1 #LyX 2.1 created this file. For more info see http://www.lyx.org/
7 % DO NOT ALTER THIS PREAMBLE!!!
9 % This preamble is designed to ensure that the file prints
10 % out as advertised. If you mess with this preamble,
11 % parts of this document may not print out as expected. If you
12 % have problems LaTeXing this file, please contact
13 % the documentation team
14 % email: lyx-docs@lists.lyx.org
20 % set fonts for nicer pdf view
21 \IfFileExists{lmodern.sty}
22 {\usepackage{lmodern}}{}
24 \fi % end if pdflatex is used
26 % solves the following problem:
27 % If the dection number consits of too many numerals the section heading
28 % will be printed in the TOC without a space between it and the section number.
29 % As solution more space between the number and the heading is inserted:
30 \renewcommand{\l@subsection}{\@dottedtocline{2}{1.5em}{2.8em}}
31 \renewcommand{\l@subsubsection}{\@dottedtocline{3}{4.3em}{3.6em}}
33 % increase link area for cross-references and autoname them,
34 \AtBeginDocument{\renewcommand{\ref}[1]{\mbox{\autoref{#1}}}}
35 \@ifundefined{extrasenglish}{\usepackage[english]{babel}}{}
36 \addto\extrasenglish{%
37 \renewcommand*{\equationautorefname}[1]{}%
38 \renewcommand{\sectionautorefname}{sec.\negthinspace}%
39 \renewcommand{\subsectionautorefname}{sec.\negthinspace}%
40 \renewcommand{\subsubsectionautorefname}{sec.\negthinspace}%
43 % don't load packages twice
44 % see first footnote in sec. 9.3
45 \@ifundefined{textcolor}{\usepackage{color}}{}
47 % the pages of the TOC are numbered roman
48 % and a PDF-bookmark for the TOC is added
50 \let\myTOC\tableofcontents
51 \renewcommand{\tableofcontents}{%
53 \pdfbookmark[1]{\contentsname}{}
56 \pagenumbering{arabic}}
58 % insert additional vertical space of 1.5 mm between footnotes,
60 \renewcommand{\footnote}[1]{\myFoot{#1\vspace{1.5mm}}}
62 % provides caption formatting
63 \setkomafont{captionlabel}{\bfseries}
65 % enables calculation of values
68 % for multiple columns used in sec. 24.7
74 % for the Fourier transformation symbol
77 % define a color, used in sec.9.3
78 \definecolor{darkgreen}{cmyk}{0.5, 0, 1, 0.5}
80 % declare operators (see sec. 10.4 and sec. 15.2)
81 \DeclareMathOperator*{\Lozenge}{\blacklozenge}
82 \DeclareMathOperator{\sgn}{sgn}
84 % example definitions for sec. 20.1
85 \newcommand{\gr}{\Longrightarrow}
86 \newcommand{\us}[1]{\underline{#1}}
87 \newcommand{\fb}[3]{\framebox#1#2{$#3$}}
88 \newcommand{\cb}[3][white]{\fcolorbox{#2}{#1}{$#3$}}
89 \newcommand{\fracS}[3][]{\genfrac{}{}{#1}{}{#2}{#3}}
91 % example macro from sec. 19.4
92 %\def\tagform@#1{\maketag@@@{|#1|}}
95 % ------------------------------------
96 % used to check for needed LaTeX packages
99 % check for package undertilde
100 % used for the command \utilde
101 \newboolean{undertilde}
102 \IfFileExists{undertilde.sty}
103 {\usepackage{undertilde}
104 \setboolean{undertilde}{true}}
105 {\setboolean{undertilde}{false}}
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 1
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, mathtools, mhchem, undertilde
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 Standard
9543 \begin_inset VSpace bigskip
9549 \begin_layout Standard
9550 LyX also supports a tilde under the character if the LaTeX-package
9555 \begin_inset Index idx
9558 \begin_layout Plain Layout
9559 Packages ! undertilde
9564 is installed on your system:
9567 \begin_layout Standard
9571 \begin_layout Plain Layout
9581 \begin_inset Note Note
9584 \begin_layout Plain Layout
9585 The following table will only be displayed when the LaTeX-package
9597 \begin_layout Standard
9600 \begin_inset Tabular
9601 <lyxtabular version="3" rows="2" columns="2">
9602 <features rotate="0" tabularvalignment="middle">
9603 <column alignment="center" valignment="top" width="0pt">
9604 <column alignment="center" valignment="top" width="0pt">
9606 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
9609 \begin_layout Plain Layout
9615 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
9618 \begin_layout Plain Layout
9626 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
9629 \begin_layout Plain Layout
9633 \begin_inset space \textvisiblespace{}
9641 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
9644 \begin_layout Plain Layout
9645 \begin_inset Formula $\raisebox{5mm}{}\utilde{A}$
9661 \begin_layout Standard
9665 \begin_layout Plain Layout
9675 \begin_inset Note Note
9678 \begin_layout Plain Layout
9679 The following will be displayed when the LaTeX-package
9691 \begin_layout Standard
9692 You need to install the LaTeX-package
9696 to see the rest of this subsection in the output.
9699 \begin_layout Standard
9703 \begin_layout Plain Layout
9715 \begin_layout Subsection
9716 Accents for several Characters
9717 \begin_inset Index idx
9720 \begin_layout Plain Layout
9721 Accents ! for several characters
9729 \begin_layout Standard
9730 \begin_inset space \hfill{}
9734 \begin_inset Tabular
9735 <lyxtabular version="3" rows="5" columns="2">
9736 <features rotate="0" tabularvalignment="middle">
9737 <column alignment="center" valignment="top" width="0pt">
9738 <column alignment="center" valignment="top" width="0pt">
9740 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
9743 \begin_layout Plain Layout
9749 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
9752 \begin_layout Plain Layout
9754 \begin_inset Note Note
9757 \begin_layout Plain Layout
9764 is only used as spacer.
9776 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
9779 \begin_layout Plain Layout
9783 \begin_inset space \textvisiblespace{}
9791 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
9794 \begin_layout Plain Layout
9795 \begin_inset Formula $\raisebox{6mm}{}\overleftarrow{A=B}\raisebox{-2mm}{}$
9805 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
9808 \begin_layout Plain Layout
9812 \begin_inset space \textvisiblespace{}
9820 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
9823 \begin_layout Plain Layout
9824 \begin_inset Formula $\raisebox{5mm}{}\underleftarrow{A=B}\raisebox{-3mm}{}$
9834 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
9837 \begin_layout Plain Layout
9841 \begin_inset space \textvisiblespace{}
9849 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
9852 \begin_layout Plain Layout
9853 \begin_inset Formula $\raisebox{6mm}{}\overleftrightarrow{A=B}\raisebox{-2mm}{}$
9863 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
9866 \begin_layout Plain Layout
9870 \begin_inset space \textvisiblespace{}
9878 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
9881 \begin_layout Plain Layout
9882 \begin_inset Formula $\raisebox{5mm}{}\underleftrightarrow{A=B}\raisebox{-3mm}{}$
9896 \begin_inset space \hfill{}
9900 \begin_inset Tabular
9901 <lyxtabular version="3" rows="5" columns="2">
9902 <features rotate="0" tabularvalignment="middle">
9903 <column alignment="center" valignment="top" width="0pt">
9904 <column alignment="center" valignment="top" width="0pt">
9906 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
9909 \begin_layout Plain Layout
9915 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
9918 \begin_layout Plain Layout
9926 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
9929 \begin_layout Plain Layout
9933 \begin_inset space \textvisiblespace{}
9941 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
9944 \begin_layout Plain Layout
9945 \begin_inset Formula $\raisebox{6mm}{}\overrightarrow{A=B}\raisebox{-2mm}{}$
9955 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
9958 \begin_layout Plain Layout
9962 \begin_inset space \textvisiblespace{}
9970 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
9973 \begin_layout Plain Layout
9974 \begin_inset Formula $\raisebox{5mm}{}\underrightarrow{A=B}\raisebox{-3mm}{}$
9984 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
9987 \begin_layout Plain Layout
9991 \begin_inset space \textvisiblespace{}
9999 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
10002 \begin_layout Plain Layout
10003 \begin_inset Formula $\raisebox{6mm}{}\widetilde{A=B}\raisebox{-2mm}{}$
10013 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
10016 \begin_layout Plain Layout
10020 \begin_inset space \textvisiblespace{}
10028 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
10031 \begin_layout Plain Layout
10032 \begin_inset Formula $\raisebox{6mm}{}\widehat{A=B}\raisebox{-2mm}{}$
10046 \begin_inset space \hfill{}
10052 \begin_layout Standard
10053 \begin_inset VSpace medskip
10056 With these commands as many characters as you like can be accented.
10069 will only be set in the output with a length of three characters, as shown
10070 in the following example:
10071 \begin_inset Formula
10073 \widetilde{A+B=C-D}
10081 \begin_layout Standard
10089 \begin_inset Index idx
10092 \begin_layout Plain Layout
10107 \begin_inset Index idx
10110 \begin_layout Plain Layout
10118 described in the previous subsection it is also possible to accent several
10125 \begin_inset space \textvisiblespace{}
10129 \begin_inset Formula $\downarrow$
10135 \begin_inset Formula
10137 \underset{***}{A=B}
10145 \begin_layout Standard
10146 \begin_inset Newpage newpage
10152 \begin_layout Section
10154 \begin_inset CommandInset label
10161 \begin_inset Index idx
10164 \begin_layout Plain Layout
10173 \begin_layout Subsection
10175 \begin_inset CommandInset label
10177 name "sub:Predefined-Space"
10182 \begin_inset Index idx
10185 \begin_layout Plain Layout
10186 Space ! horizontal ! predefined
10194 \begin_layout Standard
10195 Sometimes it is necessary to insert horizontal space into a formula.
10196 This is done by inserting a protected space (shortcut
10199 arg "command-alternatives space-insert protected ; math-space"
10204 \begin_inset Quotes eld
10210 \begin_inset space \textvisiblespace{}
10216 \begin_inset Quotes erd
10219 appears and by pressing
10223 several times one can select one of eight different space sizes.
10224 The spaces can also be inserted using the math toolbar button
10225 \begin_inset Graphics
10226 filename ../images/math/space.png
10231 or special commands.
10232 Independent from the inserted command, one can select the size again by
10240 \begin_layout Standard
10243 \begin_inset Tabular
10244 <lyxtabular version="3" rows="6" columns="3">
10245 <features rotate="0" tabularvalignment="middle">
10246 <column alignment="center" valignment="top">
10247 <column alignment="center" valignment="top" width="15col%">
10248 <column alignment="center" valignment="top">
10250 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
10253 \begin_layout Plain Layout
10259 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
10262 \begin_layout Plain Layout
10272 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
10275 \begin_layout Plain Layout
10283 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
10286 \begin_layout Plain Layout
10294 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
10297 \begin_layout Plain Layout
10303 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
10306 \begin_layout Plain Layout
10307 \begin_inset Formula $A\, B$
10317 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
10320 \begin_layout Plain Layout
10328 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
10331 \begin_layout Plain Layout
10337 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
10340 \begin_layout Plain Layout
10341 \begin_inset Formula $A\: B$
10351 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
10354 \begin_layout Plain Layout
10362 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
10365 \begin_layout Plain Layout
10371 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
10374 \begin_layout Plain Layout
10375 \begin_inset Formula $A\; B$
10385 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
10388 \begin_layout Plain Layout
10396 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
10399 \begin_layout Plain Layout
10405 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
10408 \begin_layout Plain Layout
10409 \begin_inset Formula $A\quad B$
10419 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
10422 \begin_layout Plain Layout
10430 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
10433 \begin_layout Plain Layout
10439 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
10442 \begin_layout Plain Layout
10443 \begin_inset Formula $A\qquad B$
10457 \begin_inset space \hfill{}
10461 \begin_inset Tabular
10462 <lyxtabular version="3" rows="6" columns="3">
10463 <features rotate="0" tabularvalignment="middle">
10464 <column alignment="center" valignment="top">
10465 <column alignment="center" valignment="top" width="15col%">
10466 <column alignment="center" valignment="top">
10468 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
10471 \begin_layout Plain Layout
10477 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
10480 \begin_layout Plain Layout
10490 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
10493 \begin_layout Plain Layout
10501 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
10504 \begin_layout Plain Layout
10512 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
10515 \begin_layout Plain Layout
10521 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
10524 \begin_layout Plain Layout
10525 \begin_inset Formula $A\hfill B$
10535 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
10538 \begin_layout Plain Layout
10546 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
10549 \begin_layout Plain Layout
10555 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
10558 \begin_layout Plain Layout
10559 \begin_inset Formula $A\hspace*{1em}B$
10569 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
10572 \begin_layout Plain Layout
10580 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
10583 \begin_layout Plain Layout
10589 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
10592 \begin_layout Plain Layout
10593 \begin_inset Formula $A\hspace{1em}B$
10603 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
10606 \begin_layout Plain Layout
10610 \begin_inset space \textvisiblespace{}
10618 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
10621 \begin_layout Plain Layout
10627 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
10630 \begin_layout Plain Layout
10631 \begin_inset Formula $A\ B$
10641 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
10644 \begin_layout Plain Layout
10652 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
10655 \begin_layout Plain Layout
10661 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
10664 \begin_layout Plain Layout
10665 \begin_inset Formula $A\! B$
10681 \begin_layout Standard
10683 \begin_inset space ~
10687 \begin_inset space \thinspace{}
10691 \begin_inset space \thinspace{}
10694 7 are variable spaces which are explained in
10695 \begin_inset CommandInset ref
10697 reference "sub:Variable-Space"
10703 \begin_inset space ~
10706 9 seems to produce no space.
10707 It is displayed red in LyX contrary to the other sizes, because it is a
10709 There are two more negative spaces:
10712 \begin_layout Standard
10714 \begin_inset Tabular
10715 <lyxtabular version="3" rows="3" columns="3">
10716 <features rotate="0" tabularvalignment="middle">
10717 <column alignment="center" valignment="middle" width="6.8cm">
10718 <column alignment="center" valignment="top" width="0pt">
10719 <column alignment="center" valignment="top" width="0pt">
10721 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
10724 \begin_layout Plain Layout
10730 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
10733 \begin_layout Plain Layout
10741 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
10744 \begin_layout Plain Layout
10754 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
10757 \begin_layout Plain Layout
10762 keystrokes after inserting the protected space
10767 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
10770 \begin_layout Plain Layout
10776 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
10779 \begin_layout Plain Layout
10787 <cell multicolumn="1" alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
10790 \begin_layout Plain Layout
10796 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
10799 \begin_layout Plain Layout
10800 \begin_inset Formula $A\negmedspace B$
10808 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
10811 \begin_layout Plain Layout
10812 \begin_inset Formula $A\negthickspace B$
10828 \begin_layout Standard
10829 Negative spaces can lead to characters overlapping each other.
10830 Thus they can be used to enforce ligatures, which are e.
10831 \begin_inset space \thinspace{}
10835 \begin_inset space \space{}
10838 useful for summation operators:
10841 \begin_layout Standard
10843 \begin_inset Tabular
10844 <lyxtabular version="3" rows="3" columns="2">
10845 <features rotate="0" tabularvalignment="middle">
10846 <column alignment="center" valignment="top">
10847 <column alignment="center" valignment="top">
10849 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
10852 \begin_layout Plain Layout
10858 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
10861 \begin_layout Plain Layout
10863 \begin_inset Note Note
10866 \begin_layout Plain Layout
10873 is only used as spacer.
10885 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
10888 \begin_layout Plain Layout
10894 \begin_inset space \textvisiblespace{}
10902 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
10905 \begin_layout Plain Layout
10906 \begin_inset Formula $\raisebox{4.5mm}{}\sum\sum f_{kl}\raisebox{-2.5mm}{}$
10916 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
10919 \begin_layout Plain Layout
10927 \begin_inset space \textvisiblespace{}
10935 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
10938 \begin_layout Plain Layout
10939 \begin_inset Formula $\raisebox{4.5mm}{}\sum\negmedspace\sum f_{kl}\raisebox{-2.5mm}{}$
10955 \begin_layout Standard
10957 \begin_inset VSpace medskip
10963 \begin_layout Standard
10965 Relations like for example equal signs, are always surrounded by space.
10966 To suppress this, the equal sign is placed into a TeX-brace.
10967 The following example demonstrates this:
10970 \begin_layout Standard
10972 \begin_inset Tabular
10973 <lyxtabular version="3" rows="2" columns="2">
10974 <features rotate="0" tabularvalignment="middle">
10975 <column alignment="center" valignment="top" width="0pt">
10976 <column alignment="center" valignment="top" width="0pt">
10978 <cell alignment="center" valignment="top" usebox="none">
10981 \begin_layout Plain Layout
10987 <cell alignment="center" valignment="top" usebox="none">
10990 \begin_layout Plain Layout
10991 \begin_inset Formula $A=B$
11001 <cell alignment="center" valignment="top" usebox="none">
11004 \begin_layout Plain Layout
11005 \begin_inset Note Note
11008 \begin_layout Plain Layout
11015 is only used as spacer.
11021 \begin_inset Formula $\raisebox{5mm}{}$
11024 equation without space
11029 <cell multicolumn="1" alignment="center" valignment="top" usebox="none">
11032 \begin_layout Plain Layout
11033 \begin_inset Formula $A{=}B$
11049 \begin_layout Standard
11051 The command for the last formula is:
11056 \begin_inset Formula $\to$
11062 \begin_layout Standard
11063 \begin_inset VSpace bigskip
11069 \begin_layout Standard
11070 Spaces are needed for physical units, because the space between the value
11071 and the unit is the smallest one and not a normal space.
11072 For units in text, the smallest space is inserted via the menu
11074 Insert\SpecialChar \menuseparator
11075 Formatting\SpecialChar \menuseparator
11077 \begin_inset space ~
11085 arg "space-insert thin"
11091 \begin_layout Standard
11092 An example to visualize the difference:
11095 \begin_layout Standard
11096 \begin_inset Tabular
11097 <lyxtabular version="3" rows="2" columns="2">
11098 <features rotate="0" tabularvalignment="middle">
11099 <column alignment="left" valignment="top">
11100 <column alignment="left" valignment="top">
11102 <cell alignment="center" valignment="top" usebox="none">
11105 \begin_layout Plain Layout
11107 \begin_inset Formula $\cdot$
11115 <cell alignment="center" valignment="top" usebox="none">
11118 \begin_layout Plain Layout
11119 space between value and unit
11126 <cell alignment="center" valignment="top" usebox="none">
11129 \begin_layout Plain Layout
11131 \begin_inset space \thinspace{}
11135 \begin_inset Formula $\cdot$
11143 <cell alignment="center" valignment="top" usebox="none">
11146 \begin_layout Plain Layout
11147 smallest space between value and unit
11160 \begin_layout Subsection
11165 \begin_layout Plain Layout
11178 \begin_layout Plain Layout
11179 for vertical space in formulas see
11180 \begin_inset CommandInset ref
11182 reference "sub:Line-Separation"
11195 \begin_layout Plain Layout
11203 \begin_inset Note Note
11206 \begin_layout Plain Layout
11209 texorpdfstring is used to avoid that the footnote appears in the PDF-bookmark.
11212 \begin_layout Plain Layout
11215 texorpdfstring is in section
11216 \begin_inset CommandInset ref
11218 reference "sub:Formulas-in-Section"
11228 \begin_inset CommandInset label
11230 name "sub:Variable-Space"
11235 \begin_inset Index idx
11238 \begin_layout Plain Layout
11239 Space ! horizontal ! variable
11247 \begin_layout Standard
11248 Space with a defined length can be inserted with the command
11255 \begin_inset Index idx
11258 \begin_layout Plain Layout
11268 \begin_inset Quotes eld
11274 \begin_inset space \textvisiblespace{}
11280 \begin_inset Quotes erd
11284 The length can be specified by left-clicking on the
11285 \begin_inset Quotes eld
11291 \begin_inset space \textvisiblespace{}
11297 \begin_inset Quotes erd
11301 The length may also be negative.
11302 When a space would be the first character in a line it would be omitted.
11303 To force its output use the command
11315 or left-click on the
11316 \begin_inset Quotes eld
11322 \begin_inset space \textvisiblespace{}
11328 \begin_inset Quotes erd
11331 and check the option
11336 \begin_inset Newline newline
11339 To insert as much space as is available, the command
11346 \begin_inset Index idx
11349 \begin_layout Plain Layout
11360 \begin_layout Standard
11361 \begin_inset VSpace -1mm
11367 \begin_layout Standard
11369 \begin_inset Tabular
11370 <lyxtabular version="3" rows="4" columns="2">
11371 <features rotate="0" tabularvalignment="middle">
11372 <column alignment="center" valignment="top">
11373 <column alignment="center" valignment="top">
11375 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
11378 \begin_layout Plain Layout
11386 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
11389 \begin_layout Plain Layout
11397 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
11400 \begin_layout Plain Layout
11404 \begin_inset space \textvisiblespace{}
11410 \begin_inset space \thinspace{}
11418 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
11421 \begin_layout Plain Layout
11422 \begin_inset Formula $A=B\hspace{3cm}A\not=C$
11432 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
11435 \begin_layout Plain Layout
11439 \begin_inset space \textvisiblespace{}
11445 \begin_inset space \thinspace{}
11453 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
11456 \begin_layout Plain Layout
11457 \begin_inset Formula $A\hspace{-1mm}A\not=A$
11467 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
11470 \begin_layout Plain Layout
11474 \begin_inset space \textvisiblespace{}
11482 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
11485 \begin_layout Plain Layout
11486 \begin_inset Formula $A=A\hfill B=B$
11502 \begin_layout Standard
11503 In the last example the available space is given by the longest column entry
11505 In an inline formula the space depends on the length of the line in which
11513 Thus, when the line uses the full width, no space will be created.
11520 only has an effect on displayed formulas when the formula style
11525 (Formula styles are explained in
11526 \begin_inset CommandInset ref
11528 reference "sec:Formula-Styles"
11535 \begin_layout Standard
11542 , there are the commands
11554 that fill the space with a pattern, see
11555 \begin_inset CommandInset ref
11557 reference "sub:Ellipses"
11564 \begin_layout Standard
11565 For text, variable space can be inserted via the menu
11567 Insert\SpecialChar \menuseparator
11568 Formatting\SpecialChar \menuseparator
11570 \begin_inset space ~
11578 \begin_layout Standard
11579 This is a line with
11580 \begin_inset space \hspace{}
11585 \begin_inset space \thinspace{}
11591 \begin_layout Standard
11592 This is a line with
11593 \begin_inset space \hfill{}
11599 \begin_layout Subsection
11600 Space besides inline Formulas
11601 \begin_inset Index idx
11604 \begin_layout Plain Layout
11605 Space ! besides inline formulas
11613 \begin_layout Standard
11614 The space that surrounds inline formulas can be adjusted with the length
11622 \begin_inset Index idx
11625 \begin_layout Plain Layout
11634 The value of a length is set with the command
11641 \begin_inset Index idx
11644 \begin_layout Plain Layout
11652 which has the following scheme:
11655 \begin_layout Standard
11660 setlength{length name}{value}
11663 \begin_layout Standard
11671 \begin_inset space \thinspace{}
11677 \begin_layout Standard
11687 \begin_layout Standard
11688 is inserted in TeX-mode.
11690 \begin_inset space \thinspace{}
11693 mm space will now be set around all inline formulas:
11697 \begin_layout Plain Layout
11711 \begin_layout Standard
11712 This is a line with an inline formula
11713 \begin_inset Formula $A=B$
11717 \begin_inset space \thinspace{}
11720 mm surrounding space.
11724 \begin_layout Plain Layout
11738 \begin_layout Standard
11739 To return to the predefined value,
11745 is set to the value 0
11746 \begin_inset space \thinspace{}
11752 \begin_layout Section
11754 \begin_inset Index idx
11757 \begin_layout Plain Layout
11764 \begin_inset Index idx
11767 \begin_layout Plain Layout
11772 \begin_layout Plain Layout
11783 \begin_layout Plain Layout
11798 \begin_layout Standard
11799 Boxes for text are described in chapter
11806 \begin_inset space ~
11814 \begin_layout Subsection
11816 \begin_inset CommandInset label
11818 name "sub:Boxes-with-Frame"
11823 \begin_inset Index idx
11826 \begin_layout Plain Layout
11835 \begin_layout Standard
11836 It is possible to frame a formula or part of one with the commands
11843 \begin_inset Index idx
11846 \begin_layout Plain Layout
11861 \begin_inset Index idx
11864 \begin_layout Plain Layout
11875 \begin_layout Standard
11876 When one of these commands is inserted in a formula, a blue box appears
11877 within a frame to enter formula parts.
11884 an additional formula has to be created by
11888 within this box, because the box content will otherwise be treated as mathemati
11896 is used, a new formula is automatically created inside the frame.
11899 \begin_layout Standard
11906 is not suitable to frame displayed formulas because the formula will always
11907 be set in the size of the text.
11914 is in contrary not suitable to frame inline formulas, because the formula
11915 will always be set in the size of a displayed formula.
11918 \begin_layout Standard
11932 \begin_inset Index idx
11935 \begin_layout Plain Layout
11943 where additionally the frame width and the alignment can be specified.
11950 is used in the following scheme:
11953 \begin_layout Standard
11958 framebox[frame width][position]{box content}
11961 \begin_layout Standard
11962 The position can either be
11979 right aligns the formula in the box.
11980 When no position is given, the formula will be centered.
11981 \begin_inset Newline newline
11984 If no width is given, also no position can be given.
11985 In this case the frame width is adjusted to the box content like for
11994 \begin_layout Standard
12001 is inserted, a box appears containing three blue boxes.
12002 The first two boxes are surrounded by brackets and denote the two optional
12004 The third box is for formula parts like for
12013 \begin_layout Standard
12014 \begin_inset Newpage newpage
12020 \begin_layout Standard
12022 \begin_inset Tabular
12023 <lyxtabular version="3" rows="5" columns="2">
12024 <features rotate="0" tabularvalignment="middle">
12025 <column alignment="center" valignment="top">
12026 <column alignment="center" valignment="top">
12028 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
12031 \begin_layout Plain Layout
12037 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
12040 \begin_layout Plain Layout
12042 \begin_inset Note Note
12045 \begin_layout Plain Layout
12052 is only used as spacer.
12064 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
12067 \begin_layout Plain Layout
12071 \begin_inset space \textvisiblespace{}
12081 \begin_inset space \textvisiblespace{}
12089 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
12092 \begin_layout Plain Layout
12093 \begin_inset Formula $\raisebox{6mm}{}\fbox{\ensuremath{\int A=B}}\raisebox{-4mm}{}$
12103 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
12106 \begin_layout Plain Layout
12110 \begin_inset space \textvisiblespace{}
12116 \begin_inset space \textvisiblespace{}
12124 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
12127 \begin_layout Plain Layout
12128 \begin_inset Formula $\raisebox{8.5mm}{}\boxed{\int A=B}\raisebox{-6.5mm}{}$
12138 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
12141 \begin_layout Plain Layout
12145 \begin_inset space \textvisiblespace{}
12153 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
12156 \begin_layout Plain Layout
12157 \begin_inset Formula $\raisebox{6mm}{}A+\fbox{B}\raisebox{-3mm}{}$
12167 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
12170 \begin_layout Plain Layout
12174 \begin_inset space \textvisiblespace{}
12178 \begin_inset Formula $\to$
12182 \begin_inset Formula $\to$
12192 \begin_inset space \textvisiblespace{}
12196 \begin_inset Formula $\downarrow$
12204 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
12207 \begin_layout Plain Layout
12208 \begin_inset Formula $\raisebox{6mm}{}$
12212 \begin_inset Formula $\framebox[20mm][]{\ensuremath{\frac{A}{B}}}$
12216 \begin_inset Formula $\raisebox{-4mm}{}$
12232 \begin_layout Standard
12233 The frame thickness can also be adjusted.
12234 To do this the following commands have to be inserted in TeX-mode before
12238 \begin_layout Standard
12248 \begin_inset Quotes eld
12252 \begin_inset Quotes erd
12266 \begin_inset Quotes eld
12270 \begin_inset Quotes erd
12276 \begin_layout Standard
12277 \begin_inset Quotes eld
12281 \begin_inset Quotes erd
12284 specifies the minimal distance between the frame and the first character
12286 An example for this is the following framed formula:
12290 \begin_layout Plain Layout
12302 \begin_inset Formula
12309 Before this formula the commands
12312 \begin_layout Standard
12334 \begin_layout Standard
12335 were inserted in TeX-mode.
12336 The given values are used for all following boxes.
12339 \begin_layout Standard
12340 To return to the standard frame size, the command
12343 \begin_layout Standard
12368 \begin_layout Plain Layout
12382 \begin_layout Standard
12383 is inserted in TeX-mode before the next formula.
12386 \begin_layout Subsection
12387 Boxes without Frame
12388 \begin_inset CommandInset label
12390 name "sub:Boxes-without-Frame"
12395 \begin_inset Index idx
12398 \begin_layout Plain Layout
12399 Boxes ! without frame
12407 \begin_layout Standard
12408 For boxes without a frame there are the following box commands:
12415 \begin_inset Index idx
12418 \begin_layout Plain Layout
12433 \begin_inset Index idx
12436 \begin_layout Plain Layout
12451 \begin_inset Index idx
12454 \begin_layout Plain Layout
12465 \begin_layout Standard
12472 a box can be super- or subscripted.
12473 But in contrary to normal super- and subscripting, the characters in the
12474 box keep their font size.
