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
500 \begin_inset Newline newline
503 To create a display style formula
504 \begin_inset Index idx
507 \begin_layout Plain Layout
508 Formula ! display style
513 which will appear bigger, has a different format, and will be in a separate
514 paragraph, use one of these shortcuts:
523 \begin_layout Standard
524 To change a display style formula to an inline formula, set the cursor into
525 the formula and use one of the shortcuts
533 Edit\SpecialChar \menuseparator
534 Math\SpecialChar \menuseparator
538 The same way is used to change an inline formula to a display style formula.
541 \begin_layout Standard
542 To display parts of an inline formula in the size of a display style formula,
550 \begin_inset Index idx
553 \begin_layout Plain Layout
562 Then a new blue box appears in which the desired formula part is inserted.
565 \begin_layout Standard
566 Only inline formulas are allowed inside tables.
569 \begin_layout Standard
574 can be turned on in the menu
576 View\SpecialChar \menuseparator
580 When you click there on
581 \begin_inset Quotes eld
585 \begin_inset Quotes erd
588 the toolbar will be shown permanently at the bottom; this state is visualized
593 menu with a checkmark.
594 When you click in this state again on
595 \begin_inset Quotes eld
599 \begin_inset Quotes erd
610 is only shown when the cursor is within a formula; this state is visualized
611 by the renaming of the menu entry from
612 \begin_inset Quotes eld
616 \begin_inset Quotes erd
620 \begin_inset Quotes eld
628 \begin_inset Quotes erd
634 \begin_layout Standard
636 \begin_inset Index idx
639 \begin_layout Plain Layout
645 is invoked by pressing the toolbar button
653 Insert\SpecialChar \menuseparator
658 \begin_layout Plain Layout
674 \begin_inset Note Note
677 \begin_layout Plain Layout
678 In LyX there are three
679 \begin_inset Quotes eld
683 \begin_inset Quotes erd
686 that appear in the output with sub- and superscript letters: TeX, LaTeX
690 \begin_layout Plain Layout
691 To avoid that these names are recognized as proper names, a TeX-brace pair
700 \begin_layout Standard
701 To change the LaTeX-preamble
702 \begin_inset Index idx
705 \begin_layout Plain Layout
713 Document\SpecialChar \menuseparator
714 Settings\SpecialChar \menuseparator
719 \begin_layout Plain Layout
735 \begin_layout Standard
736 To edit matrices, case differentiations and multiline formulas subsequently,
739 Edit\SpecialChar \menuseparator
744 Edit\SpecialChar \menuseparator
746 \begin_inset space \thinspace{}
750 \begin_inset space \thinspace{}
760 When lines and columns are swapped via the menu, the column or line where
761 the cursor is in is exchanged with the column to the right or the line
763 Is the cursor in the last column or row, the exchange is done with the
764 column to the left or the line above.
767 \begin_layout Standard
768 To write text in formulas
772 \begin_layout Plain Layout
773 For multiline formulas the command
780 \begin_inset CommandInset ref
782 reference "sub:Text-in-multiline"
796 \begin_inset Index idx
799 \begin_layout Plain Layout
806 \begin_inset Index idx
809 \begin_layout Plain Layout
816 This mode is invoked with the shortcut
822 or by the insertion of the command
829 \begin_inset Index idx
832 \begin_layout Plain Layout
841 The text appears black in LyX and can therefore be distinguished from the
842 other formula parts which appear blue.
843 In the output mathematical text is set upright, in contrary to other formula
847 \begin_layout Subsection*
851 \begin_layout Standard
852 Most of the LaTeX-commands for math constructs have the following scheme:
855 \begin_layout Standard
871 \begin_layout Standard
872 A command always starts with a backslash
873 \begin_inset Quotes gld
883 \begin_inset Quotes grd
887 To omit optional arguments, also omit the associated brackets.
888 The braces around the required arguments are named in this document as
890 \begin_inset Index idx
893 \begin_layout Plain Layout
900 If you add in a formula a left brace to a command name, LyX automatically
902 In all other cases TeX-braces are created in formulas with the command
910 TeX-braces appear red in LyX, in contrary to normal braces which appear
912 In TeX-mode no command is needed to get TeX-braces.
913 TeX-braces don't appear in the output.
916 \begin_layout Standard
917 When commands without arguments, like commands for symbols are entered in
918 TeX-mode, a space character must
922 be behind the command to end it.
923 This space doesn't appear in the output.
924 When the space should appear in the output, the space must be followed
925 by a protected space in normal text.
928 \begin_layout Standard
929 A protected space is inserted with
932 arg "command-alternatives space-insert protected ; math-space"
938 \begin_layout Subsection*
939 \begin_inset Newpage newpage
945 \begin_layout Itemize
947 \begin_inset space \textvisiblespace{}
950 denotes a space character to be input.
953 \begin_layout Itemize
955 \begin_inset Formula $\to$
958 denotes the usage of the corresponding arrow key on the keyboard.
963 key can often be used instead of
964 \begin_inset Formula $\to$
968 \begin_inset Formula $\downarrow$
976 \begin_inset Formula $\leftarrow$
980 \begin_inset Formula $\uparrow$
986 \begin_layout Subsection*
990 \begin_layout Standard
992 \begin_inset Float table
998 \begin_layout Plain Layout
1000 \begin_inset Caption Standard
1002 \begin_layout Plain Layout
1003 \begin_inset CommandInset label
1005 name "tab:Available-units"
1017 \begin_layout Plain Layout
1019 \begin_inset Tabular
1020 <lyxtabular version="3" rows="13" columns="2">
1021 <features rotate="0" tabularvalignment="middle">
1022 <column alignment="center" valignment="top">
1023 <column alignment="center" valignment="top">
1025 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
1028 \begin_layout Plain Layout
1034 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
1037 \begin_layout Plain Layout
1045 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
1048 \begin_layout Plain Layout
1054 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
1057 \begin_layout Plain Layout
1065 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
1068 \begin_layout Plain Layout
1074 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
1077 \begin_layout Plain Layout
1085 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
1088 \begin_layout Plain Layout
1094 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
1097 \begin_layout Plain Layout
1099 \begin_inset space \thinspace{}
1103 \begin_inset space \thinspace{}
1113 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
1116 \begin_layout Plain Layout
1122 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
1125 \begin_layout Plain Layout
1127 \begin_inset space \thinspace{}
1131 \begin_inset space \thinspace{}
1141 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
1144 \begin_layout Plain Layout
1150 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
1153 \begin_layout Plain Layout
1155 \begin_inset space \thinspace{}
1159 \begin_inset space \thinspace{}
1169 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
1172 \begin_layout Plain Layout
1178 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
1181 \begin_layout Plain Layout
1183 \begin_inset space \thinspace{}
1187 \begin_inset space \thinspace{}
1197 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
1200 \begin_layout Plain Layout
1206 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
1209 \begin_layout Plain Layout
1211 \begin_inset space \thinspace{}
1215 \begin_inset space \thinspace{}
1225 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
1228 \begin_layout Plain Layout
1234 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
1237 \begin_layout Plain Layout
1239 \begin_inset space \thinspace{}
1243 \begin_inset Formula $\approx$
1247 \begin_inset space \thinspace{}
1257 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
1260 \begin_layout Plain Layout
1266 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
1269 \begin_layout Plain Layout
1271 \begin_inset space \thinspace{}
1275 \begin_inset space \thinspace{}
1285 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
1288 \begin_layout Plain Layout
1294 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
1297 \begin_layout Plain Layout
1301 \begin_inset Quotes eld
1307 \begin_inset Quotes erd
1317 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
1320 \begin_layout Plain Layout
1326 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
1329 \begin_layout Plain Layout
1331 \begin_inset Quotes eld
1339 \begin_inset Quotes erd
1349 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
1352 \begin_layout Plain Layout
1358 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
1361 \begin_layout Plain Layout
1363 \begin_inset space \thinspace{}
1367 \begin_inset Formula $\nicefrac{1}{18}$
1371 \begin_inset space \thinspace{}
1392 \begin_layout Standard
1393 \begin_inset Newpage newpage
1399 \begin_layout Section
1403 \begin_layout Subsection
1405 \begin_inset Index idx
1408 \begin_layout Plain Layout
1415 \begin_inset Index idx
1418 \begin_layout Plain Layout
1425 \begin_inset Index idx
1428 \begin_layout Plain Layout
1433 \begin_layout Plain Layout
1444 \begin_layout Plain Layout
1457 \begin_inset Index idx
1460 \begin_layout Plain Layout
1465 \begin_layout Plain Layout
1476 \begin_layout Plain Layout
1491 \begin_layout Standard
1492 Indices are created with an underscore
1493 \begin_inset Quotes eld
1497 \begin_inset Quotes erd
1500 or via the math toolbar button
1503 arg "math-subscript"
1506 , exponents with a caret
1507 \begin_inset Quotes eld
1511 \begin_inset Quotes erd
1514 or via the math toolbar button
1517 arg "math-superscript"
1523 \begin_layout Standard
1525 \begin_inset Tabular
1526 <lyxtabular version="3" rows="4" columns="2">
1527 <features rotate="0" tabularvalignment="middle">
1528 <column alignment="center" valignment="top" width="0pt">
1529 <column alignment="center" valignment="top" width="0pt">
1531 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
1534 \begin_layout Plain Layout
1540 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
1543 \begin_layout Plain Layout
1545 \begin_inset Note Note
1548 \begin_layout Plain Layout
1555 is only used as spacer.
1567 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
1570 \begin_layout Plain Layout
1576 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
1579 \begin_layout Plain Layout
1580 \begin_inset Formula $B_{V}$
1590 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
1593 \begin_layout Plain Layout
1599 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
1602 \begin_layout Plain Layout
1603 \begin_inset Formula $\raisebox{5mm}{}B^{V}$
1613 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
1616 \begin_layout Plain Layout
1618 \begin_inset space \textvisiblespace{}
1626 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
1629 \begin_layout Plain Layout
1630 \begin_inset Formula $\raisebox{5mm}{}B^{A}$
1646 \begin_layout Standard
1647 As the caret is in some languages an accent, vowels will be accentuated
1648 in this case and not set as exponents
1652 \begin_layout Plain Layout
1653 Depending on the used keyboard settings this can also happen for characters
1660 To get exponents in this case, press
1664 after the caret as in the last example.
1667 \begin_layout Subsection
1669 \begin_inset CommandInset label
1671 name "sub:Fractions"
1676 \begin_inset Index idx
1679 \begin_layout Plain Layout
1688 \begin_layout Standard
1689 Fractions are generated with the command
1696 \begin_inset Index idx
1699 \begin_layout Plain Layout
1707 or via the math toolbar button
1710 arg "math-insert \\frac"
1714 The font size is adjusted automatically, depending on whether the fraction
1715 is in an inline or display style formula.
1716 With the math toolbar button
1719 arg "math-insert \\frac-square"
1722 you can select different fraction types.
1725 \begin_layout Standard
1733 \begin_inset Index idx
1736 \begin_layout Plain Layout
1744 a fraction can be created that always has the size of a display style formula.
1752 \begin_inset Index idx
1755 \begin_layout Plain Layout
1763 the fraction appears always with the size of an inline formula.
1767 \begin_layout Standard
1768 A line with the fraction
1769 \begin_inset Formula $\frac{1}{2}$
1772 that was created with the command
1781 \begin_layout Standard
1782 A line with the fraction
1783 \begin_inset Formula $\dfrac{1}{2}$
1786 that was created with the command
1795 \begin_layout Standard
1797 \begin_inset Tabular
1798 <lyxtabular version="3" rows="4" columns="2">
1799 <features rotate="0" tabularvalignment="middle">
1800 <column alignment="center" valignment="top" width="0pt">
1801 <column alignment="center" valignment="top" width="0pt">
1803 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
1806 \begin_layout Plain Layout
1812 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
1815 \begin_layout Plain Layout
1817 \begin_inset Note Note
1820 \begin_layout Plain Layout
1827 is only used as spacer.
1839 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
1842 \begin_layout Plain Layout
1846 \begin_inset space \textvisiblespace{}
1850 \begin_inset Formula $\downarrow$
1858 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
1861 \begin_layout Plain Layout
1862 \begin_inset Formula $\raisebox{4.5mm}{}\frac{A}{B}\raisebox{-2.5mm}{}$
1872 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
1875 \begin_layout Plain Layout
1879 \begin_inset space \textvisiblespace{}
1883 \begin_inset Formula $\downarrow$
1891 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
1894 \begin_layout Plain Layout
1895 \begin_inset Formula $\raisebox{7mm}{}\dfrac{A}{B}\raisebox{-4mm}{}$
1905 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
1908 \begin_layout Plain Layout
1912 \begin_inset space \textvisiblespace{}
1918 \begin_inset space \textvisiblespace{}
1922 \begin_inset Formula $\downarrow$
1926 \begin_inset Formula $\downarrow\downarrow$
1934 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
1937 \begin_layout Plain Layout
1938 \begin_inset Formula $\raisebox{8mm}{}\dfrac{e^{\frac{1}{2}}}{3}\raisebox{-4mm}{}$
1954 \begin_layout Standard
1955 \begin_inset VSpace bigskip
1959 \begin_inset Newpage newpage
1962 For nested fractions the command
1969 \begin_inset Index idx
1972 \begin_layout Plain Layout
1982 \begin_inset VSpace -3mm
1988 \begin_layout Standard
1989 \begin_inset Formula
1991 \textrm{created with \textbf{\textbackslash frac}} & & \textrm{created with \textbf{\textbackslash cfrac}}\\
1992 \frac{A}{B+\frac{C+\frac{E}{F}}{D}} & & \cfrac{A}{B+\cfrac{C+\cfrac{E}{F}}{D}}
2000 \begin_layout Standard
2001 The command for the example above is:
2004 \begin_layout Standard
2010 \begin_inset space \textvisiblespace{}
2014 \begin_inset Formula $\downarrow$
2020 \begin_inset space \textvisiblespace{}
2026 \begin_inset space \textvisiblespace{}
2030 \begin_inset Formula $\downarrow$
2034 \begin_inset Formula $\downarrow$
2040 \begin_layout Standard
2041 \begin_inset VSpace medskip
2047 \begin_layout Standard
2054 sets the fraction always in the size of a displayed formula, also when
2055 it is part of another fraction.
2058 \begin_layout Standard
2059 It is possible to specify the alignment of the numerator.
2066 is used to left align it, the command
2079 centers the numerator.
2080 These fractions demonstrate the different alignments:
2083 \begin_layout Standard
2086 \begin_inset Formula
2088 \cfrac[l]{A}{B+C}\,,\,\cfrac{A}{B+C}\,,\,\cfrac[r]{A}{B+C}
2096 \begin_layout Standard
2097 \begin_inset Note Greyedout
2100 \begin_layout Plain Layout
2117 are no real LaTeX commands but represent the command
2121 cfrac[alignment]{numerator}{denominator}
2124 Therefore you cannot use them in TeX code.
2132 \begin_layout Standard
2133 \begin_inset VSpace medskip
2136 It is often advantageous to combine
2149 \begin_inset Formula
2151 \cfrac{A}{B+\cfrac{C+\frac{E}{F}}{D}}
2159 \begin_layout Standard
2160 For inline fractions with a sloped fraction stroke you can use the command
2168 \begin_inset Index idx
2171 \begin_layout Plain Layout
2180 \begin_inset Formula $\nicefrac{5}{31}$
2190 \begin_inset Index idx
2193 \begin_layout Plain Layout
2202 \begin_inset Formula $\unitfrac{5}{31}$
2205 There is furthermore the command
2211 that offers to write a fraction in combination with a number:
2212 \begin_inset Formula $\unitfrac[2]{1}{3}$
2218 \begin_layout Standard
2219 \begin_inset Note Greyedout
2222 \begin_layout Plain Layout
2233 is not a real LaTeX command but the command
2234 \begin_inset Newline newline
2241 unitfrac[number]{numerator}{denominator}
2244 Therefore you cannot use it in TeX code.
2252 \begin_layout Standard
2253 How to define own fractions where the fraction stroke can be changed, is
2255 \begin_inset CommandInset ref
2257 reference "sub:Self-defined-Fractions"
2264 \begin_layout Standard
2265 \begin_inset Newpage newpage
2271 \begin_layout Subsection
2273 \begin_inset Index idx
2276 \begin_layout Plain Layout
2285 \begin_layout Standard
2286 Square roots are created with
2293 \begin_inset Index idx
2296 \begin_layout Plain Layout
2304 or the math toolbar button
2307 arg "math-insert \\sqrt"
2310 , all other roots with the command
2317 \begin_inset Index idx
2320 \begin_layout Plain Layout
2328 or with the math toolbar button
2331 arg "math-insert \\root"
2337 \begin_layout Standard
2339 \begin_inset Tabular
2340 <lyxtabular version="3" rows="3" columns="2">
2341 <features rotate="0" tabularvalignment="middle">
2342 <column alignment="center" valignment="top" width="0pt">
2343 <column alignment="center" valignment="top" width="0pt">
2345 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
2348 \begin_layout Plain Layout
2354 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
2357 \begin_layout Plain Layout
2359 \begin_inset Note Note
2362 \begin_layout Plain Layout
2369 is only used as spacer.
2381 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
2384 \begin_layout Plain Layout
2388 \begin_inset space \textvisiblespace{}
2396 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
2399 \begin_layout Plain Layout
2400 \begin_inset Formula $\raisebox{4.5mm}{}\sqrt{A-B}$
2410 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
2413 \begin_layout Plain Layout
2417 \begin_inset space \textvisiblespace{}
2421 \begin_inset Formula $\downarrow$
2429 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
2432 \begin_layout Plain Layout
2433 \begin_inset Formula $\raisebox{4.5mm}{}\sqrt[3]{A-B}$
2449 \begin_layout Standard
2450 A square root can also be created with
2456 when the root index field is left empty.
2459 \begin_layout Standard
2460 With certain indices the distance to the root is too small, like in this
2462 \begin_inset Formula $\sqrt[\beta]{B}$
2466 \begin_inset Newline newline
2470 \begin_inset Formula $\beta$
2474 To avoid this, the commands
2481 \begin_inset Index idx
2484 \begin_layout Plain Layout
2499 \begin_inset Index idx
2502 \begin_layout Plain Layout
2510 are used with the following scheme:
2513 \begin_layout Standard
2527 \begin_layout Standard
2528 Distance is the number of Big Points (unit bp;
2529 \begin_inset Formula $\mathrm{72\, bp=1\, inch}$
2532 ), that the index should be moved to the left or top, resp..
2533 The commands are written to the index.
2534 This way the command
2535 \begin_inset Newline newline
2545 \begin_inset Formula $\to$
2551 \begin_inset Formula $\to$
2557 \begin_inset space \textvisiblespace{}
2561 \begin_inset Formula $\to$
2565 \begin_inset Newline newline
2570 produces a correct typeset formula:
2571 \begin_inset Formula $\sqrt[\leftroot{-1}\uproot{2}\beta]{B}$
2577 \begin_layout Subsection
2578 Binomial Coefficients
2579 \begin_inset Index idx
2582 \begin_layout Plain Layout
2583 Binomial coefficients
2591 \begin_layout Standard
2592 Binomial coefficients are inserted with the command
2599 \begin_inset Index idx
2602 \begin_layout Plain Layout
2610 or with the submenu of the math toolbar button
2613 arg "math-insert \\frac-square"
2629 there are the commands
2636 \begin_inset Index idx
2639 \begin_layout Plain Layout
2654 \begin_inset Index idx
2657 \begin_layout Plain Layout
2666 For other brackets around binomial coeficients there are the commands
2673 \begin_inset Index idx
2676 \begin_layout Plain Layout
2691 \begin_inset Index idx
2694 \begin_layout Plain Layout
2705 \begin_layout Standard
2707 \begin_inset Tabular
2708 <lyxtabular version="3" rows="6" columns="2">
2709 <features rotate="0" tabularvalignment="middle">
2710 <column alignment="center" valignment="top" width="0pt">
2711 <column alignment="center" valignment="top" width="0pt">
2713 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
2716 \begin_layout Plain Layout
2722 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
2725 \begin_layout Plain Layout
2727 \begin_inset Note Note
2730 \begin_layout Plain Layout
2737 is only used as spacer.
2749 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
2752 \begin_layout Plain Layout
2756 \begin_inset space \textvisiblespace{}
2760 \begin_inset Formula $\downarrow$
2768 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
2771 \begin_layout Plain Layout
2772 \begin_inset Formula $\raisebox{5mm}{}\binom{A}{B}\raisebox{-2.5mm}{}$
2782 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
2785 \begin_layout Plain Layout
2789 \begin_inset space \textvisiblespace{}
2793 \begin_inset Formula $\downarrow$
2801 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
2804 \begin_layout Plain Layout
2805 \begin_inset Formula $\raisebox{5mm}{}\dbinom{A}{B}\raisebox{-2.5mm}{}$
2815 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
2818 \begin_layout Plain Layout
2822 \begin_inset space \textvisiblespace{}
2826 \begin_inset Formula $\downarrow$
2834 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
2837 \begin_layout Plain Layout
2838 \begin_inset Formula $\raisebox{5mm}{}\tbinom{A}{B}\raisebox{-2.5mm}{}$
2848 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
2851 \begin_layout Plain Layout
2855 \begin_inset space \textvisiblespace{}
2859 \begin_inset Formula $\downarrow$
2867 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
2870 \begin_layout Plain Layout
2871 \begin_inset Formula $\raisebox{5mm}{}{A \brack B}\raisebox{-2.5mm}{}$
2881 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
2884 \begin_layout Plain Layout
2888 \begin_inset space \textvisiblespace{}
2892 \begin_inset Formula $\downarrow$
2900 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
2903 \begin_layout Plain Layout
2904 \begin_inset Formula $\raisebox{5mm}{}{A \brace B}\raisebox{-2.5mm}{}$
2920 \begin_layout Subsection
2921 Case Differentiations
2922 \begin_inset Index idx
2925 \begin_layout Plain Layout
2926 Case differentiations
2934 \begin_layout Standard
2936 \begin_inset Tabular
2937 <lyxtabular version="3" rows="3" columns="2">
2938 <features rotate="0" tabularvalignment="middle">
2939 <column alignment="center" valignment="top" width="0pt">
2940 <column alignment="center" valignment="top" width="0pt">
2942 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
2945 \begin_layout Plain Layout
2951 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
2954 \begin_layout Plain Layout
2962 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
2965 \begin_layout Plain Layout
2969 \begin_inset space \textvisiblespace{}
2973 \begin_inset Formula $\to$
2977 \begin_inset Index idx
2980 \begin_layout Plain Layout
2993 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
2996 \begin_layout Plain Layout
2997 \begin_inset Formula $\begin{cases}
3008 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
3011 \begin_layout Plain Layout
3015 \begin_inset space \textvisiblespace{}
3021 arg "newline-insert newline"
3029 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
3032 \begin_layout Plain Layout
3033 \begin_inset Formula $\begin{cases}
3034 A & \textrm{for }x>0\\
3035 B & \textrm{for }x=0
3052 \begin_layout Standard
3059 or pressing the math toolbar button
3062 arg "math-insert \\cases"
3065 you can create new lines with the shortcut
3068 arg "newline-insert newline"
3071 or the table toolbar button
3074 arg "inset-modify tabular append-row"
3080 \begin_layout Standard
3087 is also available via the menu
3089 Insert\SpecialChar \menuseparator
3090 Math\SpecialChar \menuseparator
3096 \begin_layout Subsection
3098 \begin_inset Index idx
3101 \begin_layout Plain Layout
3110 \begin_layout Standard
3118 \begin_inset Index idx
3121 \begin_layout Plain Layout
3129 every character can be displayed canceled.
3130 The characters are quasi accentuated by a slash.
3133 \begin_layout Standard
3135 \begin_inset Tabular
3136 <lyxtabular version="3" rows="4" columns="2">
3137 <features rotate="0" tabularvalignment="middle">
3138 <column alignment="center" valignment="top" width="0pt">
3139 <column alignment="center" valignment="top" width="0pt">
3141 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
3144 \begin_layout Plain Layout
3150 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
3153 \begin_layout Plain Layout
3161 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
3164 \begin_layout Plain Layout
3172 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
3175 \begin_layout Plain Layout
3176 \begin_inset Formula $\not=$
3186 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
3189 \begin_layout Plain Layout
3199 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
3202 \begin_layout Plain Layout
3203 \begin_inset Formula $\not\le$
3213 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
3216 \begin_layout Plain Layout
3226 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
3229 \begin_layout Plain Layout
3230 \begin_inset Formula $\not\parallel$
3246 \begin_layout Standard
3247 The last example shows that not all negations look good.
3248 Therefore there are special commands for some negations (see
3249 \begin_inset CommandInset ref
3251 reference "sub:Mathematical-Symbols"
3256 \begin_inset CommandInset ref
3258 reference "sec:Relations"
3265 \begin_layout Subsection
3267 \begin_inset CommandInset label
3269 name "sub:Placeholders"
3274 \begin_inset Index idx
3277 \begin_layout Plain Layout
3284 \begin_inset Index idx
3287 \begin_layout Plain Layout
3288 Chemical characters ! Isotopes
3294 \begin_inset Index idx
3297 \begin_layout Plain Layout
3302 \begin_layout Plain Layout
3313 \begin_layout Plain Layout
3328 \begin_layout Standard
3330 \begin_inset space \thinspace{}
3334 \begin_inset space \space{}
3341 \begin_layout Plain Layout
3342 Typesetting isotopes and chemical symbols is described in
3343 \begin_inset CommandInset ref
3345 reference "sub:Chemical-Symbols-and"
3354 the following problem occurs:
3357 \begin_layout Standard
3359 \begin_inset Tabular
3360 <lyxtabular version="3" rows="2" columns="2">
3361 <features rotate="0" tabularvalignment="middle">
3362 <column alignment="center" valignment="top" width="0pt">
3363 <column alignment="center" valignment="top" width="0pt">
3365 <cell alignment="center" valignment="top" usebox="none">
3368 \begin_layout Plain Layout
3369 Indices created with sub- and superscripts:
3374 <cell alignment="center" valignment="top" usebox="none">
3377 \begin_layout Plain Layout
3378 \begin_inset Formula $_{9}^{19}\mathrm{F}\raisebox{-3mm}{}$
3388 <cell alignment="center" valignment="top" usebox="none">
3391 \begin_layout Plain Layout
3397 <cell alignment="center" valignment="top" usebox="none">
3400 \begin_layout Plain Layout
3401 \begin_inset Formula $_{\phantom{1}9}^{19}\mathrm{F}$
3415 \begin_inset Note Note
3418 \begin_layout Plain Layout
3425 is only used as spacer.
3433 \begin_layout Standard
3434 The shorter index is by default placed below or above the first character
3435 of the longer index.
3436 To avoid this there is the command
3443 \begin_inset Index idx
3446 \begin_layout Plain Layout
3454 or the math toolbar button
3455 \begin_inset space \thinspace{}
3462 \begin_layout Plain Layout
3463 can be found in the submenu of the toolbar button
3468 arg "math-insert \\space"
3477 \begin_inset Graphics
3478 filename ../images/math/phantom.png
3483 that creates one or more phantom characters.
3490 a small blue box appears that is superposed with two red arrows.
3491 The arrows indicate that the complete width and height of the box content
3492 will be created as placeholder.
3493 Phantom characters are accordingly placeholders with the size of the characters.
3496 \begin_layout Standard
3498 \begin_inset Tabular
3499 <lyxtabular version="3" rows="4" columns="2">
3500 <features rotate="0" tabularvalignment="middle">
3501 <column alignment="center" valignment="top">
3502 <column alignment="center" valignment="top">
3504 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
3507 \begin_layout Plain Layout
3513 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
3516 \begin_layout Plain Layout
3518 \begin_inset Note Note
3521 \begin_layout Plain Layout
3528 is only used as spacer.
3540 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
3543 \begin_layout Plain Layout
3545 \begin_inset space \textvisiblespace{}
3551 \begin_inset space \textvisiblespace{}
3555 \begin_inset Formula $\to$
3559 \begin_inset space \textvisiblespace{}
3567 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
3570 \begin_layout Plain Layout
3571 \begin_inset Formula $\raisebox{4.5mm}{}{}_{\phantom{1}9}^{19}\mathrm{F}\raisebox{-2.5mm}{}$
3581 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
3584 \begin_layout Plain Layout
3586 \begin_inset space \textvisiblespace{}
3592 \begin_inset space \textvisiblespace{}
3596 \begin_inset Formula $\to$
3600 \begin_inset space \textvisiblespace{}
3608 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
3611 \begin_layout Plain Layout
3612 \begin_inset Formula $\raisebox{4.5mm}{}{}_{\phantom{23}9}^{235}\mathrm{F}\raisebox{-2.5mm}{}$
3622 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
3625 \begin_layout Plain Layout
3629 \begin_inset space \textvisiblespace{}
3635 \begin_inset space \textvisiblespace{}
3639 \begin_inset Formula $\to$
3643 \begin_inset space \textvisiblespace{}
3651 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
3654 \begin_layout Plain Layout
3655 \begin_inset Formula $\raisebox{4.5mm}{}\Lambda_{MMt}^{\phantom{ii}t}\raisebox{-2.5mm}{}$
3671 \begin_layout Standard
3672 Furthermore there are the commands
3679 \begin_inset Index idx
3682 \begin_layout Plain Layout
3691 \begin_inset space ~
3695 \begin_inset Graphics
3696 filename ../images/math/vphantom.png
3708 \begin_inset Index idx
3711 \begin_layout Plain Layout
3720 \begin_inset space ~
3724 \begin_inset Graphics
3725 filename ../images/math/hphantom.png
3737 creates only space for the maximal height of the characters in the box
3738 but not for its width.
3745 creates only space for the width of the box content.
3746 Therefore the boxes of both commands have only one red arrow.
3749 \begin_layout Standard
3750 For example the command
3755 \begin_inset space \textvisiblespace{}
3762 creates space for the height of the integral sign,
3766 \begin_layout Plain Layout
3773 creates an integral sign, see
3774 \begin_inset CommandInset ref
3776 reference "sub:Big-Operators"
3785 because this is the larger character.
3786 An example application is in
3787 \begin_inset CommandInset ref
3789 reference "sub:Multiline-Brackets"
3796 \begin_layout Standard
3797 Placeholders can also be used for text when they are inserted via the menu
3800 Insert\SpecialChar \menuseparator
3801 Formatting\SpecialChar \menuseparator
3807 \begin_layout Standard
3809 \begin_inset Newline newline
3813 \begin_inset Phantom Phantom
3816 \begin_layout Plain Layout
3825 \begin_layout Subsection
3827 \begin_inset Index idx
3830 \begin_layout Plain Layout
3837 \begin_inset Index idx
3840 \begin_layout Plain Layout
3841 Formula ! underlined
3849 \begin_layout Standard
3851 \begin_inset Tabular
3852 <lyxtabular version="3" rows="4" columns="2">
3853 <features rotate="0" tabularvalignment="middle">
3854 <column alignment="center" valignment="top" width="0pt">
3855 <column alignment="center" valignment="top" width="0pt">
3857 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
3860 \begin_layout Plain Layout
3866 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
3869 \begin_layout Plain Layout
3871 \begin_inset Note Note
3874 \begin_layout Plain Layout
3881 is only used as spacer.
3893 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
3896 \begin_layout Plain Layout
3900 \begin_inset space \textvisiblespace{}
3904 \begin_inset Index idx
3907 \begin_layout Plain Layout
3920 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
3923 \begin_layout Plain Layout
3924 \begin_inset Formula $\raisebox{5mm}{}\overline{A+B}$
3934 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
3937 \begin_layout Plain Layout
3941 \begin_inset space \textvisiblespace{}
3945 \begin_inset Index idx
3948 \begin_layout Plain Layout
3961 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
3964 \begin_layout Plain Layout
3965 \begin_inset Formula $\underline{A+B}\raisebox{-2.5mm}{}$
3975 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
3978 \begin_layout Plain Layout
3982 \begin_inset space \textvisiblespace{}
3988 \begin_inset space \textvisiblespace{}
3996 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
3999 \begin_layout Plain Layout
4000 \begin_inset Formula $\raisebox{5mm}{}\overline{\underline{A+B}}\raisebox{-2.5mm}{}$
4016 \begin_layout Standard
4017 In the last example it doesn't matter if first
4032 \begin_layout Standard
4033 To double underline use
4042 \begin_layout Standard
4043 It is possible to place up to 6 lines above or below characters.
4046 \begin_layout Standard
4047 \begin_inset VSpace bigskip
4050 Custom lines can be created using the command
4057 \begin_inset Index idx
4060 \begin_layout Plain Layout
4068 which has the following scheme:
4071 \begin_layout Standard
4076 rule[vertical offset]{length}{thickness}
4079 \begin_layout Standard
4080 The optional vertical offset shifts the line upwards (or downwards, when
4081 the value is negative).
4083 \begin_inset CommandInset ref
4085 reference "tab:Available-units"
4089 can be used for the values.
4090 Here are two example lines created with the commands
4091 \begin_inset Newline newline
4098 rule[-2ex]{3cm}{2pt}
4109 \begin_layout Standard
4111 \begin_inset Formula $\rule[-2ex]{3cm}{2pt}\rule{2cm}{1pt}$
4117 \begin_layout Standard
4124 can also be used for text when a line is inserted via the menu
4126 Insert\SpecialChar \menuseparator
4127 Formatting\SpecialChar \menuseparator
4129 \begin_inset space ~
4137 \begin_layout Standard
4139 \begin_inset CommandInset line
4150 \begin_layout Subsection
4152 \begin_inset CommandInset label
4159 \begin_inset Index idx
4162 \begin_layout Plain Layout
4171 \begin_layout Standard
4172 There are different types of ellipses available.
4176 \begin_layout Plain Layout
4177 In the math toolbar in the submenu of the button
4180 arg "math-insert \\ldots"
4188 For listings dots at the baseline are used (
4195 \begin_inset Index idx
4198 \begin_layout Plain Layout
4206 ), while for operations dots are needed that are on the same height as the
4214 \begin_inset Index idx
4217 \begin_layout Plain Layout
4226 When using the command
4233 \begin_inset Index idx
4236 \begin_layout Plain Layout
4244 , LaTeX decides on the basis of the next character what type is used.
4247 \begin_layout Standard
4249 \begin_inset Tabular
4250 <lyxtabular version="3" rows="9" columns="2">
4251 <features rotate="0" tabularvalignment="middle">
4252 <column alignment="center" valignment="top" width="0pt">
4253 <column alignment="center" valignment="top" width="0pt">
4255 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
4258 \begin_layout Plain Layout
4264 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
4267 \begin_layout Plain Layout
4275 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
4278 \begin_layout Plain Layout
4280 \begin_inset space \textvisiblespace{}
4286 \begin_inset space \textvisiblespace{}
4294 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
4297 \begin_layout Plain Layout
4298 \begin_inset Formula $A_{1},\dots,A_{n}$
4308 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
4311 \begin_layout Plain Layout
4313 \begin_inset space \textvisiblespace{}
4319 \begin_inset space \textvisiblespace{}
4327 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
4330 \begin_layout Plain Layout
4331 \begin_inset Formula $A_{1}+\dots+A_{n}$
4341 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
4344 \begin_layout Plain Layout
4346 \begin_inset space \textvisiblespace{}
4352 \begin_inset space \textvisiblespace{}
4360 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
4363 \begin_layout Plain Layout
4364 \begin_inset Formula $A_{1},\ldots,A_{n}$
4374 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
4377 \begin_layout Plain Layout
4379 \begin_inset space \textvisiblespace{}
4385 \begin_inset space \textvisiblespace{}
4393 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
4396 \begin_layout Plain Layout
4397 \begin_inset Formula $A_{1}+\cdots+A_{n}$
4407 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
4410 \begin_layout Plain Layout
4418 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
4421 \begin_layout Plain Layout
4422 \begin_inset Formula $\vdots$
4432 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
4435 \begin_layout Plain Layout
4443 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
4446 \begin_layout Plain Layout
4447 \begin_inset Formula $\ddots$
4457 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
4460 \begin_layout Plain Layout
4468 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
4471 \begin_layout Plain Layout
4472 \begin_inset Formula $\iddots$
4482 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
4485 \begin_layout Plain Layout
4487 \begin_inset space \thinspace{}
4490 matrix with the different dots
4495 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
4498 \begin_layout Plain Layout
4499 \begin_inset Formula $\begin{array}{ccc}
4500 A_{11} & \cdots & A_{1m}\\
4501 \vdots & \ddots & \vdots\\
4502 A_{n1} & \cdots & A_{nm}
4519 \begin_layout Standard
4520 The ellipses available in menu
4522 Insert\SpecialChar \menuseparator
4524 \begin_inset space ~
4538 \begin_layout Standard
4539 \begin_inset VSpace medskip
4548 , one of the options
4550 Use mathdots package (automatically)
4552 must be set in the document settings under
4555 \begin_inset space ~
4561 \begin_inset Newline newline
4566 Use mathdots package
4568 will improve the appearance of all dots in the documents if their font
4569 style or size is not the default.
4572 \begin_layout Standard
4573 \begin_inset VSpace medskip
4576 Specially for matrices there are ellipses that span over several columns.
4577 They are created with the command
4584 \begin_inset Index idx
4587 \begin_layout Plain Layout
4595 , that has the following scheme:
4598 \begin_layout Standard
4603 hdotsfor[distance]{number of columns}
4606 \begin_layout Standard
4607 The number of columns specifies how many columns should be spanned.
4608 Distance is a factor for the distance between the dots.
4611 \begin_layout Standard
4612 In the following matrix the command
4618 was inserted in the first box of the second line, to get an ellipsis with
4619 a dot distance twice as long as with the command
4626 \begin_inset Formula
4628 \left(\begin{array}{cccc}
4637 Note that the matrix fields that should be spanned must be empty, otherwise
4638 you get LaTeX-errors.
4641 \begin_layout Standard
4642 \begin_inset VSpace bigskip
4645 Furthermore you can fill with the command
4652 \begin_inset Index idx
4655 \begin_layout Plain Layout
4663 the rest of a line with dots.
4664 The effect of these commands is the same as with
4671 \begin_inset CommandInset ref
4673 reference "sub:Variable-Space"
4680 \begin_layout Standard
4681 For example the command
4686 \begin_inset space \textvisiblespace{}
4694 \begin_layout Standard
4695 \begin_inset Formula $A\dotfill B$
4701 \begin_layout Standard
4708 there is for a line the command
4715 \begin_inset Index idx
4718 \begin_layout Plain Layout
4729 \begin_layout Standard
4730 \begin_inset Formula $A\hrulefill B$
4736 \begin_layout Standard
4737 To use the commands for text, they have to be inserted in TeX-mode.
4740 \begin_layout Section
4742 \begin_inset CommandInset label
4749 \begin_inset Index idx
4752 \begin_layout Plain Layout
4761 \begin_layout Standard
4762 Matrices can be inserted via the math toolbar button
4765 arg "dialog-show mathmatrix"
4770 Insert\SpecialChar \menuseparator
4771 Math\SpecialChar \menuseparator
4775 In the matrix dialog you can specify the number of columns and rows, the
4776 alignment and the decoration.
