layout
2746 is only used as spacer.
2758 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
2761 \begin_layout Plain Layout
2765 \begin_inset space \textvisiblespace{}
2769 \begin_inset Formula $\downarrow$
2777 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
2780 \begin_layout Plain Layout
2781 \begin_inset Formula $\raisebox{5mm}{}\binom{A}{B}\raisebox{-2.5mm}{}$
2791 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
2794 \begin_layout Plain Layout
2798 \begin_inset space \textvisiblespace{}
2802 \begin_inset Formula $\downarrow$
2810 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
2813 \begin_layout Plain Layout
2814 \begin_inset Formula $\raisebox{5mm}{}\dbinom{A}{B}\raisebox{-2.5mm}{}$
2824 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
2827 \begin_layout Plain Layout
2831 \begin_inset space \textvisiblespace{}
2835 \begin_inset Formula $\downarrow$
2843 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
2846 \begin_layout Plain Layout
2847 \begin_inset Formula $\raisebox{5mm}{}\tbinom{A}{B}\raisebox{-2.5mm}{}$
2857 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
2860 \begin_layout Plain Layout
2864 \begin_inset space \textvisiblespace{}
2868 \begin_inset Formula $\downarrow$
2876 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
2879 \begin_layout Plain Layout
2880 \begin_inset Formula $\raisebox{5mm}{}{A \brack B}\raisebox{-2.5mm}{}$
2890 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
2893 \begin_layout Plain Layout
2897 \begin_inset space \textvisiblespace{}
2901 \begin_inset Formula $\downarrow$
2909 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
2912 \begin_layout Plain Layout
2913 \begin_inset Formula $\raisebox{5mm}{}{A \brace B}\raisebox{-2.5mm}{}$
2929 \begin_layout Subsection
2930 Case Differentiations
2931 \begin_inset Index idx
2934 \begin_layout Plain Layout
2935 Case differentiations
2943 \begin_layout Standard
2945 \begin_inset Tabular
2946 <lyxtabular version="3" rows="3" columns="2">
2947 <features rotate="0" tabularvalignment="middle">
2948 <column alignment="center" valignment="top" width="0pt">
2949 <column alignment="center" valignment="top" width="0pt">
2951 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
2954 \begin_layout Plain Layout
2960 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
2963 \begin_layout Plain Layout
2971 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
2974 \begin_layout Plain Layout
2978 \begin_inset space \textvisiblespace{}
2982 \begin_inset Formula $\to$
2986 \begin_inset Index idx
2989 \begin_layout Plain Layout
3002 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
3005 \begin_layout Plain Layout
3006 \begin_inset Formula $\begin{cases}
3017 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
3020 \begin_layout Plain Layout
3024 \begin_inset space \textvisiblespace{}
3030 arg "newline-insert newline"
3038 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
3041 \begin_layout Plain Layout
3042 \begin_inset Formula $\begin{cases}
3043 A & \textrm{for }x>0\\
3044 B & \textrm{for }x=0
3061 \begin_layout Standard
3068 or pressing the math toolbar button
3069 \begin_inset Graphics
3070 filename ../images/math/cases.png
3075 you can create new lines with the shortcut
3078 arg "newline-insert newline"
3081 or the table toolbar button
3082 \begin_inset Graphics
3083 filename ../images/tabular-feature_append-row.png
3091 \begin_layout Standard
3098 is also available via the menu
3100 Insert\SpecialChar \menuseparator
3101 Math\SpecialChar \menuseparator
3107 \begin_layout Subsection
3109 \begin_inset Index idx
3112 \begin_layout Plain Layout
3121 \begin_layout Standard
3129 \begin_inset Index idx
3132 \begin_layout Plain Layout
3140 every character can be displayed canceled.
3141 The characters are quasi accentuated by a slash.
3144 \begin_layout Standard
3146 \begin_inset Tabular
3147 <lyxtabular version="3" rows="4" columns="2">
3148 <features rotate="0" tabularvalignment="middle">
3149 <column alignment="center" valignment="top" width="0pt">
3150 <column alignment="center" valignment="top" width="0pt">
3152 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
3155 \begin_layout Plain Layout
3161 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
3164 \begin_layout Plain Layout
3172 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
3175 \begin_layout Plain Layout
3183 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
3186 \begin_layout Plain Layout
3187 \begin_inset Formula $\not=$
3197 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
3200 \begin_layout Plain Layout
3210 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
3213 \begin_layout Plain Layout
3214 \begin_inset Formula $\not\le$
3224 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
3227 \begin_layout Plain Layout
3237 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
3240 \begin_layout Plain Layout
3241 \begin_inset Formula $\not\parallel$
3257 \begin_layout Standard
3258 The last example shows that not all negations look good.
3259 Therefore there are special commands for some negations (see
3260 \begin_inset CommandInset ref
3262 reference "sub:Mathematical-Symbols"
3267 \begin_inset CommandInset ref
3269 reference "sec:Relations"
3276 \begin_layout Subsection
3278 \begin_inset CommandInset label
3280 name "sub:Placeholders"
3285 \begin_inset Index idx
3288 \begin_layout Plain Layout
3295 \begin_inset Index idx
3298 \begin_layout Plain Layout
3299 Chemical characters ! Isotopes
3305 \begin_inset Index idx
3308 \begin_layout Plain Layout
3313 \begin_layout Plain Layout
3324 \begin_layout Plain Layout
3339 \begin_layout Standard
3341 \begin_inset space \thinspace{}
3345 \begin_inset space \space{}
3352 \begin_layout Plain Layout
3353 Typesetting isotopes and chemical symbols is described in
3354 \begin_inset CommandInset ref
3356 reference "sub:Chemical-Symbols-and"
3365 the following problem occurs:
3368 \begin_layout Standard
3370 \begin_inset Tabular
3371 <lyxtabular version="3" rows="2" columns="2">
3372 <features rotate="0" tabularvalignment="middle">
3373 <column alignment="center" valignment="top" width="0pt">
3374 <column alignment="center" valignment="top" width="0pt">
3376 <cell alignment="center" valignment="top" usebox="none">
3379 \begin_layout Plain Layout
3380 Indices created with sub- and superscripts:
3385 <cell alignment="center" valignment="top" usebox="none">
3388 \begin_layout Plain Layout
3389 \begin_inset Formula $_{9}^{19}\mathrm{F}\raisebox{-3mm}{}$
3399 <cell alignment="center" valignment="top" usebox="none">
3402 \begin_layout Plain Layout
3408 <cell alignment="center" valignment="top" usebox="none">
3411 \begin_layout Plain Layout
3412 \begin_inset Formula $_{\phantom{1}9}^{19}\mathrm{F}$
3426 \begin_inset Note Note
3429 \begin_layout Plain Layout
3436 is only used as spacer.
3444 \begin_layout Standard
3445 The shorter index is by default placed below or above the first character
3446 of the longer index.
3447 To avoid this there is the command
3454 \begin_inset Index idx
3457 \begin_layout Plain Layout
3465 or the math toolbar button
3466 \begin_inset space \thinspace{}
3473 \begin_layout Plain Layout
3474 can be found in the submenu of the toolbar button
3475 \begin_inset Graphics
3476 filename ../images/math/space.png
3487 \begin_inset Graphics
3488 filename ../images/math/phantom.png
3493 that creates one or more phantom characters.
3500 a small blue box appears that is superposed with two red arrows.
3501 The arrows indicate that the complete width and height of the box content
3502 will be created as placeholder.
3503 Phantom characters are accordingly placeholders with the size of the characters.
3506 \begin_layout Standard
3508 \begin_inset Tabular
3509 <lyxtabular version="3" rows="4" columns="2">
3510 <features rotate="0" tabularvalignment="middle">
3511 <column alignment="center" valignment="top">
3512 <column alignment="center" valignment="top">
3514 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
3517 \begin_layout Plain Layout
3523 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
3526 \begin_layout Plain Layout
3528 \begin_inset Note Note
3531 \begin_layout Plain Layout
3538 is only used as spacer.
3550 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
3553 \begin_layout Plain Layout
3555 \begin_inset space \textvisiblespace{}
3561 \begin_inset space \textvisiblespace{}
3565 \begin_inset Formula $\to$
3569 \begin_inset space \textvisiblespace{}
3577 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
3580 \begin_layout Plain Layout
3581 \begin_inset Formula $\raisebox{4.5mm}{}{}_{\phantom{1}9}^{19}\mathrm{F}\raisebox{-2.5mm}{}$
3591 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
3594 \begin_layout Plain Layout
3596 \begin_inset space \textvisiblespace{}
3602 \begin_inset space \textvisiblespace{}
3606 \begin_inset Formula $\to$
3610 \begin_inset space \textvisiblespace{}
3618 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
3621 \begin_layout Plain Layout
3622 \begin_inset Formula $\raisebox{4.5mm}{}{}_{\phantom{23}9}^{235}\mathrm{F}\raisebox{-2.5mm}{}$
3632 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
3635 \begin_layout Plain Layout
3639 \begin_inset space \textvisiblespace{}
3645 \begin_inset space \textvisiblespace{}
3649 \begin_inset Formula $\to$
3653 \begin_inset space \textvisiblespace{}
3661 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
3664 \begin_layout Plain Layout
3665 \begin_inset Formula $\raisebox{4.5mm}{}\Lambda_{MMt}^{\phantom{ii}t}\raisebox{-2.5mm}{}$
3681 \begin_layout Standard
3682 Furthermore there are the commands
3689 \begin_inset Index idx
3692 \begin_layout Plain Layout
3701 \begin_inset space ~
3705 \begin_inset Graphics
3706 filename ../images/math/vphantom.png
3718 \begin_inset Index idx
3721 \begin_layout Plain Layout
3730 \begin_inset space ~
3734 \begin_inset Graphics
3735 filename ../images/math/hphantom.png
3747 creates only space for the maximal height of the characters in the box
3748 but not for its width.
3755 creates only space for the width of the box content.
3756 Therefore the boxes of both commands have only one red arrow.
3759 \begin_layout Standard
3760 For example the command
3765 \begin_inset space \textvisiblespace{}
3772 creates space for the height of the integral sign,
3776 \begin_layout Plain Layout
3783 creates an integral sign, see
3784 \begin_inset CommandInset ref
3786 reference "sub:Big-Operators"
3795 because this is the larger character.
3796 An example application is in
3797 \begin_inset CommandInset ref
3799 reference "sub:Multiline-Brackets"
3806 \begin_layout Standard
3807 Placeholders can also be used for text when they are inserted via the menu
3810 Insert\SpecialChar \menuseparator
3811 Formatting\SpecialChar \menuseparator
3817 \begin_layout Standard
3819 \begin_inset Newline newline
3823 \begin_inset Phantom Phantom
3826 \begin_layout Plain Layout
3835 \begin_layout Subsection
3837 \begin_inset Index idx
3840 \begin_layout Plain Layout
3847 \begin_inset Index idx
3850 \begin_layout Plain Layout
3851 Formula ! underlined
3859 \begin_layout Standard
3861 \begin_inset Tabular
3862 <lyxtabular version="3" rows="4" columns="2">
3863 <features rotate="0" tabularvalignment="middle">
3864 <column alignment="center" valignment="top" width="0pt">
3865 <column alignment="center" valignment="top" width="0pt">
3867 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
3870 \begin_layout Plain Layout
3876 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
3879 \begin_layout Plain Layout
3881 \begin_inset Note Note
3884 \begin_layout Plain Layout
3891 is only used as spacer.
3903 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
3906 \begin_layout Plain Layout
3910 \begin_inset space \textvisiblespace{}
3914 \begin_inset Index idx
3917 \begin_layout Plain Layout
3930 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
3933 \begin_layout Plain Layout
3934 \begin_inset Formula $\raisebox{5mm}{}\overline{A+B}$
3944 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
3947 \begin_layout Plain Layout
3951 \begin_inset space \textvisiblespace{}
3955 \begin_inset Index idx
3958 \begin_layout Plain Layout
3971 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
3974 \begin_layout Plain Layout
3975 \begin_inset Formula $\underline{A+B}\raisebox{-2.5mm}{}$
3985 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
3988 \begin_layout Plain Layout
3992 \begin_inset space \textvisiblespace{}
3998 \begin_inset space \textvisiblespace{}
4006 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
4009 \begin_layout Plain Layout
4010 \begin_inset Formula $\raisebox{5mm}{}\overline{\underline{A+B}}\raisebox{-2.5mm}{}$
4026 \begin_layout Standard
4027 In the last example it doesn't matter if first
4042 \begin_layout Standard
4043 To double underline use
4052 \begin_layout Standard
4053 It is possible to place up to 6 lines above or below characters.
4056 \begin_layout Standard
4057 \begin_inset VSpace bigskip
4060 Custom lines can be created using the command
4067 \begin_inset Index idx
4070 \begin_layout Plain Layout
4078 which has the following scheme:
4081 \begin_layout Standard
4086 rule[vertical offset]{length}{thickness}
4089 \begin_layout Standard
4090 The optional vertical offset shifts the line upwards (or downwards, when
4091 the value is negative).
4093 \begin_inset CommandInset ref
4095 reference "tab:Available-units"
4099 can be used for the values.
4100 Here are two example lines created with the commands
4101 \begin_inset Newline newline
4108 rule[-2ex]{3cm}{2pt}
4119 \begin_layout Standard
4121 \begin_inset Formula $\rule[-2ex]{3cm}{2pt}\rule{2cm}{1pt}$
4127 \begin_layout Standard
4134 can also be used for text when a line is inserted via the menu
4136 Insert\SpecialChar \menuseparator
4137 Formatting\SpecialChar \menuseparator
4139 \begin_inset space ~
4147 \begin_layout Standard
4149 \begin_inset CommandInset line
4160 \begin_layout Subsection
4162 \begin_inset CommandInset label
4169 \begin_inset Index idx
4172 \begin_layout Plain Layout
4181 \begin_layout Standard
4182 There are different types of ellipses available.
4186 \begin_layout Plain Layout
4187 In the math toolbar in the submenu of the button
4188 \begin_inset Graphics
4189 filename ../images/math/ldots.png
4199 For listings dots at the baseline are used (
4206 \begin_inset Index idx
4209 \begin_layout Plain Layout
4217 ), while for operations dots are needed that are on the same height as the
4225 \begin_inset Index idx
4228 \begin_layout Plain Layout
4237 When using the command
4244 \begin_inset Index idx
4247 \begin_layout Plain Layout
4255 , LaTeX decides on the basis of the next character what type is used.
4258 \begin_layout Standard
4260 \begin_inset Tabular
4261 <lyxtabular version="3" rows="9" columns="2">
4262 <features rotate="0" tabularvalignment="middle">
4263 <column alignment="center" valignment="top" width="0pt">
4264 <column alignment="center" valignment="top" width="0pt">
4266 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
4269 \begin_layout Plain Layout
4275 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
4278 \begin_layout Plain Layout
4286 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
4289 \begin_layout Plain Layout
4291 \begin_inset space \textvisiblespace{}
4297 \begin_inset space \textvisiblespace{}
4305 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
4308 \begin_layout Plain Layout
4309 \begin_inset Formula $A_{1},\dots,A_{n}$
4319 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
4322 \begin_layout Plain Layout
4324 \begin_inset space \textvisiblespace{}
4330 \begin_inset space \textvisiblespace{}
4338 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
4341 \begin_layout Plain Layout
4342 \begin_inset Formula $A_{1}+\dots+A_{n}$
4352 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
4355 \begin_layout Plain Layout
4357 \begin_inset space \textvisiblespace{}
4363 \begin_inset space \textvisiblespace{}
4371 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
4374 \begin_layout Plain Layout
4375 \begin_inset Formula $A_{1},\ldots,A_{n}$
4385 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
4388 \begin_layout Plain Layout
4390 \begin_inset space \textvisiblespace{}
4396 \begin_inset space \textvisiblespace{}
4404 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
4407 \begin_layout Plain Layout
4408 \begin_inset Formula $A_{1}+\cdots+A_{n}$
4418 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
4421 \begin_layout Plain Layout
4429 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
4432 \begin_layout Plain Layout
4433 \begin_inset Formula $\vdots$
4443 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
4446 \begin_layout Plain Layout
4454 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
4457 \begin_layout Plain Layout
4458 \begin_inset Formula $\ddots$
4468 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
4471 \begin_layout Plain Layout
4479 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
4482 \begin_layout Plain Layout
4483 \begin_inset Formula $\iddots$
4493 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
4496 \begin_layout Plain Layout
4498 \begin_inset space \thinspace{}
4501 matrix with the different dots
4506 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
4509 \begin_layout Plain Layout
4510 \begin_inset Formula $\begin{array}{ccc}
4511 A_{11} & \cdots & A_{1m}\\
4512 \vdots & \ddots & \vdots\\
4513 A_{n1} & \cdots & A_{nm}
4530 \begin_layout Standard
4531 The ellipses available in menu
4533 Insert\SpecialChar \menuseparator
4535 \begin_inset space ~
4549 \begin_layout Standard
4550 \begin_inset VSpace medskip
4559 , one of the options
4561 Use mathdots package (automatically)
4563 must be set in the document settings under
4566 \begin_inset space ~
4572 \begin_inset Newline newline
4577 Use mathdots package
4579 will improve the appearance of all dots in the documents if their font
4580 style or size is not the default.
4583 \begin_layout Standard
4584 \begin_inset VSpace medskip
4587 Specially for matrices there are ellipses that span over several columns.
4588 They are created with the command
4595 \begin_inset Index idx
4598 \begin_layout Plain Layout
4606 , that has the following scheme:
4609 \begin_layout Standard
4614 hdotsfor[distance]{number of columns}
4617 \begin_layout Standard
4618 The number of columns specifies how many columns should be spanned.
4619 Distance is a factor for the distance between the dots.
4622 \begin_layout Standard
4623 In the following matrix the command
4629 was inserted in the first box of the second line, to get an ellipsis with
4630 a dot distance twice as long as with the command
4637 \begin_inset Formula
4639 \left(\begin{array}{cccc}
4648 Note that the matrix fields that should be spanned must be empty, otherwise
4649 you get LaTeX-errors.
4652 \begin_layout Standard
4653 \begin_inset VSpace bigskip
4656 Furthermore you can fill with the command
4663 \begin_inset Index idx
4666 \begin_layout Plain Layout
4674 the rest of a line with dots.
4675 The effect of these commands is the same as with
4682 \begin_inset CommandInset ref
4684 reference "sub:Variable-Space"
4691 \begin_layout Standard
4692 For example the command
4697 \begin_inset space \textvisiblespace{}
4705 \begin_layout Standard
4706 \begin_inset Formula $A\dotfill B$
4712 \begin_layout Standard
4719 there is for a line the command
4726 \begin_inset Index idx
4729 \begin_layout Plain Layout
4740 \begin_layout Standard
4741 \begin_inset Formula $A\hrulefill B$
4747 \begin_layout Standard
4748 To use the commands for text, they have to be inserted in TeX-mode.
4751 \begin_layout Section
4753 \begin_inset CommandInset label
4760 \begin_inset Index idx
4763 \begin_layout Plain Layout
4772 \begin_layout Standard
4773 Matrices can be inserted via the math toolbar button
4774 \begin_inset Graphics
4775 filename ../images/dialog-show_mathmatrix.png
4782 Insert\SpecialChar \menuseparator
4783 Math\SpecialChar \menuseparator
4787 In the matrix dialog you can specify the number of columns and rows, the
4788 alignment and the decoration.
4789 The vertical alignment is only of importance for matrices in inline formulas:
4792 \begin_layout Standard
4793 The first matrix is top
4794 \begin_inset Formula $\begin{array}[t]{cccc}
4802 \begin_inset Formula $\begin{array}{cccc}
4809 and the third bottom
4810 \begin_inset Formula $\begin{array}[b]{cccc}
4820 \begin_layout Standard
4821 The horizontal alignment specifies how the column entries should be aligned.
4822 It is set by entering a letter for every column.
4827 denotes left aligned,
4836 To create for example a 4
4841 \begin_inset space ~
4844 matrix where the first column is left aligned, the second and third are
4845 centered and the last one is right aligned, one enters for the horizontal
4851 Normally in a matrix all columns are centered, therefore the default for
4859 \begin_layout Standard
4860 Horizontal alignment:
4863 \begin_layout Standard
4869 \begin_inset Formula $\begin{array}{lll}
4881 \begin_inset Formula $\begin{array}{ccc}
4893 \begin_inset Formula $\begin{array}{rrr}
4903 \begin_layout Standard
4904 To add or delete rows and columns subsequently, the math toolbar buttons
4906 \begin_inset Graphics
4907 filename ../images/tabular-feature_append-row.png
4913 \begin_inset Graphics
4914 filename ../images/tabular-feature_delete-row.png
4920 \begin_inset space \thinspace{}
4925 Edit\SpecialChar \menuseparator
4929 New rows can also be created with
4932 arg "newline-insert newline"
4938 \begin_layout Standard
4939 \begin_inset VSpace bigskip
4946 adds parentheses in the selected style around the matrix.
4947 Alternatively, parentheses can can either be created with the commands
4955 \begin_inset Index idx
4958 \begin_layout Plain Layout
4973 \begin_inset Index idx
4976 \begin_layout Plain Layout
4987 \begin_inset space ~
4993 \begin_inset CommandInset ref
4995 reference "sub:Automatic-Bracket-Size"
4999 , or by using the following commands:
5000 \begin_inset VSpace medskip
5006 \begin_layout Standard
5007 \begin_inset space \hfill{}
5011 \begin_inset Tabular
5012 <lyxtabular version="3" rows="4" columns="2">
5013 <features rotate="0" tabularvalignment="middle">
5014 <column alignment="center" valignment="top">
5015 <column alignment="center" valignment="top">
5017 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
5020 \begin_layout Plain Layout
5026 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
5029 \begin_layout Plain Layout
5031 \begin_inset Note Note
5034 \begin_layout Plain Layout
5041 is only used as spacer.
5053 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
5056 \begin_layout Plain Layout
5060 \begin_inset space \textvisiblespace{}
5068 \begin_inset space \thinspace{}
5076 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
5079 \begin_layout Plain Layout
5080 \begin_inset Formula $\raisebox{7.5mm}{}\begin{bmatrix}\begin{array}{cc}
5081 0 & \textrm{-}\mathrm{i}\\
5083 \end{array}\end{bmatrix}\raisebox{-5.3mm}{}$
5093 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
5096 \begin_layout Plain Layout
5100 \begin_inset space \textvisiblespace{}
5108 \begin_inset space \thinspace{}
5116 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
5119 \begin_layout Plain Layout
5120 \begin_inset Formula $\raisebox{7.5mm}{}\begin{Bmatrix}\begin{array}{cc}
5121 0 & \textrm{-}\mathrm{i}\\
5123 \end{array}\end{Bmatrix}\raisebox{-5.3mm}{}$
5133 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
5136 \begin_layout Plain Layout
5140 \begin_inset space \textvisiblespace{}
5148 \begin_inset space \thinspace{}
5156 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
5159 \begin_layout Plain Layout
5160 \begin_inset Formula $\raisebox{7.5mm}{}\begin{pmatrix}\begin{array}{cc}
5161 0 & \textrm{-}\mathrm{i}\\
5163 \end{array}\end{pmatrix}\raisebox{-5.3mm}{}$
5177 \begin_inset space \hfill{}
5181 \begin_inset Tabular
5182 <lyxtabular version="3" rows="4" columns="2">
5183 <features rotate="0" tabularvalignment="middle">
5184 <column alignment="center" valignment="top">
5185 <column alignment="center" valignment="top">
5187 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
5190 \begin_layout Plain Layout
5196 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
5199 \begin_layout Plain Layout
5207 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
5210 \begin_layout Plain Layout
5214 \begin_inset space \textvisiblespace{}
5222 \begin_inset space \thinspace{}
5230 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
5233 \begin_layout Plain Layout
5234 \begin_inset Formula $\raisebox{7.5mm}{}\begin{vmatrix}\begin{array}{cc}
5235 0 & \textrm{-}\mathrm{i}\\
5237 \end{array}\end{vmatrix}\raisebox{-5.3mm}{}$
5247 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
5250 \begin_layout Plain Layout
5254 \begin_inset space \textvisiblespace{}
5262 \begin_inset space \thinspace{}
5270 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
5273 \begin_layout Plain Layout
5274 \begin_inset Formula $\raisebox{7.5mm}{}\begin{Vmatrix}\begin{array}{cc}
5275 0 & \textrm{-}\mathrm{i}\\
5277 \end{array}\end{Vmatrix}\raisebox{-5.3mm}{}$
5287 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
5290 \begin_layout Plain Layout
5294 \begin_inset space \textvisiblespace{}
5302 \begin_inset space \thinspace{}
5310 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
5313 \begin_layout Plain Layout
5314 \begin_inset Formula $\raisebox{7.5mm}{}\begin{matrix}\begin{array}{cc}
5315 0 & \textrm{-}\mathrm{i}\\
5317 \end{array}\end{matrix}\raisebox{-5.3mm}{}$
5331 \begin_inset space \hfill{}
5337 \begin_layout Standard
5338 \begin_inset VSpace medskip
5342 \begin_inset space \thinspace{}
5346 \begin_inset space \space{}
5355 is inserted, a blue box appears between two vertical lines where the matrix
5357 \begin_inset Newline newline
5360 Note that decorated matrices ignore the vertical alignment.
5363 \begin_layout Standard
5364 \begin_inset VSpace bigskip
5367 As all multiline formulas are matrices, the length
5374 \begin_inset Index idx
5377 \begin_layout Plain Layout
5385 that is described in
5386 \begin_inset CommandInset ref
5388 reference "sub:Column-Separation"
5392 can also be used to change the column separation of matrices.
5395 \begin_layout Standard
5396 To change the row separation, the command
5403 \begin_inset Index idx
5406 \begin_layout Plain Layout
5415 It is used as follows:
5418 \begin_layout Standard
5425 arraystretch}{stretch factor}
5426 \begin_inset Index idx
5429 \begin_layout Plain Layout
5440 \begin_layout Standard
5447 assigns the stretch factor to the predefined command
5455 \begin_inset space \thinspace{}
5459 \begin_inset space \space{}
5462 the row separation, use the factor 2.
5463 This is then used for all following matrices.
5464 To go back to the original separation, assign the factor 1 to
5473 \begin_layout Standard
5474 To set matrices into a text line, the command
5481 \begin_inset Index idx
5484 \begin_layout Plain Layout
5493 When it is inserted a blue box with two dashed lines appears.
5494 In this box the matrix is inserted.
5497 \begin_layout Standard
5499 \begin_inset Formula $\left(\begin{smallmatrix}A & B\\
5501 \end{smallmatrix}\right)$
5507 \begin_layout Section
5508 Brackets and Delimiters
5509 \begin_inset Index idx
5512 \begin_layout Plain Layout
5519 \begin_inset Index idx
5522 \begin_layout Plain Layout
5531 \begin_layout Subsection
5532 Vertical Brackets and Delimiters
5533 \begin_inset Index idx
5536 \begin_layout Plain Layout
5545 \begin_layout Standard
5546 \begin_inset space \hfill{}
5550 \begin_inset Tabular
5551 <lyxtabular version="3" rows="9" columns="2">
5552 <features rotate="0" tabularvalignment="middle">
5553 <column alignment="center" valignment="top" width="0pt">
5554 <column alignment="center" valignment="top" width="0pt">
5556 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
5559 \begin_layout Plain Layout
5565 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
5568 \begin_layout Plain Layout
5576 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
5579 \begin_layout Plain Layout
5585 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
5588 \begin_layout Plain Layout
5589 \begin_inset Formula $($
5599 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
5602 \begin_layout Plain Layout
5608 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
5611 \begin_layout Plain Layout
5612 \begin_inset Formula $\{$
5622 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
5625 \begin_layout Plain Layout
5631 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
5634 \begin_layout Plain Layout
5635 \begin_inset Formula $[$
5645 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
5648 \begin_layout Plain Layout
5656 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
5659 \begin_layout Plain Layout
5660 \begin_inset Formula $\langle$
5670 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
5673 \begin_layout Plain Layout
5681 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
5684 \begin_layout Plain Layout
5685 \begin_inset Formula $\lceil$
5695 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
5698 \begin_layout Plain Layout
5706 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
5709 \begin_layout Plain Layout
5710 \begin_inset Formula $\lfloor$
5720 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
5723 \begin_layout Plain Layout
5729 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
5732 \begin_layout Plain Layout
5733 \begin_inset Formula $/$
5743 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
5746 \begin_layout Plain Layout
5752 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
5755 \begin_layout Plain Layout
5756 \begin_inset Formula $|$
5770 \begin_inset space \hfill{}
5774 \begin_inset Tabular
5775 <lyxtabular version="3" rows="9" columns="2">
5776 <features rotate="0" tabularvalignment="middle">
5777 <column alignment="center" valignment="top" width="0pt">
5778 <column alignment="center" valignment="top" width="0pt">
5780 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
5783 \begin_layout Plain Layout
5789 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
5792 \begin_layout Plain Layout
5800 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
5803 \begin_layout Plain Layout
5809 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
5812 \begin_layout Plain Layout
5813 \begin_inset Formula $)$
5823 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
5826 \begin_layout Plain Layout
5832 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
5835 \begin_layout Plain Layout
5836 \begin_inset Formula $\}$
5846 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
5849 \begin_layout Plain Layout
5855 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
5858 \begin_layout Plain Layout
5859 \begin_inset Formula $]$
5869 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
5872 \begin_layout Plain Layout
5880 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
5883 \begin_layout Plain Layout
5884 \begin_inset Formula $\rangle$
5894 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
5897 \begin_layout Plain Layout
5905 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
5908 \begin_layout Plain Layout
5909 \begin_inset Formula $\rceil$
5919 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
5922 \begin_layout Plain Layout
5930 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
5933 \begin_layout Plain Layout
5934 \begin_inset Formula $\rfloor$
5944 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
5947 \begin_layout Plain Layout
5957 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
5960 \begin_layout Plain Layout
5961 \begin_inset Formula $\backslash$
5971 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
5974 \begin_layout Plain Layout
5982 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
5985 \begin_layout Plain Layout
5986 \begin_inset Formula $\|$
6000 \begin_inset space \hfill{}
6006 \begin_layout Standard
6009 \begin_inset Note Greyedout
6012 \begin_layout Plain Layout
6017 In TeX-mode the command
6024 \begin_inset Index idx
6027 \begin_layout Plain Layout
6035 must be used for the backslash, because the command
6043 produces a line break there.
6051 \begin_layout Standard
6052 For all characters listed above the size can be adjusted with the commands
6053 described in the following two subsections.
6054 When using these commands, the characters < and > can directly be used
6055 instead of the commands
6070 \begin_layout Subsubsection
6072 \begin_inset CommandInset label
6074 name "sub:Manual-Bracket-Size"
6079 \begin_inset Index idx
6082 \begin_layout Plain Layout
6083 Bracket size ! manual
6091 \begin_layout Standard
6092 The bracket size can be specified manually by the LaTeX-commands
6099 \begin_inset Index idx
6102 \begin_layout Plain Layout
6135 denotes the smallest and
6141 the largest bracket size.
6144 \begin_layout Standard
6145 These commands are used to emphasize levels of brackets:
6148 \begin_layout Standard
6150 \begin_inset Tabular
6151 <lyxtabular version="3" rows="2" columns="2">
6152 <features rotate="0" tabularvalignment="middle">
6153 <column alignment="center" valignment="top" width="0pt">
6154 <column alignment="center" valignment="top" width="0pt">
6156 <cell alignment="center" valignment="top" usebox="none">
6159 \begin_layout Plain Layout
6160 all brackets in the same size:
6165 <cell alignment="center" valignment="top" usebox="none">
6168 \begin_layout Plain Layout
6169 \begin_inset Formula $((A+B)(A-B))^{C}\raisebox{-4mm}{}$
6179 <cell alignment="center" valignment="top" usebox="none">
6182 \begin_layout Plain Layout
6188 <cell alignment="center" valignment="top" usebox="none">
6191 \begin_layout Plain Layout
6192 \begin_inset Formula $\Big((A+B)(A-B)\Big)^{C}$
6206 \begin_inset Note Note
6209 \begin_layout Plain Layout
6216 is only used as spacer.
6224 \begin_layout Standard
6225 For the second formula the command
6232 \begin_inset space \textvisiblespace{}
6240 \begin_layout Standard
6241 Here is an overview about all bracket sizes:
6244 \begin_layout Standard
6261 \begin_inset space \textvisiblespace{}
6269 \begin_inset space \textvisiblespace{}
6273 \begin_inset space \textvisiblespace{}
6283 \begin_layout Standard
6285 \begin_inset Formula $\Bigg(\exp\bigg<\Big[\big\{\ln(3x)\big\}^{2}\sin(x)\Big]^{A}\bigg>\Bigg)^{0,5}$
6291 \begin_layout Standard
6298 -commands there is the variant
6305 \begin_inset Index idx
6308 \begin_layout Plain Layout
6316 that adds a bit more space between the bracket and its content, and the
6330 \begin_inset Index idx
6333 \begin_layout Plain Layout
6343 , that don't add additional space.
6348 at the end of the command
6354 is for a left bracket; for a right bracket this will be replaced by an
6360 A left or right bracket can each be an opening or closing bracket.
6363 \begin_layout Standard
6364 In the following table is a comparison of the variants:
6367 \begin_layout Standard
6369 \begin_inset Tabular
6370 <lyxtabular version="3" rows="5" columns="2">
6371 <features rotate="0" tabularvalignment="middle">
6372 <column alignment="center" valignment="middle">
6373 <column alignment="center" valignment="middle">
6375 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
6378 \begin_layout Plain Layout
6384 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
6387 \begin_layout Plain Layout
6389 \begin_inset Note Note
6392 \begin_layout Plain Layout
6399 is only used as spacer.
6411 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
6414 \begin_layout Plain Layout
6424 \begin_inset space \textvisiblespace{}
6434 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
6437 \begin_layout Plain Layout
6438 \begin_inset Formula $\raisebox{5.5mm}{}\Bigm(\bigm(\ln(3x)\bigm)^{2}\Bigm)\raisebox{-3.25mm}{}$
6448 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
6451 \begin_layout Plain Layout
6461 \begin_inset space \textvisiblespace{}
6471 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
6474 \begin_layout Plain Layout
6475 \begin_inset Formula $\raisebox{5.5mm}{}\Big(\big(\ln(3x)\big)^{2}\Big)\raisebox{-3.25mm}{}$
6485 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
6488 \begin_layout Plain Layout
6498 \begin_inset space \textvisiblespace{}
6508 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
6511 \begin_layout Plain Layout
6512 \begin_inset Formula $\raisebox{5.5mm}{}\Bigl(\bigl(\ln(3x)\bigr)^{2}\Bigr)\raisebox{-3.25mm}{}$
6522 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
6525 \begin_layout Plain Layout
6537 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
6540 \begin_layout Plain Layout
6541 \begin_inset Formula $\raisebox{4.5mm}{}\bigl)\ln(3x)\bigr(\raisebox{-2mm}{}$
6557 \begin_layout Subsubsection
6558 Automatic Bracket Size
6559 \begin_inset CommandInset label
6561 name "sub:Automatic-Bracket-Size"
6566 \begin_inset Index idx
6569 \begin_layout Plain Layout
6570 Bracket size ! automatic
6578 \begin_layout Standard
6579 Brackets with variable size can be inserted with the commands
6586 \begin_inset Index idx
6589 \begin_layout Plain Layout
6604 \begin_inset Index idx
6607 \begin_layout Plain Layout
6615 or via the math toolbar button
6616 \begin_inset Graphics
6617 filename ../images/dialog-show_mathdelimiter.png
6635 the wanted bracket must be inserted.
6636 The bracket size will then automatically be calculated for the output.
6639 \begin_layout Standard
6641 normal bracket: The command
6648 \begin_inset space \textvisiblespace{}
6652 \begin_inset Formula $\downarrow$
6656 \begin_inset space \textvisiblespace{}
6662 \begin_inset Formula
6672 \begin_layout Standard
6674 multiline bracket: The command
6683 \begin_inset space \textvisiblespace{}
6687 \begin_inset Formula $\downarrow$
6691 \begin_inset space \textvisiblespace{}
6699 \begin_inset Formula
6701 \ln\left(\frac{A}{C}\right)
6709 \begin_layout Standard
6725 \begin_inset space ~
6731 This has the advantage that you can see in LyX immediately the real bracket
6732 size and that the matching right bracket will be created too.