12481 is used in the following scheme:
12484 \begin_layout Standard
12489 raisebox{height}{box content}
12492 \begin_layout Standard
12493 When the box should contain a formula, an extra formula is needed like for
12504 \begin_inset Note Greyedout
12507 \begin_layout Plain Layout
12518 this extra formula is created by pressing
12522 twice instead of once because LyX doesn't yet support
12536 \begin_layout Standard
12538 \begin_inset Tabular
12539 <lyxtabular version="3" rows="4" columns="2">
12540 <features rotate="0" tabularvalignment="middle">
12541 <column alignment="center" valignment="top">
12542 <column alignment="center" valignment="top">
12544 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
12547 \begin_layout Plain Layout
12553 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
12556 \begin_layout Plain Layout
12564 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
12567 \begin_layout Plain Layout
12571 \begin_inset Formula $\to$
12577 \begin_inset Formula $\to$
12585 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
12588 \begin_layout Plain Layout
12589 \begin_inset Formula $H\raisebox{2mm}{al}lo$
12599 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
12602 \begin_layout Plain Layout
12606 \begin_inset Formula $\to$
12612 \begin_inset Formula $\to$
12620 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
12623 \begin_layout Plain Layout
12624 \begin_inset Formula $H\raisebox{-2mm}{al}lo$
12634 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
12637 \begin_layout Plain Layout
12641 \begin_inset Formula $\to$
12657 \begin_inset space \textvisiblespace{}
12665 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
12668 \begin_layout Plain Layout
12669 \begin_inset Formula $A=\raisebox{-2mm}{\mbox{\ensuremath{\sqrt{B}}}}$
12685 \begin_layout Standard
12710 , with the difference that there is no frame.
12713 \begin_layout Subsection
12715 \begin_inset CommandInset label
12717 name "sub:Colored-Boxes"
12722 \begin_inset Index idx
12725 \begin_layout Plain Layout
12734 \begin_layout Standard
12735 To be able to use all commands explained in this section, the LaTeX-package
12744 \begin_layout Plain Layout
12749 is part of every LaTeX standard installation.
12755 \begin_inset Index idx
12758 \begin_layout Plain Layout
12764 has to be loaded in the LaTeX-preamble with the line
12768 \begin_layout Plain Layout
12769 When text is colored somewhere in the document with a predefined color,
12770 LyX loads the LaTeX-package
12775 Thus it is possible that the package is loaded twice, but this does not
12782 \begin_inset Note Note
12785 \begin_layout Plain Layout
12786 To avoid that the package is loaded twice, a macro was inserted to the LaTeX-pre
12795 \begin_layout Standard
12803 \begin_layout Standard
12804 \begin_inset VSpace medskip
12807 To color boxes, the command
12814 \begin_inset Index idx
12817 \begin_layout Plain Layout
12825 is used in the following scheme:
12828 \begin_layout Standard
12833 colorbox{color}{box content}
12836 \begin_layout Standard
12837 The box content can also be a box and a
12843 can also be part of another box (see the 2nd and 3rd example).
12844 When the box should contain a formula, an extra formula has to be created,
12845 the same way as for
12855 \begin_layout Plain Layout
12856 This also applies for the command
12870 \begin_layout Standard
12871 One of the following predefined colors can be chosen:
12874 \begin_layout Standard
12908 \begin_layout Standard
12910 \begin_inset Tabular
12911 <lyxtabular version="3" rows="4" columns="2">
12912 <features rotate="0" tabularvalignment="middle">
12913 <column alignment="center" valignment="top">
12914 <column alignment="center" valignment="top">
12916 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
12919 \begin_layout Plain Layout
12925 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
12928 \begin_layout Plain Layout
12930 \begin_inset Note Note
12933 \begin_layout Plain Layout
12940 is only used as spacer.
12952 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
12955 \begin_layout Plain Layout
12959 \begin_inset Formula $\to$
12969 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
12972 \begin_layout Plain Layout
12973 \begin_inset Formula $\raisebox{6mm}{}\colorbox{yellow}{A=B}\raisebox{-3mm}{}$
12983 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
12986 \begin_layout Plain Layout
12990 \begin_inset Formula $\to$
12998 \begin_inset space \textvisiblespace{}
13006 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
13009 \begin_layout Plain Layout
13010 \begin_inset Formula $\raisebox{6mm}{}\colorbox{green}{\fbox{A=B}}\raisebox{-3mm}{}$
13020 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
13023 \begin_layout Plain Layout
13027 \begin_inset space \textvisiblespace{}
13033 \begin_inset Formula $\to$
13049 \begin_inset space \textvisiblespace{}
13057 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
13060 \begin_layout Plain Layout
13061 \begin_inset Formula $\raisebox{7mm}{}\fbox{\colorbox{green}{\mbox{\ensuremath{\int C=D}}}}\raisebox{-5mm}{}$
13077 \begin_layout Standard
13084 only colors the box but not the characters in the box.
13085 To color all characters, the whole formula is highlighted and the desired
13086 color is chosen in the
13089 \begin_inset space ~
13095 The dialog can be called with the toolbar button
13096 \begin_inset Graphics
13097 filename ../images/dialog-show_character.png
13104 Edit\SpecialChar \menuseparator
13106 \begin_inset space ~
13109 Style\SpecialChar \menuseparator
13113 The formula number then has the same color as the formula.
13114 When the formula number should get another color than the formula characters,
13115 the color must be changed within the formula.
13118 \begin_layout Standard
13122 \begin_layout Standard
13125 \begin_inset Formula
13127 \int A=B\label{eq:red}
13135 \begin_inset Formula
13137 \textcolor{red}{\int A=B}\label{eq:redgreen}
13145 \begin_layout Standard
13147 \begin_inset CommandInset ref
13153 is completely colored red.
13154 \begin_inset Newline newline
13158 \begin_inset CommandInset ref
13160 reference "eq:redgreen"
13164 was first completely colored green to set the color for the formula number.
13165 Subsequently the formula characters were colored red.
13168 \begin_layout Standard
13169 \begin_inset VSpace bigskip
13172 To color the frame different than the rest of the box, the command
13179 \begin_inset Index idx
13182 \begin_layout Plain Layout
13190 is used in the following scheme:
13193 \begin_layout Standard
13198 fcolorbox{frame color}{color}{box content}
13201 \begin_layout Standard
13208 is an extension of the command
13215 The frame width is set, like for
13238 \begin_layout Plain Layout
13250 \begin_inset Formula
13252 \fcolorbox{cyan}{magenta}{A=B}
13261 \begin_layout Plain Layout
13275 \begin_layout Standard
13276 This formula was created with the command
13277 \begin_inset Newline newline
13285 \begin_inset Formula $\to$
13291 \begin_inset Formula $\to$
13301 \begin_layout Standard
13302 \begin_inset VSpace bigskip
13305 To use other colors than the predefined ones, they have to be defined first.
13308 \begin_layout Standard
13309 One can for example define the color
13310 \begin_inset Quotes eld
13318 \begin_inset Quotes erd
13321 with the LaTeX-preamble line:
13324 \begin_layout Standard
13329 definecolor{darkgreen}{cmyk}{0.5,
13344 \begin_inset Index idx
13347 \begin_layout Plain Layout
13358 \begin_layout Standard
13363 is the color space that denotes the colors
13380 The four comma separated numbers are the portion factor for the corresponding
13381 colors of the color space.
13382 The factors can be in the range of 0
13383 \begin_inset space \thinspace{}
13387 \begin_inset space \thinspace{}
13395 also the color space
13399 can be used for definitions.
13416 , so that there are in this case three portion factors for the corresponding
13418 Furthermore there is the color space
13422 with one portion factor for the gray value.
13425 \begin_layout Standard
13426 As example a framed box with the new defined color
13430 where the characters have been colored
13435 \begin_inset Formula
13437 \colorbox{darkgreen}{\color{yellow}\boxed{\int A\,\mathrm{d}x=\frac{\sqrt[5]{B}}{\ln\left(\frac{1}{3}\right)}}}
13445 \begin_layout Standard
13446 Self-defined colors can also be used for text with the help of the command
13454 \begin_inset Index idx
13457 \begin_layout Plain Layout
13466 \begin_layout Standard
13470 \begin_layout Plain Layout
13474 textcolor{darkgreen}{
13480 \begin_inset Quotes eld
13484 \begin_inset Quotes erd
13491 \begin_layout Plain Layout
13501 \begin_layout Standard
13509 \begin_inset Index idx
13512 \begin_layout Plain Layout
13520 is used in the scheme
13524 textcolor{color}{characters to color}
13529 \begin_layout Subsection
13531 \begin_inset CommandInset label
13533 name "sub:Paragraph-Boxes"
13538 \begin_inset Index idx
13541 \begin_layout Plain Layout
13542 Boxes ! as paragraph
13550 \begin_layout Standard
13551 A box that can contain several lines and paragraphs, a so-called paragraph
13552 box (parbox), can be created with the menu
13554 Insert\SpecialChar \menuseparator
13557 or the toolbar button
13558 \begin_inset Graphics
13559 filename ../images/box-insert.png
13567 \begin_layout Standard
13568 The following example shows a framed parbox in a line:
13571 \begin_layout Standard
13572 \begin_inset VSpace medskip
13576 \begin_inset Box Boxed
13586 height_special "totalheight"
13589 \begin_layout Plain Layout
13590 This is a paragraph box.
13592 \begin_inset space \thinspace{}
13595 cm long and can also contain formulas:
13596 \begin_inset Formula $\int A\,\mathrm{d}s=C$
13607 \begin_layout Standard
13608 \begin_inset VSpace medskip
13614 \begin_layout Standard
13615 Such a box is created by right-clicking on the gray box inset.
13616 A dialog pops up showing the box properties.
13630 \begin_inset space \thinspace{}
13635 Vertical Box Alignment
13640 \begin_layout Standard
13641 \begin_inset VSpace medskip
13644 In LaTeX a parbox is created with the command
13651 \begin_inset Index idx
13654 \begin_layout Plain Layout
13662 which has the following scheme:
13665 \begin_layout Standard
13670 parbox[position]{width}{box content}
13673 \begin_layout Standard
13688 \begin_inset Quotes eld
13692 \begin_inset Quotes erd
13695 means that the box is aligned within the surrounding text with its last
13702 \begin_inset Quotes eld
13706 \begin_inset Quotes erd
13709 this is done with the first line.
13710 When no position is given, the box will be vertically centered, see section
13718 \begin_inset space ~
13723 manual for examples.
13726 \begin_layout Standard
13727 \begin_inset VSpace bigskip
13730 To frame formulas completely, including the formula number, the formula
13731 must be set into a parbox.
13732 To do this, the command
13746 is inserted in TeX-mode before the formula.
13754 \begin_inset Index idx
13757 \begin_layout Plain Layout
13765 is hereby the line width set for the document.
13766 Because the frame is outside the parbox, 2
13767 \begin_inset space \thinspace{}
13770 times the frame separation and the frame thickness must be subtracted from
13772 As this is not automatically done by LyX due to a bug
13776 \begin_layout Plain Layout
13777 \begin_inset CommandInset href
13779 name "LyX-bug #4483"
13780 target "http://www.lyx.org/trac/ticket/4483"
13789 , TeX-mode has to be used.
13790 To be able to multiply and subtract in arguments, the LaTeX-package
13798 \begin_layout Plain Layout
13803 is part of every LaTeX standard installation.
13809 \begin_inset Index idx
13812 \begin_layout Plain Layout
13818 must be loaded in the LaTeX-preamble with the line
13821 \begin_layout Standard
13829 \begin_layout Standard
13830 Behind the formula both boxes are closed by entering
13835 Here is an example:
13839 \begin_layout Plain Layout
13853 \begin_layout Standard
13857 \begin_layout Plain Layout
13875 \begin_inset Formula
13877 \int A\,\mathrm{d}x=\frac{\sqrt[5]{B}}{\ln\left(\frac{1}{3}\right)}
13886 \begin_layout Plain Layout
13897 \begin_layout Plain Layout
13911 \begin_layout Standard
13912 \begin_inset VSpace medskip
13915 As a parbox is used as the argument of
13921 , there is in this case no difference between
13936 \begin_layout Standard
13937 \begin_inset VSpace bigskip
13940 Paragraph boxes are very useful to comment formulas directly.
13947 is used in combination with the command
13961 \begin_inset CommandInset ref
13963 reference "sub:User-defined-Numbering"
13970 \begin_layout Standard
13971 An example of a formula commented with
13980 \begin_layout Standard
13984 \begin_layout Plain Layout
13997 This is a description.
13998 It is distinctly separated from the formula and multiline.
14002 \begin_layout Plain Layout
14014 \begin_layout Standard
14015 Such a formula must be inserted completely in TeX-mode because LyX does
14016 not yet support the command
14023 The formula is created with the following command sequence:
14026 \begin_layout Standard
14039 is inserted in TeX-mode.
14043 \begin_layout Plain Layout
14044 When the formula style
14056 can also be replaced by
14063 (formula styles see
14064 \begin_inset CommandInset ref
14066 reference "sec:Formula-Styles"
14075 Then the description follows as normal text and finally
14081 is inserted in TeX-mode.
14094 hereby create a displayed formula.
14097 \begin_layout Standard
14104 can be seen in this example that was
14105 \begin_inset Quotes eld
14109 \begin_inset Quotes erd
14112 using the mathematical textmode:
14113 \begin_inset Formula
14115 5x-7b=3b\textrm{This is a description. It is not separated from the formula ...}
14123 \begin_layout Section
14125 \begin_inset Index idx
14128 \begin_layout Plain Layout
14137 \begin_layout Subsection
14139 \begin_inset CommandInset label
14141 name "sub:Big-Operators"
14146 \begin_inset Index idx
14149 \begin_layout Plain Layout
14156 \begin_inset Index idx
14159 \begin_layout Plain Layout
14166 \begin_inset Index idx
14169 \begin_layout Plain Layout
14178 \begin_layout Standard
14179 To be able to use all integral operators listed here, the option
14181 Use esint package automatically
14183 must be set in the document settings under
14186 \begin_inset space ~
14194 \begin_layout Standard
14195 \begin_inset space \hfill{}
14199 \begin_inset Tabular
14200 <lyxtabular version="3" rows="11" columns="2">
14201 <features rotate="0" tabularvalignment="middle">
14202 <column alignment="center" valignment="top" width="0pt">
14203 <column alignment="center" valignment="top" width="0pt">
14205 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
14208 \begin_layout Plain Layout
14214 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
14217 \begin_layout Plain Layout
14225 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
14228 \begin_layout Plain Layout
14232 \begin_inset Index idx
14235 \begin_layout Plain Layout
14248 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
14251 \begin_layout Plain Layout
14252 \begin_inset Formula $\int$
14262 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
14265 \begin_layout Plain Layout
14273 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
14276 \begin_layout Plain Layout
14277 \begin_inset Formula $\oint$
14287 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
14290 \begin_layout Plain Layout
14298 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
14301 \begin_layout Plain Layout
14302 \begin_inset Formula $\ointctrclockwise$
14312 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
14315 \begin_layout Plain Layout
14323 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
14326 \begin_layout Plain Layout
14327 \begin_inset Formula $\ointclockwise$
14337 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
14340 \begin_layout Plain Layout
14348 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
14351 \begin_layout Plain Layout
14352 \begin_inset Formula $\sqint$
14362 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
14365 \begin_layout Plain Layout
14373 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
14376 \begin_layout Plain Layout
14378 \begin_inset Formula $\fint$
14388 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
14391 \begin_layout Plain Layout
14399 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
14402 \begin_layout Plain Layout
14404 \begin_inset Formula $\landupint$
14414 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
14417 \begin_layout Plain Layout
14425 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
14428 \begin_layout Plain Layout
14430 \begin_inset Formula $\landdownint$
14440 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
14443 \begin_layout Plain Layout
14451 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
14454 \begin_layout Plain Layout
14455 \begin_inset Formula $\bigcap$
14465 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
14468 \begin_layout Plain Layout
14476 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
14479 \begin_layout Plain Layout
14480 \begin_inset Formula $\bigcup$
14494 \begin_inset space \hfill{}
14498 \begin_inset Tabular
14499 <lyxtabular version="3" rows="11" columns="2">
14500 <features rotate="0" tabularvalignment="middle">
14501 <column alignment="center" valignment="top" width="0pt">
14502 <column alignment="center" valignment="top" width="0pt">
14504 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
14507 \begin_layout Plain Layout
14513 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
14516 \begin_layout Plain Layout
14524 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
14527 \begin_layout Plain Layout
14531 \begin_inset Index idx
14534 \begin_layout Plain Layout
14547 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
14550 \begin_layout Plain Layout
14551 \begin_inset Formula $\sum$
14561 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
14564 \begin_layout Plain Layout
14568 \begin_inset Index idx
14571 \begin_layout Plain Layout
14578 \begin_layout Plain Layout
14597 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
14600 \begin_layout Plain Layout
14601 \begin_inset Formula $\prod$
14611 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
14614 \begin_layout Plain Layout
14622 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
14625 \begin_layout Plain Layout
14626 \begin_inset Formula $\coprod$
14636 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
14639 \begin_layout Plain Layout
14647 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
14650 \begin_layout Plain Layout
14651 \begin_inset Formula $\bigodot$
14661 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
14664 \begin_layout Plain Layout
14672 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
14675 \begin_layout Plain Layout
14676 \begin_inset Formula $\bigotimes$
14686 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
14689 \begin_layout Plain Layout
14697 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
14700 \begin_layout Plain Layout
14701 \begin_inset Formula $\bigoplus$
14711 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
14714 \begin_layout Plain Layout
14722 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
14725 \begin_layout Plain Layout
14726 \begin_inset Formula $\bigwedge$
14736 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
14739 \begin_layout Plain Layout
14747 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
14750 \begin_layout Plain Layout
14751 \begin_inset Formula $\bigvee$
14761 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
14764 \begin_layout Plain Layout
14772 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
14775 \begin_layout Plain Layout
14776 \begin_inset Formula $\bigsqcup$
14786 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
14789 \begin_layout Plain Layout
14797 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
14800 \begin_layout Plain Layout
14801 \begin_inset Formula $\biguplus$
14815 \begin_inset space \hfill{}
14821 \begin_layout Standard
14822 All big operators can also be inserted via the math toolbar button
14823 \begin_inset Graphics
14824 filename ../images/math/intop.png
14832 \begin_layout Standard
14833 The operators are called big because they are bigger than the sometimes
14834 equal looking binary operators.
14835 All big operators can have limits as described in the next subsection.
14838 \begin_layout Standard
14839 For all integral operators there is a second version available, ending in
14857 These operators are different from
14864 \begin_inset space \space{}
14867 in the style the operator limits are displayed, see
14868 \begin_inset CommandInset ref
14870 reference "sub:Operator-Limits"
14878 \begin_layout Subsubsection*
14879 Advice for Integrals
14882 \begin_layout Standard
14887 in an integral is an operator, that therefore has to be set upright.
14888 This is done by highlighting the
14892 and using the keyboard shortcut
14902 \begin_layout Plain Layout
14908 \begin_inset CommandInset ref
14910 reference "sub:Font-Styles"
14920 Finally the smallest space is inserted before the
14924 , as this is usual for operators.
14928 \begin_layout Standard
14930 \begin_inset Formula $\int A(x)dx$
14934 \begin_inset Newline newline
14938 \begin_inset Phantom HPhantom
14941 \begin_layout Plain Layout
14948 \begin_inset Formula $\int A(x)\,\mathrm{d}x$
14954 \begin_layout Standard
14955 For multiple integrals there are the following commands:
14956 \begin_inset VSpace medskip
14962 \begin_layout Standard
14963 \begin_inset space \hfill{}
14967 \begin_inset Tabular
14968 <lyxtabular version="3" rows="4" columns="2">
14969 <features rotate="0" tabularvalignment="middle">
14970 <column alignment="center" valignment="top">
14971 <column alignment="center" valignment="top">
14973 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
14976 \begin_layout Plain Layout
14982 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
14985 \begin_layout Plain Layout
14987 \begin_inset Note Note
14990 \begin_layout Plain Layout
14997 is only used as spacer.
15009 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
15012 \begin_layout Plain Layout
15020 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
15023 \begin_layout Plain Layout
15024 \begin_inset Formula $\raisebox{4.5mm}{}\iint\raisebox{-2.5mm}{}$
15034 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
15037 \begin_layout Plain Layout
15045 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
15048 \begin_layout Plain Layout
15049 \begin_inset Formula $\raisebox{4.5mm}{}\oiint\raisebox{-2.5mm}{}$
15059 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
15062 \begin_layout Plain Layout
15070 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
15073 \begin_layout Plain Layout
15074 \begin_inset Formula $\raisebox{4.5mm}{}\sqiint\raisebox{-2.5mm}{}$
15088 \begin_inset space \hfill{}
15092 \begin_inset Tabular
15093 <lyxtabular version="3" rows="4" columns="2">
15094 <features rotate="0" tabularvalignment="middle">
15095 <column alignment="center" valignment="top">
15096 <column alignment="center" valignment="top">
15098 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
15101 \begin_layout Plain Layout
15107 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
15110 \begin_layout Plain Layout
15118 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
15121 \begin_layout Plain Layout
15129 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
15132 \begin_layout Plain Layout
15133 \begin_inset Formula $\raisebox{4.5mm}{}\iiint\raisebox{-2.5mm}{}$
15143 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
15146 \begin_layout Plain Layout
15154 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
15157 \begin_layout Plain Layout
15158 \begin_inset Formula $\raisebox{4.5mm}{}\iiiint\raisebox{-2.5mm}{}$
15168 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
15171 \begin_layout Plain Layout
15179 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
15182 \begin_layout Plain Layout
15183 \begin_inset Formula $\raisebox{4.5mm}{}\dotsint\raisebox{-2.5mm}{}$
15197 \begin_inset space \hfill{}
15203 \begin_layout Standard
15204 \begin_inset Newpage newpage
15210 \begin_layout Subsection
15212 \begin_inset CommandInset label
15214 name "sub:Operator-Limits"
15219 \begin_inset Index idx
15222 \begin_layout Plain Layout
15231 \begin_layout Standard
15232 Limits are created by super- and subscripts:
15235 \begin_layout Standard
15237 \begin_inset Tabular
15238 <lyxtabular version="3" rows="2" columns="2">
15239 <features rotate="0" tabularvalignment="middle">
15240 <column alignment="center" valignment="top" width="0pt">
15241 <column alignment="center" valignment="top" width="0pt">
15243 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
15246 \begin_layout Plain Layout
15252 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
15255 \begin_layout Plain Layout
15257 \begin_inset Note Note
15260 \begin_layout Plain Layout
15267 is only used as spacer.
15279 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
15282 \begin_layout Plain Layout
15288 \begin_inset space \textvisiblespace{}
15292 \begin_inset Formula $\to$
15296 \begin_inset Formula $\to$
15304 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
15307 \begin_layout Plain Layout
15308 \begin_inset Formula $\raisebox{5mm}{}\prod_{0}^{\infty}A(x)\raisebox{-2.5mm}{}$
15324 \begin_layout Standard
15325 Limits of inline formulas are set right beside the operator.
15326 Limits in displayed formulas are set above or below the operator, except
15327 for integral limits.
15330 \begin_layout Standard
15331 To force that the limits are set beside the operator, the cursor is set
15332 directly behind the operator and the limits type is changed with the menu
15335 Edit\SpecialChar \menuseparator
15336 Math\SpecialChar \menuseparator
15355 \begin_layout Standard
15356 The default limits type is this:
15357 \begin_inset Formula
15359 \sum_{x=0}^{\infty}\frac{1}{x^{2}}
15364 This is how it looks when the limits type was changed to
15371 \begin_inset Formula
15373 \sum\nolimits _{x=0}^{\infty}\frac{1}{x^{2}}
15378 For integrals, except those ending with
15394 etc., the limits are by default set beside the operator.
15395 But for multiple integrals the limits are often set below the operator.
15396 In the following example the limits type was therefore set to
15400 and so set below the integrals:
15401 \begin_inset Formula
15403 \iiint\limits _{V}X\,\mathrm{d}V=U\label{eq:VolInt}
15411 \begin_layout Standard
15412 \begin_inset VSpace medskip
15415 To specify conditions for limits, the commands
15422 \begin_inset Index idx
15425 \begin_layout Plain Layout
15440 \begin_inset Index idx
15443 \begin_layout Plain Layout
15452 To create for example this expression
15453 \begin_inset Formula
15455 \sum_{\begin{subarray}{c}
15459 \end{subarray}}^{n}k^{-2}\label{eq:substack}
15467 \begin_layout Standard
15468 the following has to be done:
15469 \begin_inset Newline newline
15481 \begin_inset space \textvisiblespace{}
15487 One is now in a blue box under the summation operator and insert there
15493 \begin_inset space \textvisiblespace{}
15499 The blue box is now within a purple box and now several lines can be written
15501 A new line is created by inserting a line break (
15504 arg "newline-insert newline"
15509 \begin_inset Newline newline
15514 0<k<1000 Ctrl+Return
15515 \begin_inset Newline newline
15520 is typed in, a new box appears below for the new line.
15523 \begin_layout Standard
15524 The alignment of the lines can be changed to left aligned with the
15534 Edit\SpecialChar \menuseparator
15538 To get right alignment,
15543 \begin_inset space \textvisiblespace{}
15548 is inserted at the beginning of the line.
15551 \begin_layout Standard
15564 with the difference that the lines are always centered.
15567 \begin_layout Standard
15568 \begin_inset VSpace bigskip
15572 \begin_inset CommandInset ref
15574 reference "eq:substack"
15578 there can be too much space beside an operator, because the characters
15579 following the operator are set beside the limits.
15580 To avoid this the command
15587 \begin_inset Index idx
15590 \begin_layout Plain Layout
15599 It sets the width of its content to 0
15600 \begin_inset space \thinspace{}
15604 \begin_inset Newline newline
15608 \begin_inset CommandInset ref
15610 reference "eq:substack"
15614 , one uses the command
15617 \begin_layout Standard
15627 \begin_inset space \textvisiblespace{}
15630 0<k<1000 Ctrl+Return
15633 \begin_layout Standard
15634 to create the lower limit.
15635 The summand is now directly behind the summation operator:
15636 \begin_inset Formula
15638 \sum_{\mathclap{\substack{0<k<1000\\
15650 \begin_layout Standard
15651 \begin_inset VSpace bigskip
15657 \begin_layout Standard
15658 When several consecutive operators have limits the typesetting of the limits
15659 looks often imperfect in the output, see this example:
15660 \begin_inset Formula
15662 \text{a)}\lim_{n\to\infty}\max_{p\ge n}\quad\text{b)}\lim_{n\to\infty}\max_{p^{2}\ge n}\quad\text{c)}\lim_{n\to\infty}\sup_{p^{2}\ge nK}\quad\text{d)}\limsup_{n\to\infty}\max_{p\ge n}
15667 To improve the typesetting set in the document settings under
15670 \begin_inset space ~
15680 \begin_inset Index idx
15683 \begin_layout Plain Layout
15684 Packages ! mathtools
15692 \begin_inset space ~
15698 Then insert into your formula the command
15705 \begin_inset Index idx
15708 \begin_layout Plain Layout
15716 directly before the first operator.
15717 The example will then look like this:
15718 \begin_inset Formula
15720 \text{a)}\adjustlimits\lim_{n\to\infty}\max_{p\ge n}\quad\text{b)}\adjustlimits\lim_{n\to\infty}\max_{p^{2}\ge n}\quad\text{c)}\adjustlimits\lim_{n\to\infty}\sup_{p^{2}\ge nK}\quad\text{d)}\adjustlimits\limsup_{n\to\infty}\max_{p\ge n}
15728 \begin_layout Standard
15729 \begin_inset VSpace bigskip
15732 How to use one limit for several operators is described in
15733 \begin_inset CommandInset ref
15735 reference "sub:Self-defined-Operators"
15742 \begin_layout Subsection
15743 Decoration for Operators
15744 \begin_inset Index idx
15747 \begin_layout Plain Layout
15748 Operators ! Decoration
15756 \begin_layout Standard
15764 \begin_inset Index idx
15767 \begin_layout Plain Layout
15782 \begin_inset Index idx
15785 \begin_layout Plain Layout
15793 characters can be placed above or below an operator, respectively.
15801 \begin_inset Index idx
15804 \begin_layout Plain Layout
15812 characters can be set before and behind a big operator.
15815 \begin_layout Standard
15817 \begin_inset space ~
15829 \begin_layout Itemize
15836 is used to set characters at the corners of the operator
15839 \begin_layout Itemize
15846 is used to set characters before and/or behind the operator (this variant
15847 represents LaTeX's original
15856 \begin_layout Itemize
15863 is used to set characters at the left corners and/or behind the operator
15866 \begin_layout Itemize
15873 is used to set characters at the right corners and/or before the operator
15876 \begin_layout Standard
15877 For example the command
15882 \begin_inset space \textvisiblespace{}
15888 \begin_inset space \textvisiblespace{}
15892 \begin_inset Formula $\to$
15896 \begin_inset Formula $\to$
15900 \begin_inset space \textvisiblespace{}
15910 \begin_inset Formula
15912 \sideset{}{'}\sum_{k=1}^{n}
15920 \begin_layout Standard
15921 \begin_inset Note Greyedout
15924 \begin_layout Plain Layout
15931 can only be used to decorate big operators, binary operators are not allowed.
15939 \begin_layout Standard
15952 can also be used to decorate symbols and characters.