4777 The vertical alignment is only of importance for matrices in inline formulas:
4780 \begin_layout Standard
4781 The first matrix is top
4782 \begin_inset Formula $\begin{array}[t]{cccc}
4790 \begin_inset Formula $\begin{array}{cccc}
4797 and the third bottom
4798 \begin_inset Formula $\begin{array}[b]{cccc}
4808 \begin_layout Standard
4809 The horizontal alignment specifies how the column entries should be aligned.
4810 It is set by entering a letter for every column.
4815 denotes left aligned,
4824 To create for example a 4
4829 \begin_inset space ~
4832 matrix where the first column is left aligned, the second and third are
4833 centered and the last one is right aligned, one enters for the horizontal
4839 Normally in a matrix all columns are centered, therefore the default for
4847 \begin_layout Standard
4848 Horizontal alignment:
4851 \begin_layout Standard
4857 \begin_inset Formula $\begin{array}{lll}
4869 \begin_inset Formula $\begin{array}{ccc}
4881 \begin_inset Formula $\begin{array}{rrr}
4891 \begin_layout Standard
4892 To add or delete rows and columns subsequently, the math toolbar buttons
4896 arg "inset-modify tabular append-row"
4902 arg "inset-modify tabular delete-row"
4906 \begin_inset space \thinspace{}
4911 Edit\SpecialChar \menuseparator
4915 New rows can also be created with
4918 arg "newline-insert newline"
4924 \begin_layout Standard
4925 \begin_inset VSpace bigskip
4932 adds parentheses in the selected style around the matrix.
4933 Alternatively, parentheses can can either be created with the commands
4941 \begin_inset Index idx
4944 \begin_layout Plain Layout
4959 \begin_inset Index idx
4962 \begin_layout Plain Layout
4973 \begin_inset space ~
4979 \begin_inset CommandInset ref
4981 reference "sub:Automatic-Bracket-Size"
4985 , or by using the following commands:
4986 \begin_inset VSpace medskip
4992 \begin_layout Standard
4993 \begin_inset space \hfill{}
4997 \begin_inset Tabular
4998 <lyxtabular version="3" rows="4" columns="2">
4999 <features rotate="0" tabularvalignment="middle">
5000 <column alignment="center" valignment="top">
5001 <column alignment="center" valignment="top">
5003 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
5006 \begin_layout Plain Layout
5012 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
5015 \begin_layout Plain Layout
5017 \begin_inset Note Note
5020 \begin_layout Plain Layout
5027 is only used as spacer.
5039 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
5042 \begin_layout Plain Layout
5046 \begin_inset space \textvisiblespace{}
5054 \begin_inset space \thinspace{}
5062 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
5065 \begin_layout Plain Layout
5066 \begin_inset Formula $\raisebox{7.5mm}{}\begin{bmatrix}\begin{array}{cc}
5067 0 & \textrm{-}\mathrm{i}\\
5069 \end{array}\end{bmatrix}\raisebox{-5.3mm}{}$
5079 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
5082 \begin_layout Plain Layout
5086 \begin_inset space \textvisiblespace{}
5094 \begin_inset space \thinspace{}
5102 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
5105 \begin_layout Plain Layout
5106 \begin_inset Formula $\raisebox{7.5mm}{}\begin{Bmatrix}\begin{array}{cc}
5107 0 & \textrm{-}\mathrm{i}\\
5109 \end{array}\end{Bmatrix}\raisebox{-5.3mm}{}$
5119 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
5122 \begin_layout Plain Layout
5126 \begin_inset space \textvisiblespace{}
5134 \begin_inset space \thinspace{}
5142 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
5145 \begin_layout Plain Layout
5146 \begin_inset Formula $\raisebox{7.5mm}{}\begin{pmatrix}\begin{array}{cc}
5147 0 & \textrm{-}\mathrm{i}\\
5149 \end{array}\end{pmatrix}\raisebox{-5.3mm}{}$
5163 \begin_inset space \hfill{}
5167 \begin_inset Tabular
5168 <lyxtabular version="3" rows="4" columns="2">
5169 <features rotate="0" tabularvalignment="middle">
5170 <column alignment="center" valignment="top">
5171 <column alignment="center" valignment="top">
5173 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
5176 \begin_layout Plain Layout
5182 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
5185 \begin_layout Plain Layout
5193 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
5196 \begin_layout Plain Layout
5200 \begin_inset space \textvisiblespace{}
5208 \begin_inset space \thinspace{}
5216 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
5219 \begin_layout Plain Layout
5220 \begin_inset Formula $\raisebox{7.5mm}{}\begin{vmatrix}\begin{array}{cc}
5221 0 & \textrm{-}\mathrm{i}\\
5223 \end{array}\end{vmatrix}\raisebox{-5.3mm}{}$
5233 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
5236 \begin_layout Plain Layout
5240 \begin_inset space \textvisiblespace{}
5248 \begin_inset space \thinspace{}
5256 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
5259 \begin_layout Plain Layout
5260 \begin_inset Formula $\raisebox{7.5mm}{}\begin{Vmatrix}\begin{array}{cc}
5261 0 & \textrm{-}\mathrm{i}\\
5263 \end{array}\end{Vmatrix}\raisebox{-5.3mm}{}$
5273 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
5276 \begin_layout Plain Layout
5280 \begin_inset space \textvisiblespace{}
5288 \begin_inset space \thinspace{}
5296 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
5299 \begin_layout Plain Layout
5300 \begin_inset Formula $\raisebox{7.5mm}{}\begin{matrix}\begin{array}{cc}
5301 0 & \textrm{-}\mathrm{i}\\
5303 \end{array}\end{matrix}\raisebox{-5.3mm}{}$
5317 \begin_inset space \hfill{}
5323 \begin_layout Standard
5324 \begin_inset VSpace medskip
5328 \begin_inset space \thinspace{}
5332 \begin_inset space \space{}
5341 is inserted, a blue box appears between two vertical lines where the matrix
5343 \begin_inset Newline newline
5346 Note that decorated matrices ignore the vertical alignment.
5349 \begin_layout Standard
5350 \begin_inset VSpace bigskip
5353 As all multiline formulas are matrices, the length
5360 \begin_inset Index idx
5363 \begin_layout Plain Layout
5371 that is described in
5372 \begin_inset CommandInset ref
5374 reference "sub:Column-Separation"
5378 can also be used to change the column separation of matrices.
5381 \begin_layout Standard
5382 To change the row separation, the command
5389 \begin_inset Index idx
5392 \begin_layout Plain Layout
5401 It is used as follows:
5404 \begin_layout Standard
5411 arraystretch}{stretch factor}
5412 \begin_inset Index idx
5415 \begin_layout Plain Layout
5426 \begin_layout Standard
5433 assigns the stretch factor to the predefined command
5441 \begin_inset space \thinspace{}
5445 \begin_inset space \space{}
5448 the row separation, use the factor 2.
5449 This is then used for all following matrices.
5450 To go back to the original separation, assign the factor 1 to
5459 \begin_layout Standard
5460 To set matrices into a text line, the command
5467 \begin_inset Index idx
5470 \begin_layout Plain Layout
5479 When it is inserted a blue box with two dashed lines appears.
5480 In this box the matrix is inserted.
5483 \begin_layout Standard
5485 \begin_inset Formula $\left(\begin{smallmatrix}A & B\\
5487 \end{smallmatrix}\right)$
5493 \begin_layout Section
5494 Brackets and Delimiters
5495 \begin_inset Index idx
5498 \begin_layout Plain Layout
5505 \begin_inset Index idx
5508 \begin_layout Plain Layout
5517 \begin_layout Subsection
5518 Vertical Brackets and Delimiters
5519 \begin_inset Index idx
5522 \begin_layout Plain Layout
5531 \begin_layout Standard
5532 \begin_inset space \hfill{}
5536 \begin_inset Tabular
5537 <lyxtabular version="3" rows="9" columns="2">
5538 <features rotate="0" tabularvalignment="middle">
5539 <column alignment="center" valignment="top" width="0pt">
5540 <column alignment="center" valignment="top" width="0pt">
5542 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
5545 \begin_layout Plain Layout
5551 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
5554 \begin_layout Plain Layout
5562 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
5565 \begin_layout Plain Layout
5571 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
5574 \begin_layout Plain Layout
5575 \begin_inset Formula $($
5585 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
5588 \begin_layout Plain Layout
5594 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
5597 \begin_layout Plain Layout
5598 \begin_inset Formula $\{$
5608 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
5611 \begin_layout Plain Layout
5617 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
5620 \begin_layout Plain Layout
5621 \begin_inset Formula $[$
5631 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
5634 \begin_layout Plain Layout
5642 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
5645 \begin_layout Plain Layout
5646 \begin_inset Formula $\langle$
5656 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
5659 \begin_layout Plain Layout
5667 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
5670 \begin_layout Plain Layout
5671 \begin_inset Formula $\lceil$
5681 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
5684 \begin_layout Plain Layout
5692 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
5695 \begin_layout Plain Layout
5696 \begin_inset Formula $\lfloor$
5706 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
5709 \begin_layout Plain Layout
5715 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
5718 \begin_layout Plain Layout
5719 \begin_inset Formula $/$
5729 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
5732 \begin_layout Plain Layout
5738 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
5741 \begin_layout Plain Layout
5742 \begin_inset Formula $|$
5756 \begin_inset space \hfill{}
5760 \begin_inset Tabular
5761 <lyxtabular version="3" rows="9" columns="2">
5762 <features rotate="0" tabularvalignment="middle">
5763 <column alignment="center" valignment="top" width="0pt">
5764 <column alignment="center" valignment="top" width="0pt">
5766 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
5769 \begin_layout Plain Layout
5775 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
5778 \begin_layout Plain Layout
5786 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
5789 \begin_layout Plain Layout
5795 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
5798 \begin_layout Plain Layout
5799 \begin_inset Formula $)$
5809 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
5812 \begin_layout Plain Layout
5818 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
5821 \begin_layout Plain Layout
5822 \begin_inset Formula $\}$
5832 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
5835 \begin_layout Plain Layout
5841 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
5844 \begin_layout Plain Layout
5845 \begin_inset Formula $]$
5855 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
5858 \begin_layout Plain Layout
5866 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
5869 \begin_layout Plain Layout
5870 \begin_inset Formula $\rangle$
5880 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
5883 \begin_layout Plain Layout
5891 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
5894 \begin_layout Plain Layout
5895 \begin_inset Formula $\rceil$
5905 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
5908 \begin_layout Plain Layout
5916 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
5919 \begin_layout Plain Layout
5920 \begin_inset Formula $\rfloor$
5930 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
5933 \begin_layout Plain Layout
5943 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
5946 \begin_layout Plain Layout
5947 \begin_inset Formula $\backslash$
5957 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
5960 \begin_layout Plain Layout
5968 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
5971 \begin_layout Plain Layout
5972 \begin_inset Formula $\|$
5986 \begin_inset space \hfill{}
5992 \begin_layout Standard
5995 \begin_inset Note Greyedout
5998 \begin_layout Plain Layout
6003 In TeX-mode the command
6010 \begin_inset Index idx
6013 \begin_layout Plain Layout
6021 must be used for the backslash, because the command
6029 produces a line break there.
6037 \begin_layout Standard
6038 For all characters listed above the size can be adjusted with the commands
6039 described in the following two subsections.
6040 When using these commands, the characters < and > can directly be used
6041 instead of the commands
6056 \begin_layout Subsubsection
6058 \begin_inset CommandInset label
6060 name "sub:Manual-Bracket-Size"
6065 \begin_inset Index idx
6068 \begin_layout Plain Layout
6069 Bracket size ! manual
6077 \begin_layout Standard
6078 The bracket size can be specified manually by the LaTeX-commands
6085 \begin_inset Index idx
6088 \begin_layout Plain Layout
6121 denotes the smallest and
6127 the largest bracket size.
6130 \begin_layout Standard
6131 These commands are used to emphasize levels of brackets:
6134 \begin_layout Standard
6136 \begin_inset Tabular
6137 <lyxtabular version="3" rows="2" columns="2">
6138 <features rotate="0" tabularvalignment="middle">
6139 <column alignment="center" valignment="top" width="0pt">
6140 <column alignment="center" valignment="top" width="0pt">
6142 <cell alignment="center" valignment="top" usebox="none">
6145 \begin_layout Plain Layout
6146 all brackets in the same size:
6151 <cell alignment="center" valignment="top" usebox="none">
6154 \begin_layout Plain Layout
6155 \begin_inset Formula $((A+B)(A-B))^{C}\raisebox{-4mm}{}$
6165 <cell alignment="center" valignment="top" usebox="none">
6168 \begin_layout Plain Layout
6174 <cell alignment="center" valignment="top" usebox="none">
6177 \begin_layout Plain Layout
6178 \begin_inset Formula $\Big((A+B)(A-B)\Big)^{C}$
6192 \begin_inset Note Note
6195 \begin_layout Plain Layout
6202 is only used as spacer.
6210 \begin_layout Standard
6211 For the second formula the command
6218 \begin_inset space \textvisiblespace{}
6226 \begin_layout Standard
6227 Here is an overview about all bracket sizes:
6230 \begin_layout Standard
6247 \begin_inset space \textvisiblespace{}
6255 \begin_inset space \textvisiblespace{}
6259 \begin_inset space \textvisiblespace{}
6269 \begin_layout Standard
6271 \begin_inset Formula $\Bigg(\exp\bigg<\Big[\big\{\ln(3x)\big\}^{2}\sin(x)\Big]^{A}\bigg>\Bigg)^{0,5}$
6277 \begin_layout Standard
6284 -commands there is the variant
6291 \begin_inset Index idx
6294 \begin_layout Plain Layout
6302 that adds a bit more space between the bracket and its content, and the
6316 \begin_inset Index idx
6319 \begin_layout Plain Layout
6329 , that don't add additional space.
6334 at the end of the command
6340 is for a left bracket; for a right bracket this will be replaced by an
6346 A left or right bracket can each be an opening or closing bracket.
6349 \begin_layout Standard
6350 In the following table is a comparison of the variants:
6353 \begin_layout Standard
6355 \begin_inset Tabular
6356 <lyxtabular version="3" rows="5" columns="2">
6357 <features rotate="0" tabularvalignment="middle">
6358 <column alignment="center" valignment="middle">
6359 <column alignment="center" valignment="middle">
6361 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
6364 \begin_layout Plain Layout
6370 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
6373 \begin_layout Plain Layout
6375 \begin_inset Note Note
6378 \begin_layout Plain Layout
6385 is only used as spacer.
6397 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
6400 \begin_layout Plain Layout
6410 \begin_inset space \textvisiblespace{}
6420 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
6423 \begin_layout Plain Layout
6424 \begin_inset Formula $\raisebox{5.5mm}{}\Bigm(\bigm(\ln(3x)\bigm)^{2}\Bigm)\raisebox{-3.25mm}{}$
6434 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
6437 \begin_layout Plain Layout
6447 \begin_inset space \textvisiblespace{}
6457 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
6460 \begin_layout Plain Layout
6461 \begin_inset Formula $\raisebox{5.5mm}{}\Big(\big(\ln(3x)\big)^{2}\Big)\raisebox{-3.25mm}{}$
6471 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
6474 \begin_layout Plain Layout
6484 \begin_inset space \textvisiblespace{}
6494 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
6497 \begin_layout Plain Layout
6498 \begin_inset Formula $\raisebox{5.5mm}{}\Bigl(\bigl(\ln(3x)\bigr)^{2}\Bigr)\raisebox{-3.25mm}{}$
6508 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
6511 \begin_layout Plain Layout
6523 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
6526 \begin_layout Plain Layout
6527 \begin_inset Formula $\raisebox{4.5mm}{}\bigl)\ln(3x)\bigr(\raisebox{-2mm}{}$
6543 \begin_layout Subsubsection
6544 Automatic Bracket Size
6545 \begin_inset CommandInset label
6547 name "sub:Automatic-Bracket-Size"
6552 \begin_inset Index idx
6555 \begin_layout Plain Layout
6556 Bracket size ! automatic
6564 \begin_layout Standard
6565 Brackets with variable size can be inserted with the commands
6572 \begin_inset Index idx
6575 \begin_layout Plain Layout
6590 \begin_inset Index idx
6593 \begin_layout Plain Layout
6601 or via the math toolbar button
6604 arg "dialog-show mathdelimiter"
6620 the wanted bracket must be inserted.
6621 The bracket size will then automatically be calculated for the output.
6624 \begin_layout Standard
6626 normal bracket: The command
6633 \begin_inset space \textvisiblespace{}
6637 \begin_inset Formula $\downarrow$
6641 \begin_inset space \textvisiblespace{}
6647 \begin_inset Formula
6657 \begin_layout Standard
6659 multiline bracket: The command
6668 \begin_inset space \textvisiblespace{}
6672 \begin_inset Formula $\downarrow$
6676 \begin_inset space \textvisiblespace{}
6684 \begin_inset Formula
6686 \ln\left(\frac{A}{C}\right)
6694 \begin_layout Standard
6710 \begin_inset space ~
6716 This has the advantage that you can see in LyX immediately the real bracket
6717 size and that the matching right bracket will be created too.
6718 \begin_inset Newline newline
6721 The command for the last example would then be:
6732 \begin_inset space \textvisiblespace{}
6736 \begin_inset Formula $\downarrow$
6742 \begin_layout Standard
6743 To omit a left or right bracket, a dot is inserted for the omitted bracket.
6744 For example the command
6751 \begin_inset space \textvisiblespace{}
6755 \begin_inset Formula $\downarrow$
6759 \begin_inset space \textvisiblespace{}
6769 \begin_inset Formula
6771 \left.\frac{A}{B}\right\}
6790 will be converted by LyX to brackets in the right size when the document
6791 is reloaded and an omitted bracket will appear as dashed line.
6794 \begin_layout Standard
6795 \begin_inset VSpace bigskip
6798 Because all popular LaTeX-Distributions use eTeX, an extension to LaTeX,
6806 \begin_inset Index idx
6809 \begin_layout Plain Layout
6817 is additionally available for all brackets and limits.
6818 With this command the height of the following character is adapted to the
6819 one of the surrounding brackets, what is e.
6820 \begin_inset space \thinspace{}
6824 \begin_inset space \space{}
6827 needed for physical vectors:
6828 \begin_inset Formula
6830 \left\langle \phi\:\middle|\: J=\frac{3}{2}\,,\, M_{J}\right\rangle
6835 For physical vectors there is a special LaTeX-package, described in
6836 \begin_inset CommandInset ref
6838 reference "sub:Physical-Vectors"
6845 \begin_layout Subsection
6847 \begin_inset Index idx
6850 \begin_layout Plain Layout
6851 Brackets ! horizontal
6859 \begin_layout Standard
6861 \begin_inset Tabular
6862 <lyxtabular version="3" rows="4" columns="2">
6863 <features rotate="0" tabularvalignment="middle">
6864 <column alignment="center" valignment="top" width="0pt">
6865 <column alignment="center" valignment="top" width="0pt">
6867 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
6870 \begin_layout Plain Layout
6872 \begin_inset Note Note
6875 \begin_layout Plain Layout
6882 is only used as spacer.
6892 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
6895 \begin_layout Plain Layout
6903 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
6906 \begin_layout Plain Layout
6910 \begin_layout Plain Layout
6922 \begin_inset space \textvisiblespace{}
6926 \begin_inset space \textvisiblespace{}
6933 \begin_layout Plain Layout
6941 \begin_inset Index idx
6944 \begin_layout Plain Layout
6957 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
6960 \begin_layout Plain Layout
6961 \begin_inset Formula $\overbrace{A+B}^{3}$
6971 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
6974 \begin_layout Plain Layout
6978 \begin_layout Plain Layout
6990 \begin_inset space \textvisiblespace{}
6994 \begin_inset space \textvisiblespace{}
7001 \begin_layout Plain Layout
7009 \begin_inset Index idx
7012 \begin_layout Plain Layout
7025 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
7028 \begin_layout Plain Layout
7029 \begin_inset Formula $\underbrace{A+B}_{5}$
7039 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
7042 \begin_layout Plain Layout
7046 \begin_inset space \textvisiblespace{}
7052 \begin_inset space \textvisiblespace{}
7056 \begin_inset space \textvisiblespace{}
7060 \begin_inset space \textvisiblespace{}
7064 \begin_inset space \textvisiblespace{}
7068 \begin_inset space \textvisiblespace{}
7072 \begin_inset space \textvisiblespace{}
7080 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
7083 \begin_layout Plain Layout
7084 \begin_inset Formula $\overbrace{\underbrace{A+B_{w}}_{7}}^{C}$
7100 \begin_layout Standard
7101 In the last example it doesn't matter if
7113 is inserted at first.
7116 \begin_layout Standard
7117 \begin_inset VSpace bigskip
7120 When brackets are needed that overlap each other, multiline formulas, as
7122 \begin_inset CommandInset ref
7124 reference "sec:Multiline-Formulas"
7129 \begin_inset Formula
7131 A & = & \underbrace{gggg+bbqq}_{r}+\: dddd\\
7132 & & \hphantom{gggg+\:}\underbrace{\hphantom{bbqq+dddd}}_{s}
7137 In the first row the formula is inserted together with the first brace.
7138 It is hereby important that the space command
7142 \begin_layout Plain Layout
7143 Space commands are explained in
7144 \begin_inset CommandInset ref
7146 reference "sub:Predefined-Space"
7161 is inserted before the first
7162 \begin_inset Formula $d$
7165 , because the brace that ends behind the
7166 \begin_inset Formula $q$
7169 prevents that the following
7170 \begin_inset Quotes eld
7174 \begin_inset Quotes erd
7177 is surrounded by space.
7181 \begin_layout Plain Layout
7182 because a bracket is not handled as a character, see
7183 \begin_inset CommandInset ref
7185 reference "sub:Binary-Operators"
7194 In the second row the second brace is inserted.
7195 As it should begin before the
7196 \begin_inset Formula $b$
7211 \begin_layout Plain Layout
7219 \begin_inset CommandInset ref
7221 reference "sub:Placeholders"
7230 This space is needed because the
7231 \begin_inset Quotes eld
7235 \begin_inset Quotes erd
7238 is also surrounded by space in the formula.
7239 The brace is placed under the command
7248 \begin_layout Standard
7249 It gets more complicated when brackets overlap each other, like in the following
7254 \begin_layout Plain Layout
7266 \begin_inset Formula
7268 & & \hphantom{gggg+\:}\overbrace{\hphantom{bbqq+dddd}}^{s}\\
7269 A & = & \underbrace{gggg+bbqq}_{r}+\: dddd
7278 \begin_layout Plain Layout
7289 The first formula row is the same as the second row of the previous example,
7290 with the difference that the brace is above.
7291 The second row contains the formula together with the second brace.
7292 To avoid that there is space between the upper brace in the first row and
7293 the formula, the row spacing needs to be reduced.
7294 This is not easily possible due to a bug in LyX
7298 \begin_layout Plain Layout
7299 \begin_inset CommandInset href
7301 name "LyX-bug #1505"
7302 target "http://www.lyx.org/trac/ticket/1505"
7312 As a solution for the problem, the global formula row separation
7319 \begin_inset Index idx
7322 \begin_layout Plain Layout
7330 must be changed to -6
7331 \begin_inset space \thinspace{}
7334 pt before the formula with the command
7349 is set back after the formula to the standard value of 3
7350 \begin_inset space \thinspace{}
7353 pt using the same command.
7354 More about the row separation in formulas is explained in
7355 \begin_inset CommandInset ref
7357 reference "sub:Line-Separation"
7364 \begin_layout Section
7366 \begin_inset Index idx
7369 \begin_layout Plain Layout
7378 \begin_layout Standard
7379 Arrows can be inserted via the math toolbar button
7382 arg "math-insert \\leftarrow"
7385 or the commands listed in the following subsections.
7388 \begin_layout Subsection
7390 \begin_inset Index idx
7393 \begin_layout Plain Layout
7402 \begin_layout Standard
7403 \begin_inset space \hfill{}
7407 \begin_inset Tabular
7408 <lyxtabular version="3" rows="8" columns="2">
7409 <features rotate="0" tabularvalignment="middle">
7410 <column alignment="center" valignment="top" width="0pt">
7411 <column alignment="center" valignment="top" width="0pt">
7413 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
7416 \begin_layout Plain Layout
7422 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
7425 \begin_layout Plain Layout
7433 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
7436 \begin_layout Plain Layout
7444 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
7447 \begin_layout Plain Layout
7448 \begin_inset Formula $\gets$
7458 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
7461 \begin_layout Plain Layout
7469 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
7472 \begin_layout Plain Layout
7473 \begin_inset Formula $\Leftarrow$
7483 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
7486 \begin_layout Plain Layout
7494 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
7497 \begin_layout Plain Layout
7498 \begin_inset Formula $\longleftarrow$
7508 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
7511 \begin_layout Plain Layout
7519 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
7522 \begin_layout Plain Layout
7523 \begin_inset Formula $\Longleftarrow$
7533 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
7536 \begin_layout Plain Layout
7544 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
7547 \begin_layout Plain Layout
7548 \begin_inset Formula $\leftharpoonup$
7558 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
7561 \begin_layout Plain Layout
7569 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
7572 \begin_layout Plain Layout
7573 \begin_inset Formula $\leftharpoondown$
7583 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
7586 \begin_layout Plain Layout
7594 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
7597 \begin_layout Plain Layout
7598 \begin_inset Formula $\hookleftarrow$
7612 \begin_inset space \hfill{}
7616 \begin_inset Tabular
7617 <lyxtabular version="3" rows="8" columns="2">
7618 <features rotate="0" tabularvalignment="middle">
7619 <column alignment="center" valignment="top" width="0pt">
7620 <column alignment="center" valignment="top" width="0pt">
7622 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
7625 \begin_layout Plain Layout
7631 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
7634 \begin_layout Plain Layout
7642 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
7645 \begin_layout Plain Layout
7653 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
7656 \begin_layout Plain Layout
7657 \begin_inset Formula $\to$
7667 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
7670 \begin_layout Plain Layout
7678 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
7681 \begin_layout Plain Layout
7682 \begin_inset Formula $\Rightarrow$
7692 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
7695 \begin_layout Plain Layout
7703 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
7706 \begin_layout Plain Layout
7707 \begin_inset Formula $\longrightarrow$
7717 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
7720 \begin_layout Plain Layout
7728 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
7731 \begin_layout Plain Layout
7732 \begin_inset Formula $\Longrightarrow$
7742 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
7745 \begin_layout Plain Layout
7753 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
7756 \begin_layout Plain Layout
7757 \begin_inset Formula $\rightharpoonup$
7767 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
7770 \begin_layout Plain Layout
7778 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
7781 \begin_layout Plain Layout
7782 \begin_inset Formula $\rightharpoondown$
7792 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
7795 \begin_layout Plain Layout
7803 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
7806 \begin_layout Plain Layout
7807 \begin_inset Formula $\hookrightarrow$
7821 \begin_inset space \hfill{}
7827 \begin_layout Standard
7828 \begin_inset space \hfill{}
7832 \begin_inset Tabular
7833 <lyxtabular version="3" rows="6" columns="2">
7834 <features rotate="0" tabularvalignment="middle">
7835 <column alignment="center" valignment="top" width="0pt">
7836 <column alignment="center" valignment="top" width="0pt">
7838 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
7841 \begin_layout Plain Layout
7847 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
7850 \begin_layout Plain Layout
7858 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
7861 \begin_layout Plain Layout
7869 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
7872 \begin_layout Plain Layout
7873 \begin_inset Formula $\leftrightarrow$
7883 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
7886 \begin_layout Plain Layout
7894 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
7897 \begin_layout Plain Layout
7898 \begin_inset Formula $\Leftrightarrow$
7908 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
7911 \begin_layout Plain Layout
7919 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
7922 \begin_layout Plain Layout
7923 \begin_inset Formula $\longleftrightarrow$
7933 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
7936 \begin_layout Plain Layout
7944 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
7947 \begin_layout Plain Layout
7948 \begin_inset Formula $\Longleftrightarrow$
7958 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
7961 \begin_layout Plain Layout
7969 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
7972 \begin_layout Plain Layout
7973 \begin_inset Formula $\rightleftharpoons$
7987 \begin_inset space \hspace{}
7992 \begin_inset space \hfill{}
7996 \begin_inset Tabular
7997 <lyxtabular version="3" rows="5" columns="2">
7998 <features rotate="0" tabularvalignment="middle">
7999 <column alignment="center" valignment="top" width="0pt">
8000 <column alignment="center" valignment="top" width="0pt">
8002 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
8005 \begin_layout Plain Layout
8011 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
8014 \begin_layout Plain Layout
8022 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
8025 \begin_layout Plain Layout
8033 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
8036 \begin_layout Plain Layout
8037 \begin_inset Formula $\mapsto$
8047 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
8050 \begin_layout Plain Layout
8058 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
8061 \begin_layout Plain Layout
8062 \begin_inset Formula $\longmapsto$
8072 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
8075 \begin_layout Plain Layout
8083 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
8086 \begin_layout Plain Layout
8087 \begin_inset Formula $\leadsto$
8097 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
8100 \begin_layout Plain Layout
8108 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
8111 \begin_layout Plain Layout
8112 \begin_inset Formula $\dasharrow$
8126 \begin_inset space \hfill{}
8132 \begin_layout Standard
8133 \begin_inset VSpace medskip
8136 Arrows used as accents like e.
8137 \begin_inset space \thinspace{}
8141 \begin_inset space \space{}
8144 vector arrows are listed in
8145 \begin_inset CommandInset ref
8147 reference "sec:Accents"
8154 \begin_layout Standard
8155 \begin_inset VSpace bigskip
8158 Furthermore there are the labeled arrows
8159 \begin_inset Index idx
8162 \begin_layout Plain Layout
8175 \begin_inset Index idx
8178 \begin_layout Plain Layout
8193 \begin_inset Index idx
8196 \begin_layout Plain Layout
8203 \begin_layout Plain Layout
8218 When inserting one of these commands in a formula, an arrow with two blue
8219 boxes appear where the label can be inserted.
8220 The length of the arrow adapts to the label width.
8223 \begin_layout Standard
8225 \begin_inset Tabular
8226 <lyxtabular version="3" rows="3" columns="2">
8227 <features rotate="0" tabularvalignment="middle">
8228 <column alignment="center" valignment="top" width="0pt">
8229 <column alignment="center" valignment="top" width="0pt">
8231 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
8234 \begin_layout Plain Layout
8240 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
8243 \begin_layout Plain Layout
8245 \begin_inset Note Note
8248 \begin_layout Plain Layout
8255 is only used as spacer.
8267 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
8270 \begin_layout Plain Layout
8274 \begin_inset space \textvisiblespace{}
8278 \begin_inset Formula $\downarrow$
8282 \begin_inset Formula $\to$
8290 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
8293 \begin_layout Plain Layout
8294 \begin_inset Formula $\raisebox{5mm}{}F(a)\xleftarrow[x>0]{x=a}F(x)\raisebox{-4mm}{}$
8304 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
8307 \begin_layout Plain Layout
8311 \begin_inset space \textvisiblespace{}
8315 \begin_inset Formula $\downarrow$
8319 \begin_inset Formula $\to$
8327 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
8330 \begin_layout Plain Layout
8331 \begin_inset Formula $\raisebox{5mm}{}F(x)\xrightarrow[x>0]{x=a}F(a)\raisebox{-4mm}{}$
8347 \begin_layout Subsection
8348 Vertical and diagonal Arrows
8349 \begin_inset Index idx
8352 \begin_layout Plain Layout
8359 \begin_inset Index idx
8362 \begin_layout Plain Layout
8371 \begin_layout Standard
8372 \begin_inset space \hfill{}
8376 \begin_inset Tabular
8377 <lyxtabular version="3" rows="7" columns="2">
8378 <features rotate="0" tabularvalignment="middle">
8379 <column alignment="center" valignment="top" width="0pt">
8380 <column alignment="center" valignment="top" width="0pt">
8382 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
8385 \begin_layout Plain Layout
8391 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
8394 \begin_layout Plain Layout
8402 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
8405 \begin_layout Plain Layout
8413 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
8416 \begin_layout Plain Layout
8417 \begin_inset Formula $\uparrow$
8427 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
8430 \begin_layout Plain Layout
8438 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
8441 \begin_layout Plain Layout
8442 \begin_inset Formula $\Uparrow$
8452 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
8455 \begin_layout Plain Layout
8463 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
8466 \begin_layout Plain Layout
8467 \begin_inset Formula $\updownarrow$
8477 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
8480 \begin_layout Plain Layout
8488 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
8491 \begin_layout Plain Layout
8492 \begin_inset Formula $\Updownarrow$
8502 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
8505 \begin_layout Plain Layout
8513 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
8516 \begin_layout Plain Layout
8517 \begin_inset Formula $\Downarrow$
8527 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
8530 \begin_layout Plain Layout
8538 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
8541 \begin_layout Plain Layout
8542 \begin_inset Formula $\downarrow$
8556 \begin_inset space \hfill{}
8560 \begin_inset Tabular
8561 <lyxtabular version="3" rows="5" columns="2">
8562 <features rotate="0" tabularvalignment="middle">
8563 <column alignment="center" valignment="top" width="0pt">
8564 <column alignment="center" valignment="top" width="0pt">
8566 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
8569 \begin_layout Plain Layout
8575 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
8578 \begin_layout Plain Layout
8586 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
8589 \begin_layout Plain Layout
8597 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
8600 \begin_layout Plain Layout
8601 \begin_inset Formula $\nearrow$
8611 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
8614 \begin_layout Plain Layout
8622 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
8625 \begin_layout Plain Layout
8626 \begin_inset Formula $\searrow$
8636 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
8639 \begin_layout Plain Layout
8647 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
8650 \begin_layout Plain Layout
8651 \begin_inset Formula $\swarrow$
8661 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
8664 \begin_layout Plain Layout
8672 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
8675 \begin_layout Plain Layout
8676 \begin_inset Formula $\nwarrow$
8690 \begin_inset space \hfill{}
8696 \begin_layout Standard
8697 \begin_inset VSpace medskip
8700 Vertical arrows can be used also as delimiters together with the commands
8702 \begin_inset CommandInset ref
8704 reference "sub:Manual-Bracket-Size"
8709 \begin_inset CommandInset ref
8711 reference "sub:Automatic-Bracket-Size"
8718 \begin_layout Section
8720 \begin_inset CommandInset label
8727 \begin_inset Index idx
8730 \begin_layout Plain Layout
8739 \begin_layout Standard
8740 Accents can be inserted via the math toolbar button
8741 \begin_inset Graphics
8742 filename ../images/math/hat.png
8747 or the commands listed in the following subsections.
8750 \begin_layout Subsection
8751 Accents for one Character
8755 \begin_layout Plain Layout
8768 \begin_layout Plain Layout
8770 \begin_inset CommandInset ref
8772 reference "sub:Accents-in-Text"
8785 \begin_layout Plain Layout
8793 \begin_inset Note Note
8796 \begin_layout Plain Layout
8803 is used to avoid that the footnote appears in the PDF-bookmark.
8806 \begin_layout Plain Layout
8814 \begin_inset CommandInset ref
8816 reference "sub:Formulas-in-Section"
8826 \begin_inset CommandInset label
8828 name "sub:Accents-for-one"
8833 \begin_inset Index idx
8836 \begin_layout Plain Layout
8837 Accents ! for one character
8845 \begin_layout Standard
8846 \begin_inset space \hfill{}
8850 \begin_inset Tabular
8851 <lyxtabular version="3" rows="8" columns="2">
8852 <features rotate="0" tabularvalignment="middle">
8853 <column alignment="center" valignment="top" width="0pt">
8854 <column alignment="center" valignment="top" width="0pt">
8856 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
8859 \begin_layout Plain Layout
8865 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
8868 \begin_layout Plain Layout
8870 \begin_inset Note Note
8873 \begin_layout Plain Layout
8880 is only used as spacer.
8892 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
8895 \begin_layout Plain Layout
8899 \begin_inset space \textvisiblespace{}
8907 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
8910 \begin_layout Plain Layout
8911 \begin_inset Formula $\raisebox{5mm}{}\dot{A}$
8921 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
8924 \begin_layout Plain Layout
8928 \begin_inset space \textvisiblespace{}
8936 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
8939 \begin_layout Plain Layout
8940 \begin_inset Formula $\raisebox{5mm}{}\ddot{A}$
8950 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
8953 \begin_layout Plain Layout
8957 \begin_inset space \textvisiblespace{}
8965 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
8968 \begin_layout Plain Layout
8969 \begin_inset Formula $\raisebox{5mm}{}\dddot{A}$
8979 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
8982 \begin_layout Plain Layout
8986 \begin_inset space \textvisiblespace{}
8994 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
8997 \begin_layout Plain Layout
8998 \begin_inset Formula $\raisebox{5mm}{}\ddddot{A}$
9008 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
9011 \begin_layout Plain Layout
9015 \begin_inset space \textvisiblespace{}
9019 \begin_inset Index idx
9022 \begin_layout Plain Layout
9033 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
9036 \begin_layout Plain Layout
9037 \begin_inset Formula $\raisebox{5mm}{}\vec{A}$
9047 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
9050 \begin_layout Plain Layout
9054 \begin_inset space \textvisiblespace{}
9062 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
9065 \begin_layout Plain Layout
9066 \begin_inset Formula $\raisebox{5mm}{}\bar{A}$
9076 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
9079 \begin_layout Plain Layout
9083 \begin_inset space \textvisiblespace{}
9091 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
9094 \begin_layout Plain Layout
9095 \begin_inset Formula $\raisebox{5mm}{}\mathring{A}$
9109 \begin_inset space \hfill{}
9113 \begin_inset Tabular
9114 <lyxtabular version="3" rows="7" columns="2">
9115 <features rotate="0" tabularvalignment="middle">
9116 <column alignment="center" valignment="top" width="0pt">
9117 <column alignment="center" valignment="top" width="0pt">
9119 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
9122 \begin_layout Plain Layout
9128 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
9131 \begin_layout Plain Layout
9139 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
9142 \begin_layout Plain Layout
9146 \begin_inset space \textvisiblespace{}
9154 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
9157 \begin_layout Plain Layout
9158 \begin_inset Formula $\raisebox{5mm}{}\tilde{A}$
9168 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
9171 \begin_layout Plain Layout
9175 \begin_inset space \textvisiblespace{}
9183 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
9186 \begin_layout Plain Layout
9187 \begin_inset Formula $\raisebox{5mm}{}\hat{A}$
9197 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
9200 \begin_layout Plain Layout
9204 \begin_inset space \textvisiblespace{}
9212 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
9215 \begin_layout Plain Layout
9216 \begin_inset Formula $\raisebox{5mm}{}\check{A}$
9226 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
9229 \begin_layout Plain Layout
9233 \begin_inset space \textvisiblespace{}
9241 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
9244 \begin_layout Plain Layout
9245 \begin_inset Formula $\raisebox{5mm}{}\acute{A}$
9255 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
9258 \begin_layout Plain Layout
9262 \begin_inset space \textvisiblespace{}
9270 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
9273 \begin_layout Plain Layout
9274 \begin_inset Formula $\raisebox{5mm}{}\grave{A}$
9284 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
9287 \begin_layout Plain Layout
9291 \begin_inset space \textvisiblespace{}
9299 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
9302 \begin_layout Plain Layout
9303 \begin_inset Formula $\raisebox{5mm}{}\breve{A}$
9317 \begin_inset space \hfill{}
9323 \begin_layout Standard
9324 \begin_inset VSpace bigskip
9330 \begin_layout Standard
9331 You can directly insert accents like é to formulas.
9332 LyX will transform them to the corresponding accent command.
9334 \begin_inset Index idx
9337 \begin_layout Plain Layout
9343 it is better to insert a quotation mark before the vowel.