6733 \begin_inset Newline newline
6736 The command for the last example would then be:
6747 \begin_inset space \textvisiblespace{}
6751 \begin_inset Formula $\downarrow$
6757 \begin_layout Standard
6758 To omit a left or right bracket, a dot is inserted for the omitted bracket.
6759 For example the command
6766 \begin_inset space \textvisiblespace{}
6770 \begin_inset Formula $\downarrow$
6774 \begin_inset space \textvisiblespace{}
6784 \begin_inset Formula
6786 \left.\frac{A}{B}\right\}
6805 will be converted by LyX to brackets in the right size when the document
6806 is reloaded and an omitted bracket will appear as dashed line.
6809 \begin_layout Standard
6810 \begin_inset VSpace bigskip
6813 Because all popular LaTeX-Distributions use eTeX, an extension to LaTeX,
6821 \begin_inset Index idx
6824 \begin_layout Plain Layout
6832 is additionally available for all brackets and limits.
6833 With this command the height of the following character is adapted to the
6834 one of the surrounding brackets, what is e.
6835 \begin_inset space \thinspace{}
6839 \begin_inset space \space{}
6842 needed for physical vectors:
6843 \begin_inset Formula
6845 \left\langle \phi\:\middle|\: J=\frac{3}{2}\,,\, M_{J}\right\rangle
6850 For physical vectors there is a special LaTeX-package, described in
6851 \begin_inset CommandInset ref
6853 reference "sub:Physical-Vectors"
6860 \begin_layout Subsection
6862 \begin_inset Index idx
6865 \begin_layout Plain Layout
6866 Brackets ! horizontal
6874 \begin_layout Standard
6876 \begin_inset Tabular
6877 <lyxtabular version="3" rows="4" columns="2">
6878 <features rotate="0" tabularvalignment="middle">
6879 <column alignment="center" valignment="top" width="0pt">
6880 <column alignment="center" valignment="top" width="0pt">
6882 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
6885 \begin_layout Plain Layout
6887 \begin_inset Note Note
6890 \begin_layout Plain Layout
6897 is only used as spacer.
6907 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
6910 \begin_layout Plain Layout
6918 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
6921 \begin_layout Plain Layout
6925 \begin_layout Plain Layout
6937 \begin_inset space \textvisiblespace{}
6941 \begin_inset space \textvisiblespace{}
6948 \begin_layout Plain Layout
6956 \begin_inset Index idx
6959 \begin_layout Plain Layout
6972 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
6975 \begin_layout Plain Layout
6976 \begin_inset Formula $\overbrace{A+B}^{3}$
6986 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
6989 \begin_layout Plain Layout
6993 \begin_layout Plain Layout
7005 \begin_inset space \textvisiblespace{}
7009 \begin_inset space \textvisiblespace{}
7016 \begin_layout Plain Layout
7024 \begin_inset Index idx
7027 \begin_layout Plain Layout
7040 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
7043 \begin_layout Plain Layout
7044 \begin_inset Formula $\underbrace{A+B}_{5}$
7054 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
7057 \begin_layout Plain Layout
7061 \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{}
7087 \begin_inset space \textvisiblespace{}
7095 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
7098 \begin_layout Plain Layout
7099 \begin_inset Formula $\overbrace{\underbrace{A+B_{w}}_{7}}^{C}$
7115 \begin_layout Standard
7116 In the last example it doesn't matter if
7128 is inserted at first.
7131 \begin_layout Standard
7132 \begin_inset VSpace bigskip
7135 When brackets are needed that overlap each other, multiline formulas, as
7137 \begin_inset CommandInset ref
7139 reference "sec:Multiline-Formulas"
7144 \begin_inset Formula
7146 A & = & \underbrace{gggg+bbqq}_{r}+\: dddd\\
7147 & & \hphantom{gggg+\:}\underbrace{\hphantom{bbqq+dddd}}_{s}
7152 In the first row the formula is inserted together with the first brace.
7153 It is hereby important that the space command
7157 \begin_layout Plain Layout
7158 Space commands are explained in
7159 \begin_inset CommandInset ref
7161 reference "sub:Predefined-Space"
7176 is inserted before the first
7177 \begin_inset Formula $d$
7180 , because the brace that ends behind the
7181 \begin_inset Formula $q$
7184 prevents that the following
7185 \begin_inset Quotes eld
7189 \begin_inset Quotes erd
7192 is surrounded by space.
7196 \begin_layout Plain Layout
7197 because a bracket is not handled as a character, see
7198 \begin_inset CommandInset ref
7200 reference "sub:Binary-Operators"
7209 In the second row the second brace is inserted.
7210 As it should begin before the
7211 \begin_inset Formula $b$
7226 \begin_layout Plain Layout
7234 \begin_inset CommandInset ref
7236 reference "sub:Placeholders"
7245 This space is needed because the
7246 \begin_inset Quotes eld
7250 \begin_inset Quotes erd
7253 is also surrounded by space in the formula.
7254 The brace is placed under the command
7263 \begin_layout Standard
7264 It gets more complicated when brackets overlap each other, like in the following
7269 \begin_layout Plain Layout
7281 \begin_inset Formula
7283 & & \hphantom{gggg+\:}\overbrace{\hphantom{bbqq+dddd}}^{s}\\
7284 A & = & \underbrace{gggg+bbqq}_{r}+\: dddd
7293 \begin_layout Plain Layout
7304 The first formula row is the same as the second row of the previous example,
7305 with the difference that the brace is above.
7306 The second row contains the formula together with the second brace.
7307 To avoid that there is space between the upper brace in the first row and
7308 the formula, the row spacing needs to be reduced.
7309 This is not easily possible due to a bug in LyX
7313 \begin_layout Plain Layout
7314 \begin_inset CommandInset href
7316 name "LyX-bug #1505"
7317 target "http://www.lyx.org/trac/ticket/1505"
7327 As a solution for the problem, the global formula row separation
7334 \begin_inset Index idx
7337 \begin_layout Plain Layout
7345 must be changed to -6
7346 \begin_inset space \thinspace{}
7349 pt before the formula with the command
7364 is set back after the formula to the standard value of 3
7365 \begin_inset space \thinspace{}
7368 pt using the same command.
7369 More about the row separation in formulas is explained in
7370 \begin_inset CommandInset ref
7372 reference "sub:Line-Separation"
7379 \begin_layout Section
7381 \begin_inset Index idx
7384 \begin_layout Plain Layout
7393 \begin_layout Standard
7394 Arrows can be inserted via the math toolbar button
7395 \begin_inset Graphics
7396 filename ../images/math/leftarrow.png
7401 or the commands listed in the following subsections.
7404 \begin_layout Subsection
7406 \begin_inset Index idx
7409 \begin_layout Plain Layout
7418 \begin_layout Standard
7419 \begin_inset space \hfill{}
7423 \begin_inset Tabular
7424 <lyxtabular version="3" rows="8" columns="2">
7425 <features rotate="0" tabularvalignment="middle">
7426 <column alignment="center" valignment="top" width="0pt">
7427 <column alignment="center" valignment="top" width="0pt">
7429 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
7432 \begin_layout Plain Layout
7438 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
7441 \begin_layout Plain Layout
7449 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
7452 \begin_layout Plain Layout
7460 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
7463 \begin_layout Plain Layout
7464 \begin_inset Formula $\gets$
7474 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
7477 \begin_layout Plain Layout
7485 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
7488 \begin_layout Plain Layout
7489 \begin_inset Formula $\Leftarrow$
7499 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
7502 \begin_layout Plain Layout
7510 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
7513 \begin_layout Plain Layout
7514 \begin_inset Formula $\longleftarrow$
7524 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
7527 \begin_layout Plain Layout
7535 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
7538 \begin_layout Plain Layout
7539 \begin_inset Formula $\Longleftarrow$
7549 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
7552 \begin_layout Plain Layout
7560 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
7563 \begin_layout Plain Layout
7564 \begin_inset Formula $\leftharpoonup$
7574 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
7577 \begin_layout Plain Layout
7585 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
7588 \begin_layout Plain Layout
7589 \begin_inset Formula $\leftharpoondown$
7599 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
7602 \begin_layout Plain Layout
7610 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
7613 \begin_layout Plain Layout
7614 \begin_inset Formula $\hookleftarrow$
7628 \begin_inset space \hfill{}
7632 \begin_inset Tabular
7633 <lyxtabular version="3" rows="8" columns="2">
7634 <features rotate="0" tabularvalignment="middle">
7635 <column alignment="center" valignment="top" width="0pt">
7636 <column alignment="center" valignment="top" width="0pt">
7638 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
7641 \begin_layout Plain Layout
7647 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
7650 \begin_layout Plain Layout
7658 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
7661 \begin_layout Plain Layout
7669 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
7672 \begin_layout Plain Layout
7673 \begin_inset Formula $\to$
7683 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
7686 \begin_layout Plain Layout
7694 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
7697 \begin_layout Plain Layout
7698 \begin_inset Formula $\Rightarrow$
7708 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
7711 \begin_layout Plain Layout
7719 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
7722 \begin_layout Plain Layout
7723 \begin_inset Formula $\longrightarrow$
7733 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
7736 \begin_layout Plain Layout
7744 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
7747 \begin_layout Plain Layout
7748 \begin_inset Formula $\Longrightarrow$
7758 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
7761 \begin_layout Plain Layout
7769 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
7772 \begin_layout Plain Layout
7773 \begin_inset Formula $\rightharpoonup$
7783 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
7786 \begin_layout Plain Layout
7794 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
7797 \begin_layout Plain Layout
7798 \begin_inset Formula $\rightharpoondown$
7808 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
7811 \begin_layout Plain Layout
7819 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
7822 \begin_layout Plain Layout
7823 \begin_inset Formula $\hookrightarrow$
7837 \begin_inset space \hfill{}
7843 \begin_layout Standard
7844 \begin_inset space \hfill{}
7848 \begin_inset Tabular
7849 <lyxtabular version="3" rows="6" columns="2">
7850 <features rotate="0" tabularvalignment="middle">
7851 <column alignment="center" valignment="top" width="0pt">
7852 <column alignment="center" valignment="top" width="0pt">
7854 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
7857 \begin_layout Plain Layout
7863 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
7866 \begin_layout Plain Layout
7874 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
7877 \begin_layout Plain Layout
7885 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
7888 \begin_layout Plain Layout
7889 \begin_inset Formula $\leftrightarrow$
7899 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
7902 \begin_layout Plain Layout
7910 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
7913 \begin_layout Plain Layout
7914 \begin_inset Formula $\Leftrightarrow$
7924 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
7927 \begin_layout Plain Layout
7935 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
7938 \begin_layout Plain Layout
7939 \begin_inset Formula $\longleftrightarrow$
7949 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
7952 \begin_layout Plain Layout
7960 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
7963 \begin_layout Plain Layout
7964 \begin_inset Formula $\Longleftrightarrow$
7974 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
7977 \begin_layout Plain Layout
7985 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
7988 \begin_layout Plain Layout
7989 \begin_inset Formula $\rightleftharpoons$
8003 \begin_inset space \hspace{}
8008 \begin_inset space \hfill{}
8012 \begin_inset Tabular
8013 <lyxtabular version="3" rows="5" columns="2">
8014 <features rotate="0" tabularvalignment="middle">
8015 <column alignment="center" valignment="top" width="0pt">
8016 <column alignment="center" valignment="top" width="0pt">
8018 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
8021 \begin_layout Plain Layout
8027 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
8030 \begin_layout Plain Layout
8038 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
8041 \begin_layout Plain Layout
8049 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
8052 \begin_layout Plain Layout
8053 \begin_inset Formula $\mapsto$
8063 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
8066 \begin_layout Plain Layout
8074 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
8077 \begin_layout Plain Layout
8078 \begin_inset Formula $\longmapsto$
8088 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
8091 \begin_layout Plain Layout
8099 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
8102 \begin_layout Plain Layout
8103 \begin_inset Formula $\leadsto$
8113 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
8116 \begin_layout Plain Layout
8124 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
8127 \begin_layout Plain Layout
8128 \begin_inset Formula $\dasharrow$
8142 \begin_inset space \hfill{}
8148 \begin_layout Standard
8149 \begin_inset VSpace medskip
8152 Arrows used as accents like e.
8153 \begin_inset space \thinspace{}
8157 \begin_inset space \space{}
8160 vector arrows are listed in
8161 \begin_inset CommandInset ref
8163 reference "sec:Accents"
8170 \begin_layout Standard
8171 \begin_inset VSpace bigskip
8174 Furthermore there are the labeled arrows
8175 \begin_inset Index idx
8178 \begin_layout Plain Layout
8191 \begin_inset Index idx
8194 \begin_layout Plain Layout
8209 \begin_inset Index idx
8212 \begin_layout Plain Layout
8219 \begin_layout Plain Layout
8234 When inserting one of these commands in a formula, an arrow with two blue
8235 boxes appear where the label can be inserted.
8236 The length of the arrow adapts to the label width.
8239 \begin_layout Standard
8241 \begin_inset Tabular
8242 <lyxtabular version="3" rows="3" columns="2">
8243 <features rotate="0" tabularvalignment="middle">
8244 <column alignment="center" valignment="top" width="0pt">
8245 <column alignment="center" valignment="top" width="0pt">
8247 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
8250 \begin_layout Plain Layout
8256 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
8259 \begin_layout Plain Layout
8261 \begin_inset Note Note
8264 \begin_layout Plain Layout
8271 is only used as spacer.
8283 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
8286 \begin_layout Plain Layout
8290 \begin_inset space \textvisiblespace{}
8294 \begin_inset Formula $\downarrow$
8298 \begin_inset Formula $\to$
8306 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
8309 \begin_layout Plain Layout
8310 \begin_inset Formula $\raisebox{5mm}{}F(a)\xleftarrow[x>0]{x=a}F(x)\raisebox{-4mm}{}$
8320 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
8323 \begin_layout Plain Layout
8327 \begin_inset space \textvisiblespace{}
8331 \begin_inset Formula $\downarrow$
8335 \begin_inset Formula $\to$
8343 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
8346 \begin_layout Plain Layout
8347 \begin_inset Formula $\raisebox{5mm}{}F(x)\xrightarrow[x>0]{x=a}F(a)\raisebox{-4mm}{}$
8363 \begin_layout Subsection
8364 Vertical and diagonal Arrows
8365 \begin_inset Index idx
8368 \begin_layout Plain Layout
8375 \begin_inset Index idx
8378 \begin_layout Plain Layout
8387 \begin_layout Standard
8388 \begin_inset space \hfill{}
8392 \begin_inset Tabular
8393 <lyxtabular version="3" rows="7" columns="2">
8394 <features rotate="0" tabularvalignment="middle">
8395 <column alignment="center" valignment="top" width="0pt">
8396 <column alignment="center" valignment="top" width="0pt">
8398 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
8401 \begin_layout Plain Layout
8407 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
8410 \begin_layout Plain Layout
8418 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
8421 \begin_layout Plain Layout
8429 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
8432 \begin_layout Plain Layout
8433 \begin_inset Formula $\uparrow$
8443 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
8446 \begin_layout Plain Layout
8454 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
8457 \begin_layout Plain Layout
8458 \begin_inset Formula $\Uparrow$
8468 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
8471 \begin_layout Plain Layout
8479 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
8482 \begin_layout Plain Layout
8483 \begin_inset Formula $\updownarrow$
8493 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
8496 \begin_layout Plain Layout
8504 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
8507 \begin_layout Plain Layout
8508 \begin_inset Formula $\Updownarrow$
8518 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
8521 \begin_layout Plain Layout
8529 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
8532 \begin_layout Plain Layout
8533 \begin_inset Formula $\Downarrow$
8543 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
8546 \begin_layout Plain Layout
8554 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
8557 \begin_layout Plain Layout
8558 \begin_inset Formula $\downarrow$
8572 \begin_inset space \hfill{}
8576 \begin_inset Tabular
8577 <lyxtabular version="3" rows="5" columns="2">
8578 <features rotate="0" tabularvalignment="middle">
8579 <column alignment="center" valignment="top" width="0pt">
8580 <column alignment="center" valignment="top" width="0pt">
8582 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
8585 \begin_layout Plain Layout
8591 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
8594 \begin_layout Plain Layout
8602 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
8605 \begin_layout Plain Layout
8613 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
8616 \begin_layout Plain Layout
8617 \begin_inset Formula $\nearrow$
8627 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
8630 \begin_layout Plain Layout
8638 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
8641 \begin_layout Plain Layout
8642 \begin_inset Formula $\searrow$
8652 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
8655 \begin_layout Plain Layout
8663 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
8666 \begin_layout Plain Layout
8667 \begin_inset Formula $\swarrow$
8677 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
8680 \begin_layout Plain Layout
8688 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
8691 \begin_layout Plain Layout
8692 \begin_inset Formula $\nwarrow$
8706 \begin_inset space \hfill{}
8712 \begin_layout Standard
8713 \begin_inset VSpace medskip
8716 Vertical arrows can be used also as delimiters together with the commands
8718 \begin_inset CommandInset ref
8720 reference "sub:Manual-Bracket-Size"
8725 \begin_inset CommandInset ref
8727 reference "sub:Automatic-Bracket-Size"
8734 \begin_layout Section
8736 \begin_inset CommandInset label
8743 \begin_inset Index idx
8746 \begin_layout Plain Layout
8755 \begin_layout Standard
8756 Accents can be inserted via the math toolbar button
8757 \begin_inset Graphics
8758 filename ../images/math/hat.png
8763 or the commands listed in the following subsections.
8766 \begin_layout Subsection
8767 Accents for one Character
8771 \begin_layout Plain Layout
8784 \begin_layout Plain Layout
8786 \begin_inset CommandInset ref
8788 reference "sub:Accents-in-Text"
8801 \begin_layout Plain Layout
8809 \begin_inset Note Note
8812 \begin_layout Plain Layout
8819 is used to avoid that the footnote appears in the PDF-bookmark.
8822 \begin_layout Plain Layout
8830 \begin_inset CommandInset ref
8832 reference "sub:Formulas-in-Section"
8842 \begin_inset CommandInset label
8844 name "sub:Accents-for-one"
8849 \begin_inset Index idx
8852 \begin_layout Plain Layout
8853 Accents ! for one character
8861 \begin_layout Standard
8862 \begin_inset space \hfill{}
8866 \begin_inset Tabular
8867 <lyxtabular version="3" rows="8" columns="2">
8868 <features rotate="0" tabularvalignment="middle">
8869 <column alignment="center" valignment="top" width="0pt">
8870 <column alignment="center" valignment="top" width="0pt">
8872 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
8875 \begin_layout Plain Layout
8881 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
8884 \begin_layout Plain Layout
8886 \begin_inset Note Note
8889 \begin_layout Plain Layout
8896 is only used as spacer.
8908 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
8911 \begin_layout Plain Layout
8915 \begin_inset space \textvisiblespace{}
8923 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
8926 \begin_layout Plain Layout
8927 \begin_inset Formula $\raisebox{5mm}{}\dot{A}$
8937 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
8940 \begin_layout Plain Layout
8944 \begin_inset space \textvisiblespace{}
8952 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
8955 \begin_layout Plain Layout
8956 \begin_inset Formula $\raisebox{5mm}{}\ddot{A}$
8966 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
8969 \begin_layout Plain Layout
8973 \begin_inset space \textvisiblespace{}
8981 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
8984 \begin_layout Plain Layout
8985 \begin_inset Formula $\raisebox{5mm}{}\dddot{A}$
8995 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
8998 \begin_layout Plain Layout
9002 \begin_inset space \textvisiblespace{}
9010 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
9013 \begin_layout Plain Layout
9014 \begin_inset Formula $\raisebox{5mm}{}\ddddot{A}$
9024 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
9027 \begin_layout Plain Layout
9031 \begin_inset space \textvisiblespace{}
9035 \begin_inset Index idx
9038 \begin_layout Plain Layout
9049 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
9052 \begin_layout Plain Layout
9053 \begin_inset Formula $\raisebox{5mm}{}\vec{A}$
9063 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
9066 \begin_layout Plain Layout
9070 \begin_inset space \textvisiblespace{}
9078 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
9081 \begin_layout Plain Layout
9082 \begin_inset Formula $\raisebox{5mm}{}\bar{A}$
9092 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
9095 \begin_layout Plain Layout
9099 \begin_inset space \textvisiblespace{}
9107 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
9110 \begin_layout Plain Layout
9111 \begin_inset Formula $\raisebox{5mm}{}\mathring{A}$
9125 \begin_inset space \hfill{}
9129 \begin_inset Tabular
9130 <lyxtabular version="3" rows="7" columns="2">
9131 <features rotate="0" tabularvalignment="middle">
9132 <column alignment="center" valignment="top" width="0pt">
9133 <column alignment="center" valignment="top" width="0pt">
9135 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
9138 \begin_layout Plain Layout
9144 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
9147 \begin_layout Plain Layout
9155 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
9158 \begin_layout Plain Layout
9162 \begin_inset space \textvisiblespace{}
9170 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
9173 \begin_layout Plain Layout
9174 \begin_inset Formula $\raisebox{5mm}{}\tilde{A}$
9184 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
9187 \begin_layout Plain Layout
9191 \begin_inset space \textvisiblespace{}
9199 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
9202 \begin_layout Plain Layout
9203 \begin_inset Formula $\raisebox{5mm}{}\hat{A}$
9213 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
9216 \begin_layout Plain Layout
9220 \begin_inset space \textvisiblespace{}
9228 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
9231 \begin_layout Plain Layout
9232 \begin_inset Formula $\raisebox{5mm}{}\check{A}$
9242 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
9245 \begin_layout Plain Layout
9249 \begin_inset space \textvisiblespace{}
9257 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
9260 \begin_layout Plain Layout
9261 \begin_inset Formula $\raisebox{5mm}{}\acute{A}$
9271 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
9274 \begin_layout Plain Layout
9278 \begin_inset space \textvisiblespace{}
9286 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
9289 \begin_layout Plain Layout
9290 \begin_inset Formula $\raisebox{5mm}{}\grave{A}$
9300 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
9303 \begin_layout Plain Layout
9307 \begin_inset space \textvisiblespace{}
9315 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
9318 \begin_layout Plain Layout
9319 \begin_inset Formula $\raisebox{5mm}{}\breve{A}$
9333 \begin_inset space \hfill{}
9339 \begin_layout Standard
9340 \begin_inset VSpace bigskip
9346 \begin_layout Standard
9347 You can directly insert accents like é to formulas.
9348 LyX will transform them to the corresponding accent command.
9350 \begin_inset Index idx
9353 \begin_layout Plain Layout
9359 it is better to insert a quotation mark before the vowel.
9360 These two characters are then treated by LaTeX as
9364 character when the formula part with the umlaut is marked as German.
9372 \begin_inset Quotes eld
9376 \begin_inset Quotes erd
9379 umlauts are created as demonstrated in the following example:
9382 \begin_layout Standard
9383 \begin_inset VSpace -2mm
9389 \begin_layout Standard
9391 \begin_inset Tabular
9392 <lyxtabular version="3" rows="3" columns="2">
9393 <features rotate="0" tabularvalignment="middle">
9394 <column alignment="center" valignment="top">
9395 <column alignment="center" valignment="top">
9397 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
9400 \begin_layout Plain Layout
9406 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
9409 \begin_layout Plain Layout
9411 \begin_inset Note Note
9414 \begin_layout Plain Layout
9422 \begin_inset space \thinspace{}
9425 pt space are only used as spacer.
9437 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
9440 \begin_layout Plain Layout
9443 \begin_inset Quotes grd
9451 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
9454 \begin_layout Plain Layout
9455 \begin_inset space \hspace{}
9462 \begin_inset Formula $"i$
9472 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
9475 \begin_layout Plain Layout
9479 \begin_inset space \textvisiblespace{}
9487 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
9490 \begin_layout Plain Layout
9491 \begin_inset Formula $\raisebox{5mm}{}\ddot{i}$
9507 \begin_layout Standard
9508 Another advantage to
9514 is that umlauts can directly be converted to mathematical text because
9515 the accent commands above are
9521 in mathematical text
9524 To convert an accented character to mathematical text, only the character
9525 under the accent may be converted.
9526 This applies also for all other conversions, e.
9527 \begin_inset space \thinspace{}
9531 \begin_inset space \space{}
9537 \begin_layout Standard
9538 In mathematical text, umlauts and other accented characters can directly
9542 \begin_layout Subsection
9543 Accents for several Characters
9544 \begin_inset Index idx
9547 \begin_layout Plain Layout
9548 Accents ! for several characters
9556 \begin_layout Standard
9557 \begin_inset space \hfill{}
9561 \begin_inset Tabular
9562 <lyxtabular version="3" rows="5" columns="2">
9563 <features rotate="0" tabularvalignment="middle">
9564 <column alignment="center" valignment="top" width="0pt">
9565 <column alignment="center" valignment="top" width="0pt">
9567 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
9570 \begin_layout Plain Layout
9576 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
9579 \begin_layout Plain Layout
9581 \begin_inset Note Note
9584 \begin_layout Plain Layout
9591 is only used as spacer.
9603 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
9606 \begin_layout Plain Layout
9610 \begin_inset space \textvisiblespace{}
9618 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
9621 \begin_layout Plain Layout
9622 \begin_inset Formula $\raisebox{6mm}{}\overleftarrow{A=B}\raisebox{-2mm}{}$
9632 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
9635 \begin_layout Plain Layout
9639 \begin_inset space \textvisiblespace{}
9647 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
9650 \begin_layout Plain Layout
9651 \begin_inset Formula $\raisebox{5mm}{}\underleftarrow{A=B}\raisebox{-3mm}{}$
9661 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
9664 \begin_layout Plain Layout
9668 \begin_inset space \textvisiblespace{}
9676 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
9679 \begin_layout Plain Layout
9680 \begin_inset Formula $\raisebox{6mm}{}\overleftrightarrow{A=B}\raisebox{-2mm}{}$
9690 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
9693 \begin_layout Plain Layout
9697 \begin_inset space \textvisiblespace{}
9705 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
9708 \begin_layout Plain Layout
9709 \begin_inset Formula $\raisebox{5mm}{}\underleftrightarrow{A=B}\raisebox{-3mm}{}$
9723 \begin_inset space \hfill{}
9727 \begin_inset Tabular
9728 <lyxtabular version="3" rows="5" columns="2">
9729 <features rotate="0" tabularvalignment="middle">
9730 <column alignment="center" valignment="top" width="0pt">
9731 <column alignment="center" valignment="top" width="0pt">
9733 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
9736 \begin_layout Plain Layout
9742 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
9745 \begin_layout Plain Layout
9753 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
9756 \begin_layout Plain Layout
9760 \begin_inset space \textvisiblespace{}
9768 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
9771 \begin_layout Plain Layout
9772 \begin_inset Formula $\raisebox{6mm}{}\overrightarrow{A=B}\raisebox{-2mm}{}$
9782 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
9785 \begin_layout Plain Layout
9789 \begin_inset space \textvisiblespace{}
9797 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
9800 \begin_layout Plain Layout
9801 \begin_inset Formula $\raisebox{5mm}{}\underrightarrow{A=B}\raisebox{-3mm}{}$
9811 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
9814 \begin_layout Plain Layout
9818 \begin_inset space \textvisiblespace{}
9826 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
9829 \begin_layout Plain Layout
9830 \begin_inset Formula $\raisebox{6mm}{}\widetilde{A=B}\raisebox{-2mm}{}$
9840 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
9843 \begin_layout Plain Layout
9847 \begin_inset space \textvisiblespace{}
9855 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
9858 \begin_layout Plain Layout
9859 \begin_inset Formula $\raisebox{6mm}{}\widehat{A=B}\raisebox{-2mm}{}$
9873 \begin_inset space \hfill{}
9879 \begin_layout Standard
9880 \begin_inset VSpace medskip
9883 With these commands as many characters as you like can be accented.
9896 will only be set in the output with a length of three characters, as shown
9897 in the following example:
9898 \begin_inset Formula
9908 \begin_layout Standard
9916 \begin_inset Index idx
9919 \begin_layout Plain Layout
9934 \begin_inset Index idx
9937 \begin_layout Plain Layout
9945 described in the previous subsection it is also possible to accent several
9952 \begin_inset space \textvisiblespace{}
9956 \begin_inset Formula $\downarrow$
9962 \begin_inset Formula
9972 \begin_layout Standard
9973 \begin_inset Newpage newpage
9979 \begin_layout Section
9981 \begin_inset CommandInset label
9988 \begin_inset Index idx
9991 \begin_layout Plain Layout
10000 \begin_layout Subsection
10002 \begin_inset CommandInset label
10004 name "sub:Predefined-Space"
10009 \begin_inset Index idx
10012 \begin_layout Plain Layout
10013 Space ! horizontal ! predefined
10021 \begin_layout Standard
10022 Sometimes it is necessary to insert horizontal space into a formula.
10023 This is done by inserting a protected space (shortcut
10026 arg "command-alternatives space-insert protected ; math-space"
10031 \begin_inset Quotes eld
10037 \begin_inset space \textvisiblespace{}
10043 \begin_inset Quotes erd
10046 appears and by pressing
10050 several times one can select one of eight different space sizes.
10051 The spaces can also be inserted using the math toolbar button
10052 \begin_inset Graphics
10053 filename ../images/math/space.png
10058 or special commands.
10059 Independent from the inserted command, one can select the size again by
10067 \begin_layout Standard
10070 \begin_inset VSpace -5mm
10074 \begin_inset Tabular
10075 <lyxtabular version="3" rows="3" columns="7">
10076 <features rotate="0" tabularvalignment="middle">
10077 <column alignment="center" valignment="middle" width="6.8cm">
10078 <column alignment="center" valignment="top">
10079 <column alignment="center" valignment="top">
10080 <column alignment="center" valignment="top">
10081 <column alignment="center" valignment="top">
10082 <column alignment="center" valignment="top">
10083 <column alignment="center" valignment="top">
10085 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
10088 \begin_layout Plain Layout
10094 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
10097 \begin_layout Plain Layout
10105 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
10108 \begin_layout Plain Layout
10116 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
10119 \begin_layout Plain Layout
10127 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
10130 \begin_layout Plain Layout
10138 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
10141 \begin_layout Plain Layout
10149 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
10152 \begin_layout Plain Layout
10162 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
10165 \begin_layout Plain Layout
10170 keystrokes after inserting the protected space
10175 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
10178 \begin_layout Plain Layout
10184 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
10187 \begin_layout Plain Layout
10193 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
10196 \begin_layout Plain Layout
10202 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
10205 \begin_layout Plain Layout
10211 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
10214 \begin_layout Plain Layout
10220 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
10223 \begin_layout Plain Layout
10231 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
10234 \begin_layout Plain Layout
10240 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
10243 \begin_layout Plain Layout
10244 \begin_inset Formula $A\, B$
10252 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
10255 \begin_layout Plain Layout
10256 \begin_inset Formula $A\: B$
10264 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
10267 \begin_layout Plain Layout
10268 \begin_inset Formula $A\; B$
10276 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
10279 \begin_layout Plain Layout
10280 \begin_inset Formula $A\quad B$
10288 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
10291 \begin_layout Plain Layout
10292 \begin_inset Formula $A\qquad B$
10300 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
10303 \begin_layout Plain Layout
10304 \begin_inset Formula $A\! B$
10320 \begin_layout Standard
10321 The last size seem to produce no space.
10322 It is displayed red in LyX contrary to the other sizes, because it is a
10324 There are two more negative spaces:
10327 \begin_layout Standard
10329 \begin_inset Tabular
10330 <lyxtabular version="3" rows="3" columns="3">
10331 <features rotate="0" tabularvalignment="middle">
10332 <column alignment="center" valignment="middle" width="6.8cm">
10333 <column alignment="center" valignment="top" width="0pt">
10334 <column alignment="center" valignment="top" width="0pt">
10336 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
10339 \begin_layout Plain Layout
10345 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
10348 \begin_layout Plain Layout
10356 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
10359 \begin_layout Plain Layout
10369 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
10372 \begin_layout Plain Layout
10377 keystrokes after inserting the protected space
10382 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
10385 \begin_layout Plain Layout
10391 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
10394 \begin_layout Plain Layout
10402 <cell multicolumn="1" alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
10405 \begin_layout Plain Layout
10411 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
10414 \begin_layout Plain Layout
10415 \begin_inset Formula $A\negmedspace B$
10423 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
10426 \begin_layout Plain Layout
10427 \begin_inset Formula $A\negthickspace B$
10443 \begin_layout Standard
10444 Negative spaces can lead to characters overlapping each other.
10445 Thus they can be used to enforce ligatures, which are e.
10446 \begin_inset space \thinspace{}
10450 \begin_inset space \space{}
10453 useful for summation operators:
10456 \begin_layout Standard
10458 \begin_inset Tabular
10459 <lyxtabular version="3" rows="3" columns="2">
10460 <features rotate="0" tabularvalignment="middle">
10461 <column alignment="center" valignment="top">
10462 <column alignment="center" valignment="top">
10464 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
10467 \begin_layout Plain Layout
10473 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
10476 \begin_layout Plain Layout
10478 \begin_inset Note Note
10481 \begin_layout Plain Layout
10488 is only used as spacer.
10500 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
10503 \begin_layout Plain Layout
10509 \begin_inset space \textvisiblespace{}
10517 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
10520 \begin_layout Plain Layout
10521 \begin_inset Formula $\raisebox{4.5mm}{}\sum\sum f_{kl}\raisebox{-2.5mm}{}$
10531 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
10534 \begin_layout Plain Layout
10542 \begin_inset space \textvisiblespace{}
10550 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
10553 \begin_layout Plain Layout
10554 \begin_inset Formula $\raisebox{4.5mm}{}\sum\negmedspace\sum f_{kl}\raisebox{-2.5mm}{}$
10570 \begin_layout Standard
10571 Relations like for example equal signs, are always surrounded by space.
10572 To suppress this, the equal sign is placed into a TeX-brace.
10573 The following example demonstrates this:
10576 \begin_layout Standard
10578 \begin_inset Tabular
10579 <lyxtabular version="3" rows="2" columns="2">
10580 <features rotate="0" tabularvalignment="middle">
10581 <column alignment="center" valignment="top" width="0pt">
10582 <column alignment="center" valignment="top" width="0pt">
10584 <cell alignment="center" valignment="top" usebox="none">
10587 \begin_layout Plain Layout
10593 <cell alignment="center" valignment="top" usebox="none">
10596 \begin_layout Plain Layout
10597 \begin_inset Formula $A=B$
10607 <cell alignment="center" valignment="top" usebox="none">
10610 \begin_layout Plain Layout
10611 \begin_inset Note Note
10614 \begin_layout Plain Layout
10621 is only used as spacer.
10627 \begin_inset Formula $\raisebox{5mm}{}$
10630 equation without space
10635 <cell multicolumn="1" alignment="center" valignment="top" usebox="none">
10638 \begin_layout Plain Layout
10639 \begin_inset Formula $A{=}B$
10655 \begin_layout Standard
10657 The command for the last formula is:
10662 \begin_inset Formula $\to$
10668 \begin_layout Standard
10669 \begin_inset VSpace bigskip
10672 Spaces are needed for physical units, because the space between the value
10673 and the unit is the smallest one and not a normal space.
10674 For units in text, the smallest space is inserted via the menu
10676 Insert\SpecialChar \menuseparator
10677 Formatting\SpecialChar \menuseparator
10679 \begin_inset space ~
10687 arg "space-insert thin"
10693 \begin_layout Standard
10694 An example to visualize the difference:
10697 \begin_layout Standard
10698 \begin_inset Tabular
10699 <lyxtabular version="3" rows="2" columns="2">
10700 <features rotate="0" tabularvalignment="middle">
10701 <column alignment="left" valignment="top">
10702 <column alignment="left" valignment="top">
10704 <cell alignment="center" valignment="top" usebox="none">
10707 \begin_layout Plain Layout
10709 \begin_inset Formula $\cdot$
10717 <cell alignment="center" valignment="top" usebox="none">
10720 \begin_layout Plain Layout
10721 space between value and unit
10728 <cell alignment="center" valignment="top" usebox="none">
10731 \begin_layout Plain Layout
10733 \begin_inset space \thinspace{}
10737 \begin_inset Formula $\cdot$
10745 <cell alignment="center" valignment="top" usebox="none">
10748 \begin_layout Plain Layout
10749 smallest space between value and unit
10762 \begin_layout Subsection
10767 \begin_layout Plain Layout
10780 \begin_layout Plain Layout
10781 for vertical space in formulas see
10782 \begin_inset CommandInset ref
10784 reference "sub:Line-Separation"
10797 \begin_layout Plain Layout
10805 \begin_inset Note Note
10808 \begin_layout Plain Layout
10811 texorpdfstring is used to avoid that the footnote appears in the PDF-bookmark.
