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
3466 arg "math-insert \\space"
3475 \begin_inset Graphics
3476 filename ../images/math/phantom.png
3481 that creates one or more phantom characters.
3488 a small blue box appears that is superposed with two red arrows.
3489 The arrows indicate that the complete width and height of the box content
3490 will be created as placeholder.
3491 Phantom characters are accordingly placeholders with the size of the characters.
3494 \begin_layout Standard
3496 \begin_inset Tabular
3497 <lyxtabular version="3" rows="4" columns="2">
3498 <features rotate="0" tabularvalignment="middle">
3499 <column alignment="center" valignment="top">
3500 <column alignment="center" valignment="top">
3502 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
3505 \begin_layout Plain Layout
3511 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
3514 \begin_layout Plain Layout
3516 \begin_inset Note Note
3519 \begin_layout Plain Layout
3526 is only used as spacer.
3538 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
3541 \begin_layout Plain Layout
3543 \begin_inset space \textvisiblespace{}
3549 \begin_inset space \textvisiblespace{}
3553 \begin_inset Formula $\to$
3557 \begin_inset space \textvisiblespace{}
3565 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
3568 \begin_layout Plain Layout
3569 \begin_inset Formula $\raisebox{4.5mm}{}{}_{\phantom{1}9}^{19}\mathrm{F}\raisebox{-2.5mm}{}$
3579 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
3582 \begin_layout Plain Layout
3584 \begin_inset space \textvisiblespace{}
3590 \begin_inset space \textvisiblespace{}
3594 \begin_inset Formula $\to$
3598 \begin_inset space \textvisiblespace{}
3606 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
3609 \begin_layout Plain Layout
3610 \begin_inset Formula $\raisebox{4.5mm}{}{}_{\phantom{23}9}^{235}\mathrm{F}\raisebox{-2.5mm}{}$
3620 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
3623 \begin_layout Plain Layout
3627 \begin_inset space \textvisiblespace{}
3633 \begin_inset space \textvisiblespace{}
3637 \begin_inset Formula $\to$
3641 \begin_inset space \textvisiblespace{}
3649 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
3652 \begin_layout Plain Layout
3653 \begin_inset Formula $\raisebox{4.5mm}{}\Lambda_{MMt}^{\phantom{ii}t}\raisebox{-2.5mm}{}$
3669 \begin_layout Standard
3670 Furthermore there are the commands
3677 \begin_inset Index idx
3680 \begin_layout Plain Layout
3689 \begin_inset space ~
3693 \begin_inset Graphics
3694 filename ../images/math/vphantom.png
3706 \begin_inset Index idx
3709 \begin_layout Plain Layout
3718 \begin_inset space ~
3722 \begin_inset Graphics
3723 filename ../images/math/hphantom.png
3735 creates only space for the maximal height of the characters in the box
3736 but not for its width.
3743 creates only space for the width of the box content.
3744 Therefore the boxes of both commands have only one red arrow.
3747 \begin_layout Standard
3748 For example the command
3753 \begin_inset space \textvisiblespace{}
3760 creates space for the height of the integral sign,
3764 \begin_layout Plain Layout
3771 creates an integral sign, see
3772 \begin_inset CommandInset ref
3774 reference "sub:Big-Operators"
3783 because this is the larger character.
3784 An example application is in
3785 \begin_inset CommandInset ref
3787 reference "sub:Multiline-Brackets"
3794 \begin_layout Standard
3795 Placeholders can also be used for text when they are inserted via the menu
3798 Insert\SpecialChar \menuseparator
3799 Formatting\SpecialChar \menuseparator
3805 \begin_layout Standard
3807 \begin_inset Newline newline
3811 \begin_inset Phantom Phantom
3814 \begin_layout Plain Layout
3823 \begin_layout Subsection
3825 \begin_inset Index idx
3828 \begin_layout Plain Layout
3835 \begin_inset Index idx
3838 \begin_layout Plain Layout
3839 Formula ! underlined
3847 \begin_layout Standard
3849 \begin_inset Tabular
3850 <lyxtabular version="3" rows="4" columns="2">
3851 <features rotate="0" tabularvalignment="middle">
3852 <column alignment="center" valignment="top" width="0pt">
3853 <column alignment="center" valignment="top" width="0pt">
3855 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
3858 \begin_layout Plain Layout
3864 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
3867 \begin_layout Plain Layout
3869 \begin_inset Note Note
3872 \begin_layout Plain Layout
3879 is only used as spacer.
3891 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
3894 \begin_layout Plain Layout
3898 \begin_inset space \textvisiblespace{}
3902 \begin_inset Index idx
3905 \begin_layout Plain Layout
3918 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
3921 \begin_layout Plain Layout
3922 \begin_inset Formula $\raisebox{5mm}{}\overline{A+B}$
3932 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
3935 \begin_layout Plain Layout
3939 \begin_inset space \textvisiblespace{}
3943 \begin_inset Index idx
3946 \begin_layout Plain Layout
3959 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
3962 \begin_layout Plain Layout
3963 \begin_inset Formula $\underline{A+B}\raisebox{-2.5mm}{}$
3973 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
3976 \begin_layout Plain Layout
3980 \begin_inset space \textvisiblespace{}
3986 \begin_inset space \textvisiblespace{}
3994 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
3997 \begin_layout Plain Layout
3998 \begin_inset Formula $\raisebox{5mm}{}\overline{\underline{A+B}}\raisebox{-2.5mm}{}$
4014 \begin_layout Standard
4015 In the last example it doesn't matter if first
4030 \begin_layout Standard
4031 To double underline use
4040 \begin_layout Standard
4041 It is possible to place up to 6 lines above or below characters.
4044 \begin_layout Standard
4045 \begin_inset VSpace bigskip
4048 Custom lines can be created using the command
4055 \begin_inset Index idx
4058 \begin_layout Plain Layout
4066 which has the following scheme:
4069 \begin_layout Standard
4074 rule[vertical offset]{length}{thickness}
4077 \begin_layout Standard
4078 The optional vertical offset shifts the line upwards (or downwards, when
4079 the value is negative).
4081 \begin_inset CommandInset ref
4083 reference "tab:Available-units"
4087 can be used for the values.
4088 Here are two example lines created with the commands
4089 \begin_inset Newline newline
4096 rule[-2ex]{3cm}{2pt}
4107 \begin_layout Standard
4109 \begin_inset Formula $\rule[-2ex]{3cm}{2pt}\rule{2cm}{1pt}$
4115 \begin_layout Standard
4122 can also be used for text when a line is inserted via the menu
4124 Insert\SpecialChar \menuseparator
4125 Formatting\SpecialChar \menuseparator
4127 \begin_inset space ~
4135 \begin_layout Standard
4137 \begin_inset CommandInset line
4148 \begin_layout Subsection
4150 \begin_inset CommandInset label
4157 \begin_inset Index idx
4160 \begin_layout Plain Layout
4169 \begin_layout Standard
4170 There are different types of ellipses available.
4174 \begin_layout Plain Layout
4175 In the math toolbar in the submenu of the button
4178 arg "math-insert \\ldots"
4186 For listings dots at the baseline are used (
4193 \begin_inset Index idx
4196 \begin_layout Plain Layout
4204 ), while for operations dots are needed that are on the same height as the
4212 \begin_inset Index idx
4215 \begin_layout Plain Layout
4224 When using the command
4231 \begin_inset Index idx
4234 \begin_layout Plain Layout
4242 , LaTeX decides on the basis of the next character what type is used.
4245 \begin_layout Standard
4247 \begin_inset Tabular
4248 <lyxtabular version="3" rows="9" columns="2">
4249 <features rotate="0" tabularvalignment="middle">
4250 <column alignment="center" valignment="top" width="0pt">
4251 <column alignment="center" valignment="top" width="0pt">
4253 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
4256 \begin_layout Plain Layout
4262 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
4265 \begin_layout Plain Layout
4273 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
4276 \begin_layout Plain Layout
4278 \begin_inset space \textvisiblespace{}
4284 \begin_inset space \textvisiblespace{}
4292 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
4295 \begin_layout Plain Layout
4296 \begin_inset Formula $A_{1},\dots,A_{n}$
4306 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
4309 \begin_layout Plain Layout
4311 \begin_inset space \textvisiblespace{}
4317 \begin_inset space \textvisiblespace{}
4325 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
4328 \begin_layout Plain Layout
4329 \begin_inset Formula $A_{1}+\dots+A_{n}$
4339 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
4342 \begin_layout Plain Layout
4344 \begin_inset space \textvisiblespace{}
4350 \begin_inset space \textvisiblespace{}
4358 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
4361 \begin_layout Plain Layout
4362 \begin_inset Formula $A_{1},\ldots,A_{n}$
4372 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
4375 \begin_layout Plain Layout
4377 \begin_inset space \textvisiblespace{}
4383 \begin_inset space \textvisiblespace{}
4391 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
4394 \begin_layout Plain Layout
4395 \begin_inset Formula $A_{1}+\cdots+A_{n}$
4405 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
4408 \begin_layout Plain Layout
4416 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
4419 \begin_layout Plain Layout
4420 \begin_inset Formula $\vdots$
4430 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
4433 \begin_layout Plain Layout
4441 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
4444 \begin_layout Plain Layout
4445 \begin_inset Formula $\ddots$
4455 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
4458 \begin_layout Plain Layout
4466 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
4469 \begin_layout Plain Layout
4470 \begin_inset Formula $\iddots$
4480 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
4483 \begin_layout Plain Layout
4485 \begin_inset space \thinspace{}
4488 matrix with the different dots
4493 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
4496 \begin_layout Plain Layout
4497 \begin_inset Formula $\begin{array}{ccc}
4498 A_{11} & \cdots & A_{1m}\\
4499 \vdots & \ddots & \vdots\\
4500 A_{n1} & \cdots & A_{nm}
4517 \begin_layout Standard
4518 The ellipses available in menu
4520 Insert\SpecialChar \menuseparator
4522 \begin_inset space ~
4536 \begin_layout Standard
4537 \begin_inset VSpace medskip
4546 , one of the options
4548 Use mathdots package (automatically)
4550 must be set in the document settings under
4553 \begin_inset space ~
4559 \begin_inset Newline newline
4564 Use mathdots package
4566 will improve the appearance of all dots in the documents if their font
4567 style or size is not the default.
4570 \begin_layout Standard
4571 \begin_inset VSpace medskip
4574 Specially for matrices there are ellipses that span over several columns.
4575 They are created with the command
4582 \begin_inset Index idx
4585 \begin_layout Plain Layout
4593 , that has the following scheme:
4596 \begin_layout Standard
4601 hdotsfor[distance]{number of columns}
4604 \begin_layout Standard
4605 The number of columns specifies how many columns should be spanned.
4606 Distance is a factor for the distance between the dots.
4609 \begin_layout Standard
4610 In the following matrix the command
4616 was inserted in the first box of the second line, to get an ellipsis with
4617 a dot distance twice as long as with the command
4624 \begin_inset Formula
4626 \left(\begin{array}{cccc}
4635 Note that the matrix fields that should be spanned must be empty, otherwise
4636 you get LaTeX-errors.
4639 \begin_layout Standard
4640 \begin_inset VSpace bigskip
4643 Furthermore you can fill with the command
4650 \begin_inset Index idx
4653 \begin_layout Plain Layout
4661 the rest of a line with dots.
4662 The effect of these commands is the same as with
4669 \begin_inset CommandInset ref
4671 reference "sub:Variable-Space"
4678 \begin_layout Standard
4679 For example the command
4684 \begin_inset space \textvisiblespace{}
4692 \begin_layout Standard
4693 \begin_inset Formula $A\dotfill B$
4699 \begin_layout Standard
4706 there is for a line the command
4713 \begin_inset Index idx
4716 \begin_layout Plain Layout
4727 \begin_layout Standard
4728 \begin_inset Formula $A\hrulefill B$
4734 \begin_layout Standard
4735 To use the commands for text, they have to be inserted in TeX-mode.
4738 \begin_layout Section
4740 \begin_inset CommandInset label
4747 \begin_inset Index idx
4750 \begin_layout Plain Layout
4759 \begin_layout Standard
4760 Matrices can be inserted via the math toolbar button
4763 arg "dialog-show mathmatrix"
4768 Insert\SpecialChar \menuseparator
4769 Math\SpecialChar \menuseparator
4773 In the matrix dialog you can specify the number of columns and rows, the
4774 alignment and the decoration.
4775 The vertical alignment is only of importance for matrices in inline formulas:
4778 \begin_layout Standard
4779 The first matrix is top
4780 \begin_inset Formula $\begin{array}[t]{cccc}
4788 \begin_inset Formula $\begin{array}{cccc}
4795 and the third bottom
4796 \begin_inset Formula $\begin{array}[b]{cccc}
4806 \begin_layout Standard
4807 The horizontal alignment specifies how the column entries should be aligned.
4808 It is set by entering a letter for every column.
4813 denotes left aligned,
4822 To create for example a 4
4827 \begin_inset space ~
4830 matrix where the first column is left aligned, the second and third are
4831 centered and the last one is right aligned, one enters for the horizontal
4837 Normally in a matrix all columns are centered, therefore the default for
4845 \begin_layout Standard
4846 Horizontal alignment:
4849 \begin_layout Standard
4855 \begin_inset Formula $\begin{array}{lll}
4867 \begin_inset Formula $\begin{array}{ccc}
4879 \begin_inset Formula $\begin{array}{rrr}
4889 \begin_layout Standard
4890 To add or delete rows and columns subsequently, the math toolbar buttons
4894 arg "inset-modify tabular append-row"
4900 arg "inset-modify tabular delete-row"
4904 \begin_inset space \thinspace{}
4909 Edit\SpecialChar \menuseparator
4913 New rows can also be created with
4916 arg "newline-insert newline"
4922 \begin_layout Standard
4923 \begin_inset VSpace bigskip
4930 adds parentheses in the selected style around the matrix.
4931 Alternatively, parentheses can can either be created with the commands
4939 \begin_inset Index idx
4942 \begin_layout Plain Layout
4957 \begin_inset Index idx
4960 \begin_layout Plain Layout
4971 \begin_inset space ~
4977 \begin_inset CommandInset ref
4979 reference "sub:Automatic-Bracket-Size"
4983 , or by using the following commands:
4984 \begin_inset VSpace medskip
4990 \begin_layout Standard
4991 \begin_inset space \hfill{}
4995 \begin_inset Tabular
4996 <lyxtabular version="3" rows="4" columns="2">
4997 <features rotate="0" tabularvalignment="middle">
4998 <column alignment="center" valignment="top">
4999 <column alignment="center" valignment="top">
5001 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
5004 \begin_layout Plain Layout
5010 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
5013 \begin_layout Plain Layout
5015 \begin_inset Note Note
5018 \begin_layout Plain Layout
5025 is only used as spacer.
5037 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
5040 \begin_layout Plain Layout
5044 \begin_inset space \textvisiblespace{}
5052 \begin_inset space \thinspace{}
5060 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
5063 \begin_layout Plain Layout
5064 \begin_inset Formula $\raisebox{7.5mm}{}\begin{bmatrix}\begin{array}{cc}
5065 0 & \textrm{-}\mathrm{i}\\
5067 \end{array}\end{bmatrix}\raisebox{-5.3mm}{}$
5077 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
5080 \begin_layout Plain Layout
5084 \begin_inset space \textvisiblespace{}
5092 \begin_inset space \thinspace{}
5100 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
5103 \begin_layout Plain Layout
5104 \begin_inset Formula $\raisebox{7.5mm}{}\begin{Bmatrix}\begin{array}{cc}
5105 0 & \textrm{-}\mathrm{i}\\
5107 \end{array}\end{Bmatrix}\raisebox{-5.3mm}{}$
5117 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
5120 \begin_layout Plain Layout
5124 \begin_inset space \textvisiblespace{}
5132 \begin_inset space \thinspace{}
5140 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
5143 \begin_layout Plain Layout
5144 \begin_inset Formula $\raisebox{7.5mm}{}\begin{pmatrix}\begin{array}{cc}
5145 0 & \textrm{-}\mathrm{i}\\
5147 \end{array}\end{pmatrix}\raisebox{-5.3mm}{}$
5161 \begin_inset space \hfill{}
5165 \begin_inset Tabular
5166 <lyxtabular version="3" rows="4" columns="2">
5167 <features rotate="0" tabularvalignment="middle">
5168 <column alignment="center" valignment="top">
5169 <column alignment="center" valignment="top">
5171 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
5174 \begin_layout Plain Layout
5180 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
5183 \begin_layout Plain Layout
5191 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
5194 \begin_layout Plain Layout
5198 \begin_inset space \textvisiblespace{}
5206 \begin_inset space \thinspace{}
5214 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
5217 \begin_layout Plain Layout
5218 \begin_inset Formula $\raisebox{7.5mm}{}\begin{vmatrix}\begin{array}{cc}
5219 0 & \textrm{-}\mathrm{i}\\
5221 \end{array}\end{vmatrix}\raisebox{-5.3mm}{}$
5231 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
5234 \begin_layout Plain Layout
5238 \begin_inset space \textvisiblespace{}
5246 \begin_inset space \thinspace{}
5254 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
5257 \begin_layout Plain Layout
5258 \begin_inset Formula $\raisebox{7.5mm}{}\begin{Vmatrix}\begin{array}{cc}
5259 0 & \textrm{-}\mathrm{i}\\
5261 \end{array}\end{Vmatrix}\raisebox{-5.3mm}{}$
5271 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
5274 \begin_layout Plain Layout
5278 \begin_inset space \textvisiblespace{}
5286 \begin_inset space \thinspace{}
5294 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
5297 \begin_layout Plain Layout
5298 \begin_inset Formula $\raisebox{7.5mm}{}\begin{matrix}\begin{array}{cc}
5299 0 & \textrm{-}\mathrm{i}\\
5301 \end{array}\end{matrix}\raisebox{-5.3mm}{}$
5315 \begin_inset space \hfill{}
5321 \begin_layout Standard
5322 \begin_inset VSpace medskip
5326 \begin_inset space \thinspace{}
5330 \begin_inset space \space{}
5339 is inserted, a blue box appears between two vertical lines where the matrix
5341 \begin_inset Newline newline
5344 Note that decorated matrices ignore the vertical alignment.
5347 \begin_layout Standard
5348 \begin_inset VSpace bigskip
5351 As all multiline formulas are matrices, the length
5358 \begin_inset Index idx
5361 \begin_layout Plain Layout
5369 that is described in
5370 \begin_inset CommandInset ref
5372 reference "sub:Column-Separation"
5376 can also be used to change the column separation of matrices.
5379 \begin_layout Standard
5380 To change the row separation, the command
5387 \begin_inset Index idx
5390 \begin_layout Plain Layout
5399 It is used as follows:
5402 \begin_layout Standard
5409 arraystretch}{stretch factor}
5410 \begin_inset Index idx
5413 \begin_layout Plain Layout
5424 \begin_layout Standard
5431 assigns the stretch factor to the predefined command
5439 \begin_inset space \thinspace{}
5443 \begin_inset space \space{}
5446 the row separation, use the factor 2.
5447 This is then used for all following matrices.
5448 To go back to the original separation, assign the factor 1 to
5457 \begin_layout Standard
5458 To set matrices into a text line, the command
5465 \begin_inset Index idx
5468 \begin_layout Plain Layout
5477 When it is inserted a blue box with two dashed lines appears.
5478 In this box the matrix is inserted.
5481 \begin_layout Standard
5483 \begin_inset Formula $\left(\begin{smallmatrix}A & B\\
5485 \end{smallmatrix}\right)$
5491 \begin_layout Section
5492 Brackets and Delimiters
5493 \begin_inset Index idx
5496 \begin_layout Plain Layout
5503 \begin_inset Index idx
5506 \begin_layout Plain Layout
5515 \begin_layout Subsection
5516 Vertical Brackets and Delimiters
5517 \begin_inset Index idx
5520 \begin_layout Plain Layout
5529 \begin_layout Standard
5530 \begin_inset space \hfill{}
5534 \begin_inset Tabular
5535 <lyxtabular version="3" rows="9" columns="2">
5536 <features rotate="0" tabularvalignment="middle">
5537 <column alignment="center" valignment="top" width="0pt">
5538 <column alignment="center" valignment="top" width="0pt">
5540 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
5543 \begin_layout Plain Layout
5549 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
5552 \begin_layout Plain Layout
5560 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
5563 \begin_layout Plain Layout
5569 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
5572 \begin_layout Plain Layout
5573 \begin_inset Formula $($
5583 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
5586 \begin_layout Plain Layout
5592 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
5595 \begin_layout Plain Layout
5596 \begin_inset Formula $\{$
5606 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
5609 \begin_layout Plain Layout
5615 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
5618 \begin_layout Plain Layout
5619 \begin_inset Formula $[$
5629 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
5632 \begin_layout Plain Layout
5640 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
5643 \begin_layout Plain Layout
5644 \begin_inset Formula $\langle$
5654 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
5657 \begin_layout Plain Layout
5665 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
5668 \begin_layout Plain Layout
5669 \begin_inset Formula $\lceil$
5679 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
5682 \begin_layout Plain Layout
5690 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
5693 \begin_layout Plain Layout
5694 \begin_inset Formula $\lfloor$
5704 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
5707 \begin_layout Plain Layout
5713 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
5716 \begin_layout Plain Layout
5717 \begin_inset Formula $/$
5727 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
5730 \begin_layout Plain Layout
5736 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
5739 \begin_layout Plain Layout
5740 \begin_inset Formula $|$
5754 \begin_inset space \hfill{}
5758 \begin_inset Tabular
5759 <lyxtabular version="3" rows="9" columns="2">
5760 <features rotate="0" tabularvalignment="middle">
5761 <column alignment="center" valignment="top" width="0pt">
5762 <column alignment="center" valignment="top" width="0pt">
5764 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
5767 \begin_layout Plain Layout
5773 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
5776 \begin_layout Plain Layout
5784 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
5787 \begin_layout Plain Layout
5793 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
5796 \begin_layout Plain Layout
5797 \begin_inset Formula $)$
5807 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
5810 \begin_layout Plain Layout
5816 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
5819 \begin_layout Plain Layout
5820 \begin_inset Formula $\}$
5830 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
5833 \begin_layout Plain Layout
5839 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
5842 \begin_layout Plain Layout
5843 \begin_inset Formula $]$
5853 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
5856 \begin_layout Plain Layout
5864 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
5867 \begin_layout Plain Layout
5868 \begin_inset Formula $\rangle$
5878 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
5881 \begin_layout Plain Layout
5889 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
5892 \begin_layout Plain Layout
5893 \begin_inset Formula $\rceil$
5903 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
5906 \begin_layout Plain Layout
5914 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
5917 \begin_layout Plain Layout
5918 \begin_inset Formula $\rfloor$
5928 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
5931 \begin_layout Plain Layout
5941 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
5944 \begin_layout Plain Layout
5945 \begin_inset Formula $\backslash$
5955 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
5958 \begin_layout Plain Layout
5966 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
5969 \begin_layout Plain Layout
5970 \begin_inset Formula $\|$
5984 \begin_inset space \hfill{}
5990 \begin_layout Standard
5993 \begin_inset Note Greyedout
5996 \begin_layout Plain Layout
6001 In TeX-mode the command
6008 \begin_inset Index idx
6011 \begin_layout Plain Layout
6019 must be used for the backslash, because the command
6027 produces a line break there.
6035 \begin_layout Standard
6036 For all characters listed above the size can be adjusted with the commands
6037 described in the following two subsections.
6038 When using these commands, the characters < and > can directly be used
6039 instead of the commands
6054 \begin_layout Subsubsection
6056 \begin_inset CommandInset label
6058 name "sub:Manual-Bracket-Size"
6063 \begin_inset Index idx
6066 \begin_layout Plain Layout
6067 Bracket size ! manual
6075 \begin_layout Standard
6076 The bracket size can be specified manually by the LaTeX-commands
6083 \begin_inset Index idx
6086 \begin_layout Plain Layout
6119 denotes the smallest and
6125 the largest bracket size.
6128 \begin_layout Standard
6129 These commands are used to emphasize levels of brackets:
6132 \begin_layout Standard
6134 \begin_inset Tabular
6135 <lyxtabular version="3" rows="2" columns="2">
6136 <features rotate="0" tabularvalignment="middle">
6137 <column alignment="center" valignment="top" width="0pt">
6138 <column alignment="center" valignment="top" width="0pt">
6140 <cell alignment="center" valignment="top" usebox="none">
6143 \begin_layout Plain Layout
6144 all brackets in the same size:
6149 <cell alignment="center" valignment="top" usebox="none">
6152 \begin_layout Plain Layout
6153 \begin_inset Formula $((A+B)(A-B))^{C}\raisebox{-4mm}{}$
6163 <cell alignment="center" valignment="top" usebox="none">
6166 \begin_layout Plain Layout
6172 <cell alignment="center" valignment="top" usebox="none">
6175 \begin_layout Plain Layout
6176 \begin_inset Formula $\Big((A+B)(A-B)\Big)^{C}$
6190 \begin_inset Note Note
6193 \begin_layout Plain Layout
6200 is only used as spacer.
6208 \begin_layout Standard
6209 For the second formula the command
6216 \begin_inset space \textvisiblespace{}
6224 \begin_layout Standard
6225 Here is an overview about all bracket sizes:
6228 \begin_layout Standard
6245 \begin_inset space \textvisiblespace{}
6253 \begin_inset space \textvisiblespace{}
6257 \begin_inset space \textvisiblespace{}
6267 \begin_layout Standard
6269 \begin_inset Formula $\Bigg(\exp\bigg<\Big[\big\{\ln(3x)\big\}^{2}\sin(x)\Big]^{A}\bigg>\Bigg)^{0,5}$
6275 \begin_layout Standard
6282 -commands there is the variant
6289 \begin_inset Index idx
6292 \begin_layout Plain Layout
6300 that adds a bit more space between the bracket and its content, and the
6314 \begin_inset Index idx
6317 \begin_layout Plain Layout
6327 , that don't add additional space.