9344 These two characters are then treated by LaTeX as
9348 character when the formula part with the umlaut is marked as German.
9356 \begin_inset Quotes eld
9360 \begin_inset Quotes erd
9363 umlauts are created as demonstrated in the following example:
9366 \begin_layout Standard
9367 \begin_inset VSpace -2mm
9373 \begin_layout Standard
9375 \begin_inset Tabular
9376 <lyxtabular version="3" rows="3" columns="2">
9377 <features rotate="0" tabularvalignment="middle">
9378 <column alignment="center" valignment="top">
9379 <column alignment="center" valignment="top">
9381 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
9384 \begin_layout Plain Layout
9390 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
9393 \begin_layout Plain Layout
9395 \begin_inset Note Note
9398 \begin_layout Plain Layout
9406 \begin_inset space \thinspace{}
9409 pt space are only used as spacer.
9421 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
9424 \begin_layout Plain Layout
9427 \begin_inset Quotes grd
9435 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
9438 \begin_layout Plain Layout
9439 \begin_inset space \hspace{}
9446 \begin_inset Formula $"i$
9456 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
9459 \begin_layout Plain Layout
9463 \begin_inset space \textvisiblespace{}
9471 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
9474 \begin_layout Plain Layout
9475 \begin_inset Formula $\raisebox{5mm}{}\ddot{i}$
9491 \begin_layout Standard
9492 Another advantage to
9498 is that umlauts can directly be converted to mathematical text because
9499 the accent commands above are
9505 in mathematical text
9508 To convert an accented character to mathematical text, only the character
9509 under the accent may be converted.
9510 This applies also for all other conversions, e.
9511 \begin_inset space \thinspace{}
9515 \begin_inset space \space{}
9521 \begin_layout Standard
9522 In mathematical text, umlauts and other accented characters can directly
9526 \begin_layout Standard
9527 \begin_inset VSpace bigskip
9533 \begin_layout Standard
9534 LyX also supports a tilde under the character if the LaTeX-package
9539 \begin_inset Index idx
9542 \begin_layout Plain Layout
9543 Packages ! undertilde
9548 is installed on your system:
9551 \begin_layout Standard
9555 \begin_layout Plain Layout
9565 \begin_inset Note Note
9568 \begin_layout Plain Layout
9569 The following table will only be displayed when the LaTeX-package
9581 \begin_layout Standard
9584 \begin_inset Tabular
9585 <lyxtabular version="3" rows="2" columns="2">
9586 <features rotate="0" tabularvalignment="middle">
9587 <column alignment="center" valignment="top" width="0pt">
9588 <column alignment="center" valignment="top" width="0pt">
9590 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
9593 \begin_layout Plain Layout
9599 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
9602 \begin_layout Plain Layout
9610 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
9613 \begin_layout Plain Layout
9617 \begin_inset space \textvisiblespace{}
9625 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
9628 \begin_layout Plain Layout
9629 \begin_inset Formula $\raisebox{5mm}{}\utilde{A}$
9645 \begin_layout Standard
9649 \begin_layout Plain Layout
9659 \begin_inset Note Note
9662 \begin_layout Plain Layout
9663 The following will be displayed when the LaTeX-package
9675 \begin_layout Standard
9676 You need to install the LaTeX-package
9680 to see the rest of this subsection in the output.
9683 \begin_layout Standard
9687 \begin_layout Plain Layout
9699 \begin_layout Subsection
9700 Accents for several Characters
9701 \begin_inset Index idx
9704 \begin_layout Plain Layout
9705 Accents ! for several characters
9713 \begin_layout Standard
9714 \begin_inset space \hfill{}
9718 \begin_inset Tabular
9719 <lyxtabular version="3" rows="5" columns="2">
9720 <features rotate="0" tabularvalignment="middle">
9721 <column alignment="center" valignment="top" width="0pt">
9722 <column alignment="center" valignment="top" width="0pt">
9724 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
9727 \begin_layout Plain Layout
9733 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
9736 \begin_layout Plain Layout
9738 \begin_inset Note Note
9741 \begin_layout Plain Layout
9748 is only used as spacer.
9760 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
9763 \begin_layout Plain Layout
9767 \begin_inset space \textvisiblespace{}
9775 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
9778 \begin_layout Plain Layout
9779 \begin_inset Formula $\raisebox{6mm}{}\overleftarrow{A=B}\raisebox{-2mm}{}$
9789 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
9792 \begin_layout Plain Layout
9796 \begin_inset space \textvisiblespace{}
9804 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
9807 \begin_layout Plain Layout
9808 \begin_inset Formula $\raisebox{5mm}{}\underleftarrow{A=B}\raisebox{-3mm}{}$
9818 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
9821 \begin_layout Plain Layout
9825 \begin_inset space \textvisiblespace{}
9833 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
9836 \begin_layout Plain Layout
9837 \begin_inset Formula $\raisebox{6mm}{}\overleftrightarrow{A=B}\raisebox{-2mm}{}$
9847 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
9850 \begin_layout Plain Layout
9854 \begin_inset space \textvisiblespace{}
9862 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
9865 \begin_layout Plain Layout
9866 \begin_inset Formula $\raisebox{5mm}{}\underleftrightarrow{A=B}\raisebox{-3mm}{}$
9880 \begin_inset space \hfill{}
9884 \begin_inset Tabular
9885 <lyxtabular version="3" rows="5" columns="2">
9886 <features rotate="0" tabularvalignment="middle">
9887 <column alignment="center" valignment="top" width="0pt">
9888 <column alignment="center" valignment="top" width="0pt">
9890 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
9893 \begin_layout Plain Layout
9899 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
9902 \begin_layout Plain Layout
9910 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
9913 \begin_layout Plain Layout
9917 \begin_inset space \textvisiblespace{}
9925 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
9928 \begin_layout Plain Layout
9929 \begin_inset Formula $\raisebox{6mm}{}\overrightarrow{A=B}\raisebox{-2mm}{}$
9939 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
9942 \begin_layout Plain Layout
9946 \begin_inset space \textvisiblespace{}
9954 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
9957 \begin_layout Plain Layout
9958 \begin_inset Formula $\raisebox{5mm}{}\underrightarrow{A=B}\raisebox{-3mm}{}$
9968 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
9971 \begin_layout Plain Layout
9975 \begin_inset space \textvisiblespace{}
9983 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
9986 \begin_layout Plain Layout
9987 \begin_inset Formula $\raisebox{6mm}{}\widetilde{A=B}\raisebox{-2mm}{}$
9997 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
10000 \begin_layout Plain Layout
10004 \begin_inset space \textvisiblespace{}
10012 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
10015 \begin_layout Plain Layout
10016 \begin_inset Formula $\raisebox{6mm}{}\widehat{A=B}\raisebox{-2mm}{}$
10030 \begin_inset space \hfill{}
10036 \begin_layout Standard
10037 \begin_inset VSpace medskip
10040 With these commands as many characters as you like can be accented.
10053 will only be set in the output with a length of three characters, as shown
10054 in the following example:
10055 \begin_inset Formula
10057 \widetilde{A+B=C-D}
10065 \begin_layout Standard
10073 \begin_inset Index idx
10076 \begin_layout Plain Layout
10091 \begin_inset Index idx
10094 \begin_layout Plain Layout
10102 described in the previous subsection it is also possible to accent several
10109 \begin_inset space \textvisiblespace{}
10113 \begin_inset Formula $\downarrow$
10119 \begin_inset Formula
10121 \underset{***}{A=B}
10129 \begin_layout Standard
10130 \begin_inset Newpage newpage
10136 \begin_layout Section
10138 \begin_inset CommandInset label
10145 \begin_inset Index idx
10148 \begin_layout Plain Layout
10157 \begin_layout Subsection
10159 \begin_inset CommandInset label
10161 name "sub:Predefined-Space"
10166 \begin_inset Index idx
10169 \begin_layout Plain Layout
10170 Space ! horizontal ! predefined
10178 \begin_layout Standard
10179 Sometimes it is necessary to insert horizontal space into a formula.
10180 This is done by inserting a protected space (shortcut
10183 arg "command-alternatives space-insert protected ; math-space"
10188 \begin_inset Quotes eld
10194 \begin_inset space \textvisiblespace{}
10200 \begin_inset Quotes erd
10203 appears and by pressing
10207 several times one can select one of eight different space sizes.
10208 The spaces can also be inserted using the math toolbar button
10209 \begin_inset Graphics
10210 filename ../images/math/space.png
10215 or special commands.
10216 Independent from the inserted command, one can select the size again by
10224 \begin_layout Standard
10227 \begin_inset Tabular
10228 <lyxtabular version="3" rows="6" columns="3">
10229 <features rotate="0" tabularvalignment="middle">
10230 <column alignment="center" valignment="top">
10231 <column alignment="center" valignment="top" width="15col%">
10232 <column alignment="center" valignment="top">
10234 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
10237 \begin_layout Plain Layout
10243 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
10246 \begin_layout Plain Layout
10256 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
10259 \begin_layout Plain Layout
10267 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
10270 \begin_layout Plain Layout
10278 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
10281 \begin_layout Plain Layout
10287 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
10290 \begin_layout Plain Layout
10291 \begin_inset Formula $A\, B$
10301 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
10304 \begin_layout Plain Layout
10312 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
10315 \begin_layout Plain Layout
10321 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
10324 \begin_layout Plain Layout
10325 \begin_inset Formula $A\: B$
10335 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
10338 \begin_layout Plain Layout
10346 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
10349 \begin_layout Plain Layout
10355 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
10358 \begin_layout Plain Layout
10359 \begin_inset Formula $A\; B$
10369 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
10372 \begin_layout Plain Layout
10380 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
10383 \begin_layout Plain Layout
10389 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
10392 \begin_layout Plain Layout
10393 \begin_inset Formula $A\quad B$
10403 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
10406 \begin_layout Plain Layout
10414 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
10417 \begin_layout Plain Layout
10423 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
10426 \begin_layout Plain Layout
10427 \begin_inset Formula $A\qquad B$
10441 \begin_inset space \hfill{}
10445 \begin_inset Tabular
10446 <lyxtabular version="3" rows="6" columns="3">
10447 <features rotate="0" tabularvalignment="middle">
10448 <column alignment="center" valignment="top">
10449 <column alignment="center" valignment="top" width="15col%">
10450 <column alignment="center" valignment="top">
10452 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
10455 \begin_layout Plain Layout
10461 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
10464 \begin_layout Plain Layout
10474 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
10477 \begin_layout Plain Layout
10485 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
10488 \begin_layout Plain Layout
10496 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
10499 \begin_layout Plain Layout
10505 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
10508 \begin_layout Plain Layout
10509 \begin_inset Formula $A\hfill B$
10519 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
10522 \begin_layout Plain Layout
10530 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
10533 \begin_layout Plain Layout
10539 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
10542 \begin_layout Plain Layout
10543 \begin_inset Formula $A\hspace*{1em}B$
10553 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
10556 \begin_layout Plain Layout
10564 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
10567 \begin_layout Plain Layout
10573 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
10576 \begin_layout Plain Layout
10577 \begin_inset Formula $A\hspace{1em}B$
10587 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
10590 \begin_layout Plain Layout
10594 \begin_inset space \textvisiblespace{}
10602 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
10605 \begin_layout Plain Layout
10611 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
10614 \begin_layout Plain Layout
10615 \begin_inset Formula $A\ B$
10625 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
10628 \begin_layout Plain Layout
10636 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
10639 \begin_layout Plain Layout
10645 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
10648 \begin_layout Plain Layout
10649 \begin_inset Formula $A\! B$
10665 \begin_layout Standard
10667 \begin_inset space ~
10671 \begin_inset space \thinspace{}
10675 \begin_inset space \thinspace{}
10678 7 are variable spaces which are explained in
10679 \begin_inset CommandInset ref
10681 reference "sub:Variable-Space"
10687 \begin_inset space ~
10690 9 seems to produce no space.
10691 It is displayed red in LyX contrary to the other sizes, because it is a
10693 There are two more negative spaces:
10696 \begin_layout Standard
10698 \begin_inset Tabular
10699 <lyxtabular version="3" rows="3" columns="3">
10700 <features rotate="0" tabularvalignment="middle">
10701 <column alignment="center" valignment="middle" width="6.8cm">
10702 <column alignment="center" valignment="top" width="0pt">
10703 <column alignment="center" valignment="top" width="0pt">
10705 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
10708 \begin_layout Plain Layout
10714 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
10717 \begin_layout Plain Layout
10725 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
10728 \begin_layout Plain Layout
10738 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
10741 \begin_layout Plain Layout
10746 keystrokes after inserting the protected space
10751 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
10754 \begin_layout Plain Layout
10760 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
10763 \begin_layout Plain Layout
10771 <cell multicolumn="1" alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
10774 \begin_layout Plain Layout
10780 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
10783 \begin_layout Plain Layout
10784 \begin_inset Formula $A\negmedspace B$
10792 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
10795 \begin_layout Plain Layout
10796 \begin_inset Formula $A\negthickspace B$
10812 \begin_layout Standard
10813 Negative spaces can lead to characters overlapping each other.
10814 Thus they can be used to enforce ligatures, which are e.
10815 \begin_inset space \thinspace{}
10819 \begin_inset space \space{}
10822 useful for summation operators:
10825 \begin_layout Standard
10827 \begin_inset Tabular
10828 <lyxtabular version="3" rows="3" columns="2">
10829 <features rotate="0" tabularvalignment="middle">
10830 <column alignment="center" valignment="top">
10831 <column alignment="center" valignment="top">
10833 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
10836 \begin_layout Plain Layout
10842 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
10845 \begin_layout Plain Layout
10847 \begin_inset Note Note
10850 \begin_layout Plain Layout
10857 is only used as spacer.
10869 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
10872 \begin_layout Plain Layout
10878 \begin_inset space \textvisiblespace{}
10886 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
10889 \begin_layout Plain Layout
10890 \begin_inset Formula $\raisebox{4.5mm}{}\sum\sum f_{kl}\raisebox{-2.5mm}{}$
10900 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
10903 \begin_layout Plain Layout
10911 \begin_inset space \textvisiblespace{}
10919 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
10922 \begin_layout Plain Layout
10923 \begin_inset Formula $\raisebox{4.5mm}{}\sum\negmedspace\sum f_{kl}\raisebox{-2.5mm}{}$
10939 \begin_layout Standard
10941 \begin_inset VSpace medskip
10947 \begin_layout Standard
10949 Relations like for example equal signs, are always surrounded by space.
10950 To suppress this, the equal sign is placed into a TeX-brace.
10951 The following example demonstrates this:
10954 \begin_layout Standard
10956 \begin_inset Tabular
10957 <lyxtabular version="3" rows="2" columns="2">
10958 <features rotate="0" tabularvalignment="middle">
10959 <column alignment="center" valignment="top" width="0pt">
10960 <column alignment="center" valignment="top" width="0pt">
10962 <cell alignment="center" valignment="top" usebox="none">
10965 \begin_layout Plain Layout
10971 <cell alignment="center" valignment="top" usebox="none">
10974 \begin_layout Plain Layout
10975 \begin_inset Formula $A=B$
10985 <cell alignment="center" valignment="top" usebox="none">
10988 \begin_layout Plain Layout
10989 \begin_inset Note Note
10992 \begin_layout Plain Layout
10999 is only used as spacer.
11005 \begin_inset Formula $\raisebox{5mm}{}$
11008 equation without space
11013 <cell multicolumn="1" alignment="center" valignment="top" usebox="none">
11016 \begin_layout Plain Layout
11017 \begin_inset Formula $A{=}B$
11033 \begin_layout Standard
11035 The command for the last formula is:
11040 \begin_inset Formula $\to$
11046 \begin_layout Standard
11047 \begin_inset VSpace bigskip
11053 \begin_layout Standard
11054 Spaces are needed for physical units, because the space between the value
11055 and the unit is the smallest one and not a normal space.
11056 For units in text, the smallest space is inserted via the menu
11058 Insert\SpecialChar \menuseparator
11059 Formatting\SpecialChar \menuseparator
11061 \begin_inset space ~
11069 arg "space-insert thin"
11075 \begin_layout Standard
11076 An example to visualize the difference:
11079 \begin_layout Standard
11080 \begin_inset Tabular
11081 <lyxtabular version="3" rows="2" columns="2">
11082 <features rotate="0" tabularvalignment="middle">
11083 <column alignment="left" valignment="top">
11084 <column alignment="left" valignment="top">
11086 <cell alignment="center" valignment="top" usebox="none">
11089 \begin_layout Plain Layout
11091 \begin_inset Formula $\cdot$
11099 <cell alignment="center" valignment="top" usebox="none">
11102 \begin_layout Plain Layout
11103 space between value and unit
11110 <cell alignment="center" valignment="top" usebox="none">
11113 \begin_layout Plain Layout
11115 \begin_inset space \thinspace{}
11119 \begin_inset Formula $\cdot$
11127 <cell alignment="center" valignment="top" usebox="none">
11130 \begin_layout Plain Layout
11131 smallest space between value and unit
11144 \begin_layout Subsection
11149 \begin_layout Plain Layout
11162 \begin_layout Plain Layout
11163 for vertical space in formulas see
11164 \begin_inset CommandInset ref
11166 reference "sub:Line-Separation"
11179 \begin_layout Plain Layout
11187 \begin_inset Note Note
11190 \begin_layout Plain Layout
11193 texorpdfstring is used to avoid that the footnote appears in the PDF-bookmark.
11196 \begin_layout Plain Layout
11199 texorpdfstring is in section
11200 \begin_inset CommandInset ref
11202 reference "sub:Formulas-in-Section"
11212 \begin_inset CommandInset label
11214 name "sub:Variable-Space"
11219 \begin_inset Index idx
11222 \begin_layout Plain Layout
11223 Space ! horizontal ! variable
11231 \begin_layout Standard
11232 Space with a defined length can be inserted with the command
11239 \begin_inset Index idx
11242 \begin_layout Plain Layout
11252 \begin_inset Quotes eld
11258 \begin_inset space \textvisiblespace{}
11264 \begin_inset Quotes erd
11268 The length can be specified by left-clicking on the
11269 \begin_inset Quotes eld
11275 \begin_inset space \textvisiblespace{}
11281 \begin_inset Quotes erd
11285 The length may also be negative.
11286 When a space would be the first character in a line it would be omitted.
11287 To force its output use the command
11299 or left-click on the
11300 \begin_inset Quotes eld
11306 \begin_inset space \textvisiblespace{}
11312 \begin_inset Quotes erd
11315 and check the option
11320 \begin_inset Newline newline
11323 To insert as much space as is available, the command
11330 \begin_inset Index idx
11333 \begin_layout Plain Layout
11344 \begin_layout Standard
11345 \begin_inset VSpace -1mm
11351 \begin_layout Standard
11353 \begin_inset Tabular
11354 <lyxtabular version="3" rows="4" columns="2">
11355 <features rotate="0" tabularvalignment="middle">
11356 <column alignment="center" valignment="top">
11357 <column alignment="center" valignment="top">
11359 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
11362 \begin_layout Plain Layout
11370 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
11373 \begin_layout Plain Layout
11381 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
11384 \begin_layout Plain Layout
11388 \begin_inset space \textvisiblespace{}
11394 \begin_inset space \thinspace{}
11402 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
11405 \begin_layout Plain Layout
11406 \begin_inset Formula $A=B\hspace{3cm}A\not=C$
11416 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
11419 \begin_layout Plain Layout
11423 \begin_inset space \textvisiblespace{}
11429 \begin_inset space \thinspace{}
11437 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
11440 \begin_layout Plain Layout
11441 \begin_inset Formula $A\hspace{-1mm}A\not=A$
11451 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
11454 \begin_layout Plain Layout
11458 \begin_inset space \textvisiblespace{}
11466 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
11469 \begin_layout Plain Layout
11470 \begin_inset Formula $A=A\hfill B=B$
11486 \begin_layout Standard
11487 In the last example the available space is given by the longest column entry
11489 In an inline formula the space depends on the length of the line in which
11497 Thus, when the line uses the full width, no space will be created.
11504 only has an effect on displayed formulas when the formula style
11509 (Formula styles are explained in
11510 \begin_inset CommandInset ref
11512 reference "sec:Formula-Styles"
11519 \begin_layout Standard
11526 , there are the commands
11538 that fill the space with a pattern, see
11539 \begin_inset CommandInset ref
11541 reference "sub:Ellipses"
11548 \begin_layout Standard
11549 For text, variable space can be inserted via the menu
11551 Insert\SpecialChar \menuseparator
11552 Formatting\SpecialChar \menuseparator
11554 \begin_inset space ~
11562 \begin_layout Standard
11563 This is a line with
11564 \begin_inset space \hspace{}
11569 \begin_inset space \thinspace{}
11575 \begin_layout Standard
11576 This is a line with
11577 \begin_inset space \hfill{}
11583 \begin_layout Subsection
11584 Space besides inline Formulas
11585 \begin_inset Index idx
11588 \begin_layout Plain Layout
11589 Space ! besides inline formulas
11597 \begin_layout Standard
11598 The space that surrounds inline formulas can be adjusted with the length
11606 \begin_inset Index idx
11609 \begin_layout Plain Layout
11618 The value of a length is set with the command
11625 \begin_inset Index idx
11628 \begin_layout Plain Layout
11636 which has the following scheme:
11639 \begin_layout Standard
11644 setlength{length name}{value}
11647 \begin_layout Standard
11655 \begin_inset space \thinspace{}
11661 \begin_layout Standard
11671 \begin_layout Standard
11672 is inserted in TeX-mode.
11674 \begin_inset space \thinspace{}
11677 mm space will now be set around all inline formulas:
11681 \begin_layout Plain Layout
11695 \begin_layout Standard
11696 This is a line with an inline formula
11697 \begin_inset Formula $A=B$
11701 \begin_inset space \thinspace{}
11704 mm surrounding space.
11708 \begin_layout Plain Layout
11722 \begin_layout Standard
11723 To return to the predefined value,
11729 is set to the value 0
11730 \begin_inset space \thinspace{}
11736 \begin_layout Section
11738 \begin_inset Index idx
11741 \begin_layout Plain Layout
11748 \begin_inset Index idx
11751 \begin_layout Plain Layout
11756 \begin_layout Plain Layout
11767 \begin_layout Plain Layout
11782 \begin_layout Standard
11783 Boxes for text are described in chapter
11790 \begin_inset space ~
11798 \begin_layout Subsection
11800 \begin_inset CommandInset label
11802 name "sub:Boxes-with-Frame"
11807 \begin_inset Index idx
11810 \begin_layout Plain Layout
11819 \begin_layout Standard
11820 It is possible to frame a formula or part of one with the commands
11827 \begin_inset Index idx
11830 \begin_layout Plain Layout
11845 \begin_inset Index idx
11848 \begin_layout Plain Layout
11859 \begin_layout Standard
11860 When one of these commands is inserted in a formula, a blue box appears
11861 within a frame to enter formula parts.
11868 an additional formula has to be created by
11872 within this box, because the box content will otherwise be treated as mathemati
11880 is used, a new formula is automatically created inside the frame.
11883 \begin_layout Standard
11890 is not suitable to frame displayed formulas because the formula will always
11891 be set in the size of the text.
11898 is in contrary not suitable to frame inline formulas, because the formula
11899 will always be set in the size of a displayed formula.
11902 \begin_layout Standard
11916 \begin_inset Index idx
11919 \begin_layout Plain Layout
11927 where additionally the frame width and the alignment can be specified.
11934 is used in the following scheme:
11937 \begin_layout Standard
11942 framebox[frame width][position]{box content}
11945 \begin_layout Standard
11946 The position can either be
11963 right aligns the formula in the box.
11964 When no position is given, the formula will be centered.
11965 \begin_inset Newline newline
11968 If no width is given, also no position can be given.
11969 In this case the frame width is adjusted to the box content like for
11978 \begin_layout Standard
11985 is inserted, a box appears containing three blue boxes.
11986 The first two boxes are surrounded by brackets and denote the two optional
11988 The third box is for formula parts like for
11997 \begin_layout Standard
11998 \begin_inset Newpage newpage
12004 \begin_layout Standard
12006 \begin_inset Tabular
12007 <lyxtabular version="3" rows="5" columns="2">
12008 <features rotate="0" tabularvalignment="middle">
12009 <column alignment="center" valignment="top">
12010 <column alignment="center" valignment="top">
12012 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
12015 \begin_layout Plain Layout
12021 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
12024 \begin_layout Plain Layout
12026 \begin_inset Note Note
12029 \begin_layout Plain Layout
12036 is only used as spacer.
12048 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
12051 \begin_layout Plain Layout
12055 \begin_inset space \textvisiblespace{}
12065 \begin_inset space \textvisiblespace{}
12073 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
12076 \begin_layout Plain Layout
12077 \begin_inset Formula $\raisebox{6mm}{}\fbox{\ensuremath{\int A=B}}\raisebox{-4mm}{}$
12087 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
12090 \begin_layout Plain Layout
12094 \begin_inset space \textvisiblespace{}
12100 \begin_inset space \textvisiblespace{}
12108 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
12111 \begin_layout Plain Layout
12112 \begin_inset Formula $\raisebox{8.5mm}{}\boxed{\int A=B}\raisebox{-6.5mm}{}$
12122 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
12125 \begin_layout Plain Layout
12129 \begin_inset space \textvisiblespace{}
12137 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
12140 \begin_layout Plain Layout
12141 \begin_inset Formula $\raisebox{6mm}{}A+\fbox{B}\raisebox{-3mm}{}$
12151 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
12154 \begin_layout Plain Layout
12158 \begin_inset space \textvisiblespace{}
12162 \begin_inset Formula $\to$
12166 \begin_inset Formula $\to$
12176 \begin_inset space \textvisiblespace{}
12180 \begin_inset Formula $\downarrow$
12188 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
12191 \begin_layout Plain Layout
12192 \begin_inset Formula $\raisebox{6mm}{}$
12196 \begin_inset Formula $\framebox[20mm][]{\ensuremath{\frac{A}{B}}}$
12200 \begin_inset Formula $\raisebox{-4mm}{}$
12216 \begin_layout Standard
12217 The frame thickness can also be adjusted.
12218 To do this the following commands have to be inserted in TeX-mode before
12222 \begin_layout Standard
12232 \begin_inset Quotes eld
12236 \begin_inset Quotes erd
12250 \begin_inset Quotes eld
12254 \begin_inset Quotes erd
12260 \begin_layout Standard
12261 \begin_inset Quotes eld
12265 \begin_inset Quotes erd
12268 specifies the minimal distance between the frame and the first character
12270 An example for this is the following framed formula:
12274 \begin_layout Plain Layout
12286 \begin_inset Formula
12293 Before this formula the commands
12296 \begin_layout Standard
12318 \begin_layout Standard
12319 were inserted in TeX-mode.
12320 The given values are used for all following boxes.
12323 \begin_layout Standard
12324 To return to the standard frame size, the command
12327 \begin_layout Standard
12352 \begin_layout Plain Layout
12366 \begin_layout Standard
12367 is inserted in TeX-mode before the next formula.
12370 \begin_layout Subsection
12371 Boxes without Frame
12372 \begin_inset CommandInset label
12374 name "sub:Boxes-without-Frame"
12379 \begin_inset Index idx
12382 \begin_layout Plain Layout
12383 Boxes ! without frame
12391 \begin_layout Standard
12392 For boxes without a frame there are the following box commands:
12399 \begin_inset Index idx
12402 \begin_layout Plain Layout
12417 \begin_inset Index idx
12420 \begin_layout Plain Layout
12435 \begin_inset Index idx
12438 \begin_layout Plain Layout
12449 \begin_layout Standard
12456 a box can be super- or subscripted.
12457 But in contrary to normal super- and subscripting, the characters in the
12458 box keep their font size.
12465 is used in the following scheme:
12468 \begin_layout Standard
12473 raisebox{height}{box content}
12476 \begin_layout Standard
12477 When the box should contain a formula, an extra formula is needed like for
12488 \begin_inset Note Greyedout
12491 \begin_layout Plain Layout
12502 this extra formula is created by pressing
12506 twice instead of once because LyX doesn't yet support
12520 \begin_layout Standard
12522 \begin_inset Tabular
12523 <lyxtabular version="3" rows="4" columns="2">
12524 <features rotate="0" tabularvalignment="middle">
12525 <column alignment="center" valignment="top">
12526 <column alignment="center" valignment="top">
12528 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
12531 \begin_layout Plain Layout
12537 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
12540 \begin_layout Plain Layout
12548 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
12551 \begin_layout Plain Layout
12555 \begin_inset Formula $\to$
12561 \begin_inset Formula $\to$
12569 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
12572 \begin_layout Plain Layout
12573 \begin_inset Formula $H\raisebox{2mm}{al}lo$
12583 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
12586 \begin_layout Plain Layout
12590 \begin_inset Formula $\to$
12596 \begin_inset Formula $\to$
12604 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
12607 \begin_layout Plain Layout
12608 \begin_inset Formula $H\raisebox{-2mm}{al}lo$
12618 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
12621 \begin_layout Plain Layout
12625 \begin_inset Formula $\to$
12641 \begin_inset space \textvisiblespace{}
12649 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
12652 \begin_layout Plain Layout
12653 \begin_inset Formula $A=\raisebox{-2mm}{\mbox{\ensuremath{\sqrt{B}}}}$
12669 \begin_layout Standard
12694 , with the difference that there is no frame.
12697 \begin_layout Subsection
12699 \begin_inset CommandInset label
12701 name "sub:Colored-Boxes"
12706 \begin_inset Index idx
12709 \begin_layout Plain Layout
12718 \begin_layout Standard
12719 To be able to use all commands explained in this section, the LaTeX-package
12728 \begin_layout Plain Layout
12733 is part of every LaTeX standard installation.
12739 \begin_inset Index idx
12742 \begin_layout Plain Layout
12748 has to be loaded in the LaTeX-preamble with the line
12752 \begin_layout Plain Layout
12753 When text is colored somewhere in the document with a predefined color,
12754 LyX loads the LaTeX-package
12759 Thus it is possible that the package is loaded twice, but this does not
12766 \begin_inset Note Note
12769 \begin_layout Plain Layout
12770 To avoid that the package is loaded twice, a macro was inserted to the LaTeX-pre
12779 \begin_layout Standard
12787 \begin_layout Standard
12788 \begin_inset VSpace medskip
12791 To color boxes, the command
12798 \begin_inset Index idx
12801 \begin_layout Plain Layout
12809 is used in the following scheme:
12812 \begin_layout Standard
12817 colorbox{color}{box content}
12820 \begin_layout Standard
12821 The box content can also be a box and a
12827 can also be part of another box (see the 2nd and 3rd example).
12828 When the box should contain a formula, an extra formula has to be created,
12829 the same way as for
12839 \begin_layout Plain Layout
12840 This also applies for the command
12854 \begin_layout Standard
12855 One of the following predefined colors can be chosen:
12858 \begin_layout Standard
12892 \begin_layout Standard
12894 \begin_inset Tabular
12895 <lyxtabular version="3" rows="4" columns="2">
12896 <features rotate="0" tabularvalignment="middle">
12897 <column alignment="center" valignment="top">
12898 <column alignment="center" valignment="top">
12900 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
12903 \begin_layout Plain Layout
12909 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
12912 \begin_layout Plain Layout
12914 \begin_inset Note Note
12917 \begin_layout Plain Layout
12924 is only used as spacer.
12936 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
12939 \begin_layout Plain Layout
12943 \begin_inset Formula $\to$
12953 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
12956 \begin_layout Plain Layout
12957 \begin_inset Formula $\raisebox{6mm}{}\colorbox{yellow}{A=B}\raisebox{-3mm}{}$
12967 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
12970 \begin_layout Plain Layout
12974 \begin_inset Formula $\to$
12982 \begin_inset space \textvisiblespace{}
12990 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
12993 \begin_layout Plain Layout
12994 \begin_inset Formula $\raisebox{6mm}{}\colorbox{green}{\fbox{A=B}}\raisebox{-3mm}{}$
13004 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
13007 \begin_layout Plain Layout
13011 \begin_inset space \textvisiblespace{}
13017 \begin_inset Formula $\to$
13033 \begin_inset space \textvisiblespace{}
13041 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
13044 \begin_layout Plain Layout
13045 \begin_inset Formula $\raisebox{7mm}{}\fbox{\colorbox{green}{\mbox{\ensuremath{\int C=D}}}}\raisebox{-5mm}{}$
13061 \begin_layout Standard
13068 only colors the box but not the characters in the box.
13069 To color all characters, the whole formula is highlighted and the desired
13070 color is chosen in the
13073 \begin_inset space ~
13079 The dialog can be called with the toolbar button
13080 \begin_inset Graphics
13081 filename ../images/dialog-show_character.png
13088 Edit\SpecialChar \menuseparator
13090 \begin_inset space ~
13093 Style\SpecialChar \menuseparator
13097 The formula number then has the same color as the formula.
13098 When the formula number should get another color than the formula characters,
13099 the color must be changed within the formula.
13102 \begin_layout Standard
13106 \begin_layout Standard
13109 \begin_inset Formula
13111 \int A=B\label{eq:red}
13119 \begin_inset Formula
13121 \textcolor{red}{\int A=B}\label{eq:redgreen}
13129 \begin_layout Standard
13131 \begin_inset CommandInset ref
13137 is completely colored red.
13138 \begin_inset Newline newline
13142 \begin_inset CommandInset ref
13144 reference "eq:redgreen"
13148 was first completely colored green to set the color for the formula number.
13149 Subsequently the formula characters were colored red.
13152 \begin_layout Standard
13153 \begin_inset VSpace bigskip
13156 To color the frame different than the rest of the box, the command
13163 \begin_inset Index idx
13166 \begin_layout Plain Layout
13174 is used in the following scheme:
13177 \begin_layout Standard
13182 fcolorbox{frame color}{color}{box content}
13185 \begin_layout Standard
13192 is an extension of the command
13199 The frame width is set, like for
13222 \begin_layout Plain Layout
13234 \begin_inset Formula
13236 \fcolorbox{cyan}{magenta}{A=B}
13245 \begin_layout Plain Layout
13259 \begin_layout Standard
13260 This formula was created with the command
13261 \begin_inset Newline newline
13269 \begin_inset Formula $\to$
13275 \begin_inset Formula $\to$
13285 \begin_layout Standard
13286 \begin_inset VSpace bigskip
13289 To use other colors than the predefined ones, they have to be defined first.
13292 \begin_layout Standard
13293 One can for example define the color
13294 \begin_inset Quotes eld
13302 \begin_inset Quotes erd
13305 with the LaTeX-preamble line:
13308 \begin_layout Standard
13313 definecolor{darkgreen}{cmyk}{0.5,
13328 \begin_inset Index idx
13331 \begin_layout Plain Layout
13342 \begin_layout Standard
13347 is the color space that denotes the colors
13364 The four comma separated numbers are the portion factor for the corresponding
13365 colors of the color space.
13366 The factors can be in the range of 0
13367 \begin_inset space \thinspace{}
13371 \begin_inset space \thinspace{}
13379 also the color space
13383 can be used for definitions.
13400 , so that there are in this case three portion factors for the corresponding
13402 Furthermore there is the color space
13406 with one portion factor for the gray value.
13409 \begin_layout Standard
13410 As example a framed box with the new defined color
13414 where the characters have been colored
13419 \begin_inset Formula
13421 \colorbox{darkgreen}{\color{yellow}\boxed{\int A\,\mathrm{d}x=\frac{\sqrt[5]{B}}{\ln\left(\frac{1}{3}\right)}}}
13429 \begin_layout Standard
13430 Self-defined colors can also be used for text with the help of the command
13438 \begin_inset Index idx
13441 \begin_layout Plain Layout
13450 \begin_layout Standard
13454 \begin_layout Plain Layout
13458 textcolor{darkgreen}{
13464 \begin_inset Quotes eld
13468 \begin_inset Quotes erd
13475 \begin_layout Plain Layout
13485 \begin_layout Standard
13493 \begin_inset Index idx
13496 \begin_layout Plain Layout
13504 is used in the scheme
13508 textcolor{color}{characters to color}
13513 \begin_layout Subsection
13515 \begin_inset CommandInset label
13517 name "sub:Paragraph-Boxes"
13522 \begin_inset Index idx
13525 \begin_layout Plain Layout
13526 Boxes ! as paragraph
13534 \begin_layout Standard
13535 A box that can contain several lines and paragraphs, a so-called paragraph
13536 box (parbox), can be created with the menu
13538 Insert\SpecialChar \menuseparator
13541 or the toolbar button
13542 \begin_inset Graphics
13543 filename ../images/box-insert.png
13551 \begin_layout Standard
13552 The following example shows a framed parbox in a line:
13555 \begin_layout Standard
13556 \begin_inset VSpace medskip
13560 \begin_inset Box Boxed
13570 height_special "totalheight"
13573 \begin_layout Plain Layout
13574 This is a paragraph box.
13576 \begin_inset space \thinspace{}
13579 cm long and can also contain formulas:
13580 \begin_inset Formula $\int A\,\mathrm{d}s=C$
13591 \begin_layout Standard
13592 \begin_inset VSpace medskip
13598 \begin_layout Standard
13599 Such a box is created by right-clicking on the gray box inset.
13600 A dialog pops up showing the box properties.
13614 \begin_inset space \thinspace{}
13619 Vertical Box Alignment
13624 \begin_layout Standard
13625 \begin_inset VSpace medskip
13628 In LaTeX a parbox is created with the command
13635 \begin_inset Index idx
13638 \begin_layout Plain Layout
13646 which has the following scheme:
13649 \begin_layout Standard
13654 parbox[position]{width}{box content}
13657 \begin_layout Standard
13672 \begin_inset Quotes eld
13676 \begin_inset Quotes erd
13679 means that the box is aligned within the surrounding text with its last
13686 \begin_inset Quotes eld
13690 \begin_inset Quotes erd
13693 this is done with the first line.
13694 When no position is given, the box will be vertically centered, see section
13702 \begin_inset space ~
13707 manual for examples.
13710 \begin_layout Standard
13711 \begin_inset VSpace bigskip
13714 To frame formulas completely, including the formula number, the formula
13715 must be set into a parbox.
13716 To do this, the command
13730 is inserted in TeX-mode before the formula.
13738 \begin_inset Index idx
13741 \begin_layout Plain Layout
13749 is hereby the line width set for the document.
13750 Because the frame is outside the parbox, 2
13751 \begin_inset space \thinspace{}
13754 times the frame separation and the frame thickness must be subtracted from
13756 As this is not automatically done by LyX due to a bug
13760 \begin_layout Plain Layout
13761 \begin_inset CommandInset href
13763 name "LyX-bug #4483"
13764 target "http://www.lyx.org/trac/ticket/4483"
13773 , TeX-mode has to be used.