15953 For example, the command
15958 \begin_inset space \textvisiblespace{}
15964 \begin_inset space \textvisiblespace{}
15970 \begin_inset Formula $\uparrow$
15978 \begin_inset Formula
15980 \overset{a}{\maltese}
15988 \begin_layout Subsection
15990 \begin_inset CommandInset label
15992 name "sub:Binary-Operators"
15997 \begin_inset Index idx
16000 \begin_layout Plain Layout
16009 \begin_layout Standard
16010 Binary operators are surrounded by space when there is a character before
16012 \begin_inset VSpace medskip
16018 \begin_layout Standard
16019 \begin_inset space \hfill{}
16023 \begin_inset Tabular
16024 <lyxtabular version="3" rows="13" columns="2">
16025 <features rotate="0" tabularvalignment="middle">
16026 <column alignment="center" valignment="top" width="0pt">
16027 <column alignment="center" valignment="top" width="0pt">
16029 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
16032 \begin_layout Plain Layout
16034 \begin_inset Note Note
16037 \begin_layout Plain Layout
16044 is only used as spacer.
16054 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
16057 \begin_layout Plain Layout
16065 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
16068 \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 $+$
16088 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
16091 \begin_layout Plain Layout
16097 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
16100 \begin_layout Plain Layout
16101 \begin_inset Formula $-$
16111 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
16114 \begin_layout Plain Layout
16122 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
16125 \begin_layout Plain Layout
16126 \begin_inset Formula $\pm$
16136 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
16139 \begin_layout Plain Layout
16147 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
16150 \begin_layout Plain Layout
16151 \begin_inset Formula $\mp$
16161 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
16164 \begin_layout Plain Layout
16172 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
16175 \begin_layout Plain Layout
16176 \begin_inset Formula $\cdot$
16186 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
16189 \begin_layout Plain Layout
16197 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
16200 \begin_layout Plain Layout
16201 \begin_inset Formula $\times$
16211 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
16214 \begin_layout Plain Layout
16222 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
16225 \begin_layout Plain Layout
16226 \begin_inset Formula $\div$
16236 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
16239 \begin_layout Plain Layout
16243 \begin_layout Plain Layout
16256 \begin_layout Plain Layout
16268 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
16271 \begin_layout Plain Layout
16272 \begin_inset Formula $*$
16282 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
16285 \begin_layout Plain Layout
16293 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
16296 \begin_layout Plain Layout
16297 \begin_inset Formula $\star$
16307 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
16310 \begin_layout Plain Layout
16318 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
16321 \begin_layout Plain Layout
16322 \begin_inset Formula $\circ$
16332 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
16335 \begin_layout Plain Layout
16343 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
16346 \begin_layout Plain Layout
16347 \begin_inset Formula $\diamond$
16357 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
16360 \begin_layout Plain Layout
16368 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
16371 \begin_layout Plain Layout
16372 \begin_inset Formula $\bullet$
16386 \begin_inset space \hfill{}
16390 \begin_inset Tabular
16391 <lyxtabular version="3" rows="13" columns="2">
16392 <features rotate="0" tabularvalignment="middle">
16393 <column alignment="center" valignment="top" width="0pt">
16394 <column alignment="center" valignment="top" width="0pt">
16396 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
16399 \begin_layout Plain Layout
16405 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
16408 \begin_layout Plain Layout
16416 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
16419 \begin_layout Plain Layout
16427 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
16430 \begin_layout Plain Layout
16431 \begin_inset Formula $\nabla$
16441 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
16444 \begin_layout Plain Layout
16452 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
16455 \begin_layout Plain Layout
16456 \begin_inset Formula $\bigtriangledown$
16466 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
16469 \begin_layout Plain Layout
16477 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
16480 \begin_layout Plain Layout
16481 \begin_inset Formula $\bigtriangleup$
16491 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
16494 \begin_layout Plain Layout
16502 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
16505 \begin_layout Plain Layout
16506 \begin_inset Formula $\Box$
16516 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
16519 \begin_layout Plain Layout
16527 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
16530 \begin_layout Plain Layout
16531 \begin_inset Formula $\cap$
16541 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
16544 \begin_layout Plain Layout
16552 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
16555 \begin_layout Plain Layout
16556 \begin_inset Formula $\cup$
16566 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
16569 \begin_layout Plain Layout
16577 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
16580 \begin_layout Plain Layout
16581 \begin_inset Formula $\dagger$
16591 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
16594 \begin_layout Plain Layout
16602 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
16605 \begin_layout Plain Layout
16606 \begin_inset Formula $\ddagger$
16616 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
16619 \begin_layout Plain Layout
16627 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
16630 \begin_layout Plain Layout
16631 \begin_inset Formula $\wr$
16641 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
16644 \begin_layout Plain Layout
16652 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
16655 \begin_layout Plain Layout
16656 \begin_inset Formula $\bigcirc$
16666 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
16669 \begin_layout Plain Layout
16677 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
16680 \begin_layout Plain Layout
16681 \begin_inset Formula $\wedge$
16691 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
16694 \begin_layout Plain Layout
16702 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
16705 \begin_layout Plain Layout
16706 \begin_inset Formula $\vee$
16720 \begin_inset space \hfill{}
16724 \begin_inset Tabular
16725 <lyxtabular version="3" rows="13" columns="2">
16726 <features rotate="0" tabularvalignment="middle">
16727 <column alignment="center" valignment="top" width="0pt">
16728 <column alignment="center" valignment="top" width="0pt">
16730 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
16733 \begin_layout Plain Layout
16739 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
16742 \begin_layout Plain Layout
16750 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
16753 \begin_layout Plain Layout
16761 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
16764 \begin_layout Plain Layout
16765 \begin_inset Formula $\oplus$
16775 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
16778 \begin_layout Plain Layout
16786 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
16789 \begin_layout Plain Layout
16790 \begin_inset Formula $\ominus$
16800 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
16803 \begin_layout Plain Layout
16811 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
16814 \begin_layout Plain Layout
16815 \begin_inset Formula $\otimes$
16825 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
16828 \begin_layout Plain Layout
16836 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
16839 \begin_layout Plain Layout
16840 \begin_inset Formula $\oslash$
16850 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
16853 \begin_layout Plain Layout
16861 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
16864 \begin_layout Plain Layout
16865 \begin_inset Formula $\odot$
16875 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
16878 \begin_layout Plain Layout
16886 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
16889 \begin_layout Plain Layout
16890 \begin_inset Formula $\amalg$
16900 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
16903 \begin_layout Plain Layout
16911 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
16914 \begin_layout Plain Layout
16915 \begin_inset Formula $\uplus$
16925 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
16928 \begin_layout Plain Layout
16936 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
16939 \begin_layout Plain Layout
16940 \begin_inset Formula $\setminus$
16950 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
16953 \begin_layout Plain Layout
16961 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
16964 \begin_layout Plain Layout
16965 \begin_inset Formula $\sqcap$
16975 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
16978 \begin_layout Plain Layout
16986 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
16989 \begin_layout Plain Layout
16990 \begin_inset Formula $\sqcup$
17000 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
17003 \begin_layout Plain Layout
17011 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
17014 \begin_layout Plain Layout
17015 \begin_inset Formula $\triangleleft$
17025 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
17028 \begin_layout Plain Layout
17036 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
17039 \begin_layout Plain Layout
17040 \begin_inset Formula $\triangleright$
17054 \begin_inset space \hfill{}
17060 \begin_layout Standard
17061 All binary operators can also be inserted via the math toolbar button
17062 \begin_inset Graphics
17063 filename ../images/math/pm.png
17071 \begin_layout Standard
17072 To typeset the Laplace operator also
17089 \begin_inset Formula $\nabla^{2}$
17092 ) can be used instead of
17101 \begin_layout Standard
17108 Insert\SpecialChar \menuseparator
17120 \begin_layout Subsection
17121 Self-defined Operators
17122 \begin_inset CommandInset label
17124 name "sub:Self-defined-Operators"
17129 \begin_inset Index idx
17132 \begin_layout Plain Layout
17133 Operators ! self-defined
17141 \begin_layout Standard
17142 With the help of the command
17146 DeclareMathOperator
17149 \begin_inset Index idx
17152 \begin_layout Plain Layout
17157 DeclareMathOperator
17162 custom operators can be defined in the LaTeX-preamble.
17163 Its command scheme is:
17166 \begin_layout Standard
17171 DeclareMathOperator{new command}{display}
17174 \begin_layout Standard
17175 Display can be characters or symbols that define how the operator looks
17177 To define a big operator a * is set behind the command.
17178 All self-defined big operators can have limits as described in
17179 \begin_inset CommandInset ref
17181 reference "sub:Operator-Limits"
17188 \begin_layout Standard
17189 For example the LaTeX-preamble line
17192 \begin_layout Standard
17197 DeclareMathOperator*{
17204 \begin_layout Standard
17205 defines the command
17211 , that inserts a big operator consisting of the lozenge symbol from
17212 \begin_inset CommandInset ref
17214 reference "sub:Miscellaneous-Symbols"
17219 \begin_inset Formula
17221 \Lozenge_{n=1}^{\infty}
17226 The command for this formula is:
17237 \begin_inset Formula $\to$
17243 \begin_layout Standard
17244 \begin_inset VSpace bigskip
17247 When self-defined operators are not used several times in the document,
17248 they can also be defined with the commands
17255 \begin_inset Index idx
17258 \begin_layout Plain Layout
17273 \begin_inset Index idx
17276 \begin_layout Plain Layout
17284 , which have the following scheme:
17287 \begin_layout Standard
17301 \begin_layout Standard
17308 defines big operators,
17317 \begin_layout Standard
17325 \begin_inset space \thinspace{}
17329 \begin_inset space \space{}
17332 be used to use one limit for several operators:
17335 \begin_layout Standard
17336 \begin_inset Formula
17338 \mathop{\sum\negmedspace\sum}_{i,j=1}^{N}
17346 \begin_layout Standard
17347 The command for the formula above is:
17348 \begin_inset Newline newline
17364 \begin_inset space \textvisiblespace{}
17370 \begin_inset Formula $\to$
17376 \begin_inset space \textvisiblespace{}
17384 \begin_layout Section
17386 \begin_inset Index idx
17389 \begin_layout Plain Layout
17398 \begin_layout Subsection
17400 \begin_inset CommandInset label
17402 name "sub:Font-Styles"
17407 \begin_inset Index idx
17410 \begin_layout Plain Layout
17419 \begin_layout Standard
17420 Latin letters in formulas can be set in one of the following font styles:
17421 \begin_inset VSpace -2mm
17427 \begin_layout Standard
17429 \begin_inset Tabular
17430 <lyxtabular version="3" rows="7" columns="3">
17431 <features rotate="0" tabularvalignment="middle">
17432 <column alignment="center" valignment="top">
17433 <column alignment="center" valignment="top">
17434 <column alignment="center" valignment="top">
17436 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
17439 \begin_layout Plain Layout
17445 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
17448 \begin_layout Plain Layout
17454 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
17457 \begin_layout Plain Layout
17465 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
17468 \begin_layout Plain Layout
17474 \begin_inset space \textvisiblespace{}
17484 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
17487 \begin_layout Plain Layout
17488 \begin_inset Formula $\mathbb{ABC}$
17496 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
17499 \begin_layout Plain Layout
17512 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
17515 \begin_layout Plain Layout
17521 \begin_inset space \textvisiblespace{}
17531 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
17534 \begin_layout Plain Layout
17535 \begin_inset Formula $\mathbf{AbC}$
17543 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
17546 \begin_layout Plain Layout
17559 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
17562 \begin_layout Plain Layout
17568 \begin_inset space \textvisiblespace{}
17578 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
17581 \begin_layout Plain Layout
17582 \begin_inset Formula $\boldsymbol{AbC}$
17590 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
17593 \begin_layout Plain Layout
17596 arg "font-boldsymbol"
17606 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
17609 \begin_layout Plain Layout
17615 \begin_inset space \textvisiblespace{}
17625 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
17628 \begin_layout Plain Layout
17629 \begin_inset Formula $\mathcal{ABC}$
17637 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
17640 \begin_layout Plain Layout
17653 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
17656 \begin_layout Plain Layout
17662 \begin_inset space \textvisiblespace{}
17672 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
17675 \begin_layout Plain Layout
17676 \begin_inset Formula $\mathfrak{AbC}$
17684 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
17687 \begin_layout Plain Layout
17695 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
17698 \begin_layout Plain Layout
17704 \begin_inset space \textvisiblespace{}
17714 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
17717 \begin_layout Plain Layout
17718 \begin_inset Formula $\mathscr{AbC}$
17726 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
17729 \begin_layout Plain Layout
17743 \begin_layout Standard
17745 \begin_inset Tabular
17746 <lyxtabular version="3" rows="5" columns="3">
17747 <features rotate="0" tabularvalignment="middle">
17748 <column alignment="center" valignment="top">
17749 <column alignment="center" valignment="top">
17750 <column alignment="center" valignment="top">
17752 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
17755 \begin_layout Plain Layout
17761 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
17764 \begin_layout Plain Layout
17770 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
17773 \begin_layout Plain Layout
17781 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
17784 \begin_layout Plain Layout
17790 \begin_inset space \textvisiblespace{}
17800 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
17803 \begin_layout Plain Layout
17804 \begin_inset Formula $\mathit{AbC}$
17812 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
17815 \begin_layout Plain Layout
17823 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
17826 \begin_layout Plain Layout
17832 \begin_inset space \textvisiblespace{}
17842 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
17845 \begin_layout Plain Layout
17846 \begin_inset Formula $\mathrm{AbC}$
17854 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
17857 \begin_layout Plain Layout
17870 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
17873 \begin_layout Plain Layout
17879 \begin_inset space \textvisiblespace{}
17889 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
17892 \begin_layout Plain Layout
17893 \begin_inset Formula $\mathsf{AbC}$
17901 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
17904 \begin_layout Plain Layout
17917 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
17920 \begin_layout Plain Layout
17926 \begin_inset space \textvisiblespace{}
17936 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
17939 \begin_layout Plain Layout
17940 \begin_inset Formula $\mathtt{AbC}$
17948 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
17951 \begin_layout Plain Layout
17954 arg "font-typewriter"
17970 \begin_layout Standard
17971 \begin_inset Note Greyedout
17974 \begin_layout Plain Layout
17991 can only be used for big letters.
17999 \begin_layout Standard
18000 Predefined is the style
18009 \begin_layout Standard
18010 The style commands work also for letters in mathematical constructs:
18011 \begin_inset Formula
18013 \mathfrak{A=\frac{b}{C}}
18021 \begin_layout Standard
18022 Characters in mathematical text don't appear in a math font style but in
18023 the text font style
18030 That their style can't be set correctly via the text style dialog is a
18035 \begin_layout Plain Layout
18036 \begin_inset CommandInset href
18038 name "LyX-bug #4629"
18039 target "http://www.lyx.org/trac/ticket/4629"
18051 \begin_layout Standard
18052 Instead of the style commands the dialog
18054 Edit\SpecialChar \menuseparator
18055 Math\SpecialChar \menuseparator
18058 or the toolbar button
18059 \begin_inset Graphics
18060 filename ../images/math/font.png
18068 \begin_layout Subsection
18070 \begin_inset CommandInset label
18072 name "sub:Bold-Formulas"
18077 \begin_inset Index idx
18080 \begin_layout Plain Layout
18089 \begin_layout Standard
18090 To make a complete formula bold, the command
18096 from the previous subsection cannot be used, because it doesn't work for
18097 small Greek letters.
18098 Furthermore it prints Latin letters always upright, like in the following
18102 \begin_layout Standard
18103 \begin_inset Formula
18105 \mathbf{\int_{n}^{2}f(\theta)=\Gamma}\qquad\textrm{equation with \textbackslash mathbf}
18113 \begin_layout Standard
18114 To display the formula correctly, the command
18121 \begin_inset Formula
18123 \boldsymbol{\int_{n}^{2}f(\theta)=\Gamma\qquad\textrm{equation with \textbackslash boldsymbol}}
18128 It is also possible to set the formula in a
18130 boldmath environment
18133 This environment is created by inserting the command
18140 \begin_inset Index idx
18143 \begin_layout Plain Layout
18152 To end the environment, the command
18159 \begin_inset Index idx
18162 \begin_layout Plain Layout
18170 is inserted in TeX-mode.
18174 \begin_layout Plain Layout
18184 \begin_inset Formula
18186 \int_{n}^{2}f(\theta)=\Gamma\qquad\textrm{equation in a boldmath environment}
18195 \begin_layout Plain Layout
18207 \begin_layout Subsection
18209 \begin_inset Index idx
18212 \begin_layout Plain Layout
18221 \begin_layout Standard
18222 Formulas can be colored like normal text: Highlight a formula or a formula
18228 Here is a formula in magenta:
18229 \begin_inset Formula
18231 {\color{magenta}\int A\,\mathrm{d}x=\frac{\sqrt[5]{B}}{\ln\left(\frac{1}{3}\right)}}
18239 \begin_layout Standard
18240 You can also define your own colors as described in
18241 \begin_inset CommandInset ref
18243 reference "sub:Colored-Boxes"
18248 They can be used with the TeX code command
18255 \begin_inset Index idx
18258 \begin_layout Plain Layout
18269 \begin_layout Standard
18274 textcolor{color}{characters or formula}
18277 \begin_layout Standard
18278 The following example was colored completely dark green and partly red:
18281 \begin_layout Standard
18285 \begin_layout Plain Layout
18289 textcolor{darkgreen}{
18295 \begin_inset Formula
18297 \int A\,\mathrm{d}x=\frac{{\color{red}\sqrt[5]{B}}}{\ln\left(\frac{1}{3}\right)}
18306 \begin_layout Plain Layout
18316 \begin_layout Standard
18317 Due to a bug in LyX only complete formulas can be colored with self-defined
18322 \begin_layout Plain Layout
18323 \begin_inset CommandInset href
18325 name "LyX-bug #5269"
18326 target "http://www.lyx.org/trac/ticket/5269"
18338 \begin_layout Subsection
18340 \begin_inset CommandInset label
18342 name "sub:Font-Sizes"
18347 \begin_inset Index idx
18350 \begin_layout Plain Layout
18359 \begin_layout Standard
18360 For characters in formulas there are, analog to characters in text, the
18361 following size commands:
18364 \begin_layout Standard
18408 \begin_inset Newline newline
18430 \begin_layout Standard
18431 The size produced by the commands depends on the document font size, which
18432 corresponds to the command
18439 The other commands produce smaller or larger sizes than
18446 The font size can however not exceed a certain value.
18447 Is for example the document font size 12
18448 \begin_inset space \thinspace{}
18457 switches to the same size as
18467 \begin_layout Standard
18468 A size command is inserted in TeX-mode before the formula and sets the size
18469 for all following formula and text characters.
18470 To switch back to the initial size, the command
18476 is inserted behind the formula in TeX-mode.
18479 \begin_layout Standard
18480 Within a formula the size can be changed using the following size commands:
18483 \begin_layout Standard
18486 \begin_inset Tabular
18487 <lyxtabular version="3" rows="5" columns="2">
18488 <features rotate="0" tabularvalignment="middle">
18489 <column alignment="center" valignment="top">
18490 <column alignment="center" valignment="top">
18492 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
18495 \begin_layout Plain Layout
18501 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
18504 \begin_layout Plain Layout
18506 \begin_inset Note Note
18509 \begin_layout Plain Layout
18516 is only used as spacer.
18528 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
18531 \begin_layout Plain Layout
18535 \begin_inset Index idx
18538 \begin_layout Plain Layout
18551 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
18554 \begin_layout Plain Layout
18555 \begin_inset Formula $\raisebox{6.5mm}{}{\displaystyle E_{\mathrm{pot_{1}}}=\frac{K}{l+\frac{m}{n_{2}}}}\raisebox{-5.5mm}{}$
18565 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
18568 \begin_layout Plain Layout
18576 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
18579 \begin_layout Plain Layout
18580 \begin_inset Formula $\raisebox{4.5mm}{}{\textstyle E_{\mathrm{pot_{1}}}=\frac{K}{l+\frac{m}{n_{2}}}}\raisebox{-4mm}{}$
18590 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
18593 \begin_layout Plain Layout
18601 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
18604 \begin_layout Plain Layout
18605 \begin_inset Formula $\raisebox{4.5mm}{}{\scriptstyle E_{\mathrm{pot_{1}}}=\frac{K}{l+\frac{m}{n_{2}}}}\raisebox{-3.5mm}{}$
18615 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
18618 \begin_layout Plain Layout
18626 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
18629 \begin_layout Plain Layout
18630 \begin_inset Formula $\raisebox{4.5mm}{}{\scriptscriptstyle E_{\mathrm{pot_{1}}}=\frac{K}{l+\frac{m}{n_{2}}}}\raisebox{-3.5mm}{}$
18646 \begin_layout Standard
18647 After entering these commands, a blue box appears in which the formula parts
18651 \begin_layout Standard
18652 There is a further method to change the font size, that though only works
18653 for symbols or letters in mathematical text.
18654 To use it, one of the above text size commands is inserted in mathematical
18656 All following characters until the end of the mathematical text or until
18657 another size command will have the selected size.
18659 \begin_inset VSpace -2mm
18665 \begin_layout Standard
18669 \begin_layout Plain Layout
18679 \begin_inset Formula
18681 A=\frac{B}{c}\cdot\maltese
18687 \begin_inset Formula
18689 \maltese A\textrm{\Large\maltese\textit{A}}\textrm{\tiny\maltese\textit{A}}
18698 \begin_layout Plain Layout
18710 \begin_layout Standard
18711 \begin_inset VSpace medskip
18714 Before both formulas the command
18721 The command for the second formula is:
18722 \begin_inset Newline newline
18730 \begin_inset space \textvisiblespace{}
18736 \begin_inset space \textvisiblespace{}
18742 \begin_inset space \textvisiblespace{}
18748 \begin_inset space \textvisiblespace{}
18752 \begin_inset Formula $\to$
18756 \begin_inset Formula $\to$
18760 \begin_inset Newline newline
18764 \begin_inset space \hspace*{}
18775 \begin_inset space \textvisiblespace{}
18781 \begin_inset space \textvisiblespace{}
18787 \begin_inset space \textvisiblespace{}
18793 \begin_layout Standard
18794 If a symbol cannot be displayed in different sizes, it will always be displayed
18795 in the default size.
18798 \begin_layout Section
18800 \begin_inset Index idx
18803 \begin_layout Plain Layout
18812 \begin_layout Standard
18813 Greek letters can also be inserted via the toolbar button
18814 \begin_inset Graphics
18815 filename ../images/math/alpha.png
18821 All international typesetting norms purport that Greek letters in math
18822 have to be typeset italic/slanted.
18823 In some languages, like French or Russian, they are nevertheless sometimes
18827 \begin_layout Subsection
18829 \begin_inset Index idx
18832 \begin_layout Plain Layout
18833 Greek letters ! small
18841 \begin_layout Standard
18842 \begin_inset space \hfill{}
18846 \begin_inset Tabular
18847 <lyxtabular version="3" rows="11" columns="2">
18848 <features rotate="0" tabularvalignment="middle">
18849 <column alignment="center" valignment="top" width="0pt">
18850 <column alignment="center" valignment="top" width="0pt">
18852 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
18855 \begin_layout Plain Layout
18861 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
18864 \begin_layout Plain Layout
18872 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
18875 \begin_layout Plain Layout
18883 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
18886 \begin_layout Plain Layout
18887 \begin_inset Formula $\alpha$
18897 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
18900 \begin_layout Plain Layout
18908 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
18911 \begin_layout Plain Layout
18912 \begin_inset Formula $\beta$
18922 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
18925 \begin_layout Plain Layout
18933 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
18936 \begin_layout Plain Layout
18937 \begin_inset Formula $\gamma$
18947 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
18950 \begin_layout Plain Layout
18958 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
18961 \begin_layout Plain Layout
18962 \begin_inset Formula $\delta$
18972 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
18975 \begin_layout Plain Layout
18983 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
18986 \begin_layout Plain Layout
18987 \begin_inset Formula $\epsilon$
18997 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
19000 \begin_layout Plain Layout
19008 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
19011 \begin_layout Plain Layout
19012 \begin_inset Formula $\varepsilon$
19022 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
19025 \begin_layout Plain Layout
19033 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
19036 \begin_layout Plain Layout
19037 \begin_inset Formula $\zeta$
19047 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
19050 \begin_layout Plain Layout
19058 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
19061 \begin_layout Plain Layout
19062 \begin_inset Formula $\eta$
19072 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
19075 \begin_layout Plain Layout
19083 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
19086 \begin_layout Plain Layout
19087 \begin_inset Formula $\theta$
19097 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
19100 \begin_layout Plain Layout
19108 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
19111 \begin_layout Plain Layout
19112 \begin_inset Formula $\vartheta$
19126 \begin_inset space \hfill{}
19130 \begin_inset Tabular
19131 <lyxtabular version="3" rows="12" columns="2">
19132 <features rotate="0" tabularvalignment="middle">
19133 <column alignment="center" valignment="top" width="0pt">
19134 <column alignment="center" valignment="top" width="0pt">
19136 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
19139 \begin_layout Plain Layout
19145 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
19148 \begin_layout Plain Layout
19156 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
19159 \begin_layout Plain Layout
19167 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
19170 \begin_layout Plain Layout
19171 \begin_inset Formula $\iota$
19181 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
19184 \begin_layout Plain Layout
19192 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
19195 \begin_layout Plain Layout
19196 \begin_inset Formula $\kappa$
19206 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
19209 \begin_layout Plain Layout
19217 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
19220 \begin_layout Plain Layout
19221 \begin_inset Formula $\varkappa$
19231 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
19234 \begin_layout Plain Layout
19242 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
19245 \begin_layout Plain Layout
19246 \begin_inset Formula $\lambda$
19256 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
19259 \begin_layout Plain Layout
19267 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
19270 \begin_layout Plain Layout
19271 \begin_inset Formula $\mu$
19281 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
19284 \begin_layout Plain Layout
19292 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
19295 \begin_layout Plain Layout
19296 \begin_inset Formula $\nu$
19306 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
19309 \begin_layout Plain Layout
19317 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
19320 \begin_layout Plain Layout
19321 \begin_inset Formula $\xi$
19331 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
19334 \begin_layout Plain Layout
19340 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
19343 \begin_layout Plain Layout
19344 \begin_inset Formula $o$
19354 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
19357 \begin_layout Plain Layout
19365 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
19368 \begin_layout Plain Layout
19369 \begin_inset Formula $\pi$
19379 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
19382 \begin_layout Plain Layout
19390 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
19393 \begin_layout Plain Layout
19394 \begin_inset Formula $\varpi$
19404 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
19407 \begin_layout Plain Layout
19415 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
19418 \begin_layout Plain Layout
19419 \begin_inset Formula $\rho$
19433 \begin_inset space \hfill{}
19437 \begin_inset Tabular
19438 <lyxtabular version="3" rows="11" columns="2">
19439 <features rotate="0" tabularvalignment="middle">
19440 <column alignment="center" valignment="top" width="0pt">
19441 <column alignment="center" valignment="top" width="0pt">
19443 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
19446 \begin_layout Plain Layout
19452 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
19455 \begin_layout Plain Layout
19463 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
19466 \begin_layout Plain Layout
19474 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
19477 \begin_layout Plain Layout
19478 \begin_inset Formula $\varrho$
19488 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
19491 \begin_layout Plain Layout
19499 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
19502 \begin_layout Plain Layout
19503 \begin_inset Formula $\sigma$
19513 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
19516 \begin_layout Plain Layout
19524 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
19527 \begin_layout Plain Layout
19528 \begin_inset Formula $\varsigma$
19538 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
19541 \begin_layout Plain Layout
19549 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
19552 \begin_layout Plain Layout
19553 \begin_inset Formula $\tau$
19563 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
19566 \begin_layout Plain Layout
19574 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
19577 \begin_layout Plain Layout
19578 \begin_inset Formula $\upsilon$
19588 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
19591 \begin_layout Plain Layout
19599 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
19602 \begin_layout Plain Layout
19603 \begin_inset Formula $\phi$
19613 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
19616 \begin_layout Plain Layout
19624 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
19627 \begin_layout Plain Layout
19628 \begin_inset Formula $\varphi$
19638 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
19641 \begin_layout Plain Layout
19649 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
19652 \begin_layout Plain Layout
19653 \begin_inset Formula $\chi$
19663 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
19666 \begin_layout Plain Layout
19674 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
19677 \begin_layout Plain Layout
19678 \begin_inset Formula $\psi$
19688 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
19691 \begin_layout Plain Layout
19699 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
19702 \begin_layout Plain Layout
19703 \begin_inset Formula $\omega$
19717 \begin_inset space \hfill{}
19723 \begin_layout Standard
19724 \begin_inset VSpace medskip
19730 \begin_layout Standard
19731 How to create special upright Greek letters is explained in
19732 \begin_inset CommandInset ref
19734 reference "sub:Upright-small-Greek"
19741 \begin_layout Subsection
19743 \begin_inset Index idx
19746 \begin_layout Plain Layout
19747 Greek letters ! big
19755 \begin_layout Standard
19756 \begin_inset space \hfill{}
19760 \begin_inset Tabular
19761 <lyxtabular version="3" rows="7" columns="2">
19762 <features rotate="0" tabularvalignment="middle">
19763 <column alignment="center" valignment="top" width="0pt">
19764 <column alignment="center" valignment="top" width="0pt">
19766 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
19769 \begin_layout Plain Layout
19775 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
19778 \begin_layout Plain Layout
19786 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
19789 \begin_layout Plain Layout
19797 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
19800 \begin_layout Plain Layout
19801 \begin_inset Formula $\Gamma$
19811 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
19814 \begin_layout Plain Layout
19822 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
19825 \begin_layout Plain Layout
19826 \begin_inset Formula $\Delta$
19836 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
19839 \begin_layout Plain Layout
19847 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
19850 \begin_layout Plain Layout
19851 \begin_inset Formula $\Theta$
19861 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
19864 \begin_layout Plain Layout
19872 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
19875 \begin_layout Plain Layout
19876 \begin_inset Formula $\Lambda$
19886 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
19889 \begin_layout Plain Layout
19897 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
19900 \begin_layout Plain Layout
19901 \begin_inset Formula $\Xi$
19911 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
19914 \begin_layout Plain Layout
19922 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
19925 \begin_layout Plain Layout
19926 \begin_inset Formula $\Pi$
19940 \begin_inset space \hfill{}
19944 \begin_inset Tabular
19945 <lyxtabular version="3" rows="6" columns="2">
19946 <features rotate="0" tabularvalignment="middle">
19947 <column alignment="center" valignment="top" width="0pt">
19948 <column alignment="center" valignment="top" width="0pt">
19950 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
19953 \begin_layout Plain Layout
19959 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
19962 \begin_layout Plain Layout
19970 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
19973 \begin_layout Plain Layout
19981 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
19984 \begin_layout Plain Layout
19985 \begin_inset Formula $\Sigma$
19995 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
19998 \begin_layout Plain Layout
20006 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
20009 \begin_layout Plain Layout
20010 \begin_inset Formula $\Upsilon$
20020 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
20023 \begin_layout Plain Layout
20031 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
20034 \begin_layout Plain Layout
20035 \begin_inset Formula $\Phi$
20045 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
20048 \begin_layout Plain Layout
20056 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
20059 \begin_layout Plain Layout
20060 \begin_inset Formula $\Psi$
20070 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
20073 \begin_layout Plain Layout
20081 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
20084 \begin_layout Plain Layout
20085 \begin_inset Formula $\Omega$
20099 \begin_inset space \hfill{}
20105 \begin_layout Standard
20106 \begin_inset VSpace medskip
20109 That the big Greek letters appear upright is caused by a design bug when
20111 To get correct italic big letters, begin every command with
20116 For example the command
20123 \begin_inset Formula $\varGamma$
20127 Another way is to load the package
20135 \begin_layout Plain Layout
20140 is part of the LaTeX-package
20145 \begin_inset Index idx
20148 \begin_layout Plain Layout
20153 \begin_layout Plain Layout
20173 \begin_inset Index idx
20176 \begin_layout Plain Layout
20182 with the LaTeX-preamble line
20185 \begin_layout Standard
20190 usepackage{fixmath}
20193 \begin_layout Standard
20194 Then all big Greek letters in a document will automatically be typeset italic.
20197 \begin_layout Subsection
20199 \begin_inset Index idx
20202 \begin_layout Plain Layout
20203 Greek letters ! bold
20211 \begin_layout Standard
20212 Greek letters cannot be set with different font styles like Latin letters.
20213 They can only be made bold with the command
20220 \begin_inset Index idx
20223 \begin_layout Plain Layout
20234 \begin_layout Standard
20236 \begin_inset Tabular
20237 <lyxtabular version="3" rows="3" columns="2">
20238 <features rotate="0" tabularvalignment="middle">
20239 <column alignment="center" valignment="top">
20240 <column alignment="center" valignment="top">
20242 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
20245 \begin_layout Plain Layout
20251 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
20254 \begin_layout Plain Layout
20262 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
20265 \begin_layout Plain Layout
20277 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
20280 \begin_layout Plain Layout
20281 \begin_inset Formula $\Upsilon\boldsymbol{\Upsilon}$
20291 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
20294 \begin_layout Plain Layout
20306 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
20309 \begin_layout Plain Layout
20310 \begin_inset Formula $\theta\boldsymbol{\theta}$
20326 \begin_layout Section
20331 \begin_layout Plain Layout
20344 \begin_layout Plain Layout
20345 A list with all symbols of most of the LaTeX-packages can be found in
20346 \begin_inset CommandInset citation
20361 \begin_layout Plain Layout
20369 \begin_inset Note Note
20372 \begin_layout Plain Layout
20375 texorpdfstring is used to avoid that the footnote appears in the PDF-bookmark.