6332 at the end of the command
6338 is for a left bracket; for a right bracket this will be replaced by an
6344 A left or right bracket can each be an opening or closing bracket.
6347 \begin_layout Standard
6348 In the following table is a comparison of the variants:
6351 \begin_layout Standard
6353 \begin_inset Tabular
6354 <lyxtabular version="3" rows="5" columns="2">
6355 <features rotate="0" tabularvalignment="middle">
6356 <column alignment="center" valignment="middle">
6357 <column alignment="center" valignment="middle">
6359 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
6362 \begin_layout Plain Layout
6368 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
6371 \begin_layout Plain Layout
6373 \begin_inset Note Note
6376 \begin_layout Plain Layout
6383 is only used as spacer.
6395 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
6398 \begin_layout Plain Layout
6408 \begin_inset space \textvisiblespace{}
6418 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
6421 \begin_layout Plain Layout
6422 \begin_inset Formula $\raisebox{5.5mm}{}\Bigm(\bigm(\ln(3x)\bigm)^{2}\Bigm)\raisebox{-3.25mm}{}$
6432 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
6435 \begin_layout Plain Layout
6445 \begin_inset space \textvisiblespace{}
6455 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
6458 \begin_layout Plain Layout
6459 \begin_inset Formula $\raisebox{5.5mm}{}\Big(\big(\ln(3x)\big)^{2}\Big)\raisebox{-3.25mm}{}$
6469 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
6472 \begin_layout Plain Layout
6482 \begin_inset space \textvisiblespace{}
6492 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
6495 \begin_layout Plain Layout
6496 \begin_inset Formula $\raisebox{5.5mm}{}\Bigl(\bigl(\ln(3x)\bigr)^{2}\Bigr)\raisebox{-3.25mm}{}$
6506 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
6509 \begin_layout Plain Layout
6521 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
6524 \begin_layout Plain Layout
6525 \begin_inset Formula $\raisebox{4.5mm}{}\bigl)\ln(3x)\bigr(\raisebox{-2mm}{}$
6541 \begin_layout Subsubsection
6542 Automatic Bracket Size
6543 \begin_inset CommandInset label
6545 name "sub:Automatic-Bracket-Size"
6550 \begin_inset Index idx
6553 \begin_layout Plain Layout
6554 Bracket size ! automatic
6562 \begin_layout Standard
6563 Brackets with variable size can be inserted with the commands
6570 \begin_inset Index idx
6573 \begin_layout Plain Layout
6588 \begin_inset Index idx
6591 \begin_layout Plain Layout
6599 or via the math toolbar button
6602 arg "dialog-show mathdelimiter"
6618 the wanted bracket must be inserted.
6619 The bracket size will then automatically be calculated for the output.
6622 \begin_layout Standard
6624 normal bracket: The command
6631 \begin_inset space \textvisiblespace{}
6635 \begin_inset Formula $\downarrow$
6639 \begin_inset space \textvisiblespace{}
6645 \begin_inset Formula
6655 \begin_layout Standard
6657 multiline bracket: The command
6666 \begin_inset space \textvisiblespace{}
6670 \begin_inset Formula $\downarrow$
6674 \begin_inset space \textvisiblespace{}
6682 \begin_inset Formula
6684 \ln\left(\frac{A}{C}\right)
6692 \begin_layout Standard
6708 \begin_inset space ~
6714 This has the advantage that you can see in LyX immediately the real bracket
6715 size and that the matching right bracket will be created too.
6716 \begin_inset Newline newline
6719 The command for the last example would then be:
6730 \begin_inset space \textvisiblespace{}
6734 \begin_inset Formula $\downarrow$
6740 \begin_layout Standard
6741 To omit a left or right bracket, a dot is inserted for the omitted bracket.
6742 For example the command
6749 \begin_inset space \textvisiblespace{}
6753 \begin_inset Formula $\downarrow$
6757 \begin_inset space \textvisiblespace{}
6767 \begin_inset Formula
6769 \left.\frac{A}{B}\right\}
6788 will be converted by LyX to brackets in the right size when the document
6789 is reloaded and an omitted bracket will appear as dashed line.
6792 \begin_layout Standard
6793 \begin_inset VSpace bigskip
6796 Because all popular LaTeX-Distributions use eTeX, an extension to LaTeX,
6804 \begin_inset Index idx
6807 \begin_layout Plain Layout
6815 is additionally available for all brackets and limits.
6816 With this command the height of the following character is adapted to the
6817 one of the surrounding brackets, what is e.
6818 \begin_inset space \thinspace{}
6822 \begin_inset space \space{}
6825 needed for physical vectors:
6826 \begin_inset Formula
6828 \left\langle \phi\:\middle|\: J=\frac{3}{2}\,,\, M_{J}\right\rangle
6833 For physical vectors there is a special LaTeX-package, described in
6834 \begin_inset CommandInset ref
6836 reference "sub:Physical-Vectors"
6843 \begin_layout Subsection
6845 \begin_inset Index idx
6848 \begin_layout Plain Layout
6849 Brackets ! horizontal
6857 \begin_layout Standard
6859 \begin_inset Tabular
6860 <lyxtabular version="3" rows="4" columns="2">
6861 <features rotate="0" tabularvalignment="middle">
6862 <column alignment="center" valignment="top" width="0pt">
6863 <column alignment="center" valignment="top" width="0pt">
6865 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
6868 \begin_layout Plain Layout
6870 \begin_inset Note Note
6873 \begin_layout Plain Layout
6880 is only used as spacer.
6890 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
6893 \begin_layout Plain Layout
6901 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
6904 \begin_layout Plain Layout
6908 \begin_layout Plain Layout
6920 \begin_inset space \textvisiblespace{}
6924 \begin_inset space \textvisiblespace{}
6931 \begin_layout Plain Layout
6939 \begin_inset Index idx
6942 \begin_layout Plain Layout
6955 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
6958 \begin_layout Plain Layout
6959 \begin_inset Formula $\overbrace{A+B}^{3}$
6969 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
6972 \begin_layout Plain Layout
6976 \begin_layout Plain Layout
6988 \begin_inset space \textvisiblespace{}
6992 \begin_inset space \textvisiblespace{}
6999 \begin_layout Plain Layout
7007 \begin_inset Index idx
7010 \begin_layout Plain Layout
7023 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
7026 \begin_layout Plain Layout
7027 \begin_inset Formula $\underbrace{A+B}_{5}$
7037 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
7040 \begin_layout Plain Layout
7044 \begin_inset space \textvisiblespace{}
7050 \begin_inset space \textvisiblespace{}
7054 \begin_inset space \textvisiblespace{}
7058 \begin_inset space \textvisiblespace{}
7062 \begin_inset space \textvisiblespace{}
7066 \begin_inset space \textvisiblespace{}
7070 \begin_inset space \textvisiblespace{}
7078 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
7081 \begin_layout Plain Layout
7082 \begin_inset Formula $\overbrace{\underbrace{A+B_{w}}_{7}}^{C}$
7098 \begin_layout Standard
7099 In the last example it doesn't matter if
7111 is inserted at first.
7114 \begin_layout Standard
7115 \begin_inset VSpace bigskip
7118 When brackets are needed that overlap each other, multiline formulas, as
7120 \begin_inset CommandInset ref
7122 reference "sec:Multiline-Formulas"
7127 \begin_inset Formula
7129 A & = & \underbrace{gggg+bbqq}_{r}+\: dddd\\
7130 & & \hphantom{gggg+\:}\underbrace{\hphantom{bbqq+dddd}}_{s}
7135 In the first row the formula is inserted together with the first brace.
7136 It is hereby important that the space command
7140 \begin_layout Plain Layout
7141 Space commands are explained in
7142 \begin_inset CommandInset ref
7144 reference "sub:Predefined-Space"
7159 is inserted before the first
7160 \begin_inset Formula $d$
7163 , because the brace that ends behind the
7164 \begin_inset Formula $q$
7167 prevents that the following
7168 \begin_inset Quotes eld
7172 \begin_inset Quotes erd
7175 is surrounded by space.
7179 \begin_layout Plain Layout
7180 because a bracket is not handled as a character, see
7181 \begin_inset CommandInset ref
7183 reference "sub:Binary-Operators"
7192 In the second row the second brace is inserted.
7193 As it should begin before the
7194 \begin_inset Formula $b$
7209 \begin_layout Plain Layout
7217 \begin_inset CommandInset ref
7219 reference "sub:Placeholders"
7228 This space is needed because the
7229 \begin_inset Quotes eld
7233 \begin_inset Quotes erd
7236 is also surrounded by space in the formula.
7237 The brace is placed under the command
7246 \begin_layout Standard
7247 It gets more complicated when brackets overlap each other, like in the following
7252 \begin_layout Plain Layout
7264 \begin_inset Formula
7266 & & \hphantom{gggg+\:}\overbrace{\hphantom{bbqq+dddd}}^{s}\\
7267 A & = & \underbrace{gggg+bbqq}_{r}+\: dddd
7276 \begin_layout Plain Layout
7287 The first formula row is the same as the second row of the previous example,
7288 with the difference that the brace is above.
7289 The second row contains the formula together with the second brace.
7290 To avoid that there is space between the upper brace in the first row and
7291 the formula, the row spacing needs to be reduced.
7292 This is not easily possible due to a bug in LyX
7296 \begin_layout Plain Layout
7297 \begin_inset CommandInset href
7299 name "LyX-bug #1505"
7300 target "http://www.lyx.org/trac/ticket/1505"
7310 As a solution for the problem, the global formula row separation
7317 \begin_inset Index idx
7320 \begin_layout Plain Layout
7328 must be changed to -6
7329 \begin_inset space \thinspace{}
7332 pt before the formula with the command
7347 is set back after the formula to the standard value of 3
7348 \begin_inset space \thinspace{}
7351 pt using the same command.
7352 More about the row separation in formulas is explained in
7353 \begin_inset CommandInset ref
7355 reference "sub:Line-Separation"
7362 \begin_layout Section
7364 \begin_inset Index idx
7367 \begin_layout Plain Layout
7376 \begin_layout Standard
7377 Arrows can be inserted via the math toolbar button
7380 arg "math-insert \\leftarrow"
7383 or the commands listed in the following subsections.
7386 \begin_layout Subsection
7388 \begin_inset Index idx
7391 \begin_layout Plain Layout
7400 \begin_layout Standard
7401 \begin_inset space \hfill{}
7405 \begin_inset Tabular
7406 <lyxtabular version="3" rows="8" columns="2">
7407 <features rotate="0" tabularvalignment="middle">
7408 <column alignment="center" valignment="top" width="0pt">
7409 <column alignment="center" valignment="top" width="0pt">
7411 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
7414 \begin_layout Plain Layout
7420 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
7423 \begin_layout Plain Layout
7431 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
7434 \begin_layout Plain Layout
7442 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
7445 \begin_layout Plain Layout
7446 \begin_inset Formula $\gets$
7456 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
7459 \begin_layout Plain Layout
7467 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
7470 \begin_layout Plain Layout
7471 \begin_inset Formula $\Leftarrow$
7481 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
7484 \begin_layout Plain Layout
7492 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
7495 \begin_layout Plain Layout
7496 \begin_inset Formula $\longleftarrow$
7506 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
7509 \begin_layout Plain Layout
7517 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
7520 \begin_layout Plain Layout
7521 \begin_inset Formula $\Longleftarrow$
7531 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
7534 \begin_layout Plain Layout
7542 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
7545 \begin_layout Plain Layout
7546 \begin_inset Formula $\leftharpoonup$
7556 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
7559 \begin_layout Plain Layout
7567 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
7570 \begin_layout Plain Layout
7571 \begin_inset Formula $\leftharpoondown$
7581 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
7584 \begin_layout Plain Layout
7592 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
7595 \begin_layout Plain Layout
7596 \begin_inset Formula $\hookleftarrow$
7610 \begin_inset space \hfill{}
7614 \begin_inset Tabular
7615 <lyxtabular version="3" rows="8" columns="2">
7616 <features rotate="0" tabularvalignment="middle">
7617 <column alignment="center" valignment="top" width="0pt">
7618 <column alignment="center" valignment="top" width="0pt">
7620 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
7623 \begin_layout Plain Layout
7629 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
7632 \begin_layout Plain Layout
7640 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
7643 \begin_layout Plain Layout
7651 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
7654 \begin_layout Plain Layout
7655 \begin_inset Formula $\to$
7665 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
7668 \begin_layout Plain Layout
7676 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
7679 \begin_layout Plain Layout
7680 \begin_inset Formula $\Rightarrow$
7690 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
7693 \begin_layout Plain Layout
7701 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
7704 \begin_layout Plain Layout
7705 \begin_inset Formula $\longrightarrow$
7715 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
7718 \begin_layout Plain Layout
7726 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
7729 \begin_layout Plain Layout
7730 \begin_inset Formula $\Longrightarrow$
7740 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
7743 \begin_layout Plain Layout
7751 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
7754 \begin_layout Plain Layout
7755 \begin_inset Formula $\rightharpoonup$
7765 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
7768 \begin_layout Plain Layout
7776 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
7779 \begin_layout Plain Layout
7780 \begin_inset Formula $\rightharpoondown$
7790 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
7793 \begin_layout Plain Layout
7801 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
7804 \begin_layout Plain Layout
7805 \begin_inset Formula $\hookrightarrow$
7819 \begin_inset space \hfill{}
7825 \begin_layout Standard
7826 \begin_inset space \hfill{}
7830 \begin_inset Tabular
7831 <lyxtabular version="3" rows="6" columns="2">
7832 <features rotate="0" tabularvalignment="middle">
7833 <column alignment="center" valignment="top" width="0pt">
7834 <column alignment="center" valignment="top" width="0pt">
7836 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
7839 \begin_layout Plain Layout
7845 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
7848 \begin_layout Plain Layout
7856 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
7859 \begin_layout Plain Layout
7867 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
7870 \begin_layout Plain Layout
7871 \begin_inset Formula $\leftrightarrow$
7881 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
7884 \begin_layout Plain Layout
7892 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
7895 \begin_layout Plain Layout
7896 \begin_inset Formula $\Leftrightarrow$
7906 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
7909 \begin_layout Plain Layout
7917 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
7920 \begin_layout Plain Layout
7921 \begin_inset Formula $\longleftrightarrow$
7931 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
7934 \begin_layout Plain Layout
7942 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
7945 \begin_layout Plain Layout
7946 \begin_inset Formula $\Longleftrightarrow$
7956 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
7959 \begin_layout Plain Layout
7967 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
7970 \begin_layout Plain Layout
7971 \begin_inset Formula $\rightleftharpoons$
7985 \begin_inset space \hspace{}
7990 \begin_inset space \hfill{}
7994 \begin_inset Tabular
7995 <lyxtabular version="3" rows="5" columns="2">
7996 <features rotate="0" tabularvalignment="middle">
7997 <column alignment="center" valignment="top" width="0pt">
7998 <column alignment="center" valignment="top" width="0pt">
8000 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
8003 \begin_layout Plain Layout
8009 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
8012 \begin_layout Plain Layout
8020 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
8023 \begin_layout Plain Layout
8031 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
8034 \begin_layout Plain Layout
8035 \begin_inset Formula $\mapsto$
8045 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
8048 \begin_layout Plain Layout
8056 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
8059 \begin_layout Plain Layout
8060 \begin_inset Formula $\longmapsto$
8070 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
8073 \begin_layout Plain Layout
8081 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
8084 \begin_layout Plain Layout
8085 \begin_inset Formula $\leadsto$
8095 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
8098 \begin_layout Plain Layout
8106 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
8109 \begin_layout Plain Layout
8110 \begin_inset Formula $\dasharrow$
8124 \begin_inset space \hfill{}
8130 \begin_layout Standard
8131 \begin_inset VSpace medskip
8134 Arrows used as accents like e.
8135 \begin_inset space \thinspace{}
8139 \begin_inset space \space{}
8142 vector arrows are listed in
8143 \begin_inset CommandInset ref
8145 reference "sec:Accents"
8152 \begin_layout Standard
8153 \begin_inset VSpace bigskip
8156 Furthermore there are the labeled arrows
8157 \begin_inset Index idx
8160 \begin_layout Plain Layout
8173 \begin_inset Index idx
8176 \begin_layout Plain Layout
8191 \begin_inset Index idx
8194 \begin_layout Plain Layout
8201 \begin_layout Plain Layout
8216 When inserting one of these commands in a formula, an arrow with two blue
8217 boxes appear where the label can be inserted.
8218 The length of the arrow adapts to the label width.
8221 \begin_layout Standard
8223 \begin_inset Tabular
8224 <lyxtabular version="3" rows="3" columns="2">
8225 <features rotate="0" tabularvalignment="middle">
8226 <column alignment="center" valignment="top" width="0pt">
8227 <column alignment="center" valignment="top" width="0pt">
8229 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
8232 \begin_layout Plain Layout
8238 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
8241 \begin_layout Plain Layout
8243 \begin_inset Note Note
8246 \begin_layout Plain Layout
8253 is only used as spacer.
8265 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
8268 \begin_layout Plain Layout
8272 \begin_inset space \textvisiblespace{}
8276 \begin_inset Formula $\downarrow$
8280 \begin_inset Formula $\to$
8288 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
8291 \begin_layout Plain Layout
8292 \begin_inset Formula $\raisebox{5mm}{}F(a)\xleftarrow[x>0]{x=a}F(x)\raisebox{-4mm}{}$
8302 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
8305 \begin_layout Plain Layout
8309 \begin_inset space \textvisiblespace{}
8313 \begin_inset Formula $\downarrow$
8317 \begin_inset Formula $\to$
8325 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
8328 \begin_layout Plain Layout
8329 \begin_inset Formula $\raisebox{5mm}{}F(x)\xrightarrow[x>0]{x=a}F(a)\raisebox{-4mm}{}$
8345 \begin_layout Subsection
8346 Vertical and diagonal Arrows
8347 \begin_inset Index idx
8350 \begin_layout Plain Layout
8357 \begin_inset Index idx
8360 \begin_layout Plain Layout
8369 \begin_layout Standard
8370 \begin_inset space \hfill{}
8374 \begin_inset Tabular
8375 <lyxtabular version="3" rows="7" columns="2">
8376 <features rotate="0" tabularvalignment="middle">
8377 <column alignment="center" valignment="top" width="0pt">
8378 <column alignment="center" valignment="top" width="0pt">
8380 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
8383 \begin_layout Plain Layout
8389 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
8392 \begin_layout Plain Layout
8400 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
8403 \begin_layout Plain Layout
8411 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
8414 \begin_layout Plain Layout
8415 \begin_inset Formula $\uparrow$
8425 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
8428 \begin_layout Plain Layout
8436 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
8439 \begin_layout Plain Layout
8440 \begin_inset Formula $\Uparrow$
8450 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
8453 \begin_layout Plain Layout
8461 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
8464 \begin_layout Plain Layout
8465 \begin_inset Formula $\updownarrow$
8475 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
8478 \begin_layout Plain Layout
8486 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
8489 \begin_layout Plain Layout
8490 \begin_inset Formula $\Updownarrow$
8500 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
8503 \begin_layout Plain Layout
8511 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
8514 \begin_layout Plain Layout
8515 \begin_inset Formula $\Downarrow$
8525 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
8528 \begin_layout Plain Layout
8536 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
8539 \begin_layout Plain Layout
8540 \begin_inset Formula $\downarrow$
8554 \begin_inset space \hfill{}
8558 \begin_inset Tabular
8559 <lyxtabular version="3" rows="5" columns="2">
8560 <features rotate="0" tabularvalignment="middle">
8561 <column alignment="center" valignment="top" width="0pt">
8562 <column alignment="center" valignment="top" width="0pt">
8564 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
8567 \begin_layout Plain Layout
8573 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
8576 \begin_layout Plain Layout
8584 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
8587 \begin_layout Plain Layout
8595 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
8598 \begin_layout Plain Layout
8599 \begin_inset Formula $\nearrow$
8609 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
8612 \begin_layout Plain Layout
8620 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
8623 \begin_layout Plain Layout
8624 \begin_inset Formula $\searrow$
8634 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
8637 \begin_layout Plain Layout
8645 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
8648 \begin_layout Plain Layout
8649 \begin_inset Formula $\swarrow$
8659 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
8662 \begin_layout Plain Layout
8670 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
8673 \begin_layout Plain Layout
8674 \begin_inset Formula $\nwarrow$
8688 \begin_inset space \hfill{}
8694 \begin_layout Standard
8695 \begin_inset VSpace medskip
8698 Vertical arrows can be used also as delimiters together with the commands
8700 \begin_inset CommandInset ref
8702 reference "sub:Manual-Bracket-Size"
8707 \begin_inset CommandInset ref
8709 reference "sub:Automatic-Bracket-Size"
8716 \begin_layout Section
8718 \begin_inset CommandInset label
8725 \begin_inset Index idx
8728 \begin_layout Plain Layout
8737 \begin_layout Standard
8738 Accents can be inserted via the math toolbar button
8741 arg "math-insert \\hat"
8744 or the commands listed in the following subsections.
8747 \begin_layout Subsection
8748 Accents for one Character
8752 \begin_layout Plain Layout
8765 \begin_layout Plain Layout
8767 \begin_inset CommandInset ref
8769 reference "sub:Accents-in-Text"
8782 \begin_layout Plain Layout
8790 \begin_inset Note Note
8793 \begin_layout Plain Layout
8800 is used to avoid that the footnote appears in the PDF-bookmark.
8803 \begin_layout Plain Layout
8811 \begin_inset CommandInset ref
8813 reference "sub:Formulas-in-Section"
8823 \begin_inset CommandInset label
8825 name "sub:Accents-for-one"
8830 \begin_inset Index idx
8833 \begin_layout Plain Layout
8834 Accents ! for one character
8842 \begin_layout Standard
8843 \begin_inset space \hfill{}
8847 \begin_inset Tabular
8848 <lyxtabular version="3" rows="8" columns="2">
8849 <features rotate="0" tabularvalignment="middle">
8850 <column alignment="center" valignment="top" width="0pt">
8851 <column alignment="center" valignment="top" width="0pt">
8853 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
8856 \begin_layout Plain Layout
8862 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
8865 \begin_layout Plain Layout
8867 \begin_inset Note Note
8870 \begin_layout Plain Layout
8877 is only used as spacer.
8889 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
8892 \begin_layout Plain Layout
8896 \begin_inset space \textvisiblespace{}
8904 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
8907 \begin_layout Plain Layout
8908 \begin_inset Formula $\raisebox{5mm}{}\dot{A}$
8918 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
8921 \begin_layout Plain Layout
8925 \begin_inset space \textvisiblespace{}
8933 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
8936 \begin_layout Plain Layout
8937 \begin_inset Formula $\raisebox{5mm}{}\ddot{A}$
8947 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
8950 \begin_layout Plain Layout
8954 \begin_inset space \textvisiblespace{}
8962 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
8965 \begin_layout Plain Layout
8966 \begin_inset Formula $\raisebox{5mm}{}\dddot{A}$
8976 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
8979 \begin_layout Plain Layout
8983 \begin_inset space \textvisiblespace{}
8991 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
8994 \begin_layout Plain Layout
8995 \begin_inset Formula $\raisebox{5mm}{}\ddddot{A}$
9005 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
9008 \begin_layout Plain Layout
9012 \begin_inset space \textvisiblespace{}
9016 \begin_inset Index idx
9019 \begin_layout Plain Layout
9030 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
9033 \begin_layout Plain Layout
9034 \begin_inset Formula $\raisebox{5mm}{}\vec{A}$
9044 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
9047 \begin_layout Plain Layout
9051 \begin_inset space \textvisiblespace{}
9059 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
9062 \begin_layout Plain Layout
9063 \begin_inset Formula $\raisebox{5mm}{}\bar{A}$
9073 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
9076 \begin_layout Plain Layout
9080 \begin_inset space \textvisiblespace{}
9088 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
9091 \begin_layout Plain Layout
9092 \begin_inset Formula $\raisebox{5mm}{}\mathring{A}$
9106 \begin_inset space \hfill{}
9110 \begin_inset Tabular
9111 <lyxtabular version="3" rows="7" columns="2">
9112 <features rotate="0" tabularvalignment="middle">
9113 <column alignment="center" valignment="top" width="0pt">
9114 <column alignment="center" valignment="top" width="0pt">
9116 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
9119 \begin_layout Plain Layout
9125 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
9128 \begin_layout Plain Layout
9136 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
9139 \begin_layout Plain Layout
9143 \begin_inset space \textvisiblespace{}
9151 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
9154 \begin_layout Plain Layout
9155 \begin_inset Formula $\raisebox{5mm}{}\tilde{A}$
9165 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
9168 \begin_layout Plain Layout
9172 \begin_inset space \textvisiblespace{}
9180 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
9183 \begin_layout Plain Layout
9184 \begin_inset Formula $\raisebox{5mm}{}\hat{A}$
9194 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
9197 \begin_layout Plain Layout
9201 \begin_inset space \textvisiblespace{}
9209 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
9212 \begin_layout Plain Layout
9213 \begin_inset Formula $\raisebox{5mm}{}\check{A}$
9223 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
9226 \begin_layout Plain Layout
9230 \begin_inset space \textvisiblespace{}
9238 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
9241 \begin_layout Plain Layout
9242 \begin_inset Formula $\raisebox{5mm}{}\acute{A}$
9252 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
9255 \begin_layout Plain Layout
9259 \begin_inset space \textvisiblespace{}
9267 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
9270 \begin_layout Plain Layout
9271 \begin_inset Formula $\raisebox{5mm}{}\grave{A}$
9281 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
9284 \begin_layout Plain Layout
9288 \begin_inset space \textvisiblespace{}
9296 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
9299 \begin_layout Plain Layout
9300 \begin_inset Formula $\raisebox{5mm}{}\breve{A}$
9314 \begin_inset space \hfill{}
9320 \begin_layout Standard
9321 \begin_inset VSpace bigskip
9327 \begin_layout Standard
9328 You can directly insert accents like é to formulas.
9329 LyX will transform them to the corresponding accent command.
9331 \begin_inset Index idx
9334 \begin_layout Plain Layout
9340 it is better to insert a quotation mark before the vowel.