10814 \begin_layout Plain Layout
10817 texorpdfstring is in section
10818 \begin_inset CommandInset ref
10820 reference "sub:Formulas-in-Section"
10830 \begin_inset CommandInset label
10832 name "sub:Variable-Space"
10837 \begin_inset Index idx
10840 \begin_layout Plain Layout
10841 Space ! horizontal ! variable
10849 \begin_layout Standard
10850 Space with a defined length can be inserted with the command
10857 \begin_inset Index idx
10860 \begin_layout Plain Layout
10870 \begin_inset Quotes eld
10876 \begin_inset space \textvisiblespace{}
10882 \begin_inset Quotes erd
10886 The length can be specified by left-clicking on the
10887 \begin_inset Quotes eld
10893 \begin_inset space \textvisiblespace{}
10899 \begin_inset Quotes erd
10903 The length may also be negative.
10904 To insert as much space as is available, the command
10911 \begin_inset Index idx
10914 \begin_layout Plain Layout
10925 \begin_layout Standard
10926 \begin_inset VSpace -1mm
10932 \begin_layout Standard
10934 \begin_inset Tabular
10935 <lyxtabular version="3" rows="4" columns="2">
10936 <features rotate="0" tabularvalignment="middle">
10937 <column alignment="center" valignment="top">
10938 <column alignment="center" valignment="top">
10940 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
10943 \begin_layout Plain Layout
10951 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
10954 \begin_layout Plain Layout
10962 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
10965 \begin_layout Plain Layout
10969 \begin_inset space \textvisiblespace{}
10973 \begin_inset Formula $\to$
10979 \begin_inset space \thinspace{}
10987 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
10990 \begin_layout Plain Layout
10991 \begin_inset Formula $A=B\hspace{3cm}A\not=C$
11001 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
11004 \begin_layout Plain Layout
11008 \begin_inset space \textvisiblespace{}
11012 \begin_inset Formula $\to$
11018 \begin_inset space \thinspace{}
11026 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
11029 \begin_layout Plain Layout
11030 \begin_inset Formula $A\hspace{-1mm}A\not=A$
11040 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
11043 \begin_layout Plain Layout
11047 \begin_inset space \textvisiblespace{}
11055 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
11058 \begin_layout Plain Layout
11059 \begin_inset Formula $A=A\hfill B=B$
11075 \begin_layout Standard
11076 In the last example the available space is given by the longest column entry
11078 In an inline formula the space depends on the length of the line in which
11086 Thus, when the line uses the full width, no space will be created.
11093 only has an effect on displayed formulas when the formula style
11098 (Formula styles are explained in
11099 \begin_inset CommandInset ref
11101 reference "sec:Formula-Styles"
11108 \begin_layout Standard
11115 , there are the commands
11127 that fill the space with a pattern, see
11128 \begin_inset CommandInset ref
11130 reference "sub:Ellipses"
11137 \begin_layout Standard
11138 For text, variable space can be inserted via the menu
11140 Insert\SpecialChar \menuseparator
11141 Formatting\SpecialChar \menuseparator
11143 \begin_inset space ~
11151 \begin_layout Standard
11152 This is a line with
11153 \begin_inset space \hspace{}
11158 \begin_inset space \thinspace{}
11164 \begin_layout Standard
11165 This is a line with
11166 \begin_inset space \hfill{}
11172 \begin_layout Subsection
11173 Space besides inline Formulas
11174 \begin_inset Index idx
11177 \begin_layout Plain Layout
11178 Space ! besides inline formulas
11186 \begin_layout Standard
11187 The space that surrounds inline formulas can be adjusted with the length
11195 \begin_inset Index idx
11198 \begin_layout Plain Layout
11207 The value of a length is set with the command
11214 \begin_inset Index idx
11217 \begin_layout Plain Layout
11225 which has the following scheme:
11228 \begin_layout Standard
11233 setlength{length name}{value}
11236 \begin_layout Standard
11244 \begin_inset space \thinspace{}
11250 \begin_layout Standard
11260 \begin_layout Standard
11261 is inserted in TeX-mode.
11263 \begin_inset space \thinspace{}
11266 mm space will now be set around all inline formulas:
11270 \begin_layout Plain Layout
11284 \begin_layout Standard
11285 This is a line with an inline formula
11286 \begin_inset Formula $A=B$
11290 \begin_inset space \thinspace{}
11293 mm surrounding space.
11297 \begin_layout Plain Layout
11311 \begin_layout Standard
11312 To return to the predefined value,
11318 is set to the value 0
11319 \begin_inset space \thinspace{}
11325 \begin_layout Section
11327 \begin_inset Index idx
11330 \begin_layout Plain Layout
11337 \begin_inset Index idx
11340 \begin_layout Plain Layout
11345 \begin_layout Plain Layout
11356 \begin_layout Plain Layout
11371 \begin_layout Standard
11372 Boxes for text are described in chapter
11379 \begin_inset space ~
11387 \begin_layout Subsection
11389 \begin_inset CommandInset label
11391 name "sub:Boxes-with-Frame"
11396 \begin_inset Index idx
11399 \begin_layout Plain Layout
11408 \begin_layout Standard
11409 It is possible to frame a formula or part of one with the commands
11416 \begin_inset Index idx
11419 \begin_layout Plain Layout
11434 \begin_inset Index idx
11437 \begin_layout Plain Layout
11448 \begin_layout Standard
11449 When one of these commands is inserted in a formula, a blue box appears
11450 within a frame to enter formula parts.
11457 an additional formula has to be created by
11461 within this box, because the box content will otherwise be treated as mathemati
11469 is used, a new formula is automatically created inside the frame.
11472 \begin_layout Standard
11479 is not suitable to frame displayed formulas because the formula will always
11480 be set in the size of the text.
11487 is in contrary not suitable to frame inline formulas, because the formula
11488 will always be set in the size of a displayed formula.
11491 \begin_layout Standard
11505 \begin_inset Index idx
11508 \begin_layout Plain Layout
11516 where additionally the frame width and the alignment can be specified.
11523 is used in the following scheme:
11526 \begin_layout Standard
11531 framebox[frame width][position]{box content}
11534 \begin_layout Standard
11535 The position can either be
11552 right aligns the formula in the box.
11553 When no position is given, the formula will be centered.
11554 \begin_inset Newline newline
11557 If no width is given, also no position can be given.
11558 In this case the frame width is adjusted to the box content like for
11567 \begin_layout Standard
11574 is inserted, a box appears containing three blue boxes.
11575 The first two boxes are surrounded by brackets and denote the two optional
11577 The third box is for formula parts like for
11586 \begin_layout Standard
11587 \begin_inset Newpage newpage
11593 \begin_layout Standard
11595 \begin_inset Tabular
11596 <lyxtabular version="3" rows="5" columns="2">
11597 <features rotate="0" tabularvalignment="middle">
11598 <column alignment="center" valignment="top">
11599 <column alignment="center" valignment="top">
11601 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
11604 \begin_layout Plain Layout
11610 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
11613 \begin_layout Plain Layout
11615 \begin_inset Note Note
11618 \begin_layout Plain Layout
11625 is only used as spacer.
11637 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
11640 \begin_layout Plain Layout
11644 \begin_inset space \textvisiblespace{}
11654 \begin_inset space \textvisiblespace{}
11662 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
11665 \begin_layout Plain Layout
11666 \begin_inset Formula $\raisebox{6mm}{}\fbox{\ensuremath{\int A=B}}\raisebox{-4mm}{}$
11676 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
11679 \begin_layout Plain Layout
11683 \begin_inset space \textvisiblespace{}
11689 \begin_inset space \textvisiblespace{}
11697 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
11700 \begin_layout Plain Layout
11701 \begin_inset Formula $\raisebox{8.5mm}{}\boxed{\int A=B}\raisebox{-6.5mm}{}$
11711 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
11714 \begin_layout Plain Layout
11718 \begin_inset space \textvisiblespace{}
11726 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
11729 \begin_layout Plain Layout
11730 \begin_inset Formula $\raisebox{6mm}{}A+\fbox{B}\raisebox{-3mm}{}$
11740 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
11743 \begin_layout Plain Layout
11747 \begin_inset space \textvisiblespace{}
11751 \begin_inset Formula $\to$
11755 \begin_inset Formula $\to$
11765 \begin_inset space \textvisiblespace{}
11769 \begin_inset Formula $\downarrow$
11777 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
11780 \begin_layout Plain Layout
11781 \begin_inset Formula $\raisebox{6mm}{}$
11785 \begin_inset Formula $\framebox[20mm][]{\ensuremath{\frac{A}{B}}}$
11789 \begin_inset Formula $\raisebox{-4mm}{}$
11805 \begin_layout Standard
11806 The frame thickness can also be adjusted.
11807 To do this the following commands have to be inserted in TeX-mode before
11811 \begin_layout Standard
11821 \begin_inset Quotes eld
11825 \begin_inset Quotes erd
11839 \begin_inset Quotes eld
11843 \begin_inset Quotes erd
11849 \begin_layout Standard
11850 \begin_inset Quotes eld
11854 \begin_inset Quotes erd
11857 specifies the minimal distance between the frame and the first character
11859 An example for this is the following framed formula:
11863 \begin_layout Plain Layout
11875 \begin_inset Formula
11882 Before this formula the commands
11885 \begin_layout Standard
11907 \begin_layout Standard
11908 were inserted in TeX-mode.
11909 The given values are used for all following boxes.
11912 \begin_layout Standard
11913 To return to the standard frame size, the command
11916 \begin_layout Standard
11941 \begin_layout Plain Layout
11955 \begin_layout Standard
11956 is inserted in TeX-mode before the next formula.
11959 \begin_layout Subsection
11960 Boxes without Frame
11961 \begin_inset CommandInset label
11963 name "sub:Boxes-without-Frame"
11968 \begin_inset Index idx
11971 \begin_layout Plain Layout
11972 Boxes ! without frame
11980 \begin_layout Standard
11981 For boxes without a frame there are the following box commands:
11988 \begin_inset Index idx
11991 \begin_layout Plain Layout
12006 \begin_inset Index idx
12009 \begin_layout Plain Layout
12024 \begin_inset Index idx
12027 \begin_layout Plain Layout
12038 \begin_layout Standard
12045 a box can be super- or subscripted.
12046 But in contrary to normal super- and subscripting, the characters in the
12047 box keep their font size.
12054 is used in the following scheme:
12057 \begin_layout Standard
12062 raisebox{height}{box content}
12065 \begin_layout Standard
12066 When the box should contain a formula, an extra formula is needed like for
12077 \begin_inset Note Greyedout
12080 \begin_layout Plain Layout
12091 this extra formula is created by pressing
12095 twice instead of once because LyX doesn't yet support
12109 \begin_layout Standard
12111 \begin_inset Tabular
12112 <lyxtabular version="3" rows="4" columns="2">
12113 <features rotate="0" tabularvalignment="middle">
12114 <column alignment="center" valignment="top">
12115 <column alignment="center" valignment="top">
12117 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
12120 \begin_layout Plain Layout
12126 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
12129 \begin_layout Plain Layout
12137 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
12140 \begin_layout Plain Layout
12144 \begin_inset Formula $\to$
12150 \begin_inset Formula $\to$
12158 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
12161 \begin_layout Plain Layout
12162 \begin_inset Formula $H\raisebox{2mm}{al}lo$
12172 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
12175 \begin_layout Plain Layout
12179 \begin_inset Formula $\to$
12185 \begin_inset Formula $\to$
12193 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
12196 \begin_layout Plain Layout
12197 \begin_inset Formula $H\raisebox{-2mm}{al}lo$
12207 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
12210 \begin_layout Plain Layout
12214 \begin_inset Formula $\to$
12230 \begin_inset space \textvisiblespace{}
12238 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
12241 \begin_layout Plain Layout
12242 \begin_inset Formula $A=\raisebox{-2mm}{\mbox{\ensuremath{\sqrt{B}}}}$
12258 \begin_layout Standard
12283 , with the difference that there is no frame.
12286 \begin_layout Subsection
12288 \begin_inset CommandInset label
12290 name "sub:Colored-Boxes"
12295 \begin_inset Index idx
12298 \begin_layout Plain Layout
12307 \begin_layout Standard
12308 To be able to use all commands explained in this section, the LaTeX-package
12317 \begin_layout Plain Layout
12322 is part of every LaTeX standard installation.
12328 \begin_inset Index idx
12331 \begin_layout Plain Layout
12337 has to be loaded in the LaTeX-preamble with the line
12341 \begin_layout Plain Layout
12342 When text is colored somewhere in the document with a predefined color,
12343 LyX loads the LaTeX-package
12348 Thus it is possible that the package is loaded twice, but this does not
12355 \begin_inset Note Note
12358 \begin_layout Plain Layout
12359 To avoid that the package is loaded twice, a macro was inserted to the LaTeX-pre
12368 \begin_layout Standard
12376 \begin_layout Standard
12377 \begin_inset VSpace medskip
12380 To color boxes, the command
12387 \begin_inset Index idx
12390 \begin_layout Plain Layout
12398 is used in the following scheme:
12401 \begin_layout Standard
12406 colorbox{color}{box content}
12409 \begin_layout Standard
12410 The box content can also be a box and a
12416 can also be part of another box (see the 2nd and 3rd example).
12417 When the box should contain a formula, an extra formula has to be created,
12418 the same way as for
12428 \begin_layout Plain Layout
12429 This also applies for the command
12443 \begin_layout Standard
12444 One of the following predefined colors can be chosen:
12447 \begin_layout Standard
12481 \begin_layout Standard
12483 \begin_inset Tabular
12484 <lyxtabular version="3" rows="4" columns="2">
12485 <features rotate="0" tabularvalignment="middle">
12486 <column alignment="center" valignment="top">
12487 <column alignment="center" valignment="top">
12489 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
12492 \begin_layout Plain Layout
12498 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
12501 \begin_layout Plain Layout
12503 \begin_inset Note Note
12506 \begin_layout Plain Layout
12513 is only used as spacer.
12525 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
12528 \begin_layout Plain Layout
12532 \begin_inset Formula $\to$
12542 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
12545 \begin_layout Plain Layout
12546 \begin_inset Formula $\raisebox{6mm}{}\colorbox{yellow}{A=B}\raisebox{-3mm}{}$
12556 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
12559 \begin_layout Plain Layout
12563 \begin_inset Formula $\to$
12571 \begin_inset space \textvisiblespace{}
12579 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
12582 \begin_layout Plain Layout
12583 \begin_inset Formula $\raisebox{6mm}{}\colorbox{green}{\fbox{A=B}}\raisebox{-3mm}{}$
12593 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
12596 \begin_layout Plain Layout
12600 \begin_inset space \textvisiblespace{}
12606 \begin_inset Formula $\to$
12622 \begin_inset space \textvisiblespace{}
12630 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
12633 \begin_layout Plain Layout
12634 \begin_inset Formula $\raisebox{7mm}{}\fbox{\colorbox{green}{\mbox{\ensuremath{\int C=D}}}}\raisebox{-5mm}{}$
12650 \begin_layout Standard
12657 only colors the box but not the characters in the box.
12658 To color all characters, the whole formula is highlighted and the desired
12659 color is chosen in the
12662 \begin_inset space ~
12668 The dialog can be called with the toolbar button
12669 \begin_inset Graphics
12670 filename ../images/dialog-show_character.png
12677 Edit\SpecialChar \menuseparator
12679 \begin_inset space ~
12682 Style\SpecialChar \menuseparator
12686 The formula number then has the same color as the formula.
12687 When the formula number should get another color than the formula characters,
12688 the color must be changed within the formula.
12691 \begin_layout Standard
12695 \begin_layout Standard
12698 \begin_inset Formula
12700 \int A=B\label{eq:red}
12708 \begin_inset Formula
12710 \textcolor{red}{\int A=B}\label{eq:redgreen}
12718 \begin_layout Standard
12720 \begin_inset CommandInset ref
12726 is completely colored red.
12727 \begin_inset Newline newline
12731 \begin_inset CommandInset ref
12733 reference "eq:redgreen"
12737 was first completely colored green to set the color for the formula number.
12738 Subsequently the formula characters were colored red.
12741 \begin_layout Standard
12742 \begin_inset VSpace bigskip
12745 To color the frame different than the rest of the box, the command
12752 \begin_inset Index idx
12755 \begin_layout Plain Layout
12763 is used in the following scheme:
12766 \begin_layout Standard
12771 fcolorbox{frame color}{color}{box content}
12774 \begin_layout Standard
12781 is an extension of the command
12788 The frame width is set, like for
12811 \begin_layout Plain Layout
12823 \begin_inset Formula
12825 \fcolorbox{cyan}{magenta}{A=B}
12834 \begin_layout Plain Layout
12848 \begin_layout Standard
12849 This formula was created with the command
12850 \begin_inset Newline newline
12858 \begin_inset Formula $\to$
12864 \begin_inset Formula $\to$
12874 \begin_layout Standard
12875 \begin_inset VSpace bigskip
12878 To use other colors than the predefined ones, they have to be defined first.
12881 \begin_layout Standard
12882 One can for example define the color
12883 \begin_inset Quotes eld
12891 \begin_inset Quotes erd
12894 with the LaTeX-preamble line:
12897 \begin_layout Standard
12902 definecolor{darkgreen}{cmyk}{0.5,
12917 \begin_inset Index idx
12920 \begin_layout Plain Layout
12931 \begin_layout Standard
12936 is the color space that denotes the colors
12953 The four comma separated numbers are the portion factor for the corresponding
12954 colors of the color space.
12955 The factors can be in the range of 0
12956 \begin_inset space \thinspace{}
12960 \begin_inset space \thinspace{}
12968 also the color space
12972 can be used for definitions.
12989 , so that there are in this case three portion factors for the corresponding
12991 Furthermore there is the color space
12995 with one portion factor for the gray value.
12998 \begin_layout Standard
12999 As example a framed box with the new defined color
13003 where the characters have been colored
13008 \begin_inset Formula
13010 \colorbox{darkgreen}{\color{yellow}\boxed{\int A\,\mathrm{d}x=\frac{\sqrt[5]{B}}{\ln\left(\frac{1}{3}\right)}}}
13018 \begin_layout Standard
13019 Self-defined colors can also be used for text with the help of the command
13027 \begin_inset Index idx
13030 \begin_layout Plain Layout
13039 \begin_layout Standard
13043 \begin_layout Plain Layout
13047 textcolor{darkgreen}{
13053 \begin_inset Quotes eld
13057 \begin_inset Quotes erd
13064 \begin_layout Plain Layout
13074 \begin_layout Standard
13082 \begin_inset Index idx
13085 \begin_layout Plain Layout
13093 is used in the scheme
13097 textcolor{color}{characters to color}
13102 \begin_layout Subsection
13104 \begin_inset CommandInset label
13106 name "sub:Paragraph-Boxes"
13111 \begin_inset Index idx
13114 \begin_layout Plain Layout
13115 Boxes ! as paragraph
13123 \begin_layout Standard
13124 A box that can contain several lines and paragraphs, a so-called paragraph
13125 box (parbox), can be created with the menu
13127 Insert\SpecialChar \menuseparator
13130 or the toolbar button
13131 \begin_inset Graphics
13132 filename ../images/box-insert.png
13140 \begin_layout Standard
13141 The following example shows a framed parbox in a line:
13144 \begin_layout Standard
13145 \begin_inset VSpace medskip
13149 \begin_inset Box Boxed
13159 height_special "totalheight"
13162 \begin_layout Plain Layout
13163 This is a paragraph box.
13165 \begin_inset space \thinspace{}
13168 cm long and can also contain formulas:
13169 \begin_inset Formula $\int A\,\mathrm{d}s=C$
13180 \begin_layout Standard
13181 \begin_inset VSpace medskip
13187 \begin_layout Standard
13188 Such a box is created by right-clicking on the gray box inset.
13189 A dialog pops up showing the box properties.
13203 \begin_inset space \thinspace{}
13208 Vertical Box Alignment
13213 \begin_layout Standard
13214 \begin_inset VSpace medskip
13217 In LaTeX a parbox is created with the command
13224 \begin_inset Index idx
13227 \begin_layout Plain Layout
13235 which has the following scheme:
13238 \begin_layout Standard
13243 parbox[position]{width}{box content}
13246 \begin_layout Standard
13261 \begin_inset Quotes eld
13265 \begin_inset Quotes erd
13268 means that the box is aligned within the surrounding text with its last
13275 \begin_inset Quotes eld
13279 \begin_inset Quotes erd
13282 this is done with the first line.
13283 When no position is given, the box will be vertically centered, see section
13291 \begin_inset space ~
13296 manual for examples.
13299 \begin_layout Standard
13300 \begin_inset VSpace bigskip
13303 To frame formulas completely, including the formula number, the formula
13304 must be set into a parbox.
13305 To do this, the command
13319 is inserted in TeX-mode before the formula.
13327 \begin_inset Index idx
13330 \begin_layout Plain Layout
13338 is hereby the line width set for the document.
13339 Because the frame is outside the parbox, 2
13340 \begin_inset space \thinspace{}
13343 times the frame separation and the frame thickness must be subtracted from
13345 As this is not automatically done by LyX due to a bug
13349 \begin_layout Plain Layout
13350 \begin_inset CommandInset href
13352 name "LyX-bug #4483"
13353 target "http://www.lyx.org/trac/ticket/4483"
13362 , TeX-mode has to be used.
13363 To be able to multiply and subtract in arguments, the LaTeX-package
13371 \begin_layout Plain Layout
13376 is part of every LaTeX standard installation.
13382 \begin_inset Index idx
13385 \begin_layout Plain Layout
13391 must be loaded in the LaTeX-preamble with the line
13394 \begin_layout Standard
13402 \begin_layout Standard
13403 Behind the formula both boxes are closed by entering
13408 Here is an example:
13412 \begin_layout Plain Layout
13426 \begin_layout Standard
13430 \begin_layout Plain Layout
13448 \begin_inset Formula
13450 \int A\,\mathrm{d}x=\frac{\sqrt[5]{B}}{\ln\left(\frac{1}{3}\right)}
13459 \begin_layout Plain Layout
13470 \begin_layout Plain Layout
13484 \begin_layout Standard
13485 \begin_inset VSpace medskip
13488 As a parbox is used as the argument of
13494 , there is in this case no difference between
13509 \begin_layout Standard
13510 \begin_inset VSpace bigskip
13513 Paragraph boxes are very useful to comment formulas directly.
13520 is used in combination with the command
13534 \begin_inset CommandInset ref
13536 reference "sub:User-defined-Numbering"
13543 \begin_layout Standard
13544 An example of a formula commented with
13553 \begin_layout Standard
13557 \begin_layout Plain Layout
13570 This is a description.
13571 It is distinctly separated from the formula and multiline.
13575 \begin_layout Plain Layout
13587 \begin_layout Standard
13588 Such a formula must be inserted completely in TeX-mode because LyX does
13589 not yet support the command
13596 The formula is created with the following command sequence:
13599 \begin_layout Standard
13612 is inserted in TeX-mode.
13616 \begin_layout Plain Layout
13617 When the formula style
13629 can also be replaced by
13636 (formula styles see
13637 \begin_inset CommandInset ref
13639 reference "sec:Formula-Styles"
13648 Then the description follows as normal text and finally
13654 is inserted in TeX-mode.
13667 hereby create a displayed formula.
13670 \begin_layout Standard
13677 can be seen in this example that was
13678 \begin_inset Quotes eld
13682 \begin_inset Quotes erd
13685 using the mathematical textmode:
13686 \begin_inset Formula
13688 5x-7b=3b\textrm{This is a description. It is not separated from the formula ...}
13696 \begin_layout Section
13698 \begin_inset Index idx
13701 \begin_layout Plain Layout
13710 \begin_layout Subsection
13712 \begin_inset CommandInset label
13714 name "sub:Big-Operators"
13719 \begin_inset Index idx
13722 \begin_layout Plain Layout
13729 \begin_inset Index idx
13732 \begin_layout Plain Layout
13739 \begin_inset Index idx
13742 \begin_layout Plain Layout
13751 \begin_layout Standard
13752 To be able to use all integral operators listed here, the option
13754 Use esint package automatically
13756 must be set in the document settings under
13759 \begin_inset space ~
13767 \begin_layout Standard
13768 \begin_inset space \hfill{}
13772 \begin_inset Tabular
13773 <lyxtabular version="3" rows="11" columns="2">
13774 <features rotate="0" tabularvalignment="middle">
13775 <column alignment="center" valignment="top" width="0pt">
13776 <column alignment="center" valignment="top" width="0pt">
13778 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
13781 \begin_layout Plain Layout
13787 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
13790 \begin_layout Plain Layout
13798 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
13801 \begin_layout Plain Layout
13805 \begin_inset Index idx
13808 \begin_layout Plain Layout
13821 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
13824 \begin_layout Plain Layout
13825 \begin_inset Formula $\int$
13835 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
13838 \begin_layout Plain Layout
13846 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
13849 \begin_layout Plain Layout
13850 \begin_inset Formula $\oint$
13860 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
13863 \begin_layout Plain Layout
13871 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
13874 \begin_layout Plain Layout
13875 \begin_inset Formula $\ointctrclockwise$
13885 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
13888 \begin_layout Plain Layout
13896 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
13899 \begin_layout Plain Layout
13900 \begin_inset Formula $\ointclockwise$
13910 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
13913 \begin_layout Plain Layout
13921 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
13924 \begin_layout Plain Layout
13925 \begin_inset Formula $\sqint$
13935 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
13938 \begin_layout Plain Layout
13946 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
13949 \begin_layout Plain Layout
13951 \begin_inset Formula $\fint$
13961 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
13964 \begin_layout Plain Layout
13972 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
13975 \begin_layout Plain Layout
13977 \begin_inset Formula $\landupint$
13987 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
13990 \begin_layout Plain Layout
13998 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
14001 \begin_layout Plain Layout
14003 \begin_inset Formula $\landdownint$
14013 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
14016 \begin_layout Plain Layout
14024 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
14027 \begin_layout Plain Layout
14028 \begin_inset Formula $\bigcap$
14038 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
14041 \begin_layout Plain Layout
14049 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
14052 \begin_layout Plain Layout
14053 \begin_inset Formula $\bigcup$
14067 \begin_inset space \hfill{}
14071 \begin_inset Tabular
14072 <lyxtabular version="3" rows="11" columns="2">
14073 <features rotate="0" tabularvalignment="middle">
14074 <column alignment="center" valignment="top" width="0pt">
14075 <column alignment="center" valignment="top" width="0pt">
14077 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
14080 \begin_layout Plain Layout
14086 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
14089 \begin_layout Plain Layout
14097 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
14100 \begin_layout Plain Layout
14104 \begin_inset Index idx
14107 \begin_layout Plain Layout
14120 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
14123 \begin_layout Plain Layout
14124 \begin_inset Formula $\sum$
14134 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
14137 \begin_layout Plain Layout
14141 \begin_inset Index idx
14144 \begin_layout Plain Layout
14151 \begin_layout Plain Layout
14170 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
14173 \begin_layout Plain Layout
14174 \begin_inset Formula $\prod$
14184 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
14187 \begin_layout Plain Layout
14195 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
14198 \begin_layout Plain Layout
14199 \begin_inset Formula $\coprod$
14209 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
14212 \begin_layout Plain Layout
14220 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
14223 \begin_layout Plain Layout
14224 \begin_inset Formula $\bigodot$
14234 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
14237 \begin_layout Plain Layout
14245 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
14248 \begin_layout Plain Layout
14249 \begin_inset Formula $\bigotimes$
14259 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
14262 \begin_layout Plain Layout
14270 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
14273 \begin_layout Plain Layout
14274 \begin_inset Formula $\bigoplus$
14284 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
14287 \begin_layout Plain Layout
14295 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
14298 \begin_layout Plain Layout
14299 \begin_inset Formula $\bigwedge$
14309 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
14312 \begin_layout Plain Layout
14320 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
14323 \begin_layout Plain Layout
14324 \begin_inset Formula $\bigvee$
14334 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
14337 \begin_layout Plain Layout
14345 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
14348 \begin_layout Plain Layout
14349 \begin_inset Formula $\bigsqcup$
14359 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
14362 \begin_layout Plain Layout
14370 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
14373 \begin_layout Plain Layout
14374 \begin_inset Formula $\biguplus$
14388 \begin_inset space \hfill{}
14394 \begin_layout Standard
14395 All big operators can also be inserted via the math toolbar button
14396 \begin_inset Graphics
14397 filename ../images/math/intop.png
14405 \begin_layout Standard
14406 The operators are called big because they are bigger than the sometimes
14407 equal looking binary operators.
14408 All big operators can have limits as described in the next subsection.
14411 \begin_layout Standard
14412 For all integral operators there is a second version available, ending in
14430 These operators are different from
14437 \begin_inset space \space{}
14440 in the style the operator limits are displayed, see
14441 \begin_inset CommandInset ref
14443 reference "sub:Operator-Limits"
14451 \begin_layout Subsubsection*
14452 Advice for Integrals
14455 \begin_layout Standard
14460 in an integral is an operator, that therefore has to be set upright.
14461 This is done by highlighting the
14465 and using the keyboard shortcut
14475 \begin_layout Plain Layout
14481 \begin_inset CommandInset ref
14483 reference "sub:Font-Styles"
14493 Finally the smallest space is inserted before the
14497 , as this is usual for operators.
14501 \begin_layout Standard
14503 \begin_inset Formula $\int A(x)dx$
14507 \begin_inset Newline newline
14511 \begin_inset Phantom HPhantom
14514 \begin_layout Plain Layout
14521 \begin_inset Formula $\int A(x)\,\mathrm{d}x$
14527 \begin_layout Standard
14528 For multiple integrals there are the following commands:
14529 \begin_inset VSpace medskip
14535 \begin_layout Standard
14536 \begin_inset space \hfill{}
14540 \begin_inset Tabular
14541 <lyxtabular version="3" rows="4" columns="2">
14542 <features rotate="0" tabularvalignment="middle">
14543 <column alignment="center" valignment="top">
14544 <column alignment="center" valignment="top">
14546 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
14549 \begin_layout Plain Layout
14555 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
14558 \begin_layout Plain Layout
14560 \begin_inset Note Note
14563 \begin_layout Plain Layout
14570 is only used as spacer.
14582 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
14585 \begin_layout Plain Layout
14593 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
14596 \begin_layout Plain Layout
14597 \begin_inset Formula $\raisebox{4.5mm}{}\iint\raisebox{-2.5mm}{}$
14607 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
14610 \begin_layout Plain Layout
14618 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
14621 \begin_layout Plain Layout
14622 \begin_inset Formula $\raisebox{4.5mm}{}\oiint\raisebox{-2.5mm}{}$
14632 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
14635 \begin_layout Plain Layout
14643 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
14646 \begin_layout Plain Layout
14647 \begin_inset Formula $\raisebox{4.5mm}{}\sqiint\raisebox{-2.5mm}{}$
14661 \begin_inset space \hfill{}
14665 \begin_inset Tabular
14666 <lyxtabular version="3" rows="4" columns="2">
14667 <features rotate="0" tabularvalignment="middle">
14668 <column alignment="center" valignment="top">
14669 <column alignment="center" valignment="top">
14671 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
14674 \begin_layout Plain Layout
14680 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
14683 \begin_layout Plain Layout
14691 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
14694 \begin_layout Plain Layout
14702 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
14705 \begin_layout Plain Layout
14706 \begin_inset Formula $\raisebox{4.5mm}{}\iiint\raisebox{-2.5mm}{}$
14716 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
14719 \begin_layout Plain Layout
14727 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
14730 \begin_layout Plain Layout
14731 \begin_inset Formula $\raisebox{4.5mm}{}\iiiint\raisebox{-2.5mm}{}$
14741 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
14744 \begin_layout Plain Layout
14752 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
14755 \begin_layout Plain Layout
14756 \begin_inset Formula $\raisebox{4.5mm}{}\dotsint\raisebox{-2.5mm}{}$
14770 \begin_inset space \hfill{}
14776 \begin_layout Standard
14777 \begin_inset Newpage newpage
14783 \begin_layout Subsection
14785 \begin_inset CommandInset label
14787 name "sub:Operator-Limits"
14792 \begin_inset Index idx
14795 \begin_layout Plain Layout
14804 \begin_layout Standard
14805 Limits are created by super- and subscripts:
14808 \begin_layout Standard
14810 \begin_inset Tabular
14811 <lyxtabular version="3" rows="2" columns="2">
14812 <features rotate="0" tabularvalignment="middle">
14813 <column alignment="center" valignment="top" width="0pt">
14814 <column alignment="center" valignment="top" width="0pt">
14816 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
14819 \begin_layout Plain Layout
14825 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
14828 \begin_layout Plain Layout
14830 \begin_inset Note Note
14833 \begin_layout Plain Layout
14840 is only used as spacer.
14852 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
14855 \begin_layout Plain Layout
14861 \begin_inset space \textvisiblespace{}
14865 \begin_inset Formula $\to$
14869 \begin_inset Formula $\to$
14877 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
14880 \begin_layout Plain Layout
14881 \begin_inset Formula $\raisebox{5mm}{}\prod_{0}^{\infty}A(x)\raisebox{-2.5mm}{}$
14897 \begin_layout Standard
14898 Limits of inline formulas are set right beside the operator.
14899 Limits in displayed formulas are set above or below the operator, except
14900 for integral limits.
14903 \begin_layout Standard
14904 To force that the limits are set beside the operator, the cursor is set
14905 directly behind the operator and the limits type is changed with the menu
14908 Edit\SpecialChar \menuseparator
14909 Math\SpecialChar \menuseparator
14928 \begin_layout Standard
14929 The default limits type is this:
14930 \begin_inset Formula
14932 \sum_{x=0}^{\infty}\frac{1}{x^{2}}
14937 This is how it looks when the limits type was changed to
14944 \begin_inset Formula
14946 \sum\nolimits _{x=0}^{\infty}\frac{1}{x^{2}}
14951 For integrals, except those ending with
14967 etc., the limits are by default set beside the operator.
14968 But for multiple integrals the limits are often set below the operator.
14969 In the following example the limits type was therefore set to
14973 and so set below the integrals:
14974 \begin_inset Formula
14976 \iiint\limits _{V}X\,\mathrm{d}V=U\label{eq:VolInt}
14984 \begin_layout Standard
14985 \begin_inset VSpace medskip
14988 To specify conditions for limits, the commands
14995 \begin_inset Index idx
14998 \begin_layout Plain Layout
15013 \begin_inset Index idx
15016 \begin_layout Plain Layout
15025 To create for example this expression
15026 \begin_inset Formula
15028 \sum_{\begin{subarray}{c}
15032 \end{subarray}}^{n}k^{-2}\label{eq:substack}
15040 \begin_layout Standard
15041 the following has to be done:
15042 \begin_inset Newline newline
15054 \begin_inset space \textvisiblespace{}
15060 One is now in a blue box under the summation operator and insert there
15066 \begin_inset space \textvisiblespace{}
15072 The blue box is now within a purple box and now several lines can be written
15074 A new line is created by inserting a line break (
15077 arg "newline-insert newline"
15082 \begin_inset Newline newline
15087 0<k<1000 Ctrl+Return
15088 \begin_inset Newline newline
15093 is typed in, a new box appears below for the new line.
15096 \begin_layout Standard
15097 The alignment of the lines can be changed to left aligned with the
15107 Edit\SpecialChar \menuseparator
15111 To get right alignment,
15116 \begin_inset space \textvisiblespace{}
15121 is inserted at the beginning of the line.
15124 \begin_layout Standard
15137 with the difference that the lines are always centered.
15140 \begin_layout Standard
15141 \begin_inset VSpace bigskip
15145 \begin_inset CommandInset ref
15147 reference "eq:substack"
15151 there can be too much space beside an operator, because the characters
15152 following the operator are set beside the limits.
15155 \begin_layout Standard
15156 To avoid this, the following macro can be used in the LaTeX-preamble:
15159 \begin_layout Standard
15173 \begin_inset Newline newline
15185 \begin_inset Newline newline
15192 mathclapinternal #1#2{
15196 mathsurround =0pt #1{#2}$}}
15199 \begin_layout Standard
15200 This defines the command
15207 \begin_inset Index idx
15210 \begin_layout Plain Layout
15218 that sets the width of the limit to 0
15219 \begin_inset space \thinspace{}
15223 The command scheme is
15226 \begin_layout Standard
15234 \begin_layout Standard
15235 where the limit can consist of several conditions.
15238 \begin_layout Standard
15240 \begin_inset CommandInset ref
15242 reference "eq:substack"
15246 , one uses the command
15249 \begin_layout Standard
15259 \begin_inset space \textvisiblespace{}
15262 0<k<1000 Ctrl+Return
15265 \begin_layout Standard
15266 to create the lower limit.