20378 \begin_layout Plain Layout
20381 texorpdfstring is in section
20382 \begin_inset CommandInset ref
20384 reference "sub:Formulas-in-Section"
20394 \begin_inset Index idx
20397 \begin_layout Plain Layout
20406 \begin_layout Standard
20407 Many of the symbols listed in this section can also be inserted via the
20409 \begin_inset Graphics
20410 filename ../images/math/nabla.png
20416 \begin_inset Graphics
20417 filename ../images/math/digamma.png
20425 \begin_layout Subsection
20426 Mathematical Symbols
20427 \begin_inset CommandInset label
20429 name "sub:Mathematical-Symbols"
20434 \begin_inset Index idx
20437 \begin_layout Plain Layout
20438 Symbols ! mathematical
20446 \begin_layout Standard
20447 \begin_inset space \hfill{}
20451 \begin_inset Tabular
20452 <lyxtabular version="3" rows="10" columns="2">
20453 <features rotate="0" tabularvalignment="middle">
20454 <column alignment="center" valignment="top" width="0pt">
20455 <column alignment="center" valignment="top" width="0pt">
20457 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
20460 \begin_layout Plain Layout
20466 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
20469 \begin_layout Plain Layout
20477 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
20480 \begin_layout Plain Layout
20488 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
20491 \begin_layout Plain Layout
20492 \begin_inset Formula $\neg$
20502 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
20505 \begin_layout Plain Layout
20513 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
20516 \begin_layout Plain Layout
20517 \begin_inset Formula $\Im$
20527 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
20530 \begin_layout Plain Layout
20538 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
20541 \begin_layout Plain Layout
20542 \begin_inset Formula $\Re$
20552 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
20555 \begin_layout Plain Layout
20563 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
20566 \begin_layout Plain Layout
20567 \begin_inset Formula $\aleph$
20577 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
20580 \begin_layout Plain Layout
20588 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
20591 \begin_layout Plain Layout
20592 \begin_inset Formula $\partial$
20602 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
20605 \begin_layout Plain Layout
20613 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
20616 \begin_layout Plain Layout
20617 \begin_inset Formula $\infty$
20627 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
20630 \begin_layout Plain Layout
20638 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
20641 \begin_layout Plain Layout
20642 \begin_inset Formula $\wp$
20652 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
20655 \begin_layout Plain Layout
20663 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
20666 \begin_layout Plain Layout
20667 \begin_inset Formula $\imath$
20677 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
20680 \begin_layout Plain Layout
20688 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
20691 \begin_layout Plain Layout
20692 \begin_inset Formula $\jmath$
20706 \begin_inset space \hfill{}
20710 \begin_inset Tabular
20711 <lyxtabular version="3" rows="10" columns="2">
20712 <features rotate="0" tabularvalignment="middle">
20713 <column alignment="center" valignment="top" width="0pt">
20714 <column alignment="center" valignment="top" width="0pt">
20716 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
20719 \begin_layout Plain Layout
20725 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
20728 \begin_layout Plain Layout
20730 \begin_inset Note Note
20733 \begin_layout Plain Layout
20740 is only used as spacer.
20752 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
20755 \begin_layout Plain Layout
20763 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
20766 \begin_layout Plain Layout
20767 \begin_inset Formula $\forall$
20777 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
20780 \begin_layout Plain Layout
20788 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
20791 \begin_layout Plain Layout
20792 \begin_inset Formula $\exists$
20802 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
20805 \begin_layout Plain Layout
20813 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
20816 \begin_layout Plain Layout
20817 \begin_inset Formula $\nexists$
20827 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
20830 \begin_layout Plain Layout
20838 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
20841 \begin_layout Plain Layout
20842 \begin_inset Formula $\emptyset$
20852 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
20855 \begin_layout Plain Layout
20863 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
20866 \begin_layout Plain Layout
20867 \begin_inset Formula $\varnothing$
20877 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
20880 \begin_layout Plain Layout
20888 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
20891 \begin_layout Plain Layout
20892 \begin_inset Formula $\dag$
20902 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
20905 \begin_layout Plain Layout
20913 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
20916 \begin_layout Plain Layout
20917 \begin_inset Formula $\ddag$
20927 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
20930 \begin_layout Plain Layout
20938 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
20941 \begin_layout Plain Layout
20945 \begin_layout Plain Layout
20955 \begin_inset Formula $\complement$
20962 \begin_layout Plain Layout
20976 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
20979 \begin_layout Plain Layout
20987 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
20990 \begin_layout Plain Layout
20991 \begin_inset Formula $\Bbbk$
21005 \begin_inset space \hfill{}
21009 \begin_inset Tabular
21010 <lyxtabular version="3" rows="10" columns="2">
21011 <features rotate="0" tabularvalignment="middle">
21012 <column alignment="center" valignment="top" width="0pt">
21013 <column alignment="center" valignment="top" width="0pt">
21015 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
21018 \begin_layout Plain Layout
21024 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
21027 \begin_layout Plain Layout
21035 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
21038 \begin_layout Plain Layout
21046 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
21049 \begin_layout Plain Layout
21050 \begin_inset Formula $\prime$
21060 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
21063 \begin_layout Plain Layout
21071 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
21074 \begin_layout Plain Layout
21075 \begin_inset Formula $\backprime$
21085 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
21088 \begin_layout Plain Layout
21096 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
21099 \begin_layout Plain Layout
21100 \begin_inset Formula $\mho$
21110 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
21113 \begin_layout Plain Layout
21121 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
21124 \begin_layout Plain Layout
21125 \begin_inset Formula $\triangle$
21135 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
21138 \begin_layout Plain Layout
21146 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
21149 \begin_layout Plain Layout
21150 \begin_inset Formula $\angle$
21160 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
21163 \begin_layout Plain Layout
21171 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
21174 \begin_layout Plain Layout
21175 \begin_inset Formula $\measuredangle$
21185 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
21188 \begin_layout Plain Layout
21196 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
21199 \begin_layout Plain Layout
21200 \begin_inset Formula $\sphericalangle$
21210 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
21213 \begin_layout Plain Layout
21221 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
21224 \begin_layout Plain Layout
21225 \begin_inset Formula $\top$
21235 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
21238 \begin_layout Plain Layout
21246 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
21249 \begin_layout Plain Layout
21250 \begin_inset Formula $\bot$
21264 \begin_inset space \hfill{}
21270 \begin_layout Subsection
21271 Miscellaneous Symbols
21272 \begin_inset CommandInset label
21274 name "sub:Miscellaneous-Symbols"
21279 \begin_inset Index idx
21282 \begin_layout Plain Layout
21283 Symbols ! miscellaneous
21291 \begin_layout Standard
21294 \begin_inset Tabular
21295 <lyxtabular version="3" rows="10" columns="2">
21296 <features rotate="0" tabularvalignment="middle">
21297 <column alignment="center" valignment="top" width="0pt">
21298 <column alignment="center" valignment="top" width="0pt">
21300 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
21303 \begin_layout Plain Layout
21309 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
21312 \begin_layout Plain Layout
21320 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
21323 \begin_layout Plain Layout
21331 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
21334 \begin_layout Plain Layout
21335 \begin_inset Formula $\flat$
21345 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
21348 \begin_layout Plain Layout
21356 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
21359 \begin_layout Plain Layout
21360 \begin_inset Formula $\natural$
21370 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
21373 \begin_layout Plain Layout
21381 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
21384 \begin_layout Plain Layout
21385 \begin_inset Formula $\sharp$
21395 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
21398 \begin_layout Plain Layout
21406 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
21409 \begin_layout Plain Layout
21410 \begin_inset Formula $\surd$
21420 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
21423 \begin_layout Plain Layout
21431 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
21434 \begin_layout Plain Layout
21435 \begin_inset Formula $\checkmark$
21445 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
21448 \begin_layout Plain Layout
21456 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
21459 \begin_layout Plain Layout
21460 \begin_inset Formula $\yen$
21470 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
21473 \begin_layout Plain Layout
21481 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
21484 \begin_layout Plain Layout
21485 \begin_inset Formula $\pounds$
21495 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
21498 \begin_layout Plain Layout
21504 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
21507 \begin_layout Plain Layout
21508 \begin_inset Formula $\$$
21518 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
21521 \begin_layout Plain Layout
21527 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
21530 \begin_layout Plain Layout
21531 \begin_inset Formula $§$
21545 \begin_inset Tabular
21546 <lyxtabular version="3" rows="10" columns="2">
21547 <features rotate="0" tabularvalignment="middle">
21548 <column alignment="center" valignment="top">
21549 <column alignment="center" valignment="top">
21551 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
21554 \begin_layout Plain Layout
21560 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
21563 \begin_layout Plain Layout
21571 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
21574 \begin_layout Plain Layout
21582 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
21585 \begin_layout Plain Layout
21586 \begin_inset Formula $\hbar$
21596 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
21599 \begin_layout Plain Layout
21607 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
21610 \begin_layout Plain Layout
21611 \begin_inset Formula $\hslash$
21621 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
21624 \begin_layout Plain Layout
21632 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
21635 \begin_layout Plain Layout
21636 \begin_inset Formula $\clubsuit$
21646 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
21649 \begin_layout Plain Layout
21657 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
21660 \begin_layout Plain Layout
21661 \begin_inset Formula $\spadesuit$
21671 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
21674 \begin_layout Plain Layout
21682 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
21685 \begin_layout Plain Layout
21686 \begin_inset Formula $\bigstar$
21696 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
21699 \begin_layout Plain Layout
21707 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
21710 \begin_layout Plain Layout
21711 \begin_inset Formula $\blacklozenge$
21721 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
21724 \begin_layout Plain Layout
21732 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
21735 \begin_layout Plain Layout
21736 \begin_inset Formula $\blacktriangle$
21746 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
21749 \begin_layout Plain Layout
21757 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
21760 \begin_layout Plain Layout
21761 \begin_inset Formula $\blacktriangledown$
21771 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
21774 \begin_layout Plain Layout
21782 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
21785 \begin_layout Plain Layout
21786 \begin_inset Formula $\bullet$
21800 \begin_inset Tabular
21801 <lyxtabular version="3" rows="10" columns="2">
21802 <features rotate="0" tabularvalignment="middle">
21803 <column alignment="center" valignment="top" width="0pt">
21804 <column alignment="center" valignment="top" width="0pt">
21806 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
21809 \begin_layout Plain Layout
21815 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
21818 \begin_layout Plain Layout
21826 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
21829 \begin_layout Plain Layout
21837 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
21840 \begin_layout Plain Layout
21841 \begin_inset Formula $\diamondsuit$
21851 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
21854 \begin_layout Plain Layout
21862 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
21865 \begin_layout Plain Layout
21866 \begin_inset Formula $\Diamond$
21876 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
21879 \begin_layout Plain Layout
21887 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
21890 \begin_layout Plain Layout
21891 \begin_inset Formula $\heartsuit$
21901 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
21904 \begin_layout Plain Layout
21912 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
21915 \begin_layout Plain Layout
21916 \begin_inset Formula $\P$
21926 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
21929 \begin_layout Plain Layout
21937 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
21940 \begin_layout Plain Layout
21941 \begin_inset Formula $\copyright$
21951 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
21954 \begin_layout Plain Layout
21962 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
21965 \begin_layout Plain Layout
21966 \begin_inset Formula $\circledR$
21976 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
21979 \begin_layout Plain Layout
21987 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
21990 \begin_layout Plain Layout
21991 \begin_inset Formula $\maltese$
22001 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
22004 \begin_layout Plain Layout
22012 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
22015 \begin_layout Plain Layout
22016 \begin_inset Formula $\diagup$
22026 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
22029 \begin_layout Plain Layout
22037 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
22040 \begin_layout Plain Layout
22041 \begin_inset Formula $\diagdown$
22057 \begin_layout Standard
22058 \begin_inset VSpace medskip
22064 \begin_layout Standard
22065 Some symbols can be displayed in different sizes, see
22066 \begin_inset CommandInset ref
22068 reference "sub:Font-Sizes"
22075 \begin_layout Subsection
22077 \begin_inset Index idx
22080 \begin_layout Plain Layout
22081 Symbols ! Euro-symbol
22087 \begin_inset Index idx
22090 \begin_layout Plain Layout
22097 \begin_layout Plain Layout
22114 \begin_layout Standard
22115 To use the Euro symbol in formulas, the LaTeX-package
22120 \begin_inset Index idx
22123 \begin_layout Plain Layout
22129 must be installed and loaded with the LaTeX-preamble line
22132 \begin_layout Standard
22137 usepackage[gennarrow]{eurosym}
22140 \begin_layout Standard
22141 The Euro symbol can now be inserted with the command
22148 \begin_inset Index idx
22151 \begin_layout Plain Layout
22162 \begin_layout Standard
22163 The Euro symbol can directly be inserted with the € key in mathematical
22164 text, without having
22179 can also be inserted in TeX-mode.
22180 The official currency symbol can then be inserted with the command
22187 \begin_inset Index idx
22190 \begin_layout Plain Layout
22198 , that is only available in TeX-mode.
22201 \begin_layout Standard
22205 \begin_layout Plain Layout
22215 \begin_inset Note Note
22218 \begin_layout Plain Layout
22219 The following table will only be displayed when the LaTeX-package
22231 \begin_layout Standard
22232 An overview about the different Euro symbols:
22235 \begin_layout Standard
22237 \begin_inset Tabular
22238 <lyxtabular version="3" rows="4" columns="3">
22239 <features rotate="0" tabularvalignment="middle">
22240 <column alignment="center" valignment="top" width="0pt">
22241 <column alignment="center" valignment="top" width="0pt">
22242 <column alignment="center" valignment="top" width="0pt">
22244 <cell multicolumn="1" alignment="center" valignment="top" bottomline="true" usebox="none">
22247 \begin_layout Plain Layout
22253 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
22256 \begin_layout Plain Layout
22262 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
22265 \begin_layout Plain Layout
22273 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
22276 \begin_layout Plain Layout
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 $\euro$
22307 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
22310 \begin_layout Plain Layout
22316 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
22319 \begin_layout Plain Layout
22325 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
22328 \begin_layout Plain Layout
22329 \begin_inset Formula $\mbox{€}$
22339 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
22342 \begin_layout Plain Layout
22348 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
22351 \begin_layout Plain Layout
22359 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
22362 \begin_layout Plain Layout
22366 \begin_layout Plain Layout
22388 \begin_layout Standard
22392 \begin_layout Plain Layout
22402 \begin_inset Note Note
22405 \begin_layout Plain Layout
22406 The following will be displayed when the LaTeX-package
22418 \begin_layout Standard
22419 You need to install the LaTeX-package
22423 to see the rest of this subsection in the output.
22426 \begin_layout Standard
22430 \begin_layout Plain Layout
22442 \begin_layout Section
22444 \begin_inset CommandInset label
22446 name "sec:Relations"
22451 \begin_inset Index idx
22454 \begin_layout Plain Layout
22461 \begin_inset Index idx
22464 \begin_layout Plain Layout
22469 \begin_layout Plain Layout
22480 \begin_layout Plain Layout
22495 \begin_layout Standard
22496 All relations can also be inserted via the toolbar button
22497 \begin_inset Graphics
22498 filename ../images/math/leq.png
22506 \begin_layout Standard
22507 \begin_inset space \hfill{}
22511 \begin_inset Tabular
22512 <lyxtabular version="3" rows="17" columns="2">
22513 <features rotate="0" tabularvalignment="middle">
22514 <column alignment="center" valignment="top" width="0pt">
22515 <column alignment="center" valignment="top" width="0pt">
22517 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
22520 \begin_layout Plain Layout
22526 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
22529 \begin_layout Plain Layout
22537 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
22540 \begin_layout Plain Layout
22546 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
22549 \begin_layout Plain Layout
22550 \begin_inset Formula $<$
22560 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
22563 \begin_layout Plain Layout
22571 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
22574 \begin_layout Plain Layout
22575 \begin_inset Formula $\le$
22585 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
22588 \begin_layout Plain Layout
22596 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
22599 \begin_layout Plain Layout
22600 \begin_inset Formula $\ll$
22610 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
22613 \begin_layout Plain Layout
22621 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
22624 \begin_layout Plain Layout
22625 \begin_inset Formula $\prec$
22635 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
22638 \begin_layout Plain Layout
22646 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
22649 \begin_layout Plain Layout
22650 \begin_inset Formula $\preceq$
22660 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
22663 \begin_layout Plain Layout
22671 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
22674 \begin_layout Plain Layout
22675 \begin_inset Formula $\subset$
22685 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
22688 \begin_layout Plain Layout
22696 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
22699 \begin_layout Plain Layout
22700 \begin_inset Formula $\subseteq$
22710 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
22713 \begin_layout Plain Layout
22721 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
22724 \begin_layout Plain Layout
22725 \begin_inset Formula $\sqsubseteq$
22735 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
22738 \begin_layout Plain Layout
22746 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
22749 \begin_layout Plain Layout
22750 \begin_inset Formula $\in$
22760 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
22763 \begin_layout Plain Layout
22771 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
22774 \begin_layout Plain Layout
22775 \begin_inset Formula $\vdash$
22785 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
22788 \begin_layout Plain Layout
22796 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
22799 \begin_layout Plain Layout
22800 \begin_inset Formula $\smile$
22810 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
22813 \begin_layout Plain Layout
22821 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
22824 \begin_layout Plain Layout
22825 \begin_inset Formula $\lhd$
22835 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
22838 \begin_layout Plain Layout
22846 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
22849 \begin_layout Plain Layout
22850 \begin_inset Formula $\unlhd$
22860 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
22863 \begin_layout Plain Layout
22871 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
22874 \begin_layout Plain Layout
22875 \begin_inset Formula $\gtrless$
22885 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
22888 \begin_layout Plain Layout
22896 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
22899 \begin_layout Plain Layout
22900 \begin_inset Formula $\mid$
22910 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
22913 \begin_layout Plain Layout
22921 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
22924 \begin_layout Plain Layout
22925 \begin_inset Formula $\nmid$
22939 \begin_inset space \hfill{}
22943 \begin_inset Tabular
22944 <lyxtabular version="3" rows="17" columns="2">
22945 <features rotate="0" tabularvalignment="middle">
22946 <column alignment="center" valignment="top" width="0pt">
22947 <column alignment="center" valignment="top" width="0pt">
22949 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
22952 \begin_layout Plain Layout
22958 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
22961 \begin_layout Plain Layout
22969 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
22972 \begin_layout Plain Layout
22978 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
22981 \begin_layout Plain Layout
22982 \begin_inset Formula $=$
22992 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
22995 \begin_layout Plain Layout
23003 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
23006 \begin_layout Plain Layout
23007 \begin_inset Formula $\not=$
23017 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
23020 \begin_layout Plain Layout
23028 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
23031 \begin_layout Plain Layout
23032 \begin_inset Formula $\equiv$
23042 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
23045 \begin_layout Plain Layout
23053 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
23056 \begin_layout Plain Layout
23057 \begin_inset Formula $\sim$
23067 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
23070 \begin_layout Plain Layout
23078 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
23081 \begin_layout Plain Layout
23082 \begin_inset Formula $\simeq$
23092 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
23095 \begin_layout Plain Layout
23103 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
23106 \begin_layout Plain Layout
23107 \begin_inset Formula $\approx$
23117 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
23120 \begin_layout Plain Layout
23128 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
23131 \begin_layout Plain Layout
23132 \begin_inset Formula $\cong$
23142 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
23145 \begin_layout Plain Layout
23153 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
23156 \begin_layout Plain Layout
23157 \begin_inset Formula $\bowtie$
23167 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
23170 \begin_layout Plain Layout
23178 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
23181 \begin_layout Plain Layout
23182 \begin_inset Formula $\notin$
23192 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
23195 \begin_layout Plain Layout
23203 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
23206 \begin_layout Plain Layout
23207 \begin_inset Formula $\perp$
23217 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
23220 \begin_layout Plain Layout
23228 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
23231 \begin_layout Plain Layout
23232 \begin_inset Formula $\propto$
23242 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
23245 \begin_layout Plain Layout
23253 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
23256 \begin_layout Plain Layout
23257 \begin_inset Formula $\asymp$
23267 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
23270 \begin_layout Plain Layout
23278 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
23281 \begin_layout Plain Layout
23282 \begin_inset Formula $\doteq$
23292 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
23295 \begin_layout Plain Layout
23303 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
23306 \begin_layout Plain Layout
23307 \begin_inset Formula $\circeq$
23317 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
23320 \begin_layout Plain Layout
23328 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
23331 \begin_layout Plain Layout
23332 \begin_inset Formula $\models$
23342 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
23345 \begin_layout Plain Layout
23353 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
23356 \begin_layout Plain Layout
23357 \begin_inset Formula $\widehat{=}$
23371 \begin_inset space \hfill{}
23375 \begin_inset Tabular
23376 <lyxtabular version="3" rows="17" columns="2">
23377 <features rotate="0" tabularvalignment="middle">
23378 <column alignment="center" valignment="top" width="0pt">
23379 <column alignment="center" valignment="top" width="0pt">
23381 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
23384 \begin_layout Plain Layout
23390 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
23393 \begin_layout Plain Layout
23401 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
23404 \begin_layout Plain Layout
23410 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
23413 \begin_layout Plain Layout
23414 \begin_inset Formula $>$
23424 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
23427 \begin_layout Plain Layout
23435 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
23438 \begin_layout Plain Layout
23439 \begin_inset Formula $\ge$
23449 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
23452 \begin_layout Plain Layout
23460 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
23463 \begin_layout Plain Layout
23464 \begin_inset Formula $\gg$
23474 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
23477 \begin_layout Plain Layout
23485 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
23488 \begin_layout Plain Layout
23489 \begin_inset Formula $\succ$
23499 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
23502 \begin_layout Plain Layout
23510 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
23513 \begin_layout Plain Layout
23514 \begin_inset Formula $\succeq$
23524 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
23527 \begin_layout Plain Layout
23535 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
23538 \begin_layout Plain Layout
23539 \begin_inset Formula $\supset$
23549 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
23552 \begin_layout Plain Layout
23560 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
23563 \begin_layout Plain Layout
23564 \begin_inset Formula $\supseteq$
23574 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
23577 \begin_layout Plain Layout
23585 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
23588 \begin_layout Plain Layout
23589 \begin_inset Formula $\sqsupseteq$
23599 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
23602 \begin_layout Plain Layout
23610 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
23613 \begin_layout Plain Layout
23614 \begin_inset Formula $\ni$
23624 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
23627 \begin_layout Plain Layout
23635 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
23638 \begin_layout Plain Layout
23639 \begin_inset Formula $\dashv$
23649 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
23652 \begin_layout Plain Layout
23660 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
23663 \begin_layout Plain Layout
23664 \begin_inset Formula $\frown$
23674 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
23677 \begin_layout Plain Layout
23685 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
23688 \begin_layout Plain Layout
23689 \begin_inset Formula $\rhd$
23699 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
23702 \begin_layout Plain Layout
23710 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
23713 \begin_layout Plain Layout
23714 \begin_inset Formula $\unrhd$
23724 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
23727 \begin_layout Plain Layout
23735 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
23738 \begin_layout Plain Layout
23739 \begin_inset Formula $\lessgtr$
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" rightline="true" usebox="none">
23763 \begin_layout Plain Layout
23764 \begin_inset Formula $\parallel$
23774 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
23777 \begin_layout Plain Layout
23785 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
23788 \begin_layout Plain Layout
23789 \begin_inset Formula $\nparallel$
23803 \begin_inset space \hfill{}
23809 \begin_layout Standard
23810 \begin_inset VSpace medskip
23825 are bigger than the equal looking operators
23840 \begin_layout Standard
23841 Relations are, in contrary to symbols, always surrounded by space.
23844 \begin_layout Standard
23845 Relations with labels can be created with the command
23852 \begin_inset Index idx
23855 \begin_layout Plain Layout
23866 \begin_layout Standard
23868 \begin_inset Tabular
23869 <lyxtabular version="3" rows="2" columns="2">
23870 <features rotate="0" tabularvalignment="middle">
23871 <column alignment="center" valignment="top">
23872 <column alignment="center" valignment="top">
23874 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
23877 \begin_layout Plain Layout
23883 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
23886 \begin_layout Plain Layout
23888 \begin_inset Note Note
23891 \begin_layout Plain Layout
23898 is only used as spacer.