9341 These two characters are then treated by LaTeX as
9345 character when the formula part with the umlaut is marked as German.
9353 \begin_inset Quotes eld
9357 \begin_inset Quotes erd
9360 umlauts are created as demonstrated in the following example:
9363 \begin_layout Standard
9364 \begin_inset VSpace -2mm
9370 \begin_layout Standard
9372 \begin_inset Tabular
9373 <lyxtabular version="3" rows="3" columns="2">
9374 <features rotate="0" tabularvalignment="middle">
9375 <column alignment="center" valignment="top">
9376 <column alignment="center" valignment="top">
9378 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
9381 \begin_layout Plain Layout
9387 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
9390 \begin_layout Plain Layout
9392 \begin_inset Note Note
9395 \begin_layout Plain Layout
9403 \begin_inset space \thinspace{}
9406 pt space are only used as spacer.
9418 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
9421 \begin_layout Plain Layout
9424 \begin_inset Quotes grd
9432 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
9435 \begin_layout Plain Layout
9436 \begin_inset space \hspace{}
9443 \begin_inset Formula $"i$
9453 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
9456 \begin_layout Plain Layout
9460 \begin_inset space \textvisiblespace{}
9468 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
9471 \begin_layout Plain Layout
9472 \begin_inset Formula $\raisebox{5mm}{}\ddot{i}$
9488 \begin_layout Standard
9489 Another advantage to
9495 is that umlauts can directly be converted to mathematical text because
9496 the accent commands above are
9502 in mathematical text
9505 To convert an accented character to mathematical text, only the character
9506 under the accent may be converted.
9507 This applies also for all other conversions, e.
9508 \begin_inset space \thinspace{}
9512 \begin_inset space \space{}
9518 \begin_layout Standard
9519 In mathematical text, umlauts and other accented characters can directly
9523 \begin_layout Standard
9524 \begin_inset VSpace bigskip
9530 \begin_layout Standard
9531 LyX also supports a tilde under the character if the LaTeX-package
9536 \begin_inset Index idx
9539 \begin_layout Plain Layout
9540 Packages ! undertilde
9545 is installed on your system:
9548 \begin_layout Standard
9552 \begin_layout Plain Layout
9562 \begin_inset Note Note
9565 \begin_layout Plain Layout
9566 The following table will only be displayed when the LaTeX-package
9578 \begin_layout Standard
9581 \begin_inset Tabular
9582 <lyxtabular version="3" rows="2" columns="2">
9583 <features rotate="0" tabularvalignment="middle">
9584 <column alignment="center" valignment="top" width="0pt">
9585 <column alignment="center" valignment="top" width="0pt">
9587 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
9590 \begin_layout Plain Layout
9596 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
9599 \begin_layout Plain Layout
9607 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
9610 \begin_layout Plain Layout
9614 \begin_inset space \textvisiblespace{}
9622 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
9625 \begin_layout Plain Layout
9626 \begin_inset Formula $\raisebox{5mm}{}\utilde{A}$
9642 \begin_layout Standard
9646 \begin_layout Plain Layout
9656 \begin_inset Note Note
9659 \begin_layout Plain Layout
9660 The following will be displayed when the LaTeX-package
9672 \begin_layout Standard
9673 You need to install the LaTeX-package
9677 to see the rest of this subsection in the output.
9680 \begin_layout Standard
9684 \begin_layout Plain Layout
9696 \begin_layout Subsection
9697 Accents for several Characters
9698 \begin_inset Index idx
9701 \begin_layout Plain Layout
9702 Accents ! for several characters
9710 \begin_layout Standard
9711 \begin_inset space \hfill{}
9715 \begin_inset Tabular
9716 <lyxtabular version="3" rows="5" columns="2">
9717 <features rotate="0" tabularvalignment="middle">
9718 <column alignment="center" valignment="top" width="0pt">
9719 <column alignment="center" valignment="top" width="0pt">
9721 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
9724 \begin_layout Plain Layout
9730 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
9733 \begin_layout Plain Layout
9735 \begin_inset Note Note
9738 \begin_layout Plain Layout
9745 is only used as spacer.
9757 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
9760 \begin_layout Plain Layout
9764 \begin_inset space \textvisiblespace{}
9772 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
9775 \begin_layout Plain Layout
9776 \begin_inset Formula $\raisebox{6mm}{}\overleftarrow{A=B}\raisebox{-2mm}{}$
9786 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
9789 \begin_layout Plain Layout
9793 \begin_inset space \textvisiblespace{}
9801 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
9804 \begin_layout Plain Layout
9805 \begin_inset Formula $\raisebox{5mm}{}\underleftarrow{A=B}\raisebox{-3mm}{}$
9815 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
9818 \begin_layout Plain Layout
9822 \begin_inset space \textvisiblespace{}
9830 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
9833 \begin_layout Plain Layout
9834 \begin_inset Formula $\raisebox{6mm}{}\overleftrightarrow{A=B}\raisebox{-2mm}{}$
9844 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
9847 \begin_layout Plain Layout
9851 \begin_inset space \textvisiblespace{}
9859 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
9862 \begin_layout Plain Layout
9863 \begin_inset Formula $\raisebox{5mm}{}\underleftrightarrow{A=B}\raisebox{-3mm}{}$
9877 \begin_inset space \hfill{}
9881 \begin_inset Tabular
9882 <lyxtabular version="3" rows="5" columns="2">
9883 <features rotate="0" tabularvalignment="middle">
9884 <column alignment="center" valignment="top" width="0pt">
9885 <column alignment="center" valignment="top" width="0pt">
9887 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
9890 \begin_layout Plain Layout
9896 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
9899 \begin_layout Plain Layout
9907 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
9910 \begin_layout Plain Layout
9914 \begin_inset space \textvisiblespace{}
9922 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
9925 \begin_layout Plain Layout
9926 \begin_inset Formula $\raisebox{6mm}{}\overrightarrow{A=B}\raisebox{-2mm}{}$
9936 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
9939 \begin_layout Plain Layout
9943 \begin_inset space \textvisiblespace{}
9951 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
9954 \begin_layout Plain Layout
9955 \begin_inset Formula $\raisebox{5mm}{}\underrightarrow{A=B}\raisebox{-3mm}{}$
9965 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
9968 \begin_layout Plain Layout
9972 \begin_inset space \textvisiblespace{}
9980 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
9983 \begin_layout Plain Layout
9984 \begin_inset Formula $\raisebox{6mm}{}\widetilde{A=B}\raisebox{-2mm}{}$
9994 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
9997 \begin_layout Plain Layout
10001 \begin_inset space \textvisiblespace{}
10009 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
10012 \begin_layout Plain Layout
10013 \begin_inset Formula $\raisebox{6mm}{}\widehat{A=B}\raisebox{-2mm}{}$
10027 \begin_inset space \hfill{}
10033 \begin_layout Standard
10034 \begin_inset VSpace medskip
10037 With these commands as many characters as you like can be accented.
10050 will only be set in the output with a length of three characters, as shown
10051 in the following example:
10052 \begin_inset Formula
10054 \widetilde{A+B=C-D}
10062 \begin_layout Standard
10070 \begin_inset Index idx
10073 \begin_layout Plain Layout
10088 \begin_inset Index idx
10091 \begin_layout Plain Layout
10099 described in the previous subsection it is also possible to accent several
10106 \begin_inset space \textvisiblespace{}
10110 \begin_inset Formula $\downarrow$
10116 \begin_inset Formula
10118 \underset{***}{A=B}
10126 \begin_layout Standard
10127 \begin_inset Newpage newpage
10133 \begin_layout Section
10135 \begin_inset CommandInset label
10142 \begin_inset Index idx
10145 \begin_layout Plain Layout
10154 \begin_layout Subsection
10156 \begin_inset CommandInset label
10158 name "sub:Predefined-Space"
10163 \begin_inset Index idx
10166 \begin_layout Plain Layout
10167 Space ! horizontal ! predefined
10175 \begin_layout Standard
10176 Sometimes it is necessary to insert horizontal space into a formula.
10177 This is done by inserting a protected space (shortcut
10180 arg "command-alternatives space-insert protected ; math-space"
10185 \begin_inset Quotes eld
10191 \begin_inset space \textvisiblespace{}
10197 \begin_inset Quotes erd
10200 appears and by pressing
10204 several times one can select one of eight different space sizes.
10205 The spaces can also be inserted using the math toolbar button
10208 arg "math-insert \\space"
10211 or special commands.
10212 Independent from the inserted command, one can select the size again by
10220 \begin_layout Standard
10223 \begin_inset Tabular
10224 <lyxtabular version="3" rows="6" columns="3">
10225 <features rotate="0" tabularvalignment="middle">
10226 <column alignment="center" valignment="top">
10227 <column alignment="center" valignment="top" width="15col%">
10228 <column alignment="center" valignment="top">
10230 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
10233 \begin_layout Plain Layout
10239 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
10242 \begin_layout Plain Layout
10252 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
10255 \begin_layout Plain Layout
10263 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
10266 \begin_layout Plain Layout
10274 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
10277 \begin_layout Plain Layout
10283 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
10286 \begin_layout Plain Layout
10287 \begin_inset Formula $A\, B$
10297 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
10300 \begin_layout Plain Layout
10308 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
10311 \begin_layout Plain Layout
10317 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
10320 \begin_layout Plain Layout
10321 \begin_inset Formula $A\: B$
10331 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
10334 \begin_layout Plain Layout
10342 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
10345 \begin_layout Plain Layout
10351 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
10354 \begin_layout Plain Layout
10355 \begin_inset Formula $A\; B$
10365 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
10368 \begin_layout Plain Layout
10376 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
10379 \begin_layout Plain Layout
10385 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
10388 \begin_layout Plain Layout
10389 \begin_inset Formula $A\quad B$
10399 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
10402 \begin_layout Plain Layout
10410 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
10413 \begin_layout Plain Layout
10419 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
10422 \begin_layout Plain Layout
10423 \begin_inset Formula $A\qquad B$
10437 \begin_inset space \hfill{}
10441 \begin_inset Tabular
10442 <lyxtabular version="3" rows="6" columns="3">
10443 <features rotate="0" tabularvalignment="middle">
10444 <column alignment="center" valignment="top">
10445 <column alignment="center" valignment="top" width="15col%">
10446 <column alignment="center" valignment="top">
10448 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
10451 \begin_layout Plain Layout
10457 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
10460 \begin_layout Plain Layout
10470 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
10473 \begin_layout Plain Layout
10481 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
10484 \begin_layout Plain Layout
10492 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
10495 \begin_layout Plain Layout
10501 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
10504 \begin_layout Plain Layout
10505 \begin_inset Formula $A\hfill B$
10515 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
10518 \begin_layout Plain Layout
10526 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
10529 \begin_layout Plain Layout
10535 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
10538 \begin_layout Plain Layout
10539 \begin_inset Formula $A\hspace*{1em}B$
10549 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
10552 \begin_layout Plain Layout
10560 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
10563 \begin_layout Plain Layout
10569 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
10572 \begin_layout Plain Layout
10573 \begin_inset Formula $A\hspace{1em}B$
10583 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
10586 \begin_layout Plain Layout
10590 \begin_inset space \textvisiblespace{}
10598 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
10601 \begin_layout Plain Layout
10607 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
10610 \begin_layout Plain Layout
10611 \begin_inset Formula $A\ B$
10621 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
10624 \begin_layout Plain Layout
10632 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
10635 \begin_layout Plain Layout
10641 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
10644 \begin_layout Plain Layout
10645 \begin_inset Formula $A\! B$
10661 \begin_layout Standard
10663 \begin_inset space ~
10667 \begin_inset space \thinspace{}
10671 \begin_inset space \thinspace{}
10674 7 are variable spaces which are explained in
10675 \begin_inset CommandInset ref
10677 reference "sub:Variable-Space"
10683 \begin_inset space ~
10686 9 seems to produce no space.
10687 It is displayed red in LyX contrary to the other sizes, because it is a
10689 There are two more negative spaces:
10692 \begin_layout Standard
10694 \begin_inset Tabular
10695 <lyxtabular version="3" rows="3" columns="3">
10696 <features rotate="0" tabularvalignment="middle">
10697 <column alignment="center" valignment="middle" width="6.8cm">
10698 <column alignment="center" valignment="top" width="0pt">
10699 <column alignment="center" valignment="top" width="0pt">
10701 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
10704 \begin_layout Plain Layout
10710 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
10713 \begin_layout Plain Layout
10721 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
10724 \begin_layout Plain Layout
10734 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
10737 \begin_layout Plain Layout
10742 keystrokes after inserting the protected space
10747 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
10750 \begin_layout Plain Layout
10756 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
10759 \begin_layout Plain Layout
10767 <cell multicolumn="1" alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
10770 \begin_layout Plain Layout
10776 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
10779 \begin_layout Plain Layout
10780 \begin_inset Formula $A\negmedspace B$
10788 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
10791 \begin_layout Plain Layout
10792 \begin_inset Formula $A\negthickspace B$
10808 \begin_layout Standard
10809 Negative spaces can lead to characters overlapping each other.
10810 Thus they can be used to enforce ligatures, which are e.
10811 \begin_inset space \thinspace{}
10815 \begin_inset space \space{}
10818 useful for summation operators:
10821 \begin_layout Standard
10823 \begin_inset Tabular
10824 <lyxtabular version="3" rows="3" columns="2">
10825 <features rotate="0" tabularvalignment="middle">
10826 <column alignment="center" valignment="top">
10827 <column alignment="center" valignment="top">
10829 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
10832 \begin_layout Plain Layout
10838 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
10841 \begin_layout Plain Layout
10843 \begin_inset Note Note
10846 \begin_layout Plain Layout
10853 is only used as spacer.
10865 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
10868 \begin_layout Plain Layout
10874 \begin_inset space \textvisiblespace{}
10882 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
10885 \begin_layout Plain Layout
10886 \begin_inset Formula $\raisebox{4.5mm}{}\sum\sum f_{kl}\raisebox{-2.5mm}{}$
10896 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
10899 \begin_layout Plain Layout
10907 \begin_inset space \textvisiblespace{}
10915 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
10918 \begin_layout Plain Layout
10919 \begin_inset Formula $\raisebox{4.5mm}{}\sum\negmedspace\sum f_{kl}\raisebox{-2.5mm}{}$
10935 \begin_layout Standard
10937 \begin_inset VSpace medskip
10943 \begin_layout Standard
10945 Relations like for example equal signs, are always surrounded by space.
10946 To suppress this, the equal sign is placed into a TeX-brace.
10947 The following example demonstrates this:
10950 \begin_layout Standard
10952 \begin_inset Tabular
10953 <lyxtabular version="3" rows="2" columns="2">
10954 <features rotate="0" tabularvalignment="middle">
10955 <column alignment="center" valignment="top" width="0pt">
10956 <column alignment="center" valignment="top" width="0pt">
10958 <cell alignment="center" valignment="top" usebox="none">
10961 \begin_layout Plain Layout
10967 <cell alignment="center" valignment="top" usebox="none">
10970 \begin_layout Plain Layout
10971 \begin_inset Formula $A=B$
10981 <cell alignment="center" valignment="top" usebox="none">
10984 \begin_layout Plain Layout
10985 \begin_inset Note Note
10988 \begin_layout Plain Layout
10995 is only used as spacer.
11001 \begin_inset Formula $\raisebox{5mm}{}$
11004 equation without space
11009 <cell multicolumn="1" alignment="center" valignment="top" usebox="none">
11012 \begin_layout Plain Layout
11013 \begin_inset Formula $A{=}B$
11029 \begin_layout Standard
11031 The command for the last formula is:
11036 \begin_inset Formula $\to$
11042 \begin_layout Standard
11043 \begin_inset VSpace bigskip
11049 \begin_layout Standard
11050 Spaces are needed for physical units, because the space between the value
11051 and the unit is the smallest one and not a normal space.
11052 For units in text, the smallest space is inserted via the menu
11054 Insert\SpecialChar \menuseparator
11055 Formatting\SpecialChar \menuseparator
11057 \begin_inset space ~
11065 arg "space-insert thin"
11071 \begin_layout Standard
11072 An example to visualize the difference:
11075 \begin_layout Standard
11076 \begin_inset Tabular
11077 <lyxtabular version="3" rows="2" columns="2">
11078 <features rotate="0" tabularvalignment="middle">
11079 <column alignment="left" valignment="top">
11080 <column alignment="left" valignment="top">
11082 <cell alignment="center" valignment="top" usebox="none">
11085 \begin_layout Plain Layout
11087 \begin_inset Formula $\cdot$
11095 <cell alignment="center" valignment="top" usebox="none">
11098 \begin_layout Plain Layout
11099 space between value and unit
11106 <cell alignment="center" valignment="top" usebox="none">
11109 \begin_layout Plain Layout
11111 \begin_inset space \thinspace{}
11115 \begin_inset Formula $\cdot$
11123 <cell alignment="center" valignment="top" usebox="none">
11126 \begin_layout Plain Layout
11127 smallest space between value and unit
11140 \begin_layout Subsection
11145 \begin_layout Plain Layout
11158 \begin_layout Plain Layout
11159 for vertical space in formulas see
11160 \begin_inset CommandInset ref
11162 reference "sub:Line-Separation"
11175 \begin_layout Plain Layout
11183 \begin_inset Note Note
11186 \begin_layout Plain Layout
11189 texorpdfstring is used to avoid that the footnote appears in the PDF-bookmark.
11192 \begin_layout Plain Layout
11195 texorpdfstring is in section
11196 \begin_inset CommandInset ref
11198 reference "sub:Formulas-in-Section"
11208 \begin_inset CommandInset label
11210 name "sub:Variable-Space"
11215 \begin_inset Index idx
11218 \begin_layout Plain Layout
11219 Space ! horizontal ! variable
11227 \begin_layout Standard
11228 Space with a defined length can be inserted with the command
11235 \begin_inset Index idx
11238 \begin_layout Plain Layout
11248 \begin_inset Quotes eld
11254 \begin_inset space \textvisiblespace{}
11260 \begin_inset Quotes erd
11264 The length can be specified by left-clicking on the
11265 \begin_inset Quotes eld
11271 \begin_inset space \textvisiblespace{}
11277 \begin_inset Quotes erd
11281 The length may also be negative.
11282 When a space would be the first character in a line it would be omitted.
11283 To force its output use the command
11295 or left-click on the
11296 \begin_inset Quotes eld
11302 \begin_inset space \textvisiblespace{}
11308 \begin_inset Quotes erd
11311 and check the option
11316 \begin_inset Newline newline
11319 To insert as much space as is available, the command
11326 \begin_inset Index idx
11329 \begin_layout Plain Layout
11340 \begin_layout Standard
11341 \begin_inset VSpace -1mm
11347 \begin_layout Standard
11349 \begin_inset Tabular
11350 <lyxtabular version="3" rows="4" columns="2">
11351 <features rotate="0" tabularvalignment="middle">
11352 <column alignment="center" valignment="top">
11353 <column alignment="center" valignment="top">
11355 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
11358 \begin_layout Plain Layout
11366 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
11369 \begin_layout Plain Layout
11377 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
11380 \begin_layout Plain Layout
11384 \begin_inset space \textvisiblespace{}
11390 \begin_inset space \thinspace{}
11398 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
11401 \begin_layout Plain Layout
11402 \begin_inset Formula $A=B\hspace{3cm}A\not=C$
11412 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
11415 \begin_layout Plain Layout
11419 \begin_inset space \textvisiblespace{}
11425 \begin_inset space \thinspace{}
11433 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
11436 \begin_layout Plain Layout
11437 \begin_inset Formula $A\hspace{-1mm}A\not=A$
11447 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
11450 \begin_layout Plain Layout
11454 \begin_inset space \textvisiblespace{}
11462 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
11465 \begin_layout Plain Layout
11466 \begin_inset Formula $A=A\hfill B=B$
11482 \begin_layout Standard
11483 In the last example the available space is given by the longest column entry
11485 In an inline formula the space depends on the length of the line in which
11493 Thus, when the line uses the full width, no space will be created.
11500 only has an effect on displayed formulas when the formula style
11505 (Formula styles are explained in
11506 \begin_inset CommandInset ref
11508 reference "sec:Formula-Styles"
11515 \begin_layout Standard
11522 , there are the commands
11534 that fill the space with a pattern, see
11535 \begin_inset CommandInset ref
11537 reference "sub:Ellipses"
11544 \begin_layout Standard
11545 For text, variable space can be inserted via the menu
11547 Insert\SpecialChar \menuseparator
11548 Formatting\SpecialChar \menuseparator
11550 \begin_inset space ~
11558 \begin_layout Standard
11559 This is a line with
11560 \begin_inset space \hspace{}
11565 \begin_inset space \thinspace{}
11571 \begin_layout Standard
11572 This is a line with
11573 \begin_inset space \hfill{}
11579 \begin_layout Subsection
11580 Space besides inline Formulas
11581 \begin_inset Index idx
11584 \begin_layout Plain Layout
11585 Space ! besides inline formulas
11593 \begin_layout Standard
11594 The space that surrounds inline formulas can be adjusted with the length
11602 \begin_inset Index idx
11605 \begin_layout Plain Layout
11614 The value of a length is set with the command
11621 \begin_inset Index idx
11624 \begin_layout Plain Layout
11632 which has the following scheme:
11635 \begin_layout Standard
11640 setlength{length name}{value}
11643 \begin_layout Standard
11651 \begin_inset space \thinspace{}
11657 \begin_layout Standard
11667 \begin_layout Standard
11668 is inserted in TeX-mode.
11670 \begin_inset space \thinspace{}
11673 mm space will now be set around all inline formulas:
11677 \begin_layout Plain Layout
11691 \begin_layout Standard
11692 This is a line with an inline formula
11693 \begin_inset Formula $A=B$
11697 \begin_inset space \thinspace{}
11700 mm surrounding space.
11704 \begin_layout Plain Layout
11718 \begin_layout Standard
11719 To return to the predefined value,
11725 is set to the value 0
11726 \begin_inset space \thinspace{}
11732 \begin_layout Section
11734 \begin_inset Index idx
11737 \begin_layout Plain Layout
11744 \begin_inset Index idx
11747 \begin_layout Plain Layout
11752 \begin_layout Plain Layout
11763 \begin_layout Plain Layout
11778 \begin_layout Standard
11779 Boxes for text are described in chapter
11786 \begin_inset space ~
11794 \begin_layout Subsection
11796 \begin_inset CommandInset label
11798 name "sub:Boxes-with-Frame"
11803 \begin_inset Index idx
11806 \begin_layout Plain Layout
11815 \begin_layout Standard
11816 It is possible to frame a formula or part of one with the commands
11823 \begin_inset Index idx
11826 \begin_layout Plain Layout
11841 \begin_inset Index idx
11844 \begin_layout Plain Layout
11855 \begin_layout Standard
11856 When one of these commands is inserted in a formula, a blue box appears
11857 within a frame to enter formula parts.
11864 an additional formula has to be created by
11868 within this box, because the box content will otherwise be treated as mathemati
11876 is used, a new formula is automatically created inside the frame.
11879 \begin_layout Standard
11886 is not suitable to frame displayed formulas because the formula will always
11887 be set in the size of the text.
11894 is in contrary not suitable to frame inline formulas, because the formula
11895 will always be set in the size of a displayed formula.
11898 \begin_layout Standard
11912 \begin_inset Index idx
11915 \begin_layout Plain Layout
11923 where additionally the frame width and the alignment can be specified.
11930 is used in the following scheme:
11933 \begin_layout Standard
11938 framebox[frame width][position]{box content}
11941 \begin_layout Standard
11942 The position can either be
11959 right aligns the formula in the box.
11960 When no position is given, the formula will be centered.
11961 \begin_inset Newline newline
11964 If no width is given, also no position can be given.
11965 In this case the frame width is adjusted to the box content like for
11974 \begin_layout Standard
11981 is inserted, a box appears containing three blue boxes.
11982 The first two boxes are surrounded by brackets and denote the two optional
11984 The third box is for formula parts like for
11993 \begin_layout Standard
11994 \begin_inset Newpage newpage
12000 \begin_layout Standard
12002 \begin_inset Tabular
12003 <lyxtabular version="3" rows="5" columns="2">
12004 <features rotate="0" tabularvalignment="middle">
12005 <column alignment="center" valignment="top">
12006 <column alignment="center" valignment="top">
12008 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
12011 \begin_layout Plain Layout
12017 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
12020 \begin_layout Plain Layout
12022 \begin_inset Note Note
12025 \begin_layout Plain Layout
12032 is only used as spacer.