13774 To be able to multiply and subtract in arguments, the LaTeX-package
13782 \begin_layout Plain Layout
13787 is part of every LaTeX standard installation.
13793 \begin_inset Index idx
13796 \begin_layout Plain Layout
13802 must be loaded in the LaTeX-preamble with the line
13805 \begin_layout Standard
13813 \begin_layout Standard
13814 Behind the formula both boxes are closed by entering
13819 Here is an example:
13823 \begin_layout Plain Layout
13837 \begin_layout Standard
13841 \begin_layout Plain Layout
13859 \begin_inset Formula
13861 \int A\,\mathrm{d}x=\frac{\sqrt[5]{B}}{\ln\left(\frac{1}{3}\right)}
13870 \begin_layout Plain Layout
13881 \begin_layout Plain Layout
13895 \begin_layout Standard
13896 \begin_inset VSpace medskip
13899 As a parbox is used as the argument of
13905 , there is in this case no difference between
13920 \begin_layout Standard
13921 \begin_inset VSpace bigskip
13924 Paragraph boxes are very useful to comment formulas directly.
13931 is used in combination with the command
13945 \begin_inset CommandInset ref
13947 reference "sub:User-defined-Numbering"
13954 \begin_layout Standard
13955 An example of a formula commented with
13964 \begin_layout Standard
13968 \begin_layout Plain Layout
13981 This is a description.
13982 It is distinctly separated from the formula and multiline.
13986 \begin_layout Plain Layout
13998 \begin_layout Standard
13999 Such a formula must be inserted completely in TeX-mode because LyX does
14000 not yet support the command
14007 The formula is created with the following command sequence:
14010 \begin_layout Standard
14023 is inserted in TeX-mode.
14027 \begin_layout Plain Layout
14028 When the formula style
14040 can also be replaced by
14047 (formula styles see
14048 \begin_inset CommandInset ref
14050 reference "sec:Formula-Styles"
14059 Then the description follows as normal text and finally
14065 is inserted in TeX-mode.
14078 hereby create a displayed formula.
14081 \begin_layout Standard
14088 can be seen in this example that was
14089 \begin_inset Quotes eld
14093 \begin_inset Quotes erd
14096 using the mathematical textmode:
14097 \begin_inset Formula
14099 5x-7b=3b\textrm{This is a description. It is not separated from the formula ...}
14107 \begin_layout Section
14109 \begin_inset Index idx
14112 \begin_layout Plain Layout
14121 \begin_layout Subsection
14123 \begin_inset CommandInset label
14125 name "sub:Big-Operators"
14130 \begin_inset Index idx
14133 \begin_layout Plain Layout
14140 \begin_inset Index idx
14143 \begin_layout Plain Layout
14150 \begin_inset Index idx
14153 \begin_layout Plain Layout
14162 \begin_layout Standard
14163 To be able to use all integral operators listed here, the option
14165 Use esint package automatically
14167 must be set in the document settings under
14170 \begin_inset space ~
14178 \begin_layout Standard
14179 \begin_inset space \hfill{}
14183 \begin_inset Tabular
14184 <lyxtabular version="3" rows="11" columns="2">
14185 <features rotate="0" tabularvalignment="middle">
14186 <column alignment="center" valignment="top" width="0pt">
14187 <column alignment="center" valignment="top" width="0pt">
14189 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
14192 \begin_layout Plain Layout
14198 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
14201 \begin_layout Plain Layout
14209 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
14212 \begin_layout Plain Layout
14216 \begin_inset Index idx
14219 \begin_layout Plain Layout
14232 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
14235 \begin_layout Plain Layout
14236 \begin_inset Formula $\int$
14246 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
14249 \begin_layout Plain Layout
14257 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
14260 \begin_layout Plain Layout
14261 \begin_inset Formula $\oint$
14271 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
14274 \begin_layout Plain Layout
14282 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
14285 \begin_layout Plain Layout
14286 \begin_inset Formula $\ointctrclockwise$
14296 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
14299 \begin_layout Plain Layout
14307 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
14310 \begin_layout Plain Layout
14311 \begin_inset Formula $\ointclockwise$
14321 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
14324 \begin_layout Plain Layout
14332 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
14335 \begin_layout Plain Layout
14336 \begin_inset Formula $\sqint$
14346 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
14349 \begin_layout Plain Layout
14357 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
14360 \begin_layout Plain Layout
14362 \begin_inset Formula $\fint$
14372 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
14375 \begin_layout Plain Layout
14383 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
14386 \begin_layout Plain Layout
14388 \begin_inset Formula $\landupint$
14398 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
14401 \begin_layout Plain Layout
14409 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
14412 \begin_layout Plain Layout
14414 \begin_inset Formula $\landdownint$
14424 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
14427 \begin_layout Plain Layout
14435 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
14438 \begin_layout Plain Layout
14439 \begin_inset Formula $\bigcap$
14449 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
14452 \begin_layout Plain Layout
14460 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
14463 \begin_layout Plain Layout
14464 \begin_inset Formula $\bigcup$
14478 \begin_inset space \hfill{}
14482 \begin_inset Tabular
14483 <lyxtabular version="3" rows="11" columns="2">
14484 <features rotate="0" tabularvalignment="middle">
14485 <column alignment="center" valignment="top" width="0pt">
14486 <column alignment="center" valignment="top" width="0pt">
14488 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
14491 \begin_layout Plain Layout
14497 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
14500 \begin_layout Plain Layout
14508 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
14511 \begin_layout Plain Layout
14515 \begin_inset Index idx
14518 \begin_layout Plain Layout
14531 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
14534 \begin_layout Plain Layout
14535 \begin_inset Formula $\sum$
14545 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
14548 \begin_layout Plain Layout
14552 \begin_inset Index idx
14555 \begin_layout Plain Layout
14562 \begin_layout Plain Layout
14581 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
14584 \begin_layout Plain Layout
14585 \begin_inset Formula $\prod$
14595 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
14598 \begin_layout Plain Layout
14606 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
14609 \begin_layout Plain Layout
14610 \begin_inset Formula $\coprod$
14620 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
14623 \begin_layout Plain Layout
14631 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
14634 \begin_layout Plain Layout
14635 \begin_inset Formula $\bigodot$
14645 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
14648 \begin_layout Plain Layout
14656 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
14659 \begin_layout Plain Layout
14660 \begin_inset Formula $\bigotimes$
14670 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
14673 \begin_layout Plain Layout
14681 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
14684 \begin_layout Plain Layout
14685 \begin_inset Formula $\bigoplus$
14695 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
14698 \begin_layout Plain Layout
14706 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
14709 \begin_layout Plain Layout
14710 \begin_inset Formula $\bigwedge$
14720 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
14723 \begin_layout Plain Layout
14731 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
14734 \begin_layout Plain Layout
14735 \begin_inset Formula $\bigvee$
14745 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
14748 \begin_layout Plain Layout
14756 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
14759 \begin_layout Plain Layout
14760 \begin_inset Formula $\bigsqcup$
14770 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
14773 \begin_layout Plain Layout
14781 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
14784 \begin_layout Plain Layout
14785 \begin_inset Formula $\biguplus$
14799 \begin_inset space \hfill{}
14805 \begin_layout Standard
14806 All big operators can also be inserted via the math toolbar button
14807 \begin_inset Graphics
14808 filename ../images/math/intop.png
14816 \begin_layout Standard
14817 The operators are called big because they are bigger than the sometimes
14818 equal looking binary operators.
14819 All big operators can have limits as described in the next subsection.
14822 \begin_layout Standard
14823 For all integral operators there is a second version available, ending in
14841 These operators are different from
14848 \begin_inset space \space{}
14851 in the style the operator limits are displayed, see
14852 \begin_inset CommandInset ref
14854 reference "sub:Operator-Limits"
14862 \begin_layout Subsubsection*
14863 Advice for Integrals
14866 \begin_layout Standard
14871 in an integral is an operator, that therefore has to be set upright.
14872 This is done by highlighting the
14876 and using the keyboard shortcut
14886 \begin_layout Plain Layout
14892 \begin_inset CommandInset ref
14894 reference "sub:Font-Styles"
14904 Finally the smallest space is inserted before the
14908 , as this is usual for operators.
14912 \begin_layout Standard
14914 \begin_inset Formula $\int A(x)dx$
14918 \begin_inset Newline newline
14922 \begin_inset Phantom HPhantom
14925 \begin_layout Plain Layout
14932 \begin_inset Formula $\int A(x)\,\mathrm{d}x$
14938 \begin_layout Standard
14939 For multiple integrals there are the following commands:
14940 \begin_inset VSpace medskip
14946 \begin_layout Standard
14947 \begin_inset space \hfill{}
14951 \begin_inset Tabular
14952 <lyxtabular version="3" rows="4" columns="2">
14953 <features rotate="0" tabularvalignment="middle">
14954 <column alignment="center" valignment="top">
14955 <column alignment="center" valignment="top">
14957 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
14960 \begin_layout Plain Layout
14966 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
14969 \begin_layout Plain Layout
14971 \begin_inset Note Note
14974 \begin_layout Plain Layout
14981 is only used as spacer.
14993 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
14996 \begin_layout Plain Layout
15004 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
15007 \begin_layout Plain Layout
15008 \begin_inset Formula $\raisebox{4.5mm}{}\iint\raisebox{-2.5mm}{}$
15018 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
15021 \begin_layout Plain Layout
15029 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
15032 \begin_layout Plain Layout
15033 \begin_inset Formula $\raisebox{4.5mm}{}\oiint\raisebox{-2.5mm}{}$
15043 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
15046 \begin_layout Plain Layout
15054 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
15057 \begin_layout Plain Layout
15058 \begin_inset Formula $\raisebox{4.5mm}{}\sqiint\raisebox{-2.5mm}{}$
15072 \begin_inset space \hfill{}
15076 \begin_inset Tabular
15077 <lyxtabular version="3" rows="4" columns="2">
15078 <features rotate="0" tabularvalignment="middle">
15079 <column alignment="center" valignment="top">
15080 <column alignment="center" valignment="top">
15082 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
15085 \begin_layout Plain Layout
15091 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
15094 \begin_layout Plain Layout
15102 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
15105 \begin_layout Plain Layout
15113 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
15116 \begin_layout Plain Layout
15117 \begin_inset Formula $\raisebox{4.5mm}{}\iiint\raisebox{-2.5mm}{}$
15127 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
15130 \begin_layout Plain Layout
15138 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
15141 \begin_layout Plain Layout
15142 \begin_inset Formula $\raisebox{4.5mm}{}\iiiint\raisebox{-2.5mm}{}$
15152 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
15155 \begin_layout Plain Layout
15163 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
15166 \begin_layout Plain Layout
15167 \begin_inset Formula $\raisebox{4.5mm}{}\dotsint\raisebox{-2.5mm}{}$
15181 \begin_inset space \hfill{}
15187 \begin_layout Standard
15188 \begin_inset Newpage newpage
15194 \begin_layout Subsection
15196 \begin_inset CommandInset label
15198 name "sub:Operator-Limits"
15203 \begin_inset Index idx
15206 \begin_layout Plain Layout
15215 \begin_layout Standard
15216 Limits are created by super- and subscripts:
15219 \begin_layout Standard
15221 \begin_inset Tabular
15222 <lyxtabular version="3" rows="2" columns="2">
15223 <features rotate="0" tabularvalignment="middle">
15224 <column alignment="center" valignment="top" width="0pt">
15225 <column alignment="center" valignment="top" width="0pt">
15227 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
15230 \begin_layout Plain Layout
15236 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
15239 \begin_layout Plain Layout
15241 \begin_inset Note Note
15244 \begin_layout Plain Layout
15251 is only used as spacer.
15263 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
15266 \begin_layout Plain Layout
15272 \begin_inset space \textvisiblespace{}
15276 \begin_inset Formula $\to$
15280 \begin_inset Formula $\to$
15288 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
15291 \begin_layout Plain Layout
15292 \begin_inset Formula $\raisebox{5mm}{}\prod_{0}^{\infty}A(x)\raisebox{-2.5mm}{}$
15308 \begin_layout Standard
15309 Limits of inline formulas are set right beside the operator.
15310 Limits in displayed formulas are set above or below the operator, except
15311 for integral limits.
15314 \begin_layout Standard
15315 To force that the limits are set beside the operator, the cursor is set
15316 directly behind the operator and the limits type is changed with the menu
15319 Edit\SpecialChar \menuseparator
15320 Math\SpecialChar \menuseparator
15339 \begin_layout Standard
15340 The default limits type is this:
15341 \begin_inset Formula
15343 \sum_{x=0}^{\infty}\frac{1}{x^{2}}
15348 This is how it looks when the limits type was changed to
15355 \begin_inset Formula
15357 \sum\nolimits _{x=0}^{\infty}\frac{1}{x^{2}}
15362 For integrals, except those ending with
15378 etc., the limits are by default set beside the operator.
15379 But for multiple integrals the limits are often set below the operator.
15380 In the following example the limits type was therefore set to
15384 and so set below the integrals:
15385 \begin_inset Formula
15387 \iiint\limits _{V}X\,\mathrm{d}V=U\label{eq:VolInt}
15395 \begin_layout Standard
15396 \begin_inset VSpace medskip
15399 To specify conditions for limits, the commands
15406 \begin_inset Index idx
15409 \begin_layout Plain Layout
15424 \begin_inset Index idx
15427 \begin_layout Plain Layout
15436 To create for example this expression
15437 \begin_inset Formula
15439 \sum_{\begin{subarray}{c}
15443 \end{subarray}}^{n}k^{-2}\label{eq:substack}
15451 \begin_layout Standard
15452 the following has to be done:
15453 \begin_inset Newline newline
15465 \begin_inset space \textvisiblespace{}
15471 One is now in a blue box under the summation operator and insert there
15477 \begin_inset space \textvisiblespace{}
15483 The blue box is now within a purple box and now several lines can be written
15485 A new line is created by inserting a line break (
15488 arg "newline-insert newline"
15493 \begin_inset Newline newline
15498 0<k<1000 Ctrl+Return
15499 \begin_inset Newline newline
15504 is typed in, a new box appears below for the new line.
15507 \begin_layout Standard
15508 The alignment of the lines can be changed to left aligned with the
15518 Edit\SpecialChar \menuseparator
15522 To get right alignment,
15527 \begin_inset space \textvisiblespace{}
15532 is inserted at the beginning of the line.
15535 \begin_layout Standard
15548 with the difference that the lines are always centered.
15551 \begin_layout Standard
15552 \begin_inset VSpace bigskip
15556 \begin_inset CommandInset ref
15558 reference "eq:substack"
15562 there can be too much space beside an operator, because the characters
15563 following the operator are set beside the limits.
15564 To avoid this the command
15571 \begin_inset Index idx
15574 \begin_layout Plain Layout
15583 It sets the width of its content to 0
15584 \begin_inset space \thinspace{}
15588 \begin_inset Newline newline
15592 \begin_inset CommandInset ref
15594 reference "eq:substack"
15598 , one uses the command
15601 \begin_layout Standard
15611 \begin_inset space \textvisiblespace{}
15614 0<k<1000 Ctrl+Return
15617 \begin_layout Standard
15618 to create the lower limit.
15619 The summand is now directly behind the summation operator:
15620 \begin_inset Formula
15622 \sum_{\mathclap{\substack{0<k<1000\\
15634 \begin_layout Standard
15635 \begin_inset VSpace bigskip
15641 \begin_layout Standard
15642 When several consecutive operators have limits the typesetting of the limits
15643 looks often imperfect in the output, see this example:
15644 \begin_inset Formula
15646 \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}
15651 To improve the typesetting set in the document settings under
15654 \begin_inset space ~
15664 \begin_inset Index idx
15667 \begin_layout Plain Layout
15668 Packages ! mathtools
15676 \begin_inset space ~
15682 Then insert into your formula the command
15689 \begin_inset Index idx
15692 \begin_layout Plain Layout
15700 directly before the first operator.
15701 The example will then look like this:
15702 \begin_inset Formula
15704 \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}
15712 \begin_layout Standard
15713 \begin_inset VSpace bigskip
15716 How to use one limit for several operators is described in
15717 \begin_inset CommandInset ref
15719 reference "sub:Self-defined-Operators"
15726 \begin_layout Subsection
15727 Decoration for Operators
15728 \begin_inset Index idx
15731 \begin_layout Plain Layout
15732 Operators ! Decoration
15740 \begin_layout Standard
15748 \begin_inset Index idx
15751 \begin_layout Plain Layout
15766 \begin_inset Index idx
15769 \begin_layout Plain Layout
15777 characters can be placed above or below an operator, respectively.
15785 \begin_inset Index idx
15788 \begin_layout Plain Layout
15796 characters can be set before and behind a big operator.
15799 \begin_layout Standard
15801 \begin_inset space ~
15813 \begin_layout Itemize
15820 is used to set characters at the corners of the operator
15823 \begin_layout Itemize
15830 is used to set characters before and/or behind the operator (this variant
15831 represents LaTeX's original
15840 \begin_layout Itemize
15847 is used to set characters at the left corners and/or behind the operator
15850 \begin_layout Itemize
15857 is used to set characters at the right corners and/or before the operator
15860 \begin_layout Standard
15861 For example the command
15866 \begin_inset space \textvisiblespace{}
15872 \begin_inset space \textvisiblespace{}
15876 \begin_inset Formula $\to$
15880 \begin_inset Formula $\to$
15884 \begin_inset space \textvisiblespace{}
15894 \begin_inset Formula
15896 \sideset{}{'}\sum_{k=1}^{n}
15904 \begin_layout Standard
15905 \begin_inset Note Greyedout
15908 \begin_layout Plain Layout
15915 can only be used to decorate big operators, binary operators are not allowed.
15923 \begin_layout Standard
15936 can also be used to decorate symbols and characters.
15937 For example, the command
15942 \begin_inset space \textvisiblespace{}
15948 \begin_inset space \textvisiblespace{}
15954 \begin_inset Formula $\uparrow$
15962 \begin_inset Formula
15964 \overset{a}{\maltese}
15972 \begin_layout Subsection
15974 \begin_inset CommandInset label
15976 name "sub:Binary-Operators"
15981 \begin_inset Index idx
15984 \begin_layout Plain Layout
15993 \begin_layout Standard
15994 Binary operators are surrounded by space when there is a character before
15996 \begin_inset VSpace medskip
16002 \begin_layout Standard
16003 \begin_inset space \hfill{}
16007 \begin_inset Tabular
16008 <lyxtabular version="3" rows="13" columns="2">
16009 <features rotate="0" tabularvalignment="middle">
16010 <column alignment="center" valignment="top" width="0pt">
16011 <column alignment="center" valignment="top" width="0pt">
16013 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
16016 \begin_layout Plain Layout
16018 \begin_inset Note Note
16021 \begin_layout Plain Layout
16028 is only used as spacer.
16038 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
16041 \begin_layout Plain Layout
16049 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
16052 \begin_layout Plain Layout
16058 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
16061 \begin_layout Plain Layout
16062 \begin_inset Formula $+$
16072 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
16075 \begin_layout Plain Layout
16081 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
16084 \begin_layout Plain Layout
16085 \begin_inset Formula $-$
16095 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
16098 \begin_layout Plain Layout
16106 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
16109 \begin_layout Plain Layout
16110 \begin_inset Formula $\pm$
16120 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
16123 \begin_layout Plain Layout
16131 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
16134 \begin_layout Plain Layout
16135 \begin_inset Formula $\mp$
16145 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
16148 \begin_layout Plain Layout
16156 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
16159 \begin_layout Plain Layout
16160 \begin_inset Formula $\cdot$
16170 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
16173 \begin_layout Plain Layout
16181 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
16184 \begin_layout Plain Layout
16185 \begin_inset Formula $\times$
16195 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
16198 \begin_layout Plain Layout
16206 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
16209 \begin_layout Plain Layout
16210 \begin_inset Formula $\div$
16220 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
16223 \begin_layout Plain Layout
16227 \begin_layout Plain Layout
16240 \begin_layout Plain Layout
16252 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
16255 \begin_layout Plain Layout
16256 \begin_inset Formula $*$
16266 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
16269 \begin_layout Plain Layout
16277 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
16280 \begin_layout Plain Layout
16281 \begin_inset Formula $\star$
16291 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
16294 \begin_layout Plain Layout
16302 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
16305 \begin_layout Plain Layout
16306 \begin_inset Formula $\circ$
16316 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
16319 \begin_layout Plain Layout
16327 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
16330 \begin_layout Plain Layout
16331 \begin_inset Formula $\diamond$
16341 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
16344 \begin_layout Plain Layout
16352 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
16355 \begin_layout Plain Layout
16356 \begin_inset Formula $\bullet$
16370 \begin_inset space \hfill{}
16374 \begin_inset Tabular
16375 <lyxtabular version="3" rows="13" columns="2">
16376 <features rotate="0" tabularvalignment="middle">
16377 <column alignment="center" valignment="top" width="0pt">
16378 <column alignment="center" valignment="top" width="0pt">
16380 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
16383 \begin_layout Plain Layout
16389 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
16392 \begin_layout Plain Layout
16400 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
16403 \begin_layout Plain Layout
16411 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
16414 \begin_layout Plain Layout
16415 \begin_inset Formula $\nabla$
16425 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
16428 \begin_layout Plain Layout
16436 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
16439 \begin_layout Plain Layout
16440 \begin_inset Formula $\bigtriangledown$
16450 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
16453 \begin_layout Plain Layout
16461 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
16464 \begin_layout Plain Layout
16465 \begin_inset Formula $\bigtriangleup$
16475 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
16478 \begin_layout Plain Layout
16486 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
16489 \begin_layout Plain Layout
16490 \begin_inset Formula $\Box$
16500 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
16503 \begin_layout Plain Layout
16511 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
16514 \begin_layout Plain Layout
16515 \begin_inset Formula $\cap$
16525 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
16528 \begin_layout Plain Layout
16536 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
16539 \begin_layout Plain Layout
16540 \begin_inset Formula $\cup$
16550 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
16553 \begin_layout Plain Layout
16561 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
16564 \begin_layout Plain Layout
16565 \begin_inset Formula $\dagger$
16575 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
16578 \begin_layout Plain Layout
16586 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
16589 \begin_layout Plain Layout
16590 \begin_inset Formula $\ddagger$
16600 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
16603 \begin_layout Plain Layout
16611 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
16614 \begin_layout Plain Layout
16615 \begin_inset Formula $\wr$
16625 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
16628 \begin_layout Plain Layout
16636 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
16639 \begin_layout Plain Layout
16640 \begin_inset Formula $\bigcirc$
16650 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
16653 \begin_layout Plain Layout
16661 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
16664 \begin_layout Plain Layout
16665 \begin_inset Formula $\wedge$
16675 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
16678 \begin_layout Plain Layout
16686 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
16689 \begin_layout Plain Layout
16690 \begin_inset Formula $\vee$
16704 \begin_inset space \hfill{}
16708 \begin_inset Tabular
16709 <lyxtabular version="3" rows="13" columns="2">
16710 <features rotate="0" tabularvalignment="middle">
16711 <column alignment="center" valignment="top" width="0pt">
16712 <column alignment="center" valignment="top" width="0pt">
16714 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
16717 \begin_layout Plain Layout
16723 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
16726 \begin_layout Plain Layout
16734 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
16737 \begin_layout Plain Layout
16745 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
16748 \begin_layout Plain Layout
16749 \begin_inset Formula $\oplus$
16759 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
16762 \begin_layout Plain Layout
16770 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
16773 \begin_layout Plain Layout
16774 \begin_inset Formula $\ominus$
16784 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
16787 \begin_layout Plain Layout
16795 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
16798 \begin_layout Plain Layout
16799 \begin_inset Formula $\otimes$
16809 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
16812 \begin_layout Plain Layout
16820 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
16823 \begin_layout Plain Layout
16824 \begin_inset Formula $\oslash$
16834 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
16837 \begin_layout Plain Layout
16845 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
16848 \begin_layout Plain Layout
16849 \begin_inset Formula $\odot$
16859 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
16862 \begin_layout Plain Layout
16870 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
16873 \begin_layout Plain Layout
16874 \begin_inset Formula $\amalg$
16884 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
16887 \begin_layout Plain Layout
16895 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
16898 \begin_layout Plain Layout
16899 \begin_inset Formula $\uplus$
16909 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
16912 \begin_layout Plain Layout
16920 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
16923 \begin_layout Plain Layout
16924 \begin_inset Formula $\setminus$
16934 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
16937 \begin_layout Plain Layout
16945 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
16948 \begin_layout Plain Layout
16949 \begin_inset Formula $\sqcap$
16959 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
16962 \begin_layout Plain Layout
16970 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
16973 \begin_layout Plain Layout
16974 \begin_inset Formula $\sqcup$
16984 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
16987 \begin_layout Plain Layout
16995 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
16998 \begin_layout Plain Layout
16999 \begin_inset Formula $\triangleleft$
17009 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
17012 \begin_layout Plain Layout
17020 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
17023 \begin_layout Plain Layout
17024 \begin_inset Formula $\triangleright$
17038 \begin_inset space \hfill{}
17044 \begin_layout Standard
17045 All binary operators can also be inserted via the math toolbar button
17046 \begin_inset Graphics
17047 filename ../images/math/pm.png
17055 \begin_layout Standard
17056 To typeset the Laplace operator also
17073 \begin_inset Formula $\nabla^{2}$
17076 ) can be used instead of
17085 \begin_layout Standard
17092 Insert\SpecialChar \menuseparator
17104 \begin_layout Subsection
17105 Self-defined Operators
17106 \begin_inset CommandInset label
17108 name "sub:Self-defined-Operators"
17113 \begin_inset Index idx
17116 \begin_layout Plain Layout
17117 Operators ! self-defined
17125 \begin_layout Standard
17126 With the help of the command
17130 DeclareMathOperator
17133 \begin_inset Index idx
17136 \begin_layout Plain Layout
17141 DeclareMathOperator
17146 custom operators can be defined in the LaTeX-preamble.
17147 Its command scheme is:
17150 \begin_layout Standard
17155 DeclareMathOperator{new command}{display}
17158 \begin_layout Standard
17159 Display can be characters or symbols that define how the operator looks
17161 To define a big operator a * is set behind the command.
17162 All self-defined big operators can have limits as described in
17163 \begin_inset CommandInset ref
17165 reference "sub:Operator-Limits"
17172 \begin_layout Standard
17173 For example the LaTeX-preamble line
17176 \begin_layout Standard
17181 DeclareMathOperator*{
17188 \begin_layout Standard
17189 defines the command
17195 , that inserts a big operator consisting of the lozenge symbol from
17196 \begin_inset CommandInset ref
17198 reference "sub:Miscellaneous-Symbols"
17203 \begin_inset Formula
17205 \Lozenge_{n=1}^{\infty}
17210 The command for this formula is:
17221 \begin_inset Formula $\to$
17227 \begin_layout Standard
17228 \begin_inset VSpace bigskip
17231 When self-defined operators are not used several times in the document,
17232 they can also be defined with the commands
17239 \begin_inset Index idx
17242 \begin_layout Plain Layout
17257 \begin_inset Index idx
17260 \begin_layout Plain Layout
17268 , which have the following scheme:
17271 \begin_layout Standard
17285 \begin_layout Standard
17292 defines big operators,
17301 \begin_layout Standard
17309 \begin_inset space \thinspace{}
17313 \begin_inset space \space{}
17316 be used to use one limit for several operators:
17319 \begin_layout Standard
17320 \begin_inset Formula
17322 \mathop{\sum\negmedspace\sum}_{i,j=1}^{N}
17330 \begin_layout Standard
17331 The command for the formula above is:
17332 \begin_inset Newline newline
17348 \begin_inset space \textvisiblespace{}
17354 \begin_inset Formula $\to$
17360 \begin_inset space \textvisiblespace{}
17368 \begin_layout Section
17370 \begin_inset Index idx
17373 \begin_layout Plain Layout
17382 \begin_layout Subsection
17384 \begin_inset CommandInset label
17386 name "sub:Font-Styles"
17391 \begin_inset Index idx
17394 \begin_layout Plain Layout
17403 \begin_layout Standard
17404 Latin letters in formulas can be set in one of the following font styles:
17405 \begin_inset VSpace -2mm
17411 \begin_layout Standard
17413 \begin_inset Tabular
17414 <lyxtabular version="3" rows="7" columns="3">
17415 <features rotate="0" tabularvalignment="middle">
17416 <column alignment="center" valignment="top">
17417 <column alignment="center" valignment="top">
17418 <column alignment="center" valignment="top">
17420 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
17423 \begin_layout Plain Layout
17429 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
17432 \begin_layout Plain Layout
17438 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
17441 \begin_layout Plain Layout
17449 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
17452 \begin_layout Plain Layout
17458 \begin_inset space \textvisiblespace{}
17468 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
17471 \begin_layout Plain Layout
17472 \begin_inset Formula $\mathbb{ABC}$
17480 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
17483 \begin_layout Plain Layout
17496 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
17499 \begin_layout Plain Layout
17505 \begin_inset space \textvisiblespace{}
17515 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
17518 \begin_layout Plain Layout
17519 \begin_inset Formula $\mathbf{AbC}$
17527 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
17530 \begin_layout Plain Layout
17543 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
17546 \begin_layout Plain Layout
17552 \begin_inset space \textvisiblespace{}
17562 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
17565 \begin_layout Plain Layout
17566 \begin_inset Formula $\boldsymbol{AbC}$
17574 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
17577 \begin_layout Plain Layout
17580 arg "font-boldsymbol"
17590 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
17593 \begin_layout Plain Layout
17599 \begin_inset space \textvisiblespace{}
17609 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
17612 \begin_layout Plain Layout
17613 \begin_inset Formula $\mathcal{ABC}$
17621 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
17624 \begin_layout Plain Layout
17637 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
17640 \begin_layout Plain Layout
17646 \begin_inset space \textvisiblespace{}
17656 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
17659 \begin_layout Plain Layout
17660 \begin_inset Formula $\mathfrak{AbC}$
17668 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
17671 \begin_layout Plain Layout
17679 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
17682 \begin_layout Plain Layout
17688 \begin_inset space \textvisiblespace{}
17698 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
17701 \begin_layout Plain Layout
17702 \begin_inset Formula $\mathscr{AbC}$
17710 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
17713 \begin_layout Plain Layout
17727 \begin_layout Standard
17729 \begin_inset Tabular
17730 <lyxtabular version="3" rows="5" columns="3">
17731 <features rotate="0" tabularvalignment="middle">
17732 <column alignment="center" valignment="top">
17733 <column alignment="center" valignment="top">
17734 <column alignment="center" valignment="top">
17736 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
17739 \begin_layout Plain Layout
17745 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
17748 \begin_layout Plain Layout
17754 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
17757 \begin_layout Plain Layout
17765 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
17768 \begin_layout Plain Layout
17774 \begin_inset space \textvisiblespace{}
17784 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
17787 \begin_layout Plain Layout
17788 \begin_inset Formula $\mathit{AbC}$
17796 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
17799 \begin_layout Plain Layout
17807 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
17810 \begin_layout Plain Layout
17816 \begin_inset space \textvisiblespace{}
17826 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
17829 \begin_layout Plain Layout
17830 \begin_inset Formula $\mathrm{AbC}$
17838 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
17841 \begin_layout Plain Layout
17854 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
17857 \begin_layout Plain Layout
17863 \begin_inset space \textvisiblespace{}
17873 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
17876 \begin_layout Plain Layout
17877 \begin_inset Formula $\mathsf{AbC}$
17885 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
17888 \begin_layout Plain Layout
17901 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
17904 \begin_layout Plain Layout
17910 \begin_inset space \textvisiblespace{}
17920 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
17923 \begin_layout Plain Layout
17924 \begin_inset Formula $\mathtt{AbC}$
17932 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
17935 \begin_layout Plain Layout
17938 arg "font-typewriter"
17954 \begin_layout Standard
17955 \begin_inset Note Greyedout
17958 \begin_layout Plain Layout
17975 can only be used for big letters.
17983 \begin_layout Standard
17984 Predefined is the style
17993 \begin_layout Standard
17994 The style commands work also for letters in mathematical constructs:
17995 \begin_inset Formula
17997 \mathfrak{A=\frac{b}{C}}
18005 \begin_layout Standard
18006 Characters in mathematical text don't appear in a math font style but in
18007 the text font style
18014 That their style can't be set correctly via the text style dialog is a
18019 \begin_layout Plain Layout
18020 \begin_inset CommandInset href
18022 name "LyX-bug #4629"
18023 target "http://www.lyx.org/trac/ticket/4629"
18035 \begin_layout Standard
18036 Instead of the style commands the dialog
18038 Edit\SpecialChar \menuseparator
18039 Math\SpecialChar \menuseparator
18042 or the toolbar button
18043 \begin_inset Graphics
18044 filename ../images/math/font.png
18052 \begin_layout Subsection
18054 \begin_inset CommandInset label
18056 name "sub:Bold-Formulas"
18061 \begin_inset Index idx
18064 \begin_layout Plain Layout
18073 \begin_layout Standard
18074 To make a complete formula bold, the command
18080 from the previous subsection cannot be used, because it doesn't work for
18081 small Greek letters.
18082 Furthermore it prints Latin letters always upright, like in the following
18086 \begin_layout Standard
18087 \begin_inset Formula
18089 \mathbf{\int_{n}^{2}f(\theta)=\Gamma}\qquad\textrm{equation with \textbackslash mathbf}
18097 \begin_layout Standard
18098 To display the formula correctly, the command
18105 \begin_inset Formula
18107 \boldsymbol{\int_{n}^{2}f(\theta)=\Gamma\qquad\textrm{equation with \textbackslash boldsymbol}}
18112 It is also possible to set the formula in a
18114 boldmath environment
18117 This environment is created by inserting the command
18124 \begin_inset Index idx
18127 \begin_layout Plain Layout
18136 To end the environment, the command
18143 \begin_inset Index idx
18146 \begin_layout Plain Layout
18154 is inserted in TeX-mode.
18158 \begin_layout Plain Layout
18168 \begin_inset Formula
18170 \int_{n}^{2}f(\theta)=\Gamma\qquad\textrm{equation in a boldmath environment}
18179 \begin_layout Plain Layout
18191 \begin_layout Subsection
18193 \begin_inset Index idx
18196 \begin_layout Plain Layout
18205 \begin_layout Standard
18206 Formulas can be colored like normal text: Highlight a formula or a formula
18212 Here is a formula in magenta:
18213 \begin_inset Formula
18215 {\color{magenta}\int A\,\mathrm{d}x=\frac{\sqrt[5]{B}}{\ln\left(\frac{1}{3}\right)}}
18223 \begin_layout Standard
18224 You can also define your own colors as described in
18225 \begin_inset CommandInset ref
18227 reference "sub:Colored-Boxes"
18232 They can be used with the TeX code command
18239 \begin_inset Index idx
18242 \begin_layout Plain Layout
18253 \begin_layout Standard
18258 textcolor{color}{characters or formula}
18261 \begin_layout Standard
18262 The following example was colored completely dark green and partly red:
18265 \begin_layout Standard
18269 \begin_layout Plain Layout
18273 textcolor{darkgreen}{
18279 \begin_inset Formula
18281 \int A\,\mathrm{d}x=\frac{{\color{red}\sqrt[5]{B}}}{\ln\left(\frac{1}{3}\right)}
18290 \begin_layout Plain Layout
18300 \begin_layout Standard
18301 Due to a bug in LyX only complete formulas can be colored with self-defined
18306 \begin_layout Plain Layout
18307 \begin_inset CommandInset href
18309 name "LyX-bug #5269"
18310 target "http://www.lyx.org/trac/ticket/5269"
18322 \begin_layout Subsection
18324 \begin_inset CommandInset label
18326 name "sub:Font-Sizes"
18331 \begin_inset Index idx
18334 \begin_layout Plain Layout
18343 \begin_layout Standard
18344 For characters in formulas there are, analog to characters in text, the
18345 following size commands:
18348 \begin_layout Standard
18392 \begin_inset Newline newline
18414 \begin_layout Standard
18415 The size produced by the commands depends on the document font size, which
18416 corresponds to the command
18423 The other commands produce smaller or larger sizes than
18430 The font size can however not exceed a certain value.
18431 Is for example the document font size 12
18432 \begin_inset space \thinspace{}
18441 switches to the same size as
18451 \begin_layout Standard
18452 A size command is inserted in TeX-mode before the formula and sets the size
18453 for all following formula and text characters.
18454 To switch back to the initial size, the command
18460 is inserted behind the formula in TeX-mode.
18463 \begin_layout Standard
18464 Within a formula the size can be changed using the following size commands:
18467 \begin_layout Standard
18470 \begin_inset Tabular
18471 <lyxtabular version="3" rows="5" columns="2">
18472 <features rotate="0" tabularvalignment="middle">
18473 <column alignment="center" valignment="top">
18474 <column alignment="center" valignment="top">
18476 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
18479 \begin_layout Plain Layout
18485 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
18488 \begin_layout Plain Layout
18490 \begin_inset Note Note
18493 \begin_layout Plain Layout
18500 is only used as spacer.
18512 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
18515 \begin_layout Plain Layout
18519 \begin_inset Index idx
18522 \begin_layout Plain Layout
18535 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
18538 \begin_layout Plain Layout
18539 \begin_inset Formula $\raisebox{6.5mm}{}{\displaystyle E_{\mathrm{pot_{1}}}=\frac{K}{l+\frac{m}{n_{2}}}}\raisebox{-5.5mm}{}$
18549 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
18552 \begin_layout Plain Layout
18560 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
18563 \begin_layout Plain Layout
18564 \begin_inset Formula $\raisebox{4.5mm}{}{\textstyle E_{\mathrm{pot_{1}}}=\frac{K}{l+\frac{m}{n_{2}}}}\raisebox{-4mm}{}$
18574 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
18577 \begin_layout Plain Layout
18585 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
18588 \begin_layout Plain Layout
18589 \begin_inset Formula $\raisebox{4.5mm}{}{\scriptstyle E_{\mathrm{pot_{1}}}=\frac{K}{l+\frac{m}{n_{2}}}}\raisebox{-3.5mm}{}$
18599 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
18602 \begin_layout Plain Layout
18610 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
18613 \begin_layout Plain Layout
18614 \begin_inset Formula $\raisebox{4.5mm}{}{\scriptscriptstyle E_{\mathrm{pot_{1}}}=\frac{K}{l+\frac{m}{n_{2}}}}\raisebox{-3.5mm}{}$
18630 \begin_layout Standard
18631 After entering these commands, a blue box appears in which the formula parts
18635 \begin_layout Standard
18636 There is a further method to change the font size, that though only works
18637 for symbols or letters in mathematical text.
18638 To use it, one of the above text size commands is inserted in mathematical
18640 All following characters until the end of the mathematical text or until
18641 another size command will have the selected size.