23910 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
23913 \begin_layout Plain Layout
23917 \begin_inset space \textvisiblespace{}
23925 \begin_inset space \textvisiblespace{}
23929 \begin_inset Formula $\downarrow$
23935 \begin_inset space \textvisiblespace{}
23939 \begin_inset space \textvisiblespace{}
23947 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
23950 \begin_layout Plain Layout
23951 \begin_inset Formula $\raisebox{5mm}{}A(r)\stackrel{r\to\infty}{\approx}B$
23967 \begin_layout Section
23971 \begin_layout Subsection
23972 Predefined Functions
23973 \begin_inset CommandInset label
23975 name "sub:Predefined-Functions"
23980 \begin_inset Index idx
23983 \begin_layout Plain Layout
23984 Functions ! predefined
23992 \begin_layout Standard
23993 In general, variables are set
23997 in mathematical expressions, but not function names, because
23998 \begin_inset Formula $sin$
24001 could be misunderstood as
24002 \begin_inset Formula $s\cdot i\cdot n$
24006 Therefore there are predefined functionswhich are additionally a bit separated
24008 They are inserted as commands starting with a backslash before their name.
24011 \begin_layout Standard
24013 \begin_inset Tabular
24014 <lyxtabular version="3" rows="2" columns="4">
24015 <features rotate="0" tabularvalignment="middle">
24016 <column alignment="center" valignment="top" width="0pt">
24017 <column alignment="center" valignment="top" width="0pt">
24018 <column alignment="center" valignment="top" width="0pt">
24019 <column alignment="center" valignment="top" width="0pt">
24021 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
24024 \begin_layout Plain Layout
24030 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
24033 \begin_layout Plain Layout
24039 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
24042 \begin_layout Plain Layout
24048 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
24051 \begin_layout Plain Layout
24059 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
24062 \begin_layout Plain Layout
24068 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
24071 \begin_layout Plain Layout
24072 \begin_inset Formula $Asin(x)+B$
24080 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
24083 \begin_layout Plain Layout
24091 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
24094 \begin_layout Plain Layout
24095 \begin_inset Formula $A\sin(x)+B$
24111 \begin_layout Standard
24112 The following functions are predefined:
24115 \begin_layout Standard
24116 \begin_inset VSpace -2mm
24122 \begin_layout Standard
24124 \begin_inset Tabular
24125 <lyxtabular version="3" rows="9" columns="4">
24126 <features rotate="0" tabularvalignment="middle">
24127 <column alignment="center" valignment="top" width="0pt">
24128 <column alignment="center" valignment="top" width="0pt">
24129 <column alignment="center" valignment="top" width="0pt">
24130 <column alignment="center" valignment="top" width="0pt">
24132 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
24135 \begin_layout Plain Layout
24141 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
24144 \begin_layout Plain Layout
24150 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
24153 \begin_layout Plain Layout
24159 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
24162 \begin_layout Plain Layout
24170 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
24173 \begin_layout Plain Layout
24181 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
24184 \begin_layout Plain Layout
24192 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
24195 \begin_layout Plain Layout
24203 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
24206 \begin_layout Plain Layout
24216 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
24219 \begin_layout Plain Layout
24227 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
24230 \begin_layout Plain Layout
24238 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
24241 \begin_layout Plain Layout
24249 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
24252 \begin_layout Plain Layout
24262 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
24265 \begin_layout Plain Layout
24273 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
24276 \begin_layout Plain Layout
24284 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
24287 \begin_layout Plain Layout
24295 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
24298 \begin_layout Plain Layout
24308 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
24311 \begin_layout Plain Layout
24319 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
24322 \begin_layout Plain Layout
24330 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
24333 \begin_layout Plain Layout
24341 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
24344 \begin_layout Plain Layout
24354 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
24357 \begin_layout Plain Layout
24365 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
24368 \begin_layout Plain Layout
24376 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
24379 \begin_layout Plain Layout
24387 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
24390 \begin_layout Plain Layout
24400 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
24403 \begin_layout Plain Layout
24411 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
24414 \begin_layout Plain Layout
24422 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
24425 \begin_layout Plain Layout
24433 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
24436 \begin_layout Plain Layout
24446 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
24449 \begin_layout Plain Layout
24457 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
24460 \begin_layout Plain Layout
24468 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
24471 \begin_layout Plain Layout
24479 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
24482 \begin_layout Plain Layout
24492 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
24495 \begin_layout Plain Layout
24503 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
24506 \begin_layout Plain Layout
24514 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
24517 \begin_layout Plain Layout
24525 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
24528 \begin_layout Plain Layout
24544 \begin_layout Standard
24545 They can also be inserted with the math toolbar button
24546 \begin_inset Graphics
24547 filename ../images/math/functions.png
24555 \begin_layout Subsection
24556 Self-defined Functions
24557 \begin_inset Index idx
24560 \begin_layout Plain Layout
24561 Functions ! self-defined
24569 \begin_layout Standard
24570 To use a function that is not predefined, like for example the sign function
24571 sgn(x), there are two possibilities:
24574 \begin_layout Itemize
24575 Define the function by inserting the following line to the LaTeX-preamble
24579 \begin_layout Plain Layout
24584 DeclareMathOperator
24587 \begin_inset CommandInset ref
24589 reference "sub:Self-defined-Operators"
24599 \begin_inset Newline newline
24603 \begin_inset VSpace -3mm
24607 \begin_inset Newline newline
24614 DeclareMathOperator{
24619 \begin_inset Index idx
24622 \begin_layout Plain Layout
24627 DeclareMathOperator
24633 \begin_inset Newline newline
24637 \begin_inset VSpace -2mm
24641 \begin_inset Newline newline
24644 Now the new defined function can be called with the command
24653 \begin_layout Itemize
24654 Write the formula as usual, mark the formula name, in our example the letters
24659 , and change it to mathematical text.
24660 Finally, a space is inserted between prefactor and function.
24663 \begin_layout Standard
24664 The result is the same with both methods as with a predefined function
24668 \begin_layout Plain Layout
24669 In LyX self-defined functions are displayed red, predefined ones black.
24677 \begin_layout Standard
24679 \begin_inset Tabular
24680 <lyxtabular version="3" rows="3" columns="2">
24681 <features rotate="0" tabularvalignment="middle">
24682 <column alignment="center" valignment="top" width="0pt">
24683 <column alignment="center" valignment="top" width="0pt">
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" bottomline="true" leftline="true" usebox="none">
24708 \begin_layout Plain Layout
24716 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
24719 \begin_layout Plain Layout
24720 \begin_inset Formula $A\sgn(x)+B$
24730 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
24733 \begin_layout Plain Layout
24737 \begin_inset Formula $\underbrace{\textrm{sgn}}_{\textrm{Alt+M}\,\textrm{M}}$
24745 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
24748 \begin_layout Plain Layout
24749 \begin_inset Formula $A\,\textrm{sgn}(x)+B$
24765 \begin_layout Standard
24766 The first method is more suitable when the self-defined function should
24767 be used several times.
24770 \begin_layout Subsection
24772 \begin_inset Index idx
24775 \begin_layout Plain Layout
24784 \begin_layout Standard
24785 For limits, in addition to the commands
24792 \begin_inset Index idx
24795 \begin_layout Plain Layout
24815 the following functions are defined:
24818 \begin_layout Standard
24820 \begin_inset Tabular
24821 <lyxtabular version="3" rows="5" columns="2">
24822 <features rotate="0" tabularvalignment="middle">
24823 <column alignment="center" valignment="top">
24824 <column alignment="center" valignment="top">
24826 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
24829 \begin_layout Plain Layout
24835 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
24838 \begin_layout Plain Layout
24840 \begin_inset Note Note
24843 \begin_layout Plain Layout
24850 is only used as spacer.
24862 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
24865 \begin_layout Plain Layout
24873 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
24876 \begin_layout Plain Layout
24877 \begin_inset Formula $\varliminf$
24887 <cell alignment="center" valignment="top" leftline="true" usebox="none">
24890 \begin_layout Plain Layout
24898 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
24901 \begin_layout Plain Layout
24902 \begin_inset Formula $\varlimsup$
24912 <cell alignment="center" valignment="top" leftline="true" usebox="none">
24915 \begin_layout Plain Layout
24923 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
24926 \begin_layout Plain Layout
24927 \begin_inset Formula $\varprojlim$
24937 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
24940 \begin_layout Plain Layout
24948 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
24951 \begin_layout Plain Layout
24952 \begin_inset Formula $\varinjlim$
24956 \begin_inset Formula $\raisebox{-2.5mm}{}$
24972 \begin_layout Standard
24973 \begin_inset VSpace medskip
24976 The limit is created by inserting a subscript.
24977 It is set right beside the function in an inline formula:
24980 \begin_layout Standard
24982 \begin_inset Tabular
24983 <lyxtabular version="3" rows="2" columns="2">
24984 <features rotate="0" tabularvalignment="middle">
24985 <column alignment="center" valignment="top" width="0pt">
24986 <column alignment="center" valignment="top" width="0pt">
24988 <cell alignment="center" valignment="top" usebox="none">
24991 \begin_layout Plain Layout
24997 <cell alignment="center" valignment="top" usebox="none">
25000 \begin_layout Plain Layout
25001 \begin_inset space \hspace{}
25006 \begin_inset Note Note
25009 \begin_layout Plain Layout
25016 are used here as spacer.
25028 <cell alignment="center" valignment="top" usebox="none">
25031 \begin_layout Plain Layout
25037 \begin_inset space \textvisiblespace{}
25041 \begin_inset space \textvisiblespace{}
25049 <cell alignment="center" valignment="top" usebox="none">
25052 \begin_layout Plain Layout
25053 \begin_inset Formula $\hspace{1cm}\raisebox{5mm}{}\lim_{x\to A}x=B$
25069 \begin_layout Standard
25070 In a displayed formula the limit is set below the formula, as usual:
25071 \begin_inset Formula
25081 \begin_layout Standard
25082 \begin_inset VSpace medskip
25088 \begin_layout Standard
25089 How to adjust the typesetting of the limits see
25090 \begin_inset CommandInset ref
25092 reference "sub:Operator-Limits"
25099 \begin_layout Subsection
25101 \begin_inset Index idx
25104 \begin_layout Plain Layout
25105 Functions ! modulo-
25113 \begin_layout Standard
25114 The modulo-function is special, because it exists in four variants.
25115 The variants in a displayed formula are:
25116 \begin_inset Formula
25118 \underline{\textrm{Command}\raisebox{-0.9mm}{}} & & \underline{\textrm{Result}}\\
25119 \mathrm{a\backslash mod\textrm{␣}b} & & a\mod b\\
25120 \mathrm{a\backslash pmod\textrm{␣}b} & & a\pmod b\\
25121 \mathrm{a\backslash bmod\textrm{␣}b} & & a\bmod b\\
25122 \mathrm{a\backslash pod\textrm{␣}b} & & a\pod b
25130 \begin_layout Standard
25131 In an inline formula less space is set before the function names for all
25133 By default the modulo-functions take only the first following character
25135 To use more than one character, one has to put them into TeX-braces:
25136 \begin_inset Formula
25138 \underline{\textrm{Command}\raisebox{-0.9mm}{}} & & \underline{\textrm{Result}}\\
25139 \mathrm{a\backslash pod\textrm{␣}bcd} & & a\pod bcd\\
25140 \mathrm{a\backslash pod\backslash\{bc\to d} & & a\pod{bc}d
25148 \begin_layout Section
25150 \begin_inset Index idx
25153 \begin_layout Plain Layout
25162 \begin_layout Subsection
25163 Special Characters in Mathematical Text
25166 \begin_layout Standard
25167 The following commands can only be used in mathematical text or in TeX-mode:
25170 \begin_layout Standard
25171 \begin_inset space \hfill{}
25175 \begin_inset Tabular
25176 <lyxtabular version="3" rows="8" columns="2">
25177 <features rotate="0" tabularvalignment="middle">
25178 <column alignment="block" valignment="top">
25179 <column alignment="block" valignment="top">
25181 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
25184 \begin_layout Plain Layout
25190 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
25193 \begin_layout Plain Layout
25201 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
25204 \begin_layout Plain Layout
25212 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
25215 \begin_layout Plain Layout
25216 \begin_inset Formula $\textrm{œ}$
25226 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
25229 \begin_layout Plain Layout
25237 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
25240 \begin_layout Plain Layout
25241 \begin_inset Formula $\textrm{Œ}$
25251 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
25254 \begin_layout Plain Layout
25262 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
25265 \begin_layout Plain Layout
25266 \begin_inset Formula $\textrm{æ}$
25276 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
25279 \begin_layout Plain Layout
25287 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
25290 \begin_layout Plain Layout
25291 \begin_inset Formula $\textrm{Æ}$
25301 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
25304 \begin_layout Plain Layout
25312 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
25315 \begin_layout Plain Layout
25316 \begin_inset Formula $\textrm{\aa}$
25326 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
25329 \begin_layout Plain Layout
25333 \begin_inset Index idx
25336 \begin_layout Plain Layout
25343 \begin_layout Plain Layout
25364 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
25367 \begin_layout Plain Layout
25368 \begin_inset Formula $\textrm{Å}$
25378 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
25381 \begin_layout Plain Layout
25389 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
25392 \begin_layout Plain Layout
25393 \begin_inset Formula $\textrm{ı}$
25407 \begin_inset space \hfill{}
25411 \begin_inset Tabular
25412 <lyxtabular version="3" rows="8" columns="2">
25413 <features rotate="0" tabularvalignment="middle">
25414 <column alignment="block" valignment="top">
25415 <column alignment="center" valignment="top">
25417 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
25420 \begin_layout Plain Layout
25422 \begin_inset Note Note
25425 \begin_layout Plain Layout
25427 \begin_inset space \thinspace{}
25430 mm is used for separation, because otherwise the output will be ¡ and ¿
25441 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
25444 \begin_layout Plain Layout
25452 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
25455 \begin_layout Plain Layout
25463 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
25466 \begin_layout Plain Layout
25467 \begin_inset Formula $\textrm{ø}$
25477 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
25480 \begin_layout Plain Layout
25488 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
25491 \begin_layout Plain Layout
25492 \begin_inset Formula $\textrm{Ø}$
25502 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
25505 \begin_layout Plain Layout
25513 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
25516 \begin_layout Plain Layout
25517 \begin_inset Formula $\textrm{ł}$
25527 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
25530 \begin_layout Plain Layout
25538 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
25541 \begin_layout Plain Layout
25542 \begin_inset Formula $\textrm{Ł}$
25552 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
25555 \begin_layout Plain Layout
25557 \begin_inset space \hspace{}
25562 \begin_inset space \textvisiblespace{}
25570 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
25573 \begin_layout Plain Layout
25574 \begin_inset Formula $\textrm{!`}$
25584 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
25587 \begin_layout Plain Layout
25589 \begin_inset space \hspace{}
25594 \begin_inset space \textvisiblespace{}
25602 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
25605 \begin_layout Plain Layout
25606 \begin_inset Formula $\textrm{?`}$
25616 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
25619 \begin_layout Plain Layout
25627 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
25630 \begin_layout Plain Layout
25631 \begin_inset Formula $\textrm{ȷ}$
25645 \begin_inset space \hfill{}
25651 \begin_layout Standard
25653 \begin_inset Formula $\textrm{\textrm{Å}}$
25657 \begin_inset Formula $\textrm{\textrm{Ø}}$
25660 can also be inserted via the math toolbar button
25661 \begin_inset Graphics
25662 filename ../images/math/digamma.png
25670 \begin_layout Standard
25671 An exception are the commands
25674 \begin_inset space \hspace{}
25683 \begin_inset space \hspace{}
25689 , because they can be inserted in LyX directly to text.
25692 \begin_layout Subsection
25694 \begin_inset CommandInset label
25696 name "sub:Accents-in-Text"
25701 \begin_inset Index idx
25704 \begin_layout Plain Layout
25713 \begin_layout Standard
25714 With the following commands all letters can be accented.
25715 The commands must be inserted in TeX-mode.
25718 \begin_layout Standard
25719 \begin_inset space \hfill{}
25723 \begin_inset Tabular
25724 <lyxtabular version="3" rows="8" columns="2">
25725 <features rotate="0" tabularvalignment="middle">
25726 <column alignment="block" valignment="top">
25727 <column alignment="block" valignment="top">
25729 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
25732 \begin_layout Plain Layout
25738 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
25741 \begin_layout Plain Layout
25749 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
25752 \begin_layout Plain Layout
25756 \begin_inset Quotes grd
25764 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
25767 \begin_layout Plain Layout
25771 \begin_layout Plain Layout
25787 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
25790 \begin_layout Plain Layout
25798 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
25801 \begin_layout Plain Layout
25805 \begin_layout Plain Layout
25821 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
25824 \begin_layout Plain Layout
25828 \begin_inset space \textvisiblespace{}
25836 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
25839 \begin_layout Plain Layout
25843 \begin_layout Plain Layout
25859 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
25862 \begin_layout Plain Layout
25870 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
25873 \begin_layout Plain Layout
25877 \begin_layout Plain Layout
25893 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
25896 \begin_layout Plain Layout
25900 \begin_inset space \textvisiblespace{}
25908 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
25911 \begin_layout Plain Layout
25915 \begin_layout Plain Layout
25931 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
25934 \begin_layout Plain Layout
25938 \begin_inset space \textvisiblespace{}
25946 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
25949 \begin_layout Plain Layout
25953 \begin_layout Plain Layout
25969 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
25972 \begin_layout Plain Layout
25976 \begin_inset space \textvisiblespace{}
25984 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
25987 \begin_layout Plain Layout
25991 \begin_layout Plain Layout
26011 \begin_inset space \hfill{}
26015 \begin_inset Tabular
26016 <lyxtabular version="3" rows="8" columns="2">
26017 <features rotate="0" tabularvalignment="middle">
26018 <column alignment="block" valignment="top">
26019 <column alignment="center" valignment="top">
26021 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
26024 \begin_layout Plain Layout
26030 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
26033 \begin_layout Plain Layout
26041 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
26044 \begin_layout Plain Layout
26048 \begin_inset space \textvisiblespace{}
26056 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
26059 \begin_layout Plain Layout
26063 \begin_layout Plain Layout
26079 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
26082 \begin_layout Plain Layout
26090 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
26093 \begin_layout Plain Layout
26097 \begin_layout Plain Layout
26113 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
26116 \begin_layout Plain Layout
26120 \begin_inset Index idx
26123 \begin_layout Plain Layout
26134 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
26137 \begin_layout Plain Layout
26141 \begin_layout Plain Layout
26157 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
26160 \begin_layout Plain Layout
26168 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
26171 \begin_layout Plain Layout
26175 \begin_layout Plain Layout
26191 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
26194 \begin_layout Plain Layout
26198 \begin_inset space \textvisiblespace{}
26206 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
26209 \begin_layout Plain Layout
26213 \begin_layout Plain Layout
26229 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
26232 \begin_layout Plain Layout
26236 \begin_inset space \textvisiblespace{}
26244 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
26247 \begin_layout Plain Layout
26251 \begin_layout Plain Layout
26267 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
26270 \begin_layout Plain Layout
26274 \begin_inset space \textvisiblespace{}
26282 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
26285 \begin_layout Plain Layout
26289 \begin_layout Plain Layout
26309 \begin_inset space \hfill{}
26315 \begin_layout Standard
26316 \begin_inset VSpace medskip
26325 also two different characters can be accented.
26331 \begin_inset space \textvisiblespace{}
26340 \begin_layout Plain Layout
26352 \begin_layout Standard
26365 can in combination with vowels directly be inserted with the keyboard without
26367 The same applies for the tilde
26371 \begin_layout Plain Layout
26372 This only applies for keyboards where the tilde is defined as accent.
26381 in combination with
26396 \begin_layout Standard
26439 and accents that are inserted directly with the keyboard are also available
26440 in mathematical text.
26441 For the other accents there are special math commands to be used in formulas,
26443 \begin_inset CommandInset ref
26445 reference "sub:Accents-for-one"
26452 \begin_layout Standard
26453 \begin_inset VSpace bigskip
26456 Furthermore, with the command
26463 \begin_inset Index idx
26466 \begin_layout Plain Layout
26474 all numbers and letters can be set into a circle, quasi accented with a
26475 circle, similar to the copyright symbol.
26478 \begin_layout Standard
26480 \begin_inset Tabular
26481 <lyxtabular version="3" rows="3" columns="2">
26482 <features rotate="0" tabularvalignment="middle">
26483 <column alignment="center" valignment="top">
26484 <column alignment="center" valignment="top">
26486 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
26489 \begin_layout Plain Layout
26495 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
26498 \begin_layout Plain Layout
26500 \begin_inset Note Note
26503 \begin_layout Plain Layout
26510 is only used as spacer.
26522 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
26525 \begin_layout Plain Layout
26533 <cell multicolumn="1" alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
26536 \begin_layout Plain Layout
26540 \begin_layout Plain Layout
26556 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
26559 \begin_layout Plain Layout
26570 raisebox{-1.5pt}{W}}
26575 <cell multicolumn="1" alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
26578 \begin_layout Plain Layout
26579 \begin_inset Formula $\raisebox{4.5mm}{}$
26586 \begin_layout Plain Layout
26604 \begin_inset Formula $\raisebox{-2mm}{}$
26620 \begin_layout Standard
26621 One has to take care that the character fits in the circle.
26632 \begin_layout Plain Layout
26634 \begin_inset CommandInset ref
26636 reference "sub:Font-Sizes"
26645 specifies thereby the size of the circle.
26656 \begin_layout Plain Layout
26658 \begin_inset CommandInset ref
26660 reference "sub:Boxes-without-Frame"
26669 the character can be centered.
26672 \begin_layout Subsection
26674 \begin_inset Index idx
26677 \begin_layout Plain Layout
26686 \begin_layout Standard
26687 Old-style figures (also known as old-style numerals) are created with the
26695 \begin_inset Index idx
26698 \begin_layout Plain Layout
26707 The command can be used in formulas and in TeX-mode.
26708 The command scheme is:
26711 \begin_layout Standard
26716 oldstylenums{number}
26719 \begin_layout Standard
26724 oldstylenums{0123456789
26727 \begin_inset Formula $\oldstylenums{0123456789}$
26733 \begin_layout Section
26735 \begin_inset CommandInset label
26737 name "sec:Formula-Styles"
26742 \begin_inset Index idx
26745 \begin_layout Plain Layout
26754 \begin_layout Itemize
26755 There are two different alignment styles:
26759 \begin_layout Description
26760 Centered is the predefined standard
26763 \begin_layout Description
26764 Indented for this the option
26768 must be inserted in the menu
26770 Document\SpecialChar \menuseparator
26776 \begin_inset space ~
26782 \begin_layout Standard
26787 is used, the indentation can be adjusted with the length
26794 \begin_inset Index idx
26797 \begin_layout Plain Layout
26806 Should the distance be 15
26807 \begin_inset space \thinspace{}
26810 mm, the following command line is inserted in the LaTeX-preamble
26813 \begin_layout Standard
26823 \begin_layout Standard
26824 When no length is specified, the predefined value of 30
26825 \begin_inset space \thinspace{}
26832 \begin_layout Itemize
26833 And two different numbering styles:
26837 \begin_layout Description
26838 Right is the predefined standard
26841 \begin_layout Description
26842 Left for this the option
26846 must be inserted in the menu
26848 Document\SpecialChar \menuseparator
26854 \begin_inset space ~
26861 \begin_layout Standard
26870 can also be used together.
26871 In this case both options are inserted, separated by a comma.
26874 \begin_layout Standard
26875 The chosen styles are used for all displayed formulas of the document.
26876 When both, centered and indented formulas should be created in a document,
26882 The indented formulas are then set in a flalign environment, see
26883 \begin_inset CommandInset ref
26885 reference "sub:Flalign-Environment"
26892 \begin_layout Section
26894 \begin_inset CommandInset label
26896 name "sec:Multiline-Formulas"
26901 \begin_inset Index idx
26904 \begin_layout Plain Layout
26905 Formula ! multiline
26913 \begin_layout Subsection
26917 \begin_layout Standard
26918 In LyX multiline formulas are created by pressing
26923 arg "newline-insert newline"
26929 This creates either an
26931 eqnarray environment
26933 that is described in
26934 \begin_inset CommandInset ref
26936 reference "sub:Eqnarray-Environment"
26940 or, when the option
26942 Use AMS math package
26944 in the document settings is selected, an
26948 that is described in
26949 \begin_inset CommandInset ref
26951 reference "sub:Standard-align-Environment"
26956 The align environment is recommended because it provides in any case a
26957 typographically correct output.
26960 \begin_layout Standard
26961 There are other multiline formula environments that can be created via the
26964 Insert\SpecialChar \menuseparator
26968 These environments are described in the following sections.
26971 \begin_layout Standard
26972 In all multiline formula environments a new line is created by pressing
26976 arg "newline-insert newline"
26980 To add or delete lines, the math toolbar buttons
26981 \begin_inset Graphics
26982 filename ../images/tabular-feature_append-row.png
26988 \begin_inset Graphics
26989 filename ../images/tabular-feature_delete-row.png
26994 , respectively, or the menu
26996 Edit\SpecialChar \menuseparator
27002 \begin_layout Subsubsection
27004 \begin_inset CommandInset label
27006 name "sub:Line-Separation"
27011 \begin_inset Index idx
27014 \begin_layout Plain Layout
27015 Formula ! multiline ! Line separation
27023 \begin_layout Standard
27024 There is sometimes not enough space in multiline formulas between the lines:
27025 \begin_inset Formula
27027 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}\\
27028 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
27036 \begin_layout Standard
27037 In LaTeX additional line space is specified as optional argument of the
27039 This is not yet possible in LyX
27043 \begin_layout Plain Layout
27045 \begin_inset CommandInset href
27047 name "LyX-bug #1505"
27048 target "http://www.lyx.org/trac/ticket/1505"
27057 , therefore the whole formula must be inserted in TeX-mode.
27058 To add in our example space, the command
27066 is inserted at the end of the first line.
27071 \begin_layout Plain Layout
27078 \begin_layout Plain Layout
27080 B^{2}(B^{2}-2r_{g}^{2}+2x_{0}^{2}-2r_{k}^{2})+4x_{0}^{2}x^{2}+4x_{0}xD &
27083 textrm{-}4x^{2}B^{2}+4x_{0}xB^{2}
27090 \begin_layout Plain Layout
27094 left(B^{2}+x_{0}^{2}
27102 left(B^{2}-2r_{g}^{2}+2x_{0}^{2}-2r_{k}^{2}
27107 \begin_layout Plain Layout
27119 \begin_layout Standard
27120 \begin_inset VSpace bigskip
27123 To set the line separation for all lines in a formula, the length
27130 \begin_inset Index idx
27133 \begin_layout Plain Layout
27143 \begin_inset Formula $\mbox{line separation}=\mathrm{6\, pt+\backslash jot}$
27154 \begin_inset space \thinspace{}
27159 \begin_inset space \thinspace{}
27162 mm additional line separation as in the previous example, the command
27165 \begin_layout Standard
27175 \begin_layout Standard
27176 is inserted in TeX-mode before the formula.
27177 This requires that the LaTeX-package
27185 \begin_layout Plain Layout
27190 is part of every LaTeX standard installation.
27196 \begin_inset Index idx
27199 \begin_layout Plain Layout
27205 was loaded in LaTeX-preamble with the line
27208 \begin_layout Standard
27216 \begin_layout Standard
27221 \begin_layout Plain Layout
27233 \begin_inset Formula
27235 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}\\
27236 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
27244 \begin_layout Standard
27248 \begin_layout Plain Layout
27259 To get back to the predefined distance,
27265 is set to the value 3
27266 \begin_inset space \thinspace{}
27272 \begin_layout Subsubsection
27274 \begin_inset CommandInset label
27276 name "sub:Column-Separation"
27281 \begin_inset Index idx
27284 \begin_layout Plain Layout
27285 Formula ! multiline ! Column separation
27293 \begin_layout Standard
27294 Multiline formulas form a matrix.
27295 A formula in the eqnarray environment is for example a matrix with three
27297 By changing the column separation in this environment, the space beside
27298 the relation sign can be changed.
27301 \begin_layout Standard
27302 The column separation is specified with the length
27309 \begin_inset Index idx
27312 \begin_layout Plain Layout
27321 \begin_inset Newline newline
27324 column separation = 2
27325 \begin_inset space \thinspace{}
27335 \begin_inset Newline newline
27341 \begin_layout Standard
27351 \begin_layout Standard
27352 inserted in TeX-mode, sets for all following formulas a column separation
27354 \begin_inset space \thinspace{}
27358 To get back to the predefined distance,
27365 \begin_inset space \thinspace{}
27371 \begin_layout Standard
27373 \begin_inset space \thinspace{}
27376 cm column separation:
27380 \begin_layout Plain Layout
27392 \begin_inset Formula
27400 A formula with the predefined column separation for matrices of 10
27401 \begin_inset space \thinspace{}
27408 \begin_layout Plain Layout
27420 \begin_inset Formula
27431 \begin_layout Subsubsection
27433 \begin_inset Index idx
27436 \begin_layout Plain Layout
27445 \begin_layout Standard
27446 Long formulas can be typeset using these methods:
27449 \begin_layout Itemize
27450 When one side of the equation is much shorter than the line width, this
27451 one is chosen for the left side and the right side is typeset over two
27453 \begin_inset Formula
27455 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 \\
27456 & & -\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}
27461 The minus sign at the beginning of the second line does normally not appear
27462 as an operator because it is the first character of the line.
27463 Thus it would not be surrounded by space and could not be distinguished
27464 from the fraction bar.