12044 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
12047 \begin_layout Plain Layout
12051 \begin_inset space \textvisiblespace{}
12061 \begin_inset space \textvisiblespace{}
12069 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
12072 \begin_layout Plain Layout
12073 \begin_inset Formula $\raisebox{6mm}{}\fbox{\ensuremath{\int A=B}}\raisebox{-4mm}{}$
12083 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
12086 \begin_layout Plain Layout
12090 \begin_inset space \textvisiblespace{}
12096 \begin_inset space \textvisiblespace{}
12104 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
12107 \begin_layout Plain Layout
12108 \begin_inset Formula $\raisebox{8.5mm}{}\boxed{\int A=B}\raisebox{-6.5mm}{}$
12118 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
12121 \begin_layout Plain Layout
12125 \begin_inset space \textvisiblespace{}
12133 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
12136 \begin_layout Plain Layout
12137 \begin_inset Formula $\raisebox{6mm}{}A+\fbox{B}\raisebox{-3mm}{}$
12147 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
12150 \begin_layout Plain Layout
12154 \begin_inset space \textvisiblespace{}
12158 \begin_inset Formula $\to$
12162 \begin_inset Formula $\to$
12172 \begin_inset space \textvisiblespace{}
12176 \begin_inset Formula $\downarrow$
12184 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
12187 \begin_layout Plain Layout
12188 \begin_inset Formula $\raisebox{6mm}{}$
12192 \begin_inset Formula $\framebox[20mm][]{\ensuremath{\frac{A}{B}}}$
12196 \begin_inset Formula $\raisebox{-4mm}{}$
12212 \begin_layout Standard
12213 The frame thickness can also be adjusted.
12214 To do this the following commands have to be inserted in TeX-mode before
12218 \begin_layout Standard
12228 \begin_inset Quotes eld
12232 \begin_inset Quotes erd
12246 \begin_inset Quotes eld
12250 \begin_inset Quotes erd
12256 \begin_layout Standard
12257 \begin_inset Quotes eld
12261 \begin_inset Quotes erd
12264 specifies the minimal distance between the frame and the first character
12266 An example for this is the following framed formula:
12270 \begin_layout Plain Layout
12282 \begin_inset Formula
12289 Before this formula the commands
12292 \begin_layout Standard
12314 \begin_layout Standard
12315 were inserted in TeX-mode.
12316 The given values are used for all following boxes.
12319 \begin_layout Standard
12320 To return to the standard frame size, the command
12323 \begin_layout Standard
12348 \begin_layout Plain Layout
12362 \begin_layout Standard
12363 is inserted in TeX-mode before the next formula.
12366 \begin_layout Subsection
12367 Boxes without Frame
12368 \begin_inset CommandInset label
12370 name "sub:Boxes-without-Frame"
12375 \begin_inset Index idx
12378 \begin_layout Plain Layout
12379 Boxes ! without frame
12387 \begin_layout Standard
12388 For boxes without a frame there are the following box commands:
12395 \begin_inset Index idx
12398 \begin_layout Plain Layout
12413 \begin_inset Index idx
12416 \begin_layout Plain Layout
12431 \begin_inset Index idx
12434 \begin_layout Plain Layout
12445 \begin_layout Standard
12452 a box can be super- or subscripted.
12453 But in contrary to normal super- and subscripting, the characters in the
12454 box keep their font size.
12461 is used in the following scheme:
12464 \begin_layout Standard
12469 raisebox{height}{box content}
12472 \begin_layout Standard
12473 When the box should contain a formula, an extra formula is needed like for
12484 \begin_inset Note Greyedout
12487 \begin_layout Plain Layout
12498 this extra formula is created by pressing
12502 twice instead of once because LyX doesn't yet support
12516 \begin_layout Standard
12518 \begin_inset Tabular
12519 <lyxtabular version="3" rows="4" columns="2">
12520 <features rotate="0" tabularvalignment="middle">
12521 <column alignment="center" valignment="top">
12522 <column alignment="center" valignment="top">
12524 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
12527 \begin_layout Plain Layout
12533 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
12536 \begin_layout Plain Layout
12544 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
12547 \begin_layout Plain Layout
12551 \begin_inset Formula $\to$
12557 \begin_inset Formula $\to$
12565 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
12568 \begin_layout Plain Layout
12569 \begin_inset Formula $H\raisebox{2mm}{al}lo$
12579 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
12582 \begin_layout Plain Layout
12586 \begin_inset Formula $\to$
12592 \begin_inset Formula $\to$
12600 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
12603 \begin_layout Plain Layout
12604 \begin_inset Formula $H\raisebox{-2mm}{al}lo$
12614 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
12617 \begin_layout Plain Layout
12621 \begin_inset Formula $\to$
12637 \begin_inset space \textvisiblespace{}
12645 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
12648 \begin_layout Plain Layout
12649 \begin_inset Formula $A=\raisebox{-2mm}{\mbox{\ensuremath{\sqrt{B}}}}$
12665 \begin_layout Standard
12690 , with the difference that there is no frame.
12693 \begin_layout Subsection
12695 \begin_inset CommandInset label
12697 name "sub:Colored-Boxes"
12702 \begin_inset Index idx
12705 \begin_layout Plain Layout
12714 \begin_layout Standard
12715 To be able to use all commands explained in this section, the LaTeX-package
12724 \begin_layout Plain Layout
12729 is part of every LaTeX standard installation.
12735 \begin_inset Index idx
12738 \begin_layout Plain Layout
12744 has to be loaded in the LaTeX-preamble with the line
12748 \begin_layout Plain Layout
12749 When text is colored somewhere in the document with a predefined color,
12750 LyX loads the LaTeX-package
12755 Thus it is possible that the package is loaded twice, but this does not
12762 \begin_inset Note Note
12765 \begin_layout Plain Layout
12766 To avoid that the package is loaded twice, a macro was inserted to the LaTeX-pre
12775 \begin_layout Standard
12783 \begin_layout Standard
12784 \begin_inset VSpace medskip
12787 To color boxes, the command
12794 \begin_inset Index idx
12797 \begin_layout Plain Layout
12805 is used in the following scheme:
12808 \begin_layout Standard
12813 colorbox{color}{box content}
12816 \begin_layout Standard
12817 The box content can also be a box and a
12823 can also be part of another box (see the 2nd and 3rd example).
12824 When the box should contain a formula, an extra formula has to be created,
12825 the same way as for
12835 \begin_layout Plain Layout
12836 This also applies for the command
12850 \begin_layout Standard
12851 One of the following predefined colors can be chosen:
12854 \begin_layout Standard
12888 \begin_layout Standard
12890 \begin_inset Tabular
12891 <lyxtabular version="3" rows="4" columns="2">
12892 <features rotate="0" tabularvalignment="middle">
12893 <column alignment="center" valignment="top">
12894 <column alignment="center" valignment="top">
12896 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
12899 \begin_layout Plain Layout
12905 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
12908 \begin_layout Plain Layout
12910 \begin_inset Note Note
12913 \begin_layout Plain Layout
12920 is only used as spacer.
12932 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
12935 \begin_layout Plain Layout
12939 \begin_inset Formula $\to$
12949 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
12952 \begin_layout Plain Layout
12953 \begin_inset Formula $\raisebox{6mm}{}\colorbox{yellow}{A=B}\raisebox{-3mm}{}$
12963 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
12966 \begin_layout Plain Layout
12970 \begin_inset Formula $\to$
12978 \begin_inset space \textvisiblespace{}
12986 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
12989 \begin_layout Plain Layout
12990 \begin_inset Formula $\raisebox{6mm}{}\colorbox{green}{\fbox{A=B}}\raisebox{-3mm}{}$
13000 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
13003 \begin_layout Plain Layout
13007 \begin_inset space \textvisiblespace{}
13013 \begin_inset Formula $\to$
13029 \begin_inset space \textvisiblespace{}
13037 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
13040 \begin_layout Plain Layout
13041 \begin_inset Formula $\raisebox{7mm}{}\fbox{\colorbox{green}{\mbox{\ensuremath{\int C=D}}}}\raisebox{-5mm}{}$
13057 \begin_layout Standard
13064 only colors the box but not the characters in the box.
13065 To color all characters, the whole formula is highlighted and the desired
13066 color is chosen in the
13069 \begin_inset space ~
13075 The dialog can be called with the toolbar button
13078 arg "dialog-show character"
13083 Edit\SpecialChar \menuseparator
13085 \begin_inset space ~
13088 Style\SpecialChar \menuseparator
13092 The formula number then has the same color as the formula.
13093 When the formula number should get another color than the formula characters,
13094 the color must be changed within the formula.
13097 \begin_layout Standard
13101 \begin_layout Standard
13104 \begin_inset Formula
13106 \int A=B\label{eq:red}
13114 \begin_inset Formula
13116 \textcolor{red}{\int A=B}\label{eq:redgreen}
13124 \begin_layout Standard
13126 \begin_inset CommandInset ref
13132 is completely colored red.
13133 \begin_inset Newline newline
13137 \begin_inset CommandInset ref
13139 reference "eq:redgreen"
13143 was first completely colored green to set the color for the formula number.
13144 Subsequently the formula characters were colored red.
13147 \begin_layout Standard
13148 \begin_inset VSpace bigskip
13151 To color the frame different than the rest of the box, the command
13158 \begin_inset Index idx
13161 \begin_layout Plain Layout
13169 is used in the following scheme:
13172 \begin_layout Standard
13177 fcolorbox{frame color}{color}{box content}
13180 \begin_layout Standard
13187 is an extension of the command
13194 The frame width is set, like for
13217 \begin_layout Plain Layout
13229 \begin_inset Formula
13231 \fcolorbox{cyan}{magenta}{A=B}
13240 \begin_layout Plain Layout
13254 \begin_layout Standard
13255 This formula was created with the command
13256 \begin_inset Newline newline
13264 \begin_inset Formula $\to$
13270 \begin_inset Formula $\to$
13280 \begin_layout Standard
13281 \begin_inset VSpace bigskip
13284 To use other colors than the predefined ones, they have to be defined first.
13287 \begin_layout Standard
13288 One can for example define the color
13289 \begin_inset Quotes eld
13297 \begin_inset Quotes erd
13300 with the LaTeX-preamble line:
13303 \begin_layout Standard
13308 definecolor{darkgreen}{cmyk}{0.5,
13323 \begin_inset Index idx
13326 \begin_layout Plain Layout
13337 \begin_layout Standard
13342 is the color space that denotes the colors
13359 The four comma separated numbers are the portion factor for the corresponding
13360 colors of the color space.
13361 The factors can be in the range of 0
13362 \begin_inset space \thinspace{}
13366 \begin_inset space \thinspace{}
13374 also the color space
13378 can be used for definitions.
13395 , so that there are in this case three portion factors for the corresponding
13397 Furthermore there is the color space
13401 with one portion factor for the gray value.
13404 \begin_layout Standard
13405 As example a framed box with the new defined color
13409 where the characters have been colored
13414 \begin_inset Formula
13416 \colorbox{darkgreen}{\color{yellow}\boxed{\int A\,\mathrm{d}x=\frac{\sqrt[5]{B}}{\ln\left(\frac{1}{3}\right)}}}
13424 \begin_layout Standard
13425 Self-defined colors can also be used for text with the help of the command
13433 \begin_inset Index idx
13436 \begin_layout Plain Layout
13445 \begin_layout Standard
13449 \begin_layout Plain Layout
13453 textcolor{darkgreen}{
13459 \begin_inset Quotes eld
13463 \begin_inset Quotes erd
13470 \begin_layout Plain Layout
13480 \begin_layout Standard
13488 \begin_inset Index idx
13491 \begin_layout Plain Layout
13499 is used in the scheme
13503 textcolor{color}{characters to color}
13508 \begin_layout Subsection
13510 \begin_inset CommandInset label
13512 name "sub:Paragraph-Boxes"
13517 \begin_inset Index idx
13520 \begin_layout Plain Layout
13521 Boxes ! as paragraph
13529 \begin_layout Standard
13530 A box that can contain several lines and paragraphs, a so-called paragraph
13531 box (parbox), can be created with the menu
13533 Insert\SpecialChar \menuseparator
13536 or the toolbar button
13545 \begin_layout Standard
13546 The following example shows a framed parbox in a line:
13549 \begin_layout Standard
13550 \begin_inset VSpace medskip
13554 \begin_inset Box Boxed
13564 height_special "totalheight"
13567 \begin_layout Plain Layout
13568 This is a paragraph box.
13570 \begin_inset space \thinspace{}
13573 cm long and can also contain formulas:
13574 \begin_inset Formula $\int A\,\mathrm{d}s=C$
13585 \begin_layout Standard
13586 \begin_inset VSpace medskip
13592 \begin_layout Standard
13593 Such a box is created by right-clicking on the gray box inset.
13594 A dialog pops up showing the box properties.
13608 \begin_inset space \thinspace{}
13613 Vertical Box Alignment
13618 \begin_layout Standard
13619 \begin_inset VSpace medskip
13622 In LaTeX a parbox is created with the command
13629 \begin_inset Index idx
13632 \begin_layout Plain Layout
13640 which has the following scheme:
13643 \begin_layout Standard
13648 parbox[position]{width}{box content}
13651 \begin_layout Standard
13666 \begin_inset Quotes eld
13670 \begin_inset Quotes erd
13673 means that the box is aligned within the surrounding text with its last
13680 \begin_inset Quotes eld
13684 \begin_inset Quotes erd
13687 this is done with the first line.
13688 When no position is given, the box will be vertically centered, see section
13696 \begin_inset space ~
13701 manual for examples.
13704 \begin_layout Standard
13705 \begin_inset VSpace bigskip
13708 To frame formulas completely, including the formula number, the formula
13709 must be set into a parbox.
13710 To do this, the command
13724 is inserted in TeX-mode before the formula.
13732 \begin_inset Index idx
13735 \begin_layout Plain Layout
13743 is hereby the line width set for the document.
13744 Because the frame is outside the parbox, 2
13745 \begin_inset space \thinspace{}
13748 times the frame separation and the frame thickness must be subtracted from
13750 As this is not automatically done by LyX due to a bug
13754 \begin_layout Plain Layout
13755 \begin_inset CommandInset href
13757 name "LyX-bug #4483"
13758 target "http://www.lyx.org/trac/ticket/4483"
13767 , TeX-mode has to be used.
13768 To be able to multiply and subtract in arguments, the LaTeX-package
13776 \begin_layout Plain Layout
13781 is part of every LaTeX standard installation.
13787 \begin_inset Index idx
13790 \begin_layout Plain Layout
13796 must be loaded in the LaTeX-preamble with the line
13799 \begin_layout Standard
13807 \begin_layout Standard
13808 Behind the formula both boxes are closed by entering
13813 Here is an example:
13817 \begin_layout Plain Layout
13831 \begin_layout Standard
13835 \begin_layout Plain Layout
13853 \begin_inset Formula
13855 \int A\,\mathrm{d}x=\frac{\sqrt[5]{B}}{\ln\left(\frac{1}{3}\right)}
13864 \begin_layout Plain Layout
13875 \begin_layout Plain Layout
13889 \begin_layout Standard
13890 \begin_inset VSpace medskip
13893 As a parbox is used as the argument of
13899 , there is in this case no difference between
13914 \begin_layout Standard
13915 \begin_inset VSpace bigskip
13918 Paragraph boxes are very useful to comment formulas directly.
13925 is used in combination with the command
13939 \begin_inset CommandInset ref
13941 reference "sub:User-defined-Numbering"
13948 \begin_layout Standard
13949 An example of a formula commented with
13958 \begin_layout Standard
13962 \begin_layout Plain Layout
13975 This is a description.
13976 It is distinctly separated from the formula and multiline.
13980 \begin_layout Plain Layout
13992 \begin_layout Standard
13993 Such a formula must be inserted completely in TeX-mode because LyX does
13994 not yet support the command
14001 The formula is created with the following command sequence:
14004 \begin_layout Standard
14017 is inserted in TeX-mode.
14021 \begin_layout Plain Layout
14022 When the formula style
14034 can also be replaced by
14041 (formula styles see
14042 \begin_inset CommandInset ref
14044 reference "sec:Formula-Styles"
14053 Then the description follows as normal text and finally
14059 is inserted in TeX-mode.
14072 hereby create a displayed formula.
14075 \begin_layout Standard
14082 can be seen in this example that was
14083 \begin_inset Quotes eld
14087 \begin_inset Quotes erd
14090 using the mathematical textmode:
14091 \begin_inset Formula
14093 5x-7b=3b\textrm{This is a description. It is not separated from the formula ...}
14101 \begin_layout Section
14103 \begin_inset Index idx
14106 \begin_layout Plain Layout
14115 \begin_layout Subsection
14117 \begin_inset CommandInset label
14119 name "sub:Big-Operators"
14124 \begin_inset Index idx
14127 \begin_layout Plain Layout
14134 \begin_inset Index idx
14137 \begin_layout Plain Layout
14144 \begin_inset Index idx
14147 \begin_layout Plain Layout
14156 \begin_layout Standard
14157 To be able to use all integral operators listed here, the option
14159 Use esint package automatically
14161 must be set in the document settings under
14164 \begin_inset space ~
14172 \begin_layout Standard
14173 \begin_inset space \hfill{}
14177 \begin_inset Tabular
14178 <lyxtabular version="3" rows="11" columns="2">
14179 <features rotate="0" tabularvalignment="middle">
14180 <column alignment="center" valignment="top" width="0pt">
14181 <column alignment="center" valignment="top" width="0pt">
14183 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
14186 \begin_layout Plain Layout
14192 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
14195 \begin_layout Plain Layout
14203 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
14206 \begin_layout Plain Layout
14210 \begin_inset Index idx
14213 \begin_layout Plain Layout
14226 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
14229 \begin_layout Plain Layout
14230 \begin_inset Formula $\int$
14240 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
14243 \begin_layout Plain Layout
14251 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
14254 \begin_layout Plain Layout
14255 \begin_inset Formula $\oint$
14265 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
14268 \begin_layout Plain Layout
14276 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
14279 \begin_layout Plain Layout
14280 \begin_inset Formula $\ointctrclockwise$
14290 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
14293 \begin_layout Plain Layout
14301 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
14304 \begin_layout Plain Layout
14305 \begin_inset Formula $\ointclockwise$
14315 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
14318 \begin_layout Plain Layout
14326 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
14329 \begin_layout Plain Layout
14330 \begin_inset Formula $\sqint$
14340 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
14343 \begin_layout Plain Layout
14351 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
14354 \begin_layout Plain Layout
14356 \begin_inset Formula $\fint$
14366 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
14369 \begin_layout Plain Layout
14377 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
14380 \begin_layout Plain Layout
14382 \begin_inset Formula $\landupint$
14392 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
14395 \begin_layout Plain Layout
14403 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
14406 \begin_layout Plain Layout
14408 \begin_inset Formula $\landdownint$
14418 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
14421 \begin_layout Plain Layout
14429 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
14432 \begin_layout Plain Layout
14433 \begin_inset Formula $\bigcap$
14443 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
14446 \begin_layout Plain Layout
14454 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
14457 \begin_layout Plain Layout
14458 \begin_inset Formula $\bigcup$
14472 \begin_inset space \hfill{}
14476 \begin_inset Tabular
14477 <lyxtabular version="3" rows="11" columns="2">
14478 <features rotate="0" tabularvalignment="middle">
14479 <column alignment="center" valignment="top" width="0pt">
14480 <column alignment="center" valignment="top" width="0pt">
14482 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
14485 \begin_layout Plain Layout
14491 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
14494 \begin_layout Plain Layout
14502 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
14505 \begin_layout Plain Layout
14509 \begin_inset Index idx
14512 \begin_layout Plain Layout
14525 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
14528 \begin_layout Plain Layout
14529 \begin_inset Formula $\sum$
14539 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
14542 \begin_layout Plain Layout
14546 \begin_inset Index idx
14549 \begin_layout Plain Layout
14556 \begin_layout Plain Layout
14575 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
14578 \begin_layout Plain Layout
14579 \begin_inset Formula $\prod$
14589 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
14592 \begin_layout Plain Layout
14600 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
14603 \begin_layout Plain Layout
14604 \begin_inset Formula $\coprod$
14614 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
14617 \begin_layout Plain Layout
14625 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
14628 \begin_layout Plain Layout
14629 \begin_inset Formula $\bigodot$
14639 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
14642 \begin_layout Plain Layout
14650 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
14653 \begin_layout Plain Layout
14654 \begin_inset Formula $\bigotimes$
14664 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
14667 \begin_layout Plain Layout
14675 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
14678 \begin_layout Plain Layout
14679 \begin_inset Formula $\bigoplus$
14689 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
14692 \begin_layout Plain Layout
14700 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
14703 \begin_layout Plain Layout
14704 \begin_inset Formula $\bigwedge$
14714 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
14717 \begin_layout Plain Layout
14725 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
14728 \begin_layout Plain Layout
14729 \begin_inset Formula $\bigvee$
14739 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
14742 \begin_layout Plain Layout
14750 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
14753 \begin_layout Plain Layout
14754 \begin_inset Formula $\bigsqcup$
14764 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
14767 \begin_layout Plain Layout
14775 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
14778 \begin_layout Plain Layout
14779 \begin_inset Formula $\biguplus$
14793 \begin_inset space \hfill{}
14799 \begin_layout Standard
14800 All big operators can also be inserted via the math toolbar button
14803 arg "math-insert \\intop"
14809 \begin_layout Standard
14810 The operators are called big because they are bigger than the sometimes
14811 equal looking binary operators.
14812 All big operators can have limits as described in the next subsection.
14815 \begin_layout Standard
14816 For all integral operators there is a second version available, ending in
14834 These operators are different from
14841 \begin_inset space \space{}
14844 in the style the operator limits are displayed, see
14845 \begin_inset CommandInset ref
14847 reference "sub:Operator-Limits"
14855 \begin_layout Subsubsection*
14856 Advice for Integrals
14859 \begin_layout Standard
14864 in an integral is an operator, that therefore has to be set upright.
14865 This is done by highlighting the
14869 and using the keyboard shortcut
14879 \begin_layout Plain Layout
14885 \begin_inset CommandInset ref
14887 reference "sub:Font-Styles"
14897 Finally the smallest space is inserted before the
14901 , as this is usual for operators.
14905 \begin_layout Standard
14907 \begin_inset Formula $\int A(x)dx$
14911 \begin_inset Newline newline
14915 \begin_inset Phantom HPhantom
14918 \begin_layout Plain Layout
14925 \begin_inset Formula $\int A(x)\,\mathrm{d}x$
14931 \begin_layout Standard
14932 For multiple integrals there are the following commands:
14933 \begin_inset VSpace medskip
14939 \begin_layout Standard
14940 \begin_inset space \hfill{}
14944 \begin_inset Tabular
14945 <lyxtabular version="3" rows="4" columns="2">
14946 <features rotate="0" tabularvalignment="middle">
14947 <column alignment="center" valignment="top">
14948 <column alignment="center" valignment="top">
14950 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
14953 \begin_layout Plain Layout
14959 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
14962 \begin_layout Plain Layout
14964 \begin_inset Note Note
14967 \begin_layout Plain Layout
14974 is only used as spacer.
14986 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
14989 \begin_layout Plain Layout
14997 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
15000 \begin_layout Plain Layout
15001 \begin_inset Formula $\raisebox{4.5mm}{}\iint\raisebox{-2.5mm}{}$
15011 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
15014 \begin_layout Plain Layout
15022 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
15025 \begin_layout Plain Layout
15026 \begin_inset Formula $\raisebox{4.5mm}{}\oiint\raisebox{-2.5mm}{}$
15036 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
15039 \begin_layout Plain Layout
15047 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
15050 \begin_layout Plain Layout
15051 \begin_inset Formula $\raisebox{4.5mm}{}\sqiint\raisebox{-2.5mm}{}$
15065 \begin_inset space \hfill{}
15069 \begin_inset Tabular
15070 <lyxtabular version="3" rows="4" columns="2">
15071 <features rotate="0" tabularvalignment="middle">
15072 <column alignment="center" valignment="top">
15073 <column alignment="center" valignment="top">
15075 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
15078 \begin_layout Plain Layout
15084 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
15087 \begin_layout Plain Layout
15095 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
15098 \begin_layout Plain Layout
15106 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
15109 \begin_layout Plain Layout
15110 \begin_inset Formula $\raisebox{4.5mm}{}\iiint\raisebox{-2.5mm}{}$
15120 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
15123 \begin_layout Plain Layout
15131 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
15134 \begin_layout Plain Layout
15135 \begin_inset Formula $\raisebox{4.5mm}{}\iiiint\raisebox{-2.5mm}{}$
15145 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
15148 \begin_layout Plain Layout
15156 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
15159 \begin_layout Plain Layout
15160 \begin_inset Formula $\raisebox{4.5mm}{}\dotsint\raisebox{-2.5mm}{}$
15174 \begin_inset space \hfill{}
15180 \begin_layout Standard
15181 \begin_inset Newpage newpage
15187 \begin_layout Subsection
15189 \begin_inset CommandInset label
15191 name "sub:Operator-Limits"
15196 \begin_inset Index idx
15199 \begin_layout Plain Layout
15208 \begin_layout Standard
15209 Limits are created by super- and subscripts:
15212 \begin_layout Standard
15214 \begin_inset Tabular
15215 <lyxtabular version="3" rows="2" columns="2">
15216 <features rotate="0" tabularvalignment="middle">
15217 <column alignment="center" valignment="top" width="0pt">
15218 <column alignment="center" valignment="top" width="0pt">
15220 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
15223 \begin_layout Plain Layout
15229 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
15232 \begin_layout Plain Layout
15234 \begin_inset Note Note
15237 \begin_layout Plain Layout
15244 is only used as spacer.
15256 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
15259 \begin_layout Plain Layout
15265 \begin_inset space \textvisiblespace{}
15269 \begin_inset Formula $\to$
15273 \begin_inset Formula $\to$
15281 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
15284 \begin_layout Plain Layout
15285 \begin_inset Formula $\raisebox{5mm}{}\prod_{0}^{\infty}A(x)\raisebox{-2.5mm}{}$
15301 \begin_layout Standard
15302 Limits of inline formulas are set right beside the operator.
15303 Limits in displayed formulas are set above or below the operator, except
15304 for integral limits.
15307 \begin_layout Standard
15308 To force that the limits are set beside the operator, the cursor is set
15309 directly behind the operator and the limits type is changed with the menu
15312 Edit\SpecialChar \menuseparator
15313 Math\SpecialChar \menuseparator
15332 \begin_layout Standard
15333 The default limits type is this:
15334 \begin_inset Formula
15336 \sum_{x=0}^{\infty}\frac{1}{x^{2}}
15341 This is how it looks when the limits type was changed to
15348 \begin_inset Formula
15350 \sum\nolimits _{x=0}^{\infty}\frac{1}{x^{2}}
15355 For integrals, except those ending with
15371 etc., the limits are by default set beside the operator.