15267 The summand is now directly behind the summation operator:
15268 \begin_inset Formula
15270 \sum_{\mathclap{\substack{0<k<1000\\
15282 \begin_layout Standard
15283 \begin_inset VSpace bigskip
15286 How to use one limit for several operators is described in
15287 \begin_inset CommandInset ref
15289 reference "sub:Self-defined-Operators"
15296 \begin_layout Subsection
15297 Decoration for Operators
15298 \begin_inset Index idx
15301 \begin_layout Plain Layout
15302 Operators ! Decoration
15310 \begin_layout Standard
15318 \begin_inset Index idx
15321 \begin_layout Plain Layout
15336 \begin_inset Index idx
15339 \begin_layout Plain Layout
15347 characters can be placed above or below an operator, respectively.
15355 \begin_inset Index idx
15358 \begin_layout Plain Layout
15366 characters can be set before and behind a big operator.
15367 The command scheme is:
15370 \begin_layout Standard
15386 \begin_layout Standard
15393 must always be before the operator.
15394 You can decorate with several characters and even with other operators
15396 To place for example only characters behind a big operator, write nothing
15397 between the first braces but don't omit the braces.
15400 \begin_layout Standard
15401 For example the command
15406 \begin_inset Formula $\to$
15416 \begin_inset Formula $\to$
15422 \begin_inset space \textvisiblespace{}
15432 \begin_inset Formula
15434 \sideset{}{'}\sum_{k=1}^{n}
15442 \begin_layout Standard
15443 \begin_inset Note Greyedout
15446 \begin_layout Plain Layout
15453 can only be used to decorate big operators, binary operators are not allowed.
15461 \begin_layout Standard
15474 can also be used to decorate symbols and characters.
15475 For example, the command
15480 \begin_inset space \textvisiblespace{}
15486 \begin_inset space \textvisiblespace{}
15492 \begin_inset Formula $\uparrow$
15500 \begin_inset Formula
15502 \overset{a}{\maltese}
15510 \begin_layout Subsection
15512 \begin_inset CommandInset label
15514 name "sub:Binary-Operators"
15519 \begin_inset Index idx
15522 \begin_layout Plain Layout
15531 \begin_layout Standard
15532 Binary operators are surrounded by space when there is a character before
15534 \begin_inset VSpace medskip
15540 \begin_layout Standard
15541 \begin_inset space \hfill{}
15545 \begin_inset Tabular
15546 <lyxtabular version="3" rows="13" columns="2">
15547 <features rotate="0" tabularvalignment="middle">
15548 <column alignment="center" valignment="top" width="0pt">
15549 <column alignment="center" valignment="top" width="0pt">
15551 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
15554 \begin_layout Plain Layout
15556 \begin_inset Note Note
15559 \begin_layout Plain Layout
15566 is only used as spacer.
15576 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
15579 \begin_layout Plain Layout
15587 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
15590 \begin_layout Plain Layout
15596 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
15599 \begin_layout Plain Layout
15600 \begin_inset Formula $+$
15610 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
15613 \begin_layout Plain Layout
15619 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
15622 \begin_layout Plain Layout
15623 \begin_inset Formula $-$
15633 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
15636 \begin_layout Plain Layout
15644 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
15647 \begin_layout Plain Layout
15648 \begin_inset Formula $\pm$
15658 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
15661 \begin_layout Plain Layout
15669 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
15672 \begin_layout Plain Layout
15673 \begin_inset Formula $\mp$
15683 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
15686 \begin_layout Plain Layout
15694 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
15697 \begin_layout Plain Layout
15698 \begin_inset Formula $\cdot$
15708 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
15711 \begin_layout Plain Layout
15719 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
15722 \begin_layout Plain Layout
15723 \begin_inset Formula $\times$
15733 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
15736 \begin_layout Plain Layout
15744 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
15747 \begin_layout Plain Layout
15748 \begin_inset Formula $\div$
15758 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
15761 \begin_layout Plain Layout
15765 \begin_layout Plain Layout
15778 \begin_layout Plain Layout
15790 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
15793 \begin_layout Plain Layout
15794 \begin_inset Formula $*$
15804 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
15807 \begin_layout Plain Layout
15815 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
15818 \begin_layout Plain Layout
15819 \begin_inset Formula $\star$
15829 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
15832 \begin_layout Plain Layout
15840 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
15843 \begin_layout Plain Layout
15844 \begin_inset Formula $\circ$
15854 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
15857 \begin_layout Plain Layout
15865 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
15868 \begin_layout Plain Layout
15869 \begin_inset Formula $\diamond$
15879 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
15882 \begin_layout Plain Layout
15890 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
15893 \begin_layout Plain Layout
15894 \begin_inset Formula $\bullet$
15908 \begin_inset space \hfill{}
15912 \begin_inset Tabular
15913 <lyxtabular version="3" rows="13" columns="2">
15914 <features rotate="0" tabularvalignment="middle">
15915 <column alignment="center" valignment="top" width="0pt">
15916 <column alignment="center" valignment="top" width="0pt">
15918 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
15921 \begin_layout Plain Layout
15927 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
15930 \begin_layout Plain Layout
15938 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
15941 \begin_layout Plain Layout
15949 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
15952 \begin_layout Plain Layout
15953 \begin_inset Formula $\nabla$
15963 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
15966 \begin_layout Plain Layout
15974 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
15977 \begin_layout Plain Layout
15978 \begin_inset Formula $\bigtriangledown$
15988 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
15991 \begin_layout Plain Layout
15999 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
16002 \begin_layout Plain Layout
16003 \begin_inset Formula $\bigtriangleup$
16013 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
16016 \begin_layout Plain Layout
16024 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
16027 \begin_layout Plain Layout
16028 \begin_inset Formula $\Box$
16038 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
16041 \begin_layout Plain Layout
16049 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
16052 \begin_layout Plain Layout
16053 \begin_inset Formula $\cap$
16063 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
16066 \begin_layout Plain Layout
16074 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
16077 \begin_layout Plain Layout
16078 \begin_inset Formula $\cup$
16088 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
16091 \begin_layout Plain Layout
16099 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
16102 \begin_layout Plain Layout
16103 \begin_inset Formula $\dagger$
16113 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
16116 \begin_layout Plain Layout
16124 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
16127 \begin_layout Plain Layout
16128 \begin_inset Formula $\ddagger$
16138 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
16141 \begin_layout Plain Layout
16149 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
16152 \begin_layout Plain Layout
16153 \begin_inset Formula $\wr$
16163 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
16166 \begin_layout Plain Layout
16174 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
16177 \begin_layout Plain Layout
16178 \begin_inset Formula $\bigcirc$
16188 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
16191 \begin_layout Plain Layout
16199 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
16202 \begin_layout Plain Layout
16203 \begin_inset Formula $\wedge$
16213 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
16216 \begin_layout Plain Layout
16224 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
16227 \begin_layout Plain Layout
16228 \begin_inset Formula $\vee$
16242 \begin_inset space \hfill{}
16246 \begin_inset Tabular
16247 <lyxtabular version="3" rows="13" columns="2">
16248 <features rotate="0" tabularvalignment="middle">
16249 <column alignment="center" valignment="top" width="0pt">
16250 <column alignment="center" valignment="top" width="0pt">
16252 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
16255 \begin_layout Plain Layout
16261 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
16264 \begin_layout Plain Layout
16272 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
16275 \begin_layout Plain Layout
16283 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
16286 \begin_layout Plain Layout
16287 \begin_inset Formula $\oplus$
16297 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
16300 \begin_layout Plain Layout
16308 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
16311 \begin_layout Plain Layout
16312 \begin_inset Formula $\ominus$
16322 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
16325 \begin_layout Plain Layout
16333 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
16336 \begin_layout Plain Layout
16337 \begin_inset Formula $\otimes$
16347 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
16350 \begin_layout Plain Layout
16358 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
16361 \begin_layout Plain Layout
16362 \begin_inset Formula $\oslash$
16372 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
16375 \begin_layout Plain Layout
16383 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
16386 \begin_layout Plain Layout
16387 \begin_inset Formula $\odot$
16397 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
16400 \begin_layout Plain Layout
16408 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
16411 \begin_layout Plain Layout
16412 \begin_inset Formula $\amalg$
16422 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
16425 \begin_layout Plain Layout
16433 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
16436 \begin_layout Plain Layout
16437 \begin_inset Formula $\uplus$
16447 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
16450 \begin_layout Plain Layout
16458 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
16461 \begin_layout Plain Layout
16462 \begin_inset Formula $\setminus$
16472 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
16475 \begin_layout Plain Layout
16483 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
16486 \begin_layout Plain Layout
16487 \begin_inset Formula $\sqcap$
16497 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
16500 \begin_layout Plain Layout
16508 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
16511 \begin_layout Plain Layout
16512 \begin_inset Formula $\sqcup$
16522 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
16525 \begin_layout Plain Layout
16533 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
16536 \begin_layout Plain Layout
16537 \begin_inset Formula $\triangleleft$
16547 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
16550 \begin_layout Plain Layout
16558 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
16561 \begin_layout Plain Layout
16562 \begin_inset Formula $\triangleright$
16576 \begin_inset space \hfill{}
16582 \begin_layout Standard
16583 All binary operators can also be inserted via the math toolbar button
16584 \begin_inset Graphics
16585 filename ../images/math/pm.png
16593 \begin_layout Standard
16594 To typeset the Laplace operator also
16611 \begin_inset Formula $\nabla^{2}$
16614 ) can be used instead of
16623 \begin_layout Standard
16630 Insert\SpecialChar \menuseparator
16642 \begin_layout Subsection
16643 Self-defined Operators
16644 \begin_inset CommandInset label
16646 name "sub:Self-defined-Operators"
16651 \begin_inset Index idx
16654 \begin_layout Plain Layout
16655 Operators ! self-defined
16663 \begin_layout Standard
16664 With the help of the command
16668 DeclareMathOperator
16671 \begin_inset Index idx
16674 \begin_layout Plain Layout
16679 DeclareMathOperator
16684 custom operators can be defined in the LaTeX-preamble.
16685 Its command scheme is:
16688 \begin_layout Standard
16693 DeclareMathOperator{new command}{display}
16696 \begin_layout Standard
16697 Display can be characters or symbols that define how the operator looks
16699 To define a big operator a * is set behind the command.
16700 All self-defined big operators can have limits as described in
16701 \begin_inset CommandInset ref
16703 reference "sub:Operator-Limits"
16710 \begin_layout Standard
16711 For example the LaTeX-preamble line
16714 \begin_layout Standard
16719 DeclareMathOperator*{
16726 \begin_layout Standard
16727 defines the command
16733 , that inserts a big operator consisting of the lozenge symbol from
16734 \begin_inset CommandInset ref
16736 reference "sub:Miscellaneous-Symbols"
16741 \begin_inset Formula
16743 \Lozenge_{n=1}^{\infty}
16748 The command for this formula is:
16759 \begin_inset Formula $\to$
16765 \begin_layout Standard
16766 \begin_inset VSpace bigskip
16769 When self-defined operators are not used several times in the document,
16770 they can also be defined with the commands
16777 \begin_inset Index idx
16780 \begin_layout Plain Layout
16795 \begin_inset Index idx
16798 \begin_layout Plain Layout
16806 , which have the following scheme:
16809 \begin_layout Standard
16823 \begin_layout Standard
16830 defines big operators,
16839 \begin_layout Standard
16847 \begin_inset space \thinspace{}
16851 \begin_inset space \space{}
16854 be used to use one limit for several operators:
16857 \begin_layout Standard
16858 \begin_inset Formula
16860 \mathop{\sum\negmedspace\sum}_{i,j=1}^{N}
16868 \begin_layout Standard
16869 The command for the formula above is:
16870 \begin_inset Newline newline
16886 \begin_inset space \textvisiblespace{}
16892 \begin_inset Formula $\to$
16898 \begin_inset space \textvisiblespace{}
16906 \begin_layout Section
16908 \begin_inset Index idx
16911 \begin_layout Plain Layout
16920 \begin_layout Subsection
16922 \begin_inset CommandInset label
16924 name "sub:Font-Styles"
16929 \begin_inset Index idx
16932 \begin_layout Plain Layout
16941 \begin_layout Standard
16942 Latin letters in formulas can be set in one of the following font styles:
16943 \begin_inset VSpace -2mm
16949 \begin_layout Standard
16951 \begin_inset Tabular
16952 <lyxtabular version="3" rows="7" columns="3">
16953 <features rotate="0" tabularvalignment="middle">
16954 <column alignment="center" valignment="top">
16955 <column alignment="center" valignment="top">
16956 <column alignment="center" valignment="top">
16958 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
16961 \begin_layout Plain Layout
16967 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
16970 \begin_layout Plain Layout
16976 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
16979 \begin_layout Plain Layout
16987 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
16990 \begin_layout Plain Layout
16996 \begin_inset space \textvisiblespace{}
17006 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
17009 \begin_layout Plain Layout
17010 \begin_inset Formula $\mathbb{ABC}$
17018 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
17021 \begin_layout Plain Layout
17034 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
17037 \begin_layout Plain Layout
17043 \begin_inset space \textvisiblespace{}
17053 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
17056 \begin_layout Plain Layout
17057 \begin_inset Formula $\mathbf{AbC}$
17065 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
17068 \begin_layout Plain Layout
17081 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
17084 \begin_layout Plain Layout
17090 \begin_inset space \textvisiblespace{}
17100 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
17103 \begin_layout Plain Layout
17104 \begin_inset Formula $\boldsymbol{AbC}$
17112 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
17115 \begin_layout Plain Layout
17118 arg "font-boldsymbol"
17128 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
17131 \begin_layout Plain Layout
17137 \begin_inset space \textvisiblespace{}
17147 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
17150 \begin_layout Plain Layout
17151 \begin_inset Formula $\mathcal{ABC}$
17159 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
17162 \begin_layout Plain Layout
17175 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
17178 \begin_layout Plain Layout
17184 \begin_inset space \textvisiblespace{}
17194 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
17197 \begin_layout Plain Layout
17198 \begin_inset Formula $\mathfrak{AbC}$
17206 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
17209 \begin_layout Plain Layout
17217 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
17220 \begin_layout Plain Layout
17226 \begin_inset space \textvisiblespace{}
17236 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
17239 \begin_layout Plain Layout
17240 \begin_inset Formula $\mathscr{AbC}$
17248 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
17251 \begin_layout Plain Layout
17265 \begin_layout Standard
17267 \begin_inset Tabular
17268 <lyxtabular version="3" rows="5" columns="3">
17269 <features rotate="0" tabularvalignment="middle">
17270 <column alignment="center" valignment="top">
17271 <column alignment="center" valignment="top">
17272 <column alignment="center" valignment="top">
17274 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
17277 \begin_layout Plain Layout
17283 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
17286 \begin_layout Plain Layout
17292 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
17295 \begin_layout Plain Layout
17303 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
17306 \begin_layout Plain Layout
17312 \begin_inset space \textvisiblespace{}
17322 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
17325 \begin_layout Plain Layout
17326 \begin_inset Formula $\mathit{AbC}$
17334 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
17337 \begin_layout Plain Layout
17345 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
17348 \begin_layout Plain Layout
17354 \begin_inset space \textvisiblespace{}
17364 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
17367 \begin_layout Plain Layout
17368 \begin_inset Formula $\mathrm{AbC}$
17376 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
17379 \begin_layout Plain Layout
17392 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
17395 \begin_layout Plain Layout
17401 \begin_inset space \textvisiblespace{}
17411 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
17414 \begin_layout Plain Layout
17415 \begin_inset Formula $\mathsf{AbC}$
17423 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
17426 \begin_layout Plain Layout
17439 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
17442 \begin_layout Plain Layout
17448 \begin_inset space \textvisiblespace{}
17458 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
17461 \begin_layout Plain Layout
17462 \begin_inset Formula $\mathtt{AbC}$
17470 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
17473 \begin_layout Plain Layout
17476 arg "font-typewriter"
17492 \begin_layout Standard
17493 \begin_inset Note Greyedout
17496 \begin_layout Plain Layout
17513 can only be used for big letters.
17521 \begin_layout Standard
17522 Predefined is the style
17531 \begin_layout Standard
17532 The style commands work also for letters in mathematical constructs:
17533 \begin_inset Formula
17535 \mathfrak{A=\frac{b}{C}}
17543 \begin_layout Standard
17544 Characters in mathematical text don't appear in a math font style but in
17545 the text font style
17552 That their style can't be set correctly via the text style dialog is a
17557 \begin_layout Plain Layout
17558 \begin_inset CommandInset href
17560 name "LyX-bug #4629"
17561 target "http://www.lyx.org/trac/ticket/4629"
17573 \begin_layout Standard
17574 Instead of the style commands the dialog
17576 Edit\SpecialChar \menuseparator
17577 Math\SpecialChar \menuseparator
17580 or the toolbar button
17581 \begin_inset Graphics
17582 filename ../images/math/font.png
17590 \begin_layout Subsection
17592 \begin_inset CommandInset label
17594 name "sub:Bold-Formulas"
17599 \begin_inset Index idx
17602 \begin_layout Plain Layout
17611 \begin_layout Standard
17612 To make a complete formula bold, the command
17618 from the previous subsection cannot be used, because it doesn't work for
17619 small Greek letters.
17620 Furthermore it prints Latin letters always upright, like in the following
17624 \begin_layout Standard
17625 \begin_inset Formula
17627 \mathbf{\int_{n}^{2}f(\theta)=\Gamma}\qquad\textrm{equation with \textbackslash mathbf}
17635 \begin_layout Standard
17636 To display the formula correctly, the command
17643 \begin_inset Formula
17645 \boldsymbol{\int_{n}^{2}f(\theta)=\Gamma\qquad\textrm{equation with \textbackslash boldsymbol}}
17650 It is also possible to set the formula in a
17652 boldmath environment
17655 This environment is created by inserting the command
17662 \begin_inset Index idx
17665 \begin_layout Plain Layout
17674 To end the environment, the command
17681 \begin_inset Index idx
17684 \begin_layout Plain Layout
17692 is inserted in TeX-mode.
17696 \begin_layout Plain Layout
17706 \begin_inset Formula
17708 \int_{n}^{2}f(\theta)=\Gamma\qquad\textrm{equation in a boldmath environment}
17717 \begin_layout Plain Layout
17729 \begin_layout Subsection
17731 \begin_inset Index idx
17734 \begin_layout Plain Layout
17743 \begin_layout Standard
17744 Formulas can be colored like normal text: Highlight a formula or a formula
17750 Here is a formula in magenta:
17751 \begin_inset Formula
17753 {\color{magenta}\int A\,\mathrm{d}x=\frac{\sqrt[5]{B}}{\ln\left(\frac{1}{3}\right)}}
17761 \begin_layout Standard
17762 You can also define your own colors as described in
17763 \begin_inset CommandInset ref
17765 reference "sub:Colored-Boxes"
17770 They can be used with the TeX code command
17777 \begin_inset Index idx
17780 \begin_layout Plain Layout
17791 \begin_layout Standard
17796 textcolor{color}{characters or formula}
17799 \begin_layout Standard
17800 The following example was colored completely dark green and partly red:
17803 \begin_layout Standard
17807 \begin_layout Plain Layout
17811 textcolor{darkgreen}{
17817 \begin_inset Formula
17819 \int A\,\mathrm{d}x=\frac{{\color{red}\sqrt[5]{B}}}{\ln\left(\frac{1}{3}\right)}
17828 \begin_layout Plain Layout
17838 \begin_layout Standard
17839 Due to a bug in LyX only complete formulas can be colored with self-defined
17844 \begin_layout Plain Layout
17845 \begin_inset CommandInset href
17847 name "LyX-bug #5269"
17848 target "http://www.lyx.org/trac/ticket/5269"
17860 \begin_layout Subsection
17862 \begin_inset CommandInset label
17864 name "sub:Font-Sizes"
17869 \begin_inset Index idx
17872 \begin_layout Plain Layout
17881 \begin_layout Standard
17882 For characters in formulas there are, analog to characters in text, the
17883 following size commands:
17886 \begin_layout Standard
17930 \begin_inset Newline newline
17952 \begin_layout Standard
17953 The size produced by the commands depends on the document font size, which
17954 corresponds to the command
17961 The other commands produce smaller or larger sizes than
17968 The font size can however not exceed a certain value.
17969 Is for example the document font size 12
17970 \begin_inset space \thinspace{}
17979 switches to the same size as
17989 \begin_layout Standard
17990 A size command is inserted in TeX-mode before the formula and sets the size
17991 for all following formula and text characters.
17992 To switch back to the initial size, the command
17998 is inserted behind the formula in TeX-mode.
18001 \begin_layout Standard
18002 Within a formula the size can be changed using the following size commands:
18005 \begin_layout Standard
18008 \begin_inset Tabular
18009 <lyxtabular version="3" rows="5" columns="2">
18010 <features rotate="0" tabularvalignment="middle">
18011 <column alignment="center" valignment="top">
18012 <column alignment="center" valignment="top">
18014 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
18017 \begin_layout Plain Layout
18023 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
18026 \begin_layout Plain Layout
18028 \begin_inset Note Note
18031 \begin_layout Plain Layout
18038 is only used as spacer.
18050 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
18053 \begin_layout Plain Layout
18057 \begin_inset Index idx
18060 \begin_layout Plain Layout
18073 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
18076 \begin_layout Plain Layout
18077 \begin_inset Formula $\raisebox{6.5mm}{}{\displaystyle E_{\mathrm{pot_{1}}}=\frac{K}{l+\frac{m}{n_{2}}}}\raisebox{-5.5mm}{}$
18087 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
18090 \begin_layout Plain Layout
18098 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
18101 \begin_layout Plain Layout
18102 \begin_inset Formula $\raisebox{4.5mm}{}{\textstyle E_{\mathrm{pot_{1}}}=\frac{K}{l+\frac{m}{n_{2}}}}\raisebox{-4mm}{}$
18112 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
18115 \begin_layout Plain Layout
18123 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
18126 \begin_layout Plain Layout
18127 \begin_inset Formula $\raisebox{4.5mm}{}{\scriptstyle E_{\mathrm{pot_{1}}}=\frac{K}{l+\frac{m}{n_{2}}}}\raisebox{-3.5mm}{}$
18137 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
18140 \begin_layout Plain Layout
18148 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
18151 \begin_layout Plain Layout
18152 \begin_inset Formula $\raisebox{4.5mm}{}{\scriptscriptstyle E_{\mathrm{pot_{1}}}=\frac{K}{l+\frac{m}{n_{2}}}}\raisebox{-3.5mm}{}$
18168 \begin_layout Standard
18169 After entering these commands, a blue box appears in which the formula parts
18173 \begin_layout Standard
18174 There is a further method to change the font size, that though only works
18175 for symbols or letters in mathematical text.
18176 To use it, one of the above text size commands is inserted in mathematical
18178 All following characters until the end of the mathematical text or until
18179 another size command will have the selected size.
18181 \begin_inset VSpace -2mm
18187 \begin_layout Standard
18191 \begin_layout Plain Layout
18201 \begin_inset Formula
18203 A=\frac{B}{c}\cdot\maltese
18209 \begin_inset Formula
18211 \maltese A\textrm{\Large\maltese\textit{A}}\textrm{\tiny\maltese\textit{A}}
18220 \begin_layout Plain Layout
18232 \begin_layout Standard
18233 \begin_inset VSpace medskip
18236 Before both formulas the command
18243 The command for the second formula is:
18244 \begin_inset Newline newline
18252 \begin_inset space \textvisiblespace{}
18258 \begin_inset space \textvisiblespace{}
18264 \begin_inset space \textvisiblespace{}
18270 \begin_inset space \textvisiblespace{}
18274 \begin_inset Formula $\to$
18278 \begin_inset Formula $\to$
18282 \begin_inset Newline newline
18286 \begin_inset space \hspace*{}
18297 \begin_inset space \textvisiblespace{}
18303 \begin_inset space \textvisiblespace{}
18309 \begin_inset space \textvisiblespace{}
18315 \begin_layout Standard
18316 If a symbol cannot be displayed in different sizes, it will always be displayed
18317 in the default size.
18320 \begin_layout Section
18322 \begin_inset Index idx
18325 \begin_layout Plain Layout
18334 \begin_layout Standard
18335 Greek letters can also be inserted via the toolbar button
18336 \begin_inset Graphics
18337 filename ../images/math/alpha.png
18343 All international typesetting norms purport that Greek letters in math
18344 have to be typeset italic/slanted.
18345 In some languages, like French or Russian, they are nevertheless sometimes
18349 \begin_layout Subsection
18351 \begin_inset Index idx
18354 \begin_layout Plain Layout
18355 Greek letters ! small
18363 \begin_layout Standard
18364 \begin_inset space \hfill{}
18368 \begin_inset Tabular
18369 <lyxtabular version="3" rows="11" columns="2">
18370 <features rotate="0" tabularvalignment="middle">
18371 <column alignment="center" valignment="top" width="0pt">
18372 <column alignment="center" valignment="top" width="0pt">
18374 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
18377 \begin_layout Plain Layout
18383 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
18386 \begin_layout Plain Layout
18394 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
18397 \begin_layout Plain Layout
18405 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
18408 \begin_layout Plain Layout
18409 \begin_inset Formula $\alpha$
18419 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
18422 \begin_layout Plain Layout
18430 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
18433 \begin_layout Plain Layout
18434 \begin_inset Formula $\beta$
18444 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
18447 \begin_layout Plain Layout
18455 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
18458 \begin_layout Plain Layout
18459 \begin_inset Formula $\gamma$
18469 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
18472 \begin_layout Plain Layout
18480 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
18483 \begin_layout Plain Layout
18484 \begin_inset Formula $\delta$
18494 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
18497 \begin_layout Plain Layout
18505 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
18508 \begin_layout Plain Layout
18509 \begin_inset Formula $\epsilon$
18519 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
18522 \begin_layout Plain Layout
18530 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
18533 \begin_layout Plain Layout
18534 \begin_inset Formula $\varepsilon$
18544 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
18547 \begin_layout Plain Layout
18555 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
18558 \begin_layout Plain Layout
18559 \begin_inset Formula $\zeta$
18569 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
18572 \begin_layout Plain Layout
18580 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
18583 \begin_layout Plain Layout
18584 \begin_inset Formula $\eta$
18594 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
18597 \begin_layout Plain Layout
18605 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
18608 \begin_layout Plain Layout
18609 \begin_inset Formula $\theta$
18619 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
18622 \begin_layout Plain Layout
18630 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
18633 \begin_layout Plain Layout
18634 \begin_inset Formula $\vartheta$
18648 \begin_inset space \hfill{}
18652 \begin_inset Tabular
18653 <lyxtabular version="3" rows="12" columns="2">
18654 <features rotate="0" tabularvalignment="middle">
18655 <column alignment="center" valignment="top" width="0pt">
18656 <column alignment="center" valignment="top" width="0pt">
18658 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
18661 \begin_layout Plain Layout
18667 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
18670 \begin_layout Plain Layout
18678 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
18681 \begin_layout Plain Layout
18689 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
18692 \begin_layout Plain Layout
18693 \begin_inset Formula $\iota$
18703 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
18706 \begin_layout Plain Layout
18714 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
18717 \begin_layout Plain Layout
18718 \begin_inset Formula $\kappa$
18728 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
18731 \begin_layout Plain Layout
18739 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
18742 \begin_layout Plain Layout
18743 \begin_inset Formula $\varkappa$
18753 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
18756 \begin_layout Plain Layout
18764 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
18767 \begin_layout Plain Layout
18768 \begin_inset Formula $\lambda$
18778 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
18781 \begin_layout Plain Layout
18789 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
18792 \begin_layout Plain Layout
18793 \begin_inset Formula $\mu$
18803 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
18806 \begin_layout Plain Layout
18814 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
18817 \begin_layout Plain Layout
18818 \begin_inset Formula $\nu$
18828 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
18831 \begin_layout Plain Layout
18839 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
18842 \begin_layout Plain Layout
18843 \begin_inset Formula $\xi$
18853 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
18856 \begin_layout Plain Layout
18862 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
18865 \begin_layout Plain Layout
18866 \begin_inset Formula $o$
18876 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
18879 \begin_layout Plain Layout
18887 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
18890 \begin_layout Plain Layout
18891 \begin_inset Formula $\pi$
18901 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
18904 \begin_layout Plain Layout
18912 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
18915 \begin_layout Plain Layout
18916 \begin_inset Formula $\varpi$
18926 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
18929 \begin_layout Plain Layout
18937 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
18940 \begin_layout Plain Layout
18941 \begin_inset Formula $\rho$
18955 \begin_inset space \hfill{}
18959 \begin_inset Tabular
18960 <lyxtabular version="3" rows="11" columns="2">
18961 <features rotate="0" tabularvalignment="middle">
18962 <column alignment="center" valignment="top" width="0pt">
18963 <column alignment="center" valignment="top" width="0pt">
18965 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
18968 \begin_layout Plain Layout
18974 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
18977 \begin_layout Plain Layout
18985 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
18988 \begin_layout Plain Layout
18996 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
18999 \begin_layout Plain Layout
19000 \begin_inset Formula $\varrho$
19010 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
19013 \begin_layout Plain Layout
19021 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
19024 \begin_layout Plain Layout
19025 \begin_inset Formula $\sigma$
19035 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
19038 \begin_layout Plain Layout
19046 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
19049 \begin_layout Plain Layout
19050 \begin_inset Formula $\varsigma$
19060 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
19063 \begin_layout Plain Layout
19071 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
19074 \begin_layout Plain Layout
19075 \begin_inset Formula $\tau$
19085 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
19088 \begin_layout Plain Layout
19096 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
19099 \begin_layout Plain Layout
19100 \begin_inset Formula $\upsilon$
19110 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
19113 \begin_layout Plain Layout
19121 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
19124 \begin_layout Plain Layout
19125 \begin_inset Formula $\phi$
19135 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
19138 \begin_layout Plain Layout
19146 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
19149 \begin_layout Plain Layout
19150 \begin_inset Formula $\varphi$
19160 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
19163 \begin_layout Plain Layout
19171 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
19174 \begin_layout Plain Layout
19175 \begin_inset Formula $\chi$
19185 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
19188 \begin_layout Plain Layout
19196 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
19199 \begin_layout Plain Layout
19200 \begin_inset Formula $\psi$
19210 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
19213 \begin_layout Plain Layout
19221 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
19224 \begin_layout Plain Layout
19225 \begin_inset Formula $\omega$
19239 \begin_inset space \hfill{}
19245 \begin_layout Standard
19246 \begin_inset VSpace medskip
19252 \begin_layout Standard
19253 How to create special upright Greek letters is explained in
19254 \begin_inset CommandInset ref
19256 reference "sub:Upright-small-Greek"
19263 \begin_layout Subsection
19265 \begin_inset Index idx
19268 \begin_layout Plain Layout
19269 Greek letters ! big
19277 \begin_layout Standard
19278 \begin_inset space \hfill{}
19282 \begin_inset Tabular
19283 <lyxtabular version="3" rows="7" columns="2">
19284 <features rotate="0" tabularvalignment="middle">
19285 <column alignment="center" valignment="top" width="0pt">
19286 <column alignment="center" valignment="top" width="0pt">
19288 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
19291 \begin_layout Plain Layout
19297 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
19300 \begin_layout Plain Layout
19308 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
19311 \begin_layout Plain Layout
19319 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
19322 \begin_layout Plain Layout
19323 \begin_inset Formula $\Gamma$
19333 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
19336 \begin_layout Plain Layout
19344 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
19347 \begin_layout Plain Layout
19348 \begin_inset Formula $\Delta$
19358 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
19361 \begin_layout Plain Layout
19369 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
19372 \begin_layout Plain Layout
19373 \begin_inset Formula $\Theta$
19383 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
19386 \begin_layout Plain Layout
19394 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
19397 \begin_layout Plain Layout
19398 \begin_inset Formula $\Lambda$
19408 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
19411 \begin_layout Plain Layout
19419 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
19422 \begin_layout Plain Layout
19423 \begin_inset Formula $\Xi$
19433 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
19436 \begin_layout Plain Layout
19444 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
19447 \begin_layout Plain Layout
19448 \begin_inset Formula $\Pi$
19462 \begin_inset space \hfill{}
19466 \begin_inset Tabular
19467 <lyxtabular version="3" rows="6" columns="2">
19468 <features rotate="0" tabularvalignment="middle">
19469 <column alignment="center" valignment="top" width="0pt">
19470 <column alignment="center" valignment="top" width="0pt">
19472 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
19475 \begin_layout Plain Layout
19481 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
19484 \begin_layout Plain Layout
19492 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
19495 \begin_layout Plain Layout
19503 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
19506 \begin_layout Plain Layout
19507 \begin_inset Formula $\Sigma$
19517 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
19520 \begin_layout Plain Layout
19528 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
19531 \begin_layout Plain Layout
19532 \begin_inset Formula $\Upsilon$
19542 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
19545 \begin_layout Plain Layout
19553 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
19556 \begin_layout Plain Layout
19557 \begin_inset Formula $\Phi$
19567 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
19570 \begin_layout Plain Layout
19578 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
19581 \begin_layout Plain Layout
19582 \begin_inset Formula $\Psi$
19592 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
19595 \begin_layout Plain Layout
19603 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
19606 \begin_layout Plain Layout
19607 \begin_inset Formula $\Omega$
19621 \begin_inset space \hfill{}
19627 \begin_layout Standard
19628 \begin_inset VSpace medskip
19631 That the big Greek letters appear upright is caused by a design bug when
19633 To get correct italic big letters, begin every command with
19638 For example the command
19645 \begin_inset Formula $\varGamma$
19649 Another way is to load the package
19657 \begin_layout Plain Layout
19662 is part of the LaTeX-package
19667 \begin_inset Index idx
19670 \begin_layout Plain Layout
19675 \begin_layout Plain Layout
19695 \begin_inset Index idx
19698 \begin_layout Plain Layout
19704 with the LaTeX-preamble line
19707 \begin_layout Standard
19712 usepackage{fixmath}
19715 \begin_layout Standard
19716 Then all big Greek letters in a document will automatically be typeset italic.
19719 \begin_layout Subsection
19721 \begin_inset Index idx
19724 \begin_layout Plain Layout
19725 Greek letters ! bold
19733 \begin_layout Standard
19734 Greek letters cannot be set with different font styles like Latin letters.
19735 They can only be made bold with the command
19742 \begin_inset Index idx
19745 \begin_layout Plain Layout
19756 \begin_layout Standard
19758 \begin_inset Tabular
19759 <lyxtabular version="3" rows="3" columns="2">
19760 <features rotate="0" tabularvalignment="middle">
19761 <column alignment="center" valignment="top">
19762 <column alignment="center" valignment="top">
19764 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
19767 \begin_layout Plain Layout
19773 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
19776 \begin_layout Plain Layout
19784 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
19787 \begin_layout Plain Layout
19799 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
19802 \begin_layout Plain Layout
19803 \begin_inset Formula $\Upsilon\boldsymbol{\Upsilon}$
19813 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
19816 \begin_layout Plain Layout
19828 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
19831 \begin_layout Plain Layout
19832 \begin_inset Formula $\theta\boldsymbol{\theta}$
19848 \begin_layout Section
19853 \begin_layout Plain Layout
19866 \begin_layout Plain Layout
19867 A list with all symbols of most of the LaTeX-packages can be found in
19868 \begin_inset CommandInset citation
19883 \begin_layout Plain Layout
19891 \begin_inset Note Note
19894 \begin_layout Plain Layout
19897 texorpdfstring is used to avoid that the footnote appears in the PDF-bookmark.