27466 \begin_inset space \thinspace{}
27469 pt space was inserted behind the minus sign with the command
27479 \begin_layout Plain Layout
27487 \begin_inset CommandInset ref
27489 reference "sub:Variable-Space"
27499 \begin_inset Index idx
27502 \begin_layout Plain Layout
27513 \begin_layout Itemize
27514 When both sides of the equation are too long, the command
27521 \begin_inset Index idx
27524 \begin_layout Plain Layout
27533 It is inserted in the first column of the first line and causes all further
27534 insertions to overwrite the following columns:
27535 \begin_inset Formula
27537 \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 \\
27538 & & -\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 \\
27539 & & =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}
27544 After the insertion of
27550 , the cursor is in a purple box that is a bit shifted to the left from the
27552 In this the formula is inserted.
27553 \begin_inset Newline newline
27556 The content of the further lines is inserted to the second or another formula
27558 The greater the column number where it was inserted, the larger the indentation.
27559 \begin_inset VSpace medskip
27563 \begin_inset Newline newline
27567 \begin_inset Note Greyedout
27570 \begin_layout Plain Layout
27571 Note the following when using
27580 \begin_layout Itemize
27581 The formula doesn't use the full page width.
27583 \begin_inset space \thinspace{}
27587 \begin_inset space \space{}
27591 \begin_inset Formula $-B^{2}$
27594 is added to the first line in the above example, it would have been outside
27596 To better use the width, negative space can be inserted at the beginning
27600 \begin_layout Itemize
27601 Due to a bug in LyX the cursor cannot be set with the mouse into the first
27606 \begin_layout Plain Layout
27607 \begin_inset CommandInset href
27609 name "LyX-bug #1429"
27610 target "http://www.lyx.org/trac/ticket/1429"
27619 One can only set the cursor at the beginning of the line and move it with
27628 \begin_layout Itemize
27629 Other methods to set long formulas are offered by the environments described
27631 \begin_inset CommandInset ref
27633 reference "sub:Multline-Environment"
27638 \begin_inset CommandInset ref
27640 reference "sub:Multiline-Formula-Parts"
27647 \begin_layout Subsubsection
27649 \begin_inset CommandInset label
27651 name "sub:Multiline-Brackets"
27656 \begin_inset Index idx
27659 \begin_layout Plain Layout
27660 Brackets ! for multiline expressions
27668 \begin_layout Standard
27669 For brackets spanning multiple lines the following problem occurs:
27670 \begin_inset Formula
27672 A & = & \sin(x)\left[\prod_{R=1}^{\infty}\frac{1}{R}+\cdots\right.\\
27673 & & \left.\cdots+B-D\right]
27681 \begin_layout Standard
27682 The closing bracket is smaller than the opening bracket because brackets
27683 with variable size may not span multiple lines.
27686 \begin_layout Standard
27687 To set the bracket size for the second line correctly, the first line is
27695 \begin_inset Index idx
27698 \begin_layout Plain Layout
27706 and the second line with
27714 \begin_layout Plain Layout
27728 \begin_inset CommandInset ref
27730 reference "sub:Automatic-Bracket-Size"
27742 \begin_inset Index idx
27745 \begin_layout Plain Layout
27768 \begin_inset space \textvisiblespace{}
27778 \begin_inset space \textvisiblespace{}
27788 \begin_inset space \textvisiblespace{}
27794 \begin_inset Formula $\downarrow$
27800 \begin_inset Index idx
27803 \begin_layout Plain Layout
27811 is inserted, because the multiplication operator with its limits is the
27812 largest symbol in the first line and this should be the size for the bracket
27813 in the second line.
27816 \begin_layout Standard
27817 The result is this:
27818 \begin_inset Formula
27820 A & = & \sin(x)\left[\prod_{R=1}^{\infty}\frac{1}{R}+\cdots\right.\\
27821 & & \left.\vphantom{\prod_{R=1}^{\infty}}\cdots+B-D\right]
27829 \begin_layout Subsection
27833 \begin_layout Standard
27834 Align environments can be used for every kind of multiline formulas.
27835 They are especially useful to set several formulas side by side.
27838 \begin_layout Standard
27839 Align environments consist of columns.
27840 The odd columns are right aligned, the even ones left aligned.
27841 Every line in an Align environment can be numbered.
27844 \begin_layout Standard
27845 Align environments are created via the menu
27847 Insert\SpecialChar \menuseparator
27853 Edit\SpecialChar \menuseparator
27854 Math\SpecialChar \menuseparator
27855 Change Formula Type
27857 already existing formulas can be converted to Align environments.
27860 \begin_layout Standard
27861 To add or delete columns, the math toolbar buttons
27862 \begin_inset Graphics
27863 filename ../images/tabular-feature_append-column.png
27869 \begin_inset Graphics
27870 filename ../images/tabular-feature_delete-column.png
27875 , respectively, or the menu
27877 Edit\SpecialChar \menuseparator
27883 \begin_layout Subsubsection
27884 Standard align Environment
27885 \begin_inset CommandInset label
27887 name "sub:Standard-align-Environment"
27892 \begin_inset Index idx
27895 \begin_layout Plain Layout
27896 Formula ! multiline ! align environment
27904 \begin_layout Standard
27905 This Align environment is created by pressing
27908 arg "newline-insert newline"
27911 in a formula or by the menu
27913 Insert\SpecialChar \menuseparator
27914 Math\SpecialChar \menuseparator
27915 AMS align Environment
27920 \begin_layout Standard
27921 An example for two formulas set side by side, that are created with a four
27922 column align environment:
27923 \begin_inset Formula
27925 A & =\sin(B) & C & =D\\
27926 C & \ne A & B & \ne D
27931 As it can be seen, the formulas in this environment are placed so as if
27940 \begin_layout Plain Layout
27948 \begin_inset CommandInset ref
27950 reference "sub:Variable-Space"
27961 before the first and after every even column.
27962 When the formula style
27968 \begin_layout Plain Layout
27970 \begin_inset CommandInset ref
27972 reference "sec:Formula-Styles"
27983 is used, the formula is set without the
27989 before the first column.
27992 \begin_layout Subsubsection
27993 Alignat Environment
27994 \begin_inset Index idx
27997 \begin_layout Plain Layout
27998 Formula ! multiline ! alignat environment
28006 \begin_layout Standard
28007 The alignat environment has no predefined column separation.
28008 It can be inserted manually with the spaces that are described
28009 \begin_inset CommandInset ref
28011 reference "sub:Space"
28018 \begin_layout Standard
28019 The above example in the alignat environment where 1
28020 \begin_inset space \thinspace{}
28023 cm space was inserted at the beginning of the second formula:
28024 \begin_inset Formula
28025 \begin{alignat*}{2}
28026 A & =\sin(B) & \hspace{1cm}C & =D\\
28027 C & \ne A & B & \ne D
28032 Because the column separation can be set separately for every column, this
28033 environment is especially suitable to set three and more formulas side
28037 \begin_layout Subsubsection
28038 Flalign Environment
28039 \begin_inset CommandInset label
28041 name "sub:Flalign-Environment"
28046 \begin_inset Index idx
28049 \begin_layout Plain Layout
28050 Formula ! multiline ! flalign environment
28058 \begin_layout Standard
28059 In this environment the first two columns are always set as much as possible
28060 to the left and the last two ones to the right.
28062 \begin_inset Formula
28064 A & =1 & B & =2 & C & =3\\
28065 X & =\textrm{-}1 & Y & =\textrm{-}2 & Z & =4
28073 \begin_layout Standard
28074 By creating a flalign environment with an odd number of columns where an
28075 empty TeX-brace is inserted to the last column, several formulas in a document
28076 can be set to the left, although the formula style
28081 As example the indented formula
28082 \begin_inset CommandInset ref
28084 reference "eq:VolInt"
28089 \begin_inset Formula
28091 \hspace{30pt}\iiint\limits _{V}X\,\mathrm{d}V & =U & {}
28096 The first two columns contain the formula.
28097 To indent it as with the formula style
28102 \begin_inset space \thinspace{}
28105 pt space was inserted at the beginning of the first column.
28108 \begin_layout Subsection
28109 Eqnarray Environment
28110 \begin_inset CommandInset label
28112 name "sub:Eqnarray-Environment"
28117 \begin_inset Index idx
28120 \begin_layout Plain Layout
28121 Formula ! multiline ! eqnarray environment
28129 \begin_layout Standard
28130 When this environment has been created, three blue boxes appear.
28131 The content of the first box is right aligned, the content of the last
28133 The content of the middle box appears centered and a bit smaller, because
28134 it is designed to insert there only relation characters.
28135 \begin_inset Formula
28137 \frac{ABC}{D} & \frac{ABC}{D} & \frac{ABC}{D}\\
28147 \begin_layout Subsection
28149 \begin_inset Index idx
28152 \begin_layout Plain Layout
28153 Formula ! multiline ! gather environment
28161 \begin_layout Standard
28162 This environment consists of only one centered column.
28163 Every line can be numbered.
28164 \begin_inset Formula
28175 \begin_layout Subsection
28176 Multline Environment
28177 \begin_inset CommandInset label
28179 name "sub:Multline-Environment"
28184 \begin_inset Index idx
28187 \begin_layout Plain Layout
28188 Formula ! multiline ! multline environment
28196 \begin_layout Standard
28197 The multline environment consists, like the gather environment, of only
28199 But the first line is left aligned, the last one right aligned.
28200 All other lines are centered.
28201 Therefore this environment is suitable for long formulas.
28203 \begin_inset CommandInset ref
28205 reference "eq:lefteqn"
28209 in the multline environment:
28210 \begin_inset Formula
28212 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}\\
28213 -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}\\
28214 =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}}
28222 \begin_layout Standard
28223 In the output only the last (first) line of a multline environment appears
28224 numbered when the document numbering is right (left).
28228 \begin_layout Plain Layout
28229 numbering styles see
28230 \begin_inset CommandInset ref
28232 reference "sec:Formula-Styles"
28244 \begin_layout Standard
28252 \begin_inset Index idx
28255 \begin_layout Plain Layout
28270 \begin_inset Index idx
28273 \begin_layout Plain Layout
28281 a centered line can be right or left aligned, respectively.
28282 The commands are used as follows:
28285 \begin_layout Standard
28290 shoveright{line content}
28296 shoveleft{line content}
28299 \begin_layout Standard
28300 \begin_inset VSpace medskip
28310 \begin_inset Index idx
28313 \begin_layout Plain Layout
28321 specifies the distance of the first line from the left page margin.
28322 Predefined is the length 0
28323 \begin_inset space \thinspace{}
28329 \begin_layout Standard
28330 As example the above formula where the command
28333 \begin_layout Standard
28343 \begin_layout Standard
28344 was inserted in TeX-mode before:
28348 \begin_layout Plain Layout
28360 \begin_inset Formula
28362 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}\\
28363 \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}}\\
28364 =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}}
28373 \begin_layout Plain Layout
28384 The second line was left aligned using
28393 \begin_layout Subsection
28394 Multiline Formula Parts
28395 \begin_inset CommandInset label
28397 name "sub:Multiline-Formula-Parts"
28402 \begin_inset Index idx
28405 \begin_layout Plain Layout
28406 Formula ! multiline ! formula parts
28414 \begin_layout Standard
28415 To display only parts of a formula with multiple lines, one of the following
28416 environments is used:
28433 They can be inserted via the menu
28435 Insert\SpecialChar \menuseparator
28438 or by using the commands described in this section.
28441 \begin_layout Standard
28442 The first three have the same properties as the corresponding multiline
28443 formula environments, but it is possible to set further formula parts beside
28446 \begin_inset Formula
28448 \left.\begin{aligned}\Delta x\Delta p & \ge\frac{\hbar}{2}\\
28449 \Delta E\Delta t & \ge\frac{\hbar}{2}
28451 \right\} \textrm{Uncertainty relations}
28459 \begin_layout Standard
28460 To get this formula, a displayed formula is created where the command
28467 \begin_inset Index idx
28470 \begin_layout Plain Layout
28479 A purple box appears around the blue formula box where now columns and
28480 lines can be added.
28481 Outside the multiline environment other formula parts can be set, like
28485 \begin_layout Standard
28486 The aligned environment is also suitable for long formulas whose lines are
28487 horizontally aligned.
28488 Using aligned in a displayed formula has the advantage that the formula
28489 number is vertically centered behind the lines.
28491 \begin_inset CommandInset ref
28493 reference "eq:shortlong"
28497 in the aligned environment:
28498 \begin_inset Formula
28500 \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}|}\\
28501 & -\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}|}
28510 \begin_layout Standard
28511 To use the environments
28530 \begin_inset Index idx
28533 \begin_layout Plain Layout
28548 \begin_inset Index idx
28551 \begin_layout Plain Layout
28566 \begin_inset Index idx
28569 \begin_layout Plain Layout
28577 are inserted, respectively.
28578 The split environment has the same properties as the aligned environment
28579 but it can only have two columns.
28582 \begin_layout Subsection
28583 Text in multiline Formulas
28584 \begin_inset CommandInset label
28586 name "sub:Text-in-multiline"
28591 \begin_inset Index idx
28594 \begin_layout Plain Layout
28601 \begin_inset Index idx
28604 \begin_layout Plain Layout
28605 Formula ! multiline ! text
28613 \begin_layout Standard
28614 In the Align environments, and the multline and gather environment, text
28615 can be inserted that will appear in a separate line and doesn't affect
28616 the column alignment.
28617 To do this, the command
28624 \begin_inset Index idx
28627 \begin_layout Plain Layout
28635 is used in the following scheme:
28638 \begin_layout Standard
28646 \begin_layout Standard
28647 The text should not be longer than a line because it cannot be hyphenated.
28648 As LyX doesn't yet support
28654 directly, the text is written as mathematical text.
28661 must hereby be at the beginning of a line and appears in the output above
28663 An example where the text was inserted at the beginning of the second line:
28664 \begin_inset Formula
28666 I & =a\sqrt{2}\int_{0}^{2\pi}\sqrt{1+\cos(\phi)}\;\mathrm{d}\phi\\
28667 \intertext{\text{integrand is symmetric to \ensuremath{\phi=\pi}, therefore}} & =2a\sqrt{2}\int_{0}^{\pi}\sqrt{1+\cos(\phi)}\;\mathrm{d}\phi
28675 \begin_layout Section
28677 \begin_inset Index idx
28680 \begin_layout Plain Layout
28687 \begin_inset Index idx
28690 \begin_layout Plain Layout
28691 Formula ! numbering|see
28695 \begin_layout Plain Layout
28706 \begin_layout Plain Layout
28721 \begin_layout Subsection
28725 \begin_layout Standard
28726 Numbered formulas can be created with the menu
28728 Insert\SpecialChar \menuseparator
28729 Math\SpecialChar \menuseparator
28731 \begin_inset space ~
28739 \begin_inset space ~
28745 Existing formulas can be numbered with the menu
28747 Edit\SpecialChar \menuseparator
28748 Math\SpecialChar \menuseparator
28750 \begin_inset space ~
28758 arg "math-number-toggle"
28762 The formula number is displayed in LyX behind the formula as a number sign
28764 The number sign is replaced in the output by the formula number.
28767 \begin_layout Standard
28768 When numbering is turned on in multiline formulas, all lines will be numbered.
28769 But the numbering can be controlled with the menu
28771 Edit\SpecialChar \menuseparator
28772 Math\SpecialChar \menuseparator
28774 \begin_inset space ~
28778 \begin_inset space ~
28782 \begin_inset space ~
28790 arg "math-number-line-toggle"
28796 \begin_layout Standard
28797 Except for inline formulas, all formulas can be numbered with two different
28799 \begin_inset CommandInset ref
28801 reference "sec:Formula-Styles"
28808 \begin_layout Subsection
28810 \begin_inset Index idx
28813 \begin_layout Plain Layout
28814 Cross-references ! to formulas
28822 \begin_layout Standard
28823 All labeled formulas can be cross-referenced.
28824 A label is added by the menu
28826 Insert\SpecialChar \menuseparator
28829 or the toolbar button
28830 \begin_inset Graphics
28831 filename ../images/label-insert.png
28837 The cursor must hereby be inside a displayed formula.
28838 Alternatively you can right-click on the formula and choose
28843 A dialog pops up displaying the prefix
28848 The label is inserted there behind the prefix.
28849 The predefined prefix means
28850 \begin_inset Quotes eld
28854 \begin_inset Quotes erd
28857 and makes it easier to find labels in large documents because it marks
28858 it as formula label to divide it from e.
28859 \begin_inset space \thinspace{}
28863 \begin_inset space \space{}
28867 To change a label, the menu
28869 Insert\SpecialChar \menuseparator
28872 is used again or you right-click on a formula and then on
28879 \begin_layout Standard
28880 The name of the label is displayed in LyX within two parentheses behind
28882 A formula with a label is always numbered.
28885 \begin_layout Standard
28886 Cross-references are inserted via the menu
28888 Insert\SpecialChar \menuseparator
28891 or with the toolbar button
28892 \begin_inset Graphics
28893 filename ../images/dialog-show-new-inset_ref.png
28899 A formula cross-reference appears in the output as formula number.
28900 When in the cross-reference dialog window the format
28904 is chosen, the cross-reference appears in the output as formula number
28906 \begin_inset Newline newline
28909 By right-clicking on a cross-reference in LyX, one jumps to the formula
28910 that is referenced.
28913 \begin_layout Standard
28914 Here are as examples cross-references to formulas of the following subsections:
28915 \begin_inset Note Note
28918 \begin_layout Plain Layout
28919 Note the different cross-reference types.
28927 \begin_layout Standard
28929 \begin_inset CommandInset ref
28936 \begin_inset CommandInset ref
28944 \begin_inset CommandInset ref
28950 ) big Latin letters are used for the numbering in contrary to (
28951 \begin_inset CommandInset ref
28960 \begin_layout Standard
28961 \begin_inset VSpace medskip
28964 When the argument of
28972 \begin_layout Plain Layout
28980 \begin_inset CommandInset ref
28982 reference "sub:User-defined-Numbering"
28993 contains a box like in
28994 \begin_inset CommandInset ref
28996 reference "sub:Paragraph-Boxes"
29000 , the formula cannot be referenced.
29003 \begin_layout Subsection
29005 \begin_inset Index idx
29008 \begin_layout Plain Layout
29009 Formula numbering ! subnumbering
29017 \begin_layout Standard
29018 With the help of the commands
29022 begin{subequations}
29030 formulas can be subnumbered.
29031 Both commands are inserted in TeX-mode.
29034 \begin_layout Standard
29036 \begin_inset Formula
29047 \begin_layout Plain Layout
29051 addtocounter{equation}{-1}
29060 \begin_layout Plain Layout
29064 begin{subequations}
29070 \begin_inset VSpace -5mm
29074 \begin_inset Formula
29082 \begin_inset Formula
29092 \begin_layout Standard
29096 \begin_layout Plain Layout
29108 \begin_layout Standard
29109 To create the example, the following is done:
29112 \begin_layout Enumerate
29113 first formula is inserted
29116 \begin_layout Enumerate
29121 addtocounter{equation}{-1}
29123 begin{subequations}
29124 \begin_inset Index idx
29127 \begin_layout Plain Layout
29136 \begin_inset Newline newline
29141 is inserted after the first formula
29144 \begin_layout Enumerate
29145 second formula is inserted
29148 \begin_layout Enumerate
29149 third formula is inserted
29152 \begin_layout Enumerate
29159 is inserted after the third formula
29162 \begin_layout Standard
29163 Every formula between the commands
29175 is subnumbered as a, b,
29176 \begin_inset Newline linebreak
29179 c, \SpecialChar \ldots{}
29180 For multiline formulas every line will be subnumbered.
29181 All subnumbered formulas are treated as
29186 But as every numbered formula increases the counter
29190 by one, the command
29196 is needed to decrease it.
29197 Otherwise the formulas
29198 \begin_inset CommandInset ref
29205 \begin_inset CommandInset ref
29212 \begin_inset CommandInset ref
29218 would be numbered as
29219 \begin_inset CommandInset ref
29226 \begin_inset CommandInset ref
29233 \begin_inset CommandInset ref
29242 \begin_layout Standard
29243 By inserting the commands in TeX-mode, a space is created between the first
29246 \begin_inset space \thinspace{}
29249 mm vertical space is inserted after the command
29253 begin{subequations}
29256 When the formula style
29262 \begin_layout Plain Layout
29264 \begin_inset CommandInset ref
29266 reference "sec:Formula-Styles"
29278 \begin_inset space \thinspace{}
29281 mm space is inserted instead.
29284 \begin_layout Standard
29285 Here is an example for a multiline formula where the numbering was turned
29286 off for the second line:
29290 \begin_layout Plain Layout
29294 begin{subequations}
29300 \begin_inset Formula
29302 A & = & (B-Z)^{2}=(B-Z)(B-Z)\label{eq:d}\\
29303 & = & B^{2}-ZB-BZ+Z^{2}\nonumber \\
29304 & = & B^{2}-2BZ+Z^{2}\label{eq:f}
29313 \begin_layout Plain Layout
29325 \begin_layout Subsection
29326 User-defined Numbering
29327 \begin_inset CommandInset label
29329 name "sub:User-defined-Numbering"
29334 \begin_inset Index idx
29337 \begin_layout Plain Layout
29338 Formula numbering ! user-defined
29346 \begin_layout Standard
29347 \begin_inset Index idx
29350 \begin_layout Plain Layout
29351 Formula numbering ! self-defined delimiters
29356 With the standard numbering parentheses are set around the formula number.
29357 To replace the parentheses for example by vertical bars, the following
29358 line is added to the LaTeX-preamble:
29361 \begin_layout Standard
29373 \begin_inset Note Note
29376 \begin_layout Plain Layout
29377 This macro is already declared in the LaTeX-preamble for testing.
29378 To activate it, remove the percent sign at the beginning.
29386 \begin_layout Standard
29387 To use other characters, the vertical bars besides the
29391 are replaced by one ore more characters.
29392 To get only the formula number the vertical bars are omitted.
29395 \begin_layout Standard
29396 \begin_inset VSpace bigskip
29399 When there should be an expression of your choice instead of the consecutive
29400 formula number in parentheses behind the formula, the command
29407 \begin_inset Index idx
29410 \begin_layout Plain Layout
29419 \begin_inset Formula
29421 A+B=C\tag{something}\label{eq:tag}
29426 In this example the command
29431 \begin_inset space \textvisiblespace{}
29436 was inserted in the formula.
29439 \begin_layout Standard
29445 \begin_inset space \textvisiblespace{}
29450 is inserted instead, the star prevents the parentheses around the expression:
29451 \begin_inset Formula
29453 A+B=C\tag*{something}
29461 \begin_layout Standard
29462 \begin_inset VSpace bigskip
29465 To restart the formula numbering with new document parts or sections, the
29466 following command is used:
29469 \begin_layout Standard
29474 @addtoreset{equation}{part}
29477 \begin_inset Index idx
29480 \begin_layout Plain Layout
29485 \begin_layout Plain Layout
29496 \begin_layout Plain Layout
29509 \begin_layout Plain Layout
29520 \begin_layout Plain Layout
29533 \begin_inset Newline newline
29537 \begin_inset Newline newline
29544 @addtoreset{equation}{section}
29547 \begin_layout Standard
29548 To be able to use these commands in TeX-mode, the
29549 \begin_inset Quotes eld
29553 \begin_inset Quotes erd
29556 character has to be made
29557 \begin_inset Quotes eld
29561 \begin_inset Quotes erd
29564 for LaTeX using the command
29578 So the command sequence in TeX-mode is:
29581 \begin_layout Standard
29587 \begin_inset Newline newline
29592 @addtoreset{equation}{section}
29593 \begin_inset Newline newline
29601 \begin_layout Standard
29602 In the LaTeX-preamble
29614 can be omitted as they are automatically internally inserted by LyX.
29617 \begin_layout Standard
29632 \begin_layout Plain Layout
29637 is part of the LaTeX-package
29642 \begin_inset Index idx
29645 \begin_layout Plain Layout
29646 Packages ! carlisle
29651 that is part of every LaTeX standard installation.
29657 \begin_inset Index idx
29660 \begin_layout Plain Layout
29661 Packages ! remreset
29666 has to be loaded in the LaTeX-preamble with the line
29669 \begin_layout Standard
29674 usepackage{remreset}
29677 \begin_layout Standard
29685 \begin_inset Index idx
29688 \begin_layout Plain Layout
29693 \begin_layout Plain Layout
29704 \begin_layout Plain Layout
29717 \begin_layout Plain Layout
29728 \begin_layout Plain Layout
29740 can be used with the same scheme as
29749 \begin_layout Standard
29750 \begin_inset VSpace bigskip
29753 Sometimes formulas should be numbered in the following form:
29756 \begin_layout Standard
29759 (section number.formula number)
29762 \begin_layout Standard
29763 The formula number should start with every section with
29764 \begin_inset Quotes eld
29768 \begin_inset Quotes erd
29774 \begin_layout Standard
29775 For this case there is the command
29782 \begin_inset Index idx
29785 \begin_layout Plain Layout
29793 , which is used with the following scheme:
29796 \begin_layout Standard
29801 numberwithin{counter}{sectioning}
29804 \begin_layout Standard
29805 Counter denotes what kind of numbering is affected, sectioning denotes what
29806 number is before the dot.
29809 \begin_layout Standard
29810 Thus in our case the following LaTeX-preamble or TeX code line is used:
29813 \begin_layout Standard
29818 numberwithin{equation}{section}
29821 \begin_layout Standard
29822 This is the result:
29826 \begin_layout Plain Layout
29830 numberwithin{equation}{section}
29836 \begin_inset Formula
29846 \begin_layout Standard
29848 \begin_inset space \thinspace{}
29852 \begin_inset space \space{}
29855 tables so that the number of the part is the sectioning,
29856 \begin_inset Newline newline
29863 numberwithin{table}{part}
29868 \begin_layout Standard
29869 To go back to the standard numbering or to prevent this kind of numbering
29870 when it is defined by the document class, the following command is inserted
29871 as TeX code or to the LaTeX-preamble:
29874 \begin_layout Standard
29884 \begin_inset Index idx
29887 \begin_layout Plain Layout
29901 \begin_layout Plain Layout
29917 \begin_inset Newline newline
29925 \begin_inset Newline newline
29937 \begin_layout Standard
29944 uses internally the command
29950 , described above, that also needs to be reverted.
29954 \begin_layout Plain Layout
29961 \begin_layout Plain Layout
29965 @removefromreset{equation}{section}
29968 \begin_layout Plain Layout
29980 \begin_layout Subsection
29981 Numbering with Roman Numbers and Letters
29982 \begin_inset Index idx
29985 \begin_layout Plain Layout
29986 Formula numbering ! with letters
29992 \begin_inset Index idx
29995 \begin_layout Plain Layout
29996 Formula numbering ! with Roman numbers
30004 \begin_layout Standard
30005 Formulas can also be numbered with Roman numbers and Latin letters.
30006 To number for example with small Roman numbers, the command
30009 \begin_layout Standard
30021 \begin_layout Standard
30022 is inserted before the formula in TeX-mode.
30030 \begin_inset Index idx
30033 \begin_layout Plain Layout
30041 redefines the predefined command
30057 \begin_layout Plain Layout
30064 has the same scheme like the command
30070 that is described in
30071 \begin_inset CommandInset ref
30073 reference "sub:The-Command-newcommand"
30086 is the formula counter.
30093 is used as prefix for a counter, the value of the counter is output as
30095 When a formula is numbered, LaTeX sets internally the command
30101 behind the formula.
30107 \begin_inset Index idx
30110 \begin_layout Plain Layout
30120 outputs the counter as small Roman number.
30123 \begin_layout Standard
30124 All formulas behind the command
30134 are now numbered Roman.
30135 To switch to numbering with big Roman numbers, the command is inserted
30149 \begin_inset Index idx
30152 \begin_layout Plain Layout
30164 \begin_inset Quotes eld
30168 \begin_inset Quotes erd
30171 with small Latin letters there is the command
30178 \begin_inset Index idx
30181 \begin_layout Plain Layout
30189 , for big ones there is the command
30196 \begin_inset Index idx
30199 \begin_layout Plain Layout
30212 \begin_layout Standard
30213 \begin_inset Note Greyedout
30216 \begin_layout Plain Layout
30223 \begin_inset space ~
30226 formulas can be numbered with Latin letters in one document.
30234 \begin_layout Standard
30238 \begin_layout Plain Layout
30254 \begin_layout Standard
30255 \begin_inset Formula
30257 A=\textrm{small roman}
30266 \begin_layout Plain Layout
30280 \begin_inset Formula
30282 B=\textrm{big Roman}\label{eq:Rom}
30291 \begin_layout Plain Layout
30305 \begin_inset Formula
30307 C=\textrm{small Latin}
30316 \begin_layout Plain Layout
30330 \begin_inset Formula
30332 D=\textrm{big Latin}\label{eq:Lat}
30340 \begin_layout Standard
30341 To switch back to the default numbering, insert the command:
30344 \begin_layout Standard
30354 \begin_inset Index idx
30357 \begin_layout Plain Layout
30368 \begin_layout Standard
30372 \begin_layout Plain Layout
30386 \begin_inset Formula
30396 \begin_layout Standard
30397 \begin_inset VSpace medskip
30400 As you see, formulas are numbered serially independent from the numbering
30402 When then numbering should start with
30403 \begin_inset Quotes eld
30407 \begin_inset Quotes erd
30410 when the style is changed, new equation counters have to be defined.
30411 A description about this can be found in the file
30412 \begin_inset CommandInset href
30414 name "Formula-numbering.lyx"
30415 target "run:Formula-numbering.lyx"
30422 \begin_layout Standard
30423 \begin_inset Newpage newpage
30429 \begin_layout Section
30430 Chemical Symbols and Equations
30431 \begin_inset CommandInset label
30433 name "sub:Chemical-Symbols-and"
30438 \begin_inset Index idx
30441 \begin_layout Plain Layout
30442 Chemical characters ! Symbols
30448 \begin_inset Index idx
30451 \begin_layout Plain Layout
30458 \begin_inset Index idx
30461 \begin_layout Plain Layout
30470 \begin_layout Standard
30471 An example text from chemistry:
30474 \begin_layout Quote
30476 \begin_inset Formula $\mathrm{SO_{4}^{2-}}$
30479 -ion reacts with two
30480 \begin_inset Formula $\mathrm{Na^{+}}$
30483 -ions to sodium sulfate
30484 \begin_inset Formula $\left(\mathrm{Na_{2}SO_{4}}\right)$
30488 The chemical equation for this is:
30489 \begin_inset Formula
30491 \mathrm{2\, Na^{+}+SO_{4}^{2-}\longrightarrow Na_{2}SO_{4}}\label{eq:chem-reaction}
30499 \begin_layout Standard
30500 This chemical equation can directly be created as formula.
30501 To avoid that the symbols appear italic, everything is highlighted and
30502 changed by the shortcut
30508 to the upright font style.