15372 But for multiple integrals the limits are often set below the operator.
15373 In the following example the limits type was therefore set to
15377 and so set below the integrals:
15378 \begin_inset Formula
15380 \iiint\limits _{V}X\,\mathrm{d}V=U\label{eq:VolInt}
15388 \begin_layout Standard
15389 \begin_inset VSpace medskip
15392 To specify conditions for limits, the commands
15399 \begin_inset Index idx
15402 \begin_layout Plain Layout
15417 \begin_inset Index idx
15420 \begin_layout Plain Layout
15429 To create for example this expression
15430 \begin_inset Formula
15432 \sum_{\begin{subarray}{c}
15436 \end{subarray}}^{n}k^{-2}\label{eq:substack}
15444 \begin_layout Standard
15445 the following has to be done:
15446 \begin_inset Newline newline
15458 \begin_inset space \textvisiblespace{}
15464 One is now in a blue box under the summation operator and insert there
15470 \begin_inset space \textvisiblespace{}
15476 The blue box is now within a purple box and now several lines can be written
15478 A new line is created by inserting a line break (
15481 arg "newline-insert newline"
15486 \begin_inset Newline newline
15491 0<k<1000 Ctrl+Return
15492 \begin_inset Newline newline
15497 is typed in, a new box appears below for the new line.
15500 \begin_layout Standard
15501 The alignment of the lines can be changed to left aligned with the
15511 Edit\SpecialChar \menuseparator
15515 To get right alignment,
15520 \begin_inset space \textvisiblespace{}
15525 is inserted at the beginning of the line.
15528 \begin_layout Standard
15541 with the difference that the lines are always centered.
15544 \begin_layout Standard
15545 \begin_inset VSpace bigskip
15549 \begin_inset CommandInset ref
15551 reference "eq:substack"
15555 there can be too much space beside an operator, because the characters
15556 following the operator are set beside the limits.
15557 To avoid this the command
15564 \begin_inset Index idx
15567 \begin_layout Plain Layout
15576 It sets the width of its content to 0
15577 \begin_inset space \thinspace{}
15581 \begin_inset Newline newline
15585 \begin_inset CommandInset ref
15587 reference "eq:substack"
15591 , one uses the command
15594 \begin_layout Standard
15604 \begin_inset space \textvisiblespace{}
15607 0<k<1000 Ctrl+Return
15610 \begin_layout Standard
15611 to create the lower limit.
15612 The summand is now directly behind the summation operator:
15613 \begin_inset Formula
15615 \sum_{\mathclap{\substack{0<k<1000\\
15627 \begin_layout Standard
15628 \begin_inset VSpace bigskip
15634 \begin_layout Standard
15635 When several consecutive operators have limits the typesetting of the limits
15636 looks often imperfect in the output, see this example:
15637 \begin_inset Formula
15639 \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}
15644 To improve the typesetting set in the document settings under
15647 \begin_inset space ~
15657 \begin_inset Index idx
15660 \begin_layout Plain Layout
15661 Packages ! mathtools
15669 \begin_inset space ~
15675 Then insert into your formula the command
15682 \begin_inset Index idx
15685 \begin_layout Plain Layout
15693 directly before the first operator.
15694 The example will then look like this:
15695 \begin_inset Formula
15697 \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}
15705 \begin_layout Standard
15706 \begin_inset VSpace bigskip
15709 How to use one limit for several operators is described in
15710 \begin_inset CommandInset ref
15712 reference "sub:Self-defined-Operators"
15719 \begin_layout Subsection
15720 Decoration for Operators
15721 \begin_inset Index idx
15724 \begin_layout Plain Layout
15725 Operators ! Decoration
15733 \begin_layout Standard
15741 \begin_inset Index idx
15744 \begin_layout Plain Layout
15759 \begin_inset Index idx
15762 \begin_layout Plain Layout
15770 characters can be placed above or below an operator, respectively.
15778 \begin_inset Index idx
15781 \begin_layout Plain Layout
15789 characters can be set before and behind a big operator.
15792 \begin_layout Standard
15794 \begin_inset space ~
15806 \begin_layout Itemize
15813 is used to set characters at the corners of the operator
15816 \begin_layout Itemize
15823 is used to set characters before and/or behind the operator (this variant
15824 represents LaTeX's original
15833 \begin_layout Itemize
15840 is used to set characters at the left corners and/or behind the operator
15843 \begin_layout Itemize
15850 is used to set characters at the right corners and/or before the operator
15853 \begin_layout Standard
15854 For example the command
15859 \begin_inset space \textvisiblespace{}
15865 \begin_inset space \textvisiblespace{}
15869 \begin_inset Formula $\to$
15873 \begin_inset Formula $\to$
15877 \begin_inset space \textvisiblespace{}
15887 \begin_inset Formula
15889 \sideset{}{'}\sum_{k=1}^{n}
15897 \begin_layout Standard
15898 \begin_inset Note Greyedout
15901 \begin_layout Plain Layout
15908 can only be used to decorate big operators, binary operators are not allowed.
15916 \begin_layout Standard
15929 can also be used to decorate symbols and characters.
15930 For example, the command
15935 \begin_inset space \textvisiblespace{}
15941 \begin_inset space \textvisiblespace{}
15947 \begin_inset Formula $\uparrow$
15955 \begin_inset Formula
15957 \overset{a}{\maltese}
15965 \begin_layout Subsection
15967 \begin_inset CommandInset label
15969 name "sub:Binary-Operators"
15974 \begin_inset Index idx
15977 \begin_layout Plain Layout
15986 \begin_layout Standard
15987 Binary operators are surrounded by space when there is a character before
15989 \begin_inset VSpace medskip
15995 \begin_layout Standard
15996 \begin_inset space \hfill{}
16000 \begin_inset Tabular
16001 <lyxtabular version="3" rows="13" columns="2">
16002 <features rotate="0" tabularvalignment="middle">
16003 <column alignment="center" valignment="top" width="0pt">
16004 <column alignment="center" valignment="top" width="0pt">
16006 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
16009 \begin_layout Plain Layout
16011 \begin_inset Note Note
16014 \begin_layout Plain Layout
16021 is only used as spacer.
16031 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
16034 \begin_layout Plain Layout
16042 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
16045 \begin_layout Plain Layout
16051 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
16054 \begin_layout Plain Layout
16055 \begin_inset Formula $+$
16065 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
16068 \begin_layout Plain Layout
16074 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
16077 \begin_layout Plain Layout
16078 \begin_inset Formula $-$
16088 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
16091 \begin_layout Plain Layout
16099 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
16102 \begin_layout Plain Layout
16103 \begin_inset Formula $\pm$
16113 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
16116 \begin_layout Plain Layout
16124 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
16127 \begin_layout Plain Layout
16128 \begin_inset Formula $\mp$
16138 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
16141 \begin_layout Plain Layout
16149 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
16152 \begin_layout Plain Layout
16153 \begin_inset Formula $\cdot$
16163 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
16166 \begin_layout Plain Layout
16174 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
16177 \begin_layout Plain Layout
16178 \begin_inset Formula $\times$
16188 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
16191 \begin_layout Plain Layout
16199 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
16202 \begin_layout Plain Layout
16203 \begin_inset Formula $\div$
16213 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
16216 \begin_layout Plain Layout
16220 \begin_layout Plain Layout
16233 \begin_layout Plain Layout
16245 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
16248 \begin_layout Plain Layout
16249 \begin_inset Formula $*$
16259 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
16262 \begin_layout Plain Layout
16270 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
16273 \begin_layout Plain Layout
16274 \begin_inset Formula $\star$
16284 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
16287 \begin_layout Plain Layout
16295 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
16298 \begin_layout Plain Layout
16299 \begin_inset Formula $\circ$
16309 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
16312 \begin_layout Plain Layout
16320 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
16323 \begin_layout Plain Layout
16324 \begin_inset Formula $\diamond$
16334 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
16337 \begin_layout Plain Layout
16345 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
16348 \begin_layout Plain Layout
16349 \begin_inset Formula $\bullet$
16363 \begin_inset space \hfill{}
16367 \begin_inset Tabular
16368 <lyxtabular version="3" rows="13" columns="2">
16369 <features rotate="0" tabularvalignment="middle">
16370 <column alignment="center" valignment="top" width="0pt">
16371 <column alignment="center" valignment="top" width="0pt">
16373 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
16376 \begin_layout Plain Layout
16382 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
16385 \begin_layout Plain Layout
16393 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
16396 \begin_layout Plain Layout
16404 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
16407 \begin_layout Plain Layout
16408 \begin_inset Formula $\nabla$
16418 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
16421 \begin_layout Plain Layout
16429 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
16432 \begin_layout Plain Layout
16433 \begin_inset Formula $\bigtriangledown$
16443 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
16446 \begin_layout Plain Layout
16454 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
16457 \begin_layout Plain Layout
16458 \begin_inset Formula $\bigtriangleup$
16468 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
16471 \begin_layout Plain Layout
16479 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
16482 \begin_layout Plain Layout
16483 \begin_inset Formula $\Box$
16493 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
16496 \begin_layout Plain Layout
16504 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
16507 \begin_layout Plain Layout
16508 \begin_inset Formula $\cap$
16518 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
16521 \begin_layout Plain Layout
16529 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
16532 \begin_layout Plain Layout
16533 \begin_inset Formula $\cup$
16543 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
16546 \begin_layout Plain Layout
16554 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
16557 \begin_layout Plain Layout
16558 \begin_inset Formula $\dagger$
16568 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
16571 \begin_layout Plain Layout
16579 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
16582 \begin_layout Plain Layout
16583 \begin_inset Formula $\ddagger$
16593 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
16596 \begin_layout Plain Layout
16604 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
16607 \begin_layout Plain Layout
16608 \begin_inset Formula $\wr$
16618 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
16621 \begin_layout Plain Layout
16629 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
16632 \begin_layout Plain Layout
16633 \begin_inset Formula $\bigcirc$
16643 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
16646 \begin_layout Plain Layout
16654 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
16657 \begin_layout Plain Layout
16658 \begin_inset Formula $\wedge$
16668 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
16671 \begin_layout Plain Layout
16679 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
16682 \begin_layout Plain Layout
16683 \begin_inset Formula $\vee$
16697 \begin_inset space \hfill{}
16701 \begin_inset Tabular
16702 <lyxtabular version="3" rows="13" columns="2">
16703 <features rotate="0" tabularvalignment="middle">
16704 <column alignment="center" valignment="top" width="0pt">
16705 <column alignment="center" valignment="top" width="0pt">
16707 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
16710 \begin_layout Plain Layout
16716 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
16719 \begin_layout Plain Layout
16727 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
16730 \begin_layout Plain Layout
16738 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
16741 \begin_layout Plain Layout
16742 \begin_inset Formula $\oplus$
16752 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
16755 \begin_layout Plain Layout
16763 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
16766 \begin_layout Plain Layout
16767 \begin_inset Formula $\ominus$
16777 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
16780 \begin_layout Plain Layout
16788 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
16791 \begin_layout Plain Layout
16792 \begin_inset Formula $\otimes$
16802 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
16805 \begin_layout Plain Layout
16813 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
16816 \begin_layout Plain Layout
16817 \begin_inset Formula $\oslash$
16827 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
16830 \begin_layout Plain Layout
16838 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
16841 \begin_layout Plain Layout
16842 \begin_inset Formula $\odot$
16852 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
16855 \begin_layout Plain Layout
16863 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
16866 \begin_layout Plain Layout
16867 \begin_inset Formula $\amalg$
16877 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
16880 \begin_layout Plain Layout
16888 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
16891 \begin_layout Plain Layout
16892 \begin_inset Formula $\uplus$
16902 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
16905 \begin_layout Plain Layout
16913 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
16916 \begin_layout Plain Layout
16917 \begin_inset Formula $\setminus$
16927 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
16930 \begin_layout Plain Layout
16938 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
16941 \begin_layout Plain Layout
16942 \begin_inset Formula $\sqcap$
16952 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
16955 \begin_layout Plain Layout
16963 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
16966 \begin_layout Plain Layout
16967 \begin_inset Formula $\sqcup$
16977 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
16980 \begin_layout Plain Layout
16988 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
16991 \begin_layout Plain Layout
16992 \begin_inset Formula $\triangleleft$
17002 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
17005 \begin_layout Plain Layout
17013 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
17016 \begin_layout Plain Layout
17017 \begin_inset Formula $\triangleright$
17031 \begin_inset space \hfill{}
17037 \begin_layout Standard
17038 All binary operators can also be inserted via the math toolbar button
17041 arg "math-insert \\pm"
17047 \begin_layout Standard
17048 To typeset the Laplace operator also
17065 \begin_inset Formula $\nabla^{2}$
17068 ) can be used instead of
17077 \begin_layout Standard
17084 Insert\SpecialChar \menuseparator
17096 \begin_layout Subsection
17097 Self-defined Operators
17098 \begin_inset CommandInset label
17100 name "sub:Self-defined-Operators"
17105 \begin_inset Index idx
17108 \begin_layout Plain Layout
17109 Operators ! self-defined
17117 \begin_layout Standard
17118 With the help of the command
17122 DeclareMathOperator
17125 \begin_inset Index idx
17128 \begin_layout Plain Layout
17133 DeclareMathOperator
17138 custom operators can be defined in the LaTeX-preamble.
17139 Its command scheme is:
17142 \begin_layout Standard
17147 DeclareMathOperator{new command}{display}
17150 \begin_layout Standard
17151 Display can be characters or symbols that define how the operator looks
17153 To define a big operator a * is set behind the command.
17154 All self-defined big operators can have limits as described in
17155 \begin_inset CommandInset ref
17157 reference "sub:Operator-Limits"
17164 \begin_layout Standard
17165 For example the LaTeX-preamble line
17168 \begin_layout Standard
17173 DeclareMathOperator*{
17180 \begin_layout Standard
17181 defines the command
17187 , that inserts a big operator consisting of the lozenge symbol from
17188 \begin_inset CommandInset ref
17190 reference "sub:Miscellaneous-Symbols"
17195 \begin_inset Formula
17197 \Lozenge_{n=1}^{\infty}
17202 The command for this formula is:
17213 \begin_inset Formula $\to$
17219 \begin_layout Standard
17220 \begin_inset VSpace bigskip
17223 When self-defined operators are not used several times in the document,
17224 they can also be defined with the commands
17231 \begin_inset Index idx
17234 \begin_layout Plain Layout
17249 \begin_inset Index idx
17252 \begin_layout Plain Layout
17260 , which have the following scheme:
17263 \begin_layout Standard
17277 \begin_layout Standard
17284 defines big operators,
17293 \begin_layout Standard
17301 \begin_inset space \thinspace{}
17305 \begin_inset space \space{}
17308 be used to use one limit for several operators:
17311 \begin_layout Standard
17312 \begin_inset Formula
17314 \mathop{\sum\negmedspace\sum}_{i,j=1}^{N}
17322 \begin_layout Standard
17323 The command for the formula above is:
17324 \begin_inset Newline newline
17340 \begin_inset space \textvisiblespace{}
17346 \begin_inset Formula $\to$
17352 \begin_inset space \textvisiblespace{}
17360 \begin_layout Section
17362 \begin_inset Index idx
17365 \begin_layout Plain Layout
17374 \begin_layout Subsection
17376 \begin_inset CommandInset label
17378 name "sub:Font-Styles"
17383 \begin_inset Index idx
17386 \begin_layout Plain Layout
17395 \begin_layout Standard
17396 Latin letters in formulas can be set in one of the following font styles:
17397 \begin_inset VSpace -2mm
17403 \begin_layout Standard
17405 \begin_inset Tabular
17406 <lyxtabular version="3" rows="7" columns="3">
17407 <features rotate="0" tabularvalignment="middle">
17408 <column alignment="center" valignment="top">
17409 <column alignment="center" valignment="top">
17410 <column alignment="center" valignment="top">
17412 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
17415 \begin_layout Plain Layout
17421 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
17424 \begin_layout Plain Layout
17430 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
17433 \begin_layout Plain Layout
17441 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
17444 \begin_layout Plain Layout
17450 \begin_inset space \textvisiblespace{}
17460 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
17463 \begin_layout Plain Layout
17464 \begin_inset Formula $\mathbb{ABC}$
17472 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
17475 \begin_layout Plain Layout
17488 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
17491 \begin_layout Plain Layout
17497 \begin_inset space \textvisiblespace{}
17507 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
17510 \begin_layout Plain Layout
17511 \begin_inset Formula $\mathbf{AbC}$
17519 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
17522 \begin_layout Plain Layout
17535 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
17538 \begin_layout Plain Layout
17544 \begin_inset space \textvisiblespace{}
17554 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
17557 \begin_layout Plain Layout
17558 \begin_inset Formula $\boldsymbol{AbC}$
17566 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
17569 \begin_layout Plain Layout
17572 arg "font-boldsymbol"
17582 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
17585 \begin_layout Plain Layout
17591 \begin_inset space \textvisiblespace{}
17601 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
17604 \begin_layout Plain Layout
17605 \begin_inset Formula $\mathcal{ABC}$
17613 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
17616 \begin_layout Plain Layout
17629 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
17632 \begin_layout Plain Layout
17638 \begin_inset space \textvisiblespace{}
17648 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
17651 \begin_layout Plain Layout
17652 \begin_inset Formula $\mathfrak{AbC}$
17660 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
17663 \begin_layout Plain Layout
17671 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
17674 \begin_layout Plain Layout
17680 \begin_inset space \textvisiblespace{}
17690 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
17693 \begin_layout Plain Layout
17694 \begin_inset Formula $\mathscr{AbC}$
17702 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
17705 \begin_layout Plain Layout
17719 \begin_layout Standard
17721 \begin_inset Tabular
17722 <lyxtabular version="3" rows="5" columns="3">
17723 <features rotate="0" tabularvalignment="middle">
17724 <column alignment="center" valignment="top">
17725 <column alignment="center" valignment="top">
17726 <column alignment="center" valignment="top">
17728 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
17731 \begin_layout Plain Layout
17737 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
17740 \begin_layout Plain Layout
17746 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
17749 \begin_layout Plain Layout
17757 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
17760 \begin_layout Plain Layout
17766 \begin_inset space \textvisiblespace{}
17776 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
17779 \begin_layout Plain Layout
17780 \begin_inset Formula $\mathit{AbC}$
17788 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
17791 \begin_layout Plain Layout
17799 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
17802 \begin_layout Plain Layout
17808 \begin_inset space \textvisiblespace{}
17818 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
17821 \begin_layout Plain Layout
17822 \begin_inset Formula $\mathrm{AbC}$
17830 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
17833 \begin_layout Plain Layout
17846 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
17849 \begin_layout Plain Layout
17855 \begin_inset space \textvisiblespace{}
17865 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
17868 \begin_layout Plain Layout
17869 \begin_inset Formula $\mathsf{AbC}$
17877 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
17880 \begin_layout Plain Layout
17893 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
17896 \begin_layout Plain Layout
17902 \begin_inset space \textvisiblespace{}
17912 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
17915 \begin_layout Plain Layout
17916 \begin_inset Formula $\mathtt{AbC}$
17924 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
17927 \begin_layout Plain Layout
17930 arg "font-typewriter"
17946 \begin_layout Standard
17947 \begin_inset Note Greyedout
17950 \begin_layout Plain Layout
17967 can only be used for big letters.
17975 \begin_layout Standard
17976 Predefined is the style
17985 \begin_layout Standard
17986 The style commands work also for letters in mathematical constructs:
17987 \begin_inset Formula
17989 \mathfrak{A=\frac{b}{C}}
17997 \begin_layout Standard
17998 Characters in mathematical text don't appear in a math font style but in
17999 the text font style
18006 That their style can't be set correctly via the text style dialog is a
18011 \begin_layout Plain Layout
18012 \begin_inset CommandInset href
18014 name "LyX-bug #4629"
18015 target "http://www.lyx.org/trac/ticket/4629"
18027 \begin_layout Standard
18028 Instead of the style commands the dialog
18030 Edit\SpecialChar \menuseparator
18031 Math\SpecialChar \menuseparator
18034 or the toolbar button
18037 arg "math-insert \\font"
18043 \begin_layout Subsection
18045 \begin_inset CommandInset label
18047 name "sub:Bold-Formulas"
18052 \begin_inset Index idx
18055 \begin_layout Plain Layout
18064 \begin_layout Standard
18065 To make a complete formula bold, the command
18071 from the previous subsection cannot be used, because it doesn't work for
18072 small Greek letters.
18073 Furthermore it prints Latin letters always upright, like in the following
18077 \begin_layout Standard
18078 \begin_inset Formula
18080 \mathbf{\int_{n}^{2}f(\theta)=\Gamma}\qquad\textrm{equation with \textbackslash mathbf}
18088 \begin_layout Standard
18089 To display the formula correctly, the command
18096 \begin_inset Formula
18098 \boldsymbol{\int_{n}^{2}f(\theta)=\Gamma\qquad\textrm{equation with \textbackslash boldsymbol}}
18103 It is also possible to set the formula in a
18105 boldmath environment
18108 This environment is created by inserting the command
18115 \begin_inset Index idx
18118 \begin_layout Plain Layout
18127 To end the environment, the command
18134 \begin_inset Index idx
18137 \begin_layout Plain Layout
18145 is inserted in TeX-mode.
18149 \begin_layout Plain Layout
18159 \begin_inset Formula
18161 \int_{n}^{2}f(\theta)=\Gamma\qquad\textrm{equation in a boldmath environment}
18170 \begin_layout Plain Layout
18182 \begin_layout Subsection
18184 \begin_inset Index idx
18187 \begin_layout Plain Layout
18196 \begin_layout Standard
18197 Formulas can be colored like normal text: Highlight a formula or a formula
18203 Here is a formula in magenta:
18204 \begin_inset Formula
18206 {\color{magenta}\int A\,\mathrm{d}x=\frac{\sqrt[5]{B}}{\ln\left(\frac{1}{3}\right)}}
18214 \begin_layout Standard
18215 You can also define your own colors as described in
18216 \begin_inset CommandInset ref
18218 reference "sub:Colored-Boxes"
18223 They can be used with the TeX code command
18230 \begin_inset Index idx
18233 \begin_layout Plain Layout
18244 \begin_layout Standard
18249 textcolor{color}{characters or formula}
18252 \begin_layout Standard
18253 The following example was colored completely dark green and partly red:
18256 \begin_layout Standard
18260 \begin_layout Plain Layout
18264 textcolor{darkgreen}{
18270 \begin_inset Formula
18272 \int A\,\mathrm{d}x=\frac{{\color{red}\sqrt[5]{B}}}{\ln\left(\frac{1}{3}\right)}
18281 \begin_layout Plain Layout
18291 \begin_layout Standard
18292 Due to a bug in LyX only complete formulas can be colored with self-defined
18297 \begin_layout Plain Layout
18298 \begin_inset CommandInset href
18300 name "LyX-bug #5269"
18301 target "http://www.lyx.org/trac/ticket/5269"
18313 \begin_layout Subsection
18315 \begin_inset CommandInset label
18317 name "sub:Font-Sizes"
18322 \begin_inset Index idx
18325 \begin_layout Plain Layout
18334 \begin_layout Standard
18335 For characters in formulas there are, analog to characters in text, the
18336 following size commands:
18339 \begin_layout Standard
18383 \begin_inset Newline newline
18405 \begin_layout Standard
18406 The size produced by the commands depends on the document font size, which
18407 corresponds to the command
18414 The other commands produce smaller or larger sizes than
18421 The font size can however not exceed a certain value.
18422 Is for example the document font size 12
18423 \begin_inset space \thinspace{}
18432 switches to the same size as
18442 \begin_layout Standard
18443 A size command is inserted in TeX-mode before the formula and sets the size
18444 for all following formula and text characters.
18445 To switch back to the initial size, the command
18451 is inserted behind the formula in TeX-mode.
18454 \begin_layout Standard
18455 Within a formula the size can be changed using the following size commands
18456 or the toolbar button
18459 arg "math-insert \\style"
18465 \begin_layout Standard
18468 \begin_inset Tabular
18469 <lyxtabular version="3" rows="5" columns="2">
18470 <features rotate="0" tabularvalignment="middle">
18471 <column alignment="center" valignment="top">
18472 <column alignment="center" valignment="top">
18474 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
18477 \begin_layout Plain Layout
18483 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
18486 \begin_layout Plain Layout
18488 \begin_inset Note Note
18491 \begin_layout Plain Layout
18498 is only used as spacer.
18510 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
18513 \begin_layout Plain Layout
18517 \begin_inset Index idx
18520 \begin_layout Plain Layout
18533 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
18536 \begin_layout Plain Layout
18537 \begin_inset Formula $\raisebox{6.5mm}{}{\displaystyle E_{\mathrm{pot_{1}}}=\frac{K}{l+\frac{m}{n_{2}}}}\raisebox{-5.5mm}{}$
18547 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
18550 \begin_layout Plain Layout
18558 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
18561 \begin_layout Plain Layout
18562 \begin_inset Formula $\raisebox{4.5mm}{}{\textstyle E_{\mathrm{pot_{1}}}=\frac{K}{l+\frac{m}{n_{2}}}}\raisebox{-4mm}{}$
18572 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
18575 \begin_layout Plain Layout
18583 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
18586 \begin_layout Plain Layout
18587 \begin_inset Formula $\raisebox{4.5mm}{}{\scriptstyle E_{\mathrm{pot_{1}}}=\frac{K}{l+\frac{m}{n_{2}}}}\raisebox{-3.5mm}{}$
18597 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
18600 \begin_layout Plain Layout
18608 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
18611 \begin_layout Plain Layout
18612 \begin_inset Formula $\raisebox{4.5mm}{}{\scriptscriptstyle E_{\mathrm{pot_{1}}}=\frac{K}{l+\frac{m}{n_{2}}}}\raisebox{-3.5mm}{}$
18628 \begin_layout Standard
18629 After entering these commands, a blue box appears in which the formula parts
18633 \begin_layout Standard
18634 There is a further method to change the font size, that though only works
18635 for symbols or letters in mathematical text.