19900 \begin_layout Plain Layout
19903 texorpdfstring is in section
19904 \begin_inset CommandInset ref
19906 reference "sub:Formulas-in-Section"
19916 \begin_inset Index idx
19919 \begin_layout Plain Layout
19928 \begin_layout Standard
19929 Many of the symbols listed in this section can also be inserted via the
19931 \begin_inset Graphics
19932 filename ../images/math/nabla.png
19938 \begin_inset Graphics
19939 filename ../images/math/digamma.png
19947 \begin_layout Subsection
19948 Mathematical Symbols
19949 \begin_inset CommandInset label
19951 name "sub:Mathematical-Symbols"
19956 \begin_inset Index idx
19959 \begin_layout Plain Layout
19960 Symbols ! mathematical
19968 \begin_layout Standard
19969 \begin_inset space \hfill{}
19973 \begin_inset Tabular
19974 <lyxtabular version="3" rows="10" columns="2">
19975 <features rotate="0" tabularvalignment="middle">
19976 <column alignment="center" valignment="top" width="0pt">
19977 <column alignment="center" valignment="top" width="0pt">
19979 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
19982 \begin_layout Plain Layout
19988 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
19991 \begin_layout Plain Layout
19999 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
20002 \begin_layout Plain Layout
20010 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
20013 \begin_layout Plain Layout
20014 \begin_inset Formula $\neg$
20024 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
20027 \begin_layout Plain Layout
20035 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
20038 \begin_layout Plain Layout
20039 \begin_inset Formula $\Im$
20049 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
20052 \begin_layout Plain Layout
20060 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
20063 \begin_layout Plain Layout
20064 \begin_inset Formula $\Re$
20074 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
20077 \begin_layout Plain Layout
20085 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
20088 \begin_layout Plain Layout
20089 \begin_inset Formula $\aleph$
20099 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
20102 \begin_layout Plain Layout
20110 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
20113 \begin_layout Plain Layout
20114 \begin_inset Formula $\partial$
20124 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
20127 \begin_layout Plain Layout
20135 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
20138 \begin_layout Plain Layout
20139 \begin_inset Formula $\infty$
20149 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
20152 \begin_layout Plain Layout
20160 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
20163 \begin_layout Plain Layout
20164 \begin_inset Formula $\wp$
20174 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
20177 \begin_layout Plain Layout
20185 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
20188 \begin_layout Plain Layout
20189 \begin_inset Formula $\imath$
20199 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
20202 \begin_layout Plain Layout
20210 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
20213 \begin_layout Plain Layout
20214 \begin_inset Formula $\jmath$
20228 \begin_inset space \hfill{}
20232 \begin_inset Tabular
20233 <lyxtabular version="3" rows="10" columns="2">
20234 <features rotate="0" tabularvalignment="middle">
20235 <column alignment="center" valignment="top" width="0pt">
20236 <column alignment="center" valignment="top" width="0pt">
20238 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
20241 \begin_layout Plain Layout
20247 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
20250 \begin_layout Plain Layout
20252 \begin_inset Note Note
20255 \begin_layout Plain Layout
20262 is only used as spacer.
20274 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
20277 \begin_layout Plain Layout
20285 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
20288 \begin_layout Plain Layout
20289 \begin_inset Formula $\forall$
20299 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
20302 \begin_layout Plain Layout
20310 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
20313 \begin_layout Plain Layout
20314 \begin_inset Formula $\exists$
20324 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
20327 \begin_layout Plain Layout
20335 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
20338 \begin_layout Plain Layout
20339 \begin_inset Formula $\nexists$
20349 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
20352 \begin_layout Plain Layout
20360 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
20363 \begin_layout Plain Layout
20364 \begin_inset Formula $\emptyset$
20374 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
20377 \begin_layout Plain Layout
20385 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
20388 \begin_layout Plain Layout
20389 \begin_inset Formula $\varnothing$
20399 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
20402 \begin_layout Plain Layout
20410 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
20413 \begin_layout Plain Layout
20414 \begin_inset Formula $\dag$
20424 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
20427 \begin_layout Plain Layout
20435 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
20438 \begin_layout Plain Layout
20439 \begin_inset Formula $\ddag$
20449 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
20452 \begin_layout Plain Layout
20460 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
20463 \begin_layout Plain Layout
20467 \begin_layout Plain Layout
20477 \begin_inset Formula $\complement$
20484 \begin_layout Plain Layout
20498 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
20501 \begin_layout Plain Layout
20509 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
20512 \begin_layout Plain Layout
20513 \begin_inset Formula $\Bbbk$
20527 \begin_inset space \hfill{}
20531 \begin_inset Tabular
20532 <lyxtabular version="3" rows="10" columns="2">
20533 <features rotate="0" tabularvalignment="middle">
20534 <column alignment="center" valignment="top" width="0pt">
20535 <column alignment="center" valignment="top" width="0pt">
20537 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
20540 \begin_layout Plain Layout
20546 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
20549 \begin_layout Plain Layout
20557 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
20560 \begin_layout Plain Layout
20568 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
20571 \begin_layout Plain Layout
20572 \begin_inset Formula $\prime$
20582 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
20585 \begin_layout Plain Layout
20593 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
20596 \begin_layout Plain Layout
20597 \begin_inset Formula $\backprime$
20607 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
20610 \begin_layout Plain Layout
20618 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
20621 \begin_layout Plain Layout
20622 \begin_inset Formula $\mho$
20632 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
20635 \begin_layout Plain Layout
20643 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
20646 \begin_layout Plain Layout
20647 \begin_inset Formula $\triangle$
20657 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
20660 \begin_layout Plain Layout
20668 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
20671 \begin_layout Plain Layout
20672 \begin_inset Formula $\angle$
20682 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
20685 \begin_layout Plain Layout
20693 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
20696 \begin_layout Plain Layout
20697 \begin_inset Formula $\measuredangle$
20707 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
20710 \begin_layout Plain Layout
20718 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
20721 \begin_layout Plain Layout
20722 \begin_inset Formula $\sphericalangle$
20732 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
20735 \begin_layout Plain Layout
20743 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
20746 \begin_layout Plain Layout
20747 \begin_inset Formula $\top$
20757 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
20760 \begin_layout Plain Layout
20768 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
20771 \begin_layout Plain Layout
20772 \begin_inset Formula $\bot$
20786 \begin_inset space \hfill{}
20792 \begin_layout Subsection
20793 Miscellaneous Symbols
20794 \begin_inset CommandInset label
20796 name "sub:Miscellaneous-Symbols"
20801 \begin_inset Index idx
20804 \begin_layout Plain Layout
20805 Symbols ! miscellaneous
20813 \begin_layout Standard
20816 \begin_inset Tabular
20817 <lyxtabular version="3" rows="10" columns="2">
20818 <features rotate="0" tabularvalignment="middle">
20819 <column alignment="center" valignment="top" width="0pt">
20820 <column alignment="center" valignment="top" width="0pt">
20822 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
20825 \begin_layout Plain Layout
20831 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
20834 \begin_layout Plain Layout
20842 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
20845 \begin_layout Plain Layout
20853 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
20856 \begin_layout Plain Layout
20857 \begin_inset Formula $\flat$
20867 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
20870 \begin_layout Plain Layout
20878 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
20881 \begin_layout Plain Layout
20882 \begin_inset Formula $\natural$
20892 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
20895 \begin_layout Plain Layout
20903 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
20906 \begin_layout Plain Layout
20907 \begin_inset Formula $\sharp$
20917 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
20920 \begin_layout Plain Layout
20928 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
20931 \begin_layout Plain Layout
20932 \begin_inset Formula $\surd$
20942 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
20945 \begin_layout Plain Layout
20953 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
20956 \begin_layout Plain Layout
20957 \begin_inset Formula $\checkmark$
20967 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
20970 \begin_layout Plain Layout
20978 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
20981 \begin_layout Plain Layout
20982 \begin_inset Formula $\yen$
20992 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
20995 \begin_layout Plain Layout
21003 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
21006 \begin_layout Plain Layout
21007 \begin_inset Formula $\pounds$
21017 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
21020 \begin_layout Plain Layout
21026 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
21029 \begin_layout Plain Layout
21030 \begin_inset Formula $\$$
21040 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
21043 \begin_layout Plain Layout
21049 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
21052 \begin_layout Plain Layout
21053 \begin_inset Formula $§$
21067 \begin_inset Tabular
21068 <lyxtabular version="3" rows="10" columns="2">
21069 <features rotate="0" tabularvalignment="middle">
21070 <column alignment="center" valignment="top">
21071 <column alignment="center" valignment="top">
21073 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
21076 \begin_layout Plain Layout
21082 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
21085 \begin_layout Plain Layout
21093 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
21096 \begin_layout Plain Layout
21104 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
21107 \begin_layout Plain Layout
21108 \begin_inset Formula $\hbar$
21118 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
21121 \begin_layout Plain Layout
21129 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
21132 \begin_layout Plain Layout
21133 \begin_inset Formula $\hslash$
21143 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
21146 \begin_layout Plain Layout
21154 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
21157 \begin_layout Plain Layout
21158 \begin_inset Formula $\clubsuit$
21168 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
21171 \begin_layout Plain Layout
21179 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
21182 \begin_layout Plain Layout
21183 \begin_inset Formula $\spadesuit$
21193 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
21196 \begin_layout Plain Layout
21204 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
21207 \begin_layout Plain Layout
21208 \begin_inset Formula $\bigstar$
21218 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
21221 \begin_layout Plain Layout
21229 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
21232 \begin_layout Plain Layout
21233 \begin_inset Formula $\blacklozenge$
21243 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
21246 \begin_layout Plain Layout
21254 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
21257 \begin_layout Plain Layout
21258 \begin_inset Formula $\blacktriangle$
21268 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
21271 \begin_layout Plain Layout
21279 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
21282 \begin_layout Plain Layout
21283 \begin_inset Formula $\blacktriangledown$
21293 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
21296 \begin_layout Plain Layout
21304 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
21307 \begin_layout Plain Layout
21308 \begin_inset Formula $\bullet$
21322 \begin_inset Tabular
21323 <lyxtabular version="3" rows="10" columns="2">
21324 <features rotate="0" tabularvalignment="middle">
21325 <column alignment="center" valignment="top" width="0pt">
21326 <column alignment="center" valignment="top" width="0pt">
21328 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
21331 \begin_layout Plain Layout
21337 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
21340 \begin_layout Plain Layout
21348 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
21351 \begin_layout Plain Layout
21359 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
21362 \begin_layout Plain Layout
21363 \begin_inset Formula $\diamondsuit$
21373 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
21376 \begin_layout Plain Layout
21384 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
21387 \begin_layout Plain Layout
21388 \begin_inset Formula $\Diamond$
21398 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
21401 \begin_layout Plain Layout
21409 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
21412 \begin_layout Plain Layout
21413 \begin_inset Formula $\heartsuit$
21423 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
21426 \begin_layout Plain Layout
21434 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
21437 \begin_layout Plain Layout
21438 \begin_inset Formula $\P$
21448 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
21451 \begin_layout Plain Layout
21459 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
21462 \begin_layout Plain Layout
21463 \begin_inset Formula $\copyright$
21473 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
21476 \begin_layout Plain Layout
21484 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
21487 \begin_layout Plain Layout
21488 \begin_inset Formula $\circledR$
21498 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
21501 \begin_layout Plain Layout
21509 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
21512 \begin_layout Plain Layout
21513 \begin_inset Formula $\maltese$
21523 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
21526 \begin_layout Plain Layout
21534 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
21537 \begin_layout Plain Layout
21538 \begin_inset Formula $\diagup$
21548 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
21551 \begin_layout Plain Layout
21559 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
21562 \begin_layout Plain Layout
21563 \begin_inset Formula $\diagdown$
21579 \begin_layout Standard
21580 \begin_inset VSpace medskip
21586 \begin_layout Standard
21587 Some symbols can be displayed in different sizes, see
21588 \begin_inset CommandInset ref
21590 reference "sub:Font-Sizes"
21597 \begin_layout Subsection
21599 \begin_inset Index idx
21602 \begin_layout Plain Layout
21603 Symbols ! Euro-symbol
21609 \begin_inset Index idx
21612 \begin_layout Plain Layout
21619 \begin_layout Plain Layout
21636 \begin_layout Standard
21637 To use the Euro symbol in formulas, the LaTeX-package
21642 \begin_inset Index idx
21645 \begin_layout Plain Layout
21651 must be installed and loaded with the LaTeX-preamble line
21654 \begin_layout Standard
21659 usepackage[gennarrow]{eurosym}
21662 \begin_layout Standard
21663 The Euro symbol can now be inserted with the command
21670 \begin_inset Index idx
21673 \begin_layout Plain Layout
21684 \begin_layout Standard
21685 The Euro symbol can directly be inserted with the € key in mathematical
21686 text, without having
21701 can also be inserted in TeX-mode.
21702 The official currency symbol can then be inserted with the command
21709 \begin_inset Index idx
21712 \begin_layout Plain Layout
21720 , that is only available in TeX-mode.
21723 \begin_layout Standard
21727 \begin_layout Plain Layout
21737 \begin_inset Note Note
21740 \begin_layout Plain Layout
21741 The following table will only be displayed when the LaTeX-package
21753 \begin_layout Standard
21754 An overview about the different Euro symbols:
21757 \begin_layout Standard
21759 \begin_inset Tabular
21760 <lyxtabular version="3" rows="4" columns="3">
21761 <features rotate="0" tabularvalignment="middle">
21762 <column alignment="center" valignment="top" width="0pt">
21763 <column alignment="center" valignment="top" width="0pt">
21764 <column alignment="center" valignment="top" width="0pt">
21766 <cell multicolumn="1" alignment="center" valignment="top" bottomline="true" usebox="none">
21769 \begin_layout Plain Layout
21775 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
21778 \begin_layout Plain Layout
21784 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
21787 \begin_layout Plain Layout
21795 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
21798 \begin_layout Plain Layout
21804 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
21807 \begin_layout Plain Layout
21815 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
21818 \begin_layout Plain Layout
21819 \begin_inset Formula $\euro$
21829 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
21832 \begin_layout Plain Layout
21838 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
21841 \begin_layout Plain Layout
21847 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
21850 \begin_layout Plain Layout
21851 \begin_inset Formula $\mbox{€}$
21861 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
21864 \begin_layout Plain Layout
21870 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
21873 \begin_layout Plain Layout
21881 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
21884 \begin_layout Plain Layout
21888 \begin_layout Plain Layout
21910 \begin_layout Standard
21914 \begin_layout Plain Layout
21924 \begin_inset Note Note
21927 \begin_layout Plain Layout
21928 The following will be displayed when the LaTeX-package
21940 \begin_layout Standard
21941 You need to install the LaTeX-package
21945 to see the rest of this subsection in the output.
21948 \begin_layout Standard
21952 \begin_layout Plain Layout
21964 \begin_layout Section
21966 \begin_inset CommandInset label
21968 name "sec:Relations"
21973 \begin_inset Index idx
21976 \begin_layout Plain Layout
21983 \begin_inset Index idx
21986 \begin_layout Plain Layout
21991 \begin_layout Plain Layout
22002 \begin_layout Plain Layout
22017 \begin_layout Standard
22018 All relations can also be inserted via the toolbar button
22019 \begin_inset Graphics
22020 filename ../images/math/leq.png
22028 \begin_layout Standard
22029 \begin_inset space \hfill{}
22033 \begin_inset Tabular
22034 <lyxtabular version="3" rows="17" columns="2">
22035 <features rotate="0" tabularvalignment="middle">
22036 <column alignment="center" valignment="top" width="0pt">
22037 <column alignment="center" valignment="top" width="0pt">
22039 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
22042 \begin_layout Plain Layout
22048 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
22051 \begin_layout Plain Layout
22059 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
22062 \begin_layout Plain Layout
22068 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
22071 \begin_layout Plain Layout
22072 \begin_inset Formula $<$
22082 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
22085 \begin_layout Plain Layout
22093 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
22096 \begin_layout Plain Layout
22097 \begin_inset Formula $\le$
22107 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
22110 \begin_layout Plain Layout
22118 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
22121 \begin_layout Plain Layout
22122 \begin_inset Formula $\ll$
22132 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
22135 \begin_layout Plain Layout
22143 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
22146 \begin_layout Plain Layout
22147 \begin_inset Formula $\prec$
22157 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
22160 \begin_layout Plain Layout
22168 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
22171 \begin_layout Plain Layout
22172 \begin_inset Formula $\preceq$
22182 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
22185 \begin_layout Plain Layout
22193 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
22196 \begin_layout Plain Layout
22197 \begin_inset Formula $\subset$
22207 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
22210 \begin_layout Plain Layout
22218 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
22221 \begin_layout Plain Layout
22222 \begin_inset Formula $\subseteq$
22232 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
22235 \begin_layout Plain Layout
22243 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
22246 \begin_layout Plain Layout
22247 \begin_inset Formula $\sqsubseteq$
22257 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
22260 \begin_layout Plain Layout
22268 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
22271 \begin_layout Plain Layout
22272 \begin_inset Formula $\in$
22282 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
22285 \begin_layout Plain Layout
22293 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
22296 \begin_layout Plain Layout
22297 \begin_inset Formula $\vdash$
22307 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
22310 \begin_layout Plain Layout
22318 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
22321 \begin_layout Plain Layout
22322 \begin_inset Formula $\smile$
22332 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
22335 \begin_layout Plain Layout
22343 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
22346 \begin_layout Plain Layout
22347 \begin_inset Formula $\lhd$
22357 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
22360 \begin_layout Plain Layout
22368 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
22371 \begin_layout Plain Layout
22372 \begin_inset Formula $\unlhd$
22382 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
22385 \begin_layout Plain Layout
22393 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
22396 \begin_layout Plain Layout
22397 \begin_inset Formula $\gtrless$
22407 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
22410 \begin_layout Plain Layout
22418 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
22421 \begin_layout Plain Layout
22422 \begin_inset Formula $\mid$
22432 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
22435 \begin_layout Plain Layout
22443 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
22446 \begin_layout Plain Layout
22447 \begin_inset Formula $\nmid$
22461 \begin_inset space \hfill{}
22465 \begin_inset Tabular
22466 <lyxtabular version="3" rows="17" columns="2">
22467 <features rotate="0" tabularvalignment="middle">
22468 <column alignment="center" valignment="top" width="0pt">
22469 <column alignment="center" valignment="top" width="0pt">
22471 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
22474 \begin_layout Plain Layout
22480 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
22483 \begin_layout Plain Layout
22491 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
22494 \begin_layout Plain Layout
22500 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
22503 \begin_layout Plain Layout
22504 \begin_inset Formula $=$
22514 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
22517 \begin_layout Plain Layout
22525 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
22528 \begin_layout Plain Layout
22529 \begin_inset Formula $\not=$
22539 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
22542 \begin_layout Plain Layout
22550 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
22553 \begin_layout Plain Layout
22554 \begin_inset Formula $\equiv$
22564 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
22567 \begin_layout Plain Layout
22575 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
22578 \begin_layout Plain Layout
22579 \begin_inset Formula $\sim$
22589 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
22592 \begin_layout Plain Layout
22600 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
22603 \begin_layout Plain Layout
22604 \begin_inset Formula $\simeq$
22614 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
22617 \begin_layout Plain Layout
22625 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
22628 \begin_layout Plain Layout
22629 \begin_inset Formula $\approx$
22639 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
22642 \begin_layout Plain Layout
22650 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
22653 \begin_layout Plain Layout
22654 \begin_inset Formula $\cong$
22664 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
22667 \begin_layout Plain Layout
22675 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
22678 \begin_layout Plain Layout
22679 \begin_inset Formula $\bowtie$
22689 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
22692 \begin_layout Plain Layout
22700 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
22703 \begin_layout Plain Layout
22704 \begin_inset Formula $\notin$
22714 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
22717 \begin_layout Plain Layout
22725 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
22728 \begin_layout Plain Layout
22729 \begin_inset Formula $\perp$
22739 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
22742 \begin_layout Plain Layout
22750 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
22753 \begin_layout Plain Layout
22754 \begin_inset Formula $\propto$
22764 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
22767 \begin_layout Plain Layout
22775 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
22778 \begin_layout Plain Layout
22779 \begin_inset Formula $\asymp$
22789 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
22792 \begin_layout Plain Layout
22800 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
22803 \begin_layout Plain Layout
22804 \begin_inset Formula $\doteq$
22814 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
22817 \begin_layout Plain Layout
22825 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
22828 \begin_layout Plain Layout
22829 \begin_inset Formula $\circeq$
22839 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
22842 \begin_layout Plain Layout
22850 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
22853 \begin_layout Plain Layout
22854 \begin_inset Formula $\models$
22864 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
22867 \begin_layout Plain Layout
22875 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
22878 \begin_layout Plain Layout
22879 \begin_inset Formula $\widehat{=}$
22893 \begin_inset space \hfill{}
22897 \begin_inset Tabular
22898 <lyxtabular version="3" rows="17" columns="2">
22899 <features rotate="0" tabularvalignment="middle">
22900 <column alignment="center" valignment="top" width="0pt">
22901 <column alignment="center" valignment="top" width="0pt">
22903 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
22906 \begin_layout Plain Layout
22912 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
22915 \begin_layout Plain Layout
22923 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
22926 \begin_layout Plain Layout
22932 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
22935 \begin_layout Plain Layout
22936 \begin_inset Formula $>$
22946 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
22949 \begin_layout Plain Layout
22957 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
22960 \begin_layout Plain Layout
22961 \begin_inset Formula $\ge$
22971 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
22974 \begin_layout Plain Layout
22982 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
22985 \begin_layout Plain Layout
22986 \begin_inset Formula $\gg$
22996 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
22999 \begin_layout Plain Layout
23007 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
23010 \begin_layout Plain Layout
23011 \begin_inset Formula $\succ$
23021 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
23024 \begin_layout Plain Layout
23032 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
23035 \begin_layout Plain Layout
23036 \begin_inset Formula $\succeq$
23046 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
23049 \begin_layout Plain Layout
23057 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
23060 \begin_layout Plain Layout
23061 \begin_inset Formula $\supset$
23071 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
23074 \begin_layout Plain Layout
23082 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
23085 \begin_layout Plain Layout
23086 \begin_inset Formula $\supseteq$
23096 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
23099 \begin_layout Plain Layout
23107 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
23110 \begin_layout Plain Layout
23111 \begin_inset Formula $\sqsupseteq$
23121 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
23124 \begin_layout Plain Layout
23132 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
23135 \begin_layout Plain Layout
23136 \begin_inset Formula $\ni$
23146 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
23149 \begin_layout Plain Layout
23157 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
23160 \begin_layout Plain Layout
23161 \begin_inset Formula $\dashv$
23171 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
23174 \begin_layout Plain Layout
23182 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
23185 \begin_layout Plain Layout
23186 \begin_inset Formula $\frown$
23196 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
23199 \begin_layout Plain Layout
23207 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
23210 \begin_layout Plain Layout
23211 \begin_inset Formula $\rhd$
23221 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
23224 \begin_layout Plain Layout
23232 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
23235 \begin_layout Plain Layout
23236 \begin_inset Formula $\unrhd$
23246 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
23249 \begin_layout Plain Layout
23257 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
23260 \begin_layout Plain Layout
23261 \begin_inset Formula $\lessgtr$
23271 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
23274 \begin_layout Plain Layout
23282 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
23285 \begin_layout Plain Layout
23286 \begin_inset Formula $\parallel$
23296 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
23299 \begin_layout Plain Layout
23307 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
23310 \begin_layout Plain Layout
23311 \begin_inset Formula $\nparallel$
23325 \begin_inset space \hfill{}
23331 \begin_layout Standard
23332 \begin_inset VSpace medskip
23347 are bigger than the equal looking operators
23362 \begin_layout Standard
23363 Relations are, in contrary to symbols, always surrounded by space.
23366 \begin_layout Standard
23367 Relations with labels can be created with the command
23374 \begin_inset Index idx
23377 \begin_layout Plain Layout
23388 \begin_layout Standard
23390 \begin_inset Tabular
23391 <lyxtabular version="3" rows="2" columns="2">
23392 <features rotate="0" tabularvalignment="middle">
23393 <column alignment="center" valignment="top">
23394 <column alignment="center" valignment="top">
23396 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
23399 \begin_layout Plain Layout
23405 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
23408 \begin_layout Plain Layout
23410 \begin_inset Note Note
23413 \begin_layout Plain Layout
23420 is only used as spacer.
23432 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
23435 \begin_layout Plain Layout
23439 \begin_inset space \textvisiblespace{}
23447 \begin_inset space \textvisiblespace{}
23451 \begin_inset Formula $\downarrow$
23457 \begin_inset space \textvisiblespace{}
23461 \begin_inset space \textvisiblespace{}
23469 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
23472 \begin_layout Plain Layout
23473 \begin_inset Formula $\raisebox{5mm}{}A(r)\stackrel{r\to\infty}{\approx}B$
23489 \begin_layout Section
23493 \begin_layout Subsection
23494 Predefined Functions
23495 \begin_inset CommandInset label
23497 name "sub:Predefined-Functions"
23502 \begin_inset Index idx
23505 \begin_layout Plain Layout
23506 Functions ! predefined
23514 \begin_layout Standard
23515 In general, variables are set
23519 in mathematical expressions, but not function names, because
23520 \begin_inset Formula $sin$
23523 could be misunderstood as
23524 \begin_inset Formula $s\cdot i\cdot n$
23528 Therefore there are predefined functionswhich are additionally a bit separated
23530 They are inserted as commands starting with a backslash before their name.
23533 \begin_layout Standard
23535 \begin_inset Tabular
23536 <lyxtabular version="3" rows="2" columns="4">
23537 <features rotate="0" tabularvalignment="middle">
23538 <column alignment="center" valignment="top" width="0pt">
23539 <column alignment="center" valignment="top" width="0pt">
23540 <column alignment="center" valignment="top" width="0pt">
23541 <column alignment="center" valignment="top" width="0pt">
23543 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
23546 \begin_layout Plain Layout
23552 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
23555 \begin_layout Plain Layout
23561 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
23564 \begin_layout Plain Layout
23570 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
23573 \begin_layout Plain Layout
23581 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
23584 \begin_layout Plain Layout
23590 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
23593 \begin_layout Plain Layout
23594 \begin_inset Formula $Asin(x)+B$
23602 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
23605 \begin_layout Plain Layout
23613 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
23616 \begin_layout Plain Layout
23617 \begin_inset Formula $A\sin(x)+B$
23633 \begin_layout Standard
23634 The following functions are predefined:
23637 \begin_layout Standard
23638 \begin_inset VSpace -2mm
23644 \begin_layout Standard
23646 \begin_inset Tabular
23647 <lyxtabular version="3" rows="9" columns="4">
23648 <features rotate="0" tabularvalignment="middle">
23649 <column alignment="center" valignment="top" width="0pt">
23650 <column alignment="center" valignment="top" width="0pt">
23651 <column alignment="center" valignment="top" width="0pt">
23652 <column alignment="center" valignment="top" width="0pt">
23654 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
23657 \begin_layout Plain Layout
23663 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
23666 \begin_layout Plain Layout
23672 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
23675 \begin_layout Plain Layout
23681 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
23684 \begin_layout Plain Layout
23692 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
23695 \begin_layout Plain Layout
23703 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
23706 \begin_layout Plain Layout
23714 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
23717 \begin_layout Plain Layout
23725 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
23728 \begin_layout Plain Layout
23738 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
23741 \begin_layout Plain Layout
23749 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
23752 \begin_layout Plain Layout
23760 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
23763 \begin_layout Plain Layout
23771 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
23774 \begin_layout Plain Layout
23784 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
23787 \begin_layout Plain Layout
23795 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
23798 \begin_layout Plain Layout
23806 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
23809 \begin_layout Plain Layout
23817 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
23820 \begin_layout Plain Layout
23830 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
23833 \begin_layout Plain Layout
23841 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
23844 \begin_layout Plain Layout
23852 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
23855 \begin_layout Plain Layout
23863 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
23866 \begin_layout Plain Layout
23876 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
23879 \begin_layout Plain Layout
23887 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
23890 \begin_layout Plain Layout
23898 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
23901 \begin_layout Plain Layout
23909 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
23912 \begin_layout Plain Layout
23922 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
23925 \begin_layout Plain Layout
23933 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
23936 \begin_layout Plain Layout
23944 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
23947 \begin_layout Plain Layout
23955 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
23958 \begin_layout Plain Layout
23968 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
23971 \begin_layout Plain Layout
23979 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
23982 \begin_layout Plain Layout
23990 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
23993 \begin_layout Plain Layout
24001 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
24004 \begin_layout Plain Layout
24014 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
24017 \begin_layout Plain Layout
24025 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
24028 \begin_layout Plain Layout
24036 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
24039 \begin_layout Plain Layout
24047 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
24050 \begin_layout Plain Layout
24066 \begin_layout Standard
24067 They can also be inserted with the math toolbar button
24068 \begin_inset Graphics
24069 filename ../images/math/functions.png
24077 \begin_layout Subsection
24078 Self-defined Functions
24079 \begin_inset Index idx
24082 \begin_layout Plain Layout
24083 Functions ! self-defined
24091 \begin_layout Standard
24092 To use a function that is not predefined, like for example the sign function
24093 sgn(x), there are two possibilities:
24096 \begin_layout Itemize
24097 Define the function by inserting the following line to the LaTeX-preamble
24101 \begin_layout Plain Layout
24106 DeclareMathOperator
24109 \begin_inset CommandInset ref
24111 reference "sub:Self-defined-Operators"
24121 \begin_inset Newline newline
24125 \begin_inset VSpace -3mm
24129 \begin_inset Newline newline
24136 DeclareMathOperator{
24141 \begin_inset Index idx
24144 \begin_layout Plain Layout
24149 DeclareMathOperator
24155 \begin_inset Newline newline
24159 \begin_inset VSpace -2mm
24163 \begin_inset Newline newline
24166 Now the new defined function can be called with the command
24175 \begin_layout Itemize
24176 Write the formula as usual, mark the formula name, in our example the letters
24181 , and change it to mathematical text.
24182 Finally, a space is inserted between prefactor and function.
24185 \begin_layout Standard
24186 The result is the same with both methods as with a predefined function
24190 \begin_layout Plain Layout
24191 In LyX self-defined functions are displayed red, predefined ones black.
24199 \begin_layout Standard
24201 \begin_inset Tabular
24202 <lyxtabular version="3" rows="3" columns="2">
24203 <features rotate="0" tabularvalignment="middle">
24204 <column alignment="center" valignment="top" width="0pt">
24205 <column alignment="center" valignment="top" width="0pt">
24207 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
24210 \begin_layout Plain Layout
24216 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
24219 \begin_layout Plain Layout
24227 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
24230 \begin_layout Plain Layout
24238 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
24241 \begin_layout Plain Layout
24242 \begin_inset Formula $A\sgn(x)+B$
24252 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
24255 \begin_layout Plain Layout
24259 \begin_inset Formula $\underbrace{\textrm{sgn}}_{\textrm{Alt+M}\,\textrm{M}}$
24267 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
24270 \begin_layout Plain Layout
24271 \begin_inset Formula $A\,\textrm{sgn}(x)+B$
24287 \begin_layout Standard
24288 The first method is more suitable when the self-defined function should
24289 be used several times.
24292 \begin_layout Subsection
24294 \begin_inset Index idx
24297 \begin_layout Plain Layout
24306 \begin_layout Standard
24307 For limits, in addition to the commands
24314 \begin_inset Index idx
24317 \begin_layout Plain Layout
24337 the following functions are defined:
24340 \begin_layout Standard
24342 \begin_inset Tabular
24343 <lyxtabular version="3" rows="5" columns="2">
24344 <features rotate="0" tabularvalignment="middle">
24345 <column alignment="center" valignment="top">
24346 <column alignment="center" valignment="top">
24348 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
24351 \begin_layout Plain Layout
24357 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
24360 \begin_layout Plain Layout
24362 \begin_inset Note Note
24365 \begin_layout Plain Layout
24372 is only used as spacer.
24384 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
24387 \begin_layout Plain Layout
24395 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
24398 \begin_layout Plain Layout
24399 \begin_inset Formula $\varliminf$
24409 <cell alignment="center" valignment="top" leftline="true" usebox="none">
24412 \begin_layout Plain Layout
24420 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
24423 \begin_layout Plain Layout
24424 \begin_inset Formula $\varlimsup$
24434 <cell alignment="center" valignment="top" leftline="true" usebox="none">
24437 \begin_layout Plain Layout
24445 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
24448 \begin_layout Plain Layout
24449 \begin_inset Formula $\varprojlim$
24459 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
24462 \begin_layout Plain Layout
24470 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
24473 \begin_layout Plain Layout
24474 \begin_inset Formula $\varinjlim$
24478 \begin_inset Formula $\raisebox{-2.5mm}{}$
24494 \begin_layout Standard
24495 \begin_inset VSpace medskip
24498 The limit is created by inserting a subscript.
24499 It is set right beside the function in an inline formula:
24502 \begin_layout Standard
24504 \begin_inset Tabular
24505 <lyxtabular version="3" rows="2" columns="2">
24506 <features rotate="0" tabularvalignment="middle">
24507 <column alignment="center" valignment="top" width="0pt">
24508 <column alignment="center" valignment="top" width="0pt">
24510 <cell alignment="center" valignment="top" usebox="none">
24513 \begin_layout Plain Layout
24519 <cell alignment="center" valignment="top" usebox="none">
24522 \begin_layout Plain Layout
24523 \begin_inset space \hspace{}
24528 \begin_inset Note Note
24531 \begin_layout Plain Layout
24538 are used here as spacer.
24550 <cell alignment="center" valignment="top" usebox="none">
24553 \begin_layout Plain Layout
24559 \begin_inset space \textvisiblespace{}
24563 \begin_inset space \textvisiblespace{}
24571 <cell alignment="center" valignment="top" usebox="none">
24574 \begin_layout Plain Layout
24575 \begin_inset Formula $\hspace{1cm}\raisebox{5mm}{}\lim_{x\to A}x=B$
24591 \begin_layout Standard
24592 In a displayed formula the limit is set below the formula, as usual:
24593 \begin_inset Formula
24603 \begin_layout Subsection
24605 \begin_inset Index idx
24608 \begin_layout Plain Layout
24609 Functions ! modulo-
24617 \begin_layout Standard
24618 The modulo-function is special, because it exists in four variants.
24619 The variants in a displayed formula are:
24620 \begin_inset Formula
24622 \underline{\textrm{Command}\raisebox{-0.9mm}{}} & & \underline{\textrm{Result}}\\
24623 \mathrm{a\backslash mod\textrm{␣}b} & & a\mod b\\
24624 \mathrm{a\backslash pmod\textrm{␣}b} & & a\pmod b\\
24625 \mathrm{a\backslash bmod\textrm{␣}b} & & a\bmod b\\
24626 \mathrm{a\backslash pod\textrm{␣}b} & & a\pod b
24634 \begin_layout Standard
24635 In an inline formula less space is set before the function names for all
24637 By default the modulo-functions take only the first following character
24639 To use more than one character, one has to put them into TeX-braces:
24640 \begin_inset Formula
24642 \underline{\textrm{Command}\raisebox{-0.9mm}{}} & & \underline{\textrm{Result}}\\
24643 \mathrm{a\backslash pod\textrm{␣}bcd} & & a\pod bcd\\
24644 \mathrm{a\backslash pod\backslash\{bc\to d} & & a\pod{bc}d
24652 \begin_layout Section
24654 \begin_inset Index idx
24657 \begin_layout Plain Layout
24666 \begin_layout Subsection
24667 Special Characters in Mathematical Text
24670 \begin_layout Standard
24671 The following commands can only be used in mathematical text or in TeX-mode:
24674 \begin_layout Standard
24675 \begin_inset space \hfill{}
24679 \begin_inset Tabular
24680 <lyxtabular version="3" rows="8" columns="2">
24681 <features rotate="0" tabularvalignment="middle">
24682 <column alignment="block" valignment="top">
24683 <column alignment="block" valignment="top">
24685 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
24688 \begin_layout Plain Layout
24694 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
24697 \begin_layout Plain Layout
24705 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
24708 \begin_layout Plain Layout
24716 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
24719 \begin_layout Plain Layout
24720 \begin_inset Formula $\textrm{œ}$
24730 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
24733 \begin_layout Plain Layout
24741 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
24744 \begin_layout Plain Layout
24745 \begin_inset Formula $\textrm{Œ}$
24755 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
24758 \begin_layout Plain Layout
24766 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
24769 \begin_layout Plain Layout
24770 \begin_inset Formula $\textrm{æ}$
24780 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
24783 \begin_layout Plain Layout
24791 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
24794 \begin_layout Plain Layout
24795 \begin_inset Formula $\textrm{Æ}$
24805 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
24808 \begin_layout Plain Layout
24816 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
24819 \begin_layout Plain Layout
24820 \begin_inset Formula $\textrm{\aa}$
24830 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
24833 \begin_layout Plain Layout
24837 \begin_inset Index idx
24840 \begin_layout Plain Layout
24847 \begin_layout Plain Layout
24868 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
24871 \begin_layout Plain Layout
24872 \begin_inset Formula $\textrm{Å}$
24882 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
24885 \begin_layout Plain Layout
24893 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
24896 \begin_layout Plain Layout
24897 \begin_inset Formula $\textrm{ı}$
24911 \begin_inset space \hfill{}
24915 \begin_inset Tabular
24916 <lyxtabular version="3" rows="8" columns="2">
24917 <features rotate="0" tabularvalignment="middle">
24918 <column alignment="block" valignment="top">
24919 <column alignment="center" valignment="top">
24921 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
24924 \begin_layout Plain Layout
24926 \begin_inset Note Note
24929 \begin_layout Plain Layout
24931 \begin_inset space \thinspace{}
24934 mm is used for separation, because otherwise the output will be ¡ and ¿
24945 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
24948 \begin_layout Plain Layout
24956 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
24959 \begin_layout Plain Layout
24967 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
24970 \begin_layout Plain Layout
24971 \begin_inset Formula $\textrm{ø}$
24981 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
24984 \begin_layout Plain Layout
24992 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
24995 \begin_layout Plain Layout
24996 \begin_inset Formula $\textrm{Ø}$
25006 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
25009 \begin_layout Plain Layout
25017 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
25020 \begin_layout Plain Layout
25021 \begin_inset Formula $\textrm{ł}$
25031 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
25034 \begin_layout Plain Layout
25042 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
25045 \begin_layout Plain Layout
25046 \begin_inset Formula $\textrm{Ł}$
25056 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
25059 \begin_layout Plain Layout
25061 \begin_inset space \hspace{}
25066 \begin_inset space \textvisiblespace{}
25074 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
25077 \begin_layout Plain Layout
25078 \begin_inset Formula $\textrm{!`}$
25088 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
25091 \begin_layout Plain Layout
25093 \begin_inset space \hspace{}
25098 \begin_inset space \textvisiblespace{}
25106 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
25109 \begin_layout Plain Layout
25110 \begin_inset Formula $\textrm{?`}$
25120 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
25123 \begin_layout Plain Layout
25131 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
25134 \begin_layout Plain Layout
25135 \begin_inset Formula $\textrm{ȷ}$
25149 \begin_inset space \hfill{}
25155 \begin_layout Standard
25157 \begin_inset Formula $\textrm{\textrm{Å}}$
25161 \begin_inset Formula $\textrm{\textrm{Ø}}$
25164 can also be inserted via the math toolbar button
25165 \begin_inset Graphics
25166 filename ../images/math/digamma.png
25174 \begin_layout Standard
25175 An exception are the commands
25178 \begin_inset space \hspace{}
25187 \begin_inset space \hspace{}
25193 , because they can be inserted in LyX directly to text.