18643 \begin_inset VSpace -2mm
18649 \begin_layout Standard
18653 \begin_layout Plain Layout
18663 \begin_inset Formula
18665 A=\frac{B}{c}\cdot\maltese
18671 \begin_inset Formula
18673 \maltese A\textrm{\Large\maltese\textit{A}}\textrm{\tiny\maltese\textit{A}}
18682 \begin_layout Plain Layout
18694 \begin_layout Standard
18695 \begin_inset VSpace medskip
18698 Before both formulas the command
18705 The command for the second formula is:
18706 \begin_inset Newline newline
18714 \begin_inset space \textvisiblespace{}
18720 \begin_inset space \textvisiblespace{}
18726 \begin_inset space \textvisiblespace{}
18732 \begin_inset space \textvisiblespace{}
18736 \begin_inset Formula $\to$
18740 \begin_inset Formula $\to$
18744 \begin_inset Newline newline
18748 \begin_inset space \hspace*{}
18759 \begin_inset space \textvisiblespace{}
18765 \begin_inset space \textvisiblespace{}
18771 \begin_inset space \textvisiblespace{}
18777 \begin_layout Standard
18778 If a symbol cannot be displayed in different sizes, it will always be displayed
18779 in the default size.
18782 \begin_layout Section
18784 \begin_inset Index idx
18787 \begin_layout Plain Layout
18796 \begin_layout Standard
18797 Greek letters can also be inserted via the toolbar button
18798 \begin_inset Graphics
18799 filename ../images/math/alpha.png
18805 All international typesetting norms purport that Greek letters in math
18806 have to be typeset italic/slanted.
18807 In some languages, like French or Russian, they are nevertheless sometimes
18811 \begin_layout Subsection
18813 \begin_inset Index idx
18816 \begin_layout Plain Layout
18817 Greek letters ! small
18825 \begin_layout Standard
18826 \begin_inset space \hfill{}
18830 \begin_inset Tabular
18831 <lyxtabular version="3" rows="11" columns="2">
18832 <features rotate="0" tabularvalignment="middle">
18833 <column alignment="center" valignment="top" width="0pt">
18834 <column alignment="center" valignment="top" width="0pt">
18836 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
18839 \begin_layout Plain Layout
18845 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
18848 \begin_layout Plain Layout
18856 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
18859 \begin_layout Plain Layout
18867 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
18870 \begin_layout Plain Layout
18871 \begin_inset Formula $\alpha$
18881 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
18884 \begin_layout Plain Layout
18892 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
18895 \begin_layout Plain Layout
18896 \begin_inset Formula $\beta$
18906 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
18909 \begin_layout Plain Layout
18917 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
18920 \begin_layout Plain Layout
18921 \begin_inset Formula $\gamma$
18931 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
18934 \begin_layout Plain Layout
18942 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
18945 \begin_layout Plain Layout
18946 \begin_inset Formula $\delta$
18956 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
18959 \begin_layout Plain Layout
18967 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
18970 \begin_layout Plain Layout
18971 \begin_inset Formula $\epsilon$
18981 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
18984 \begin_layout Plain Layout
18992 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
18995 \begin_layout Plain Layout
18996 \begin_inset Formula $\varepsilon$
19006 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
19009 \begin_layout Plain Layout
19017 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
19020 \begin_layout Plain Layout
19021 \begin_inset Formula $\zeta$
19031 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
19034 \begin_layout Plain Layout
19042 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
19045 \begin_layout Plain Layout
19046 \begin_inset Formula $\eta$
19056 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
19059 \begin_layout Plain Layout
19067 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
19070 \begin_layout Plain Layout
19071 \begin_inset Formula $\theta$
19081 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
19084 \begin_layout Plain Layout
19092 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
19095 \begin_layout Plain Layout
19096 \begin_inset Formula $\vartheta$
19110 \begin_inset space \hfill{}
19114 \begin_inset Tabular
19115 <lyxtabular version="3" rows="12" columns="2">
19116 <features rotate="0" tabularvalignment="middle">
19117 <column alignment="center" valignment="top" width="0pt">
19118 <column alignment="center" valignment="top" width="0pt">
19120 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
19123 \begin_layout Plain Layout
19129 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
19132 \begin_layout Plain Layout
19140 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
19143 \begin_layout Plain Layout
19151 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
19154 \begin_layout Plain Layout
19155 \begin_inset Formula $\iota$
19165 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
19168 \begin_layout Plain Layout
19176 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
19179 \begin_layout Plain Layout
19180 \begin_inset Formula $\kappa$
19190 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
19193 \begin_layout Plain Layout
19201 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
19204 \begin_layout Plain Layout
19205 \begin_inset Formula $\varkappa$
19215 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
19218 \begin_layout Plain Layout
19226 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
19229 \begin_layout Plain Layout
19230 \begin_inset Formula $\lambda$
19240 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
19243 \begin_layout Plain Layout
19251 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
19254 \begin_layout Plain Layout
19255 \begin_inset Formula $\mu$
19265 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
19268 \begin_layout Plain Layout
19276 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
19279 \begin_layout Plain Layout
19280 \begin_inset Formula $\nu$
19290 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
19293 \begin_layout Plain Layout
19301 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
19304 \begin_layout Plain Layout
19305 \begin_inset Formula $\xi$
19315 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
19318 \begin_layout Plain Layout
19324 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
19327 \begin_layout Plain Layout
19328 \begin_inset Formula $o$
19338 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
19341 \begin_layout Plain Layout
19349 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
19352 \begin_layout Plain Layout
19353 \begin_inset Formula $\pi$
19363 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
19366 \begin_layout Plain Layout
19374 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
19377 \begin_layout Plain Layout
19378 \begin_inset Formula $\varpi$
19388 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
19391 \begin_layout Plain Layout
19399 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
19402 \begin_layout Plain Layout
19403 \begin_inset Formula $\rho$
19417 \begin_inset space \hfill{}
19421 \begin_inset Tabular
19422 <lyxtabular version="3" rows="11" columns="2">
19423 <features rotate="0" tabularvalignment="middle">
19424 <column alignment="center" valignment="top" width="0pt">
19425 <column alignment="center" valignment="top" width="0pt">
19427 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
19430 \begin_layout Plain Layout
19436 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
19439 \begin_layout Plain Layout
19447 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
19450 \begin_layout Plain Layout
19458 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
19461 \begin_layout Plain Layout
19462 \begin_inset Formula $\varrho$
19472 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
19475 \begin_layout Plain Layout
19483 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
19486 \begin_layout Plain Layout
19487 \begin_inset Formula $\sigma$
19497 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
19500 \begin_layout Plain Layout
19508 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
19511 \begin_layout Plain Layout
19512 \begin_inset Formula $\varsigma$
19522 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
19525 \begin_layout Plain Layout
19533 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
19536 \begin_layout Plain Layout
19537 \begin_inset Formula $\tau$
19547 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
19550 \begin_layout Plain Layout
19558 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
19561 \begin_layout Plain Layout
19562 \begin_inset Formula $\upsilon$
19572 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
19575 \begin_layout Plain Layout
19583 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
19586 \begin_layout Plain Layout
19587 \begin_inset Formula $\phi$
19597 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
19600 \begin_layout Plain Layout
19608 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
19611 \begin_layout Plain Layout
19612 \begin_inset Formula $\varphi$
19622 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
19625 \begin_layout Plain Layout
19633 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
19636 \begin_layout Plain Layout
19637 \begin_inset Formula $\chi$
19647 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
19650 \begin_layout Plain Layout
19658 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
19661 \begin_layout Plain Layout
19662 \begin_inset Formula $\psi$
19672 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
19675 \begin_layout Plain Layout
19683 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
19686 \begin_layout Plain Layout
19687 \begin_inset Formula $\omega$
19701 \begin_inset space \hfill{}
19707 \begin_layout Standard
19708 \begin_inset VSpace medskip
19714 \begin_layout Standard
19715 How to create special upright Greek letters is explained in
19716 \begin_inset CommandInset ref
19718 reference "sub:Upright-small-Greek"
19725 \begin_layout Subsection
19727 \begin_inset Index idx
19730 \begin_layout Plain Layout
19731 Greek letters ! big
19739 \begin_layout Standard
19740 \begin_inset space \hfill{}
19744 \begin_inset Tabular
19745 <lyxtabular version="3" rows="7" columns="2">
19746 <features rotate="0" tabularvalignment="middle">
19747 <column alignment="center" valignment="top" width="0pt">
19748 <column alignment="center" valignment="top" width="0pt">
19750 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
19753 \begin_layout Plain Layout
19759 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
19762 \begin_layout Plain Layout
19770 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
19773 \begin_layout Plain Layout
19781 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
19784 \begin_layout Plain Layout
19785 \begin_inset Formula $\Gamma$
19795 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
19798 \begin_layout Plain Layout
19806 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
19809 \begin_layout Plain Layout
19810 \begin_inset Formula $\Delta$
19820 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
19823 \begin_layout Plain Layout
19831 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
19834 \begin_layout Plain Layout
19835 \begin_inset Formula $\Theta$
19845 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
19848 \begin_layout Plain Layout
19856 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
19859 \begin_layout Plain Layout
19860 \begin_inset Formula $\Lambda$
19870 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
19873 \begin_layout Plain Layout
19881 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
19884 \begin_layout Plain Layout
19885 \begin_inset Formula $\Xi$
19895 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
19898 \begin_layout Plain Layout
19906 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
19909 \begin_layout Plain Layout
19910 \begin_inset Formula $\Pi$
19924 \begin_inset space \hfill{}
19928 \begin_inset Tabular
19929 <lyxtabular version="3" rows="6" columns="2">
19930 <features rotate="0" tabularvalignment="middle">
19931 <column alignment="center" valignment="top" width="0pt">
19932 <column alignment="center" valignment="top" width="0pt">
19934 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
19937 \begin_layout Plain Layout
19943 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
19946 \begin_layout Plain Layout
19954 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
19957 \begin_layout Plain Layout
19965 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
19968 \begin_layout Plain Layout
19969 \begin_inset Formula $\Sigma$
19979 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
19982 \begin_layout Plain Layout
19990 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
19993 \begin_layout Plain Layout
19994 \begin_inset Formula $\Upsilon$
20004 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
20007 \begin_layout Plain Layout
20015 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
20018 \begin_layout Plain Layout
20019 \begin_inset Formula $\Phi$
20029 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
20032 \begin_layout Plain Layout
20040 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
20043 \begin_layout Plain Layout
20044 \begin_inset Formula $\Psi$
20054 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
20057 \begin_layout Plain Layout
20065 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
20068 \begin_layout Plain Layout
20069 \begin_inset Formula $\Omega$
20083 \begin_inset space \hfill{}
20089 \begin_layout Standard
20090 \begin_inset VSpace medskip
20093 That the big Greek letters appear upright is caused by a design bug when
20095 To get correct italic big letters, begin every command with
20100 For example the command
20107 \begin_inset Formula $\varGamma$
20111 Another way is to load the package
20119 \begin_layout Plain Layout
20124 is part of the LaTeX-package
20129 \begin_inset Index idx
20132 \begin_layout Plain Layout
20137 \begin_layout Plain Layout
20157 \begin_inset Index idx
20160 \begin_layout Plain Layout
20166 with the LaTeX-preamble line
20169 \begin_layout Standard
20174 usepackage{fixmath}
20177 \begin_layout Standard
20178 Then all big Greek letters in a document will automatically be typeset italic.
20181 \begin_layout Subsection
20183 \begin_inset Index idx
20186 \begin_layout Plain Layout
20187 Greek letters ! bold
20195 \begin_layout Standard
20196 Greek letters cannot be set with different font styles like Latin letters.
20197 They can only be made bold with the command
20204 \begin_inset Index idx
20207 \begin_layout Plain Layout
20218 \begin_layout Standard
20220 \begin_inset Tabular
20221 <lyxtabular version="3" rows="3" columns="2">
20222 <features rotate="0" tabularvalignment="middle">
20223 <column alignment="center" valignment="top">
20224 <column alignment="center" valignment="top">
20226 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
20229 \begin_layout Plain Layout
20235 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
20238 \begin_layout Plain Layout
20246 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
20249 \begin_layout Plain Layout
20261 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
20264 \begin_layout Plain Layout
20265 \begin_inset Formula $\Upsilon\boldsymbol{\Upsilon}$
20275 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
20278 \begin_layout Plain Layout
20290 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
20293 \begin_layout Plain Layout
20294 \begin_inset Formula $\theta\boldsymbol{\theta}$
20310 \begin_layout Section
20315 \begin_layout Plain Layout
20328 \begin_layout Plain Layout
20329 A list with all symbols of most of the LaTeX-packages can be found in
20330 \begin_inset CommandInset citation
20345 \begin_layout Plain Layout
20353 \begin_inset Note Note
20356 \begin_layout Plain Layout
20359 texorpdfstring is used to avoid that the footnote appears in the PDF-bookmark.
20362 \begin_layout Plain Layout
20365 texorpdfstring is in section
20366 \begin_inset CommandInset ref
20368 reference "sub:Formulas-in-Section"
20378 \begin_inset Index idx
20381 \begin_layout Plain Layout
20390 \begin_layout Standard
20391 Many of the symbols listed in this section can also be inserted via the
20393 \begin_inset Graphics
20394 filename ../images/math/nabla.png
20400 \begin_inset Graphics
20401 filename ../images/math/digamma.png
20409 \begin_layout Subsection
20410 Mathematical Symbols
20411 \begin_inset CommandInset label
20413 name "sub:Mathematical-Symbols"
20418 \begin_inset Index idx
20421 \begin_layout Plain Layout
20422 Symbols ! mathematical
20430 \begin_layout Standard
20431 \begin_inset space \hfill{}
20435 \begin_inset Tabular
20436 <lyxtabular version="3" rows="10" columns="2">
20437 <features rotate="0" tabularvalignment="middle">
20438 <column alignment="center" valignment="top" width="0pt">
20439 <column alignment="center" valignment="top" width="0pt">
20441 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
20444 \begin_layout Plain Layout
20450 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
20453 \begin_layout Plain Layout
20461 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
20464 \begin_layout Plain Layout
20472 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
20475 \begin_layout Plain Layout
20476 \begin_inset Formula $\neg$
20486 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
20489 \begin_layout Plain Layout
20497 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
20500 \begin_layout Plain Layout
20501 \begin_inset Formula $\Im$
20511 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
20514 \begin_layout Plain Layout
20522 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
20525 \begin_layout Plain Layout
20526 \begin_inset Formula $\Re$
20536 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
20539 \begin_layout Plain Layout
20547 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
20550 \begin_layout Plain Layout
20551 \begin_inset Formula $\aleph$
20561 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
20564 \begin_layout Plain Layout
20572 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
20575 \begin_layout Plain Layout
20576 \begin_inset Formula $\partial$
20586 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
20589 \begin_layout Plain Layout
20597 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
20600 \begin_layout Plain Layout
20601 \begin_inset Formula $\infty$
20611 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
20614 \begin_layout Plain Layout
20622 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
20625 \begin_layout Plain Layout
20626 \begin_inset Formula $\wp$
20636 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
20639 \begin_layout Plain Layout
20647 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
20650 \begin_layout Plain Layout
20651 \begin_inset Formula $\imath$
20661 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
20664 \begin_layout Plain Layout
20672 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
20675 \begin_layout Plain Layout
20676 \begin_inset Formula $\jmath$
20690 \begin_inset space \hfill{}
20694 \begin_inset Tabular
20695 <lyxtabular version="3" rows="10" columns="2">
20696 <features rotate="0" tabularvalignment="middle">
20697 <column alignment="center" valignment="top" width="0pt">
20698 <column alignment="center" valignment="top" width="0pt">
20700 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
20703 \begin_layout Plain Layout
20709 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
20712 \begin_layout Plain Layout
20714 \begin_inset Note Note
20717 \begin_layout Plain Layout
20724 is only used as spacer.
20736 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
20739 \begin_layout Plain Layout
20747 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
20750 \begin_layout Plain Layout
20751 \begin_inset Formula $\forall$
20761 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
20764 \begin_layout Plain Layout
20772 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
20775 \begin_layout Plain Layout
20776 \begin_inset Formula $\exists$
20786 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
20789 \begin_layout Plain Layout
20797 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
20800 \begin_layout Plain Layout
20801 \begin_inset Formula $\nexists$
20811 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
20814 \begin_layout Plain Layout
20822 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
20825 \begin_layout Plain Layout
20826 \begin_inset Formula $\emptyset$
20836 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
20839 \begin_layout Plain Layout
20847 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
20850 \begin_layout Plain Layout
20851 \begin_inset Formula $\varnothing$
20861 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
20864 \begin_layout Plain Layout
20872 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
20875 \begin_layout Plain Layout
20876 \begin_inset Formula $\dag$
20886 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
20889 \begin_layout Plain Layout
20897 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
20900 \begin_layout Plain Layout
20901 \begin_inset Formula $\ddag$
20911 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
20914 \begin_layout Plain Layout
20922 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
20925 \begin_layout Plain Layout
20929 \begin_layout Plain Layout
20939 \begin_inset Formula $\complement$
20946 \begin_layout Plain Layout
20960 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
20963 \begin_layout Plain Layout
20971 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
20974 \begin_layout Plain Layout
20975 \begin_inset Formula $\Bbbk$
20989 \begin_inset space \hfill{}
20993 \begin_inset Tabular
20994 <lyxtabular version="3" rows="10" columns="2">
20995 <features rotate="0" tabularvalignment="middle">
20996 <column alignment="center" valignment="top" width="0pt">
20997 <column alignment="center" valignment="top" width="0pt">
20999 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
21002 \begin_layout Plain Layout
21008 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
21011 \begin_layout Plain Layout
21019 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
21022 \begin_layout Plain Layout
21030 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
21033 \begin_layout Plain Layout
21034 \begin_inset Formula $\prime$
21044 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
21047 \begin_layout Plain Layout
21055 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
21058 \begin_layout Plain Layout
21059 \begin_inset Formula $\backprime$
21069 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
21072 \begin_layout Plain Layout
21080 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
21083 \begin_layout Plain Layout
21084 \begin_inset Formula $\mho$
21094 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
21097 \begin_layout Plain Layout
21105 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
21108 \begin_layout Plain Layout
21109 \begin_inset Formula $\triangle$
21119 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
21122 \begin_layout Plain Layout
21130 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
21133 \begin_layout Plain Layout
21134 \begin_inset Formula $\angle$
21144 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
21147 \begin_layout Plain Layout
21155 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
21158 \begin_layout Plain Layout
21159 \begin_inset Formula $\measuredangle$
21169 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
21172 \begin_layout Plain Layout
21180 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
21183 \begin_layout Plain Layout
21184 \begin_inset Formula $\sphericalangle$
21194 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
21197 \begin_layout Plain Layout
21205 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
21208 \begin_layout Plain Layout
21209 \begin_inset Formula $\top$
21219 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
21222 \begin_layout Plain Layout
21230 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
21233 \begin_layout Plain Layout
21234 \begin_inset Formula $\bot$
21248 \begin_inset space \hfill{}
21254 \begin_layout Subsection
21255 Miscellaneous Symbols
21256 \begin_inset CommandInset label
21258 name "sub:Miscellaneous-Symbols"
21263 \begin_inset Index idx
21266 \begin_layout Plain Layout
21267 Symbols ! miscellaneous
21275 \begin_layout Standard
21278 \begin_inset Tabular
21279 <lyxtabular version="3" rows="10" columns="2">
21280 <features rotate="0" tabularvalignment="middle">
21281 <column alignment="center" valignment="top" width="0pt">
21282 <column alignment="center" valignment="top" width="0pt">
21284 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
21287 \begin_layout Plain Layout
21293 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
21296 \begin_layout Plain Layout
21304 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
21307 \begin_layout Plain Layout
21315 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
21318 \begin_layout Plain Layout
21319 \begin_inset Formula $\flat$
21329 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
21332 \begin_layout Plain Layout
21340 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
21343 \begin_layout Plain Layout
21344 \begin_inset Formula $\natural$
21354 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
21357 \begin_layout Plain Layout
21365 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
21368 \begin_layout Plain Layout
21369 \begin_inset Formula $\sharp$
21379 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
21382 \begin_layout Plain Layout
21390 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
21393 \begin_layout Plain Layout
21394 \begin_inset Formula $\surd$
21404 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
21407 \begin_layout Plain Layout
21415 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
21418 \begin_layout Plain Layout
21419 \begin_inset Formula $\checkmark$
21429 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
21432 \begin_layout Plain Layout
21440 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
21443 \begin_layout Plain Layout
21444 \begin_inset Formula $\yen$
21454 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
21457 \begin_layout Plain Layout
21465 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
21468 \begin_layout Plain Layout
21469 \begin_inset Formula $\pounds$
21479 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
21482 \begin_layout Plain Layout
21488 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
21491 \begin_layout Plain Layout
21492 \begin_inset Formula $\$$
21502 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
21505 \begin_layout Plain Layout
21511 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
21514 \begin_layout Plain Layout
21515 \begin_inset Formula $§$
21529 \begin_inset Tabular
21530 <lyxtabular version="3" rows="10" columns="2">
21531 <features rotate="0" tabularvalignment="middle">
21532 <column alignment="center" valignment="top">
21533 <column alignment="center" valignment="top">
21535 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
21538 \begin_layout Plain Layout
21544 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
21547 \begin_layout Plain Layout
21555 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
21558 \begin_layout Plain Layout
21566 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
21569 \begin_layout Plain Layout
21570 \begin_inset Formula $\hbar$
21580 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
21583 \begin_layout Plain Layout
21591 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
21594 \begin_layout Plain Layout
21595 \begin_inset Formula $\hslash$
21605 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
21608 \begin_layout Plain Layout
21616 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
21619 \begin_layout Plain Layout
21620 \begin_inset Formula $\clubsuit$
21630 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
21633 \begin_layout Plain Layout
21641 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
21644 \begin_layout Plain Layout
21645 \begin_inset Formula $\spadesuit$
21655 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
21658 \begin_layout Plain Layout
21666 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
21669 \begin_layout Plain Layout
21670 \begin_inset Formula $\bigstar$
21680 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
21683 \begin_layout Plain Layout
21691 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
21694 \begin_layout Plain Layout
21695 \begin_inset Formula $\blacklozenge$
21705 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
21708 \begin_layout Plain Layout
21716 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
21719 \begin_layout Plain Layout
21720 \begin_inset Formula $\blacktriangle$
21730 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
21733 \begin_layout Plain Layout
21741 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
21744 \begin_layout Plain Layout
21745 \begin_inset Formula $\blacktriangledown$
21755 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
21758 \begin_layout Plain Layout
21766 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
21769 \begin_layout Plain Layout
21770 \begin_inset Formula $\bullet$
21784 \begin_inset Tabular
21785 <lyxtabular version="3" rows="10" columns="2">
21786 <features rotate="0" tabularvalignment="middle">
21787 <column alignment="center" valignment="top" width="0pt">
21788 <column alignment="center" valignment="top" width="0pt">
21790 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
21793 \begin_layout Plain Layout
21799 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
21802 \begin_layout Plain Layout
21810 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
21813 \begin_layout Plain Layout
21821 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
21824 \begin_layout Plain Layout
21825 \begin_inset Formula $\diamondsuit$
21835 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
21838 \begin_layout Plain Layout
21846 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
21849 \begin_layout Plain Layout
21850 \begin_inset Formula $\Diamond$
21860 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
21863 \begin_layout Plain Layout
21871 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
21874 \begin_layout Plain Layout
21875 \begin_inset Formula $\heartsuit$
21885 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
21888 \begin_layout Plain Layout
21896 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
21899 \begin_layout Plain Layout
21900 \begin_inset Formula $\P$
21910 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
21913 \begin_layout Plain Layout
21921 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
21924 \begin_layout Plain Layout
21925 \begin_inset Formula $\copyright$
21935 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
21938 \begin_layout Plain Layout
21946 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
21949 \begin_layout Plain Layout
21950 \begin_inset Formula $\circledR$
21960 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
21963 \begin_layout Plain Layout
21971 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
21974 \begin_layout Plain Layout
21975 \begin_inset Formula $\maltese$
21985 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
21988 \begin_layout Plain Layout
21996 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
21999 \begin_layout Plain Layout
22000 \begin_inset Formula $\diagup$
22010 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
22013 \begin_layout Plain Layout
22021 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
22024 \begin_layout Plain Layout
22025 \begin_inset Formula $\diagdown$
22041 \begin_layout Standard
22042 \begin_inset VSpace medskip
22048 \begin_layout Standard
22049 Some symbols can be displayed in different sizes, see
22050 \begin_inset CommandInset ref
22052 reference "sub:Font-Sizes"
22059 \begin_layout Subsection
22061 \begin_inset Index idx
22064 \begin_layout Plain Layout
22065 Symbols ! Euro-symbol
22071 \begin_inset Index idx
22074 \begin_layout Plain Layout
22081 \begin_layout Plain Layout
22098 \begin_layout Standard
22099 To use the Euro symbol in formulas, the LaTeX-package
22104 \begin_inset Index idx
22107 \begin_layout Plain Layout
22113 must be installed and loaded with the LaTeX-preamble line
22116 \begin_layout Standard
22121 usepackage[gennarrow]{eurosym}
22124 \begin_layout Standard
22125 The Euro symbol can now be inserted with the command
22132 \begin_inset Index idx
22135 \begin_layout Plain Layout
22146 \begin_layout Standard
22147 The Euro symbol can directly be inserted with the € key in mathematical
22148 text, without having
22163 can also be inserted in TeX-mode.
22164 The official currency symbol can then be inserted with the command
22171 \begin_inset Index idx
22174 \begin_layout Plain Layout
22182 , that is only available in TeX-mode.
22185 \begin_layout Standard
22189 \begin_layout Plain Layout
22199 \begin_inset Note Note
22202 \begin_layout Plain Layout
22203 The following table will only be displayed when the LaTeX-package
22215 \begin_layout Standard
22216 An overview about the different Euro symbols:
22219 \begin_layout Standard
22221 \begin_inset Tabular
22222 <lyxtabular version="3" rows="4" columns="3">
22223 <features rotate="0" tabularvalignment="middle">
22224 <column alignment="center" valignment="top" width="0pt">
22225 <column alignment="center" valignment="top" width="0pt">
22226 <column alignment="center" valignment="top" width="0pt">
22228 <cell multicolumn="1" alignment="center" valignment="top" bottomline="true" usebox="none">
22231 \begin_layout Plain Layout
22237 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
22240 \begin_layout Plain Layout
22246 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
22249 \begin_layout Plain Layout
22257 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
22260 \begin_layout Plain Layout
22266 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
22269 \begin_layout Plain Layout
22277 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
22280 \begin_layout Plain Layout
22281 \begin_inset Formula $\euro$
22291 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
22294 \begin_layout Plain Layout
22300 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
22303 \begin_layout Plain Layout
22309 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
22312 \begin_layout Plain Layout
22313 \begin_inset Formula $\mbox{€}$
22323 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
22326 \begin_layout Plain Layout
22332 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
22335 \begin_layout Plain Layout
22343 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
22346 \begin_layout Plain Layout
22350 \begin_layout Plain Layout
22372 \begin_layout Standard
22376 \begin_layout Plain Layout
22386 \begin_inset Note Note
22389 \begin_layout Plain Layout
22390 The following will be displayed when the LaTeX-package
22402 \begin_layout Standard
22403 You need to install the LaTeX-package
22407 to see the rest of this subsection in the output.
22410 \begin_layout Standard
22414 \begin_layout Plain Layout
22426 \begin_layout Section
22428 \begin_inset CommandInset label
22430 name "sec:Relations"
22435 \begin_inset Index idx
22438 \begin_layout Plain Layout
22445 \begin_inset Index idx
22448 \begin_layout Plain Layout
22453 \begin_layout Plain Layout
22464 \begin_layout Plain Layout
22479 \begin_layout Standard
22480 All following relations can also be inserted via the toolbar button
22481 \begin_inset Graphics
22482 filename ../images/math/leq.png
22490 \begin_layout Standard
22491 \begin_inset space \hfill{}
22495 \begin_inset Tabular
22496 <lyxtabular version="3" rows="17" columns="2">
22497 <features rotate="0" tabularvalignment="middle">
22498 <column alignment="center" valignment="top" width="0pt">
22499 <column alignment="center" valignment="top" width="0pt">
22501 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
22504 \begin_layout Plain Layout
22510 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
22513 \begin_layout Plain Layout
22521 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
22524 \begin_layout Plain Layout
22530 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
22533 \begin_layout Plain Layout
22534 \begin_inset Formula $<$
22544 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
22547 \begin_layout Plain Layout
22555 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
22558 \begin_layout Plain Layout
22559 \begin_inset Formula $\le$
22569 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
22572 \begin_layout Plain Layout
22580 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
22583 \begin_layout Plain Layout
22584 \begin_inset Formula $\ll$
22594 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
22597 \begin_layout Plain Layout
22605 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
22608 \begin_layout Plain Layout
22609 \begin_inset Formula $\prec$
22619 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
22622 \begin_layout Plain Layout
22630 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
22633 \begin_layout Plain Layout
22634 \begin_inset Formula $\preceq$
22644 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
22647 \begin_layout Plain Layout
22655 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
22658 \begin_layout Plain Layout
22659 \begin_inset Formula $\subset$
22669 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
22672 \begin_layout Plain Layout
22680 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
22683 \begin_layout Plain Layout
22684 \begin_inset Formula $\subseteq$
22694 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
22697 \begin_layout Plain Layout
22705 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
22708 \begin_layout Plain Layout
22709 \begin_inset Formula $\sqsubseteq$
22719 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
22722 \begin_layout Plain Layout
22730 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
22733 \begin_layout Plain Layout
22734 \begin_inset Formula $\in$
22744 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
22747 \begin_layout Plain Layout
22755 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
22758 \begin_layout Plain Layout
22759 \begin_inset Formula $\vdash$
22769 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
22772 \begin_layout Plain Layout
22780 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
22783 \begin_layout Plain Layout
22784 \begin_inset Formula $\smile$
22794 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
22797 \begin_layout Plain Layout
22805 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
22808 \begin_layout Plain Layout
22809 \begin_inset Formula $\lhd$
22819 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
22822 \begin_layout Plain Layout
22830 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
22833 \begin_layout Plain Layout
22834 \begin_inset Formula $\unlhd$
22844 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
22847 \begin_layout Plain Layout
22855 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
22858 \begin_layout Plain Layout
22859 \begin_inset Formula $\gtrless$
22869 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
22872 \begin_layout Plain Layout
22880 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
22883 \begin_layout Plain Layout
22884 \begin_inset Formula $\mid$
22894 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
22897 \begin_layout Plain Layout
22905 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
22908 \begin_layout Plain Layout
22909 \begin_inset Formula $\nmid$
22923 \begin_inset space \hfill{}
22927 \begin_inset Tabular
22928 <lyxtabular version="3" rows="17" columns="2">
22929 <features rotate="0" tabularvalignment="middle">
22930 <column alignment="center" valignment="top" width="0pt">
22931 <column alignment="center" valignment="top" width="0pt">
22933 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
22936 \begin_layout Plain Layout
22942 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
22945 \begin_layout Plain Layout
22953 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
22956 \begin_layout Plain Layout
22962 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
22965 \begin_layout Plain Layout
22966 \begin_inset Formula $=$
22976 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
22979 \begin_layout Plain Layout
22987 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
22990 \begin_layout Plain Layout
22991 \begin_inset Formula $\not=$
23001 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
23004 \begin_layout Plain Layout
23012 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
23015 \begin_layout Plain Layout
23016 \begin_inset Formula $\equiv$
23026 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
23029 \begin_layout Plain Layout
23037 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
23040 \begin_layout Plain Layout
23041 \begin_inset Formula $\sim$
23051 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
23054 \begin_layout Plain Layout
23062 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
23065 \begin_layout Plain Layout
23066 \begin_inset Formula $\simeq$
23076 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
23079 \begin_layout Plain Layout
23087 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
23090 \begin_layout Plain Layout
23091 \begin_inset Formula $\approx$
23101 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
23104 \begin_layout Plain Layout
23112 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
23115 \begin_layout Plain Layout
23116 \begin_inset Formula $\cong$
23126 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
23129 \begin_layout Plain Layout
23137 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
23140 \begin_layout Plain Layout
23141 \begin_inset Formula $\bowtie$
23151 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
23154 \begin_layout Plain Layout
23162 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
23165 \begin_layout Plain Layout
23166 \begin_inset Formula $\notin$
23176 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
23179 \begin_layout Plain Layout
23187 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
23190 \begin_layout Plain Layout
23191 \begin_inset Formula $\perp$
23201 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
23204 \begin_layout Plain Layout
23212 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
23215 \begin_layout Plain Layout
23216 \begin_inset Formula $\propto$
23226 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
23229 \begin_layout Plain Layout
23237 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
23240 \begin_layout Plain Layout
23241 \begin_inset Formula $\asymp$
23251 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
23254 \begin_layout Plain Layout
23262 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
23265 \begin_layout Plain Layout
23266 \begin_inset Formula $\doteq$
23276 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
23279 \begin_layout Plain Layout
23287 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
23290 \begin_layout Plain Layout
23291 \begin_inset Formula $\circeq$
23301 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
23304 \begin_layout Plain Layout
23312 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
23315 \begin_layout Plain Layout
23316 \begin_inset Formula $\models$
23326 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
23329 \begin_layout Plain Layout
23337 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
23340 \begin_layout Plain Layout
23341 \begin_inset Formula $\widehat{=}$
23355 \begin_inset space \hfill{}
23359 \begin_inset Tabular
23360 <lyxtabular version="3" rows="17" columns="2">
23361 <features rotate="0" tabularvalignment="middle">
23362 <column alignment="center" valignment="top" width="0pt">
23363 <column alignment="center" valignment="top" width="0pt">
23365 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
23368 \begin_layout Plain Layout
23374 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
23377 \begin_layout Plain Layout
23385 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
23388 \begin_layout Plain Layout
23394 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
23397 \begin_layout Plain Layout
23398 \begin_inset Formula $>$
23408 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
23411 \begin_layout Plain Layout
23419 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
23422 \begin_layout Plain Layout
23423 \begin_inset Formula $\ge$
23433 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
23436 \begin_layout Plain Layout
23444 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
23447 \begin_layout Plain Layout
23448 \begin_inset Formula $\gg$
23458 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
23461 \begin_layout Plain Layout
23469 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
23472 \begin_layout Plain Layout
23473 \begin_inset Formula $\succ$
23483 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
23486 \begin_layout Plain Layout
23494 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
23497 \begin_layout Plain Layout
23498 \begin_inset Formula $\succeq$
23508 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
23511 \begin_layout Plain Layout
23519 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
23522 \begin_layout Plain Layout
23523 \begin_inset Formula $\supset$
23533 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
23536 \begin_layout Plain Layout
23544 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
23547 \begin_layout Plain Layout
23548 \begin_inset Formula $\supseteq$
23558 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
23561 \begin_layout Plain Layout
23569 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
23572 \begin_layout Plain Layout
23573 \begin_inset Formula $\sqsupseteq$
23583 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
23586 \begin_layout Plain Layout
23594 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
23597 \begin_layout Plain Layout
23598 \begin_inset Formula $\ni$
23608 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
23611 \begin_layout Plain Layout
23619 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
23622 \begin_layout Plain Layout
23623 \begin_inset Formula $\dashv$
23633 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
23636 \begin_layout Plain Layout
23644 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
23647 \begin_layout Plain Layout
23648 \begin_inset Formula $\frown$
23658 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
23661 \begin_layout Plain Layout
23669 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
23672 \begin_layout Plain Layout
23673 \begin_inset Formula $\rhd$
23683 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
23686 \begin_layout Plain Layout
23694 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
23697 \begin_layout Plain Layout
23698 \begin_inset Formula $\unrhd$
23708 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
23711 \begin_layout Plain Layout
23719 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
23722 \begin_layout Plain Layout
23723 \begin_inset Formula $\lessgtr$
23733 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
23736 \begin_layout Plain Layout
23744 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
23747 \begin_layout Plain Layout
23748 \begin_inset Formula $\parallel$
23758 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
23761 \begin_layout Plain Layout
23769 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
23772 \begin_layout Plain Layout
23773 \begin_inset Formula $\nparallel$
23787 \begin_inset space \hfill{}
23793 \begin_layout Standard
23794 \begin_inset VSpace medskip
23809 are bigger than the equal looking operators
23824 \begin_layout Standard
23825 Relations are, in contrary to symbols, always surrounded by space.
23828 \begin_layout Standard
23829 Relations with labels can be created with the command
23836 \begin_inset Index idx
23839 \begin_layout Plain Layout
23850 \begin_layout Standard
23852 \begin_inset Tabular
23853 <lyxtabular version="3" rows="2" columns="2">
23854 <features rotate="0" tabularvalignment="middle">
23855 <column alignment="center" valignment="top">
23856 <column alignment="center" valignment="top">
23858 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
23861 \begin_layout Plain Layout
23867 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
23870 \begin_layout Plain Layout
23872 \begin_inset Note Note
23875 \begin_layout Plain Layout
23882 is only used as spacer.
23894 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
23897 \begin_layout Plain Layout
23901 \begin_inset space \textvisiblespace{}
23909 \begin_inset space \textvisiblespace{}
23913 \begin_inset Formula $\downarrow$
23919 \begin_inset space \textvisiblespace{}
23923 \begin_inset space \textvisiblespace{}
23931 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
23934 \begin_layout Plain Layout
23935 \begin_inset Formula $\raisebox{5mm}{}A(r)\stackrel{r\to\infty}{\approx}B$
23951 \begin_layout Standard
23952 \begin_inset VSpace bigskip
23958 \begin_layout Standard
23959 LyX supports also many special relations.
23960 Use the toolbar button
23961 \begin_inset Graphics
23962 filename ../images/math/leq.png
23967 to see a list of possible relations.