30512 \begin_layout Plain Layout
30518 \begin_inset CommandInset ref
30520 reference "sub:Font-Styles"
30532 \begin_layout Standard
30533 A more convenient way to typeset chemical formulas is to use the command
30541 \begin_inset Index idx
30544 \begin_layout Plain Layout
30552 that is available when the LaTeX-package
30557 \begin_inset Index idx
30560 \begin_layout Plain Layout
30573 to a formula a new blue box appears where chemical formulas can be inserted
30574 in an intuitive way.
30577 \begin_layout Standard
30579 \begin_inset Tabular
30580 <lyxtabular version="3" rows="9" columns="2">
30581 <features rotate="0" tabularvalignment="middle">
30582 <column alignment="center" valignment="top">
30583 <column alignment="center" valignment="top">
30585 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
30588 \begin_layout Plain Layout
30594 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
30597 \begin_layout Plain Layout
30599 \begin_inset Note Note
30602 \begin_layout Plain Layout
30609 is only used as spacer.
30621 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
30624 \begin_layout Plain Layout
30628 \begin_inset space \textvisiblespace{}
30636 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
30639 \begin_layout Plain Layout
30640 \begin_inset Formula $\raisebox{4.5mm}{}\ce{H2CO3}\raisebox{-2mm}{}$
30650 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
30653 \begin_layout Plain Layout
30657 \begin_inset space \textvisiblespace{}
30665 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
30668 \begin_layout Plain Layout
30669 \begin_inset Formula $\raisebox{5mm}{}\ce{SO4^{2-}}\raisebox{-2mm}{}$
30679 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
30682 \begin_layout Plain Layout
30686 \begin_inset space \textvisiblespace{}
30694 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
30697 \begin_layout Plain Layout
30698 \begin_inset Formula $\raisebox{4.5mm}{}\ce{(NH4)2S}\raisebox{-2mm}{}$
30708 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
30711 \begin_layout Plain Layout
30715 \begin_inset space \textvisiblespace{}
30723 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
30726 \begin_layout Plain Layout
30727 \begin_inset Formula $\raisebox{4.5mm}{}\ce{KCr(SO4)2.12H2O}\raisebox{-2mm}{}$
30737 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
30740 \begin_layout Plain Layout
30744 \begin_inset space \textvisiblespace{}
30750 \begin_inset space \textvisiblespace{}
30756 \begin_inset space \textvisiblespace{}
30764 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
30767 \begin_layout Plain Layout
30768 \begin_inset Formula $\raisebox{4.5mm}{}\ce{A-B\dbond C\tbond D}\raisebox{-2mm}{}$
30778 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
30781 \begin_layout Plain Layout
30785 \begin_inset space \textvisiblespace{}
30789 \begin_inset Formula $\downarrow$
30793 \begin_inset Formula $\to$
30801 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
30804 \begin_layout Plain Layout
30805 \begin_inset Formula $\raisebox{5mm}{}\ce{_{90}^{227}Th+}\raisebox{-2mm}{}$
30815 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
30818 \begin_layout Plain Layout
30822 \begin_inset space \textvisiblespace{}
30826 \begin_inset space \textvisiblespace{}
30830 \begin_inset space \textvisiblespace{}
30834 \begin_inset space \textvisiblespace{}
30838 \begin_inset space \textvisiblespace{}
30846 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
30849 \begin_layout Plain Layout
30850 \begin_inset Formula $\raisebox{4.5mm}{}\ce{CO2 + C <=> 2CO}\raisebox{-2mm}{}$
30860 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
30863 \begin_layout Plain Layout
30867 \begin_inset space \textvisiblespace{}
30871 \begin_inset space \textvisiblespace{}
30875 \begin_inset space \textvisiblespace{}
30879 \begin_inset space \textvisiblespace{}
30887 \begin_inset space \textvisiblespace{}
30895 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
30898 \begin_layout Plain Layout
30899 \begin_inset Formula $\raisebox{5mm}{}\ce{CO2 + C ->[\alpha][\beta] 2CO}\raisebox{-4mm}{}$
30915 \begin_layout Standard
30916 \begin_inset Note Greyedout
30919 \begin_layout Plain Layout
30925 Inserting a formula to a
30931 box will lead to LaTeX errors due to a LyX bug.
30937 \begin_layout Plain Layout
30938 \begin_inset CommandInset href
30940 name "LyX-bug #8566"
30941 target "http://www.lyx.org/trac/ticket/8566"
30952 In this case TeX code has to be used like for
30966 \begin_layout Plain Layout
30987 \begin_layout Standard
30988 \begin_inset Note Greyedout
30991 \begin_layout Plain Layout
30997 It is not possible in LyX to use the character ^ to get an up-arrow as
31003 One instead uses a negative thin space followed by the command
31010 \begin_inset Formula $\ce{Fe + 2H+ -> Fe^{2+} + H2\negthinspace\uparrow}$
31021 \begin_layout Standard
31028 the command for equation
31029 \begin_inset space ~
31033 \begin_inset CommandInset ref
31035 reference "eq:chem-reaction"
31040 \begin_inset Newline newline
31048 \begin_inset space \textvisiblespace{}
31052 \begin_inset space \textvisiblespace{}
31056 \begin_inset space \textvisiblespace{}
31060 \begin_inset space \textvisiblespace{}
31064 \begin_inset space \textvisiblespace{}
31068 \begin_inset space \textvisiblespace{}
31074 \begin_layout Standard
31075 To create multiline chemical equations first a multiline formula is created
31077 \begin_inset CommandInset ref
31079 reference "sec:Multiline-Formulas"
31084 Afterwards the command
31090 is used in every small blue box of the formula.
31092 \begin_inset CommandInset ref
31094 reference "eq:TEOS-reaction-1"
31099 \begin_inset CommandInset ref
31101 reference "eq:TEOS-reaction-2"
31105 are an example of a multi-stage chemical reaction where every equation
31106 has its own number.
31107 \begin_inset Formula
31109 \ce{TEOS + 4O} & \ce{->} & \ce{Si(OH)4 + 4C2H4O}\label{eq:TEOS-reaction-1}\\
31110 \ce{Si(OH)4} & \ce{->} & \ce{SiO2 + 2H2O}\label{eq:TEOS-reaction-2}
31118 \begin_layout Standard
31129 package provides the command
31136 \begin_inset Index idx
31139 \begin_layout Plain Layout
31147 that has to be used for special cases.
31148 For more information about
31154 and more examples have a look at the documentation of
31159 \begin_inset CommandInset citation
31168 \begin_layout Section
31172 \begin_layout Standard
31173 LyX supports two types of commutative diagrams:
31181 that are explained in the following.
31184 \begin_layout Subsection
31186 \begin_inset Index idx
31189 \begin_layout Plain Layout
31198 \begin_layout Standard
31199 Diagrams of this type visualize relations by vertical and horizontal lines
31201 \begin_inset Formula
31203 \begin{CD}A@>>>B@>>>C\\
31214 \begin_layout Standard
31215 To get them, the command
31220 \begin_inset Index idx
31223 \begin_layout Plain Layout
31233 is inserted to a formula.
31234 A blue box appears with two dashed lines where further commands can be
31239 arg "newline-insert newline"
31242 a new line is created.
31243 Horizontal relations are inserted in odd, vertical in even formula lines.
31246 \begin_layout Standard
31247 To create the relations there are the following commands:
31250 \begin_layout Itemize
31255 creates a left arrow,
31266 \begin_layout Itemize
31271 creates an up arrow,
31279 a vertical equal sign
31282 \begin_layout Itemize
31288 is a placeholder for non-existent relations
31291 \begin_layout Standard
31292 All arrows can be labeled as follows:
31295 \begin_layout Itemize
31296 If text inserted between the first and second < or >, resp., it is placed
31298 When it is inserted between the second and third one, it appears under
31302 \begin_layout Itemize
31303 When text for vertical arrows is inserted between the first and second A
31304 or V, resp., it is placed left beside the arrow.
31305 When it is inserted between the second and third one, it appears right
31307 If the text contains an A or V, these letters must be set into a TeX-brace.
31310 \begin_layout Standard
31311 As example a diagram with all possible relations:
31314 \begin_layout Standard
31315 \begin_inset Formula
31317 \begin{CD}A@>j>>B@>>k>C@=F\\
31328 \begin_layout Standard
31329 The command for this is:
31330 \begin_inset Newline newline
31338 \begin_inset space \textvisiblespace{}
31341 A@>j>>B@>>k>C@=F Ctrl+Return
31342 \begin_inset Newline newline
31346 \begin_inset Phantom HPhantom
31349 \begin_layout Plain Layout
31355 \begin_inset space \textvisiblespace{}
31368 \begin_inset Formula $\to$
31374 \begin_inset Newline newline
31378 \begin_inset Phantom HPhantom
31381 \begin_layout Plain Layout
31387 \begin_inset space \textvisiblespace{}
31398 \begin_layout Subsection
31400 \begin_inset Index idx
31403 \begin_layout Plain Layout
31404 Diagrams ! xymatrix
31412 \begin_layout Standard
31413 To be able to use xymatrices, the LaTeX-package
31418 A xymatrix is created by inserting the command
31425 Then you are able to add new matrix columns and rows like for normal matrices,
31427 \begin_inset CommandInset ref
31429 reference "sec:Matrices"
31436 \begin_layout Standard
31437 In contrary to amscd diagrams, xymatrices supports diagonal and curved arrows,
31439 All possibilities to create commutative diagrams and decorations are explained
31444 that you find in the menu
31446 Help\SpecialChar \menuseparator
31448 \begin_inset space ~
31456 \begin_layout Subsection
31462 \begin_inset Index idx
31465 \begin_layout Plain Layout
31474 \begin_layout Standard
31479 -diagrams, the LaTeX-package
31488 -diagram is created by inserting the command
31495 Then you are able to add new matrix columns and rows like for normal matrices,
31497 \begin_inset CommandInset ref
31499 reference "sec:Matrices"
31506 \begin_layout Standard
31507 Examples how to create
31511 diagrams in LyX is given in the
31513 Feynman-diagram manual
31515 that you find in the menu
31517 Help\SpecialChar \menuseparator
31519 \begin_inset space ~
31527 \begin_layout Standard
31528 \begin_inset Newpage newpage
31534 \begin_layout Section
31535 User-defined Commands
31536 \begin_inset Index idx
31539 \begin_layout Plain Layout
31540 User-defined commands
31548 \begin_layout Standard
31549 \begin_inset Note Greyedout
31552 \begin_layout Plain Layout
31557 The names of user-defined commands and macros may only consist of Latin
31566 \begin_layout Subsection
31570 \begin_inset CommandInset label
31572 name "sub:The-Command-newcommand"
31577 \begin_inset Index idx
31580 \begin_layout Plain Layout
31581 User-defined commands !
31589 \begin_inset Index idx
31592 \begin_layout Plain Layout
31603 \begin_layout Standard
31604 Many LaTeX-commands are too long to be used frequently.
31605 But it is possible to define with the command
31611 new shorter commands.
31614 \begin_layout Standard
31615 The command scheme of
31624 \begin_layout Standard
31629 newcommand{new command name}[number of arguments][optional
31634 \begin_inset Newline newline
31638 \begin_inset Phantom HPhantom
31641 \begin_layout Plain Layout
31651 {command definition}
31654 \begin_layout Standard
31655 \begin_inset Note Greyedout
31658 \begin_layout Plain Layout
31663 Assure that the name of the new command is not already used in your document
31664 or by LaTeX-packages that you use.
31665 When you for example define the command
31677 , you get an error message because
31683 is already defined as command for
31684 \begin_inset Quotes eld
31688 \begin_inset Formula $\le$
31692 \begin_inset Quotes erd
31703 \begin_layout Standard
31704 The number of arguments is an integer in the range 0
31705 \begin_inset space \thinspace{}
31709 \begin_inset space \thinspace{}
31712 9 and specifies how many arguments the new command should have.
31713 With the optional value a value for an optional argument can be predefined.
31714 When this is done, the
31722 rgument of the new command is automatically an optional one.
31725 \begin_layout Standard
31726 Here are some examples:
31729 \begin_layout Itemize
31730 To define the command
31742 , the LaTeX-preamble line is:
31743 \begin_inset VSpace medskip
31747 \begin_inset Newline newline
31761 \begin_layout Itemize
31762 To define the command
31774 , the argument (that should be underlined) must be taken into account.
31775 For this the preamble line is:
31776 \begin_inset VSpace medskip
31780 \begin_inset Newline newline
31794 \begin_inset VSpace medskip
31798 \begin_inset Newline newline
31805 acts as argument placeholder, the
31809 behind it denotes that it is the placeholder for the first argument.
31812 \begin_layout Itemize
31820 \begin_inset space \thinspace{}
31824 \begin_inset space \space{}
31834 \begin_inset VSpace medskip
31838 \begin_inset Newline newline
31849 framebox#1#2{$#3$}}
31852 \begin_inset VSpace medskip
31856 \begin_inset Newline newline
31859 The two Dollar signs creates the extra formula needed for
31866 \begin_inset CommandInset ref
31868 reference "sub:Boxes-with-Frame"
31875 \begin_layout Itemize
31876 To create a new command for
31882 where the color for the box need not be specified, the argument for the
31883 color is defined optional:
31884 \begin_inset VSpace medskip
31888 \begin_inset Newline newline
31899 fcolorbox{#2}{#1}{$#3$}}
31902 \begin_inset VSpace medskip
31906 \begin_inset Newline newline
31909 When the color is not specified when using
31915 , the predefined color
31922 \begin_layout Standard
31923 A test of the new defined commands:
31926 \begin_layout Standard
31928 \begin_inset Tabular
31929 <lyxtabular version="3" rows="6" columns="2">
31930 <features rotate="0" tabularvalignment="middle">
31931 <column alignment="center" valignment="top">
31932 <column alignment="center" valignment="top">
31934 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
31937 \begin_layout Plain Layout
31943 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
31946 \begin_layout Plain Layout
31948 \begin_inset Note Note
31951 \begin_layout Plain Layout
31958 is only used as spacer.
31970 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
31973 \begin_layout Plain Layout
31977 \begin_inset space \textvisiblespace{}
31985 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
31988 \begin_layout Plain Layout
31989 \begin_inset Formula $A\gr B$
31999 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
32002 \begin_layout Plain Layout
32010 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
32013 \begin_layout Plain Layout
32014 \begin_inset Formula $\raisebox{4.5mm}{}\us{ABcd}\raisebox{-2mm}{}$
32024 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
32027 \begin_layout Plain Layout
32031 \begin_inset Formula $\to$
32037 \begin_inset Formula $\to$
32045 \begin_inset space \textvisiblespace{}
32053 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
32056 \begin_layout Plain Layout
32057 \begin_inset Formula $\raisebox{6mm}{}\fb{[2cm]}{}{\int A=B}\raisebox{-4mm}{}$
32067 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
32070 \begin_layout Plain Layout
32074 \begin_inset Formula $\to$
32082 \begin_inset space \textvisiblespace{}
32090 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
32093 \begin_layout Plain Layout
32094 \begin_inset Formula $\raisebox{6mm}{}\cb{red}{\int A=B}\raisebox{-4mm}{}$
32104 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
32107 \begin_layout Plain Layout
32113 \begin_inset Formula $\to$
32121 \begin_inset space \textvisiblespace{}
32129 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
32132 \begin_layout Plain Layout
32133 \begin_inset Formula $\raisebox{6mm}{}\cb[green]{red}{\int A=B}\raisebox{-4mm}{}$
32149 \begin_layout Subsection
32151 \begin_inset Index idx
32154 \begin_layout Plain Layout
32155 User-defined commands! Math macros
32161 \begin_inset Index idx
32164 \begin_layout Plain Layout
32173 \begin_layout Standard
32174 User-defined commands are especially convenient for complex expressions.
32175 When you are for example dealing with a document that has quadratic equations,
32176 the same solution type occurs several times.
32177 The general form of a quadratic equation is
32178 \begin_inset Formula
32180 0=\lambda^{2}+p\lambda+q
32185 The general form of the solution is
32186 \begin_inset Formula
32188 \lambda_{1,2}=-\frac{p}{2}\pm\sqrt{\frac{p²}{4}-q}
32196 \begin_layout Standard
32197 To define a command for the solution formula where only the three parameters
32199 \begin_inset Formula $\lambda$
32203 \begin_inset Formula $p$
32207 \begin_inset Formula $q$
32210 need to be specified and the index of
32211 \begin_inset Formula $\lambda$
32214 can be given optionally, the LaTeX-preamble line is
32215 \begin_inset Newline newline
32231 \begin_inset Newline newline
32235 \begin_inset Phantom HPhantom
32238 \begin_layout Plain Layout
32252 frac{#3^{2}}{4}-#4}}
32255 \begin_layout Standard
32256 To create with this the solution formula, the command
32257 \begin_inset Newline newline
32267 \begin_inset Formula $\to$
32273 \begin_inset Formula $\to$
32280 is inserted to a formula
32285 \begin_layout Standard
32286 The definition of the new command is unintuitive because one has to know
32287 the schemes of all used LaTeX commands, e.
32288 \begin_inset space \thinspace{}
32292 \begin_inset space \space{}
32295 that a fraction is inserted in LaTeX as
32299 frac{numerator}{denominator}
32302 Furthermore one can easily forget a brace in the definition and cannot
32303 see in LyX what the new command is doing.
32304 To avoid these problems LyX offers the possibility to use math macros instead
32314 \begin_layout Standard
32315 A math macro is created by using the menu
32317 Insert\SpecialChar \menuseparator
32318 Math\SpecialChar \menuseparator
32321 or the toolbar button
32322 \begin_inset Graphics
32323 filename ../images/math-macro_newmacroname_newcommand.png
32329 The math macro toolbar appears together with the following box where the
32331 \begin_inset Newline newline
32335 \begin_inset space \hspace*{\fill}
32339 \begin_inset Graphics
32340 filename clipart/macrobox.png
32345 \begin_inset space \hspace*{\fill}
32349 \begin_inset Newline newline
32353 \begin_inset FormulaMacro
32354 \newcommand{\qG}[4][1,\,2]{#2_{#1}=-\frac{#3}{2}\pm\sqrt{\frac{#3^{2}}{4}-#4}}
32359 newmacroname is the default name of the macro that should be changed to
32360 something sensible.
32361 The wanted formula is inserted in the first blue box.
32362 An argument placeholder is inserted with the command
32369 \begin_inset space \thinspace{}
32373 \begin_inset space \space{}
32382 or by using the macro toolbar button
32383 \begin_inset Graphics
32384 filename ../images/math-macro-add-param.png
32390 Argument placeholders are displayed red.
32392 \begin_inset space ~
32395 arguments are possible.
32396 Optional arguments are created with the toolbar button
32397 \begin_inset Graphics
32398 filename ../images/math-macro-add-optional-param.png
32404 The first non-optional argument can be transformed to an optional one with
32406 \begin_inset Graphics
32407 filename ../images/math-macro-make-optional.png
32413 In the second blue box the appearance of the macro in LyX can be defined.
32414 Normally you want to see it as it is defined, so the box is kept empty.
32415 But when you have created a macro that needs lot of space on the screen,
32416 you can insert in the box for example
32417 \begin_inset Newline newline
32447 \begin_inset Newline newline
32452 For the macro only the arguments with the macro name in front of them will
32453 then be displayed in LyX, leading to a better overview.
32454 The formula appears in the output as defined in the first box.
32455 \begin_inset Newline newline
32458 The appearance of macros in formulas can furthermore be changed for single
32459 macros by setting the cursor in the macro and using the menu
32461 View\SpecialChar \menuseparator
32463 \begin_inset space ~
32467 \begin_inset space ~
32475 \begin_layout Standard
32476 To use a macro, the macro name is inserted as command to a formula, in our
32484 Our macro looks in LyX like this:
32485 \begin_inset Newline newline
32489 \begin_inset space \hspace*{\fill}
32493 \begin_inset Graphics
32494 filename clipart/macrouse.png
32499 \begin_inset space \hspace*{\fill}
32503 \begin_inset Newline newline
32506 Here is our macro example with the arguments
32507 \begin_inset Formula $x$
32511 \begin_inset Formula $\ln(x)$
32515 \begin_inset Formula $B$
32521 \begin_layout Standard
32522 \begin_inset Formula
32532 \begin_layout Standard
32533 LyX offers in the menu
32535 Tools\SpecialChar \menuseparator
32536 Preferences\SpecialChar \menuseparator
32537 Editing\SpecialChar \menuseparator
32540 different styles to edit macros.
32541 To find the style that suits you the most, choose a style and set the cursor
32542 in a macro formula to see the difference.
32545 \begin_layout Standard
32546 A math macro is transformed internally to a
32552 command when exporting the document.
32559 command is not placed in the LaTeX-preamble, therefore macros can only
32560 be used in formulas that are in the document below the macro definition
32564 \begin_layout Standard
32565 Math macros can also be directly created from a
32572 When writing for example the command
32575 \begin_inset Newline newline
32584 xleftarrow[#2]{#1}}
32585 \begin_inset Newline newline
32590 in LyX as normal text, highlighting it completely and using then the shortcut
32595 , the command will be transformed to a math macro.
32596 Using this method you need to be careful that the
32602 command is typed correctly, otherwise you get a faulty macro leading to
32606 \begin_layout Standard
32607 Math macros currently have the problem that further formulas in macro definition
32608 s are handled wrongly.
32609 Therefore the example
32616 \begin_inset CommandInset ref
32618 reference "sub:The-Command-newcommand"
32622 cannot be created as macro.
32625 \begin_layout Standard
32626 When the cursor is in a macro definition box, you will see the macro toolbar
32630 \begin_layout Standard
32631 \begin_inset VSpace defskip
32637 \begin_layout Standard
32638 \begin_inset Graphics
32639 filename clipart/MacroToolbar.png
32644 \begin_inset Index idx
32647 \begin_layout Plain Layout
32656 \begin_layout Standard
32657 \begin_inset VSpace defskip
32663 \begin_layout Standard
32664 The macro toolbar contains from left to right the following buttons:
32667 \begin_layout Standard
32668 \begin_inset VSpace defskip
32674 \begin_layout Standard
32675 \begin_inset Tabular
32676 <lyxtabular version="3" rows="9" columns="2">
32677 <features rotate="0" islongtable="true" longtabularalignment="center">
32678 <column alignment="left" valignment="top">
32679 <column alignment="left" valignment="top" width="85col%">
32680 <row interlinespace="2.5mm">
32681 <cell alignment="center" valignment="top" usebox="none">
32684 \begin_layout Plain Layout
32685 \begin_inset Graphics
32686 filename ../images/math-macro-remove-param.png
32687 rotateOrigin center
32696 <cell alignment="center" valignment="top" usebox="none">
32699 \begin_layout Plain Layout
32702 Edit\SpecialChar \menuseparator
32703 Math\SpecialChar \menuseparator
32705 \begin_inset space ~
32708 Definition\SpecialChar \menuseparator
32709 Remove Last Argument
32715 <row interlinespace="2.5mm">
32716 <cell alignment="center" valignment="top" usebox="none">
32719 \begin_layout Plain Layout
32720 \begin_inset Graphics
32721 filename ../images/math-macro-add-param.png
32722 rotateOrigin center
32731 <cell alignment="center" valignment="top" usebox="none">
32734 \begin_layout Plain Layout
32737 Edit\SpecialChar \menuseparator
32738 Math\SpecialChar \menuseparator
32740 \begin_inset space ~
32743 Definition\SpecialChar \menuseparator
32750 <row interlinespace="2.5mm">
32751 <cell alignment="center" valignment="top" usebox="none">
32754 \begin_layout Plain Layout
32755 \begin_inset Graphics
32756 filename ../images/math-macro-make-optional.png
32757 rotateOrigin center
32766 <cell alignment="center" valignment="top" usebox="none">
32769 \begin_layout Plain Layout
32772 Edit\SpecialChar \menuseparator
32773 Math\SpecialChar \menuseparator
32775 \begin_inset space ~
32778 Definition\SpecialChar \menuseparator
32779 Make First Non-Optional into
32780 \begin_inset Newline newline
32784 \begin_inset Phantom HPhantom
32787 \begin_layout Plain Layout
32790 Edit\SpecialChar \menuseparator
32791 Math\SpecialChar \menuseparator
32793 \begin_inset space ~
32796 Definition\SpecialChar \menuseparator
32808 <row interlinespace="2.5mm">
32809 <cell alignment="center" valignment="top" usebox="none">
32812 \begin_layout Plain Layout
32813 \begin_inset Graphics
32814 filename ../images/math-macro-make-nonoptional.png
32815 rotateOrigin center
32824 <cell alignment="center" valignment="top" usebox="none">
32827 \begin_layout Plain Layout
32830 Edit\SpecialChar \menuseparator
32831 Math\SpecialChar \menuseparator
32833 \begin_inset space ~
32836 Definition\SpecialChar \menuseparator
32837 Make Last Optional into
32838 \begin_inset Newline newline
32842 \begin_inset Phantom HPhantom
32845 \begin_layout Plain Layout
32848 Edit\SpecialChar \menuseparator
32849 Math\SpecialChar \menuseparator
32851 \begin_inset space ~
32854 Definition\SpecialChar \menuseparator
32860 Non-Optional Argument
32866 <row interlinespace="2.5mm">
32867 <cell alignment="center" valignment="top" usebox="none">
32870 \begin_layout Plain Layout
32871 \begin_inset Graphics
32872 filename ../images/math-macro-remove-optional-param.png
32873 rotateOrigin center
32882 <cell alignment="center" valignment="top" usebox="none">
32885 \begin_layout Plain Layout
32888 Edit\SpecialChar \menuseparator
32889 Math\SpecialChar \menuseparator
32891 \begin_inset space ~
32894 Definition\SpecialChar \menuseparator
32895 Remove Optional Argument
32901 <row interlinespace="2.5mm">
32902 <cell alignment="center" valignment="top" usebox="none">
32905 \begin_layout Plain Layout
32906 \begin_inset Graphics
32907 filename ../images/math-macro-add-optional-param.png
32908 rotateOrigin center
32917 <cell alignment="center" valignment="top" usebox="none">
32920 \begin_layout Plain Layout
32923 Edit\SpecialChar \menuseparator
32924 Math\SpecialChar \menuseparator
32926 \begin_inset space ~
32929 Definition\SpecialChar \menuseparator
32930 Insert Optional Argument
32936 <row interlinespace="2.5mm">
32937 <cell alignment="center" valignment="top" usebox="none">
32940 \begin_layout Plain Layout
32941 \begin_inset Graphics
32942 filename ../images/math-macro-remove-greedy-param.png
32943 rotateOrigin center
32952 <cell alignment="center" valignment="top" usebox="none">
32955 \begin_layout Plain Layout
32958 Edit\SpecialChar \menuseparator
32959 Math\SpecialChar \menuseparator
32961 \begin_inset space ~
32964 Definition\SpecialChar \menuseparator
32965 Remove Last Argument
32966 \begin_inset Newline newline
32970 \begin_inset Phantom HPhantom
32973 \begin_layout Plain Layout
32976 Edit\SpecialChar \menuseparator
32977 Math\SpecialChar \menuseparator
32979 \begin_inset space ~
32982 Definition\SpecialChar \menuseparator
32988 Spitting Out To The Right
32994 <row interlinespace="2.5mm">
32995 <cell alignment="center" valignment="top" usebox="none">
32998 \begin_layout Plain Layout
32999 \begin_inset Graphics
33000 filename ../images/math-macro-append-greedy-param.png
33001 rotateOrigin center
33010 <cell alignment="center" valignment="top" usebox="none">
33013 \begin_layout Plain Layout
33016 Edit\SpecialChar \menuseparator
33017 Math\SpecialChar \menuseparator
33019 \begin_inset space ~
33022 Definition\SpecialChar \menuseparator
33024 \begin_inset Newline newline
33028 \begin_inset Phantom HPhantom
33031 \begin_layout Plain Layout
33034 Edit\SpecialChar \menuseparator
33035 Math\SpecialChar \menuseparator
33037 \begin_inset space ~
33040 Definition\SpecialChar \menuseparator
33046 Eating From The Right
33052 <row interlinespace="2.5mm">
33053 <cell alignment="center" valignment="top" usebox="none">
33056 \begin_layout Plain Layout
33057 \begin_inset Graphics
33058 filename ../images/math-macro-add-greedy-optional-param.png
33059 rotateOrigin center
33068 <cell alignment="center" valignment="top" usebox="none">
33071 \begin_layout Plain Layout
33074 Edit\SpecialChar \menuseparator
33075 Math\SpecialChar \menuseparator
33077 \begin_inset space ~
33080 Definition\SpecialChar \menuseparator
33081 Append Optional Argument
33082 \begin_inset Newline newline
33086 \begin_inset Phantom HPhantom
33089 \begin_layout Plain Layout
33092 Edit\SpecialChar \menuseparator
33093 Math\SpecialChar \menuseparator
33095 \begin_inset space ~
33098 Definition\SpecialChar \menuseparator
33104 Eating From The Right
33117 \begin_layout Section
33118 Computer Algebra Systems
33121 \begin_layout Standard
33122 LyX offers the exchange between mathematical expressions written in LyX's
33123 math editor and external applications or user defined scripts.
33124 Currently supported applications are
33141 Note that the set of supported mathematical constructs is limited only
33142 to very simple cases.
33145 \begin_layout Subsection
33149 \begin_layout Standard
33150 Write some expression in a formula, go to the
33152 Edit\SpecialChar \menuseparator
33153 Math\SpecialChar \menuseparator
33154 Use Computer Algebra System
33156 menu and choose the application you have installed on the computer.