25196 \begin_layout Subsection
25198 \begin_inset CommandInset label
25200 name "sub:Accents-in-Text"
25205 \begin_inset Index idx
25208 \begin_layout Plain Layout
25217 \begin_layout Standard
25218 With the following commands all letters can be accented.
25219 The commands must be inserted in TeX-mode.
25222 \begin_layout Standard
25223 \begin_inset space \hfill{}
25227 \begin_inset Tabular
25228 <lyxtabular version="3" rows="8" columns="2">
25229 <features rotate="0" tabularvalignment="middle">
25230 <column alignment="block" valignment="top">
25231 <column alignment="block" valignment="top">
25233 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
25236 \begin_layout Plain Layout
25242 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
25245 \begin_layout Plain Layout
25253 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
25256 \begin_layout Plain Layout
25260 \begin_inset Quotes grd
25268 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
25271 \begin_layout Plain Layout
25275 \begin_layout Plain Layout
25291 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
25294 \begin_layout Plain Layout
25302 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
25305 \begin_layout Plain Layout
25309 \begin_layout Plain Layout
25325 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
25328 \begin_layout Plain Layout
25332 \begin_inset space \textvisiblespace{}
25340 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
25343 \begin_layout Plain Layout
25347 \begin_layout Plain Layout
25363 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
25366 \begin_layout Plain Layout
25374 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
25377 \begin_layout Plain Layout
25381 \begin_layout Plain Layout
25397 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
25400 \begin_layout Plain Layout
25404 \begin_inset space \textvisiblespace{}
25412 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
25415 \begin_layout Plain Layout
25419 \begin_layout Plain Layout
25435 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
25438 \begin_layout Plain Layout
25442 \begin_inset space \textvisiblespace{}
25450 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
25453 \begin_layout Plain Layout
25457 \begin_layout Plain Layout
25473 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
25476 \begin_layout Plain Layout
25480 \begin_inset space \textvisiblespace{}
25488 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
25491 \begin_layout Plain Layout
25495 \begin_layout Plain Layout
25515 \begin_inset space \hfill{}
25519 \begin_inset Tabular
25520 <lyxtabular version="3" rows="8" columns="2">
25521 <features rotate="0" tabularvalignment="middle">
25522 <column alignment="block" valignment="top">
25523 <column alignment="center" valignment="top">
25525 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
25528 \begin_layout Plain Layout
25534 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
25537 \begin_layout Plain Layout
25545 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
25548 \begin_layout Plain Layout
25552 \begin_inset space \textvisiblespace{}
25560 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
25563 \begin_layout Plain Layout
25567 \begin_layout Plain Layout
25583 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
25586 \begin_layout Plain Layout
25594 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
25597 \begin_layout Plain Layout
25601 \begin_layout Plain Layout
25617 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
25620 \begin_layout Plain Layout
25624 \begin_inset Index idx
25627 \begin_layout Plain Layout
25638 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
25641 \begin_layout Plain Layout
25645 \begin_layout Plain Layout
25661 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
25664 \begin_layout Plain Layout
25672 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
25675 \begin_layout Plain Layout
25679 \begin_layout Plain Layout
25695 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
25698 \begin_layout Plain Layout
25702 \begin_inset space \textvisiblespace{}
25710 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
25713 \begin_layout Plain Layout
25717 \begin_layout Plain Layout
25733 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
25736 \begin_layout Plain Layout
25740 \begin_inset space \textvisiblespace{}
25748 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
25751 \begin_layout Plain Layout
25755 \begin_layout Plain Layout
25771 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
25774 \begin_layout Plain Layout
25778 \begin_inset space \textvisiblespace{}
25786 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
25789 \begin_layout Plain Layout
25793 \begin_layout Plain Layout
25813 \begin_inset space \hfill{}
25819 \begin_layout Standard
25820 \begin_inset VSpace medskip
25829 also two different characters can be accented.
25835 \begin_inset space \textvisiblespace{}
25844 \begin_layout Plain Layout
25856 \begin_layout Standard
25869 can in combination with vowels directly be inserted with the keyboard without
25871 The same applies for the tilde
25875 \begin_layout Plain Layout
25876 This only applies for keyboards where the tilde is defined as accent.
25885 in combination with
25900 \begin_layout Standard
25943 and accents that are inserted directly with the keyboard are also available
25944 in mathematical text.
25945 For the other accents there are special math commands to be used in formulas,
25947 \begin_inset CommandInset ref
25949 reference "sub:Accents-for-one"
25956 \begin_layout Standard
25957 \begin_inset VSpace bigskip
25960 Furthermore, with the command
25967 \begin_inset Index idx
25970 \begin_layout Plain Layout
25978 all numbers and letters can be set into a circle, quasi accented with a
25979 circle, similar to the copyright symbol.
25982 \begin_layout Standard
25984 \begin_inset Tabular
25985 <lyxtabular version="3" rows="3" columns="2">
25986 <features rotate="0" tabularvalignment="middle">
25987 <column alignment="center" valignment="top">
25988 <column alignment="center" valignment="top">
25990 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
25993 \begin_layout Plain Layout
25999 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
26002 \begin_layout Plain Layout
26004 \begin_inset Note Note
26007 \begin_layout Plain Layout
26014 is only used as spacer.
26026 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
26029 \begin_layout Plain Layout
26037 <cell multicolumn="1" alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
26040 \begin_layout Plain Layout
26044 \begin_layout Plain Layout
26060 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
26063 \begin_layout Plain Layout
26074 raisebox{-1.5pt}{W}}
26079 <cell multicolumn="1" alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
26082 \begin_layout Plain Layout
26083 \begin_inset Formula $\raisebox{4.5mm}{}$
26090 \begin_layout Plain Layout
26108 \begin_inset Formula $\raisebox{-2mm}{}$
26124 \begin_layout Standard
26125 One has to take care that the character fits in the circle.
26136 \begin_layout Plain Layout
26138 \begin_inset CommandInset ref
26140 reference "sub:Font-Sizes"
26149 specifies thereby the size of the circle.
26160 \begin_layout Plain Layout
26162 \begin_inset CommandInset ref
26164 reference "sub:Boxes-without-Frame"
26173 the character can be centered.
26176 \begin_layout Subsection
26178 \begin_inset Index idx
26181 \begin_layout Plain Layout
26190 \begin_layout Standard
26191 Old-style figures (also known as old-style numerals) are created with the
26199 \begin_inset Index idx
26202 \begin_layout Plain Layout
26211 The command can be used in formulas and in TeX-mode.
26212 The command scheme is:
26215 \begin_layout Standard
26220 oldstylenums{number}
26223 \begin_layout Standard
26228 oldstylenums{0123456789
26231 \begin_inset Formula $\oldstylenums{0123456789}$
26237 \begin_layout Section
26239 \begin_inset CommandInset label
26241 name "sec:Formula-Styles"
26246 \begin_inset Index idx
26249 \begin_layout Plain Layout
26258 \begin_layout Itemize
26259 There are two different alignment styles:
26263 \begin_layout Description
26264 Centered is the predefined standard
26267 \begin_layout Description
26268 Indented for this the option
26272 must be inserted in the menu
26274 Document\SpecialChar \menuseparator
26280 \begin_inset space ~
26286 \begin_layout Standard
26291 is used, the indentation can be adjusted with the length
26298 \begin_inset Index idx
26301 \begin_layout Plain Layout
26310 Should the distance be 15
26311 \begin_inset space \thinspace{}
26314 mm, the following command line is inserted in the LaTeX-preamble
26317 \begin_layout Standard
26327 \begin_layout Standard
26328 When no length is specified, the predefined value of 30
26329 \begin_inset space \thinspace{}
26336 \begin_layout Itemize
26337 And two different numbering styles:
26341 \begin_layout Description
26342 Right is the predefined standard
26345 \begin_layout Description
26346 Left for this the option
26350 must be inserted in the menu
26352 Document\SpecialChar \menuseparator
26358 \begin_inset space ~
26365 \begin_layout Standard
26374 can also be used together.
26375 In this case both options are inserted, separated by a comma.
26378 \begin_layout Standard
26379 The chosen styles are used for all displayed formulas of the document.
26380 When both, centered and indented formulas should be created in a document,
26386 The indented formulas are then set in a flalign environment, see
26387 \begin_inset CommandInset ref
26389 reference "sub:Flalign-Environment"
26396 \begin_layout Section
26398 \begin_inset CommandInset label
26400 name "sec:Multiline-Formulas"
26405 \begin_inset Index idx
26408 \begin_layout Plain Layout
26409 Formula ! multiline
26417 \begin_layout Subsection
26421 \begin_layout Standard
26422 In LyX multiline formulas are created by pressing
26427 arg "newline-insert newline"
26433 This creates either an
26435 eqnarray environment
26437 that is described in
26438 \begin_inset CommandInset ref
26440 reference "sub:Eqnarray-Environment"
26444 or, when the option
26446 Use AMS math package
26448 in the document settings is selected, an
26452 that is described in
26453 \begin_inset CommandInset ref
26455 reference "sub:Standard-align-Environment"
26460 The align environment is recommended because it provides in any case a
26461 typographically correct output.
26464 \begin_layout Standard
26465 There are other multiline formula environments that can be created via the
26468 Insert\SpecialChar \menuseparator
26472 These environments are described in the following sections.
26475 \begin_layout Standard
26476 In all multiline formula environments a new line is created by pressing
26480 arg "newline-insert newline"
26484 To add or delete lines, the math toolbar buttons
26485 \begin_inset Graphics
26486 filename ../images/tabular-feature_append-row.png
26492 \begin_inset Graphics
26493 filename ../images/tabular-feature_delete-row.png
26498 , respectively, or the menu
26500 Edit\SpecialChar \menuseparator
26506 \begin_layout Subsubsection
26508 \begin_inset CommandInset label
26510 name "sub:Line-Separation"
26515 \begin_inset Index idx
26518 \begin_layout Plain Layout
26519 Formula ! multiline ! Line separation
26527 \begin_layout Standard
26528 There is sometimes not enough space in multiline formulas between the lines:
26529 \begin_inset Formula
26531 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}\\
26532 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
26540 \begin_layout Standard
26541 In LaTeX additional line space is specified as optional argument of the
26543 This is not yet possible in LyX
26547 \begin_layout Plain Layout
26549 \begin_inset CommandInset href
26551 name "LyX-bug #1505"
26552 target "http://www.lyx.org/trac/ticket/1505"
26561 , therefore the whole formula must be inserted in TeX-mode.
26562 To add in our example space, the command
26570 is inserted at the end of the first line.
26575 \begin_layout Plain Layout
26582 \begin_layout Plain Layout
26584 B^{2}(B^{2}-2r_{g}^{2}+2x_{0}^{2}-2r_{k}^{2})+4x_{0}^{2}x^{2}+4x_{0}xD &
26587 textrm{-}4x^{2}B^{2}+4x_{0}xB^{2}
26594 \begin_layout Plain Layout
26598 left(B^{2}+x_{0}^{2}
26606 left(B^{2}-2r_{g}^{2}+2x_{0}^{2}-2r_{k}^{2}
26611 \begin_layout Plain Layout
26623 \begin_layout Standard
26624 \begin_inset VSpace bigskip
26627 To set the line separation for all lines in a formula, the length
26634 \begin_inset Index idx
26637 \begin_layout Plain Layout
26647 \begin_inset Formula $\mbox{line separation}=\mathrm{6\, pt+\backslash jot}$
26658 \begin_inset space \thinspace{}
26663 \begin_inset space \thinspace{}
26666 mm additional line separation as in the previous example, the command
26669 \begin_layout Standard
26679 \begin_layout Standard
26680 is inserted in TeX-mode before the formula.
26681 This requires that the LaTeX-package
26689 \begin_layout Plain Layout
26694 is part of every LaTeX standard installation.
26700 \begin_inset Index idx
26703 \begin_layout Plain Layout
26709 was loaded in LaTeX-preamble with the line
26712 \begin_layout Standard
26720 \begin_layout Standard
26725 \begin_layout Plain Layout
26737 \begin_inset Formula
26739 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}\\
26740 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
26748 \begin_layout Standard
26752 \begin_layout Plain Layout
26763 To get back to the predefined distance,
26769 is set to the value 3
26770 \begin_inset space \thinspace{}
26776 \begin_layout Subsubsection
26778 \begin_inset CommandInset label
26780 name "sub:Column-Separation"
26785 \begin_inset Index idx
26788 \begin_layout Plain Layout
26789 Formula ! multiline ! Column separation
26797 \begin_layout Standard
26798 Multiline formulas form a matrix.
26799 A formula in the eqnarray environment is for example a matrix with three
26801 By changing the column separation in this environment, the space beside
26802 the relation sign can be changed.
26805 \begin_layout Standard
26806 The column separation is specified with the length
26813 \begin_inset Index idx
26816 \begin_layout Plain Layout
26825 \begin_inset Newline newline
26828 column separation = 2
26829 \begin_inset space \thinspace{}
26839 \begin_inset Newline newline
26845 \begin_layout Standard
26855 \begin_layout Standard
26856 inserted in TeX-mode, sets for all following formulas a column separation
26858 \begin_inset space \thinspace{}
26862 To get back to the predefined distance,
26869 \begin_inset space \thinspace{}
26875 \begin_layout Standard
26877 \begin_inset space \thinspace{}
26880 cm column separation:
26884 \begin_layout Plain Layout
26896 \begin_inset Formula
26904 A formula with the predefined column separation for matrices of 10
26905 \begin_inset space \thinspace{}
26912 \begin_layout Plain Layout
26924 \begin_inset Formula
26935 \begin_layout Subsubsection
26937 \begin_inset Index idx
26940 \begin_layout Plain Layout
26949 \begin_layout Standard
26950 Long formulas can be typeset using these methods:
26953 \begin_layout Itemize
26954 When one side of the equation is much shorter than the line width, this
26955 one is chosen for the left side and the right side is typeset over two
26957 \begin_inset Formula
26959 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 \\
26960 & & -\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}
26965 The minus sign at the beginning of the second line does normally not appear
26966 as an operator because it is the first character of the line.
26967 Thus it would not be surrounded by space and could not be distinguished
26968 from the fraction bar.
26970 \begin_inset space \thinspace{}
26973 pt space was inserted behind the minus sign with the command
26983 \begin_layout Plain Layout
26991 \begin_inset CommandInset ref
26993 reference "sub:Variable-Space"
27003 \begin_inset Index idx
27006 \begin_layout Plain Layout
27017 \begin_layout Itemize
27018 When both sides of the equation are too long, the command
27025 \begin_inset Index idx
27028 \begin_layout Plain Layout
27037 It is inserted in the first column of the first line and causes all further
27038 insertions to overwrite the following columns:
27039 \begin_inset Formula
27041 \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 \\
27042 & & -\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 \\
27043 & & =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}
27048 After the insertion of
27054 , the cursor is in a purple box that is a bit shifted to the left from the
27056 In this the formula is inserted.
27057 \begin_inset Newline newline
27060 The content of the further lines is inserted to the second or another formula
27062 The greater the column number where it was inserted, the larger the indentation.
27063 \begin_inset VSpace medskip
27067 \begin_inset Newline newline
27071 \begin_inset Note Greyedout
27074 \begin_layout Plain Layout
27075 Note the following when using
27084 \begin_layout Itemize
27085 The formula doesn't use the full page width.
27087 \begin_inset space \thinspace{}
27091 \begin_inset space \space{}
27095 \begin_inset Formula $-B^{2}$
27098 is added to the first line in the above example, it would have been outside
27100 To better use the width, negative space can be inserted at the beginning
27104 \begin_layout Itemize
27105 Due to a bug in LyX the cursor cannot be set with the mouse into the first
27110 \begin_layout Plain Layout
27111 \begin_inset CommandInset href
27113 name "LyX-bug #1429"
27114 target "http://www.lyx.org/trac/ticket/1429"
27123 One can only set the cursor at the beginning of the line and move it with
27132 \begin_layout Itemize
27133 Other methods to set long formulas are offered by the environments described
27135 \begin_inset CommandInset ref
27137 reference "sub:Multline-Environment"
27142 \begin_inset CommandInset ref
27144 reference "sub:Multiline-Formula-Parts"
27151 \begin_layout Subsubsection
27153 \begin_inset CommandInset label
27155 name "sub:Multiline-Brackets"
27160 \begin_inset Index idx
27163 \begin_layout Plain Layout
27164 Brackets ! for multiline expressions
27172 \begin_layout Standard
27173 For brackets spanning multiple lines the following problem occurs:
27174 \begin_inset Formula
27176 A & = & \sin(x)\left[\prod_{R=1}^{\infty}\frac{1}{R}+\cdots\right.\\
27177 & & \left.\cdots+B-D\right]
27185 \begin_layout Standard
27186 The closing bracket is smaller than the opening bracket because brackets
27187 with variable size may not span multiple lines.
27190 \begin_layout Standard
27191 To set the bracket size for the second line correctly, the first line is
27199 \begin_inset Index idx
27202 \begin_layout Plain Layout
27210 and the second line with
27218 \begin_layout Plain Layout
27232 \begin_inset CommandInset ref
27234 reference "sub:Automatic-Bracket-Size"
27246 \begin_inset Index idx
27249 \begin_layout Plain Layout
27272 \begin_inset space \textvisiblespace{}
27282 \begin_inset space \textvisiblespace{}
27292 \begin_inset space \textvisiblespace{}
27298 \begin_inset Formula $\downarrow$
27304 \begin_inset Index idx
27307 \begin_layout Plain Layout
27315 is inserted, because the multiplication operator with its limits is the
27316 largest symbol in the first line and this should be the size for the bracket
27317 in the second line.
27320 \begin_layout Standard
27321 The result is this:
27322 \begin_inset Formula
27324 A & = & \sin(x)\left[\prod_{R=1}^{\infty}\frac{1}{R}+\cdots\right.\\
27325 & & \left.\vphantom{\prod_{R=1}^{\infty}}\cdots+B-D\right]
27333 \begin_layout Subsection
27337 \begin_layout Standard
27338 Align environments can be used for every kind of multiline formulas.
27339 They are especially useful to set several formulas side by side.
27342 \begin_layout Standard
27343 Align environments consist of columns.
27344 The odd columns are right aligned, the even ones left aligned.
27345 Every line in an Align environment can be numbered.
27348 \begin_layout Standard
27349 Align environments are created via the menu
27351 Insert\SpecialChar \menuseparator
27357 Edit\SpecialChar \menuseparator
27358 Math\SpecialChar \menuseparator
27359 Change Formula Type
27361 already existing formulas can be converted to Align environments.
27364 \begin_layout Standard
27365 To add or delete columns, the math toolbar buttons
27366 \begin_inset Graphics
27367 filename ../images/tabular-feature_append-column.png
27373 \begin_inset Graphics
27374 filename ../images/tabular-feature_delete-column.png
27379 , respectively, or the menu
27381 Edit\SpecialChar \menuseparator
27387 \begin_layout Subsubsection
27388 Standard align Environment
27389 \begin_inset CommandInset label
27391 name "sub:Standard-align-Environment"
27396 \begin_inset Index idx
27399 \begin_layout Plain Layout
27400 Formula ! multiline ! align environment
27408 \begin_layout Standard
27409 This Align environment is created by pressing
27412 arg "newline-insert newline"
27415 in a formula or by the menu
27417 Insert\SpecialChar \menuseparator
27418 Math\SpecialChar \menuseparator
27419 AMS align Environment
27424 \begin_layout Standard
27425 An example for two formulas set side by side, that are created with a four
27426 column align environment:
27427 \begin_inset Formula
27429 A & =\sin(B) & C & =D\\
27430 C & \ne A & B & \ne D
27435 As it can be seen, the formulas in this environment are placed so as if
27444 \begin_layout Plain Layout
27452 \begin_inset CommandInset ref
27454 reference "sub:Variable-Space"
27465 before the first and after every even column.
27466 When the formula style
27472 \begin_layout Plain Layout
27474 \begin_inset CommandInset ref
27476 reference "sec:Formula-Styles"
27487 is used, the formula is set without the
27493 before the first column.
27496 \begin_layout Subsubsection
27497 Alignat Environment
27498 \begin_inset Index idx
27501 \begin_layout Plain Layout
27502 Formula ! multiline ! alignat environment
27510 \begin_layout Standard
27511 The alignat environment has no predefined column separation.
27512 It can be inserted manually with the spaces that are described
27513 \begin_inset CommandInset ref
27515 reference "sub:Space"
27522 \begin_layout Standard
27523 The above example in the alignat environment where 1
27524 \begin_inset space \thinspace{}
27527 cm space was inserted at the beginning of the second formula:
27528 \begin_inset Formula
27529 \begin{alignat*}{2}
27530 A & =\sin(B) & \hspace{1cm}C & =D\\
27531 C & \ne A & B & \ne D
27536 Because the column separation can be set separately for every column, this
27537 environment is especially suitable to set three and more formulas side
27541 \begin_layout Subsubsection
27542 Flalign Environment
27543 \begin_inset CommandInset label
27545 name "sub:Flalign-Environment"
27550 \begin_inset Index idx
27553 \begin_layout Plain Layout
27554 Formula ! multiline ! flalign environment
27562 \begin_layout Standard
27563 In this environment the first two columns are always set as much as possible
27564 to the left and the last two ones to the right.
27566 \begin_inset Formula
27568 A & =1 & B & =2 & C & =3\\
27569 X & =\textrm{-}1 & Y & =\textrm{-}2 & Z & =4
27577 \begin_layout Standard
27578 By creating a flalign environment with an odd number of columns where an
27579 empty TeX-brace is inserted to the last column, several formulas in a document
27580 can be set to the left, although the formula style
27585 As example the indented formula
27586 \begin_inset CommandInset ref
27588 reference "eq:VolInt"
27593 \begin_inset Formula
27595 \hspace{30pt}\iiint\limits _{V}X\,\mathrm{d}V & =U & {}
27600 The first two columns contain the formula.
27601 To indent it as with the formula style
27606 \begin_inset space \thinspace{}
27609 pt space was inserted at the beginning of the first column.
27612 \begin_layout Subsection
27613 Eqnarray Environment
27614 \begin_inset CommandInset label
27616 name "sub:Eqnarray-Environment"
27621 \begin_inset Index idx
27624 \begin_layout Plain Layout
27625 Formula ! multiline ! eqnarray environment
27633 \begin_layout Standard
27634 When this environment has been created, three blue boxes appear.
27635 The content of the first box is right aligned, the content of the last
27637 The content of the middle box appears centered and a bit smaller, because
27638 it is designed to insert there only relation characters.
27639 \begin_inset Formula
27641 \frac{ABC}{D} & \frac{ABC}{D} & \frac{ABC}{D}\\
27651 \begin_layout Subsection
27653 \begin_inset Index idx
27656 \begin_layout Plain Layout
27657 Formula ! multiline ! gather environment
27665 \begin_layout Standard
27666 This environment consists of only one centered column.
27667 Every line can be numbered.
27668 \begin_inset Formula
27679 \begin_layout Subsection
27680 Multline Environment
27681 \begin_inset CommandInset label
27683 name "sub:Multline-Environment"
27688 \begin_inset Index idx
27691 \begin_layout Plain Layout
27692 Formula ! multiline ! multline environment
27700 \begin_layout Standard
27701 The multline environment consists, like the gather environment, of only
27703 But the first line is left aligned, the last one right aligned.
27704 All other lines are centered.
27705 Therefore this environment is suitable for long formulas.
27707 \begin_inset CommandInset ref
27709 reference "eq:lefteqn"
27713 in the multline environment:
27714 \begin_inset Formula
27716 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}\\
27717 -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}\\
27718 =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}}
27726 \begin_layout Standard
27727 In the output only the last (first) line of a multline environment appears
27728 numbered when the document numbering is right (left).
27732 \begin_layout Plain Layout
27733 numbering styles see
27734 \begin_inset CommandInset ref
27736 reference "sec:Formula-Styles"
27748 \begin_layout Standard
27756 \begin_inset Index idx
27759 \begin_layout Plain Layout
27774 \begin_inset Index idx
27777 \begin_layout Plain Layout
27785 a centered line can be right or left aligned, respectively.
27786 The commands are used as follows:
27789 \begin_layout Standard
27794 shoveright{line content}
27800 shoveleft{line content}
27803 \begin_layout Standard
27804 \begin_inset VSpace medskip
27814 \begin_inset Index idx
27817 \begin_layout Plain Layout
27825 specifies the distance of the first line from the left page margin.
27826 Predefined is the length 0
27827 \begin_inset space \thinspace{}
27833 \begin_layout Standard
27834 As example the above formula where the command
27837 \begin_layout Standard
27847 \begin_layout Standard
27848 was inserted in TeX-mode before:
27852 \begin_layout Plain Layout
27864 \begin_inset Formula
27866 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}\\
27867 \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}}\\
27868 =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}}
27877 \begin_layout Plain Layout
27888 The second line was left aligned using
27897 \begin_layout Subsection
27898 Multiline Formula Parts
27899 \begin_inset CommandInset label
27901 name "sub:Multiline-Formula-Parts"
27906 \begin_inset Index idx
27909 \begin_layout Plain Layout
27910 Formula ! multiline ! formula parts
27918 \begin_layout Standard
27919 To display only parts of a formula with multiple lines, one of the following
27920 environments is used:
27937 They can be inserted via the menu
27939 Insert\SpecialChar \menuseparator
27942 or by using the commands described in this section.
27945 \begin_layout Standard
27946 The first three have the same properties as the corresponding multiline
27947 formula environments, but it is possible to set further formula parts beside
27950 \begin_inset Formula
27952 \left.\begin{aligned}\Delta x\Delta p & \ge\frac{\hbar}{2}\\
27953 \Delta E\Delta t & \ge\frac{\hbar}{2}
27955 \right\} \textrm{Uncertainty relations}
27963 \begin_layout Standard
27964 To get this formula, a displayed formula is created where the command
27971 \begin_inset Index idx
27974 \begin_layout Plain Layout
27983 A purple box appears around the blue formula box where now columns and
27984 lines can be added.
27985 Outside the multiline environment other formula parts can be set, like
27989 \begin_layout Standard
27990 The aligned environment is also suitable for long formulas whose lines are
27991 horizontally aligned.
27992 Using aligned in a displayed formula has the advantage that the formula
27993 number is vertically centered behind the lines.
27995 \begin_inset CommandInset ref
27997 reference "eq:shortlong"
28001 in the aligned environment:
28002 \begin_inset Formula
28004 \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}|}\\
28005 & -\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}|}
28014 \begin_layout Standard
28015 To use the environments
28034 \begin_inset Index idx
28037 \begin_layout Plain Layout
28052 \begin_inset Index idx
28055 \begin_layout Plain Layout
28070 \begin_inset Index idx
28073 \begin_layout Plain Layout
28081 are inserted, respectively.
28082 The split environment has the same properties as the aligned environment
28083 but it can only have two columns.
28086 \begin_layout Subsection
28087 Text in multiline Formulas
28088 \begin_inset CommandInset label
28090 name "sub:Text-in-multiline"
28095 \begin_inset Index idx
28098 \begin_layout Plain Layout
28105 \begin_inset Index idx
28108 \begin_layout Plain Layout
28109 Formula ! multiline ! text
28117 \begin_layout Standard
28118 In the Align environments, and the multline and gather environment, text
28119 can be inserted that will appear in a separate line and doesn't affect
28120 the column alignment.
28121 To do this, the command
28128 \begin_inset Index idx
28131 \begin_layout Plain Layout
28139 is used in the following scheme:
28142 \begin_layout Standard
28150 \begin_layout Standard
28151 The text should not be longer than a line because it cannot be hyphenated.
28152 As LyX doesn't yet support
28158 directly, the text is written as mathematical text.
28165 must hereby be at the beginning of a line and appears in the output above
28167 An example where the text was inserted at the beginning of the second line:
28168 \begin_inset Formula
28170 I & =a\sqrt{2}\int_{0}^{2\pi}\sqrt{1+\cos(\phi)}\;\mathrm{d}\phi\\
28171 \intertext{\text{integrand is symmetric to \ensuremath{\phi=\pi}, therefore}} & =2a\sqrt{2}\int_{0}^{\pi}\sqrt{1+\cos(\phi)}\;\mathrm{d}\phi
28179 \begin_layout Section
28181 \begin_inset Index idx
28184 \begin_layout Plain Layout
28191 \begin_inset Index idx
28194 \begin_layout Plain Layout
28195 Formula ! numbering|see
28199 \begin_layout Plain Layout
28210 \begin_layout Plain Layout
28225 \begin_layout Subsection
28229 \begin_layout Standard
28230 Numbered formulas can be created with the menu
28232 Insert\SpecialChar \menuseparator
28233 Math\SpecialChar \menuseparator
28235 \begin_inset space ~
28243 \begin_inset space ~
28249 Existing formulas can be numbered with the menu
28251 Edit\SpecialChar \menuseparator
28252 Math\SpecialChar \menuseparator
28254 \begin_inset space ~
28262 arg "math-number-toggle"
28266 The formula number is displayed in LyX behind the formula as a number sign
28268 The number sign is replaced in the output by the formula number.
28271 \begin_layout Standard
28272 When numbering is turned on in multiline formulas, all lines will be numbered.
28273 But the numbering can be controlled with the menu
28275 Edit\SpecialChar \menuseparator
28276 Math\SpecialChar \menuseparator
28278 \begin_inset space ~
28282 \begin_inset space ~
28286 \begin_inset space ~
28294 arg "math-number-line-toggle"
28300 \begin_layout Standard
28301 Except for inline formulas, all formulas can be numbered with two different
28303 \begin_inset CommandInset ref
28305 reference "sec:Formula-Styles"
28312 \begin_layout Subsection
28314 \begin_inset Index idx
28317 \begin_layout Plain Layout
28318 Cross-references ! to formulas
28326 \begin_layout Standard
28327 All labeled formulas can be cross-referenced.
28328 A label is added by the menu
28330 Insert\SpecialChar \menuseparator
28333 or the toolbar button
28334 \begin_inset Graphics
28335 filename ../images/label-insert.png
28341 The cursor must hereby be inside a displayed formula.
28342 Alternatively you can right-click on the formula and choose
28347 A dialog pops up displaying the prefix
28352 The label is inserted there behind the prefix.
28353 The predefined prefix means
28354 \begin_inset Quotes eld
28358 \begin_inset Quotes erd
28361 and makes it easier to find labels in large documents because it marks
28362 it as formula label to divide it from e.
28363 \begin_inset space \thinspace{}
28367 \begin_inset space \space{}
28371 To change a label, the menu
28373 Insert\SpecialChar \menuseparator
28376 is used again or you right-click on a formula and then on
28383 \begin_layout Standard
28384 The name of the label is displayed in LyX within two parentheses behind
28386 A formula with a label is always numbered.
28389 \begin_layout Standard
28390 Cross-references are inserted via the menu
28392 Insert\SpecialChar \menuseparator
28395 or with the toolbar button
28396 \begin_inset Graphics
28397 filename ../images/dialog-show-new-inset_ref.png
28403 A formula cross-reference appears in the output as formula number.
28404 When in the cross-reference dialog window the format
28408 is chosen, the cross-reference appears in the output as formula number
28410 \begin_inset Newline newline
28413 By right-clicking on a cross-reference in LyX, one jumps to the formula
28414 that is referenced.
28417 \begin_layout Standard
28418 Here are as examples cross-references to formulas of the following subsections:
28419 \begin_inset Note Note
28422 \begin_layout Plain Layout
28423 Note the different cross-reference types.
28431 \begin_layout Standard
28433 \begin_inset CommandInset ref
28440 \begin_inset CommandInset ref
28448 \begin_inset CommandInset ref
28454 ) big Latin letters are used for the numbering in contrary to (
28455 \begin_inset CommandInset ref
28464 \begin_layout Standard
28465 \begin_inset VSpace medskip
28468 When the argument of
28476 \begin_layout Plain Layout
28484 \begin_inset CommandInset ref
28486 reference "sub:User-defined-Numbering"
28497 contains a box like in
28498 \begin_inset CommandInset ref
28500 reference "sub:Paragraph-Boxes"
28504 , the formula cannot be referenced.
28507 \begin_layout Subsection
28509 \begin_inset Index idx
28512 \begin_layout Plain Layout
28513 Formula numbering ! subnumbering
28521 \begin_layout Standard
28522 With the help of the commands
28526 begin{subequations}
28534 formulas can be subnumbered.
28535 Both commands are inserted in TeX-mode.
28538 \begin_layout Standard
28540 \begin_inset Formula
28551 \begin_layout Plain Layout
28555 addtocounter{equation}{-1}
28564 \begin_layout Plain Layout
28568 begin{subequations}
28574 \begin_inset VSpace -5mm
28578 \begin_inset Formula
28586 \begin_inset Formula
28596 \begin_layout Standard
28600 \begin_layout Plain Layout
28612 \begin_layout Standard
28613 To create the example, the following is done:
28616 \begin_layout Enumerate
28617 first formula is inserted
28620 \begin_layout Enumerate
28625 addtocounter{equation}{-1}
28627 begin{subequations}
28628 \begin_inset Index idx
28631 \begin_layout Plain Layout
28640 \begin_inset Newline newline
28645 is inserted after the first formula
28648 \begin_layout Enumerate
28649 second formula is inserted
28652 \begin_layout Enumerate
28653 third formula is inserted
28656 \begin_layout Enumerate
28663 is inserted after the third formula
28666 \begin_layout Standard
28667 Every formula between the commands
28679 is subnumbered as a, b,
28680 \begin_inset Newline linebreak
28683 c, \SpecialChar \ldots{}
28684 For multiline formulas every line will be subnumbered.
28685 All subnumbered formulas are treated as
28690 But as every numbered formula increases the counter
28694 by one, the command
28700 is needed to decrease it.
28701 Otherwise the formulas
28702 \begin_inset CommandInset ref
28709 \begin_inset CommandInset ref
28716 \begin_inset CommandInset ref
28722 would be numbered as
28723 \begin_inset CommandInset ref
28730 \begin_inset CommandInset ref
28737 \begin_inset CommandInset ref
28746 \begin_layout Standard
28747 By inserting the commands in TeX-mode, a space is created between the first
28750 \begin_inset space \thinspace{}
28753 mm vertical space is inserted after the command
28757 begin{subequations}
28760 When the formula style
28766 \begin_layout Plain Layout
28768 \begin_inset CommandInset ref
28770 reference "sec:Formula-Styles"
28782 \begin_inset space \thinspace{}
28785 mm space is inserted instead.