23970 \begin_layout Section
23974 \begin_layout Subsection
23975 Predefined Functions
23976 \begin_inset CommandInset label
23978 name "sub:Predefined-Functions"
23983 \begin_inset Index idx
23986 \begin_layout Plain Layout
23987 Functions ! predefined
23995 \begin_layout Standard
23996 In general, variables are set
24000 in mathematical expressions, but not function names, because
24001 \begin_inset Formula $sin$
24004 could be misunderstood as
24005 \begin_inset Formula $s\cdot i\cdot n$
24009 Therefore there are predefined functionswhich are additionally a bit separated
24011 They are inserted as commands starting with a backslash before their name.
24014 \begin_layout Standard
24016 \begin_inset Tabular
24017 <lyxtabular version="3" rows="2" columns="4">
24018 <features rotate="0" tabularvalignment="middle">
24019 <column alignment="center" valignment="top" width="0pt">
24020 <column alignment="center" valignment="top" width="0pt">
24021 <column alignment="center" valignment="top" width="0pt">
24022 <column alignment="center" valignment="top" width="0pt">
24024 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
24027 \begin_layout Plain Layout
24033 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
24036 \begin_layout Plain Layout
24042 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
24045 \begin_layout Plain Layout
24051 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
24054 \begin_layout Plain Layout
24062 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
24065 \begin_layout Plain Layout
24071 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
24074 \begin_layout Plain Layout
24075 \begin_inset Formula $Asin(x)+B$
24083 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
24086 \begin_layout Plain Layout
24094 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
24097 \begin_layout Plain Layout
24098 \begin_inset Formula $A\sin(x)+B$
24114 \begin_layout Standard
24115 The following functions are predefined:
24118 \begin_layout Standard
24119 \begin_inset VSpace -2mm
24125 \begin_layout Standard
24127 \begin_inset Tabular
24128 <lyxtabular version="3" rows="9" columns="4">
24129 <features rotate="0" tabularvalignment="middle">
24130 <column alignment="center" valignment="top" width="0pt">
24131 <column alignment="center" valignment="top" width="0pt">
24132 <column alignment="center" valignment="top" width="0pt">
24133 <column alignment="center" valignment="top" width="0pt">
24135 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
24138 \begin_layout Plain Layout
24144 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
24147 \begin_layout Plain Layout
24153 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
24156 \begin_layout Plain Layout
24162 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
24165 \begin_layout Plain Layout
24173 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
24176 \begin_layout Plain Layout
24184 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
24187 \begin_layout Plain Layout
24195 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
24198 \begin_layout Plain Layout
24206 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
24209 \begin_layout Plain Layout
24219 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
24222 \begin_layout Plain Layout
24230 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
24233 \begin_layout Plain Layout
24241 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
24244 \begin_layout Plain Layout
24252 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
24255 \begin_layout Plain Layout
24265 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
24268 \begin_layout Plain Layout
24276 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
24279 \begin_layout Plain Layout
24287 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
24290 \begin_layout Plain Layout
24298 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
24301 \begin_layout Plain Layout
24311 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
24314 \begin_layout Plain Layout
24322 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
24325 \begin_layout Plain Layout
24333 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
24336 \begin_layout Plain Layout
24344 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
24347 \begin_layout Plain Layout
24357 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
24360 \begin_layout Plain Layout
24368 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
24371 \begin_layout Plain Layout
24379 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
24382 \begin_layout Plain Layout
24390 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
24393 \begin_layout Plain Layout
24403 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
24406 \begin_layout Plain Layout
24414 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
24417 \begin_layout Plain Layout
24425 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
24428 \begin_layout Plain Layout
24436 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
24439 \begin_layout Plain Layout
24449 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
24452 \begin_layout Plain Layout
24460 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
24463 \begin_layout Plain Layout
24471 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
24474 \begin_layout Plain Layout
24482 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
24485 \begin_layout Plain Layout
24495 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
24498 \begin_layout Plain Layout
24506 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
24509 \begin_layout Plain Layout
24517 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
24520 \begin_layout Plain Layout
24528 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
24531 \begin_layout Plain Layout
24547 \begin_layout Standard
24548 They can also be inserted with the math toolbar button
24549 \begin_inset Graphics
24550 filename ../images/math/functions.png
24558 \begin_layout Subsection
24559 Self-defined Functions
24560 \begin_inset Index idx
24563 \begin_layout Plain Layout
24564 Functions ! self-defined
24572 \begin_layout Standard
24573 To use a function that is not predefined, like for example the sign function
24574 sgn(x), there are two possibilities:
24577 \begin_layout Itemize
24578 Define the function by inserting the following line to the LaTeX-preamble
24582 \begin_layout Plain Layout
24587 DeclareMathOperator
24590 \begin_inset CommandInset ref
24592 reference "sub:Self-defined-Operators"
24602 \begin_inset Newline newline
24606 \begin_inset VSpace -3mm
24610 \begin_inset Newline newline
24617 DeclareMathOperator{
24622 \begin_inset Index idx
24625 \begin_layout Plain Layout
24630 DeclareMathOperator
24636 \begin_inset Newline newline
24640 \begin_inset VSpace -2mm
24644 \begin_inset Newline newline
24647 Now the new defined function can be called with the command
24656 \begin_layout Itemize
24657 Write the formula as usual, mark the formula name, in our example the letters
24662 , and change it to mathematical text.
24663 Finally, a space is inserted between prefactor and function.
24666 \begin_layout Standard
24667 The result is the same with both methods as with a predefined function
24671 \begin_layout Plain Layout
24672 In LyX self-defined functions are displayed red, predefined ones black.
24680 \begin_layout Standard
24682 \begin_inset Tabular
24683 <lyxtabular version="3" rows="3" columns="2">
24684 <features rotate="0" tabularvalignment="middle">
24685 <column alignment="center" valignment="top" width="0pt">
24686 <column alignment="center" valignment="top" width="0pt">
24688 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
24691 \begin_layout Plain Layout
24697 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
24700 \begin_layout Plain Layout
24708 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
24711 \begin_layout Plain Layout
24719 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
24722 \begin_layout Plain Layout
24723 \begin_inset Formula $A\sgn(x)+B$
24733 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
24736 \begin_layout Plain Layout
24740 \begin_inset Formula $\underbrace{\textrm{sgn}}_{\textrm{Alt+M}\,\textrm{M}}$
24748 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
24751 \begin_layout Plain Layout
24752 \begin_inset Formula $A\,\textrm{sgn}(x)+B$
24768 \begin_layout Standard
24769 The first method is more suitable when the self-defined function should
24770 be used several times.
24773 \begin_layout Subsection
24775 \begin_inset Index idx
24778 \begin_layout Plain Layout
24787 \begin_layout Standard
24788 For limits, in addition to the commands
24795 \begin_inset Index idx
24798 \begin_layout Plain Layout
24818 the following functions are defined:
24821 \begin_layout Standard
24823 \begin_inset Tabular
24824 <lyxtabular version="3" rows="5" columns="2">
24825 <features rotate="0" tabularvalignment="middle">
24826 <column alignment="center" valignment="top">
24827 <column alignment="center" valignment="top">
24829 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
24832 \begin_layout Plain Layout
24838 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
24841 \begin_layout Plain Layout
24843 \begin_inset Note Note
24846 \begin_layout Plain Layout
24853 is only used as spacer.
24865 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
24868 \begin_layout Plain Layout
24876 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
24879 \begin_layout Plain Layout
24880 \begin_inset Formula $\varliminf$
24890 <cell alignment="center" valignment="top" leftline="true" usebox="none">
24893 \begin_layout Plain Layout
24901 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
24904 \begin_layout Plain Layout
24905 \begin_inset Formula $\varlimsup$
24915 <cell alignment="center" valignment="top" leftline="true" usebox="none">
24918 \begin_layout Plain Layout
24926 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
24929 \begin_layout Plain Layout
24930 \begin_inset Formula $\varprojlim$
24940 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
24943 \begin_layout Plain Layout
24951 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
24954 \begin_layout Plain Layout
24955 \begin_inset Formula $\varinjlim$
24959 \begin_inset Formula $\raisebox{-2.5mm}{}$
24975 \begin_layout Standard
24976 \begin_inset VSpace medskip
24979 The limit is created by inserting a subscript.
24980 It is set right beside the function in an inline formula:
24983 \begin_layout Standard
24985 \begin_inset Tabular
24986 <lyxtabular version="3" rows="2" columns="2">
24987 <features rotate="0" tabularvalignment="middle">
24988 <column alignment="center" valignment="top" width="0pt">
24989 <column alignment="center" valignment="top" width="0pt">
24991 <cell alignment="center" valignment="top" usebox="none">
24994 \begin_layout Plain Layout
25000 <cell alignment="center" valignment="top" usebox="none">
25003 \begin_layout Plain Layout
25004 \begin_inset space \hspace{}
25009 \begin_inset Note Note
25012 \begin_layout Plain Layout
25019 are used here as spacer.
25031 <cell alignment="center" valignment="top" usebox="none">
25034 \begin_layout Plain Layout
25040 \begin_inset space \textvisiblespace{}
25044 \begin_inset space \textvisiblespace{}
25052 <cell alignment="center" valignment="top" usebox="none">
25055 \begin_layout Plain Layout
25056 \begin_inset Formula $\hspace{1cm}\raisebox{5mm}{}\lim_{x\to A}x=B$
25072 \begin_layout Standard
25073 In a displayed formula the limit is set below the formula, as usual:
25074 \begin_inset Formula
25084 \begin_layout Standard
25085 \begin_inset VSpace medskip
25091 \begin_layout Standard
25092 How to adjust the typesetting of the limits see
25093 \begin_inset CommandInset ref
25095 reference "sub:Operator-Limits"
25102 \begin_layout Subsection
25104 \begin_inset Index idx
25107 \begin_layout Plain Layout
25108 Functions ! modulo-
25116 \begin_layout Standard
25117 The modulo-function is special, because it exists in four variants.
25118 The variants in a displayed formula are:
25119 \begin_inset Formula
25121 \underline{\textrm{Command}\raisebox{-0.9mm}{}} & & \underline{\textrm{Result}}\\
25122 \mathrm{a\backslash mod\textrm{␣}b} & & a\mod b\\
25123 \mathrm{a\backslash pmod\textrm{␣}b} & & a\pmod b\\
25124 \mathrm{a\backslash bmod\textrm{␣}b} & & a\bmod b\\
25125 \mathrm{a\backslash pod\textrm{␣}b} & & a\pod b
25133 \begin_layout Standard
25134 In an inline formula less space is set before the function names for all
25136 By default the modulo-functions take only the first following character
25138 To use more than one character, one has to put them into TeX-braces:
25139 \begin_inset Formula
25141 \underline{\textrm{Command}\raisebox{-0.9mm}{}} & & \underline{\textrm{Result}}\\
25142 \mathrm{a\backslash pod\textrm{␣}bcd} & & a\pod bcd\\
25143 \mathrm{a\backslash pod\backslash\{bc\to d} & & a\pod{bc}d
25151 \begin_layout Section
25153 \begin_inset Index idx
25156 \begin_layout Plain Layout
25165 \begin_layout Subsection
25166 Special Characters in Mathematical Text
25169 \begin_layout Standard
25170 The following commands can only be used in mathematical text or in TeX-mode:
25173 \begin_layout Standard
25174 \begin_inset space \hfill{}
25178 \begin_inset Tabular
25179 <lyxtabular version="3" rows="8" columns="2">
25180 <features rotate="0" tabularvalignment="middle">
25181 <column alignment="block" valignment="top">
25182 <column alignment="block" valignment="top">
25184 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
25187 \begin_layout Plain Layout
25193 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
25196 \begin_layout Plain Layout
25204 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
25207 \begin_layout Plain Layout
25215 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
25218 \begin_layout Plain Layout
25219 \begin_inset Formula $\textrm{œ}$
25229 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
25232 \begin_layout Plain Layout
25240 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
25243 \begin_layout Plain Layout
25244 \begin_inset Formula $\textrm{Œ}$
25254 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
25257 \begin_layout Plain Layout
25265 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
25268 \begin_layout Plain Layout
25269 \begin_inset Formula $\textrm{æ}$
25279 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
25282 \begin_layout Plain Layout
25290 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
25293 \begin_layout Plain Layout
25294 \begin_inset Formula $\textrm{Æ}$
25304 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
25307 \begin_layout Plain Layout
25315 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
25318 \begin_layout Plain Layout
25319 \begin_inset Formula $\textrm{\aa}$
25329 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
25332 \begin_layout Plain Layout
25336 \begin_inset Index idx
25339 \begin_layout Plain Layout
25346 \begin_layout Plain Layout
25367 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
25370 \begin_layout Plain Layout
25371 \begin_inset Formula $\textrm{Å}$
25381 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
25384 \begin_layout Plain Layout
25392 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
25395 \begin_layout Plain Layout
25396 \begin_inset Formula $\textrm{ı}$
25410 \begin_inset space \hfill{}
25414 \begin_inset Tabular
25415 <lyxtabular version="3" rows="8" columns="2">
25416 <features rotate="0" tabularvalignment="middle">
25417 <column alignment="block" valignment="top">
25418 <column alignment="center" valignment="top">
25420 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
25423 \begin_layout Plain Layout
25425 \begin_inset Note Note
25428 \begin_layout Plain Layout
25430 \begin_inset space \thinspace{}
25433 mm is used for separation, because otherwise the output will be ¡ and ¿
25444 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
25447 \begin_layout Plain Layout
25455 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
25458 \begin_layout Plain Layout
25466 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
25469 \begin_layout Plain Layout
25470 \begin_inset Formula $\textrm{ø}$
25480 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
25483 \begin_layout Plain Layout
25491 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
25494 \begin_layout Plain Layout
25495 \begin_inset Formula $\textrm{Ø}$
25505 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
25508 \begin_layout Plain Layout
25516 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
25519 \begin_layout Plain Layout
25520 \begin_inset Formula $\textrm{ł}$
25530 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
25533 \begin_layout Plain Layout
25541 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
25544 \begin_layout Plain Layout
25545 \begin_inset Formula $\textrm{Ł}$
25555 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
25558 \begin_layout Plain Layout
25560 \begin_inset space \hspace{}
25565 \begin_inset space \textvisiblespace{}
25573 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
25576 \begin_layout Plain Layout
25577 \begin_inset Formula $\textrm{!`}$
25587 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
25590 \begin_layout Plain Layout
25592 \begin_inset space \hspace{}
25597 \begin_inset space \textvisiblespace{}
25605 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
25608 \begin_layout Plain Layout
25609 \begin_inset Formula $\textrm{?`}$
25619 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
25622 \begin_layout Plain Layout
25630 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
25633 \begin_layout Plain Layout
25634 \begin_inset Formula $\textrm{ȷ}$
25648 \begin_inset space \hfill{}
25654 \begin_layout Standard
25656 \begin_inset Formula $\textrm{\textrm{Å}}$
25660 \begin_inset Formula $\textrm{\textrm{Ø}}$
25663 can also be inserted via the math toolbar button
25664 \begin_inset Graphics
25665 filename ../images/math/digamma.png
25673 \begin_layout Standard
25674 An exception are the commands
25677 \begin_inset space \hspace{}
25686 \begin_inset space \hspace{}
25692 , because they can be inserted in LyX directly to text.
25695 \begin_layout Subsection
25697 \begin_inset CommandInset label
25699 name "sub:Accents-in-Text"
25704 \begin_inset Index idx
25707 \begin_layout Plain Layout
25716 \begin_layout Standard
25717 With the following commands all letters can be accented.
25718 The commands must be inserted in TeX-mode.
25721 \begin_layout Standard
25722 \begin_inset space \hfill{}
25726 \begin_inset Tabular
25727 <lyxtabular version="3" rows="8" columns="2">
25728 <features rotate="0" tabularvalignment="middle">
25729 <column alignment="block" valignment="top">
25730 <column alignment="block" valignment="top">
25732 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
25735 \begin_layout Plain Layout
25741 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
25744 \begin_layout Plain Layout
25752 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
25755 \begin_layout Plain Layout
25759 \begin_inset Quotes grd
25767 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
25770 \begin_layout Plain Layout
25774 \begin_layout Plain Layout
25790 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
25793 \begin_layout Plain Layout
25801 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
25804 \begin_layout Plain Layout
25808 \begin_layout Plain Layout
25824 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
25827 \begin_layout Plain Layout
25831 \begin_inset space \textvisiblespace{}
25839 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
25842 \begin_layout Plain Layout
25846 \begin_layout Plain Layout
25862 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
25865 \begin_layout Plain Layout
25873 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
25876 \begin_layout Plain Layout
25880 \begin_layout Plain Layout
25896 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
25899 \begin_layout Plain Layout
25903 \begin_inset space \textvisiblespace{}
25911 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
25914 \begin_layout Plain Layout
25918 \begin_layout Plain Layout
25934 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
25937 \begin_layout Plain Layout
25941 \begin_inset space \textvisiblespace{}
25949 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
25952 \begin_layout Plain Layout
25956 \begin_layout Plain Layout
25972 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
25975 \begin_layout Plain Layout
25979 \begin_inset space \textvisiblespace{}
25987 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
25990 \begin_layout Plain Layout
25994 \begin_layout Plain Layout
26014 \begin_inset space \hfill{}
26018 \begin_inset Tabular
26019 <lyxtabular version="3" rows="8" columns="2">
26020 <features rotate="0" tabularvalignment="middle">
26021 <column alignment="block" valignment="top">
26022 <column alignment="center" valignment="top">
26024 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
26027 \begin_layout Plain Layout
26033 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
26036 \begin_layout Plain Layout
26044 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
26047 \begin_layout Plain Layout
26051 \begin_inset space \textvisiblespace{}
26059 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
26062 \begin_layout Plain Layout
26066 \begin_layout Plain Layout
26082 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
26085 \begin_layout Plain Layout
26093 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
26096 \begin_layout Plain Layout
26100 \begin_layout Plain Layout
26116 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
26119 \begin_layout Plain Layout
26123 \begin_inset Index idx
26126 \begin_layout Plain Layout
26137 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
26140 \begin_layout Plain Layout
26144 \begin_layout Plain Layout
26160 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
26163 \begin_layout Plain Layout
26171 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
26174 \begin_layout Plain Layout
26178 \begin_layout Plain Layout
26194 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
26197 \begin_layout Plain Layout
26201 \begin_inset space \textvisiblespace{}
26209 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
26212 \begin_layout Plain Layout
26216 \begin_layout Plain Layout
26232 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
26235 \begin_layout Plain Layout
26239 \begin_inset space \textvisiblespace{}
26247 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
26250 \begin_layout Plain Layout
26254 \begin_layout Plain Layout
26270 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
26273 \begin_layout Plain Layout
26277 \begin_inset space \textvisiblespace{}
26285 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
26288 \begin_layout Plain Layout
26292 \begin_layout Plain Layout
26312 \begin_inset space \hfill{}
26318 \begin_layout Standard
26319 \begin_inset VSpace medskip
26328 also two different characters can be accented.
26334 \begin_inset space \textvisiblespace{}
26343 \begin_layout Plain Layout
26355 \begin_layout Standard
26368 can in combination with vowels directly be inserted with the keyboard without
26370 The same applies for the tilde
26374 \begin_layout Plain Layout
26375 This only applies for keyboards where the tilde is defined as accent.
26384 in combination with
26399 \begin_layout Standard
26442 and accents that are inserted directly with the keyboard are also available
26443 in mathematical text.
26444 For the other accents there are special math commands to be used in formulas,
26446 \begin_inset CommandInset ref
26448 reference "sub:Accents-for-one"
26455 \begin_layout Standard
26456 \begin_inset VSpace bigskip
26459 Furthermore, with the command
26466 \begin_inset Index idx
26469 \begin_layout Plain Layout
26477 all numbers and letters can be set into a circle, quasi accented with a
26478 circle, similar to the copyright symbol.
26481 \begin_layout Standard
26483 \begin_inset Tabular
26484 <lyxtabular version="3" rows="3" columns="2">
26485 <features rotate="0" tabularvalignment="middle">
26486 <column alignment="center" valignment="top">
26487 <column alignment="center" valignment="top">
26489 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
26492 \begin_layout Plain Layout
26498 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
26501 \begin_layout Plain Layout
26503 \begin_inset Note Note
26506 \begin_layout Plain Layout
26513 is only used as spacer.
26525 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
26528 \begin_layout Plain Layout
26536 <cell multicolumn="1" alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
26539 \begin_layout Plain Layout
26543 \begin_layout Plain Layout
26559 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
26562 \begin_layout Plain Layout
26573 raisebox{-1.5pt}{W}}
26578 <cell multicolumn="1" alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
26581 \begin_layout Plain Layout
26582 \begin_inset Formula $\raisebox{4.5mm}{}$
26589 \begin_layout Plain Layout
26607 \begin_inset Formula $\raisebox{-2mm}{}$
26623 \begin_layout Standard
26624 One has to take care that the character fits in the circle.
26635 \begin_layout Plain Layout
26637 \begin_inset CommandInset ref
26639 reference "sub:Font-Sizes"
26648 specifies thereby the size of the circle.
26659 \begin_layout Plain Layout
26661 \begin_inset CommandInset ref
26663 reference "sub:Boxes-without-Frame"
26672 the character can be centered.
26675 \begin_layout Subsection
26677 \begin_inset Index idx
26680 \begin_layout Plain Layout
26689 \begin_layout Standard
26690 Old-style figures (also known as old-style numerals) are created with the
26698 \begin_inset Index idx
26701 \begin_layout Plain Layout
26710 The command can be used in formulas and in TeX-mode.
26711 The command scheme is:
26714 \begin_layout Standard
26719 oldstylenums{number}
26722 \begin_layout Standard
26727 oldstylenums{0123456789
26730 \begin_inset Formula $\oldstylenums{0123456789}$
26736 \begin_layout Section
26738 \begin_inset CommandInset label
26740 name "sec:Formula-Styles"
26745 \begin_inset Index idx
26748 \begin_layout Plain Layout
26757 \begin_layout Itemize
26758 There are two different alignment styles:
26762 \begin_layout Description
26763 Centered is the predefined standard
26766 \begin_layout Description
26767 Indented for this the option
26771 must be inserted in the menu
26773 Document\SpecialChar \menuseparator
26779 \begin_inset space ~
26785 \begin_layout Standard
26790 is used, the indentation can be adjusted with the length
26797 \begin_inset Index idx
26800 \begin_layout Plain Layout
26809 Should the distance be 15
26810 \begin_inset space \thinspace{}
26813 mm, the following command line is inserted in the LaTeX-preamble
26816 \begin_layout Standard
26826 \begin_layout Standard
26827 When no length is specified, the predefined value of 30
26828 \begin_inset space \thinspace{}
26835 \begin_layout Itemize
26836 And two different numbering styles:
26840 \begin_layout Description
26841 Right is the predefined standard
26844 \begin_layout Description
26845 Left for this the option
26849 must be inserted in the menu
26851 Document\SpecialChar \menuseparator
26857 \begin_inset space ~
26864 \begin_layout Standard
26873 can also be used together.
26874 In this case both options are inserted, separated by a comma.
26877 \begin_layout Standard
26878 The chosen styles are used for all displayed formulas of the document.
26879 When both, centered and indented formulas should be created in a document,
26885 The indented formulas are then set in a flalign environment, see
26886 \begin_inset CommandInset ref
26888 reference "sub:Flalign-Environment"
26895 \begin_layout Section
26897 \begin_inset CommandInset label
26899 name "sec:Multiline-Formulas"
26904 \begin_inset Index idx
26907 \begin_layout Plain Layout
26908 Formula ! multiline
26916 \begin_layout Subsection
26920 \begin_layout Standard
26921 In LyX multiline formulas are created by pressing
26926 arg "newline-insert newline"
26932 This creates either an
26934 eqnarray environment
26936 that is described in
26937 \begin_inset CommandInset ref
26939 reference "sub:Eqnarray-Environment"
26943 or, when the option
26945 Use AMS math package
26947 in the document settings is selected, an
26951 that is described in
26952 \begin_inset CommandInset ref
26954 reference "sub:Standard-align-Environment"
26959 The align environment is recommended because it provides in any case a
26960 typographically correct output.
26963 \begin_layout Standard
26964 There are other multiline formula environments that can be created via the
26967 Insert\SpecialChar \menuseparator
26971 These environments are described in the following sections.
26974 \begin_layout Standard
26975 In all multiline formula environments a new line is created by pressing
26979 arg "newline-insert newline"
26983 To add or delete lines, the math toolbar buttons
26984 \begin_inset Graphics
26985 filename ../images/tabular-feature_append-row.png
26991 \begin_inset Graphics
26992 filename ../images/tabular-feature_delete-row.png
26997 , respectively, or the menu
26999 Edit\SpecialChar \menuseparator
27005 \begin_layout Subsubsection
27007 \begin_inset CommandInset label
27009 name "sub:Line-Separation"
27014 \begin_inset Index idx
27017 \begin_layout Plain Layout
27018 Formula ! multiline ! Line separation
27026 \begin_layout Standard
27027 There is sometimes not enough space in multiline formulas between the lines:
27028 \begin_inset Formula
27030 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}\\
27031 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
27039 \begin_layout Standard
27040 In LaTeX additional line space is specified as optional argument of the
27042 This is not yet possible in LyX
27046 \begin_layout Plain Layout
27048 \begin_inset CommandInset href
27050 name "LyX-bug #1505"
27051 target "http://www.lyx.org/trac/ticket/1505"
27060 , therefore the whole formula must be inserted in TeX-mode.
27061 To add in our example space, the command
27069 is inserted at the end of the first line.
27074 \begin_layout Plain Layout
27081 \begin_layout Plain Layout
27083 B^{2}(B^{2}-2r_{g}^{2}+2x_{0}^{2}-2r_{k}^{2})+4x_{0}^{2}x^{2}+4x_{0}xD &
27086 textrm{-}4x^{2}B^{2}+4x_{0}xB^{2}
27093 \begin_layout Plain Layout
27097 left(B^{2}+x_{0}^{2}
27105 left(B^{2}-2r_{g}^{2}+2x_{0}^{2}-2r_{k}^{2}
27110 \begin_layout Plain Layout
27122 \begin_layout Standard
27123 \begin_inset VSpace bigskip
27126 To set the line separation for all lines in a formula, the length
27133 \begin_inset Index idx
27136 \begin_layout Plain Layout
27146 \begin_inset Formula $\mbox{line separation}=\mathrm{6\, pt+\backslash jot}$
27157 \begin_inset space \thinspace{}
27162 \begin_inset space \thinspace{}
27165 mm additional line separation as in the previous example, the command
27168 \begin_layout Standard
27178 \begin_layout Standard
27179 is inserted in TeX-mode before the formula.
27180 This requires that the LaTeX-package
27188 \begin_layout Plain Layout
27193 is part of every LaTeX standard installation.
27199 \begin_inset Index idx
27202 \begin_layout Plain Layout
27208 was loaded in LaTeX-preamble with the line
27211 \begin_layout Standard
27219 \begin_layout Standard
27224 \begin_layout Plain Layout
27236 \begin_inset Formula
27238 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}\\
27239 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
27247 \begin_layout Standard
27251 \begin_layout Plain Layout
27262 To get back to the predefined distance,
27268 is set to the value 3
27269 \begin_inset space \thinspace{}
27275 \begin_layout Subsubsection
27277 \begin_inset CommandInset label
27279 name "sub:Column-Separation"
27284 \begin_inset Index idx
27287 \begin_layout Plain Layout
27288 Formula ! multiline ! Column separation
27296 \begin_layout Standard
27297 Multiline formulas form a matrix.
27298 A formula in the eqnarray environment is for example a matrix with three
27300 By changing the column separation in this environment, the space beside
27301 the relation sign can be changed.
27304 \begin_layout Standard
27305 The column separation is specified with the length
27312 \begin_inset Index idx
27315 \begin_layout Plain Layout
27324 \begin_inset Newline newline
27327 column separation = 2
27328 \begin_inset space \thinspace{}
27338 \begin_inset Newline newline
27344 \begin_layout Standard
27354 \begin_layout Standard
27355 inserted in TeX-mode, sets for all following formulas a column separation
27357 \begin_inset space \thinspace{}
27361 To get back to the predefined distance,
27368 \begin_inset space \thinspace{}
27374 \begin_layout Standard
27376 \begin_inset space \thinspace{}
27379 cm column separation:
27383 \begin_layout Plain Layout
27395 \begin_inset Formula
27403 A formula with the predefined column separation for matrices of 10
27404 \begin_inset space \thinspace{}
27411 \begin_layout Plain Layout
27423 \begin_inset Formula
27434 \begin_layout Subsubsection
27436 \begin_inset Index idx
27439 \begin_layout Plain Layout
27448 \begin_layout Standard
27449 Long formulas can be typeset using these methods:
27452 \begin_layout Itemize
27453 When one side of the equation is much shorter than the line width, this
27454 one is chosen for the left side and the right side is typeset over two
27456 \begin_inset Formula
27458 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 \\
27459 & & -\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}
27464 The minus sign at the beginning of the second line does normally not appear
27465 as an operator because it is the first character of the line.
27466 Thus it would not be surrounded by space and could not be distinguished
27467 from the fraction bar.
27469 \begin_inset space \thinspace{}
27472 pt space was inserted behind the minus sign with the command
27482 \begin_layout Plain Layout
27490 \begin_inset CommandInset ref
27492 reference "sub:Variable-Space"
27502 \begin_inset Index idx
27505 \begin_layout Plain Layout
27516 \begin_layout Itemize
27517 When both sides of the equation are too long, the command
27524 \begin_inset Index idx
27527 \begin_layout Plain Layout
27536 It is inserted in the first column of the first line and causes all further
27537 insertions to overwrite the following columns:
27538 \begin_inset Formula
27540 \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 \\
27541 & & -\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 \\
27542 & & =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}
27547 After the insertion of
27553 , the cursor is in a purple box that is a bit shifted to the left from the
27555 In this the formula is inserted.
27556 \begin_inset Newline newline
27559 The content of the further lines is inserted to the second or another formula
27561 The greater the column number where it was inserted, the larger the indentation.
27562 \begin_inset VSpace medskip
27566 \begin_inset Newline newline
27570 \begin_inset Note Greyedout
27573 \begin_layout Plain Layout
27574 Note the following when using
27583 \begin_layout Itemize
27584 The formula doesn't use the full page width.
27586 \begin_inset space \thinspace{}
27590 \begin_inset space \space{}
27594 \begin_inset Formula $-B^{2}$
27597 is added to the first line in the above example, it would have been outside
27599 To better use the width, negative space can be inserted at the beginning
27603 \begin_layout Itemize
27604 Due to a bug in LyX the cursor cannot be set with the mouse into the first
27609 \begin_layout Plain Layout
27610 \begin_inset CommandInset href
27612 name "LyX-bug #1429"
27613 target "http://www.lyx.org/trac/ticket/1429"
27622 One can only set the cursor at the beginning of the line and move it with
27631 \begin_layout Itemize
27632 Other methods to set long formulas are offered by the environments described
27634 \begin_inset CommandInset ref
27636 reference "sub:Multline-Environment"
27641 \begin_inset CommandInset ref
27643 reference "sub:Multiline-Formula-Parts"
27650 \begin_layout Subsubsection
27652 \begin_inset CommandInset label
27654 name "sub:Multiline-Brackets"
27659 \begin_inset Index idx
27662 \begin_layout Plain Layout
27663 Brackets ! for multiline expressions
27671 \begin_layout Standard
27672 For brackets spanning multiple lines the following problem occurs:
27673 \begin_inset Formula
27675 A & = & \sin(x)\left[\prod_{R=1}^{\infty}\frac{1}{R}+\cdots\right.\\
27676 & & \left.\cdots+B-D\right]
27684 \begin_layout Standard
27685 The closing bracket is smaller than the opening bracket because brackets
27686 with variable size may not span multiple lines.
27689 \begin_layout Standard
27690 To set the bracket size for the second line correctly, the first line is
27698 \begin_inset Index idx
27701 \begin_layout Plain Layout
27709 and the second line with
27717 \begin_layout Plain Layout
27731 \begin_inset CommandInset ref
27733 reference "sub:Automatic-Bracket-Size"
27745 \begin_inset Index idx
27748 \begin_layout Plain Layout
27771 \begin_inset space \textvisiblespace{}
27781 \begin_inset space \textvisiblespace{}
27791 \begin_inset space \textvisiblespace{}
27797 \begin_inset Formula $\downarrow$
27803 \begin_inset Index idx
27806 \begin_layout Plain Layout
27814 is inserted, because the multiplication operator with its limits is the
27815 largest symbol in the first line and this should be the size for the bracket
27816 in the second line.
27819 \begin_layout Standard
27820 The result is this:
27821 \begin_inset Formula
27823 A & = & \sin(x)\left[\prod_{R=1}^{\infty}\frac{1}{R}+\cdots\right.\\
27824 & & \left.\vphantom{\prod_{R=1}^{\infty}}\cdots+B-D\right]
27832 \begin_layout Subsection
27836 \begin_layout Standard
27837 Align environments can be used for every kind of multiline formulas.
27838 They are especially useful to set several formulas side by side.
27841 \begin_layout Standard
27842 Align environments consist of columns.
27843 The odd columns are right aligned, the even ones left aligned.
27844 Every line in an Align environment can be numbered.
27847 \begin_layout Standard
27848 Align environments are created via the menu
27850 Insert\SpecialChar \menuseparator
27856 Edit\SpecialChar \menuseparator
27857 Math\SpecialChar \menuseparator
27858 Change Formula Type
27860 already existing formulas can be converted to Align environments.
27863 \begin_layout Standard
27864 To add or delete columns, the math toolbar buttons
27865 \begin_inset Graphics
27866 filename ../images/tabular-feature_append-column.png
27872 \begin_inset Graphics
27873 filename ../images/tabular-feature_delete-column.png
27878 , respectively, or the menu
27880 Edit\SpecialChar \menuseparator
27886 \begin_layout Subsubsection
27887 Standard align Environment
27888 \begin_inset CommandInset label
27890 name "sub:Standard-align-Environment"
27895 \begin_inset Index idx
27898 \begin_layout Plain Layout
27899 Formula ! multiline ! align environment
27907 \begin_layout Standard
27908 This Align environment is created by pressing
27911 arg "newline-insert newline"
27914 in a formula or by the menu
27916 Insert\SpecialChar \menuseparator
27917 Math\SpecialChar \menuseparator
27918 AMS align Environment
27923 \begin_layout Standard
27924 An example for two formulas set side by side, that are created with a four
27925 column align environment:
27926 \begin_inset Formula
27928 A & =\sin(B) & C & =D\\
27929 C & \ne A & B & \ne D
27934 As it can be seen, the formulas in this environment are placed so as if
27943 \begin_layout Plain Layout
27951 \begin_inset CommandInset ref
27953 reference "sub:Variable-Space"
27964 before the first and after every even column.
27965 When the formula style
27971 \begin_layout Plain Layout
27973 \begin_inset CommandInset ref
27975 reference "sec:Formula-Styles"
27986 is used, the formula is set without the
27992 before the first column.
27995 \begin_layout Subsubsection
27996 Alignat Environment
27997 \begin_inset Index idx
28000 \begin_layout Plain Layout
28001 Formula ! multiline ! alignat environment
28009 \begin_layout Standard
28010 The alignat environment has no predefined column separation.
28011 It can be inserted manually with the spaces that are described
28012 \begin_inset CommandInset ref
28014 reference "sub:Space"
28021 \begin_layout Standard
28022 The above example in the alignat environment where 1
28023 \begin_inset space \thinspace{}
28026 cm space was inserted at the beginning of the second formula:
28027 \begin_inset Formula
28028 \begin{alignat*}{2}
28029 A & =\sin(B) & \hspace{1cm}C & =D\\
28030 C & \ne A & B & \ne D
28035 Because the column separation can be set separately for every column, this
28036 environment is especially suitable to set three and more formulas side
28040 \begin_layout Subsubsection
28041 Flalign Environment
28042 \begin_inset CommandInset label
28044 name "sub:Flalign-Environment"
28049 \begin_inset Index idx
28052 \begin_layout Plain Layout
28053 Formula ! multiline ! flalign environment
28061 \begin_layout Standard
28062 In this environment the first two columns are always set as much as possible
28063 to the left and the last two ones to the right.
28065 \begin_inset Formula
28067 A & =1 & B & =2 & C & =3\\
28068 X & =\textrm{-}1 & Y & =\textrm{-}2 & Z & =4
28076 \begin_layout Standard
28077 By creating a flalign environment with an odd number of columns where an
28078 empty TeX-brace is inserted to the last column, several formulas in a document
28079 can be set to the left, although the formula style
28084 As example the indented formula
28085 \begin_inset CommandInset ref
28087 reference "eq:VolInt"
28092 \begin_inset Formula
28094 \hspace{30pt}\iiint\limits _{V}X\,\mathrm{d}V & =U & {}
28099 The first two columns contain the formula.
28100 To indent it as with the formula style
28105 \begin_inset space \thinspace{}
28108 pt space was inserted at the beginning of the first column.
28111 \begin_layout Subsection
28112 Eqnarray Environment
28113 \begin_inset CommandInset label
28115 name "sub:Eqnarray-Environment"
28120 \begin_inset Index idx
28123 \begin_layout Plain Layout
28124 Formula ! multiline ! eqnarray environment
28132 \begin_layout Standard
28133 When this environment has been created, three blue boxes appear.
28134 The content of the first box is right aligned, the content of the last
28136 The content of the middle box appears centered and a bit smaller, because
28137 it is designed to insert there only relation characters.
28138 \begin_inset Formula
28140 \frac{ABC}{D} & \frac{ABC}{D} & \frac{ABC}{D}\\
28150 \begin_layout Subsection
28152 \begin_inset Index idx
28155 \begin_layout Plain Layout
28156 Formula ! multiline ! gather environment
28164 \begin_layout Standard
28165 This environment consists of only one centered column.
28166 Every line can be numbered.
28167 \begin_inset Formula
28178 \begin_layout Subsection
28179 Multline Environment
28180 \begin_inset CommandInset label
28182 name "sub:Multline-Environment"
28187 \begin_inset Index idx
28190 \begin_layout Plain Layout
28191 Formula ! multiline ! multline environment
28199 \begin_layout Standard
28200 The multline environment consists, like the gather environment, of only
28202 But the first line is left aligned, the last one right aligned.
28203 All other lines are centered.
28204 Therefore this environment is suitable for long formulas.
28206 \begin_inset CommandInset ref
28208 reference "eq:lefteqn"
28212 in the multline environment:
28213 \begin_inset Formula
28215 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}\\
28216 -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}\\
28217 =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}}
28225 \begin_layout Standard
28226 In the output only the last (first) line of a multline environment appears
28227 numbered when the document numbering is right (left).
28231 \begin_layout Plain Layout
28232 numbering styles see
28233 \begin_inset CommandInset ref
28235 reference "sec:Formula-Styles"
28247 \begin_layout Standard
28255 \begin_inset Index idx
28258 \begin_layout Plain Layout
28273 \begin_inset Index idx
28276 \begin_layout Plain Layout
28284 a centered line can be right or left aligned, respectively.
28285 The commands are used as follows:
28288 \begin_layout Standard
28293 shoveright{line content}
28299 shoveleft{line content}
28302 \begin_layout Standard
28303 \begin_inset VSpace medskip
28313 \begin_inset Index idx
28316 \begin_layout Plain Layout
28324 specifies the distance of the first line from the left page margin.
28325 Predefined is the length 0
28326 \begin_inset space \thinspace{}
28332 \begin_layout Standard
28333 As example the above formula where the command
28336 \begin_layout Standard
28346 \begin_layout Standard
28347 was inserted in TeX-mode before:
28351 \begin_layout Plain Layout
28363 \begin_inset Formula
28365 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}\\
28366 \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}}\\
28367 =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}}
28376 \begin_layout Plain Layout
28387 The second line was left aligned using
28396 \begin_layout Subsection
28397 Multiline Formula Parts
28398 \begin_inset CommandInset label
28400 name "sub:Multiline-Formula-Parts"
28405 \begin_inset Index idx
28408 \begin_layout Plain Layout
28409 Formula ! multiline ! formula parts
28417 \begin_layout Standard
28418 To display only parts of a formula with multiple lines, one of the following
28419 environments is used:
28436 They can be inserted via the menu
28438 Insert\SpecialChar \menuseparator
28441 or by using the commands described in this section.