18636 To use it, one of the above text size commands is inserted in mathematical
18638 All following characters until the end of the mathematical text or until
18639 another size command will have the selected size.
18641 \begin_inset VSpace -2mm
18647 \begin_layout Standard
18651 \begin_layout Plain Layout
18661 \begin_inset Formula
18663 A=\frac{B}{c}\cdot\maltese
18669 \begin_inset Formula
18671 \maltese A\textrm{\Large\maltese\textit{A}}\textrm{\tiny\maltese\textit{A}}
18680 \begin_layout Plain Layout
18692 \begin_layout Standard
18693 \begin_inset VSpace medskip
18696 Before both formulas the command
18703 The command for the second formula is:
18704 \begin_inset Newline newline
18712 \begin_inset space \textvisiblespace{}
18718 \begin_inset space \textvisiblespace{}
18724 \begin_inset space \textvisiblespace{}
18730 \begin_inset space \textvisiblespace{}
18734 \begin_inset Formula $\to$
18738 \begin_inset Formula $\to$
18742 \begin_inset Newline newline
18746 \begin_inset space \hspace*{}
18757 \begin_inset space \textvisiblespace{}
18763 \begin_inset space \textvisiblespace{}
18769 \begin_inset space \textvisiblespace{}
18775 \begin_layout Standard
18776 If a symbol cannot be displayed in different sizes, it will always be displayed
18777 in the default size.
18780 \begin_layout Section
18782 \begin_inset Index idx
18785 \begin_layout Plain Layout
18794 \begin_layout Standard
18795 Greek letters can also be inserted via the toolbar button
18798 arg "math-insert \\alpha"
18802 All international typesetting norms purport that Greek letters in math
18803 have to be typeset italic/slanted.
18804 In some languages, like French or Russian, they are nevertheless sometimes
18808 \begin_layout Subsection
18810 \begin_inset Index idx
18813 \begin_layout Plain Layout
18814 Greek letters ! small
18822 \begin_layout Standard
18823 \begin_inset space \hfill{}
18827 \begin_inset Tabular
18828 <lyxtabular version="3" rows="11" columns="2">
18829 <features rotate="0" tabularvalignment="middle">
18830 <column alignment="center" valignment="top" width="0pt">
18831 <column alignment="center" valignment="top" width="0pt">
18833 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
18836 \begin_layout Plain Layout
18842 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
18845 \begin_layout Plain Layout
18853 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
18856 \begin_layout Plain Layout
18864 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
18867 \begin_layout Plain Layout
18868 \begin_inset Formula $\alpha$
18878 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
18881 \begin_layout Plain Layout
18889 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
18892 \begin_layout Plain Layout
18893 \begin_inset Formula $\beta$
18903 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
18906 \begin_layout Plain Layout
18914 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
18917 \begin_layout Plain Layout
18918 \begin_inset Formula $\gamma$
18928 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
18931 \begin_layout Plain Layout
18939 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
18942 \begin_layout Plain Layout
18943 \begin_inset Formula $\delta$
18953 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
18956 \begin_layout Plain Layout
18964 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
18967 \begin_layout Plain Layout
18968 \begin_inset Formula $\epsilon$
18978 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
18981 \begin_layout Plain Layout
18989 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
18992 \begin_layout Plain Layout
18993 \begin_inset Formula $\varepsilon$
19003 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
19006 \begin_layout Plain Layout
19014 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
19017 \begin_layout Plain Layout
19018 \begin_inset Formula $\zeta$
19028 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
19031 \begin_layout Plain Layout
19039 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
19042 \begin_layout Plain Layout
19043 \begin_inset Formula $\eta$
19053 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
19056 \begin_layout Plain Layout
19064 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
19067 \begin_layout Plain Layout
19068 \begin_inset Formula $\theta$
19078 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
19081 \begin_layout Plain Layout
19089 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
19092 \begin_layout Plain Layout
19093 \begin_inset Formula $\vartheta$
19107 \begin_inset space \hfill{}
19111 \begin_inset Tabular
19112 <lyxtabular version="3" rows="12" columns="2">
19113 <features rotate="0" tabularvalignment="middle">
19114 <column alignment="center" valignment="top" width="0pt">
19115 <column alignment="center" valignment="top" width="0pt">
19117 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
19120 \begin_layout Plain Layout
19126 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
19129 \begin_layout Plain Layout
19137 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
19140 \begin_layout Plain Layout
19148 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
19151 \begin_layout Plain Layout
19152 \begin_inset Formula $\iota$
19162 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
19165 \begin_layout Plain Layout
19173 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
19176 \begin_layout Plain Layout
19177 \begin_inset Formula $\kappa$
19187 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
19190 \begin_layout Plain Layout
19198 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
19201 \begin_layout Plain Layout
19202 \begin_inset Formula $\varkappa$
19212 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
19215 \begin_layout Plain Layout
19223 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
19226 \begin_layout Plain Layout
19227 \begin_inset Formula $\lambda$
19237 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
19240 \begin_layout Plain Layout
19248 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
19251 \begin_layout Plain Layout
19252 \begin_inset Formula $\mu$
19262 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
19265 \begin_layout Plain Layout
19273 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
19276 \begin_layout Plain Layout
19277 \begin_inset Formula $\nu$
19287 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
19290 \begin_layout Plain Layout
19298 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
19301 \begin_layout Plain Layout
19302 \begin_inset Formula $\xi$
19312 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
19315 \begin_layout Plain Layout
19321 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
19324 \begin_layout Plain Layout
19325 \begin_inset Formula $o$
19335 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
19338 \begin_layout Plain Layout
19346 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
19349 \begin_layout Plain Layout
19350 \begin_inset Formula $\pi$
19360 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
19363 \begin_layout Plain Layout
19371 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
19374 \begin_layout Plain Layout
19375 \begin_inset Formula $\varpi$
19385 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
19388 \begin_layout Plain Layout
19396 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
19399 \begin_layout Plain Layout
19400 \begin_inset Formula $\rho$
19414 \begin_inset space \hfill{}
19418 \begin_inset Tabular
19419 <lyxtabular version="3" rows="11" columns="2">
19420 <features rotate="0" tabularvalignment="middle">
19421 <column alignment="center" valignment="top" width="0pt">
19422 <column alignment="center" valignment="top" width="0pt">
19424 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
19427 \begin_layout Plain Layout
19433 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
19436 \begin_layout Plain Layout
19444 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
19447 \begin_layout Plain Layout
19455 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
19458 \begin_layout Plain Layout
19459 \begin_inset Formula $\varrho$
19469 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
19472 \begin_layout Plain Layout
19480 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
19483 \begin_layout Plain Layout
19484 \begin_inset Formula $\sigma$
19494 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
19497 \begin_layout Plain Layout
19505 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
19508 \begin_layout Plain Layout
19509 \begin_inset Formula $\varsigma$
19519 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
19522 \begin_layout Plain Layout
19530 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
19533 \begin_layout Plain Layout
19534 \begin_inset Formula $\tau$
19544 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
19547 \begin_layout Plain Layout
19555 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
19558 \begin_layout Plain Layout
19559 \begin_inset Formula $\upsilon$
19569 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
19572 \begin_layout Plain Layout
19580 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
19583 \begin_layout Plain Layout
19584 \begin_inset Formula $\phi$
19594 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
19597 \begin_layout Plain Layout
19605 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
19608 \begin_layout Plain Layout
19609 \begin_inset Formula $\varphi$
19619 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
19622 \begin_layout Plain Layout
19630 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
19633 \begin_layout Plain Layout
19634 \begin_inset Formula $\chi$
19644 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
19647 \begin_layout Plain Layout
19655 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
19658 \begin_layout Plain Layout
19659 \begin_inset Formula $\psi$
19669 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
19672 \begin_layout Plain Layout
19680 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
19683 \begin_layout Plain Layout
19684 \begin_inset Formula $\omega$
19698 \begin_inset space \hfill{}
19704 \begin_layout Standard
19705 \begin_inset VSpace medskip
19711 \begin_layout Standard
19712 How to create special upright Greek letters is explained in
19713 \begin_inset CommandInset ref
19715 reference "sub:Upright-small-Greek"
19722 \begin_layout Subsection
19724 \begin_inset Index idx
19727 \begin_layout Plain Layout
19728 Greek letters ! big
19736 \begin_layout Standard
19737 \begin_inset space \hfill{}
19741 \begin_inset Tabular
19742 <lyxtabular version="3" rows="7" columns="2">
19743 <features rotate="0" tabularvalignment="middle">
19744 <column alignment="center" valignment="top" width="0pt">
19745 <column alignment="center" valignment="top" width="0pt">
19747 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
19750 \begin_layout Plain Layout
19756 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
19759 \begin_layout Plain Layout
19767 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
19770 \begin_layout Plain Layout
19778 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
19781 \begin_layout Plain Layout
19782 \begin_inset Formula $\Gamma$
19792 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
19795 \begin_layout Plain Layout
19803 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
19806 \begin_layout Plain Layout
19807 \begin_inset Formula $\Delta$
19817 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
19820 \begin_layout Plain Layout
19828 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
19831 \begin_layout Plain Layout
19832 \begin_inset Formula $\Theta$
19842 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
19845 \begin_layout Plain Layout
19853 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
19856 \begin_layout Plain Layout
19857 \begin_inset Formula $\Lambda$
19867 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
19870 \begin_layout Plain Layout
19878 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
19881 \begin_layout Plain Layout
19882 \begin_inset Formula $\Xi$
19892 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
19895 \begin_layout Plain Layout
19903 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
19906 \begin_layout Plain Layout
19907 \begin_inset Formula $\Pi$
19921 \begin_inset space \hfill{}
19925 \begin_inset Tabular
19926 <lyxtabular version="3" rows="6" columns="2">
19927 <features rotate="0" tabularvalignment="middle">
19928 <column alignment="center" valignment="top" width="0pt">
19929 <column alignment="center" valignment="top" width="0pt">
19931 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
19934 \begin_layout Plain Layout
19940 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
19943 \begin_layout Plain Layout
19951 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
19954 \begin_layout Plain Layout
19962 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
19965 \begin_layout Plain Layout
19966 \begin_inset Formula $\Sigma$
19976 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
19979 \begin_layout Plain Layout
19987 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
19990 \begin_layout Plain Layout
19991 \begin_inset Formula $\Upsilon$
20001 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
20004 \begin_layout Plain Layout
20012 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
20015 \begin_layout Plain Layout
20016 \begin_inset Formula $\Phi$
20026 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
20029 \begin_layout Plain Layout
20037 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
20040 \begin_layout Plain Layout
20041 \begin_inset Formula $\Psi$
20051 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
20054 \begin_layout Plain Layout
20062 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
20065 \begin_layout Plain Layout
20066 \begin_inset Formula $\Omega$
20080 \begin_inset space \hfill{}
20086 \begin_layout Standard
20087 \begin_inset VSpace medskip
20090 That the big Greek letters appear upright is caused by a design bug when
20092 To get correct italic big letters, begin every command with
20097 For example the command
20104 \begin_inset Formula $\varGamma$
20108 Another way is to load the package
20116 \begin_layout Plain Layout
20121 is part of the LaTeX-package
20126 \begin_inset Index idx
20129 \begin_layout Plain Layout
20134 \begin_layout Plain Layout
20154 \begin_inset Index idx
20157 \begin_layout Plain Layout
20163 with the LaTeX-preamble line
20166 \begin_layout Standard
20171 usepackage{fixmath}
20174 \begin_layout Standard
20175 Then all big Greek letters in a document will automatically be typeset italic.
20178 \begin_layout Subsection
20180 \begin_inset Index idx
20183 \begin_layout Plain Layout
20184 Greek letters ! bold
20192 \begin_layout Standard
20193 Greek letters cannot be set with different font styles like Latin letters.
20194 They can only be made bold with the command
20201 \begin_inset Index idx
20204 \begin_layout Plain Layout
20215 \begin_layout Standard
20217 \begin_inset Tabular
20218 <lyxtabular version="3" rows="3" columns="2">
20219 <features rotate="0" tabularvalignment="middle">
20220 <column alignment="center" valignment="top">
20221 <column alignment="center" valignment="top">
20223 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
20226 \begin_layout Plain Layout
20232 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
20235 \begin_layout Plain Layout
20243 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
20246 \begin_layout Plain Layout
20258 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
20261 \begin_layout Plain Layout
20262 \begin_inset Formula $\Upsilon\boldsymbol{\Upsilon}$
20272 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
20275 \begin_layout Plain Layout
20287 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
20290 \begin_layout Plain Layout
20291 \begin_inset Formula $\theta\boldsymbol{\theta}$
20307 \begin_layout Section
20312 \begin_layout Plain Layout
20325 \begin_layout Plain Layout
20326 A list with all symbols of most of the LaTeX-packages can be found in
20327 \begin_inset CommandInset citation
20342 \begin_layout Plain Layout
20350 \begin_inset Note Note
20353 \begin_layout Plain Layout
20356 texorpdfstring is used to avoid that the footnote appears in the PDF-bookmark.
20359 \begin_layout Plain Layout
20362 texorpdfstring is in section
20363 \begin_inset CommandInset ref
20365 reference "sub:Formulas-in-Section"
20375 \begin_inset Index idx
20378 \begin_layout Plain Layout
20387 \begin_layout Standard
20388 Many of the symbols listed in this section can also be inserted via the
20392 arg "math-insert \\nabla"
20398 arg "math-insert \\digamma"
20404 \begin_layout Subsection
20405 Mathematical Symbols
20406 \begin_inset CommandInset label
20408 name "sub:Mathematical-Symbols"
20413 \begin_inset Index idx
20416 \begin_layout Plain Layout
20417 Symbols ! mathematical
20425 \begin_layout Standard
20426 \begin_inset space \hfill{}
20430 \begin_inset Tabular
20431 <lyxtabular version="3" rows="10" columns="2">
20432 <features rotate="0" tabularvalignment="middle">
20433 <column alignment="center" valignment="top" width="0pt">
20434 <column alignment="center" valignment="top" width="0pt">
20436 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
20439 \begin_layout Plain Layout
20445 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
20448 \begin_layout Plain Layout
20456 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
20459 \begin_layout Plain Layout
20467 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
20470 \begin_layout Plain Layout
20471 \begin_inset Formula $\neg$
20481 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
20484 \begin_layout Plain Layout
20492 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
20495 \begin_layout Plain Layout
20496 \begin_inset Formula $\Im$
20506 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
20509 \begin_layout Plain Layout
20517 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
20520 \begin_layout Plain Layout
20521 \begin_inset Formula $\Re$
20531 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
20534 \begin_layout Plain Layout
20542 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
20545 \begin_layout Plain Layout
20546 \begin_inset Formula $\aleph$
20556 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
20559 \begin_layout Plain Layout
20567 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
20570 \begin_layout Plain Layout
20571 \begin_inset Formula $\partial$
20581 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
20584 \begin_layout Plain Layout
20592 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
20595 \begin_layout Plain Layout
20596 \begin_inset Formula $\infty$
20606 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
20609 \begin_layout Plain Layout
20617 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
20620 \begin_layout Plain Layout
20621 \begin_inset Formula $\wp$
20631 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
20634 \begin_layout Plain Layout
20642 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
20645 \begin_layout Plain Layout
20646 \begin_inset Formula $\imath$
20656 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
20659 \begin_layout Plain Layout
20667 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
20670 \begin_layout Plain Layout
20671 \begin_inset Formula $\jmath$
20685 \begin_inset space \hfill{}
20689 \begin_inset Tabular
20690 <lyxtabular version="3" rows="10" columns="2">
20691 <features rotate="0" tabularvalignment="middle">
20692 <column alignment="center" valignment="top" width="0pt">
20693 <column alignment="center" valignment="top" width="0pt">
20695 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
20698 \begin_layout Plain Layout
20704 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
20707 \begin_layout Plain Layout
20709 \begin_inset Note Note
20712 \begin_layout Plain Layout
20719 is only used as spacer.
20731 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
20734 \begin_layout Plain Layout
20742 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
20745 \begin_layout Plain Layout
20746 \begin_inset Formula $\forall$
20756 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
20759 \begin_layout Plain Layout
20767 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
20770 \begin_layout Plain Layout
20771 \begin_inset Formula $\exists$
20781 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
20784 \begin_layout Plain Layout
20792 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
20795 \begin_layout Plain Layout
20796 \begin_inset Formula $\nexists$
20806 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
20809 \begin_layout Plain Layout
20817 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
20820 \begin_layout Plain Layout
20821 \begin_inset Formula $\emptyset$
20831 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
20834 \begin_layout Plain Layout
20842 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
20845 \begin_layout Plain Layout
20846 \begin_inset Formula $\varnothing$
20856 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
20859 \begin_layout Plain Layout
20867 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
20870 \begin_layout Plain Layout
20871 \begin_inset Formula $\dag$
20881 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
20884 \begin_layout Plain Layout
20892 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
20895 \begin_layout Plain Layout
20896 \begin_inset Formula $\ddag$
20906 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
20909 \begin_layout Plain Layout
20917 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
20920 \begin_layout Plain Layout
20924 \begin_layout Plain Layout
20934 \begin_inset Formula $\complement$
20941 \begin_layout Plain Layout
20955 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
20958 \begin_layout Plain Layout
20966 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
20969 \begin_layout Plain Layout
20970 \begin_inset Formula $\Bbbk$
20984 \begin_inset space \hfill{}
20988 \begin_inset Tabular
20989 <lyxtabular version="3" rows="10" columns="2">
20990 <features rotate="0" tabularvalignment="middle">
20991 <column alignment="center" valignment="top" width="0pt">
20992 <column alignment="center" valignment="top" width="0pt">
20994 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
20997 \begin_layout Plain Layout
21003 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
21006 \begin_layout Plain Layout
21014 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
21017 \begin_layout Plain Layout
21025 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
21028 \begin_layout Plain Layout
21029 \begin_inset Formula $\prime$
21039 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
21042 \begin_layout Plain Layout
21050 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
21053 \begin_layout Plain Layout
21054 \begin_inset Formula $\backprime$
21064 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
21067 \begin_layout Plain Layout
21075 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
21078 \begin_layout Plain Layout
21079 \begin_inset Formula $\mho$
21089 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
21092 \begin_layout Plain Layout
21100 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
21103 \begin_layout Plain Layout
21104 \begin_inset Formula $\triangle$
21114 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
21117 \begin_layout Plain Layout
21125 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
21128 \begin_layout Plain Layout
21129 \begin_inset Formula $\angle$
21139 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
21142 \begin_layout Plain Layout
21150 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
21153 \begin_layout Plain Layout
21154 \begin_inset Formula $\measuredangle$
21164 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
21167 \begin_layout Plain Layout
21175 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
21178 \begin_layout Plain Layout
21179 \begin_inset Formula $\sphericalangle$
21189 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
21192 \begin_layout Plain Layout
21200 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
21203 \begin_layout Plain Layout
21204 \begin_inset Formula $\top$
21214 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
21217 \begin_layout Plain Layout
21225 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
21228 \begin_layout Plain Layout
21229 \begin_inset Formula $\bot$
21243 \begin_inset space \hfill{}
21249 \begin_layout Subsection
21250 Miscellaneous Symbols
21251 \begin_inset CommandInset label
21253 name "sub:Miscellaneous-Symbols"
21258 \begin_inset Index idx
21261 \begin_layout Plain Layout
21262 Symbols ! miscellaneous
21270 \begin_layout Standard
21273 \begin_inset Tabular
21274 <lyxtabular version="3" rows="10" columns="2">
21275 <features rotate="0" tabularvalignment="middle">
21276 <column alignment="center" valignment="top" width="0pt">
21277 <column alignment="center" valignment="top" width="0pt">
21279 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
21282 \begin_layout Plain Layout
21288 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
21291 \begin_layout Plain Layout
21299 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
21302 \begin_layout Plain Layout
21310 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
21313 \begin_layout Plain Layout
21314 \begin_inset Formula $\flat$
21324 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
21327 \begin_layout Plain Layout
21335 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
21338 \begin_layout Plain Layout
21339 \begin_inset Formula $\natural$
21349 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
21352 \begin_layout Plain Layout
21360 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
21363 \begin_layout Plain Layout
21364 \begin_inset Formula $\sharp$
21374 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
21377 \begin_layout Plain Layout
21385 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
21388 \begin_layout Plain Layout
21389 \begin_inset Formula $\surd$
21399 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
21402 \begin_layout Plain Layout
21410 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
21413 \begin_layout Plain Layout
21414 \begin_inset Formula $\checkmark$
21424 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
21427 \begin_layout Plain Layout
21435 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
21438 \begin_layout Plain Layout
21439 \begin_inset Formula $\yen$
21449 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
21452 \begin_layout Plain Layout
21460 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
21463 \begin_layout Plain Layout
21464 \begin_inset Formula $\pounds$
21474 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
21477 \begin_layout Plain Layout
21483 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
21486 \begin_layout Plain Layout
21487 \begin_inset Formula $\$$
21497 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
21500 \begin_layout Plain Layout
21506 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
21509 \begin_layout Plain Layout
21510 \begin_inset Formula $§$
21524 \begin_inset Tabular
21525 <lyxtabular version="3" rows="10" columns="2">
21526 <features rotate="0" tabularvalignment="middle">
21527 <column alignment="center" valignment="top">
21528 <column alignment="center" valignment="top">
21530 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
21533 \begin_layout Plain Layout
21539 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
21542 \begin_layout Plain Layout
21550 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
21553 \begin_layout Plain Layout
21561 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
21564 \begin_layout Plain Layout
21565 \begin_inset Formula $\hbar$
21575 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
21578 \begin_layout Plain Layout
21586 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
21589 \begin_layout Plain Layout
21590 \begin_inset Formula $\hslash$
21600 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
21603 \begin_layout Plain Layout
21611 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
21614 \begin_layout Plain Layout
21615 \begin_inset Formula $\clubsuit$
21625 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
21628 \begin_layout Plain Layout
21636 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
21639 \begin_layout Plain Layout
21640 \begin_inset Formula $\spadesuit$
21650 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
21653 \begin_layout Plain Layout
21661 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
21664 \begin_layout Plain Layout
21665 \begin_inset Formula $\bigstar$
21675 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
21678 \begin_layout Plain Layout
21686 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
21689 \begin_layout Plain Layout
21690 \begin_inset Formula $\blacklozenge$
21700 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
21703 \begin_layout Plain Layout
21711 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
21714 \begin_layout Plain Layout
21715 \begin_inset Formula $\blacktriangle$
21725 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
21728 \begin_layout Plain Layout
21736 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
21739 \begin_layout Plain Layout
21740 \begin_inset Formula $\blacktriangledown$
21750 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
21753 \begin_layout Plain Layout
21761 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
21764 \begin_layout Plain Layout
21765 \begin_inset Formula $\bullet$
21779 \begin_inset Tabular
21780 <lyxtabular version="3" rows="10" columns="2">
21781 <features rotate="0" tabularvalignment="middle">
21782 <column alignment="center" valignment="top" width="0pt">
21783 <column alignment="center" valignment="top" width="0pt">
21785 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
21788 \begin_layout Plain Layout
21794 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
21797 \begin_layout Plain Layout
21805 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
21808 \begin_layout Plain Layout
21816 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
21819 \begin_layout Plain Layout
21820 \begin_inset Formula $\diamondsuit$
21830 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
21833 \begin_layout Plain Layout
21841 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
21844 \begin_layout Plain Layout
21845 \begin_inset Formula $\Diamond$
21855 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
21858 \begin_layout Plain Layout
21866 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
21869 \begin_layout Plain Layout
21870 \begin_inset Formula $\heartsuit$
21880 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
21883 \begin_layout Plain Layout
21891 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
21894 \begin_layout Plain Layout
21895 \begin_inset Formula $\P$
21905 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
21908 \begin_layout Plain Layout
21916 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
21919 \begin_layout Plain Layout
21920 \begin_inset Formula $\copyright$
21930 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
21933 \begin_layout Plain Layout
21941 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
21944 \begin_layout Plain Layout
21945 \begin_inset Formula $\circledR$
21955 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
21958 \begin_layout Plain Layout
21966 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
21969 \begin_layout Plain Layout
21970 \begin_inset Formula $\maltese$
21980 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
21983 \begin_layout Plain Layout
21991 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
21994 \begin_layout Plain Layout
21995 \begin_inset Formula $\diagup$
22005 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
22008 \begin_layout Plain Layout
22016 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
22019 \begin_layout Plain Layout
22020 \begin_inset Formula $\diagdown$
22036 \begin_layout Standard
22037 \begin_inset VSpace medskip
22043 \begin_layout Standard
22044 Some symbols can be displayed in different sizes, see
22045 \begin_inset CommandInset ref
22047 reference "sub:Font-Sizes"
22054 \begin_layout Subsection
22056 \begin_inset Index idx
22059 \begin_layout Plain Layout
22060 Symbols ! Euro-symbol
22066 \begin_inset Index idx
22069 \begin_layout Plain Layout
22076 \begin_layout Plain Layout
22093 \begin_layout Standard
22094 To use the Euro symbol in formulas, the LaTeX-package
22099 \begin_inset Index idx
22102 \begin_layout Plain Layout
22108 must be installed and loaded with the LaTeX-preamble line
22111 \begin_layout Standard
22116 usepackage[gennarrow]{eurosym}
22119 \begin_layout Standard
22120 The Euro symbol can now be inserted with the command
22127 \begin_inset Index idx
22130 \begin_layout Plain Layout
22141 \begin_layout Standard
22142 The Euro symbol can directly be inserted with the € key in mathematical
22143 text, without having
22158 can also be inserted in TeX-mode.
22159 The official currency symbol can then be inserted with the command
22166 \begin_inset Index idx
22169 \begin_layout Plain Layout
22177 , that is only available in TeX-mode.