28788 \begin_layout Standard
28789 Here is an example for a multiline formula where the numbering was turned
28790 off for the second line:
28794 \begin_layout Plain Layout
28798 begin{subequations}
28804 \begin_inset Formula
28806 A & = & (B-Z)^{2}=(B-Z)(B-Z)\label{eq:d}\\
28807 & = & B^{2}-ZB-BZ+Z^{2}\nonumber \\
28808 & = & B^{2}-2BZ+Z^{2}\label{eq:f}
28817 \begin_layout Plain Layout
28829 \begin_layout Subsection
28830 User-defined Numbering
28831 \begin_inset CommandInset label
28833 name "sub:User-defined-Numbering"
28838 \begin_inset Index idx
28841 \begin_layout Plain Layout
28842 Formula numbering ! user-defined
28850 \begin_layout Standard
28851 \begin_inset Index idx
28854 \begin_layout Plain Layout
28855 Formula numbering ! self-defined delimiters
28860 With the standard numbering parentheses are set around the formula number.
28861 To replace the parentheses for example by vertical bars, the following
28862 line is added to the LaTeX-preamble:
28865 \begin_layout Standard
28877 \begin_inset Note Note
28880 \begin_layout Plain Layout
28881 This macro is already declared in the LaTeX-preamble for testing.
28882 To activate it, remove the percent sign at the beginning.
28890 \begin_layout Standard
28891 To use other characters, the vertical bars besides the
28895 are replaced by one ore more characters.
28896 To get only the formula number the vertical bars are omitted.
28899 \begin_layout Standard
28900 \begin_inset VSpace bigskip
28903 When there should be an expression of your choice instead of the consecutive
28904 formula number in parentheses behind the formula, the command
28911 \begin_inset Index idx
28914 \begin_layout Plain Layout
28923 \begin_inset Formula
28925 A+B=C\tag{something}\label{eq:tag}
28930 In this example the command
28935 \begin_inset space \textvisiblespace{}
28940 was inserted in the formula.
28943 \begin_layout Standard
28949 \begin_inset space \textvisiblespace{}
28954 is inserted instead, the star prevents the parentheses around the expression:
28955 \begin_inset Formula
28957 A+B=C\tag*{something}
28965 \begin_layout Standard
28966 \begin_inset VSpace bigskip
28969 To restart the formula numbering with new document parts or sections, the
28970 following command is used:
28973 \begin_layout Standard
28978 @addtoreset{equation}{part}
28981 \begin_inset Index idx
28984 \begin_layout Plain Layout
28989 \begin_layout Plain Layout
29000 \begin_layout Plain Layout
29013 \begin_layout Plain Layout
29024 \begin_layout Plain Layout
29037 \begin_inset Newline newline
29041 \begin_inset Newline newline
29048 @addtoreset{equation}{section}
29051 \begin_layout Standard
29052 To be able to use these commands in TeX-mode, the
29053 \begin_inset Quotes eld
29057 \begin_inset Quotes erd
29060 character has to be made
29061 \begin_inset Quotes eld
29065 \begin_inset Quotes erd
29068 for LaTeX using the command
29082 So the command sequence in TeX-mode is:
29085 \begin_layout Standard
29091 \begin_inset Newline newline
29096 @addtoreset{equation}{section}
29097 \begin_inset Newline newline
29105 \begin_layout Standard
29106 In the LaTeX-preamble
29118 can be omitted as they are automatically internally inserted by LyX.
29121 \begin_layout Standard
29136 \begin_layout Plain Layout
29141 is part of the LaTeX-package
29146 \begin_inset Index idx
29149 \begin_layout Plain Layout
29150 Packages ! carlisle
29155 that is part of every LaTeX standard installation.
29161 \begin_inset Index idx
29164 \begin_layout Plain Layout
29165 Packages ! remreset
29170 has to be loaded in the LaTeX-preamble with the line
29173 \begin_layout Standard
29178 usepackage{remreset}
29181 \begin_layout Standard
29189 \begin_inset Index idx
29192 \begin_layout Plain Layout
29197 \begin_layout Plain Layout
29208 \begin_layout Plain Layout
29221 \begin_layout Plain Layout
29232 \begin_layout Plain Layout
29244 can be used with the same scheme as
29253 \begin_layout Standard
29254 \begin_inset VSpace bigskip
29257 Sometimes formulas should be numbered in the following form:
29260 \begin_layout Standard
29263 (section number.formula number)
29266 \begin_layout Standard
29267 The formula number should start with every section with
29268 \begin_inset Quotes eld
29272 \begin_inset Quotes erd
29278 \begin_layout Standard
29279 For this case there is the command
29286 \begin_inset Index idx
29289 \begin_layout Plain Layout
29297 , which is used with the following scheme:
29300 \begin_layout Standard
29305 numberwithin{counter}{sectioning}
29308 \begin_layout Standard
29309 Counter denotes what kind of numbering is affected, sectioning denotes what
29310 number is before the dot.
29313 \begin_layout Standard
29314 Thus in our case the following LaTeX-preamble or TeX code line is used:
29317 \begin_layout Standard
29322 numberwithin{equation}{section}
29325 \begin_layout Standard
29326 This is the result:
29330 \begin_layout Plain Layout
29334 numberwithin{equation}{section}
29340 \begin_inset Formula
29350 \begin_layout Standard
29352 \begin_inset space \thinspace{}
29356 \begin_inset space \space{}
29359 tables so that the number of the part is the sectioning,
29360 \begin_inset Newline newline
29367 numberwithin{table}{part}
29372 \begin_layout Standard
29373 To go back to the standard numbering or to prevent this kind of numbering
29374 when it is defined by the document class, the following command is inserted
29375 as TeX code or to the LaTeX-preamble:
29378 \begin_layout Standard
29388 \begin_inset Index idx
29391 \begin_layout Plain Layout
29405 \begin_layout Plain Layout
29421 \begin_inset Newline newline
29429 \begin_inset Newline newline
29441 \begin_layout Standard
29448 uses internally the command
29454 , described above, that also needs to be reverted.
29458 \begin_layout Plain Layout
29465 \begin_layout Plain Layout
29469 @removefromreset{equation}{section}
29472 \begin_layout Plain Layout
29484 \begin_layout Subsection
29485 Numbering with Roman Numbers and Letters
29486 \begin_inset Index idx
29489 \begin_layout Plain Layout
29490 Formula numbering ! with letters
29496 \begin_inset Index idx
29499 \begin_layout Plain Layout
29500 Formula numbering ! with Roman numbers
29508 \begin_layout Standard
29509 Formulas can also be numbered with Roman numbers and Latin letters.
29510 To number for example with small Roman numbers, the command
29513 \begin_layout Standard
29525 \begin_layout Standard
29526 is inserted before the formula in TeX-mode.
29534 \begin_inset Index idx
29537 \begin_layout Plain Layout
29545 redefines the predefined command
29561 \begin_layout Plain Layout
29568 has the same scheme like the command
29574 that is described in
29575 \begin_inset CommandInset ref
29577 reference "sub:The-Command-newcommand"
29590 is the formula counter.
29597 is used as prefix for a counter, the value of the counter is output as
29599 When a formula is numbered, LaTeX sets internally the command
29605 behind the formula.
29611 \begin_inset Index idx
29614 \begin_layout Plain Layout
29624 outputs the counter as small Roman number.
29627 \begin_layout Standard
29628 All formulas behind the command
29638 are now numbered Roman.
29639 To switch to numbering with big Roman numbers, the command is inserted
29653 \begin_inset Index idx
29656 \begin_layout Plain Layout
29668 \begin_inset Quotes eld
29672 \begin_inset Quotes erd
29675 with small Latin letters there is the command
29682 \begin_inset Index idx
29685 \begin_layout Plain Layout
29693 , for big ones there is the command
29700 \begin_inset Index idx
29703 \begin_layout Plain Layout
29716 \begin_layout Standard
29717 \begin_inset Note Greyedout
29720 \begin_layout Plain Layout
29727 \begin_inset space ~
29730 formulas can be numbered with Latin letters in one document.
29738 \begin_layout Standard
29742 \begin_layout Plain Layout
29758 \begin_layout Standard
29759 \begin_inset Formula
29761 A=\textrm{small roman}
29770 \begin_layout Plain Layout
29784 \begin_inset Formula
29786 B=\textrm{big Roman}\label{eq:Rom}
29795 \begin_layout Plain Layout
29809 \begin_inset Formula
29811 C=\textrm{small Latin}
29820 \begin_layout Plain Layout
29834 \begin_inset Formula
29836 D=\textrm{big Latin}\label{eq:Lat}
29844 \begin_layout Standard
29845 To switch back to the default numbering, insert the command:
29848 \begin_layout Standard
29858 \begin_inset Index idx
29861 \begin_layout Plain Layout
29872 \begin_layout Standard
29876 \begin_layout Plain Layout
29890 \begin_inset Formula
29900 \begin_layout Standard
29901 \begin_inset VSpace medskip
29904 As you see, formulas are numbered serially independent from the numbering
29906 When then numbering should start with
29907 \begin_inset Quotes eld
29911 \begin_inset Quotes erd
29914 when the style is changed, new equation counters have to be defined.
29915 A description about this can be found in the file
29916 \begin_inset CommandInset href
29918 name "Formula-numbering.lyx"
29919 target "run:Formula-numbering.lyx"
29926 \begin_layout Standard
29927 \begin_inset Newpage newpage
29933 \begin_layout Section
29934 Chemical Symbols and Equations
29935 \begin_inset CommandInset label
29937 name "sub:Chemical-Symbols-and"
29942 \begin_inset Index idx
29945 \begin_layout Plain Layout
29946 Chemical characters ! Symbols
29952 \begin_inset Index idx
29955 \begin_layout Plain Layout
29962 \begin_inset Index idx
29965 \begin_layout Plain Layout
29974 \begin_layout Standard
29975 An example text from chemistry:
29978 \begin_layout Quote
29980 \begin_inset Formula $\mathrm{SO_{4}^{2-}}$
29983 -ion reacts with two
29984 \begin_inset Formula $\mathrm{Na^{+}}$
29987 -ions to sodium sulfate
29988 \begin_inset Formula $\left(\mathrm{Na_{2}SO_{4}}\right)$
29992 The chemical equation for this is:
29993 \begin_inset Formula
29995 \mathrm{2\, Na^{+}+SO_{4}^{2-}\longrightarrow Na_{2}SO_{4}}\label{eq:chem-reaction}
30003 \begin_layout Standard
30004 This chemical equation can directly be created as formula.
30005 To avoid that the symbols appear italic, everything is highlighted and
30006 changed by the shortcut
30012 to the upright font style.
30016 \begin_layout Plain Layout
30022 \begin_inset CommandInset ref
30024 reference "sub:Font-Styles"
30036 \begin_layout Standard
30037 A more convenient way to typeset chemical formulas is to use the command
30045 \begin_inset Index idx
30048 \begin_layout Plain Layout
30056 that is available when the LaTeX-package
30061 \begin_inset Index idx
30064 \begin_layout Plain Layout
30077 to a formula a new blue box appears where chemical formulas can be inserted
30078 in an intuitive way.
30081 \begin_layout Standard
30083 \begin_inset Tabular
30084 <lyxtabular version="3" rows="9" columns="2">
30085 <features rotate="0" tabularvalignment="middle">
30086 <column alignment="center" valignment="top">
30087 <column alignment="center" valignment="top">
30089 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
30092 \begin_layout Plain Layout
30098 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
30101 \begin_layout Plain Layout
30103 \begin_inset Note Note
30106 \begin_layout Plain Layout
30113 is only used as spacer.
30125 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
30128 \begin_layout Plain Layout
30132 \begin_inset space \textvisiblespace{}
30140 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
30143 \begin_layout Plain Layout
30144 \begin_inset Formula $\raisebox{4.5mm}{}\ce{H2CO3}\raisebox{-2mm}{}$
30154 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
30157 \begin_layout Plain Layout
30161 \begin_inset space \textvisiblespace{}
30169 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
30172 \begin_layout Plain Layout
30173 \begin_inset Formula $\raisebox{5mm}{}\ce{SO4^{2-}}\raisebox{-2mm}{}$
30183 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
30186 \begin_layout Plain Layout
30190 \begin_inset space \textvisiblespace{}
30198 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
30201 \begin_layout Plain Layout
30202 \begin_inset Formula $\raisebox{4.5mm}{}\ce{(NH4)2S}\raisebox{-2mm}{}$
30212 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
30215 \begin_layout Plain Layout
30219 \begin_inset space \textvisiblespace{}
30227 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
30230 \begin_layout Plain Layout
30231 \begin_inset Formula $\raisebox{4.5mm}{}\ce{KCr(SO4)2.12H2O}\raisebox{-2mm}{}$
30241 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
30244 \begin_layout Plain Layout
30248 \begin_inset space \textvisiblespace{}
30254 \begin_inset space \textvisiblespace{}
30260 \begin_inset space \textvisiblespace{}
30268 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
30271 \begin_layout Plain Layout
30272 \begin_inset Formula $\raisebox{4.5mm}{}\ce{A-B\dbond C\tbond D}\raisebox{-2mm}{}$
30282 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
30285 \begin_layout Plain Layout
30289 \begin_inset space \textvisiblespace{}
30293 \begin_inset Formula $\downarrow$
30297 \begin_inset Formula $\to$
30305 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
30308 \begin_layout Plain Layout
30309 \begin_inset Formula $\raisebox{5mm}{}\ce{_{90}^{227}Th+}\raisebox{-2mm}{}$
30319 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
30322 \begin_layout Plain Layout
30326 \begin_inset space \textvisiblespace{}
30330 \begin_inset space \textvisiblespace{}
30334 \begin_inset space \textvisiblespace{}
30338 \begin_inset space \textvisiblespace{}
30342 \begin_inset space \textvisiblespace{}
30350 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
30353 \begin_layout Plain Layout
30354 \begin_inset Formula $\raisebox{4.5mm}{}\ce{CO2 + C <=> 2CO}\raisebox{-2mm}{}$
30364 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
30367 \begin_layout Plain Layout
30371 \begin_inset space \textvisiblespace{}
30375 \begin_inset space \textvisiblespace{}
30379 \begin_inset space \textvisiblespace{}
30383 \begin_inset space \textvisiblespace{}
30391 \begin_inset space \textvisiblespace{}
30399 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
30402 \begin_layout Plain Layout
30403 \begin_inset Formula $\raisebox{5mm}{}\ce{CO2 + C ->[\alpha][\beta] 2CO}\raisebox{-4mm}{}$
30419 \begin_layout Standard
30420 \begin_inset Note Greyedout
30423 \begin_layout Plain Layout
30429 Inserting a formula to a
30435 box will lead to LaTeX errors due to a LyX bug.
30441 \begin_layout Plain Layout
30442 \begin_inset CommandInset href
30444 name "LyX-bug #8566"
30445 target "http://www.lyx.org/trac/ticket/8566"
30456 In this case TeX code has to be used like for
30470 \begin_layout Plain Layout
30491 \begin_layout Standard
30492 \begin_inset Note Greyedout
30495 \begin_layout Plain Layout
30501 It is not possible in LyX to use the character ^ to get an up-arrow as
30507 One instead uses a negative thin space followed by the command
30514 \begin_inset Formula $\ce{Fe + 2H+ -> Fe^{2+} + H2\negthinspace\uparrow}$
30525 \begin_layout Standard
30532 the command for equation
30533 \begin_inset space ~
30537 \begin_inset CommandInset ref
30539 reference "eq:chem-reaction"
30544 \begin_inset Newline newline
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{}
30572 \begin_inset space \textvisiblespace{}
30578 \begin_layout Standard
30579 To create multiline chemical equations first a multiline formula is created
30581 \begin_inset CommandInset ref
30583 reference "sec:Multiline-Formulas"
30588 Afterwards the command
30594 is used in every small blue box of the formula.
30596 \begin_inset CommandInset ref
30598 reference "eq:TEOS-reaction-1"
30603 \begin_inset CommandInset ref
30605 reference "eq:TEOS-reaction-2"
30609 are an example of a multi-stage chemical reaction where every equation
30610 has its own number.
30611 \begin_inset Formula
30613 \ce{TEOS + 4O} & \ce{->} & \ce{Si(OH)4 + 4C2H4O}\label{eq:TEOS-reaction-1}\\
30614 \ce{Si(OH)4} & \ce{->} & \ce{SiO2 + 2H2O}\label{eq:TEOS-reaction-2}
30622 \begin_layout Standard
30633 package provides the command
30640 \begin_inset Index idx
30643 \begin_layout Plain Layout
30651 that has to be used for special cases.
30652 For more information about
30658 and more examples have a look at the documentation of
30663 \begin_inset CommandInset citation
30672 \begin_layout Section
30676 \begin_layout Standard
30677 LyX supports two types of commutative diagrams:
30685 that are explained in the following.
30688 \begin_layout Subsection
30690 \begin_inset Index idx
30693 \begin_layout Plain Layout
30702 \begin_layout Standard
30703 Diagrams of this type visualize relations by vertical and horizontal lines
30705 \begin_inset Formula
30707 \begin{CD}A@>>>B@>>>C\\
30718 \begin_layout Standard
30719 To get them, the command
30724 \begin_inset Index idx
30727 \begin_layout Plain Layout
30737 is inserted to a formula.
30738 A blue box appears with two dashed lines where further commands can be
30743 arg "newline-insert newline"
30746 a new line is created.
30747 Horizontal relations are inserted in odd, vertical in even formula lines.
30750 \begin_layout Standard
30751 To create the relations there are the following commands:
30754 \begin_layout Itemize
30759 creates a left arrow,
30770 \begin_layout Itemize
30775 creates an up arrow,
30783 a vertical equal sign
30786 \begin_layout Itemize
30792 is a placeholder for non-existent relations
30795 \begin_layout Standard
30796 All arrows can be labeled as follows:
30799 \begin_layout Itemize
30800 If text inserted between the first and second < or >, resp., it is placed
30802 When it is inserted between the second and third one, it appears under
30806 \begin_layout Itemize
30807 When text for vertical arrows is inserted between the first and second A
30808 or V, resp., it is placed left beside the arrow.
30809 When it is inserted between the second and third one, it appears right
30811 If the text contains an A or V, these letters must be set into a TeX-brace.
30814 \begin_layout Standard
30815 As example a diagram with all possible relations:
30818 \begin_layout Standard
30819 \begin_inset Formula
30821 \begin{CD}A@>j>>B@>>k>C@=F\\
30832 \begin_layout Standard
30833 The command for this is:
30834 \begin_inset Newline newline
30842 \begin_inset space \textvisiblespace{}
30845 A@>j>>B@>>k>C@=F Ctrl+Return
30846 \begin_inset Newline newline
30850 \begin_inset Phantom HPhantom
30853 \begin_layout Plain Layout
30859 \begin_inset space \textvisiblespace{}
30872 \begin_inset Formula $\to$
30878 \begin_inset Newline newline
30882 \begin_inset Phantom HPhantom
30885 \begin_layout Plain Layout
30891 \begin_inset space \textvisiblespace{}
30902 \begin_layout Subsection
30904 \begin_inset Index idx
30907 \begin_layout Plain Layout
30908 Diagrams ! xymatrix
30916 \begin_layout Standard
30917 To be able to use xymatrices, the LaTeX-package
30922 A xymatrix is created by inserting the command
30929 Then you are able to add new matrix columns and rows like for normal matrices,
30931 \begin_inset CommandInset ref
30933 reference "sec:Matrices"
30940 \begin_layout Standard
30941 In contrary to amscd diagrams, xymatrices supports diagonal and curved arrows,
30943 All possibilities to create commutative diagrams and decorations are explained
30948 that you find in the menu
30950 Help\SpecialChar \menuseparator
30952 \begin_inset space ~
30960 \begin_layout Subsection
30966 \begin_inset Index idx
30969 \begin_layout Plain Layout
30978 \begin_layout Standard
30983 -diagrams, the LaTeX-package
30992 -diagram is created by inserting the command
30999 Then you are able to add new matrix columns and rows like for normal matrices,
31001 \begin_inset CommandInset ref
31003 reference "sec:Matrices"
31010 \begin_layout Standard
31011 Examples how to create
31015 diagrams in LyX is given in the
31017 Feynman-diagram manual
31019 that you find in the menu
31021 Help\SpecialChar \menuseparator
31023 \begin_inset space ~
31031 \begin_layout Standard
31032 \begin_inset Newpage newpage
31038 \begin_layout Section
31039 User-defined Commands
31040 \begin_inset Index idx
31043 \begin_layout Plain Layout
31044 User-defined commands
31052 \begin_layout Standard
31053 \begin_inset Note Greyedout
31056 \begin_layout Plain Layout
31061 The names of user-defined commands and macros may only consist of Latin
31070 \begin_layout Subsection
31074 \begin_inset CommandInset label
31076 name "sub:The-Command-newcommand"
31081 \begin_inset Index idx
31084 \begin_layout Plain Layout
31085 User-defined commands !
31093 \begin_inset Index idx
31096 \begin_layout Plain Layout
31107 \begin_layout Standard
31108 Many LaTeX-commands are too long to be used frequently.
31109 But it is possible to define with the command
31115 new shorter commands.
31118 \begin_layout Standard
31119 The command scheme of
31128 \begin_layout Standard
31133 newcommand{new command name}[number of arguments][optional
31138 \begin_inset Newline newline
31142 \begin_inset Phantom HPhantom
31145 \begin_layout Plain Layout
31155 {command definition}
31158 \begin_layout Standard
31159 \begin_inset Note Greyedout
31162 \begin_layout Plain Layout
31167 Assure that the name of the new command is not already used in your document
31168 or by LaTeX-packages that you use.
31169 When you for example define the command
31181 , you get an error message because
31187 is already defined as command for
31188 \begin_inset Quotes eld
31192 \begin_inset Formula $\le$
31196 \begin_inset Quotes erd
31207 \begin_layout Standard
31208 The number of arguments is an integer in the range 0
31209 \begin_inset space \thinspace{}
31213 \begin_inset space \thinspace{}
31216 9 and specifies how many arguments the new command should have.
31217 With the optional value a value for an optional argument can be predefined.
31218 When this is done, the
31226 rgument of the new command is automatically an optional one.
31229 \begin_layout Standard
31230 Here are some examples:
31233 \begin_layout Itemize
31234 To define the command
31246 , the LaTeX-preamble line is:
31247 \begin_inset VSpace medskip
31251 \begin_inset Newline newline
31265 \begin_layout Itemize
31266 To define the command
31278 , the argument (that should be underlined) must be taken into account.
31279 For this the preamble line is:
31280 \begin_inset VSpace medskip
31284 \begin_inset Newline newline
31298 \begin_inset VSpace medskip
31302 \begin_inset Newline newline
31309 acts as argument placeholder, the
31313 behind it denotes that it is the placeholder for the first argument.
31316 \begin_layout Itemize
31324 \begin_inset space \thinspace{}
31328 \begin_inset space \space{}
31338 \begin_inset VSpace medskip
31342 \begin_inset Newline newline
31353 framebox#1#2{$#3$}}
31356 \begin_inset VSpace medskip
31360 \begin_inset Newline newline
31363 The two Dollar signs creates the extra formula needed for
31370 \begin_inset CommandInset ref
31372 reference "sub:Boxes-with-Frame"
31379 \begin_layout Itemize
31380 To create a new command for
31386 where the color for the box need not be specified, the argument for the
31387 color is defined optional:
31388 \begin_inset VSpace medskip
31392 \begin_inset Newline newline
31403 fcolorbox{#2}{#1}{$#3$}}
31406 \begin_inset VSpace medskip
31410 \begin_inset Newline newline
31413 When the color is not specified when using
31419 , the predefined color
31426 \begin_layout Standard
31427 A test of the new defined commands:
31430 \begin_layout Standard
31432 \begin_inset Tabular
31433 <lyxtabular version="3" rows="6" columns="2">
31434 <features rotate="0" tabularvalignment="middle">
31435 <column alignment="center" valignment="top">
31436 <column alignment="center" valignment="top">
31438 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
31441 \begin_layout Plain Layout
31447 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
31450 \begin_layout Plain Layout
31452 \begin_inset Note Note
31455 \begin_layout Plain Layout
31462 is only used as spacer.
31474 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
31477 \begin_layout Plain Layout
31481 \begin_inset space \textvisiblespace{}
31489 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
31492 \begin_layout Plain Layout
31493 \begin_inset Formula $A\gr B$
31503 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
31506 \begin_layout Plain Layout
31514 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
31517 \begin_layout Plain Layout
31518 \begin_inset Formula $\raisebox{4.5mm}{}\us{ABcd}\raisebox{-2mm}{}$
31528 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
31531 \begin_layout Plain Layout
31535 \begin_inset Formula $\to$
31541 \begin_inset Formula $\to$
31549 \begin_inset space \textvisiblespace{}
31557 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
31560 \begin_layout Plain Layout
31561 \begin_inset Formula $\raisebox{6mm}{}\fb{[2cm]}{}{\int A=B}\raisebox{-4mm}{}$
31571 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
31574 \begin_layout Plain Layout
31578 \begin_inset Formula $\to$
31586 \begin_inset space \textvisiblespace{}
31594 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
31597 \begin_layout Plain Layout
31598 \begin_inset Formula $\raisebox{6mm}{}\cb{red}{\int A=B}\raisebox{-4mm}{}$
31608 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
31611 \begin_layout Plain Layout
31617 \begin_inset Formula $\to$
31625 \begin_inset space \textvisiblespace{}
31633 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
31636 \begin_layout Plain Layout
31637 \begin_inset Formula $\raisebox{6mm}{}\cb[green]{red}{\int A=B}\raisebox{-4mm}{}$
31653 \begin_layout Subsection
31655 \begin_inset Index idx
31658 \begin_layout Plain Layout
31659 User-defined commands! Math macros
31665 \begin_inset Index idx
31668 \begin_layout Plain Layout
31677 \begin_layout Standard
31678 User-defined commands are especially convenient for complex expressions.
31679 When you are for example dealing with a document that has quadratic equations,
31680 the same solution type occurs several times.
31681 The general form of a quadratic equation is
31682 \begin_inset Formula
31684 0=\lambda^{2}+p\lambda+q
31689 The general form of the solution is
31690 \begin_inset Formula
31692 \lambda_{1,2}=-\frac{p}{2}\pm\sqrt{\frac{p²}{4}-q}
31700 \begin_layout Standard
31701 To define a command for the solution formula where only the three parameters
31703 \begin_inset Formula $\lambda$
31707 \begin_inset Formula $p$
31711 \begin_inset Formula $q$
31714 need to be specified and the index of
31715 \begin_inset Formula $\lambda$
31718 can be given optionally, the LaTeX-preamble line is
31719 \begin_inset Newline newline
31735 \begin_inset Newline newline
31739 \begin_inset Phantom HPhantom
31742 \begin_layout Plain Layout
31756 frac{#3^{2}}{4}-#4}}
31759 \begin_layout Standard
31760 To create with this the solution formula, the command
31761 \begin_inset Newline newline
31771 \begin_inset Formula $\to$
31777 \begin_inset Formula $\to$
31784 is inserted to a formula
31789 \begin_layout Standard
31790 The definition of the new command is unintuitive because one has to know
31791 the schemes of all used LaTeX commands, e.
31792 \begin_inset space \thinspace{}
31796 \begin_inset space \space{}
31799 that a fraction is inserted in LaTeX as
31803 frac{numerator}{denominator}
31806 Furthermore one can easily forget a brace in the definition and cannot
31807 see in LyX what the new command is doing.
31808 To avoid these problems LyX offers the possibility to use math macros instead
31818 \begin_layout Standard
31819 A math macro is created by using the menu
31821 Insert\SpecialChar \menuseparator
31822 Math\SpecialChar \menuseparator
31825 or the toolbar button
31826 \begin_inset Graphics
31827 filename ../images/math-macro_newmacroname_newcommand.png
31833 The math macro toolbar appears together with the following box where the
31835 \begin_inset Newline newline
31839 \begin_inset space \hspace*{\fill}
31843 \begin_inset Graphics
31844 filename clipart/macrobox.png
31849 \begin_inset space \hspace*{\fill}
31853 \begin_inset Newline newline
31857 \begin_inset FormulaMacro
31858 \newcommand{\qG}[4][1,\,2]{#2_{#1}=-\frac{#3}{2}\pm\sqrt{\frac{#3^{2}}{4}-#4}}
31863 newmacroname is the default name of the macro that should be changed to
31864 something sensible.
31865 The wanted formula is inserted in the first blue box.
31866 An argument placeholder is inserted with the command
31873 \begin_inset space \thinspace{}
31877 \begin_inset space \space{}
31886 or by using the macro toolbar button
31887 \begin_inset Graphics
31888 filename ../images/math-macro-add-param.png
31894 Argument placeholders are displayed red.
31896 \begin_inset space ~
31899 arguments are possible.
31900 Optional arguments are created with the toolbar button
31901 \begin_inset Graphics
31902 filename ../images/math-macro-add-optional-param.png
31908 The first non-optional argument can be transformed to an optional one with
31910 \begin_inset Graphics
31911 filename ../images/math-macro-make-optional.png
31917 In the second blue box the appearance of the macro in LyX can be defined.
31918 Normally you want to see it as it is defined, so the box is kept empty.
31919 But when you have created a macro that needs lot of space on the screen,
31920 you can insert in the box for example
31921 \begin_inset Newline newline
31951 \begin_inset Newline newline
31956 For the macro only the arguments with the macro name in front of them will
31957 then be displayed in LyX, leading to a better overview.
31958 The formula appears in the output as defined in the first box.
31959 \begin_inset Newline newline
31962 The appearance of macros in formulas can furthermore be changed for single
31963 macros by setting the cursor in the macro and using the menu
31965 View\SpecialChar \menuseparator
31967 \begin_inset space ~
31971 \begin_inset space ~
31979 \begin_layout Standard
31980 To use a macro, the macro name is inserted as command to a formula, in our
31988 Our macro looks in LyX like this:
31989 \begin_inset Newline newline
31993 \begin_inset space \hspace*{\fill}
31997 \begin_inset Graphics
31998 filename clipart/macrouse.png
32003 \begin_inset space \hspace*{\fill}
32007 \begin_inset Newline newline
32010 Here is our macro example with the arguments
32011 \begin_inset Formula $x$
32015 \begin_inset Formula $\ln(x)$
32019 \begin_inset Formula $B$
32025 \begin_layout Standard
32026 \begin_inset Formula
32036 \begin_layout Standard
32037 LyX offers in the menu
32039 Tools\SpecialChar \menuseparator
32040 Preferences\SpecialChar \menuseparator
32041 Editing\SpecialChar \menuseparator
32044 different styles to edit macros.
32045 To find the style that suits you the most, choose a style and set the cursor
32046 in a macro formula to see the difference.
32049 \begin_layout Standard
32050 A math macro is transformed internally to a
32056 command when exporting the document.
32063 command is not placed in the LaTeX-preamble, therefore macros can only
32064 be used in formulas that are in the document below the macro definition
32068 \begin_layout Standard
32069 Math macros can also be directly created from a
32076 When writing for example the command
32079 \begin_inset Newline newline
32088 xleftarrow[#2]{#1}}
32089 \begin_inset Newline newline
32094 in LyX as normal text, highlighting it completely and using then the shortcut
32099 , the command will be transformed to a math macro.
32100 Using this method you need to be careful that the
32106 command is typed correctly, otherwise you get a faulty macro leading to
32110 \begin_layout Standard
32111 Math macros currently have the problem that further formulas in macro definition
32112 s are handled wrongly.
32113 Therefore the example
32120 \begin_inset CommandInset ref
32122 reference "sub:The-Command-newcommand"
32126 cannot be created as macro.
32129 \begin_layout Standard
32130 When the cursor is in a macro definition box, you will see the macro toolbar
32134 \begin_layout Standard
32135 \begin_inset VSpace defskip
32141 \begin_layout Standard
32142 \begin_inset Graphics
32143 filename clipart/MacroToolbar.png
32148 \begin_inset Index idx
32151 \begin_layout Plain Layout
32160 \begin_layout Standard
32161 \begin_inset VSpace defskip
32167 \begin_layout Standard
32168 The macro toolbar contains from left to right the following buttons:
32171 \begin_layout Standard
32172 \begin_inset VSpace defskip
32178 \begin_layout Standard
32179 \begin_inset Tabular
32180 <lyxtabular version="3" rows="9" columns="2">
32181 <features rotate="0" islongtable="true" longtabularalignment="center">
32182 <column alignment="left" valignment="top">
32183 <column alignment="left" valignment="top" width="85col%">
32184 <row interlinespace="2.5mm">
32185 <cell alignment="center" valignment="top" usebox="none">
32188 \begin_layout Plain Layout
32189 \begin_inset Graphics
32190 filename ../images/math-macro-remove-param.png
32191 rotateOrigin center
32200 <cell alignment="center" valignment="top" usebox="none">
32203 \begin_layout Plain Layout
32206 Edit\SpecialChar \menuseparator
32207 Math\SpecialChar \menuseparator
32209 \begin_inset space ~
32212 Definition\SpecialChar \menuseparator
32213 Remove Last Argument
32219 <row interlinespace="2.5mm">
32220 <cell alignment="center" valignment="top" usebox="none">
32223 \begin_layout Plain Layout
32224 \begin_inset Graphics
32225 filename ../images/math-macro-add-param.png
32226 rotateOrigin center
32235 <cell alignment="center" valignment="top" usebox="none">
32238 \begin_layout Plain Layout
32241 Edit\SpecialChar \menuseparator
32242 Math\SpecialChar \menuseparator
32244 \begin_inset space ~
32247 Definition\SpecialChar \menuseparator
32254 <row interlinespace="2.5mm">
32255 <cell alignment="center" valignment="top" usebox="none">
32258 \begin_layout Plain Layout
32259 \begin_inset Graphics
32260 filename ../images/math-macro-make-optional.png
32261 rotateOrigin center
32270 <cell alignment="center" valignment="top" usebox="none">
32273 \begin_layout Plain Layout
32276 Edit\SpecialChar \menuseparator
32277 Math\SpecialChar \menuseparator
32279 \begin_inset space ~
32282 Definition\SpecialChar \menuseparator
32283 Make First Non-Optional into
32284 \begin_inset Newline newline
32288 \begin_inset Phantom HPhantom
32291 \begin_layout Plain Layout
32294 Edit\SpecialChar \menuseparator
32295 Math\SpecialChar \menuseparator
32297 \begin_inset space ~
32300 Definition\SpecialChar \menuseparator
32312 <row interlinespace="2.5mm">
32313 <cell alignment="center" valignment="top" usebox="none">
32316 \begin_layout Plain Layout
32317 \begin_inset Graphics
32318 filename ../images/math-macro-make-nonoptional.png
32319 rotateOrigin center
32328 <cell alignment="center" valignment="top" usebox="none">
32331 \begin_layout Plain Layout
32334 Edit\SpecialChar \menuseparator
32335 Math\SpecialChar \menuseparator
32337 \begin_inset space ~
32340 Definition\SpecialChar \menuseparator
32341 Make Last Optional into
32342 \begin_inset Newline newline
32346 \begin_inset Phantom HPhantom
32349 \begin_layout Plain Layout
32352 Edit\SpecialChar \menuseparator
32353 Math\SpecialChar \menuseparator
32355 \begin_inset space ~
32358 Definition\SpecialChar \menuseparator
32364 Non-Optional Argument
32370 <row interlinespace="2.5mm">
32371 <cell alignment="center" valignment="top" usebox="none">
32374 \begin_layout Plain Layout
32375 \begin_inset Graphics
32376 filename ../images/math-macro-remove-optional-param.png
32377 rotateOrigin center
32386 <cell alignment="center" valignment="top" usebox="none">
32389 \begin_layout Plain Layout
32392 Edit\SpecialChar \menuseparator
32393 Math\SpecialChar \menuseparator
32395 \begin_inset space ~
32398 Definition\SpecialChar \menuseparator
32399 Remove Optional Argument
32405 <row interlinespace="2.5mm">
32406 <cell alignment="center" valignment="top" usebox="none">
32409 \begin_layout Plain Layout
32410 \begin_inset Graphics
32411 filename ../images/math-macro-add-optional-param.png
32412 rotateOrigin center
32421 <cell alignment="center" valignment="top" usebox="none">
32424 \begin_layout Plain Layout
32427 Edit\SpecialChar \menuseparator
32428 Math\SpecialChar \menuseparator
32430 \begin_inset space ~
32433 Definition\SpecialChar \menuseparator
32434 Insert Optional Argument
32440 <row interlinespace="2.5mm">
32441 <cell alignment="center" valignment="top" usebox="none">
32444 \begin_layout Plain Layout
32445 \begin_inset Graphics
32446 filename ../images/math-macro-remove-greedy-param.png
32447 rotateOrigin center
32456 <cell alignment="center" valignment="top" usebox="none">
32459 \begin_layout Plain Layout
32462 Edit\SpecialChar \menuseparator
32463 Math\SpecialChar \menuseparator
32465 \begin_inset space ~
32468 Definition\SpecialChar \menuseparator
32469 Remove Last Argument
32470 \begin_inset Newline newline
32474 \begin_inset Phantom HPhantom
32477 \begin_layout Plain Layout
32480 Edit\SpecialChar \menuseparator
32481 Math\SpecialChar \menuseparator
32483 \begin_inset space ~
32486 Definition\SpecialChar \menuseparator
32492 Spitting Out To The Right
32498 <row interlinespace="2.5mm">
32499 <cell alignment="center" valignment="top" usebox="none">
32502 \begin_layout Plain Layout
32503 \begin_inset Graphics
32504 filename ../images/math-macro-append-greedy-param.png
32505 rotateOrigin center
32514 <cell alignment="center" valignment="top" usebox="none">
32517 \begin_layout Plain Layout
32520 Edit\SpecialChar \menuseparator
32521 Math\SpecialChar \menuseparator
32523 \begin_inset space ~
32526 Definition\SpecialChar \menuseparator
32528 \begin_inset Newline newline
32532 \begin_inset Phantom HPhantom
32535 \begin_layout Plain Layout
32538 Edit\SpecialChar \menuseparator
32539 Math\SpecialChar \menuseparator
32541 \begin_inset space ~
32544 Definition\SpecialChar \menuseparator
32550 Eating From The Right
32556 <row interlinespace="2.5mm">
32557 <cell alignment="center" valignment="top" usebox="none">
32560 \begin_layout Plain Layout
32561 \begin_inset Graphics
32562 filename ../images/math-macro-add-greedy-optional-param.png
32563 rotateOrigin center
32572 <cell alignment="center" valignment="top" usebox="none">
32575 \begin_layout Plain Layout
32578 Edit\SpecialChar \menuseparator
32579 Math\SpecialChar \menuseparator
32581 \begin_inset space ~
32584 Definition\SpecialChar \menuseparator
32585 Append Optional Argument
32586 \begin_inset Newline newline
32590 \begin_inset Phantom HPhantom
32593 \begin_layout Plain Layout
32596 Edit\SpecialChar \menuseparator
32597 Math\SpecialChar \menuseparator
32599 \begin_inset space ~
32602 Definition\SpecialChar \menuseparator
32608 Eating From The Right
32621 \begin_layout Section
32622 Computer Algebra Systems
32625 \begin_layout Standard
32626 LyX offers the exchange between mathematical expressions written in LyX's
32627 math editor and external applications or user defined scripts.