28444 \begin_layout Standard
28445 The first three have the same properties as the corresponding multiline
28446 formula environments, but it is possible to set further formula parts beside
28449 \begin_inset Formula
28451 \left.\begin{aligned}\Delta x\Delta p & \ge\frac{\hbar}{2}\\
28452 \Delta E\Delta t & \ge\frac{\hbar}{2}
28454 \right\} \textrm{Uncertainty relations}
28462 \begin_layout Standard
28463 To get this formula, a displayed formula is created where the command
28470 \begin_inset Index idx
28473 \begin_layout Plain Layout
28482 A purple box appears around the blue formula box where now columns and
28483 lines can be added.
28484 Outside the multiline environment other formula parts can be set, like
28488 \begin_layout Standard
28489 The aligned environment is also suitable for long formulas whose lines are
28490 horizontally aligned.
28491 Using aligned in a displayed formula has the advantage that the formula
28492 number is vertically centered behind the lines.
28494 \begin_inset CommandInset ref
28496 reference "eq:shortlong"
28500 in the aligned environment:
28501 \begin_inset Formula
28503 \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}|}\\
28504 & -\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}|}
28513 \begin_layout Standard
28514 To use the environments
28533 \begin_inset Index idx
28536 \begin_layout Plain Layout
28551 \begin_inset Index idx
28554 \begin_layout Plain Layout
28569 \begin_inset Index idx
28572 \begin_layout Plain Layout
28580 are inserted, respectively.
28581 The split environment has the same properties as the aligned environment
28582 but it can only have two columns.
28585 \begin_layout Subsection
28586 Text in multiline Formulas
28587 \begin_inset CommandInset label
28589 name "sub:Text-in-multiline"
28594 \begin_inset Index idx
28597 \begin_layout Plain Layout
28604 \begin_inset Index idx
28607 \begin_layout Plain Layout
28608 Formula ! multiline ! text
28616 \begin_layout Standard
28617 In the Align environments, and the multline and gather environment, text
28618 can be inserted that will appear in a separate line and doesn't affect
28619 the column alignment.
28620 To do this, the command
28627 \begin_inset Index idx
28630 \begin_layout Plain Layout
28638 is used in the following scheme:
28641 \begin_layout Standard
28649 \begin_layout Standard
28650 The text should not be longer than a line because it cannot be hyphenated.
28651 As LyX doesn't yet support
28657 directly, the text is written as mathematical text.
28664 must hereby be at the beginning of a line and appears in the output above
28666 An example where the text was inserted at the beginning of the second line:
28667 \begin_inset Formula
28669 I & =a\sqrt{2}\int_{0}^{2\pi}\sqrt{1+\cos(\phi)}\;\mathrm{d}\phi\\
28670 \intertext{\text{integrand is symmetric to \ensuremath{\phi=\pi}, therefore}} & =2a\sqrt{2}\int_{0}^{\pi}\sqrt{1+\cos(\phi)}\;\mathrm{d}\phi
28678 \begin_layout Section
28680 \begin_inset Index idx
28683 \begin_layout Plain Layout
28690 \begin_inset Index idx
28693 \begin_layout Plain Layout
28694 Formula ! numbering|see
28698 \begin_layout Plain Layout
28709 \begin_layout Plain Layout
28724 \begin_layout Subsection
28728 \begin_layout Standard
28729 Numbered formulas can be created with the menu
28731 Insert\SpecialChar \menuseparator
28732 Math\SpecialChar \menuseparator
28734 \begin_inset space ~
28742 \begin_inset space ~
28748 Existing formulas can be numbered with the menu
28750 Edit\SpecialChar \menuseparator
28751 Math\SpecialChar \menuseparator
28753 \begin_inset space ~
28761 arg "math-number-toggle"
28765 The formula number is displayed in LyX behind the formula as a number sign
28767 The number sign is replaced in the output by the formula number.
28770 \begin_layout Standard
28771 When numbering is turned on in multiline formulas, all lines will be numbered.
28772 But the numbering can be controlled with the menu
28774 Edit\SpecialChar \menuseparator
28775 Math\SpecialChar \menuseparator
28777 \begin_inset space ~
28781 \begin_inset space ~
28785 \begin_inset space ~
28793 arg "math-number-line-toggle"
28799 \begin_layout Standard
28800 Except for inline formulas, all formulas can be numbered with two different
28802 \begin_inset CommandInset ref
28804 reference "sec:Formula-Styles"
28811 \begin_layout Subsection
28813 \begin_inset Index idx
28816 \begin_layout Plain Layout
28817 Cross-references ! to formulas
28825 \begin_layout Standard
28826 All labeled formulas can be cross-referenced.
28827 A label is added by the menu
28829 Insert\SpecialChar \menuseparator
28832 or the toolbar button
28833 \begin_inset Graphics
28834 filename ../images/label-insert.png
28840 The cursor must hereby be inside a displayed formula.
28841 Alternatively you can right-click on the formula and choose
28846 A dialog pops up displaying the prefix
28851 The label is inserted there behind the prefix.
28852 The predefined prefix means
28853 \begin_inset Quotes eld
28857 \begin_inset Quotes erd
28860 and makes it easier to find labels in large documents because it marks
28861 it as formula label to divide it from e.
28862 \begin_inset space \thinspace{}
28866 \begin_inset space \space{}
28870 To change a label, the menu
28872 Insert\SpecialChar \menuseparator
28875 is used again or you right-click on a formula and then on
28882 \begin_layout Standard
28883 The name of the label is displayed in LyX within two parentheses behind
28885 A formula with a label is always numbered.
28888 \begin_layout Standard
28889 Cross-references are inserted via the menu
28891 Insert\SpecialChar \menuseparator
28894 or with the toolbar button
28895 \begin_inset Graphics
28896 filename ../images/dialog-show-new-inset_ref.png
28902 A formula cross-reference appears in the output as formula number.
28903 When in the cross-reference dialog window the format
28907 is chosen, the cross-reference appears in the output as formula number
28909 \begin_inset Newline newline
28912 By right-clicking on a cross-reference in LyX, one jumps to the formula
28913 that is referenced.
28916 \begin_layout Standard
28917 Here are as examples cross-references to formulas of the following subsections:
28918 \begin_inset Note Note
28921 \begin_layout Plain Layout
28922 Note the different cross-reference types.
28930 \begin_layout Standard
28932 \begin_inset CommandInset ref
28939 \begin_inset CommandInset ref
28947 \begin_inset CommandInset ref
28953 ) big Latin letters are used for the numbering in contrary to (
28954 \begin_inset CommandInset ref
28963 \begin_layout Standard
28964 \begin_inset VSpace medskip
28967 When the argument of
28975 \begin_layout Plain Layout
28983 \begin_inset CommandInset ref
28985 reference "sub:User-defined-Numbering"
28996 contains a box like in
28997 \begin_inset CommandInset ref
28999 reference "sub:Paragraph-Boxes"
29003 , the formula cannot be referenced.
29006 \begin_layout Subsection
29008 \begin_inset Index idx
29011 \begin_layout Plain Layout
29012 Formula numbering ! subnumbering
29020 \begin_layout Standard
29021 With the help of the commands
29025 begin{subequations}
29033 formulas can be subnumbered.
29034 Both commands are inserted in TeX-mode.
29037 \begin_layout Standard
29039 \begin_inset Formula
29050 \begin_layout Plain Layout
29054 addtocounter{equation}{-1}
29063 \begin_layout Plain Layout
29067 begin{subequations}
29073 \begin_inset VSpace -5mm
29077 \begin_inset Formula
29085 \begin_inset Formula
29095 \begin_layout Standard
29099 \begin_layout Plain Layout
29111 \begin_layout Standard
29112 To create the example, the following is done:
29115 \begin_layout Enumerate
29116 first formula is inserted
29119 \begin_layout Enumerate
29124 addtocounter{equation}{-1}
29126 begin{subequations}
29127 \begin_inset Index idx
29130 \begin_layout Plain Layout
29139 \begin_inset Newline newline
29144 is inserted after the first formula
29147 \begin_layout Enumerate
29148 second formula is inserted
29151 \begin_layout Enumerate
29152 third formula is inserted
29155 \begin_layout Enumerate
29162 is inserted after the third formula
29165 \begin_layout Standard
29166 Every formula between the commands
29178 is subnumbered as a, b,
29179 \begin_inset Newline linebreak
29182 c, \SpecialChar \ldots{}
29183 For multiline formulas every line will be subnumbered.
29184 All subnumbered formulas are treated as
29189 But as every numbered formula increases the counter
29193 by one, the command
29199 is needed to decrease it.
29200 Otherwise the formulas
29201 \begin_inset CommandInset ref
29208 \begin_inset CommandInset ref
29215 \begin_inset CommandInset ref
29221 would be numbered as
29222 \begin_inset CommandInset ref
29229 \begin_inset CommandInset ref
29236 \begin_inset CommandInset ref
29245 \begin_layout Standard
29246 By inserting the commands in TeX-mode, a space is created between the first
29249 \begin_inset space \thinspace{}
29252 mm vertical space is inserted after the command
29256 begin{subequations}
29259 When the formula style
29265 \begin_layout Plain Layout
29267 \begin_inset CommandInset ref
29269 reference "sec:Formula-Styles"
29281 \begin_inset space \thinspace{}
29284 mm space is inserted instead.
29287 \begin_layout Standard
29288 Here is an example for a multiline formula where the numbering was turned
29289 off for the second line:
29293 \begin_layout Plain Layout
29297 begin{subequations}
29303 \begin_inset Formula
29305 A & = & (B-Z)^{2}=(B-Z)(B-Z)\label{eq:d}\\
29306 & = & B^{2}-ZB-BZ+Z^{2}\nonumber \\
29307 & = & B^{2}-2BZ+Z^{2}\label{eq:f}
29316 \begin_layout Plain Layout
29328 \begin_layout Subsection
29329 User-defined Numbering
29330 \begin_inset CommandInset label
29332 name "sub:User-defined-Numbering"
29337 \begin_inset Index idx
29340 \begin_layout Plain Layout
29341 Formula numbering ! user-defined
29349 \begin_layout Standard
29350 \begin_inset Index idx
29353 \begin_layout Plain Layout
29354 Formula numbering ! self-defined delimiters
29359 With the standard numbering parentheses are set around the formula number.
29360 To replace the parentheses for example by vertical bars, the following
29361 line is added to the LaTeX-preamble:
29364 \begin_layout Standard
29376 \begin_inset Note Note
29379 \begin_layout Plain Layout
29380 This macro is already declared in the LaTeX-preamble for testing.
29381 To activate it, remove the percent sign at the beginning.
29389 \begin_layout Standard
29390 To use other characters, the vertical bars besides the
29394 are replaced by one ore more characters.
29395 To get only the formula number the vertical bars are omitted.
29398 \begin_layout Standard
29399 \begin_inset VSpace bigskip
29402 When there should be an expression of your choice instead of the consecutive
29403 formula number in parentheses behind the formula, the command
29410 \begin_inset Index idx
29413 \begin_layout Plain Layout
29422 \begin_inset Formula
29424 A+B=C\tag{something}\label{eq:tag}
29429 In this example the command
29434 \begin_inset space \textvisiblespace{}
29439 was inserted in the formula.
29442 \begin_layout Standard
29448 \begin_inset space \textvisiblespace{}
29453 is inserted instead, the star prevents the parentheses around the expression:
29454 \begin_inset Formula
29456 A+B=C\tag*{something}
29464 \begin_layout Standard
29465 \begin_inset VSpace bigskip
29468 To restart the formula numbering with new document parts or sections, the
29469 following command is used:
29472 \begin_layout Standard
29477 @addtoreset{equation}{part}
29480 \begin_inset Index idx
29483 \begin_layout Plain Layout
29488 \begin_layout Plain Layout
29499 \begin_layout Plain Layout
29512 \begin_layout Plain Layout
29523 \begin_layout Plain Layout
29536 \begin_inset Newline newline
29540 \begin_inset Newline newline
29547 @addtoreset{equation}{section}
29550 \begin_layout Standard
29551 To be able to use these commands in TeX-mode, the
29552 \begin_inset Quotes eld
29556 \begin_inset Quotes erd
29559 character has to be made
29560 \begin_inset Quotes eld
29564 \begin_inset Quotes erd
29567 for LaTeX using the command
29581 So the command sequence in TeX-mode is:
29584 \begin_layout Standard
29590 \begin_inset Newline newline
29595 @addtoreset{equation}{section}
29596 \begin_inset Newline newline
29604 \begin_layout Standard
29605 In the LaTeX-preamble
29617 can be omitted as they are automatically internally inserted by LyX.
29620 \begin_layout Standard
29635 \begin_layout Plain Layout
29640 is part of the LaTeX-package
29645 \begin_inset Index idx
29648 \begin_layout Plain Layout
29649 Packages ! carlisle
29654 that is part of every LaTeX standard installation.
29660 \begin_inset Index idx
29663 \begin_layout Plain Layout
29664 Packages ! remreset
29669 has to be loaded in the LaTeX-preamble with the line
29672 \begin_layout Standard
29677 usepackage{remreset}
29680 \begin_layout Standard
29688 \begin_inset Index idx
29691 \begin_layout Plain Layout
29696 \begin_layout Plain Layout
29707 \begin_layout Plain Layout
29720 \begin_layout Plain Layout
29731 \begin_layout Plain Layout
29743 can be used with the same scheme as
29752 \begin_layout Standard
29753 \begin_inset VSpace bigskip
29756 Sometimes formulas should be numbered in the following form:
29759 \begin_layout Standard
29762 (section number.formula number)
29765 \begin_layout Standard
29766 The formula number should start with every section with
29767 \begin_inset Quotes eld
29771 \begin_inset Quotes erd
29777 \begin_layout Standard
29778 For this case there is the command
29785 \begin_inset Index idx
29788 \begin_layout Plain Layout
29796 , which is used with the following scheme:
29799 \begin_layout Standard
29804 numberwithin{counter}{sectioning}
29807 \begin_layout Standard
29808 Counter denotes what kind of numbering is affected, sectioning denotes what
29809 number is before the dot.
29812 \begin_layout Standard
29813 Thus in our case the following LaTeX-preamble or TeX code line is used:
29816 \begin_layout Standard
29821 numberwithin{equation}{section}
29824 \begin_layout Standard
29825 This is the result:
29829 \begin_layout Plain Layout
29833 numberwithin{equation}{section}
29839 \begin_inset Formula
29849 \begin_layout Standard
29851 \begin_inset space \thinspace{}
29855 \begin_inset space \space{}
29858 tables so that the number of the part is the sectioning,
29859 \begin_inset Newline newline
29866 numberwithin{table}{part}
29871 \begin_layout Standard
29872 To go back to the standard numbering or to prevent this kind of numbering
29873 when it is defined by the document class, the following command is inserted
29874 as TeX code or to the LaTeX-preamble:
29877 \begin_layout Standard
29887 \begin_inset Index idx
29890 \begin_layout Plain Layout
29904 \begin_layout Plain Layout
29920 \begin_inset Newline newline
29928 \begin_inset Newline newline
29940 \begin_layout Standard
29947 uses internally the command
29953 , described above, that also needs to be reverted.
29957 \begin_layout Plain Layout
29964 \begin_layout Plain Layout
29968 @removefromreset{equation}{section}
29971 \begin_layout Plain Layout
29983 \begin_layout Subsection
29984 Numbering with Roman Numbers and Letters
29985 \begin_inset Index idx
29988 \begin_layout Plain Layout
29989 Formula numbering ! with letters
29995 \begin_inset Index idx
29998 \begin_layout Plain Layout
29999 Formula numbering ! with Roman numbers
30007 \begin_layout Standard
30008 Formulas can also be numbered with Roman numbers and Latin letters.
30009 To number for example with small Roman numbers, the command
30012 \begin_layout Standard
30024 \begin_layout Standard
30025 is inserted before the formula in TeX-mode.
30033 \begin_inset Index idx
30036 \begin_layout Plain Layout
30044 redefines the predefined command
30060 \begin_layout Plain Layout
30067 has the same scheme like the command
30073 that is described in
30074 \begin_inset CommandInset ref
30076 reference "sub:The-Command-newcommand"
30089 is the formula counter.
30096 is used as prefix for a counter, the value of the counter is output as
30098 When a formula is numbered, LaTeX sets internally the command
30104 behind the formula.
30110 \begin_inset Index idx
30113 \begin_layout Plain Layout
30123 outputs the counter as small Roman number.
30126 \begin_layout Standard
30127 All formulas behind the command
30137 are now numbered Roman.
30138 To switch to numbering with big Roman numbers, the command is inserted
30152 \begin_inset Index idx
30155 \begin_layout Plain Layout
30167 \begin_inset Quotes eld
30171 \begin_inset Quotes erd
30174 with small Latin letters there is the command
30181 \begin_inset Index idx
30184 \begin_layout Plain Layout
30192 , for big ones there is the command
30199 \begin_inset Index idx
30202 \begin_layout Plain Layout
30215 \begin_layout Standard
30216 \begin_inset Note Greyedout
30219 \begin_layout Plain Layout
30226 \begin_inset space ~
30229 formulas can be numbered with Latin letters in one document.
30237 \begin_layout Standard
30241 \begin_layout Plain Layout
30257 \begin_layout Standard
30258 \begin_inset Formula
30260 A=\textrm{small roman}
30269 \begin_layout Plain Layout
30283 \begin_inset Formula
30285 B=\textrm{big Roman}\label{eq:Rom}
30294 \begin_layout Plain Layout
30308 \begin_inset Formula
30310 C=\textrm{small Latin}
30319 \begin_layout Plain Layout
30333 \begin_inset Formula
30335 D=\textrm{big Latin}\label{eq:Lat}
30343 \begin_layout Standard
30344 To switch back to the default numbering, insert the command:
30347 \begin_layout Standard
30357 \begin_inset Index idx
30360 \begin_layout Plain Layout
30371 \begin_layout Standard
30375 \begin_layout Plain Layout
30389 \begin_inset Formula
30399 \begin_layout Standard
30400 \begin_inset VSpace medskip
30403 As you see, formulas are numbered serially independent from the numbering
30405 When then numbering should start with
30406 \begin_inset Quotes eld
30410 \begin_inset Quotes erd
30413 when the style is changed, new equation counters have to be defined.
30414 A description about this can be found in the file
30415 \begin_inset CommandInset href
30417 name "Formula-numbering.lyx"
30418 target "run:Formula-numbering.lyx"
30425 \begin_layout Standard
30426 \begin_inset Newpage newpage
30432 \begin_layout Section
30433 Chemical Symbols and Equations
30434 \begin_inset CommandInset label
30436 name "sub:Chemical-Symbols-and"
30441 \begin_inset Index idx
30444 \begin_layout Plain Layout
30445 Chemical characters ! Symbols
30451 \begin_inset Index idx
30454 \begin_layout Plain Layout
30461 \begin_inset Index idx
30464 \begin_layout Plain Layout
30473 \begin_layout Standard
30474 An example text from chemistry:
30477 \begin_layout Quote
30479 \begin_inset Formula $\mathrm{SO_{4}^{2-}}$
30482 -ion reacts with two
30483 \begin_inset Formula $\mathrm{Na^{+}}$
30486 -ions to sodium sulfate
30487 \begin_inset Formula $\left(\mathrm{Na_{2}SO_{4}}\right)$
30491 The chemical equation for this is:
30492 \begin_inset Formula
30494 \mathrm{2\, Na^{+}+SO_{4}^{2-}\longrightarrow Na_{2}SO_{4}}\label{eq:chem-reaction}
30502 \begin_layout Standard
30503 This chemical equation can directly be created as formula.
30504 To avoid that the symbols appear italic, everything is highlighted and
30505 changed by the shortcut
30511 to the upright font style.
30515 \begin_layout Plain Layout
30521 \begin_inset CommandInset ref
30523 reference "sub:Font-Styles"
30535 \begin_layout Standard
30536 A more convenient way to typeset chemical formulas is to use the command
30544 \begin_inset Index idx
30547 \begin_layout Plain Layout
30555 that is available when the LaTeX-package
30560 \begin_inset Index idx
30563 \begin_layout Plain Layout
30576 to a formula a new blue box appears where chemical formulas can be inserted
30577 in an intuitive way.
30580 \begin_layout Standard
30582 \begin_inset Tabular
30583 <lyxtabular version="3" rows="9" columns="2">
30584 <features rotate="0" tabularvalignment="middle">
30585 <column alignment="center" valignment="top">
30586 <column alignment="center" valignment="top">
30588 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
30591 \begin_layout Plain Layout
30597 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
30600 \begin_layout Plain Layout
30602 \begin_inset Note Note
30605 \begin_layout Plain Layout
30612 is only used as spacer.
30624 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
30627 \begin_layout Plain Layout
30631 \begin_inset space \textvisiblespace{}
30639 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
30642 \begin_layout Plain Layout
30643 \begin_inset Formula $\raisebox{4.5mm}{}\ce{H2CO3}\raisebox{-2mm}{}$
30653 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
30656 \begin_layout Plain Layout
30660 \begin_inset space \textvisiblespace{}
30668 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
30671 \begin_layout Plain Layout
30672 \begin_inset Formula $\raisebox{5mm}{}\ce{SO4^{2-}}\raisebox{-2mm}{}$
30682 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
30685 \begin_layout Plain Layout
30689 \begin_inset space \textvisiblespace{}
30697 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
30700 \begin_layout Plain Layout
30701 \begin_inset Formula $\raisebox{4.5mm}{}\ce{(NH4)2S}\raisebox{-2mm}{}$
30711 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
30714 \begin_layout Plain Layout
30718 \begin_inset space \textvisiblespace{}
30726 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
30729 \begin_layout Plain Layout
30730 \begin_inset Formula $\raisebox{4.5mm}{}\ce{KCr(SO4)2.12H2O}\raisebox{-2mm}{}$
30740 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
30743 \begin_layout Plain Layout
30747 \begin_inset space \textvisiblespace{}
30753 \begin_inset space \textvisiblespace{}
30759 \begin_inset space \textvisiblespace{}
30767 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
30770 \begin_layout Plain Layout
30771 \begin_inset Formula $\raisebox{4.5mm}{}\ce{A-B\dbond C\tbond D}\raisebox{-2mm}{}$
30781 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
30784 \begin_layout Plain Layout
30788 \begin_inset space \textvisiblespace{}
30792 \begin_inset Formula $\downarrow$
30796 \begin_inset Formula $\to$
30804 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
30807 \begin_layout Plain Layout
30808 \begin_inset Formula $\raisebox{5mm}{}\ce{_{90}^{227}Th+}\raisebox{-2mm}{}$
30818 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
30821 \begin_layout Plain Layout
30825 \begin_inset space \textvisiblespace{}
30829 \begin_inset space \textvisiblespace{}
30833 \begin_inset space \textvisiblespace{}
30837 \begin_inset space \textvisiblespace{}
30841 \begin_inset space \textvisiblespace{}
30849 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
30852 \begin_layout Plain Layout
30853 \begin_inset Formula $\raisebox{4.5mm}{}\ce{CO2 + C <=> 2CO}\raisebox{-2mm}{}$
30863 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
30866 \begin_layout Plain Layout
30870 \begin_inset space \textvisiblespace{}
30874 \begin_inset space \textvisiblespace{}
30878 \begin_inset space \textvisiblespace{}
30882 \begin_inset space \textvisiblespace{}
30890 \begin_inset space \textvisiblespace{}
30898 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
30901 \begin_layout Plain Layout
30902 \begin_inset Formula $\raisebox{5mm}{}\ce{CO2 + C ->[\alpha][\beta] 2CO}\raisebox{-4mm}{}$
30918 \begin_layout Standard
30919 \begin_inset Note Greyedout
30922 \begin_layout Plain Layout
30928 Inserting a formula to a
30934 box will lead to LaTeX errors due to a LyX bug.
30940 \begin_layout Plain Layout
30941 \begin_inset CommandInset href
30943 name "LyX-bug #8566"
30944 target "http://www.lyx.org/trac/ticket/8566"
30955 In this case TeX code has to be used like for
30969 \begin_layout Plain Layout
30990 \begin_layout Standard
30991 \begin_inset Note Greyedout
30994 \begin_layout Plain Layout
31000 It is not possible in LyX to use the character ^ to get an up-arrow as
31006 One instead uses a negative thin space followed by the command
31013 \begin_inset Formula $\ce{Fe + 2H+ -> Fe^{2+} + H2\negthinspace\uparrow}$
31024 \begin_layout Standard
31031 the command for equation
31032 \begin_inset space ~
31036 \begin_inset CommandInset ref
31038 reference "eq:chem-reaction"
31043 \begin_inset Newline newline
31051 \begin_inset space \textvisiblespace{}
31055 \begin_inset space \textvisiblespace{}
31059 \begin_inset space \textvisiblespace{}
31063 \begin_inset space \textvisiblespace{}
31067 \begin_inset space \textvisiblespace{}
31071 \begin_inset space \textvisiblespace{}
31077 \begin_layout Standard
31078 To create multiline chemical equations first a multiline formula is created
31080 \begin_inset CommandInset ref
31082 reference "sec:Multiline-Formulas"
31087 Afterwards the command
31093 is used in every small blue box of the formula.
31095 \begin_inset CommandInset ref
31097 reference "eq:TEOS-reaction-1"
31102 \begin_inset CommandInset ref
31104 reference "eq:TEOS-reaction-2"
31108 are an example of a multi-stage chemical reaction where every equation
31109 has its own number.
31110 \begin_inset Formula
31112 \ce{TEOS + 4O} & \ce{->} & \ce{Si(OH)4 + 4C2H4O}\label{eq:TEOS-reaction-1}\\
31113 \ce{Si(OH)4} & \ce{->} & \ce{SiO2 + 2H2O}\label{eq:TEOS-reaction-2}
31121 \begin_layout Standard
31132 package provides the command
31139 \begin_inset Index idx
31142 \begin_layout Plain Layout
31150 that has to be used for special cases.
31151 For more information about
31157 and more examples have a look at the documentation of
31162 \begin_inset CommandInset citation
31171 \begin_layout Section
31175 \begin_layout Standard
31176 LyX supports two types of commutative diagrams:
31184 that are explained in the following.
31187 \begin_layout Subsection
31189 \begin_inset Index idx
31192 \begin_layout Plain Layout
31201 \begin_layout Standard
31202 Diagrams of this type visualize relations by vertical and horizontal lines
31204 \begin_inset Formula
31206 \begin{CD}A@>>>B@>>>C\\
31217 \begin_layout Standard
31218 To get them, the command
31223 \begin_inset Index idx
31226 \begin_layout Plain Layout
31236 is inserted to a formula.
31237 A blue box appears with two dashed lines where further commands can be
31242 arg "newline-insert newline"
31245 a new line is created.
31246 Horizontal relations are inserted in odd, vertical in even formula lines.
31249 \begin_layout Standard
31250 To create the relations there are the following commands:
31253 \begin_layout Itemize
31258 creates a left arrow,
31269 \begin_layout Itemize
31274 creates an up arrow,
31282 a vertical equal sign
31285 \begin_layout Itemize
31291 is a placeholder for non-existent relations
31294 \begin_layout Standard
31295 All arrows can be labeled as follows:
31298 \begin_layout Itemize
31299 If text inserted between the first and second < or >, resp., it is placed
31301 When it is inserted between the second and third one, it appears under
31305 \begin_layout Itemize
31306 When text for vertical arrows is inserted between the first and second A
31307 or V, resp., it is placed left beside the arrow.
31308 When it is inserted between the second and third one, it appears right
31310 If the text contains an A or V, these letters must be set into a TeX-brace.
31313 \begin_layout Standard
31314 As example a diagram with all possible relations:
31317 \begin_layout Standard
31318 \begin_inset Formula
31320 \begin{CD}A@>j>>B@>>k>C@=F\\
31331 \begin_layout Standard
31332 The command for this is:
31333 \begin_inset Newline newline
31341 \begin_inset space \textvisiblespace{}
31344 A@>j>>B@>>k>C@=F Ctrl+Return
31345 \begin_inset Newline newline
31349 \begin_inset Phantom HPhantom
31352 \begin_layout Plain Layout
31358 \begin_inset space \textvisiblespace{}
31371 \begin_inset Formula $\to$
31377 \begin_inset Newline newline
31381 \begin_inset Phantom HPhantom
31384 \begin_layout Plain Layout
31390 \begin_inset space \textvisiblespace{}
31401 \begin_layout Subsection
31403 \begin_inset Index idx
31406 \begin_layout Plain Layout
31407 Diagrams ! xymatrix
31415 \begin_layout Standard
31416 To be able to use xymatrices, the LaTeX-package
31421 A xymatrix is created by inserting the command
31428 Then you are able to add new matrix columns and rows like for normal matrices,
31430 \begin_inset CommandInset ref
31432 reference "sec:Matrices"
31439 \begin_layout Standard
31440 In contrary to amscd diagrams, xymatrices supports diagonal and curved arrows,
31442 All possibilities to create commutative diagrams and decorations are explained
31447 that you find in the menu
31449 Help\SpecialChar \menuseparator
31451 \begin_inset space ~
31459 \begin_layout Subsection
31465 \begin_inset Index idx
31468 \begin_layout Plain Layout
31477 \begin_layout Standard
31482 -diagrams, the LaTeX-package
31491 -diagram is created by inserting the command
31498 Then you are able to add new matrix columns and rows like for normal matrices,
31500 \begin_inset CommandInset ref
31502 reference "sec:Matrices"
31509 \begin_layout Standard
31510 Examples how to create
31514 diagrams in LyX is given in the
31516 Feynman-diagram manual
31518 that you find in the menu
31520 Help\SpecialChar \menuseparator
31522 \begin_inset space ~
31530 \begin_layout Standard
31531 \begin_inset Newpage newpage
31537 \begin_layout Section
31538 User-defined Commands
31539 \begin_inset Index idx
31542 \begin_layout Plain Layout
31543 User-defined commands
31551 \begin_layout Standard
31552 \begin_inset Note Greyedout
31555 \begin_layout Plain Layout
31560 The names of user-defined commands and macros may only consist of Latin
31569 \begin_layout Subsection
31573 \begin_inset CommandInset label
31575 name "sub:The-Command-newcommand"
31580 \begin_inset Index idx
31583 \begin_layout Plain Layout
31584 User-defined commands !
31592 \begin_inset Index idx
31595 \begin_layout Plain Layout
31606 \begin_layout Standard
31607 Many LaTeX-commands are too long to be used frequently.
31608 But it is possible to define with the command
31614 new shorter commands.
31617 \begin_layout Standard
31618 The command scheme of
31627 \begin_layout Standard
31632 newcommand{new command name}[number of arguments][optional
31637 \begin_inset Newline newline
31641 \begin_inset Phantom HPhantom
31644 \begin_layout Plain Layout
31654 {command definition}
31657 \begin_layout Standard
31658 \begin_inset Note Greyedout
31661 \begin_layout Plain Layout
31666 Assure that the name of the new command is not already used in your document
31667 or by LaTeX-packages that you use.
31668 When you for example define the command
31680 , you get an error message because
31686 is already defined as command for
31687 \begin_inset Quotes eld
31691 \begin_inset Formula $\le$
31695 \begin_inset Quotes erd
31706 \begin_layout Standard
31707 The number of arguments is an integer in the range 0
31708 \begin_inset space \thinspace{}
31712 \begin_inset space \thinspace{}
31715 9 and specifies how many arguments the new command should have.
31716 With the optional value a value for an optional argument can be predefined.
31717 When this is done, the
31725 rgument of the new command is automatically an optional one.
31728 \begin_layout Standard
31729 Here are some examples:
31732 \begin_layout Itemize
31733 To define the command
31745 , the LaTeX-preamble line is:
31746 \begin_inset VSpace medskip
31750 \begin_inset Newline newline
31764 \begin_layout Itemize
31765 To define the command
31777 , the argument (that should be underlined) must be taken into account.
31778 For this the preamble line is:
31779 \begin_inset VSpace medskip
31783 \begin_inset Newline newline
31797 \begin_inset VSpace medskip
31801 \begin_inset Newline newline
31808 acts as argument placeholder, the
31812 behind it denotes that it is the placeholder for the first argument.
31815 \begin_layout Itemize
31823 \begin_inset space \thinspace{}
31827 \begin_inset space \space{}
31837 \begin_inset VSpace medskip
31841 \begin_inset Newline newline
31852 framebox#1#2{$#3$}}
31855 \begin_inset VSpace medskip
31859 \begin_inset Newline newline
31862 The two Dollar signs creates the extra formula needed for
31869 \begin_inset CommandInset ref
31871 reference "sub:Boxes-with-Frame"
31878 \begin_layout Itemize
31879 To create a new command for
31885 where the color for the box need not be specified, the argument for the
31886 color is defined optional:
31887 \begin_inset VSpace medskip
31891 \begin_inset Newline newline
31902 fcolorbox{#2}{#1}{$#3$}}
31905 \begin_inset VSpace medskip
31909 \begin_inset Newline newline
31912 When the color is not specified when using
31918 , the predefined color
31925 \begin_layout Standard
31926 A test of the new defined commands:
31929 \begin_layout Standard
31931 \begin_inset Tabular
31932 <lyxtabular version="3" rows="6" columns="2">
31933 <features rotate="0" tabularvalignment="middle">
31934 <column alignment="center" valignment="top">
31935 <column alignment="center" valignment="top">
31937 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
31940 \begin_layout Plain Layout
31946 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
31949 \begin_layout Plain Layout
31951 \begin_inset Note Note
31954 \begin_layout Plain Layout
31961 is only used as spacer.
31973 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
31976 \begin_layout Plain Layout
31980 \begin_inset space \textvisiblespace{}
31988 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
31991 \begin_layout Plain Layout
31992 \begin_inset Formula $A\gr B$
32002 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
32005 \begin_layout Plain Layout
32013 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
32016 \begin_layout Plain Layout
32017 \begin_inset Formula $\raisebox{4.5mm}{}\us{ABcd}\raisebox{-2mm}{}$
32027 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
32030 \begin_layout Plain Layout
32034 \begin_inset Formula $\to$
32040 \begin_inset Formula $\to$
32048 \begin_inset space \textvisiblespace{}
32056 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
32059 \begin_layout Plain Layout
32060 \begin_inset Formula $\raisebox{6mm}{}\fb{[2cm]}{}{\int A=B}\raisebox{-4mm}{}$
32070 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
32073 \begin_layout Plain Layout
32077 \begin_inset Formula $\to$
32085 \begin_inset space \textvisiblespace{}
32093 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
32096 \begin_layout Plain Layout
32097 \begin_inset Formula $\raisebox{6mm}{}\cb{red}{\int A=B}\raisebox{-4mm}{}$
32107 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
32110 \begin_layout Plain Layout
32116 \begin_inset Formula $\to$
32124 \begin_inset space \textvisiblespace{}
32132 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
32135 \begin_layout Plain Layout
32136 \begin_inset Formula $\raisebox{6mm}{}\cb[green]{red}{\int A=B}\raisebox{-4mm}{}$
32152 \begin_layout Subsection
32154 \begin_inset Index idx
32157 \begin_layout Plain Layout
32158 User-defined commands! Math macros
32164 \begin_inset Index idx
32167 \begin_layout Plain Layout
32176 \begin_layout Standard
32177 User-defined commands are especially convenient for complex expressions.
32178 When you are for example dealing with a document that has quadratic equations,
32179 the same solution type occurs several times.
32180 The general form of a quadratic equation is
32181 \begin_inset Formula
32183 0=\lambda^{2}+p\lambda+q
32188 The general form of the solution is
32189 \begin_inset Formula
32191 \lambda_{1,2}=-\frac{p}{2}\pm\sqrt{\frac{p²}{4}-q}
32199 \begin_layout Standard
32200 To define a command for the solution formula where only the three parameters
32202 \begin_inset Formula $\lambda$
32206 \begin_inset Formula $p$
32210 \begin_inset Formula $q$
32213 need to be specified and the index of
32214 \begin_inset Formula $\lambda$
32217 can be given optionally, the LaTeX-preamble line is
32218 \begin_inset Newline newline
32234 \begin_inset Newline newline
32238 \begin_inset Phantom HPhantom
32241 \begin_layout Plain Layout
32255 frac{#3^{2}}{4}-#4}}
32258 \begin_layout Standard
32259 To create with this the solution formula, the command
32260 \begin_inset Newline newline
32270 \begin_inset Formula $\to$
32276 \begin_inset Formula $\to$
32283 is inserted to a formula
32288 \begin_layout Standard
32289 The definition of the new command is unintuitive because one has to know
32290 the schemes of all used LaTeX commands, e.
32291 \begin_inset space \thinspace{}
32295 \begin_inset space \space{}
32298 that a fraction is inserted in LaTeX as
32302 frac{numerator}{denominator}
32305 Furthermore one can easily forget a brace in the definition and cannot
32306 see in LyX what the new command is doing.
32307 To avoid these problems LyX offers the possibility to use math macros instead
32317 \begin_layout Standard
32318 A math macro is created by using the menu
32320 Insert\SpecialChar \menuseparator
32321 Math\SpecialChar \menuseparator
32324 or the toolbar button
32325 \begin_inset Graphics
32326 filename ../images/math-macro_newmacroname_newcommand.png
32332 The math macro toolbar appears together with the following box where the
32334 \begin_inset Newline newline
32338 \begin_inset space \hspace*{\fill}
32342 \begin_inset Graphics
32343 filename clipart/macrobox.png
32348 \begin_inset space \hspace*{\fill}
32352 \begin_inset Newline newline
32356 \begin_inset FormulaMacro
32357 \newcommand{\qG}[4][1,\,2]{#2_{#1}=-\frac{#3}{2}\pm\sqrt{\frac{#3^{2}}{4}-#4}}
32362 newmacroname is the default name of the macro that should be changed to
32363 something sensible.
32364 The wanted formula is inserted in the first blue box.
32365 An argument placeholder is inserted with the command
32372 \begin_inset space \thinspace{}
32376 \begin_inset space \space{}
32385 or by using the macro toolbar button
32386 \begin_inset Graphics
32387 filename ../images/math-macro-add-param.png
32393 Argument placeholders are displayed red.
32395 \begin_inset space ~
32398 arguments are possible.
32399 Optional arguments are created with the toolbar button
32400 \begin_inset Graphics
32401 filename ../images/math-macro-add-optional-param.png
32407 The first non-optional argument can be transformed to an optional one with
32409 \begin_inset Graphics
32410 filename ../images/math-macro-make-optional.png
32416 In the second blue box the appearance of the macro in LyX can be defined.
32417 Normally you want to see it as it is defined, so the box is kept empty.
32418 But when you have created a macro that needs lot of space on the screen,
32419 you can insert in the box for example
32420 \begin_inset Newline newline
32450 \begin_inset Newline newline
32455 For the macro only the arguments with the macro name in front of them will
32456 then be displayed in LyX, leading to a better overview.
32457 The formula appears in the output as defined in the first box.
32458 \begin_inset Newline newline
32461 The appearance of macros in formulas can furthermore be changed for single
32462 macros by setting the cursor in the macro and using the menu
32464 View\SpecialChar \menuseparator
32466 \begin_inset space ~
32470 \begin_inset space ~
32478 \begin_layout Standard
32479 To use a macro, the macro name is inserted as command to a formula, in our
32487 Our macro looks in LyX like this:
32488 \begin_inset Newline newline
32492 \begin_inset space \hspace*{\fill}
32496 \begin_inset Graphics
32497 filename clipart/macrouse.png
32502 \begin_inset space \hspace*{\fill}
32506 \begin_inset Newline newline
32509 Here is our macro example with the arguments
32510 \begin_inset Formula $x$
32514 \begin_inset Formula $\ln(x)$
32518 \begin_inset Formula $B$
32524 \begin_layout Standard
32525 \begin_inset Formula
32535 \begin_layout Standard
32536 LyX offers in the menu
32538 Tools\SpecialChar \menuseparator
32539 Preferences\SpecialChar \menuseparator
32540 Editing\SpecialChar \menuseparator
32543 different styles to edit macros.