22180 \begin_layout Standard
22184 \begin_layout Plain Layout
22194 \begin_inset Note Note
22197 \begin_layout Plain Layout
22198 The following table will only be displayed when the LaTeX-package
22210 \begin_layout Standard
22211 An overview about the different Euro symbols:
22214 \begin_layout Standard
22216 \begin_inset Tabular
22217 <lyxtabular version="3" rows="4" columns="3">
22218 <features rotate="0" tabularvalignment="middle">
22219 <column alignment="center" valignment="top" width="0pt">
22220 <column alignment="center" valignment="top" width="0pt">
22221 <column alignment="center" valignment="top" width="0pt">
22223 <cell multicolumn="1" alignment="center" valignment="top" bottomline="true" usebox="none">
22226 \begin_layout Plain Layout
22232 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
22235 \begin_layout Plain Layout
22241 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
22244 \begin_layout Plain Layout
22252 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
22255 \begin_layout Plain Layout
22261 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
22264 \begin_layout Plain Layout
22272 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
22275 \begin_layout Plain Layout
22276 \begin_inset Formula $\euro$
22286 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
22289 \begin_layout Plain Layout
22295 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
22298 \begin_layout Plain Layout
22304 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
22307 \begin_layout Plain Layout
22308 \begin_inset Formula $\mbox{€}$
22318 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
22321 \begin_layout Plain Layout
22327 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
22330 \begin_layout Plain Layout
22338 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
22341 \begin_layout Plain Layout
22345 \begin_layout Plain Layout
22367 \begin_layout Standard
22371 \begin_layout Plain Layout
22381 \begin_inset Note Note
22384 \begin_layout Plain Layout
22385 The following will be displayed when the LaTeX-package
22397 \begin_layout Standard
22398 You need to install the LaTeX-package
22402 to see the rest of this subsection in the output.
22405 \begin_layout Standard
22409 \begin_layout Plain Layout
22421 \begin_layout Section
22423 \begin_inset CommandInset label
22425 name "sec:Relations"
22430 \begin_inset Index idx
22433 \begin_layout Plain Layout
22440 \begin_inset Index idx
22443 \begin_layout Plain Layout
22448 \begin_layout Plain Layout
22459 \begin_layout Plain Layout
22474 \begin_layout Standard
22475 All following relations can also be inserted via the toolbar button
22478 arg "math-insert \\leq"
22484 \begin_layout Standard
22485 \begin_inset space \hfill{}
22489 \begin_inset Tabular
22490 <lyxtabular version="3" rows="17" columns="2">
22491 <features rotate="0" tabularvalignment="middle">
22492 <column alignment="center" valignment="top" width="0pt">
22493 <column alignment="center" valignment="top" width="0pt">
22495 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
22498 \begin_layout Plain Layout
22504 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
22507 \begin_layout Plain Layout
22515 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
22518 \begin_layout Plain Layout
22524 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
22527 \begin_layout Plain Layout
22528 \begin_inset Formula $<$
22538 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
22541 \begin_layout Plain Layout
22549 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
22552 \begin_layout Plain Layout
22553 \begin_inset Formula $\le$
22563 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
22566 \begin_layout Plain Layout
22574 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
22577 \begin_layout Plain Layout
22578 \begin_inset Formula $\ll$
22588 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
22591 \begin_layout Plain Layout
22599 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
22602 \begin_layout Plain Layout
22603 \begin_inset Formula $\prec$
22613 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
22616 \begin_layout Plain Layout
22624 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
22627 \begin_layout Plain Layout
22628 \begin_inset Formula $\preceq$
22638 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
22641 \begin_layout Plain Layout
22649 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
22652 \begin_layout Plain Layout
22653 \begin_inset Formula $\subset$
22663 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
22666 \begin_layout Plain Layout
22674 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
22677 \begin_layout Plain Layout
22678 \begin_inset Formula $\subseteq$
22688 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
22691 \begin_layout Plain Layout
22699 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
22702 \begin_layout Plain Layout
22703 \begin_inset Formula $\sqsubseteq$
22713 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
22716 \begin_layout Plain Layout
22724 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
22727 \begin_layout Plain Layout
22728 \begin_inset Formula $\in$
22738 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
22741 \begin_layout Plain Layout
22749 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
22752 \begin_layout Plain Layout
22753 \begin_inset Formula $\vdash$
22763 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
22766 \begin_layout Plain Layout
22774 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
22777 \begin_layout Plain Layout
22778 \begin_inset Formula $\smile$
22788 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
22791 \begin_layout Plain Layout
22799 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
22802 \begin_layout Plain Layout
22803 \begin_inset Formula $\lhd$
22813 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
22816 \begin_layout Plain Layout
22824 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
22827 \begin_layout Plain Layout
22828 \begin_inset Formula $\unlhd$
22838 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
22841 \begin_layout Plain Layout
22849 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
22852 \begin_layout Plain Layout
22853 \begin_inset Formula $\gtrless$
22863 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
22866 \begin_layout Plain Layout
22874 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
22877 \begin_layout Plain Layout
22878 \begin_inset Formula $\mid$
22888 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
22891 \begin_layout Plain Layout
22899 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
22902 \begin_layout Plain Layout
22903 \begin_inset Formula $\nmid$
22917 \begin_inset space \hfill{}
22921 \begin_inset Tabular
22922 <lyxtabular version="3" rows="17" columns="2">
22923 <features rotate="0" tabularvalignment="middle">
22924 <column alignment="center" valignment="top" width="0pt">
22925 <column alignment="center" valignment="top" width="0pt">
22927 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
22930 \begin_layout Plain Layout
22936 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
22939 \begin_layout Plain Layout
22947 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
22950 \begin_layout Plain Layout
22956 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
22959 \begin_layout Plain Layout
22960 \begin_inset Formula $=$
22970 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
22973 \begin_layout Plain Layout
22981 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
22984 \begin_layout Plain Layout
22985 \begin_inset Formula $\not=$
22995 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
22998 \begin_layout Plain Layout
23006 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
23009 \begin_layout Plain Layout
23010 \begin_inset Formula $\equiv$
23020 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
23023 \begin_layout Plain Layout
23031 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
23034 \begin_layout Plain Layout
23035 \begin_inset Formula $\sim$
23045 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
23048 \begin_layout Plain Layout
23056 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
23059 \begin_layout Plain Layout
23060 \begin_inset Formula $\simeq$
23070 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
23073 \begin_layout Plain Layout
23081 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
23084 \begin_layout Plain Layout
23085 \begin_inset Formula $\approx$
23095 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
23098 \begin_layout Plain Layout
23106 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
23109 \begin_layout Plain Layout
23110 \begin_inset Formula $\cong$
23120 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
23123 \begin_layout Plain Layout
23131 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
23134 \begin_layout Plain Layout
23135 \begin_inset Formula $\bowtie$
23145 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
23148 \begin_layout Plain Layout
23156 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
23159 \begin_layout Plain Layout
23160 \begin_inset Formula $\notin$
23170 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
23173 \begin_layout Plain Layout
23181 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
23184 \begin_layout Plain Layout
23185 \begin_inset Formula $\perp$
23195 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
23198 \begin_layout Plain Layout
23206 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
23209 \begin_layout Plain Layout
23210 \begin_inset Formula $\propto$
23220 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
23223 \begin_layout Plain Layout
23231 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
23234 \begin_layout Plain Layout
23235 \begin_inset Formula $\asymp$
23245 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
23248 \begin_layout Plain Layout
23256 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
23259 \begin_layout Plain Layout
23260 \begin_inset Formula $\doteq$
23270 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
23273 \begin_layout Plain Layout
23281 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
23284 \begin_layout Plain Layout
23285 \begin_inset Formula $\circeq$
23295 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
23298 \begin_layout Plain Layout
23306 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
23309 \begin_layout Plain Layout
23310 \begin_inset Formula $\models$
23320 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
23323 \begin_layout Plain Layout
23331 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
23334 \begin_layout Plain Layout
23335 \begin_inset Formula $\widehat{=}$
23349 \begin_inset space \hfill{}
23353 \begin_inset Tabular
23354 <lyxtabular version="3" rows="17" columns="2">
23355 <features rotate="0" tabularvalignment="middle">
23356 <column alignment="center" valignment="top" width="0pt">
23357 <column alignment="center" valignment="top" width="0pt">
23359 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
23362 \begin_layout Plain Layout
23368 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
23371 \begin_layout Plain Layout
23379 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
23382 \begin_layout Plain Layout
23388 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
23391 \begin_layout Plain Layout
23392 \begin_inset Formula $>$
23402 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
23405 \begin_layout Plain Layout
23413 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
23416 \begin_layout Plain Layout
23417 \begin_inset Formula $\ge$
23427 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
23430 \begin_layout Plain Layout
23438 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
23441 \begin_layout Plain Layout
23442 \begin_inset Formula $\gg$
23452 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
23455 \begin_layout Plain Layout
23463 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
23466 \begin_layout Plain Layout
23467 \begin_inset Formula $\succ$
23477 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
23480 \begin_layout Plain Layout
23488 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
23491 \begin_layout Plain Layout
23492 \begin_inset Formula $\succeq$
23502 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
23505 \begin_layout Plain Layout
23513 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
23516 \begin_layout Plain Layout
23517 \begin_inset Formula $\supset$
23527 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
23530 \begin_layout Plain Layout
23538 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
23541 \begin_layout Plain Layout
23542 \begin_inset Formula $\supseteq$
23552 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
23555 \begin_layout Plain Layout
23563 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
23566 \begin_layout Plain Layout
23567 \begin_inset Formula $\sqsupseteq$
23577 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
23580 \begin_layout Plain Layout
23588 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
23591 \begin_layout Plain Layout
23592 \begin_inset Formula $\ni$
23602 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
23605 \begin_layout Plain Layout
23613 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
23616 \begin_layout Plain Layout
23617 \begin_inset Formula $\dashv$
23627 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
23630 \begin_layout Plain Layout
23638 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
23641 \begin_layout Plain Layout
23642 \begin_inset Formula $\frown$
23652 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
23655 \begin_layout Plain Layout
23663 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
23666 \begin_layout Plain Layout
23667 \begin_inset Formula $\rhd$
23677 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
23680 \begin_layout Plain Layout
23688 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
23691 \begin_layout Plain Layout
23692 \begin_inset Formula $\unrhd$
23702 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
23705 \begin_layout Plain Layout
23713 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
23716 \begin_layout Plain Layout
23717 \begin_inset Formula $\lessgtr$
23727 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
23730 \begin_layout Plain Layout
23738 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
23741 \begin_layout Plain Layout
23742 \begin_inset Formula $\parallel$
23752 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
23755 \begin_layout Plain Layout
23763 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
23766 \begin_layout Plain Layout
23767 \begin_inset Formula $\nparallel$
23781 \begin_inset space \hfill{}
23787 \begin_layout Standard
23788 \begin_inset VSpace medskip
23803 are bigger than the equal looking operators
23818 \begin_layout Standard
23819 LyX supports also many special relations.
23820 Use the toolbar button
23823 arg "math-insert \\leqq"
23826 to see a list of these relations.
23829 \begin_layout Standard
23830 Relations are, in contrary to symbols, always surrounded by space.
23833 \begin_layout Standard
23834 Relations with labels can be created with the command
23841 \begin_inset Index idx
23844 \begin_layout Plain Layout
23855 \begin_layout Standard
23857 \begin_inset Tabular
23858 <lyxtabular version="3" rows="2" columns="2">
23859 <features rotate="0" tabularvalignment="middle">
23860 <column alignment="center" valignment="top">
23861 <column alignment="center" valignment="top">
23863 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
23866 \begin_layout Plain Layout
23872 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
23875 \begin_layout Plain Layout
23877 \begin_inset Note Note
23880 \begin_layout Plain Layout
23887 is only used as spacer.
23899 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
23902 \begin_layout Plain Layout
23906 \begin_inset space \textvisiblespace{}
23914 \begin_inset space \textvisiblespace{}
23918 \begin_inset Formula $\downarrow$
23924 \begin_inset space \textvisiblespace{}
23928 \begin_inset space \textvisiblespace{}
23936 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
23939 \begin_layout Plain Layout
23940 \begin_inset Formula $\raisebox{5mm}{}A(r)\stackrel{r\to\infty}{\approx}B$
23956 \begin_layout Section
23960 \begin_layout Subsection
23961 Predefined Functions
23962 \begin_inset CommandInset label
23964 name "sub:Predefined-Functions"
23969 \begin_inset Index idx
23972 \begin_layout Plain Layout
23973 Functions ! predefined
23981 \begin_layout Standard
23982 In general, variables are set
23986 in mathematical expressions, but not function names, because
23987 \begin_inset Formula $sin$
23990 could be misunderstood as
23991 \begin_inset Formula $s\cdot i\cdot n$
23995 Therefore there are predefined functionswhich are additionally a bit separated
23997 They are inserted as commands starting with a backslash before their name.
24000 \begin_layout Standard
24002 \begin_inset Tabular
24003 <lyxtabular version="3" rows="2" columns="4">
24004 <features rotate="0" tabularvalignment="middle">
24005 <column alignment="center" valignment="top" width="0pt">
24006 <column alignment="center" valignment="top" width="0pt">
24007 <column alignment="center" valignment="top" width="0pt">
24008 <column alignment="center" valignment="top" width="0pt">
24010 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
24013 \begin_layout Plain Layout
24019 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
24022 \begin_layout Plain Layout
24028 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
24031 \begin_layout Plain Layout
24037 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
24040 \begin_layout Plain Layout
24048 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
24051 \begin_layout Plain Layout
24057 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
24060 \begin_layout Plain Layout
24061 \begin_inset Formula $Asin(x)+B$
24069 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
24072 \begin_layout Plain Layout
24080 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
24083 \begin_layout Plain Layout
24084 \begin_inset Formula $A\sin(x)+B$
24100 \begin_layout Standard
24101 The following functions are predefined:
24104 \begin_layout Standard
24105 \begin_inset VSpace -2mm
24111 \begin_layout Standard
24113 \begin_inset Tabular
24114 <lyxtabular version="3" rows="9" columns="4">
24115 <features rotate="0" tabularvalignment="middle">
24116 <column alignment="center" valignment="top" width="0pt">
24117 <column alignment="center" valignment="top" width="0pt">
24118 <column alignment="center" valignment="top" width="0pt">
24119 <column alignment="center" valignment="top" width="0pt">
24121 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
24124 \begin_layout Plain Layout
24130 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
24133 \begin_layout Plain Layout
24139 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
24142 \begin_layout Plain Layout
24148 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
24151 \begin_layout Plain Layout
24159 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
24162 \begin_layout Plain Layout
24170 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
24173 \begin_layout Plain Layout
24181 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
24184 \begin_layout Plain Layout
24192 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
24195 \begin_layout Plain Layout
24205 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
24208 \begin_layout Plain Layout
24216 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
24219 \begin_layout Plain Layout
24227 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
24230 \begin_layout Plain Layout
24238 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
24241 \begin_layout Plain Layout
24251 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
24254 \begin_layout Plain Layout
24262 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
24265 \begin_layout Plain Layout
24273 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
24276 \begin_layout Plain Layout
24284 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
24287 \begin_layout Plain Layout
24297 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
24300 \begin_layout Plain Layout
24308 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
24311 \begin_layout Plain Layout
24319 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
24322 \begin_layout Plain Layout
24330 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
24333 \begin_layout Plain Layout
24343 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
24346 \begin_layout Plain Layout
24354 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
24357 \begin_layout Plain Layout
24365 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
24368 \begin_layout Plain Layout
24376 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
24379 \begin_layout Plain Layout
24389 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
24392 \begin_layout Plain Layout
24400 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
24403 \begin_layout Plain Layout
24411 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
24414 \begin_layout Plain Layout
24422 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
24425 \begin_layout Plain Layout
24435 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
24438 \begin_layout Plain Layout
24446 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
24449 \begin_layout Plain Layout
24457 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
24460 \begin_layout Plain Layout
24468 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
24471 \begin_layout Plain Layout
24481 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
24484 \begin_layout Plain Layout
24492 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
24495 \begin_layout Plain Layout
24503 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
24506 \begin_layout Plain Layout
24514 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
24517 \begin_layout Plain Layout
24533 \begin_layout Standard
24534 They can also be inserted with the math toolbar button
24537 arg "math-insert \\functions"
24543 \begin_layout Subsection
24544 Self-defined Functions
24545 \begin_inset Index idx
24548 \begin_layout Plain Layout
24549 Functions ! self-defined
24557 \begin_layout Standard
24558 To use a function that is not predefined, like for example the sign function
24559 sgn(x), there are two possibilities:
24562 \begin_layout Itemize
24563 Define the function by inserting the following line to the LaTeX-preamble
24567 \begin_layout Plain Layout
24572 DeclareMathOperator
24575 \begin_inset CommandInset ref
24577 reference "sub:Self-defined-Operators"
24587 \begin_inset Newline newline
24591 \begin_inset VSpace -3mm
24595 \begin_inset Newline newline
24602 DeclareMathOperator{
24607 \begin_inset Index idx
24610 \begin_layout Plain Layout
24615 DeclareMathOperator
24621 \begin_inset Newline newline
24625 \begin_inset VSpace -2mm
24629 \begin_inset Newline newline
24632 Now the new defined function can be called with the command
24641 \begin_layout Itemize
24642 Write the formula as usual, mark the formula name, in our example the letters
24647 , and change it to mathematical text.
24648 Finally, a space is inserted between prefactor and function.
24651 \begin_layout Standard
24652 The result is the same with both methods as with a predefined function
24656 \begin_layout Plain Layout
24657 In LyX self-defined functions are displayed red, predefined ones black.
24665 \begin_layout Standard
24667 \begin_inset Tabular
24668 <lyxtabular version="3" rows="3" columns="2">
24669 <features rotate="0" tabularvalignment="middle">
24670 <column alignment="center" valignment="top" width="0pt">
24671 <column alignment="center" valignment="top" width="0pt">
24673 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
24676 \begin_layout Plain Layout
24682 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
24685 \begin_layout Plain Layout
24693 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
24696 \begin_layout Plain Layout
24704 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
24707 \begin_layout Plain Layout
24708 \begin_inset Formula $A\sgn(x)+B$
24718 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
24721 \begin_layout Plain Layout
24725 \begin_inset Formula $\underbrace{\textrm{sgn}}_{\textrm{Alt+M}\,\textrm{M}}$
24733 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
24736 \begin_layout Plain Layout
24737 \begin_inset Formula $A\,\textrm{sgn}(x)+B$
24753 \begin_layout Standard
24754 The first method is more suitable when the self-defined function should
24755 be used several times.
24758 \begin_layout Subsection
24760 \begin_inset Index idx
24763 \begin_layout Plain Layout
24772 \begin_layout Standard
24773 For limits, in addition to the commands
24780 \begin_inset Index idx
24783 \begin_layout Plain Layout
24803 the following functions are defined:
24806 \begin_layout Standard
24808 \begin_inset Tabular
24809 <lyxtabular version="3" rows="5" columns="2">
24810 <features rotate="0" tabularvalignment="middle">
24811 <column alignment="center" valignment="top">
24812 <column alignment="center" valignment="top">
24814 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
24817 \begin_layout Plain Layout
24823 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
24826 \begin_layout Plain Layout
24828 \begin_inset Note Note
24831 \begin_layout Plain Layout
24838 is only used as spacer.
24850 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
24853 \begin_layout Plain Layout
24861 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
24864 \begin_layout Plain Layout
24865 \begin_inset Formula $\varliminf$
24875 <cell alignment="center" valignment="top" leftline="true" usebox="none">
24878 \begin_layout Plain Layout
24886 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
24889 \begin_layout Plain Layout
24890 \begin_inset Formula $\varlimsup$
24900 <cell alignment="center" valignment="top" leftline="true" usebox="none">
24903 \begin_layout Plain Layout
24911 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
24914 \begin_layout Plain Layout
24915 \begin_inset Formula $\varprojlim$
24925 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
24928 \begin_layout Plain Layout
24936 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
24939 \begin_layout Plain Layout
24940 \begin_inset Formula $\varinjlim$
24944 \begin_inset Formula $\raisebox{-2.5mm}{}$
24960 \begin_layout Standard
24961 \begin_inset VSpace medskip
24964 The limit is created by inserting a subscript.
24965 It is set right beside the function in an inline formula:
24968 \begin_layout Standard
24970 \begin_inset Tabular
24971 <lyxtabular version="3" rows="2" columns="2">
24972 <features rotate="0" tabularvalignment="middle">
24973 <column alignment="center" valignment="top" width="0pt">
24974 <column alignment="center" valignment="top" width="0pt">
24976 <cell alignment="center" valignment="top" usebox="none">
24979 \begin_layout Plain Layout
24985 <cell alignment="center" valignment="top" usebox="none">
24988 \begin_layout Plain Layout
24989 \begin_inset space \hspace{}
24994 \begin_inset Note Note
24997 \begin_layout Plain Layout
25004 are used here as spacer.
25016 <cell alignment="center" valignment="top" usebox="none">
25019 \begin_layout Plain Layout
25025 \begin_inset space \textvisiblespace{}
25029 \begin_inset space \textvisiblespace{}
25037 <cell alignment="center" valignment="top" usebox="none">
25040 \begin_layout Plain Layout
25041 \begin_inset Formula $\hspace{1cm}\raisebox{5mm}{}\lim_{x\to A}x=B$
25057 \begin_layout Standard
25058 In a displayed formula the limit is set below the formula, as usual:
25059 \begin_inset Formula
25069 \begin_layout Standard
25070 \begin_inset VSpace medskip
25076 \begin_layout Standard
25077 How to adjust the typesetting of the limits see
25078 \begin_inset CommandInset ref
25080 reference "sub:Operator-Limits"
25087 \begin_layout Subsection
25089 \begin_inset Index idx
25092 \begin_layout Plain Layout
25093 Functions ! modulo-
25101 \begin_layout Standard
25102 The modulo-function is special, because it exists in four variants.
25103 The variants in a displayed formula are:
25104 \begin_inset Formula
25106 \underline{\textrm{Command}\raisebox{-0.9mm}{}} & & \underline{\textrm{Result}}\\
25107 \mathrm{a\backslash mod\textrm{␣}b} & & a\mod b\\
25108 \mathrm{a\backslash pmod\textrm{␣}b} & & a\pmod b\\
25109 \mathrm{a\backslash bmod\textrm{␣}b} & & a\bmod b\\
25110 \mathrm{a\backslash pod\textrm{␣}b} & & a\pod b
25118 \begin_layout Standard
25119 In an inline formula less space is set before the function names for all
25121 By default the modulo-functions take only the first following character
25123 To use more than one character, one has to put them into TeX-braces:
25124 \begin_inset Formula
25126 \underline{\textrm{Command}\raisebox{-0.9mm}{}} & & \underline{\textrm{Result}}\\
25127 \mathrm{a\backslash pod\textrm{␣}bcd} & & a\pod bcd\\
25128 \mathrm{a\backslash pod\backslash\{bc\to d} & & a\pod{bc}d
25136 \begin_layout Section
25138 \begin_inset Index idx
25141 \begin_layout Plain Layout
25150 \begin_layout Subsection
25151 Special Characters in Mathematical Text
25154 \begin_layout Standard
25155 The following commands can only be used in mathematical text or in TeX-mode:
25158 \begin_layout Standard
25159 \begin_inset space \hfill{}
25163 \begin_inset Tabular
25164 <lyxtabular version="3" rows="8" columns="2">
25165 <features rotate="0" tabularvalignment="middle">
25166 <column alignment="block" valignment="top">
25167 <column alignment="block" valignment="top">
25169 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
25172 \begin_layout Plain Layout
25178 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
25181 \begin_layout Plain Layout
25189 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
25192 \begin_layout Plain Layout
25200 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
25203 \begin_layout Plain Layout
25204 \begin_inset Formula $\textrm{œ}$
25214 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
25217 \begin_layout Plain Layout
25225 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
25228 \begin_layout Plain Layout
25229 \begin_inset Formula $\textrm{Œ}$
25239 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
25242 \begin_layout Plain Layout
25250 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
25253 \begin_layout Plain Layout
25254 \begin_inset Formula $\textrm{æ}$
25264 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
25267 \begin_layout Plain Layout
25275 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
25278 \begin_layout Plain Layout
25279 \begin_inset Formula $\textrm{Æ}$
25289 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
25292 \begin_layout Plain Layout
25300 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
25303 \begin_layout Plain Layout
25304 \begin_inset Formula $\textrm{\aa}$
25314 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
25317 \begin_layout Plain Layout
25321 \begin_inset Index idx
25324 \begin_layout Plain Layout
25331 \begin_layout Plain Layout
25352 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
25355 \begin_layout Plain Layout
25356 \begin_inset Formula $\textrm{Å}$
25366 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
25369 \begin_layout Plain Layout
25377 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
25380 \begin_layout Plain Layout
25381 \begin_inset Formula $\textrm{ı}$
25395 \begin_inset space \hfill{}
25399 \begin_inset Tabular
25400 <lyxtabular version="3" rows="8" columns="2">
25401 <features rotate="0" tabularvalignment="middle">
25402 <column alignment="block" valignment="top">
25403 <column alignment="center" valignment="top">
25405 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
25408 \begin_layout Plain Layout
25410 \begin_inset Note Note
25413 \begin_layout Plain Layout
25415 \begin_inset space \thinspace{}
25418 mm is used for separation, because otherwise the output will be ¡ and ¿
25429 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
25432 \begin_layout Plain Layout
25440 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
25443 \begin_layout Plain Layout
25451 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
25454 \begin_layout Plain Layout
25455 \begin_inset Formula $\textrm{ø}$
25465 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
25468 \begin_layout Plain Layout
25476 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
25479 \begin_layout Plain Layout
25480 \begin_inset Formula $\textrm{Ø}$
25490 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
25493 \begin_layout Plain Layout
25501 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
25504 \begin_layout Plain Layout
25505 \begin_inset Formula $\textrm{ł}$
25515 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
25518 \begin_layout Plain Layout
25526 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
25529 \begin_layout Plain Layout
25530 \begin_inset Formula $\textrm{Ł}$
25540 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
25543 \begin_layout Plain Layout
25545 \begin_inset space \hspace{}
25550 \begin_inset space \textvisiblespace{}
25558 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
25561 \begin_layout Plain Layout
25562 \begin_inset Formula $\textrm{!`}$
25572 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
25575 \begin_layout Plain Layout
25577 \begin_inset space \hspace{}
25582 \begin_inset space \textvisiblespace{}
25590 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
25593 \begin_layout Plain Layout
25594 \begin_inset Formula $\textrm{?`}$
25604 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
25607 \begin_layout Plain Layout
25615 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
25618 \begin_layout Plain Layout
25619 \begin_inset Formula $\textrm{ȷ}$
25633 \begin_inset space \hfill{}
25639 \begin_layout Standard
25641 \begin_inset Formula $\textrm{\textrm{Å}}$
25645 \begin_inset Formula $\textrm{\textrm{Ø}}$
25648 can also be inserted via the math toolbar button
25651 arg "math-insert \\digamma"
25657 \begin_layout Standard
25658 An exception are the commands
25661 \begin_inset space \hspace{}
25670 \begin_inset space \hspace{}
25676 , because they can be inserted in LyX directly to text.