32628 Currently supported applications are
32645 Note that the set of supported mathematical constructs is limited only
32646 to very simple cases.
32649 \begin_layout Subsection
32653 \begin_layout Standard
32654 Write some expression in a formula, go to the
32656 Edit\SpecialChar \menuseparator
32657 Math\SpecialChar \menuseparator
32658 Use Computer Algebra System
32660 menu and choose the application you have installed on the computer.
32661 After that the result of computation should show on the right side of the
32662 expression together with the
32663 \begin_inset Quotes eld
32667 \begin_inset Quotes erd
32673 \begin_layout Standard
32674 Here are few simple examples (with results from
32678 ) to show what kind of computations can be performed:
32681 \begin_layout Itemize
32682 \begin_inset Formula $\frac{37}{3}*2-\sum_{i=1}^{3}i^{i}=-\frac{22}{3}$
32688 \begin_layout Itemize
32689 \begin_inset Formula $\frac{37.0}{3}=12.33333333333333$
32695 \begin_layout Itemize
32696 \begin_inset Formula $\int_{1}^{2}\sin(x)dx=\cos1-\cos2$
32702 \begin_layout Itemize
32703 \begin_inset Formula $\det\left[\begin{array}{ccc}
32707 \end{array}\right]=-56$
32713 \begin_layout Itemize
32714 \begin_inset Formula $\lim_{x\rightarrow0}\left(\frac{\sin(x)}{x}\right)=1$
32720 \begin_layout Subsection
32724 \begin_layout Standard
32725 Currently there is no keyboard shortcut for calling the algebra applications.
32726 One can easily bind a shortcut to the
32730 LyX function (see the
32738 \begin_inset space \thinspace{}
32742 \begin_inset space \space{}
32749 key inside the math editor.
32754 one would use this shortcut definition command:
32757 \begin_layout Standard
32760 command-alternatives break-paragraph;math-extern maxima
32763 \begin_layout Section
32765 \begin_inset Index idx
32768 \begin_layout Plain Layout
32777 \begin_layout Subsection
32779 \begin_inset Index idx
32782 \begin_layout Plain Layout
32791 \begin_layout Standard
32792 Negative numbers often look ugly in formulas because the minus sign before
32793 the number is set with the same length as the minus operator sign.
32794 When writing the negative number in normal text, the minus sign appears
32798 \begin_layout Standard
32799 Thus, the problem disappears when converting the minus sign to mathematical
32803 \begin_layout Standard
32804 An example to visualize the problem:
32807 \begin_layout Standard
32809 \begin_inset Tabular
32810 <lyxtabular version="3" rows="3" columns="2">
32811 <features rotate="0" tabularvalignment="middle">
32812 <column alignment="right" valignment="top">
32813 <column alignment="left" valignment="top">
32815 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
32818 \begin_layout Plain Layout
32824 <cell alignment="center" valignment="top" topline="true" rightline="true" usebox="none">
32827 \begin_layout Plain Layout
32835 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
32838 \begin_layout Plain Layout
32844 <cell alignment="center" valignment="top" topline="true" bottomline="true" rightline="true" usebox="none">
32847 \begin_layout Plain Layout
32848 \begin_inset Formula $x=-2$
32858 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
32861 \begin_layout Plain Layout
32867 <cell alignment="center" valignment="top" topline="true" bottomline="true" rightline="true" usebox="none">
32870 \begin_layout Plain Layout
32871 \begin_inset Formula $x=\textrm{-}2$
32887 \begin_layout Subsection
32888 Comma as decimal Separator
32889 \begin_inset Index idx
32892 \begin_layout Plain Layout
32901 \begin_layout Standard
32902 In LaTeX a comma inside a formula is used, according to the English convention,
32903 as number group separator.
32904 So there will be space added behind all commas in formulas.
32907 \begin_layout Standard
32908 To avoid this, the comma is highlighted and changed to mathematical text
32918 \begin_layout Standard
32919 To use all formula commas in the document as decimal separator, the file
32928 \begin_layout Plain Layout
32933 is part of the LaTeX-package
32938 \begin_inset Index idx
32941 \begin_layout Plain Layout
32946 \begin_layout Plain Layout
32966 \begin_inset Index idx
32969 \begin_layout Plain Layout
32975 is loaded with the LaTeX-preamble line
32978 \begin_layout Standard
32986 \begin_layout Subsection
32988 \begin_inset CommandInset label
32990 name "sub:Physical-Vectors"
32995 \begin_inset Index idx
32998 \begin_layout Plain Layout
33007 \begin_layout Standard
33008 Predefined vectors are offered by the LaTeX-package
33013 \begin_inset Index idx
33016 \begin_layout Plain Layout
33022 that is loaded with the LaTeX-preamble line
33025 \begin_layout Standard
33033 \begin_layout Standard
33037 \begin_layout Plain Layout
33047 \begin_inset Note Note
33050 \begin_layout Plain Layout
33051 The following table will only be displayed when the LaTeX-package
33063 \begin_layout Standard
33064 The following commands are defined:
33067 \begin_layout Standard
33069 \begin_inset Tabular
33070 <lyxtabular version="3" rows="4" columns="2">
33071 <features rotate="0" tabularvalignment="middle">
33072 <column alignment="center" valignment="top">
33073 <column alignment="center" valignment="top">
33075 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
33078 \begin_layout Plain Layout
33084 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
33087 \begin_layout Plain Layout
33095 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
33098 \begin_layout Plain Layout
33108 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
33111 \begin_layout Plain Layout
33112 \begin_inset Formula $\Bra{\psi}$
33122 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
33125 \begin_layout Plain Layout
33135 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
33138 \begin_layout Plain Layout
33139 \begin_inset Formula $\Ket{\psi}$
33149 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
33152 \begin_layout Plain Layout
33164 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
33167 \begin_layout Plain Layout
33168 \begin_inset Formula $\Braket{\psi|\phi}$
33184 \begin_layout Standard
33191 assures that all vertical bars are set in the size of the surrounding brackets:
33192 \begin_inset Formula
33194 \Braket{\phi|J=\frac{3}{2}\,,\, M_{J}}
33203 \begin_layout Plain Layout
33213 \begin_inset Note Note
33216 \begin_layout Plain Layout
33217 The following will be displayed when the LaTeX-package
33229 \begin_layout Standard
33230 You need to install the LaTeX-package
33234 to see the rest of this subsection in the output.
33237 \begin_layout Standard
33241 \begin_layout Plain Layout
33253 \begin_layout Standard
33260 can also be achieved using the command
33266 , that is described in
33267 \begin_inset CommandInset ref
33269 reference "sub:Automatic-Bracket-Size"
33276 \begin_layout Subsection
33277 Self-defined Fractions
33278 \begin_inset CommandInset label
33280 name "sub:Self-defined-Fractions"
33285 \begin_inset Index idx
33288 \begin_layout Plain Layout
33289 Fractions ! self-defined
33297 \begin_layout Standard
33298 To define custom commands for fractions, the command
33305 \begin_inset Index idx
33308 \begin_layout Plain Layout
33315 \begin_layout Plain Layout
33329 is used in the following scheme:
33332 \begin_layout Standard
33345 bracket}{fraction bar thickness}{style}
33346 \begin_inset Newline newline
33350 \begin_inset Phantom HPhantom
33353 \begin_layout Plain Layout
33363 {numerator}{denominator}
33366 \begin_layout Standard
33367 The style is a number in the range of 0
33368 \begin_inset space \thinspace{}
33372 \begin_inset space \thinspace{}
33378 \begin_layout Standard
33380 \begin_inset Tabular
33381 <lyxtabular version="3" rows="5" columns="2">
33382 <features rotate="0" tabularvalignment="middle">
33383 <column alignment="center" valignment="top">
33384 <column alignment="center" valignment="top">
33386 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
33389 \begin_layout Plain Layout
33395 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
33398 \begin_layout Plain Layout
33406 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
33409 \begin_layout Plain Layout
33415 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
33418 \begin_layout Plain Layout
33419 display style formula
33426 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
33429 \begin_layout Plain Layout
33435 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
33438 \begin_layout Plain Layout
33446 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
33449 \begin_layout Plain Layout
33455 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
33458 \begin_layout Plain Layout
33466 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
33469 \begin_layout Plain Layout
33475 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
33478 \begin_layout Plain Layout
33492 \begin_layout Standard
33493 When no style is given, the size is adjusted to the surrounding environment
33494 like for the command
33503 \begin_layout Standard
33504 When no fraction bar thickness is given, the predefined value of 0.4
33505 \begin_inset space \thinspace{}
33511 \begin_layout Standard
33512 \begin_inset VSpace medskip
33515 For example, the commands
33528 \begin_inset CommandInset ref
33530 reference "sub:Fractions"
33534 are defined with the commands
33537 \begin_layout Standard
33546 genfrac{}{}{}{0}{#1}{#2}}
33549 \begin_layout Standard
33553 \begin_layout Standard
33562 genfrac{(}{)}{0pt}{1}{#1}{#2}}
33565 \begin_layout Standard
33566 \begin_inset VSpace medskip
33569 To define a fraction where the fraction bar thickness can be given as optional
33570 argument, the following line is inserted to the LaTeX-preamble:
33573 \begin_layout Standard
33582 genfrac{}{}{#1}{}{#2}{#3}}
33585 \begin_layout Standard
33587 \begin_inset Formula
33589 \text{Command} & & \mathrm{\backslash fracS[1mm]\backslash\{A\to\backslash\{B} & & \mathrm{\backslash fracS[5mm]\backslash\{A\to\backslash\{B}\\
33590 \text{Result} & & \fracS[1mm]{A}{B} & & \fracS[5mm]{A}{B}
33595 As one can see, the distance of the numerator and the denominator to the
33596 fraction bar is round about three times the bar thickness.
33599 \begin_layout Subsection
33601 \begin_inset Index idx
33604 \begin_layout Plain Layout
33613 \begin_layout Standard
33614 There are four ways to cancel formulas or parts of formulas:
33617 \begin_layout Standard
33621 \begin_layout Plain Layout
33631 \begin_inset Note Note
33634 \begin_layout Plain Layout
33635 The following table will only be displayed when the LaTeX-package
33647 \begin_layout Standard
33649 \begin_inset Tabular
33650 <lyxtabular version="3" rows="5" columns="2">
33651 <features rotate="0" tabularvalignment="middle">
33652 <column alignment="center" valignment="top">
33653 <column alignment="center" valignment="top">
33655 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
33658 \begin_layout Plain Layout
33664 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
33667 \begin_layout Plain Layout
33669 \begin_inset Note Note
33672 \begin_layout Plain Layout
33679 are used here as spacer.
33691 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
33694 \begin_layout Plain Layout
33698 \begin_inset space \textvisiblespace{}
33704 \begin_inset space \textvisiblespace{}
33712 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
33715 \begin_layout Plain Layout
33716 \begin_inset Formula $\raisebox{4.5mm}{}\cancel{\int A=B}\raisebox{-2.5mm}{}$
33726 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
33729 \begin_layout Plain Layout
33733 \begin_inset space \textvisiblespace{}
33739 \begin_inset space \textvisiblespace{}
33747 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
33750 \begin_layout Plain Layout
33751 \begin_inset Formula $\raisebox{4.5mm}{}\bcancel{\int A=B}\raisebox{-2.5mm}{}$
33761 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
33764 \begin_layout Plain Layout
33768 \begin_inset space \textvisiblespace{}
33774 \begin_inset space \textvisiblespace{}
33782 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
33785 \begin_layout Plain Layout
33786 \begin_inset Formula $\raisebox{4.5mm}{}\xcancel{\int A=B}\raisebox{-2.5mm}{}$
33796 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
33799 \begin_layout Plain Layout
33803 \begin_inset space \textvisiblespace{}
33809 \begin_inset space \textvisiblespace{}
33813 \begin_inset Formula $\to$
33821 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
33824 \begin_layout Plain Layout
33825 \begin_inset Formula $\raisebox{7mm}{}\cancelto{1}{\int A=B}\raisebox{-2.5mm}{}\hspace{3mm}$
33841 \begin_layout Standard
33848 is especially suitable to visualize the reduction of fractions within formulas:
33849 \begin_inset Formula
33851 \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}}}
33859 \begin_layout Standard
33860 To change the size of
33867 \begin_inset Quotes eld
33871 \begin_inset Quotes erd
33874 value one can add the LaTeX-preamble line
33877 \begin_layout Standard
33882 PassOptionsToPackage{option}{cancel}
33885 \begin_layout Standard
33894 which leads to the same size as for the canceled value, or
33898 which makes is it a bit smaller than normal.
33901 \begin_layout Standard
33902 To color the cancellation bar one adds this command as TeX code:
33905 \begin_layout Standard
33917 \begin_layout Standard
33922 can be replaced by a color of your choice.
33925 \begin_layout Standard
33929 \begin_layout Plain Layout
33945 \begin_layout Standard
33946 \begin_inset Formula
33948 \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}}}
33956 \begin_layout Standard
33960 \begin_layout Plain Layout
33974 \begin_inset Note Note
33977 \begin_layout Plain Layout
33986 \begin_layout Standard
33987 For further customizations, see the documentation of the package
33992 \begin_inset CommandInset citation
33999 \begin_inset Index idx
34002 \begin_layout Plain Layout
34011 \begin_layout Standard
34015 \begin_layout Plain Layout
34025 \begin_inset Note Note
34028 \begin_layout Plain Layout
34029 The following will be displayed when the LaTeX-package
34041 \begin_layout Standard
34042 You need to install the LaTeX-package
34046 to see the rest of this subsection in the output.
34049 \begin_layout Standard
34053 \begin_layout Plain Layout
34065 \begin_layout Standard
34066 \begin_inset Newpage newpage
34072 \begin_layout Subsection
34073 Formulas in Section Headings
34074 \begin_inset CommandInset label
34076 name "sub:Formulas-in-Section"
34081 \begin_inset Index idx
34084 \begin_layout Plain Layout
34085 Formula ! in section headings
34093 \begin_layout Standard
34094 When formulas are used in section headings, the following has to be taken
34098 \begin_layout Standard
34099 \begin_inset Note Greyedout
34102 \begin_layout Plain Layout
34108 \begin_inset Index idx
34111 \begin_layout Plain Layout
34112 Packages ! hyperref
34117 support is enabled in the document settings dialog under
34120 \begin_inset space ~
34125 , PDF-bookmarks are created for every section heading in the table of contents.
34126 If a section heading contains formulas, they are incorrectly displayed
34127 in the bookmark text, because formulas in bookmarks infringe the PDF convention
34136 \begin_layout Standard
34137 Both problems can be solved by inserting at the end of the section heading
34138 a short title with the menu
34140 Insert\SpecialChar \menuseparator
34142 \begin_inset space ~
34148 Short titles are used as alternative for multiline section headings to
34149 keep the table of contents clearly arranged.
34150 Only the short title appears in the table of contents and therefore also
34151 in the PDF-bookmark.
34154 \begin_layout Standard
34155 When formulas should be used in the table of contents but
34159 is used, one can use the following command in TeX-mode:
34162 \begin_layout Standard
34167 texorpdfstring{part}{alternative}
34168 \begin_inset Index idx
34171 \begin_layout Plain Layout
34182 \begin_layout Standard
34183 Part is the part of the heading that shouldn't appear in the PDF-bookmark.
34184 This can be characters, formulas, footnotes, but also cross-references.
34185 The alternative is used instead of the part for the bookmark.
34188 \begin_layout Standard
34189 Here are two example headings:
34190 \begin_inset VSpace -3mm
34197 \begin_layout Plain Layout
34209 \begin_layout Subsubsection
34210 Heading without formula in table of contents
34211 \begin_inset Formula $\sqrt{-1}=\mathrm{i}$
34215 \begin_inset Argument 1
34218 \begin_layout Plain Layout
34219 Heading without formula in table of contents
34227 \begin_layout Subsubsection
34228 Heading with formula in table of contents
34232 \begin_layout Plain Layout
34242 \begin_inset Formula $\sqrt{-1}=\mathrm{i}$
34249 \begin_layout Plain Layout
34259 \begin_layout Standard
34263 \begin_layout Plain Layout
34272 In the first heading a short title was used, in the second one
34281 \begin_layout Standard
34282 To get the same formatting as for the other headings, the complete heading
34291 \begin_layout Plain Layout
34293 \begin_inset CommandInset ref
34295 reference "sub:Bold-Formulas"
34307 \begin_layout Subsection
34308 Formulas in multi-column Text
34309 \begin_inset Index idx
34312 \begin_layout Plain Layout
34313 Formula ! in multi-column text
34321 \begin_layout Standard
34322 Formulas in multi-column text are often too wide to fit into a column and
34323 thus need to be set over the whole page width.
34324 This is done by using the LaTeX-package
34332 \begin_layout Plain Layout
34337 is part of every LaTeX standard installation.
34343 \begin_inset Index idx
34346 \begin_layout Plain Layout
34347 Packages ! multicol
34352 , that is loaded with the LaTeX-preamble line
34355 \begin_layout Standard
34360 usepackage{multicol}
34363 \begin_layout Standard
34364 \begin_inset Note Greyedout
34367 \begin_layout Plain Layout
34368 Note that in this case the setting
34371 \begin_inset space ~
34378 Document\SpecialChar \menuseparator
34384 \begin_inset space ~
34404 \begin_layout Standard
34405 Before the multi-column text the command
34408 \begin_layout Standard
34413 begin{multicols}{column number}
34416 \begin_layout Standard
34417 is written in TeX-mode.
34418 The column number is a number in the range of 2
34419 \begin_inset space \thinspace{}
34423 \begin_inset space \thinspace{}
34427 Before the formula the multi-column text is ended by inserting the command
34430 \begin_layout Standard
34438 \begin_layout Standard
34442 \begin_layout Standard
34443 Due to the command some space is automatically added before the formula.
34445 \begin_inset space \thinspace{}
34448 mm vertical space is inserted before the formula.
34449 When the formula style
34455 \begin_layout Plain Layout
34457 \begin_inset CommandInset ref
34459 reference "sec:Formula-Styles"
34471 \begin_inset space \thinspace{}
34474 mm space is inserted instead.
34477 \begin_layout Standard
34478 As example a multi-column text with a displayed formula:
34481 \begin_layout Standard
34487 \begin_layout Plain Layout
34491 begin{multicols}{2}
34496 Das Spektrum wird fouriertransformiert.
34497 Die Fouriertransformation wird verwendet, um die überlagerten Signale (Netzwerk
34498 , Lösungsmittel) zu trennen.
34499 Nachdem wir die Phasenverschiebung bestimmen konnten, interessiert uns
34500 nun das Aussehen des Ausgangssignals.
34501 Im Experiment haben wir es mit sehr vielen Teilchen zu tun, so dass man
34502 über alle Phasen integrieren muss.
34504 \begin_inset Formula $S$
34507 unser normiertes Ausgangssignal und
34508 \begin_inset Formula $P$
34511 die Phasenverteilungsfunktion, so ergibt sich die Beziehung
34515 \begin_layout Plain Layout
34525 \begin_inset VSpace -6mm
34529 \begin_inset Formula
34531 S(t)=S_{0}(t)\int_{-\infty}^{\infty}P(\phi,t)\mathrm{e}^{\mathrm{i}\phi}\,\mathrm{d}\phi
34540 \begin_layout Plain Layout
34544 begin{multicols}{2}
34550 \begin_inset Formula $S_{0}$
34553 das Signal ohne Gradient ist und die Normierungsbedingung
34554 \begin_inset Formula $\int_{-\infty}^{\infty}P(\phi,t)\,\mathrm{d}\phi=1$
34558 Nun dürfen wir aber nicht den Relaxationsprozess außer Acht lassen.
34560 \begin_inset Formula $\nicefrac{\pi}{2}$
34564 \begin_inset space \thinspace{}
34567 -rf-Puls beginnt sich die Magnetisierung zu entfokussieren, wodurch sich
34568 das Signal zusätzlich abschwächt.
34569 Diese Abschwächung verläuft exponentiell in Abhängigkeit der so genannten
34571 \begin_inset Formula $T_{2}$
34577 \begin_layout Standard
34583 \begin_layout Plain Layout
34595 \begin_layout Subsection
34596 Formulas with Description of Variables
34597 \begin_inset Index idx
34600 \begin_layout Plain Layout
34601 Formula ! with description of variables
34609 \begin_layout Standard
34610 To describe variables within a formula, like in formula
34611 \begin_inset CommandInset ref
34613 reference "eq:within"
34622 \begin_inset Formula $n$
34626 \begin_inset space ~
34629 matrix is used with left aligned columns for the
34630 \begin_inset Formula $n$
34637 \begin_layout Plain Layout
34639 \begin_inset CommandInset ref
34641 reference "sec:Matrices"
34650 To set the description in a smaller size, before the matrix e.
34651 \begin_inset space \thinspace{}
34655 \begin_inset space \space{}
34668 \begin_layout Plain Layout
34670 \begin_inset CommandInset ref
34672 reference "sub:Font-Sizes"
34684 \begin_layout Standard
34685 When the formula style
34691 \begin_layout Plain Layout
34693 \begin_inset CommandInset ref
34695 reference "sec:Formula-Styles"
34716 \begin_layout Plain Layout
34723 only works in formulas with the style
34728 \begin_inset CommandInset ref
34730 reference "sub:Variable-Space"
34739 is inserted before and after the matrix to have the same separation of
34740 the matrix from the equation and the side margin.
34743 \begin_layout Standard
34744 When the formula style
34748 is used, the method described in
34749 \begin_inset CommandInset ref
34751 reference "sub:Flalign-Environment"
34755 is used to indent formulas.
34757 \begin_inset CommandInset ref
34759 reference "eq:within"
34763 consists of five columns where in the first two columns contain the equation,
34764 the third the matrix and the last one an empty TeX-brace.
34765 \begin_inset Formula
34767 \hspace{30pt}F_{A} & =\rho·V·g & \footnotesize\begin{array}{ll}
34768 \rho & \textrm{density}\\
34769 V & \textrm{volume}\\
34770 g & \textrm{gravitational acceleration}
34771 \end{array} & & {}\label{eq:within}
34779 \begin_layout Subsection
34780 Upright small Greek Letters
34781 \begin_inset CommandInset label
34783 name "sub:Upright-small-Greek"
34788 \begin_inset Index idx
34791 \begin_layout Plain Layout
34792 Greek letters ! upright
34800 \begin_layout Standard
34801 Most of the math fonts only provide italic small Greek letters.
34802 But for symbols of elementary particles like pions and neutrinos, upright
34803 Greek letters are needed.
34812 \begin_layout Plain Layout
34817 is part of the LaTeX-package
34822 \begin_inset Index idx
34825 \begin_layout Plain Layout
34830 \begin_layout Plain Layout
34850 \begin_inset Index idx
34853 \begin_layout Plain Layout
34859 that is loaded with the LaTeX-preamble line
34862 \begin_layout Standard
34867 usepackage{upgreek}
34870 \begin_layout Standard
34876 \begin_layout Plain Layout
34886 \begin_inset Note Note
34889 \begin_layout Plain Layout
34890 The following table will only be displayed when the LaTeX-package
34899 They are created when the command for a small Greek letter is started with
34905 For example the command
34912 \begin_inset Formula $\uptau$
34918 \begin_layout Standard
34919 With these commands reactions of elementary particles can be typeset:
34920 \begin_inset Formula
34922 \uppi^{+}\to\upmu^{+}+\upnu_{\upmu}
34930 \begin_layout Standard
34931 The upright letters are more bold and wider than the italic ones.
34932 They should therefore not be used for units like
34933 \begin_inset Quotes eld
34937 \begin_inset Quotes erd
34943 \begin_layout Standard
34947 \begin_layout Plain Layout
34957 \begin_inset Note Note
34960 \begin_layout Plain Layout
34961 The following will be displayed when the LaTeX-package
34973 \begin_layout Standard
34974 You need to install the LaTeX-package
34978 to see the rest of this subsection in the output.
34981 \begin_layout Standard
34985 \begin_layout Plain Layout
34997 \begin_layout Subsection
34998 Text Characters in Formulas
34999 \begin_inset CommandInset label
35001 name "sub:Text-Characters-in"
35006 \begin_inset Index idx
35009 \begin_layout Plain Layout
35018 \begin_layout Standard
35019 In some cases you might want to insert text characters directly into formulas.
35020 When for example the centered dot · is often used in formulas like
35021 \begin_inset Formula $\nu=5·10^{5}\,\mathrm{Hz}$
35024 , one would have to insert the command
35034 \begin_layout Plain Layout
35036 \begin_inset CommandInset ref
35038 reference "sub:Binary-Operators"
35047 all the time, because this character is defined in all encodings as text
35049 But the encoding can be changed by this LaTeX-preamble line:
35052 \begin_layout Standard
35057 Declare Inputtext{183}{
35067 f\SpecialChar \textcompwordmark{}
35071 \begin_layout Standard
35072 The character encoding (menu
35074 Document\SpecialChar \menuseparator
35075 Settings\SpecialChar \menuseparator
35078 ) specifies what character appears when a keyboard key is pressed.
35079 When the key for the character '·' is pressed, internally the command
35086 But this command is not available in a formula so that you would get LaTeX-erro
35088 With the changed encoding the right command is chosen automatically, depending
35089 on if the character was inserted into a formula or not.
35092 \begin_layout Standard
35093 The encoding of several characters is saved in definition files.
35094 For example the encoding
35098 is defined in the file
35102 which is in the installation folder of LaTeX.
35103 Encodings should only be changed via the LaTeX-preamble and not in the
35105 Otherwise documents could not be edited by other LyX users working on other
35109 \begin_layout Standard
35110 \begin_inset VSpace medskip
35113 Besides the centered dot, in this document the degree sign ° is defined
35114 with the following LaTeX-preamble line so that it can be directly inserted
35118 \begin_layout Standard
35123 DeclareInputtext{176}{
35133 f\SpecialChar \textcompwordmark{}
35137 \begin_layout Standard
35138 \begin_inset Newpage newpage
35144 \begin_layout Section
35147 \begin_inset Index idx
35150 \begin_layout Plain Layout
35159 \begin_layout Standard
35160 This section is a summary of the most important typographic rules, listed
35165 \begin_layout Plain Layout
35166 This collection was partly taken from the German semi-official dictionary
35168 \begin_inset Quotes eld
35172 \begin_inset Quotes erd
35176 \begin_inset CommandInset citation
35182 that lists some of the ISO rules.
35183 More rules are listed in
35184 \begin_inset CommandInset citation
35198 \begin_layout Itemize
35207 \begin_layout Plain Layout
35208 done with font styles, see
35209 \begin_inset CommandInset ref
35211 reference "sub:Font-Styles"
35220 , no matter if they appear in italic text: 30
35221 \begin_inset space \thinspace{}
35225 \begin_inset Newline newline
35228 Between the value and the unit is the smallest space, see
35229 \begin_inset CommandInset ref
35231 reference "sub:Predefined-Space"
35236 \begin_inset Newline newline
35239 This convention is automatically fulfilled when the command
35246 When it is entered to a formula, two boxes appear.
35247 In the first one the value is inserted, in the second one the unit, and
35249 \begin_inset Formula $\unit[30]{km/h}$
35253 \begin_inset space \thinspace{}
35263 is not a real LaTeX command but the command
35269 , therefore you cannot use it in TeX code.
35272 \begin_layout Itemize
35273 Percent and perthousand signs are set like physical units:
35274 \begin_inset Newline newline
35278 \begin_inset space \thinspace{}
35284 \begin_layout Itemize
35285 The degree sign follows directly on the value: 15°, but not when it is used
35287 \begin_inset space \thinspace{}
35293 \begin_layout Itemize
35294 In numbers with more than four digits the smallest space is inserted before
35295 every third digit to group them:
35305 \begin_inset space \thinspace{}
35309 \begin_inset space \thinspace{}
35315 \begin_layout Itemize
35316 For dimensions like 120×90×40
35317 \begin_inset space \thinspace{}
35320 cm the multiplication sign
35321 \begin_inset Quotes eld
35325 \begin_inset Quotes erd
35329 It is available either via the command
35337 Insert\SpecialChar \menuseparator
35338 Special Character\SpecialChar \menuseparator
35344 \begin_layout Itemize
35345 Functions with names consisting of several letters are set upright to avoid
35347 \begin_inset CommandInset ref
35349 reference "sub:Predefined-Functions"
35356 \begin_layout Itemize
35357 Indices consisting of several letters, are set upright:
35358 \begin_inset Formula $E_{\mathrm{kin}}$
35362 \begin_inset Newline newline
35365 Components of matrices are set italic:
35366 \begin_inset Formula $\hat{H}_{kl}$
35372 \begin_layout Itemize
35373 The differentiation/integration operator 'd', the Euler's number 'e' and
35374 the imaginary unit 'i' should be set upright, to avoid mixing them up with
35378 \begin_layout Itemize
35379 The character that denotes a
35383 transformation is inserted either by the command
35388 \begin_inset space \textvisiblespace{}
35395 Insert\SpecialChar \menuseparator
35396 Special Character\SpecialChar \menuseparator
35397 Symbols\SpecialChar \menuseparator
35399 \begin_inset space ~
35405 \begin_inset Formula $\mathscr{F}$
35411 \begin_layout Standard
35412 \begin_inset Newpage newpage
35418 \begin_layout Section
35420 \begin_inset Index idx
35423 \begin_layout Plain Layout
35432 \begin_layout Standard
35433 Some characters and symbols can be created with several commands.
35434 Here is a list of the synonym commands:
35437 \begin_layout Standard
35438 \begin_inset VSpace bigskip
35442 \begin_inset space \hfill{}
35446 \begin_inset Tabular
35447 <lyxtabular version="3" rows="12" columns="2">
35448 <features rotate="0" tabularvalignment="middle">
35449 <column alignment="center" valignment="top" width="0pt">
35450 <column alignment="center" valignment="top" width="0pt">
35452 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
35455 \begin_layout Plain Layout
35461 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
35464 \begin_layout Plain Layout
35466 \begin_inset Note Note
35469 \begin_layout Plain Layout
35476 is only used as spacer.
35488 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
35491 \begin_layout Plain Layout
35499 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
35502 \begin_layout Plain Layout
35506 \begin_layout Plain Layout
35519 \begin_layout Plain Layout
35533 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
35536 \begin_layout Plain Layout
35544 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
35547 \begin_layout Plain Layout
35557 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
35560 \begin_layout Plain Layout
35568 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
35571 \begin_layout Plain Layout
35581 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
35584 \begin_layout Plain Layout
35592 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
35595 \begin_layout Plain Layout
35603 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
35606 \begin_layout Plain Layout
35614 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
35617 \begin_layout Plain Layout
35625 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
35628 \begin_layout Plain Layout
35636 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
35639 \begin_layout Plain Layout
35649 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
35652 \begin_layout Plain Layout
35660 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
35663 \begin_layout Plain Layout
35673 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
35676 \begin_layout Plain Layout
35684 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
35687 \begin_layout Plain Layout
35697 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
35700 \begin_layout Plain Layout
35708 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
35711 \begin_layout Plain Layout
35721 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
35724 \begin_layout Plain Layout
35732 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
35735 \begin_layout Plain Layout
35743 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
35746 \begin_layout Plain Layout
35754 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
35757 \begin_layout Plain Layout
35769 \begin_inset space \hfill{}
35773 \begin_inset Tabular
35774 <lyxtabular version="3" rows="12" columns="2">
35775 <features rotate="0" tabularvalignment="middle">
35776 <column alignment="center" valignment="top" width="0pt">
35777 <column alignment="center" valignment="top" width="0pt">
35779 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
35782 \begin_layout Plain Layout
35788 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
35791 \begin_layout Plain Layout
35799 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
35802 \begin_layout Plain Layout
35810 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
35813 \begin_layout Plain Layout
35825 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
35828 \begin_layout Plain Layout
35836 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
35839 \begin_layout Plain Layout
35849 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
35852 \begin_layout Plain Layout
35860 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
35863 \begin_layout Plain Layout
35873 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
35876 \begin_layout Plain Layout
35884 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
35887 \begin_layout Plain Layout
35895 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
35898 \begin_layout Plain Layout
35906 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
35909 \begin_layout Plain Layout
35917 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
35920 \begin_layout Plain Layout
35928 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
35931 \begin_layout Plain Layout
35941 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
35944 \begin_layout Plain Layout
35952 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
35955 \begin_layout Plain Layout
35965 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
35968 \begin_layout Plain Layout
35976 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
35979 \begin_layout Plain Layout
35989 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
35992 \begin_layout Plain Layout
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36092 The LaTeX Companion
36095 Addison Wesley, 2004
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36100 LatexCommand bibitem
36106 \begin_inset CommandInset href
36109 target "ftp://ftp.dante.de/tex-archive/info/math/voss/mathmode/Mathmode.pdf"
36113 of LaTeX's math abilities
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36127 target "http://mirrors.ctan.org/macros/latex/required/amslatex/math/amsldoc.pdf"
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36155 \begin_inset CommandInset href
36158 target "ftp://ftp.dante.de/tex-archive/info/symbols/comprehensive/symbols-a4.pdf"
36162 of all symbols available with LaTeX-packages
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36180 of the LaTeX-package
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36205 \begin_inset CommandInset href
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36208 target "http://www.tug.org/applications/hyperref/ftp/doc/manual.pdf"
36212 of the LaTeX-package
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36221 Packages ! hyperref
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36239 name "Documentation"
36240 target "http://www.ctan.org/tex-archive/macros/latex/contrib/mhchem/mhchem.pdf"
36244 of the LaTeX-package
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36269 \begin_inset CommandInset href
36272 target "http://www.tug.org/TUGboat/Articles/tb22-4/tb72perlS.pdf"
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36285 reference "sub:Operator-Limits"
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36317 Auflage, Duden 2001
36320 \begin_layout Bibliography
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36328 \begin_inset CommandInset href
36331 target "http://physics.nist.gov/Document/checklist.pdf"
36335 for reviewing manuscripts
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