32544 To find the style that suits you the most, choose a style and set the cursor
32545 in a macro formula to see the difference.
32548 \begin_layout Standard
32549 A math macro is transformed internally to a
32555 command when exporting the document.
32562 command is not placed in the LaTeX-preamble, therefore macros can only
32563 be used in formulas that are in the document below the macro definition
32567 \begin_layout Standard
32568 Math macros can also be directly created from a
32575 When writing for example the command
32578 \begin_inset Newline newline
32587 xleftarrow[#2]{#1}}
32588 \begin_inset Newline newline
32593 in LyX as normal text, highlighting it completely and using then the shortcut
32598 , the command will be transformed to a math macro.
32599 Using this method you need to be careful that the
32605 command is typed correctly, otherwise you get a faulty macro leading to
32609 \begin_layout Standard
32610 Math macros currently have the problem that further formulas in macro definition
32611 s are handled wrongly.
32612 Therefore the example
32619 \begin_inset CommandInset ref
32621 reference "sub:The-Command-newcommand"
32625 cannot be created as macro.
32628 \begin_layout Standard
32629 When the cursor is in a macro definition box, you will see the macro toolbar
32633 \begin_layout Standard
32634 \begin_inset VSpace defskip
32640 \begin_layout Standard
32641 \begin_inset Graphics
32642 filename clipart/MacroToolbar.png
32647 \begin_inset Index idx
32650 \begin_layout Plain Layout
32659 \begin_layout Standard
32660 \begin_inset VSpace defskip
32666 \begin_layout Standard
32667 The macro toolbar contains from left to right the following buttons:
32670 \begin_layout Standard
32671 \begin_inset VSpace defskip
32677 \begin_layout Standard
32678 \begin_inset Tabular
32679 <lyxtabular version="3" rows="9" columns="2">
32680 <features rotate="0" islongtable="true" longtabularalignment="center">
32681 <column alignment="left" valignment="top">
32682 <column alignment="left" valignment="top" width="85col%">
32683 <row interlinespace="2.5mm">
32684 <cell alignment="center" valignment="top" usebox="none">
32687 \begin_layout Plain Layout
32688 \begin_inset Graphics
32689 filename ../images/math-macro-remove-param.png
32690 rotateOrigin center
32699 <cell alignment="center" valignment="top" usebox="none">
32702 \begin_layout Plain Layout
32705 Edit\SpecialChar \menuseparator
32706 Math\SpecialChar \menuseparator
32708 \begin_inset space ~
32711 Definition\SpecialChar \menuseparator
32712 Remove Last Argument
32718 <row interlinespace="2.5mm">
32719 <cell alignment="center" valignment="top" usebox="none">
32722 \begin_layout Plain Layout
32723 \begin_inset Graphics
32724 filename ../images/math-macro-add-param.png
32725 rotateOrigin center
32734 <cell alignment="center" valignment="top" usebox="none">
32737 \begin_layout Plain Layout
32740 Edit\SpecialChar \menuseparator
32741 Math\SpecialChar \menuseparator
32743 \begin_inset space ~
32746 Definition\SpecialChar \menuseparator
32753 <row interlinespace="2.5mm">
32754 <cell alignment="center" valignment="top" usebox="none">
32757 \begin_layout Plain Layout
32758 \begin_inset Graphics
32759 filename ../images/math-macro-make-optional.png
32760 rotateOrigin center
32769 <cell alignment="center" valignment="top" usebox="none">
32772 \begin_layout Plain Layout
32775 Edit\SpecialChar \menuseparator
32776 Math\SpecialChar \menuseparator
32778 \begin_inset space ~
32781 Definition\SpecialChar \menuseparator
32782 Make First Non-Optional into
32783 \begin_inset Newline newline
32787 \begin_inset Phantom HPhantom
32790 \begin_layout Plain Layout
32793 Edit\SpecialChar \menuseparator
32794 Math\SpecialChar \menuseparator
32796 \begin_inset space ~
32799 Definition\SpecialChar \menuseparator
32811 <row interlinespace="2.5mm">
32812 <cell alignment="center" valignment="top" usebox="none">
32815 \begin_layout Plain Layout
32816 \begin_inset Graphics
32817 filename ../images/math-macro-make-nonoptional.png
32818 rotateOrigin center
32827 <cell alignment="center" valignment="top" usebox="none">
32830 \begin_layout Plain Layout
32833 Edit\SpecialChar \menuseparator
32834 Math\SpecialChar \menuseparator
32836 \begin_inset space ~
32839 Definition\SpecialChar \menuseparator
32840 Make Last Optional into
32841 \begin_inset Newline newline
32845 \begin_inset Phantom HPhantom
32848 \begin_layout Plain Layout
32851 Edit\SpecialChar \menuseparator
32852 Math\SpecialChar \menuseparator
32854 \begin_inset space ~
32857 Definition\SpecialChar \menuseparator
32863 Non-Optional Argument
32869 <row interlinespace="2.5mm">
32870 <cell alignment="center" valignment="top" usebox="none">
32873 \begin_layout Plain Layout
32874 \begin_inset Graphics
32875 filename ../images/math-macro-remove-optional-param.png
32876 rotateOrigin center
32885 <cell alignment="center" valignment="top" usebox="none">
32888 \begin_layout Plain Layout
32891 Edit\SpecialChar \menuseparator
32892 Math\SpecialChar \menuseparator
32894 \begin_inset space ~
32897 Definition\SpecialChar \menuseparator
32898 Remove Optional Argument
32904 <row interlinespace="2.5mm">
32905 <cell alignment="center" valignment="top" usebox="none">
32908 \begin_layout Plain Layout
32909 \begin_inset Graphics
32910 filename ../images/math-macro-add-optional-param.png
32911 rotateOrigin center
32920 <cell alignment="center" valignment="top" usebox="none">
32923 \begin_layout Plain Layout
32926 Edit\SpecialChar \menuseparator
32927 Math\SpecialChar \menuseparator
32929 \begin_inset space ~
32932 Definition\SpecialChar \menuseparator
32933 Insert Optional Argument
32939 <row interlinespace="2.5mm">
32940 <cell alignment="center" valignment="top" usebox="none">
32943 \begin_layout Plain Layout
32944 \begin_inset Graphics
32945 filename ../images/math-macro-remove-greedy-param.png
32946 rotateOrigin center
32955 <cell alignment="center" valignment="top" usebox="none">
32958 \begin_layout Plain Layout
32961 Edit\SpecialChar \menuseparator
32962 Math\SpecialChar \menuseparator
32964 \begin_inset space ~
32967 Definition\SpecialChar \menuseparator
32968 Remove Last Argument
32969 \begin_inset Newline newline
32973 \begin_inset Phantom HPhantom
32976 \begin_layout Plain Layout
32979 Edit\SpecialChar \menuseparator
32980 Math\SpecialChar \menuseparator
32982 \begin_inset space ~
32985 Definition\SpecialChar \menuseparator
32991 Spitting Out To The Right
32997 <row interlinespace="2.5mm">
32998 <cell alignment="center" valignment="top" usebox="none">
33001 \begin_layout Plain Layout
33002 \begin_inset Graphics
33003 filename ../images/math-macro-append-greedy-param.png
33004 rotateOrigin center
33013 <cell alignment="center" valignment="top" usebox="none">
33016 \begin_layout Plain Layout
33019 Edit\SpecialChar \menuseparator
33020 Math\SpecialChar \menuseparator
33022 \begin_inset space ~
33025 Definition\SpecialChar \menuseparator
33027 \begin_inset Newline newline
33031 \begin_inset Phantom HPhantom
33034 \begin_layout Plain Layout
33037 Edit\SpecialChar \menuseparator
33038 Math\SpecialChar \menuseparator
33040 \begin_inset space ~
33043 Definition\SpecialChar \menuseparator
33049 Eating From The Right
33055 <row interlinespace="2.5mm">
33056 <cell alignment="center" valignment="top" usebox="none">
33059 \begin_layout Plain Layout
33060 \begin_inset Graphics
33061 filename ../images/math-macro-add-greedy-optional-param.png
33062 rotateOrigin center
33071 <cell alignment="center" valignment="top" usebox="none">
33074 \begin_layout Plain Layout
33077 Edit\SpecialChar \menuseparator
33078 Math\SpecialChar \menuseparator
33080 \begin_inset space ~
33083 Definition\SpecialChar \menuseparator
33084 Append Optional Argument
33085 \begin_inset Newline newline
33089 \begin_inset Phantom HPhantom
33092 \begin_layout Plain Layout
33095 Edit\SpecialChar \menuseparator
33096 Math\SpecialChar \menuseparator
33098 \begin_inset space ~
33101 Definition\SpecialChar \menuseparator
33107 Eating From The Right
33120 \begin_layout Section
33121 Computer Algebra Systems
33124 \begin_layout Standard
33125 LyX offers the exchange between mathematical expressions written in LyX's
33126 math editor and external applications or user defined scripts.
33127 Currently supported applications are
33144 Note that the set of supported mathematical constructs is limited only
33145 to very simple cases.
33148 \begin_layout Subsection
33152 \begin_layout Standard
33153 Write some expression in a formula, go to the
33155 Edit\SpecialChar \menuseparator
33156 Math\SpecialChar \menuseparator
33157 Use Computer Algebra System
33159 menu and choose the application you have installed on the computer.
33160 After that the result of computation should show on the right side of the
33161 expression together with the
33162 \begin_inset Quotes eld
33166 \begin_inset Quotes erd
33172 \begin_layout Standard
33173 Here are few simple examples (with results from
33177 ) to show what kind of computations can be performed:
33180 \begin_layout Itemize
33181 \begin_inset Formula $\frac{37}{3}*2-\sum_{i=1}^{3}i^{i}=-\frac{22}{3}$
33187 \begin_layout Itemize
33188 \begin_inset Formula $\frac{37.0}{3}=12.33333333333333$
33194 \begin_layout Itemize
33195 \begin_inset Formula $\int_{1}^{2}\sin(x)dx=\cos1-\cos2$
33201 \begin_layout Itemize
33202 \begin_inset Formula $\det\left[\begin{array}{ccc}
33206 \end{array}\right]=-56$
33212 \begin_layout Itemize
33213 \begin_inset Formula $\lim_{x\rightarrow0}\left(\frac{\sin(x)}{x}\right)=1$
33219 \begin_layout Subsection
33223 \begin_layout Standard
33224 Currently there is no keyboard shortcut for calling the algebra applications.
33225 One can easily bind a shortcut to the
33229 LyX function (see the
33237 \begin_inset space \thinspace{}
33241 \begin_inset space \space{}
33248 key inside the math editor.
33253 one would use this shortcut definition command:
33256 \begin_layout Standard
33259 command-alternatives break-paragraph;math-extern maxima
33262 \begin_layout Section
33264 \begin_inset Index idx
33267 \begin_layout Plain Layout
33276 \begin_layout Subsection
33278 \begin_inset Index idx
33281 \begin_layout Plain Layout
33290 \begin_layout Standard
33291 Negative numbers often look ugly in formulas because the minus sign before
33292 the number is set with the same length as the minus operator sign.
33293 When writing the negative number in normal text, the minus sign appears
33297 \begin_layout Standard
33298 Thus, the problem disappears when converting the minus sign to mathematical
33302 \begin_layout Standard
33303 An example to visualize the problem:
33306 \begin_layout Standard
33308 \begin_inset Tabular
33309 <lyxtabular version="3" rows="3" columns="2">
33310 <features rotate="0" tabularvalignment="middle">
33311 <column alignment="right" valignment="top">
33312 <column alignment="left" valignment="top">
33314 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
33317 \begin_layout Plain Layout
33323 <cell alignment="center" valignment="top" topline="true" rightline="true" usebox="none">
33326 \begin_layout Plain Layout
33334 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
33337 \begin_layout Plain Layout
33343 <cell alignment="center" valignment="top" topline="true" bottomline="true" rightline="true" usebox="none">
33346 \begin_layout Plain Layout
33347 \begin_inset Formula $x=-2$
33357 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
33360 \begin_layout Plain Layout
33366 <cell alignment="center" valignment="top" topline="true" bottomline="true" rightline="true" usebox="none">
33369 \begin_layout Plain Layout
33370 \begin_inset Formula $x=\textrm{-}2$
33386 \begin_layout Subsection
33387 Comma as decimal Separator
33388 \begin_inset Index idx
33391 \begin_layout Plain Layout
33400 \begin_layout Standard
33401 In LaTeX a comma inside a formula is used, according to the English convention,
33402 as number group separator.
33403 So there will be space added behind all commas in formulas.
33406 \begin_layout Standard
33407 To avoid this, the comma is highlighted and changed to mathematical text
33417 \begin_layout Standard
33418 To use all formula commas in the document as decimal separator, the file
33427 \begin_layout Plain Layout
33432 is part of the LaTeX-package
33437 \begin_inset Index idx
33440 \begin_layout Plain Layout
33445 \begin_layout Plain Layout
33465 \begin_inset Index idx
33468 \begin_layout Plain Layout
33474 is loaded with the LaTeX-preamble line
33477 \begin_layout Standard
33485 \begin_layout Subsection
33487 \begin_inset CommandInset label
33489 name "sub:Physical-Vectors"
33494 \begin_inset Index idx
33497 \begin_layout Plain Layout
33506 \begin_layout Standard
33507 Predefined vectors are offered by the LaTeX-package
33512 \begin_inset Index idx
33515 \begin_layout Plain Layout
33521 that is loaded with the LaTeX-preamble line
33524 \begin_layout Standard
33532 \begin_layout Standard
33536 \begin_layout Plain Layout
33546 \begin_inset Note Note
33549 \begin_layout Plain Layout
33550 The following table will only be displayed when the LaTeX-package
33562 \begin_layout Standard
33563 The following commands are defined:
33566 \begin_layout Standard
33568 \begin_inset Tabular
33569 <lyxtabular version="3" rows="4" columns="2">
33570 <features rotate="0" tabularvalignment="middle">
33571 <column alignment="center" valignment="top">
33572 <column alignment="center" valignment="top">
33574 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
33577 \begin_layout Plain Layout
33583 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
33586 \begin_layout Plain Layout
33594 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
33597 \begin_layout Plain Layout
33607 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
33610 \begin_layout Plain Layout
33611 \begin_inset Formula $\Bra{\psi}$
33621 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
33624 \begin_layout Plain Layout
33634 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
33637 \begin_layout Plain Layout
33638 \begin_inset Formula $\Ket{\psi}$
33648 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
33651 \begin_layout Plain Layout
33663 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
33666 \begin_layout Plain Layout
33667 \begin_inset Formula $\Braket{\psi|\phi}$
33683 \begin_layout Standard
33690 assures that all vertical bars are set in the size of the surrounding brackets:
33691 \begin_inset Formula
33693 \Braket{\phi|J=\frac{3}{2}\,,\, M_{J}}
33702 \begin_layout Plain Layout
33712 \begin_inset Note Note
33715 \begin_layout Plain Layout
33716 The following will be displayed when the LaTeX-package
33728 \begin_layout Standard
33729 You need to install the LaTeX-package
33733 to see the rest of this subsection in the output.
33736 \begin_layout Standard
33740 \begin_layout Plain Layout
33752 \begin_layout Standard
33759 can also be achieved using the command
33765 , that is described in
33766 \begin_inset CommandInset ref
33768 reference "sub:Automatic-Bracket-Size"
33775 \begin_layout Subsection
33776 Self-defined Fractions
33777 \begin_inset CommandInset label
33779 name "sub:Self-defined-Fractions"
33784 \begin_inset Index idx
33787 \begin_layout Plain Layout
33788 Fractions ! self-defined
33796 \begin_layout Standard
33797 To define custom commands for fractions, the command
33804 \begin_inset Index idx
33807 \begin_layout Plain Layout
33814 \begin_layout Plain Layout
33828 is used in the following scheme:
33831 \begin_layout Standard
33844 bracket}{fraction bar thickness}{style}
33845 \begin_inset Newline newline
33849 \begin_inset Phantom HPhantom
33852 \begin_layout Plain Layout
33862 {numerator}{denominator}
33865 \begin_layout Standard
33866 The style is a number in the range of 0
33867 \begin_inset space \thinspace{}
33871 \begin_inset space \thinspace{}
33877 \begin_layout Standard
33879 \begin_inset Tabular
33880 <lyxtabular version="3" rows="5" columns="2">
33881 <features rotate="0" tabularvalignment="middle">
33882 <column alignment="center" valignment="top">
33883 <column alignment="center" valignment="top">
33885 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
33888 \begin_layout Plain Layout
33894 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
33897 \begin_layout Plain Layout
33905 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
33908 \begin_layout Plain Layout
33914 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
33917 \begin_layout Plain Layout
33918 display style formula
33925 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
33928 \begin_layout Plain Layout
33934 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
33937 \begin_layout Plain Layout
33945 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
33948 \begin_layout Plain Layout
33954 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
33957 \begin_layout Plain Layout
33965 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
33968 \begin_layout Plain Layout
33974 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
33977 \begin_layout Plain Layout
33991 \begin_layout Standard
33992 When no style is given, the size is adjusted to the surrounding environment
33993 like for the command
34002 \begin_layout Standard
34003 When no fraction bar thickness is given, the predefined value of 0.4
34004 \begin_inset space \thinspace{}
34010 \begin_layout Standard
34011 \begin_inset VSpace medskip
34014 For example, the commands
34027 \begin_inset CommandInset ref
34029 reference "sub:Fractions"
34033 are defined with the commands
34036 \begin_layout Standard
34045 genfrac{}{}{}{0}{#1}{#2}}
34048 \begin_layout Standard
34052 \begin_layout Standard
34061 genfrac{(}{)}{0pt}{1}{#1}{#2}}
34064 \begin_layout Standard
34065 \begin_inset VSpace medskip
34068 To define a fraction where the fraction bar thickness can be given as optional
34069 argument, the following line is inserted to the LaTeX-preamble:
34072 \begin_layout Standard
34081 genfrac{}{}{#1}{}{#2}{#3}}
34084 \begin_layout Standard
34086 \begin_inset Formula
34088 \text{Command} & & \mathrm{\backslash fracS[1mm]\backslash\{A\to\backslash\{B} & & \mathrm{\backslash fracS[5mm]\backslash\{A\to\backslash\{B}\\
34089 \text{Result} & & \fracS[1mm]{A}{B} & & \fracS[5mm]{A}{B}
34094 As one can see, the distance of the numerator and the denominator to the
34095 fraction bar is round about three times the bar thickness.
34098 \begin_layout Subsection
34100 \begin_inset Index idx
34103 \begin_layout Plain Layout
34112 \begin_layout Standard
34113 There are four ways to cancel formulas or parts of formulas:
34116 \begin_layout Standard
34120 \begin_layout Plain Layout
34130 \begin_inset Note Note
34133 \begin_layout Plain Layout
34134 The following table will only be displayed when the LaTeX-package
34146 \begin_layout Standard
34148 \begin_inset Tabular
34149 <lyxtabular version="3" rows="5" columns="2">
34150 <features rotate="0" tabularvalignment="middle">
34151 <column alignment="center" valignment="top">
34152 <column alignment="center" valignment="top">
34154 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
34157 \begin_layout Plain Layout
34163 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
34166 \begin_layout Plain Layout
34168 \begin_inset Note Note
34171 \begin_layout Plain Layout
34178 are used here as spacer.
34190 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
34193 \begin_layout Plain Layout
34197 \begin_inset space \textvisiblespace{}
34203 \begin_inset space \textvisiblespace{}
34211 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
34214 \begin_layout Plain Layout
34215 \begin_inset Formula $\raisebox{4.5mm}{}\cancel{\int A=B}\raisebox{-2.5mm}{}$
34225 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
34228 \begin_layout Plain Layout
34232 \begin_inset space \textvisiblespace{}
34238 \begin_inset space \textvisiblespace{}
34246 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
34249 \begin_layout Plain Layout
34250 \begin_inset Formula $\raisebox{4.5mm}{}\bcancel{\int A=B}\raisebox{-2.5mm}{}$
34260 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
34263 \begin_layout Plain Layout
34267 \begin_inset space \textvisiblespace{}
34273 \begin_inset space \textvisiblespace{}
34281 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
34284 \begin_layout Plain Layout
34285 \begin_inset Formula $\raisebox{4.5mm}{}\xcancel{\int A=B}\raisebox{-2.5mm}{}$
34295 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
34298 \begin_layout Plain Layout
34302 \begin_inset space \textvisiblespace{}
34308 \begin_inset space \textvisiblespace{}
34312 \begin_inset Formula $\to$
34320 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
34323 \begin_layout Plain Layout
34324 \begin_inset Formula $\raisebox{7mm}{}\cancelto{1}{\int A=B}\raisebox{-2.5mm}{}\hspace{3mm}$
34340 \begin_layout Standard
34347 is especially suitable to visualize the reduction of fractions within formulas:
34348 \begin_inset Formula
34350 \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}}}
34358 \begin_layout Standard
34359 To change the size of
34366 \begin_inset Quotes eld
34370 \begin_inset Quotes erd
34373 value one can add the LaTeX-preamble line
34376 \begin_layout Standard
34381 PassOptionsToPackage{option}{cancel}
34384 \begin_layout Standard
34393 which leads to the same size as for the canceled value, or
34397 which makes is it a bit smaller than normal.
34400 \begin_layout Standard
34401 To color the cancellation bar one adds this command as TeX code:
34404 \begin_layout Standard
34416 \begin_layout Standard
34421 can be replaced by a color of your choice.
34424 \begin_layout Standard
34428 \begin_layout Plain Layout
34444 \begin_layout Standard
34445 \begin_inset Formula
34447 \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}}}
34455 \begin_layout Standard
34459 \begin_layout Plain Layout
34473 \begin_inset Note Note
34476 \begin_layout Plain Layout
34485 \begin_layout Standard
34486 For further customizations, see the documentation of the package
34491 \begin_inset CommandInset citation
34498 \begin_inset Index idx
34501 \begin_layout Plain Layout
34510 \begin_layout Standard
34514 \begin_layout Plain Layout
34524 \begin_inset Note Note
34527 \begin_layout Plain Layout
34528 The following will be displayed when the LaTeX-package
34540 \begin_layout Standard
34541 You need to install the LaTeX-package
34545 to see the rest of this subsection in the output.
34548 \begin_layout Standard
34552 \begin_layout Plain Layout
34564 \begin_layout Standard
34565 \begin_inset Newpage newpage
34571 \begin_layout Subsection
34572 Formulas in Section Headings
34573 \begin_inset CommandInset label
34575 name "sub:Formulas-in-Section"
34580 \begin_inset Index idx
34583 \begin_layout Plain Layout
34584 Formula ! in section headings
34592 \begin_layout Standard
34593 When formulas are used in section headings, the following has to be taken
34597 \begin_layout Standard
34598 \begin_inset Note Greyedout
34601 \begin_layout Plain Layout
34607 \begin_inset Index idx
34610 \begin_layout Plain Layout
34611 Packages ! hyperref
34616 support is enabled in the document settings dialog under
34619 \begin_inset space ~
34624 , PDF-bookmarks are created for every section heading in the table of contents.
34625 If a section heading contains formulas, they are incorrectly displayed
34626 in the bookmark text, because formulas in bookmarks infringe the PDF convention
34635 \begin_layout Standard
34636 Both problems can be solved by inserting at the end of the section heading
34637 a short title with the menu
34639 Insert\SpecialChar \menuseparator
34641 \begin_inset space ~
34647 Short titles are used as alternative for multiline section headings to
34648 keep the table of contents clearly arranged.
34649 Only the short title appears in the table of contents and therefore also
34650 in the PDF-bookmark.
34653 \begin_layout Standard
34654 When formulas should be used in the table of contents but
34658 is used, one can use the following command in TeX-mode:
34661 \begin_layout Standard
34666 texorpdfstring{part}{alternative}
34667 \begin_inset Index idx
34670 \begin_layout Plain Layout
34681 \begin_layout Standard
34682 Part is the part of the heading that shouldn't appear in the PDF-bookmark.
34683 This can be characters, formulas, footnotes, but also cross-references.
34684 The alternative is used instead of the part for the bookmark.
34687 \begin_layout Standard
34688 Here are two example headings:
34689 \begin_inset VSpace -3mm
34696 \begin_layout Plain Layout
34708 \begin_layout Subsubsection
34709 Heading without formula in table of contents
34710 \begin_inset Formula $\sqrt{-1}=\mathrm{i}$
34714 \begin_inset Argument 1
34717 \begin_layout Plain Layout
34718 Heading without formula in table of contents
34726 \begin_layout Subsubsection
34727 Heading with formula in table of contents
34731 \begin_layout Plain Layout
34741 \begin_inset Formula $\sqrt{-1}=\mathrm{i}$
34748 \begin_layout Plain Layout
34758 \begin_layout Standard
34762 \begin_layout Plain Layout
34771 In the first heading a short title was used, in the second one
34780 \begin_layout Standard
34781 To get the same formatting as for the other headings, the complete heading
34790 \begin_layout Plain Layout
34792 \begin_inset CommandInset ref
34794 reference "sub:Bold-Formulas"
34806 \begin_layout Subsection
34807 Formulas in multi-column Text
34808 \begin_inset Index idx
34811 \begin_layout Plain Layout
34812 Formula ! in multi-column text
34820 \begin_layout Standard
34821 Formulas in multi-column text are often too wide to fit into a column and
34822 thus need to be set over the whole page width.
34823 This is done by using the LaTeX-package
34831 \begin_layout Plain Layout
34836 is part of every LaTeX standard installation.
34842 \begin_inset Index idx
34845 \begin_layout Plain Layout
34846 Packages ! multicol
34851 , that is loaded with the LaTeX-preamble line
34854 \begin_layout Standard
34859 usepackage{multicol}
34862 \begin_layout Standard
34863 \begin_inset Note Greyedout
34866 \begin_layout Plain Layout
34867 Note that in this case the setting
34870 \begin_inset space ~
34877 Document\SpecialChar \menuseparator
34883 \begin_inset space ~
34903 \begin_layout Standard
34904 Before the multi-column text the command
34907 \begin_layout Standard
34912 begin{multicols}{column number}
34915 \begin_layout Standard
34916 is written in TeX-mode.
34917 The column number is a number in the range of 2
34918 \begin_inset space \thinspace{}
34922 \begin_inset space \thinspace{}
34926 Before the formula the multi-column text is ended by inserting the command
34929 \begin_layout Standard
34937 \begin_layout Standard
34941 \begin_layout Standard
34942 Due to the command some space is automatically added before the formula.
34944 \begin_inset space \thinspace{}
34947 mm vertical space is inserted before the formula.
34948 When the formula style
34954 \begin_layout Plain Layout
34956 \begin_inset CommandInset ref
34958 reference "sec:Formula-Styles"
34970 \begin_inset space \thinspace{}
34973 mm space is inserted instead.
34976 \begin_layout Standard
34977 As example a multi-column text with a displayed formula:
34980 \begin_layout Standard
34986 \begin_layout Plain Layout
34990 begin{multicols}{2}
34995 Das Spektrum wird fouriertransformiert.
34996 Die Fouriertransformation wird verwendet, um die überlagerten Signale (Netzwerk
34997 , Lösungsmittel) zu trennen.
34998 Nachdem wir die Phasenverschiebung bestimmen konnten, interessiert uns
34999 nun das Aussehen des Ausgangssignals.
35000 Im Experiment haben wir es mit sehr vielen Teilchen zu tun, so dass man
35001 über alle Phasen integrieren muss.
35003 \begin_inset Formula $S$
35006 unser normiertes Ausgangssignal und
35007 \begin_inset Formula $P$
35010 die Phasenverteilungsfunktion, so ergibt sich die Beziehung
35014 \begin_layout Plain Layout
35024 \begin_inset VSpace -6mm
35028 \begin_inset Formula
35030 S(t)=S_{0}(t)\int_{-\infty}^{\infty}P(\phi,t)\mathrm{e}^{\mathrm{i}\phi}\,\mathrm{d}\phi
35039 \begin_layout Plain Layout
35043 begin{multicols}{2}
35049 \begin_inset Formula $S_{0}$
35052 das Signal ohne Gradient ist und die Normierungsbedingung
35053 \begin_inset Formula $\int_{-\infty}^{\infty}P(\phi,t)\,\mathrm{d}\phi=1$
35057 Nun dürfen wir aber nicht den Relaxationsprozess außer Acht lassen.
35059 \begin_inset Formula $\nicefrac{\pi}{2}$
35063 \begin_inset space \thinspace{}
35066 -rf-Puls beginnt sich die Magnetisierung zu entfokussieren, wodurch sich
35067 das Signal zusätzlich abschwächt.
35068 Diese Abschwächung verläuft exponentiell in Abhängigkeit der so genannten
35070 \begin_inset Formula $T_{2}$
35076 \begin_layout Standard
35082 \begin_layout Plain Layout
35094 \begin_layout Subsection
35095 Formulas with Description of Variables
35096 \begin_inset Index idx
35099 \begin_layout Plain Layout
35100 Formula ! with description of variables
35108 \begin_layout Standard
35109 To describe variables within a formula, like in formula
35110 \begin_inset CommandInset ref
35112 reference "eq:within"
35121 \begin_inset Formula $n$
35125 \begin_inset space ~
35128 matrix is used with left aligned columns for the
35129 \begin_inset Formula $n$
35136 \begin_layout Plain Layout
35138 \begin_inset CommandInset ref
35140 reference "sec:Matrices"
35149 To set the description in a smaller size, before the matrix e.
35150 \begin_inset space \thinspace{}
35154 \begin_inset space \space{}
35167 \begin_layout Plain Layout
35169 \begin_inset CommandInset ref
35171 reference "sub:Font-Sizes"
35183 \begin_layout Standard
35184 When the formula style
35190 \begin_layout Plain Layout
35192 \begin_inset CommandInset ref
35194 reference "sec:Formula-Styles"
35215 \begin_layout Plain Layout
35222 only works in formulas with the style
35227 \begin_inset CommandInset ref
35229 reference "sub:Variable-Space"
35238 is inserted before and after the matrix to have the same separation of
35239 the matrix from the equation and the side margin.
35242 \begin_layout Standard
35243 When the formula style
35247 is used, the method described in
35248 \begin_inset CommandInset ref
35250 reference "sub:Flalign-Environment"
35254 is used to indent formulas.
35256 \begin_inset CommandInset ref
35258 reference "eq:within"
35262 consists of five columns where in the first two columns contain the equation,
35263 the third the matrix and the last one an empty TeX-brace.
35264 \begin_inset Formula
35266 \hspace{30pt}F_{A} & =\rho·V·g & \footnotesize\begin{array}{ll}
35267 \rho & \textrm{density}\\
35268 V & \textrm{volume}\\
35269 g & \textrm{gravitational acceleration}
35270 \end{array} & & {}\label{eq:within}
35278 \begin_layout Subsection
35279 Upright small Greek Letters
35280 \begin_inset CommandInset label
35282 name "sub:Upright-small-Greek"
35287 \begin_inset Index idx
35290 \begin_layout Plain Layout
35291 Greek letters ! upright
35299 \begin_layout Standard
35300 Most of the math fonts only provide italic small Greek letters.
35301 But for symbols of elementary particles like pions and neutrinos, upright
35302 Greek letters are needed.
35311 \begin_layout Plain Layout
35316 is part of the LaTeX-package
35321 \begin_inset Index idx
35324 \begin_layout Plain Layout
35329 \begin_layout Plain Layout
35349 \begin_inset Index idx
35352 \begin_layout Plain Layout
35358 that is loaded with the LaTeX-preamble line
35361 \begin_layout Standard
35366 usepackage{upgreek}
35369 \begin_layout Standard
35375 \begin_layout Plain Layout
35385 \begin_inset Note Note
35388 \begin_layout Plain Layout
35389 The following table will only be displayed when the LaTeX-package
35398 They are created when the command for a small Greek letter is started with
35404 For example the command
35411 \begin_inset Formula $\uptau$
35417 \begin_layout Standard
35418 With these commands reactions of elementary particles can be typeset:
35419 \begin_inset Formula
35421 \uppi^{+}\to\upmu^{+}+\upnu_{\upmu}
35429 \begin_layout Standard
35430 The upright letters are more bold and wider than the italic ones.
35431 They should therefore not be used for units like
35432 \begin_inset Quotes eld
35436 \begin_inset Quotes erd
35442 \begin_layout Standard
35446 \begin_layout Plain Layout
35456 \begin_inset Note Note
35459 \begin_layout Plain Layout
35460 The following will be displayed when the LaTeX-package
35472 \begin_layout Standard
35473 You need to install the LaTeX-package
35477 to see the rest of this subsection in the output.
35480 \begin_layout Standard
35484 \begin_layout Plain Layout
35496 \begin_layout Subsection
35497 Text Characters in Formulas
35498 \begin_inset CommandInset label
35500 name "sub:Text-Characters-in"
35505 \begin_inset Index idx
35508 \begin_layout Plain Layout
35517 \begin_layout Standard
35518 In some cases you might want to insert text characters directly into formulas.
35519 When for example the centered dot · is often used in formulas like
35520 \begin_inset Formula $\nu=5·10^{5}\,\mathrm{Hz}$
35523 , one would have to insert the command
35533 \begin_layout Plain Layout
35535 \begin_inset CommandInset ref
35537 reference "sub:Binary-Operators"
35546 all the time, because this character is defined in all encodings as text
35548 But the encoding can be changed by this LaTeX-preamble line:
35551 \begin_layout Standard
35556 Declare Inputtext{183}{
35566 f\SpecialChar \textcompwordmark{}
35570 \begin_layout Standard
35571 The character encoding (menu
35573 Document\SpecialChar \menuseparator
35574 Settings\SpecialChar \menuseparator
35577 ) specifies what character appears when a keyboard key is pressed.
35578 When the key for the character '·' is pressed, internally the command
35585 But this command is not available in a formula so that you would get LaTeX-erro
35587 With the changed encoding the right command is chosen automatically, depending
35588 on if the character was inserted into a formula or not.
35591 \begin_layout Standard
35592 The encoding of several characters is saved in definition files.
35593 For example the encoding
35597 is defined in the file
35601 which is in the installation folder of LaTeX.
35602 Encodings should only be changed via the LaTeX-preamble and not in the
35604 Otherwise documents could not be edited by other LyX users working on other
35608 \begin_layout Standard
35609 \begin_inset VSpace medskip
35612 Besides the centered dot, in this document the degree sign ° is defined
35613 with the following LaTeX-preamble line so that it can be directly inserted
35617 \begin_layout Standard
35622 DeclareInputtext{176}{
35632 f\SpecialChar \textcompwordmark{}
35636 \begin_layout Standard
35637 \begin_inset Newpage newpage
35643 \begin_layout Section
35646 \begin_inset Index idx
35649 \begin_layout Plain Layout
35658 \begin_layout Standard
35659 This section is a summary of the most important typographic rules, listed
35664 \begin_layout Plain Layout
35665 This collection was partly taken from the German semi-official dictionary
35667 \begin_inset Quotes eld
35671 \begin_inset Quotes erd
35675 \begin_inset CommandInset citation
35681 that lists some of the ISO rules.
35682 More rules are listed in
35683 \begin_inset CommandInset citation
35697 \begin_layout Itemize
35706 \begin_layout Plain Layout
35707 done with font styles, see
35708 \begin_inset CommandInset ref
35710 reference "sub:Font-Styles"
35719 , no matter if they appear in italic text: 30
35720 \begin_inset space \thinspace{}
35724 \begin_inset Newline newline
35727 Between the value and the unit is the smallest space, see
35728 \begin_inset CommandInset ref
35730 reference "sub:Predefined-Space"
35735 \begin_inset Newline newline
35738 This convention is automatically fulfilled when the command
35745 When it is entered to a formula, two boxes appear.
35746 In the first one the value is inserted, in the second one the unit, and
35748 \begin_inset Formula $\unit[30]{km/h}$
35752 \begin_inset space \thinspace{}
35762 is not a real LaTeX command but the command
35768 , therefore you cannot use it in TeX code.
35771 \begin_layout Itemize
35772 Percent and perthousand signs are set like physical units:
35773 \begin_inset Newline newline
35777 \begin_inset space \thinspace{}
35783 \begin_layout Itemize
35784 The degree sign follows directly on the value: 15°, but not when it is used
35786 \begin_inset space \thinspace{}
35792 \begin_layout Itemize
35793 In numbers with more than four digits the smallest space is inserted before
35794 every third digit to group them:
35804 \begin_inset space \thinspace{}
35808 \begin_inset space \thinspace{}
35814 \begin_layout Itemize
35815 For dimensions like 120×90×40
35816 \begin_inset space \thinspace{}
35819 cm the multiplication sign
35820 \begin_inset Quotes eld
35824 \begin_inset Quotes erd
35828 It is available either via the command
35836 Insert\SpecialChar \menuseparator
35837 Special Character\SpecialChar \menuseparator
35843 \begin_layout Itemize
35844 Functions with names consisting of several letters are set upright to avoid
35846 \begin_inset CommandInset ref
35848 reference "sub:Predefined-Functions"
35855 \begin_layout Itemize
35856 Indices consisting of several letters, are set upright:
35857 \begin_inset Formula $E_{\mathrm{kin}}$
35861 \begin_inset Newline newline
35864 Components of matrices are set italic:
35865 \begin_inset Formula $\hat{H}_{kl}$
35871 \begin_layout Itemize
35872 The differentiation/integration operator 'd', the Euler's number 'e' and
35873 the imaginary unit 'i' should be set upright, to avoid mixing them up with
35877 \begin_layout Itemize
35878 The character that denotes a
35882 transformation is inserted either by the command
35887 \begin_inset space \textvisiblespace{}
35894 Insert\SpecialChar \menuseparator
35895 Special Character\SpecialChar \menuseparator
35896 Symbols\SpecialChar \menuseparator
35898 \begin_inset space ~
35904 \begin_inset Formula $\mathscr{F}$
35910 \begin_layout Standard
35911 \begin_inset Newpage newpage
35917 \begin_layout Section
35919 \begin_inset Index idx
35922 \begin_layout Plain Layout
35931 \begin_layout Standard
35932 Some characters and symbols can be created with several commands.
35933 Here is a list of the synonym commands:
35936 \begin_layout Standard
35937 \begin_inset VSpace bigskip
35941 \begin_inset space \hfill{}
35945 \begin_inset Tabular
35946 <lyxtabular version="3" rows="12" columns="2">
35947 <features rotate="0" tabularvalignment="middle">
35948 <column alignment="center" valignment="top" width="0pt">
35949 <column alignment="center" valignment="top" width="0pt">
35951 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
35954 \begin_layout Plain Layout
35960 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
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