33157 After that the result of computation should show on the right side of the
33158 expression together with the
33159 \begin_inset Quotes eld
33163 \begin_inset Quotes erd
33169 \begin_layout Standard
33170 Here are few simple examples (with results from
33174 ) to show what kind of computations can be performed:
33177 \begin_layout Itemize
33178 \begin_inset Formula $\frac{37}{3}*2-\sum_{i=1}^{3}i^{i}=-\frac{22}{3}$
33184 \begin_layout Itemize
33185 \begin_inset Formula $\frac{37.0}{3}=12.33333333333333$
33191 \begin_layout Itemize
33192 \begin_inset Formula $\int_{1}^{2}\sin(x)dx=\cos1-\cos2$
33198 \begin_layout Itemize
33199 \begin_inset Formula $\det\left[\begin{array}{ccc}
33203 \end{array}\right]=-56$
33209 \begin_layout Itemize
33210 \begin_inset Formula $\lim_{x\rightarrow0}\left(\frac{\sin(x)}{x}\right)=1$
33216 \begin_layout Subsection
33220 \begin_layout Standard
33221 Currently there is no keyboard shortcut for calling the algebra applications.
33222 One can easily bind a shortcut to the
33226 LyX function (see the
33234 \begin_inset space \thinspace{}
33238 \begin_inset space \space{}
33245 key inside the math editor.
33250 one would use this shortcut definition command:
33253 \begin_layout Standard
33256 command-alternatives break-paragraph;math-extern maxima
33259 \begin_layout Section
33261 \begin_inset Index idx
33264 \begin_layout Plain Layout
33273 \begin_layout Subsection
33275 \begin_inset Index idx
33278 \begin_layout Plain Layout
33287 \begin_layout Standard
33288 Negative numbers often look ugly in formulas because the minus sign before
33289 the number is set with the same length as the minus operator sign.
33290 When writing the negative number in normal text, the minus sign appears
33294 \begin_layout Standard
33295 Thus, the problem disappears when converting the minus sign to mathematical
33299 \begin_layout Standard
33300 An example to visualize the problem:
33303 \begin_layout Standard
33305 \begin_inset Tabular
33306 <lyxtabular version="3" rows="3" columns="2">
33307 <features rotate="0" tabularvalignment="middle">
33308 <column alignment="right" valignment="top">
33309 <column alignment="left" valignment="top">
33311 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
33314 \begin_layout Plain Layout
33320 <cell alignment="center" valignment="top" topline="true" rightline="true" usebox="none">
33323 \begin_layout Plain Layout
33331 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
33334 \begin_layout Plain Layout
33340 <cell alignment="center" valignment="top" topline="true" bottomline="true" rightline="true" usebox="none">
33343 \begin_layout Plain Layout
33344 \begin_inset Formula $x=-2$
33354 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
33357 \begin_layout Plain Layout
33363 <cell alignment="center" valignment="top" topline="true" bottomline="true" rightline="true" usebox="none">
33366 \begin_layout Plain Layout
33367 \begin_inset Formula $x=\textrm{-}2$
33383 \begin_layout Subsection
33384 Comma as decimal Separator
33385 \begin_inset Index idx
33388 \begin_layout Plain Layout
33397 \begin_layout Standard
33398 In LaTeX a comma inside a formula is used, according to the English convention,
33399 as number group separator.
33400 So there will be space added behind all commas in formulas.
33403 \begin_layout Standard
33404 To avoid this, the comma is highlighted and changed to mathematical text
33414 \begin_layout Standard
33415 To use all formula commas in the document as decimal separator, the file
33424 \begin_layout Plain Layout
33429 is part of the LaTeX-package
33434 \begin_inset Index idx
33437 \begin_layout Plain Layout
33442 \begin_layout Plain Layout
33462 \begin_inset Index idx
33465 \begin_layout Plain Layout
33471 is loaded with the LaTeX-preamble line
33474 \begin_layout Standard
33482 \begin_layout Subsection
33484 \begin_inset CommandInset label
33486 name "sub:Physical-Vectors"
33491 \begin_inset Index idx
33494 \begin_layout Plain Layout
33503 \begin_layout Standard
33504 Predefined vectors are offered by the LaTeX-package
33509 \begin_inset Index idx
33512 \begin_layout Plain Layout
33518 that is loaded with the LaTeX-preamble line
33521 \begin_layout Standard
33529 \begin_layout Standard
33533 \begin_layout Plain Layout
33543 \begin_inset Note Note
33546 \begin_layout Plain Layout
33547 The following table will only be displayed when the LaTeX-package
33559 \begin_layout Standard
33560 The following commands are defined:
33563 \begin_layout Standard
33565 \begin_inset Tabular
33566 <lyxtabular version="3" rows="4" columns="2">
33567 <features rotate="0" tabularvalignment="middle">
33568 <column alignment="center" valignment="top">
33569 <column alignment="center" valignment="top">
33571 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
33574 \begin_layout Plain Layout
33580 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
33583 \begin_layout Plain Layout
33591 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
33594 \begin_layout Plain Layout
33604 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
33607 \begin_layout Plain Layout
33608 \begin_inset Formula $\Bra{\psi}$
33618 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
33621 \begin_layout Plain Layout
33631 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
33634 \begin_layout Plain Layout
33635 \begin_inset Formula $\Ket{\psi}$
33645 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
33648 \begin_layout Plain Layout
33660 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
33663 \begin_layout Plain Layout
33664 \begin_inset Formula $\Braket{\psi|\phi}$
33680 \begin_layout Standard
33687 assures that all vertical bars are set in the size of the surrounding brackets:
33688 \begin_inset Formula
33690 \Braket{\phi|J=\frac{3}{2}\,,\, M_{J}}
33699 \begin_layout Plain Layout
33709 \begin_inset Note Note
33712 \begin_layout Plain Layout
33713 The following will be displayed when the LaTeX-package
33725 \begin_layout Standard
33726 You need to install the LaTeX-package
33730 to see the rest of this subsection in the output.
33733 \begin_layout Standard
33737 \begin_layout Plain Layout
33749 \begin_layout Standard
33756 can also be achieved using the command
33762 , that is described in
33763 \begin_inset CommandInset ref
33765 reference "sub:Automatic-Bracket-Size"
33772 \begin_layout Subsection
33773 Self-defined Fractions
33774 \begin_inset CommandInset label
33776 name "sub:Self-defined-Fractions"
33781 \begin_inset Index idx
33784 \begin_layout Plain Layout
33785 Fractions ! self-defined
33793 \begin_layout Standard
33794 To define custom commands for fractions, the command
33801 \begin_inset Index idx
33804 \begin_layout Plain Layout
33811 \begin_layout Plain Layout
33825 is used in the following scheme:
33828 \begin_layout Standard
33841 bracket}{fraction bar thickness}{style}
33842 \begin_inset Newline newline
33846 \begin_inset Phantom HPhantom
33849 \begin_layout Plain Layout
33859 {numerator}{denominator}
33862 \begin_layout Standard
33863 The style is a number in the range of 0
33864 \begin_inset space \thinspace{}
33868 \begin_inset space \thinspace{}
33874 \begin_layout Standard
33876 \begin_inset Tabular
33877 <lyxtabular version="3" rows="5" columns="2">
33878 <features rotate="0" tabularvalignment="middle">
33879 <column alignment="center" valignment="top">
33880 <column alignment="center" valignment="top">
33882 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
33885 \begin_layout Plain Layout
33891 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
33894 \begin_layout Plain Layout
33902 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
33905 \begin_layout Plain Layout
33911 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
33914 \begin_layout Plain Layout
33915 display style formula
33922 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
33925 \begin_layout Plain Layout
33931 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
33934 \begin_layout Plain Layout
33942 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
33945 \begin_layout Plain Layout
33951 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
33954 \begin_layout Plain Layout
33962 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
33965 \begin_layout Plain Layout
33971 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
33974 \begin_layout Plain Layout
33988 \begin_layout Standard
33989 When no style is given, the size is adjusted to the surrounding environment
33990 like for the command
33999 \begin_layout Standard
34000 When no fraction bar thickness is given, the predefined value of 0.4
34001 \begin_inset space \thinspace{}
34007 \begin_layout Standard
34008 \begin_inset VSpace medskip
34011 For example, the commands
34024 \begin_inset CommandInset ref
34026 reference "sub:Fractions"
34030 are defined with the commands
34033 \begin_layout Standard
34042 genfrac{}{}{}{0}{#1}{#2}}
34045 \begin_layout Standard
34049 \begin_layout Standard
34058 genfrac{(}{)}{0pt}{1}{#1}{#2}}
34061 \begin_layout Standard
34062 \begin_inset VSpace medskip
34065 To define a fraction where the fraction bar thickness can be given as optional
34066 argument, the following line is inserted to the LaTeX-preamble:
34069 \begin_layout Standard
34078 genfrac{}{}{#1}{}{#2}{#3}}
34081 \begin_layout Standard
34083 \begin_inset Formula
34085 \text{Command} & & \mathrm{\backslash fracS[1mm]\backslash\{A\to\backslash\{B} & & \mathrm{\backslash fracS[5mm]\backslash\{A\to\backslash\{B}\\
34086 \text{Result} & & \fracS[1mm]{A}{B} & & \fracS[5mm]{A}{B}
34091 As one can see, the distance of the numerator and the denominator to the
34092 fraction bar is round about three times the bar thickness.
34095 \begin_layout Subsection
34097 \begin_inset Index idx
34100 \begin_layout Plain Layout
34109 \begin_layout Standard
34110 There are four ways to cancel formulas or parts of formulas:
34113 \begin_layout Standard
34117 \begin_layout Plain Layout
34127 \begin_inset Note Note
34130 \begin_layout Plain Layout
34131 The following table will only be displayed when the LaTeX-package
34143 \begin_layout Standard
34145 \begin_inset Tabular
34146 <lyxtabular version="3" rows="5" columns="2">
34147 <features rotate="0" tabularvalignment="middle">
34148 <column alignment="center" valignment="top">
34149 <column alignment="center" valignment="top">
34151 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
34154 \begin_layout Plain Layout
34160 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
34163 \begin_layout Plain Layout
34165 \begin_inset Note Note
34168 \begin_layout Plain Layout
34175 are used here as spacer.
34187 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
34190 \begin_layout Plain Layout
34194 \begin_inset space \textvisiblespace{}
34200 \begin_inset space \textvisiblespace{}
34208 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
34211 \begin_layout Plain Layout
34212 \begin_inset Formula $\raisebox{4.5mm}{}\cancel{\int A=B}\raisebox{-2.5mm}{}$
34222 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
34225 \begin_layout Plain Layout
34229 \begin_inset space \textvisiblespace{}
34235 \begin_inset space \textvisiblespace{}
34243 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
34246 \begin_layout Plain Layout
34247 \begin_inset Formula $\raisebox{4.5mm}{}\bcancel{\int A=B}\raisebox{-2.5mm}{}$
34257 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
34260 \begin_layout Plain Layout
34264 \begin_inset space \textvisiblespace{}
34270 \begin_inset space \textvisiblespace{}
34278 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
34281 \begin_layout Plain Layout
34282 \begin_inset Formula $\raisebox{4.5mm}{}\xcancel{\int A=B}\raisebox{-2.5mm}{}$
34292 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
34295 \begin_layout Plain Layout
34299 \begin_inset space \textvisiblespace{}
34305 \begin_inset space \textvisiblespace{}
34309 \begin_inset Formula $\to$
34317 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
34320 \begin_layout Plain Layout
34321 \begin_inset Formula $\raisebox{7mm}{}\cancelto{1}{\int A=B}\raisebox{-2.5mm}{}\hspace{3mm}$
34337 \begin_layout Standard
34344 is especially suitable to visualize the reduction of fractions within formulas:
34345 \begin_inset Formula
34347 \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}}}
34355 \begin_layout Standard
34356 To change the size of
34363 \begin_inset Quotes eld
34367 \begin_inset Quotes erd
34370 value one can add the LaTeX-preamble line
34373 \begin_layout Standard
34378 PassOptionsToPackage{option}{cancel}
34381 \begin_layout Standard
34390 which leads to the same size as for the canceled value, or
34394 which makes is it a bit smaller than normal.
34397 \begin_layout Standard
34398 To color the cancellation bar one adds this command as TeX code:
34401 \begin_layout Standard
34413 \begin_layout Standard
34418 can be replaced by a color of your choice.
34421 \begin_layout Standard
34425 \begin_layout Plain Layout
34441 \begin_layout Standard
34442 \begin_inset Formula
34444 \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}}}
34452 \begin_layout Standard
34456 \begin_layout Plain Layout
34470 \begin_inset Note Note
34473 \begin_layout Plain Layout
34482 \begin_layout Standard
34483 For further customizations, see the documentation of the package
34488 \begin_inset CommandInset citation
34495 \begin_inset Index idx
34498 \begin_layout Plain Layout
34507 \begin_layout Standard
34511 \begin_layout Plain Layout
34521 \begin_inset Note Note
34524 \begin_layout Plain Layout
34525 The following will be displayed when the LaTeX-package
34537 \begin_layout Standard
34538 You need to install the LaTeX-package
34542 to see the rest of this subsection in the output.
34545 \begin_layout Standard
34549 \begin_layout Plain Layout
34561 \begin_layout Standard
34562 \begin_inset Newpage newpage
34568 \begin_layout Subsection
34569 Formulas in Section Headings
34570 \begin_inset CommandInset label
34572 name "sub:Formulas-in-Section"
34577 \begin_inset Index idx
34580 \begin_layout Plain Layout
34581 Formula ! in section headings
34589 \begin_layout Standard
34590 When formulas are used in section headings, the following has to be taken
34594 \begin_layout Standard
34595 \begin_inset Note Greyedout
34598 \begin_layout Plain Layout
34604 \begin_inset Index idx
34607 \begin_layout Plain Layout
34608 Packages ! hyperref
34613 support is enabled in the document settings dialog under
34616 \begin_inset space ~
34621 , PDF-bookmarks are created for every section heading in the table of contents.
34622 If a section heading contains formulas, they are incorrectly displayed
34623 in the bookmark text, because formulas in bookmarks infringe the PDF convention
34632 \begin_layout Standard
34633 Both problems can be solved by inserting at the end of the section heading
34634 a short title with the menu
34636 Insert\SpecialChar \menuseparator
34638 \begin_inset space ~
34644 Short titles are used as alternative for multiline section headings to
34645 keep the table of contents clearly arranged.
34646 Only the short title appears in the table of contents and therefore also
34647 in the PDF-bookmark.
34650 \begin_layout Standard
34651 When formulas should be used in the table of contents but
34655 is used, one can use the following command in TeX-mode:
34658 \begin_layout Standard
34663 texorpdfstring{part}{alternative}
34664 \begin_inset Index idx
34667 \begin_layout Plain Layout
34678 \begin_layout Standard
34679 Part is the part of the heading that shouldn't appear in the PDF-bookmark.
34680 This can be characters, formulas, footnotes, but also cross-references.
34681 The alternative is used instead of the part for the bookmark.
34684 \begin_layout Standard
34685 Here are two example headings:
34686 \begin_inset VSpace -3mm
34693 \begin_layout Plain Layout
34705 \begin_layout Subsubsection
34706 Heading without formula in table of contents
34707 \begin_inset Formula $\sqrt{-1}=\mathrm{i}$
34711 \begin_inset Argument 1
34714 \begin_layout Plain Layout
34715 Heading without formula in table of contents
34723 \begin_layout Subsubsection
34724 Heading with formula in table of contents
34728 \begin_layout Plain Layout
34738 \begin_inset Formula $\sqrt{-1}=\mathrm{i}$
34745 \begin_layout Plain Layout
34755 \begin_layout Standard
34759 \begin_layout Plain Layout
34768 In the first heading a short title was used, in the second one
34777 \begin_layout Standard
34778 To get the same formatting as for the other headings, the complete heading
34787 \begin_layout Plain Layout
34789 \begin_inset CommandInset ref
34791 reference "sub:Bold-Formulas"
34803 \begin_layout Subsection
34804 Formulas in multi-column Text
34805 \begin_inset Index idx
34808 \begin_layout Plain Layout
34809 Formula ! in multi-column text
34817 \begin_layout Standard
34818 Formulas in multi-column text are often too wide to fit into a column and
34819 thus need to be set over the whole page width.
34820 This is done by using the LaTeX-package
34828 \begin_layout Plain Layout
34833 is part of every LaTeX standard installation.
34839 \begin_inset Index idx
34842 \begin_layout Plain Layout
34843 Packages ! multicol
34848 , that is loaded with the LaTeX-preamble line
34851 \begin_layout Standard
34856 usepackage{multicol}
34859 \begin_layout Standard
34860 \begin_inset Note Greyedout
34863 \begin_layout Plain Layout
34864 Note that in this case the setting
34867 \begin_inset space ~
34874 Document\SpecialChar \menuseparator
34880 \begin_inset space ~
34900 \begin_layout Standard
34901 Before the multi-column text the command
34904 \begin_layout Standard
34909 begin{multicols}{column number}
34912 \begin_layout Standard
34913 is written in TeX-mode.
34914 The column number is a number in the range of 2
34915 \begin_inset space \thinspace{}
34919 \begin_inset space \thinspace{}
34923 Before the formula the multi-column text is ended by inserting the command
34926 \begin_layout Standard
34934 \begin_layout Standard
34938 \begin_layout Standard
34939 Due to the command some space is automatically added before the formula.
34941 \begin_inset space \thinspace{}
34944 mm vertical space is inserted before the formula.
34945 When the formula style
34951 \begin_layout Plain Layout
34953 \begin_inset CommandInset ref
34955 reference "sec:Formula-Styles"
34967 \begin_inset space \thinspace{}
34970 mm space is inserted instead.
34973 \begin_layout Standard
34974 As example a multi-column text with a displayed formula:
34977 \begin_layout Standard
34983 \begin_layout Plain Layout
34987 begin{multicols}{2}
34992 Das Spektrum wird fouriertransformiert.
34993 Die Fouriertransformation wird verwendet, um die überlagerten Signale (Netzwerk
34994 , Lösungsmittel) zu trennen.
34995 Nachdem wir die Phasenverschiebung bestimmen konnten, interessiert uns
34996 nun das Aussehen des Ausgangssignals.
34997 Im Experiment haben wir es mit sehr vielen Teilchen zu tun, so dass man
34998 über alle Phasen integrieren muss.
35000 \begin_inset Formula $S$
35003 unser normiertes Ausgangssignal und
35004 \begin_inset Formula $P$
35007 die Phasenverteilungsfunktion, so ergibt sich die Beziehung
35011 \begin_layout Plain Layout
35021 \begin_inset VSpace -6mm
35025 \begin_inset Formula
35027 S(t)=S_{0}(t)\int_{-\infty}^{\infty}P(\phi,t)\mathrm{e}^{\mathrm{i}\phi}\,\mathrm{d}\phi
35036 \begin_layout Plain Layout
35040 begin{multicols}{2}
35046 \begin_inset Formula $S_{0}$
35049 das Signal ohne Gradient ist und die Normierungsbedingung
35050 \begin_inset Formula $\int_{-\infty}^{\infty}P(\phi,t)\,\mathrm{d}\phi=1$
35054 Nun dürfen wir aber nicht den Relaxationsprozess außer Acht lassen.
35056 \begin_inset Formula $\nicefrac{\pi}{2}$
35060 \begin_inset space \thinspace{}
35063 -rf-Puls beginnt sich die Magnetisierung zu entfokussieren, wodurch sich
35064 das Signal zusätzlich abschwächt.
35065 Diese Abschwächung verläuft exponentiell in Abhängigkeit der so genannten
35067 \begin_inset Formula $T_{2}$
35073 \begin_layout Standard
35079 \begin_layout Plain Layout
35091 \begin_layout Subsection
35092 Formulas with Description of Variables
35093 \begin_inset Index idx
35096 \begin_layout Plain Layout
35097 Formula ! with description of variables
35105 \begin_layout Standard
35106 To describe variables within a formula, like in formula
35107 \begin_inset CommandInset ref
35109 reference "eq:within"
35118 \begin_inset Formula $n$
35122 \begin_inset space ~
35125 matrix is used with left aligned columns for the
35126 \begin_inset Formula $n$
35133 \begin_layout Plain Layout
35135 \begin_inset CommandInset ref
35137 reference "sec:Matrices"
35146 To set the description in a smaller size, before the matrix e.
35147 \begin_inset space \thinspace{}
35151 \begin_inset space \space{}
35164 \begin_layout Plain Layout
35166 \begin_inset CommandInset ref
35168 reference "sub:Font-Sizes"
35180 \begin_layout Standard
35181 When the formula style
35187 \begin_layout Plain Layout
35189 \begin_inset CommandInset ref
35191 reference "sec:Formula-Styles"
35212 \begin_layout Plain Layout
35219 only works in formulas with the style
35224 \begin_inset CommandInset ref
35226 reference "sub:Variable-Space"
35235 is inserted before and after the matrix to have the same separation of
35236 the matrix from the equation and the side margin.
35239 \begin_layout Standard
35240 When the formula style
35244 is used, the method described in
35245 \begin_inset CommandInset ref
35247 reference "sub:Flalign-Environment"
35251 is used to indent formulas.
35253 \begin_inset CommandInset ref
35255 reference "eq:within"
35259 consists of five columns where in the first two columns contain the equation,
35260 the third the matrix and the last one an empty TeX-brace.
35261 \begin_inset Formula
35263 \hspace{30pt}F_{A} & =\rho·V·g & \footnotesize\begin{array}{ll}
35264 \rho & \textrm{density}\\
35265 V & \textrm{volume}\\
35266 g & \textrm{gravitational acceleration}
35267 \end{array} & & {}\label{eq:within}
35275 \begin_layout Subsection
35276 Upright small Greek Letters
35277 \begin_inset CommandInset label
35279 name "sub:Upright-small-Greek"
35284 \begin_inset Index idx
35287 \begin_layout Plain Layout
35288 Greek letters ! upright
35296 \begin_layout Standard
35297 Most of the math fonts only provide italic small Greek letters.
35298 But for symbols of elementary particles like pions and neutrinos, upright
35299 Greek letters are needed.
35308 \begin_layout Plain Layout
35313 is part of the LaTeX-package
35318 \begin_inset Index idx
35321 \begin_layout Plain Layout
35326 \begin_layout Plain Layout
35346 \begin_inset Index idx
35349 \begin_layout Plain Layout
35355 that is loaded with the LaTeX-preamble line
35358 \begin_layout Standard
35363 usepackage{upgreek}
35366 \begin_layout Standard
35372 \begin_layout Plain Layout
35382 \begin_inset Note Note
35385 \begin_layout Plain Layout
35386 The following table will only be displayed when the LaTeX-package
35395 They are created when the command for a small Greek letter is started with
35401 For example the command
35408 \begin_inset Formula $\uptau$
35414 \begin_layout Standard
35415 With these commands reactions of elementary particles can be typeset:
35416 \begin_inset Formula
35418 \uppi^{+}\to\upmu^{+}+\upnu_{\upmu}
35426 \begin_layout Standard
35427 The upright letters are more bold and wider than the italic ones.
35428 They should therefore not be used for units like
35429 \begin_inset Quotes eld
35433 \begin_inset Quotes erd
35439 \begin_layout Standard
35443 \begin_layout Plain Layout
35453 \begin_inset Note Note
35456 \begin_layout Plain Layout
35457 The following will be displayed when the LaTeX-package
35469 \begin_layout Standard
35470 You need to install the LaTeX-package
35474 to see the rest of this subsection in the output.
35477 \begin_layout Standard
35481 \begin_layout Plain Layout
35493 \begin_layout Subsection
35494 Text Characters in Formulas
35495 \begin_inset CommandInset label
35497 name "sub:Text-Characters-in"
35502 \begin_inset Index idx
35505 \begin_layout Plain Layout
35514 \begin_layout Standard
35515 In some cases you might want to insert text characters directly into formulas.
35516 When for example the centered dot · is often used in formulas like
35517 \begin_inset Formula $\nu=5·10^{5}\,\mathrm{Hz}$
35520 , one would have to insert the command
35530 \begin_layout Plain Layout
35532 \begin_inset CommandInset ref
35534 reference "sub:Binary-Operators"
35543 all the time, because this character is defined in all encodings as text
35545 But the encoding can be changed by this LaTeX-preamble line:
35548 \begin_layout Standard
35553 Declare Inputtext{183}{
35563 f\SpecialChar \textcompwordmark{}
35567 \begin_layout Standard
35568 The character encoding (menu
35570 Document\SpecialChar \menuseparator
35571 Settings\SpecialChar \menuseparator
35574 ) specifies what character appears when a keyboard key is pressed.
35575 When the key for the character '·' is pressed, internally the command
35582 But this command is not available in a formula so that you would get LaTeX-erro
35584 With the changed encoding the right command is chosen automatically, depending
35585 on if the character was inserted into a formula or not.
35588 \begin_layout Standard
35589 The encoding of several characters is saved in definition files.
35590 For example the encoding
35594 is defined in the file
35598 which is in the installation folder of LaTeX.
35599 Encodings should only be changed via the LaTeX-preamble and not in the
35601 Otherwise documents could not be edited by other LyX users working on other
35605 \begin_layout Standard
35606 \begin_inset VSpace medskip
35609 Besides the centered dot, in this document the degree sign ° is defined
35610 with the following LaTeX-preamble line so that it can be directly inserted
35614 \begin_layout Standard
35619 DeclareInputtext{176}{
35629 f\SpecialChar \textcompwordmark{}
35633 \begin_layout Standard
35634 \begin_inset Newpage newpage
35640 \begin_layout Section
35643 \begin_inset Index idx
35646 \begin_layout Plain Layout
35655 \begin_layout Standard
35656 This section is a summary of the most important typographic rules, listed
35661 \begin_layout Plain Layout
35662 This collection was partly taken from the German semi-official dictionary
35664 \begin_inset Quotes eld
35668 \begin_inset Quotes erd
35672 \begin_inset CommandInset citation
35678 that lists some of the ISO rules.
35679 More rules are listed in
35680 \begin_inset CommandInset citation
35694 \begin_layout Itemize
35703 \begin_layout Plain Layout
35704 done with font styles, see
35705 \begin_inset CommandInset ref
35707 reference "sub:Font-Styles"
35716 , no matter if they appear in italic text: 30
35717 \begin_inset space \thinspace{}
35721 \begin_inset Newline newline
35724 Between the value and the unit is the smallest space, see
35725 \begin_inset CommandInset ref
35727 reference "sub:Predefined-Space"
35732 \begin_inset Newline newline
35735 This convention is automatically fulfilled when the command
35742 When it is entered to a formula, two boxes appear.
35743 In the first one the value is inserted, in the second one the unit, and
35745 \begin_inset Formula $\unit[30]{km/h}$
35749 \begin_inset space \thinspace{}
35759 is not a real LaTeX command but the command
35765 , therefore you cannot use it in TeX code.
35768 \begin_layout Itemize
35769 Percent and perthousand signs are set like physical units:
35770 \begin_inset Newline newline
35774 \begin_inset space \thinspace{}
35780 \begin_layout Itemize
35781 The degree sign follows directly on the value: 15°, but not when it is used
35783 \begin_inset space \thinspace{}
35789 \begin_layout Itemize
35790 In numbers with more than four digits the smallest space is inserted before
35791 every third digit to group them:
35801 \begin_inset space \thinspace{}
35805 \begin_inset space \thinspace{}
35811 \begin_layout Itemize
35812 For dimensions like 120×90×40
35813 \begin_inset space \thinspace{}
35816 cm the multiplication sign
35817 \begin_inset Quotes eld
35821 \begin_inset Quotes erd
35825 It is available either via the command
35833 Insert\SpecialChar \menuseparator
35834 Special Character\SpecialChar \menuseparator
35840 \begin_layout Itemize
35841 Functions with names consisting of several letters are set upright to avoid
35843 \begin_inset CommandInset ref
35845 reference "sub:Predefined-Functions"
35852 \begin_layout Itemize
35853 Indices consisting of several letters, are set upright:
35854 \begin_inset Formula $E_{\mathrm{kin}}$
35858 \begin_inset Newline newline
35861 Components of matrices are set italic:
35862 \begin_inset Formula $\hat{H}_{kl}$
35868 \begin_layout Itemize
35869 The differentiation/integration operator 'd', the Euler's number 'e' and
35870 the imaginary unit 'i' should be set upright, to avoid mixing them up with
35874 \begin_layout Itemize
35875 The character that denotes a
35879 transformation is inserted either by the command
35884 \begin_inset space \textvisiblespace{}
35891 Insert\SpecialChar \menuseparator
35892 Special Character\SpecialChar \menuseparator
35893 Symbols\SpecialChar \menuseparator
35895 \begin_inset space ~
35901 \begin_inset Formula $\mathscr{F}$
35907 \begin_layout Standard
35908 \begin_inset Newpage newpage
35914 \begin_layout Section
35916 \begin_inset Index idx
35919 \begin_layout Plain Layout
35928 \begin_layout Standard
35929 Some characters and symbols can be created with several commands.
35930 Here is a list of the synonym commands:
35933 \begin_layout Standard
35934 \begin_inset VSpace bigskip
35938 \begin_inset space \hfill{}
35942 \begin_inset Tabular
35943 <lyxtabular version="3" rows="12" columns="2">
35944 <features rotate="0" tabularvalignment="middle">
35945 <column alignment="center" valignment="top" width="0pt">
35946 <column alignment="center" valignment="top" width="0pt">
35948 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
35951 \begin_layout Plain Layout
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