25679 \begin_layout Subsection
25681 \begin_inset CommandInset label
25683 name "sub:Accents-in-Text"
25688 \begin_inset Index idx
25691 \begin_layout Plain Layout
25700 \begin_layout Standard
25701 With the following commands all letters can be accented.
25702 The commands must be inserted in TeX-mode.
25705 \begin_layout Standard
25706 \begin_inset space \hfill{}
25710 \begin_inset Tabular
25711 <lyxtabular version="3" rows="8" columns="2">
25712 <features rotate="0" tabularvalignment="middle">
25713 <column alignment="block" valignment="top">
25714 <column alignment="block" valignment="top">
25716 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
25719 \begin_layout Plain Layout
25725 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
25728 \begin_layout Plain Layout
25736 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
25739 \begin_layout Plain Layout
25743 \begin_inset Quotes grd
25751 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
25754 \begin_layout Plain Layout
25758 \begin_layout Plain Layout
25774 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
25777 \begin_layout Plain Layout
25785 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
25788 \begin_layout Plain Layout
25792 \begin_layout Plain Layout
25808 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
25811 \begin_layout Plain Layout
25815 \begin_inset space \textvisiblespace{}
25823 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
25826 \begin_layout Plain Layout
25830 \begin_layout Plain Layout
25846 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
25849 \begin_layout Plain Layout
25857 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
25860 \begin_layout Plain Layout
25864 \begin_layout Plain Layout
25880 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
25883 \begin_layout Plain Layout
25887 \begin_inset space \textvisiblespace{}
25895 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
25898 \begin_layout Plain Layout
25902 \begin_layout Plain Layout
25918 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
25921 \begin_layout Plain Layout
25925 \begin_inset space \textvisiblespace{}
25933 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
25936 \begin_layout Plain Layout
25940 \begin_layout Plain Layout
25956 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
25959 \begin_layout Plain Layout
25963 \begin_inset space \textvisiblespace{}
25971 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
25974 \begin_layout Plain Layout
25978 \begin_layout Plain Layout
25998 \begin_inset space \hfill{}
26002 \begin_inset Tabular
26003 <lyxtabular version="3" rows="8" columns="2">
26004 <features rotate="0" tabularvalignment="middle">
26005 <column alignment="block" valignment="top">
26006 <column alignment="center" valignment="top">
26008 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
26011 \begin_layout Plain Layout
26017 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
26020 \begin_layout Plain Layout
26028 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
26031 \begin_layout Plain Layout
26035 \begin_inset space \textvisiblespace{}
26043 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
26046 \begin_layout Plain Layout
26050 \begin_layout Plain Layout
26066 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
26069 \begin_layout Plain Layout
26077 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
26080 \begin_layout Plain Layout
26084 \begin_layout Plain Layout
26100 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
26103 \begin_layout Plain Layout
26107 \begin_inset Index idx
26110 \begin_layout Plain Layout
26121 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
26124 \begin_layout Plain Layout
26128 \begin_layout Plain Layout
26144 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
26147 \begin_layout Plain Layout
26155 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
26158 \begin_layout Plain Layout
26162 \begin_layout Plain Layout
26178 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
26181 \begin_layout Plain Layout
26185 \begin_inset space \textvisiblespace{}
26193 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
26196 \begin_layout Plain Layout
26200 \begin_layout Plain Layout
26216 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
26219 \begin_layout Plain Layout
26223 \begin_inset space \textvisiblespace{}
26231 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
26234 \begin_layout Plain Layout
26238 \begin_layout Plain Layout
26254 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
26257 \begin_layout Plain Layout
26261 \begin_inset space \textvisiblespace{}
26269 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
26272 \begin_layout Plain Layout
26276 \begin_layout Plain Layout
26296 \begin_inset space \hfill{}
26302 \begin_layout Standard
26303 \begin_inset VSpace medskip
26312 also two different characters can be accented.
26318 \begin_inset space \textvisiblespace{}
26327 \begin_layout Plain Layout
26339 \begin_layout Standard
26352 can in combination with vowels directly be inserted with the keyboard without
26354 The same applies for the tilde
26358 \begin_layout Plain Layout
26359 This only applies for keyboards where the tilde is defined as accent.
26368 in combination with
26383 \begin_layout Standard
26426 and accents that are inserted directly with the keyboard are also available
26427 in mathematical text.
26428 For the other accents there are special math commands to be used in formulas,
26430 \begin_inset CommandInset ref
26432 reference "sub:Accents-for-one"
26439 \begin_layout Standard
26440 \begin_inset VSpace bigskip
26443 Furthermore, with the command
26450 \begin_inset Index idx
26453 \begin_layout Plain Layout
26461 all numbers and letters can be set into a circle, quasi accented with a
26462 circle, similar to the copyright symbol.
26465 \begin_layout Standard
26467 \begin_inset Tabular
26468 <lyxtabular version="3" rows="3" columns="2">
26469 <features rotate="0" tabularvalignment="middle">
26470 <column alignment="center" valignment="top">
26471 <column alignment="center" valignment="top">
26473 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
26476 \begin_layout Plain Layout
26482 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
26485 \begin_layout Plain Layout
26487 \begin_inset Note Note
26490 \begin_layout Plain Layout
26497 is only used as spacer.
26509 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
26512 \begin_layout Plain Layout
26520 <cell multicolumn="1" alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
26523 \begin_layout Plain Layout
26527 \begin_layout Plain Layout
26543 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
26546 \begin_layout Plain Layout
26557 raisebox{-1.5pt}{W}}
26562 <cell multicolumn="1" alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
26565 \begin_layout Plain Layout
26566 \begin_inset Formula $\raisebox{4.5mm}{}$
26573 \begin_layout Plain Layout
26591 \begin_inset Formula $\raisebox{-2mm}{}$
26607 \begin_layout Standard
26608 One has to take care that the character fits in the circle.
26619 \begin_layout Plain Layout
26621 \begin_inset CommandInset ref
26623 reference "sub:Font-Sizes"
26632 specifies thereby the size of the circle.
26643 \begin_layout Plain Layout
26645 \begin_inset CommandInset ref
26647 reference "sub:Boxes-without-Frame"
26656 the character can be centered.
26659 \begin_layout Subsection
26661 \begin_inset Index idx
26664 \begin_layout Plain Layout
26673 \begin_layout Standard
26674 Old-style figures (also known as old-style numerals) are created with the
26682 \begin_inset Index idx
26685 \begin_layout Plain Layout
26694 The command can be used in formulas and in TeX-mode.
26695 The command scheme is:
26698 \begin_layout Standard
26703 oldstylenums{number}
26706 \begin_layout Standard
26711 oldstylenums{0123456789
26714 \begin_inset Formula $\oldstylenums{0123456789}$
26720 \begin_layout Section
26722 \begin_inset CommandInset label
26724 name "sec:Formula-Styles"
26729 \begin_inset Index idx
26732 \begin_layout Plain Layout
26741 \begin_layout Itemize
26742 There are two different alignment styles:
26746 \begin_layout Description
26747 Centered is the predefined standard
26750 \begin_layout Description
26751 Indented for this the option
26755 must be inserted in the menu
26757 Document\SpecialChar \menuseparator
26763 \begin_inset space ~
26769 \begin_layout Standard
26774 is used, the indentation can be adjusted with the length
26781 \begin_inset Index idx
26784 \begin_layout Plain Layout
26793 Should the distance be 15
26794 \begin_inset space \thinspace{}
26797 mm, the following command line is inserted in the LaTeX-preamble
26800 \begin_layout Standard
26810 \begin_layout Standard
26811 When no length is specified, the predefined value of 30
26812 \begin_inset space \thinspace{}
26819 \begin_layout Itemize
26820 And two different numbering styles:
26824 \begin_layout Description
26825 Right is the predefined standard
26828 \begin_layout Description
26829 Left for this the option
26833 must be inserted in the menu
26835 Document\SpecialChar \menuseparator
26841 \begin_inset space ~
26848 \begin_layout Standard
26857 can also be used together.
26858 In this case both options are inserted, separated by a comma.
26861 \begin_layout Standard
26862 The chosen styles are used for all displayed formulas of the document.
26863 When both, centered and indented formulas should be created in a document,
26869 The indented formulas are then set in a flalign environment, see
26870 \begin_inset CommandInset ref
26872 reference "sub:Flalign-Environment"
26879 \begin_layout Section
26881 \begin_inset CommandInset label
26883 name "sec:Multiline-Formulas"
26888 \begin_inset Index idx
26891 \begin_layout Plain Layout
26892 Formula ! multiline
26900 \begin_layout Subsection
26904 \begin_layout Standard
26905 In LyX multiline formulas are created by pressing
26908 arg "newline-insert newline"
26912 This creates either an
26914 eqnarray environment
26916 that is described in
26917 \begin_inset CommandInset ref
26919 reference "sub:Eqnarray-Environment"
26923 or, when the option
26925 Use AMS math package
26927 in the document settings is selected, an
26931 that is described in
26932 \begin_inset CommandInset ref
26934 reference "sub:Standard-align-Environment"
26939 The align environment is recommended because it provides in any case a
26940 typographically correct output.
26943 \begin_layout Standard
26944 There are other multiline formula environments that can be created via the
26947 Insert\SpecialChar \menuseparator
26951 These environments are described in the following sections.
26954 \begin_layout Standard
26955 In all multiline formula environments a new line is created by pressing
26959 arg "newline-insert newline"
26963 To add or delete lines, the math toolbar buttons
26966 arg "inset-modify tabular append-row"
26972 arg "inset-modify tabular delete-row"
26975 , respectively, or the menu
26977 Edit\SpecialChar \menuseparator
26983 \begin_layout Subsubsection
26985 \begin_inset CommandInset label
26987 name "sub:Line-Separation"
26992 \begin_inset Index idx
26995 \begin_layout Plain Layout
26996 Formula ! multiline ! Line separation
27004 \begin_layout Standard
27005 There is sometimes not enough space in multiline formulas between the lines:
27006 \begin_inset Formula
27008 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}\\
27009 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
27017 \begin_layout Standard
27018 In LaTeX additional line space is specified as optional argument of the
27020 This is not yet possible in LyX
27024 \begin_layout Plain Layout
27026 \begin_inset CommandInset href
27028 name "LyX-bug #1505"
27029 target "http://www.lyx.org/trac/ticket/1505"
27038 , therefore the whole formula must be inserted in TeX-mode.
27039 To add in our example space, the command
27047 is inserted at the end of the first line.
27052 \begin_layout Plain Layout
27059 \begin_layout Plain Layout
27061 B^{2}(B^{2}-2r_{g}^{2}+2x_{0}^{2}-2r_{k}^{2})+4x_{0}^{2}x^{2}+4x_{0}xD &
27064 textrm{-}4x^{2}B^{2}+4x_{0}xB^{2}
27071 \begin_layout Plain Layout
27075 left(B^{2}+x_{0}^{2}
27083 left(B^{2}-2r_{g}^{2}+2x_{0}^{2}-2r_{k}^{2}
27088 \begin_layout Plain Layout
27100 \begin_layout Standard
27101 \begin_inset VSpace bigskip
27104 To set the line separation for all lines in a formula, the length
27111 \begin_inset Index idx
27114 \begin_layout Plain Layout
27124 \begin_inset Formula $\mbox{line separation}=\mathrm{6\, pt+\backslash jot}$
27135 \begin_inset space \thinspace{}
27140 \begin_inset space \thinspace{}
27143 mm additional line separation as in the previous example, the command
27146 \begin_layout Standard
27156 \begin_layout Standard
27157 is inserted in TeX-mode before the formula.
27158 This requires that the LaTeX-package
27166 \begin_layout Plain Layout
27171 is part of every LaTeX standard installation.
27177 \begin_inset Index idx
27180 \begin_layout Plain Layout
27186 was loaded in LaTeX-preamble with the line
27189 \begin_layout Standard
27197 \begin_layout Standard
27202 \begin_layout Plain Layout
27214 \begin_inset Formula
27216 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}\\
27217 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
27225 \begin_layout Standard
27229 \begin_layout Plain Layout
27240 To get back to the predefined distance,
27246 is set to the value 3
27247 \begin_inset space \thinspace{}
27253 \begin_layout Subsubsection
27255 \begin_inset CommandInset label
27257 name "sub:Column-Separation"
27262 \begin_inset Index idx
27265 \begin_layout Plain Layout
27266 Formula ! multiline ! Column separation
27274 \begin_layout Standard
27275 Multiline formulas form a matrix.
27276 A formula in the eqnarray environment is for example a matrix with three
27278 By changing the column separation in this environment, the space beside
27279 the relation sign can be changed.
27282 \begin_layout Standard
27283 The column separation is specified with the length
27290 \begin_inset Index idx
27293 \begin_layout Plain Layout
27302 \begin_inset Newline newline
27305 column separation = 2
27306 \begin_inset space \thinspace{}
27316 \begin_inset Newline newline
27322 \begin_layout Standard
27332 \begin_layout Standard
27333 inserted in TeX-mode, sets for all following formulas a column separation
27335 \begin_inset space \thinspace{}
27339 To get back to the predefined distance,
27346 \begin_inset space \thinspace{}
27352 \begin_layout Standard
27354 \begin_inset space \thinspace{}
27357 cm column separation:
27361 \begin_layout Plain Layout
27373 \begin_inset Formula
27381 A formula with the predefined column separation for matrices of 10
27382 \begin_inset space \thinspace{}
27389 \begin_layout Plain Layout
27401 \begin_inset Formula
27412 \begin_layout Subsubsection
27414 \begin_inset Index idx
27417 \begin_layout Plain Layout
27426 \begin_layout Standard
27427 Long formulas can be typeset using these methods:
27430 \begin_layout Itemize
27431 When one side of the equation is much shorter than the line width, this
27432 one is chosen for the left side and the right side is typeset over two
27434 \begin_inset Formula
27436 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 \\
27437 & & -\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}
27442 The minus sign at the beginning of the second line does normally not appear
27443 as an operator because it is the first character of the line.
27444 Thus it would not be surrounded by space and could not be distinguished
27445 from the fraction bar.
27447 \begin_inset space \thinspace{}
27450 pt space was inserted behind the minus sign with the command
27460 \begin_layout Plain Layout
27468 \begin_inset CommandInset ref
27470 reference "sub:Variable-Space"
27480 \begin_inset Index idx
27483 \begin_layout Plain Layout
27494 \begin_layout Itemize
27495 When both sides of the equation are too long, the command
27502 \begin_inset Index idx
27505 \begin_layout Plain Layout
27514 It is inserted in the first column of the first line and causes all further
27515 insertions to overwrite the following columns:
27516 \begin_inset Formula
27518 \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 \\
27519 & & -\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 \\
27520 & & =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}
27525 After the insertion of
27531 , the cursor is in a purple box that is a bit shifted to the left from the
27533 In this the formula is inserted.
27534 \begin_inset Newline newline
27537 The content of the further lines is inserted to the second or another formula
27539 The greater the column number where it was inserted, the larger the indentation.
27540 \begin_inset VSpace medskip
27544 \begin_inset Newline newline
27548 \begin_inset Note Greyedout
27551 \begin_layout Plain Layout
27552 Note the following when using
27561 \begin_layout Itemize
27562 The formula doesn't use the full page width.
27564 \begin_inset space \thinspace{}
27568 \begin_inset space \space{}
27572 \begin_inset Formula $-B^{2}$
27575 is added to the first line in the above example, it would have been outside
27577 To better use the width, negative space can be inserted at the beginning
27581 \begin_layout Itemize
27582 Due to a bug in LyX the cursor cannot be set with the mouse into the first
27587 \begin_layout Plain Layout
27588 \begin_inset CommandInset href
27590 name "LyX-bug #1429"
27591 target "http://www.lyx.org/trac/ticket/1429"
27600 One can only set the cursor at the beginning of the line and move it with
27609 \begin_layout Itemize
27610 Other methods to set long formulas are offered by the environments described
27612 \begin_inset CommandInset ref
27614 reference "sub:Multline-Environment"
27619 \begin_inset CommandInset ref
27621 reference "sub:Multiline-Formula-Parts"
27628 \begin_layout Subsubsection
27630 \begin_inset CommandInset label
27632 name "sub:Multiline-Brackets"
27637 \begin_inset Index idx
27640 \begin_layout Plain Layout
27641 Brackets ! for multiline expressions
27649 \begin_layout Standard
27650 For brackets spanning multiple lines the following problem occurs:
27651 \begin_inset Formula
27653 A & = & \sin(x)\left[\prod_{R=1}^{\infty}\frac{1}{R}+\cdots\right.\\
27654 & & \left.\cdots+B-D\right]
27662 \begin_layout Standard
27663 The closing bracket is smaller than the opening bracket because brackets
27664 with variable size may not span multiple lines.
27667 \begin_layout Standard
27668 To set the bracket size for the second line correctly, the first line is
27676 \begin_inset Index idx
27679 \begin_layout Plain Layout
27687 and the second line with
27695 \begin_layout Plain Layout
27709 \begin_inset CommandInset ref
27711 reference "sub:Automatic-Bracket-Size"
27723 \begin_inset Index idx
27726 \begin_layout Plain Layout
27749 \begin_inset space \textvisiblespace{}
27759 \begin_inset space \textvisiblespace{}
27769 \begin_inset space \textvisiblespace{}
27775 \begin_inset Formula $\downarrow$
27781 \begin_inset Index idx
27784 \begin_layout Plain Layout
27792 is inserted, because the multiplication operator with its limits is the
27793 largest symbol in the first line and this should be the size for the bracket
27794 in the second line.
27797 \begin_layout Standard
27798 The result is this:
27799 \begin_inset Formula
27801 A & = & \sin(x)\left[\prod_{R=1}^{\infty}\frac{1}{R}+\cdots\right.\\
27802 & & \left.\vphantom{\prod_{R=1}^{\infty}}\cdots+B-D\right]
27810 \begin_layout Subsection
27814 \begin_layout Standard
27815 Align environments can be used for every kind of multiline formulas.
27816 They are especially useful to set several formulas side by side.
27819 \begin_layout Standard
27820 Align environments consist of columns.
27821 The odd columns are right aligned, the even ones left aligned.
27822 Every line in an Align environment can be numbered.
27825 \begin_layout Standard
27826 Align environments are created via the menu
27828 Insert\SpecialChar \menuseparator
27834 Edit\SpecialChar \menuseparator
27835 Math\SpecialChar \menuseparator
27836 Change Formula Type
27838 already existing formulas can be converted to Align environments.
27841 \begin_layout Standard
27842 To add or delete columns, the math toolbar buttons
27845 arg "inset-modify tabular append-column"
27851 arg "inset-modify tabular delete-column"
27854 , respectively, or the menu
27856 Edit\SpecialChar \menuseparator
27862 \begin_layout Subsubsection
27863 Standard align Environment
27864 \begin_inset CommandInset label
27866 name "sub:Standard-align-Environment"
27871 \begin_inset Index idx
27874 \begin_layout Plain Layout
27875 Formula ! multiline ! align environment
27883 \begin_layout Standard
27884 This Align environment is created by pressing
27887 arg "newline-insert newline"
27890 in a formula or by the menu
27892 Insert\SpecialChar \menuseparator
27893 Math\SpecialChar \menuseparator
27894 AMS align Environment
27899 \begin_layout Standard
27900 An example for two formulas set side by side, that are created with a four
27901 column align environment:
27902 \begin_inset Formula
27904 A & =\sin(B) & C & =D\\
27905 C & \ne A & B & \ne D
27910 As it can be seen, the formulas in this environment are placed so as if
27919 \begin_layout Plain Layout
27927 \begin_inset CommandInset ref
27929 reference "sub:Variable-Space"
27940 before the first and after every even column.
27941 When the formula style
27947 \begin_layout Plain Layout
27949 \begin_inset CommandInset ref
27951 reference "sec:Formula-Styles"
27962 is used, the formula is set without the
27968 before the first column.
27971 \begin_layout Subsubsection
27972 Alignat Environment
27973 \begin_inset Index idx
27976 \begin_layout Plain Layout
27977 Formula ! multiline ! alignat environment
27985 \begin_layout Standard
27986 The alignat environment has no predefined column separation.
27987 It can be inserted manually with the spaces that are described
27988 \begin_inset CommandInset ref
27990 reference "sub:Space"
27997 \begin_layout Standard
27998 The above example in the alignat environment where 1
27999 \begin_inset space \thinspace{}
28002 cm space was inserted at the beginning of the second formula:
28003 \begin_inset Formula
28004 \begin{alignat*}{2}
28005 A & =\sin(B) & \hspace{1cm}C & =D\\
28006 C & \ne A & B & \ne D
28011 Because the column separation can be set separately for every column, this
28012 environment is especially suitable to set three and more formulas side
28016 \begin_layout Subsubsection
28017 Flalign Environment
28018 \begin_inset CommandInset label
28020 name "sub:Flalign-Environment"
28025 \begin_inset Index idx
28028 \begin_layout Plain Layout
28029 Formula ! multiline ! flalign environment
28037 \begin_layout Standard
28038 In this environment the first two columns are always set as much as possible
28039 to the left and the last two ones to the right.
28041 \begin_inset Formula
28043 A & =1 & B & =2 & C & =3\\
28044 X & =\textrm{-}1 & Y & =\textrm{-}2 & Z & =4
28052 \begin_layout Standard
28053 By creating a flalign environment with an odd number of columns where an
28054 empty TeX-brace is inserted to the last column, several formulas in a document
28055 can be set to the left, although the formula style
28060 As example the indented formula
28061 \begin_inset CommandInset ref
28063 reference "eq:VolInt"
28068 \begin_inset Formula
28070 \hspace{30pt}\iiint\limits _{V}X\,\mathrm{d}V & =U & {}
28075 The first two columns contain the formula.
28076 To indent it as with the formula style
28081 \begin_inset space \thinspace{}
28084 pt space was inserted at the beginning of the first column.
28087 \begin_layout Subsection
28088 Eqnarray Environment
28089 \begin_inset CommandInset label
28091 name "sub:Eqnarray-Environment"
28096 \begin_inset Index idx
28099 \begin_layout Plain Layout
28100 Formula ! multiline ! eqnarray environment
28108 \begin_layout Standard
28109 When this environment has been created, three blue boxes appear.
28110 The content of the first box is right aligned, the content of the last
28112 The content of the middle box appears centered and a bit smaller, because
28113 it is designed to insert there only relation characters.
28114 \begin_inset Formula
28116 \frac{ABC}{D} & \frac{ABC}{D} & \frac{ABC}{D}\\
28126 \begin_layout Subsection
28128 \begin_inset Index idx
28131 \begin_layout Plain Layout
28132 Formula ! multiline ! gather environment
28140 \begin_layout Standard
28141 This environment consists of only one centered column.
28142 Every line can be numbered.
28143 \begin_inset Formula
28154 \begin_layout Subsection
28155 Multline Environment
28156 \begin_inset CommandInset label
28158 name "sub:Multline-Environment"
28163 \begin_inset Index idx
28166 \begin_layout Plain Layout
28167 Formula ! multiline ! multline environment
28175 \begin_layout Standard
28176 The multline environment consists, like the gather environment, of only
28178 But the first line is left aligned, the last one right aligned.
28179 All other lines are centered.
28180 Therefore this environment is suitable for long formulas.
28182 \begin_inset CommandInset ref
28184 reference "eq:lefteqn"
28188 in the multline environment:
28189 \begin_inset Formula
28191 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}\\
28192 -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}\\
28193 =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}}
28201 \begin_layout Standard
28202 In the output only the last (first) line of a multline environment appears
28203 numbered when the document numbering is right (left).
28207 \begin_layout Plain Layout
28208 numbering styles see
28209 \begin_inset CommandInset ref
28211 reference "sec:Formula-Styles"
28223 \begin_layout Standard
28231 \begin_inset Index idx
28234 \begin_layout Plain Layout
28249 \begin_inset Index idx
28252 \begin_layout Plain Layout
28260 a centered line can be right or left aligned, respectively.
28261 The commands are used as follows:
28264 \begin_layout Standard
28269 shoveright{line content}
28275 shoveleft{line content}
28278 \begin_layout Standard
28279 \begin_inset VSpace medskip
28289 \begin_inset Index idx
28292 \begin_layout Plain Layout
28300 specifies the distance of the first line from the left page margin.
28301 Predefined is the length 0
28302 \begin_inset space \thinspace{}
28308 \begin_layout Standard
28309 As example the above formula where the command
28312 \begin_layout Standard
28322 \begin_layout Standard
28323 was inserted in TeX-mode before:
28327 \begin_layout Plain Layout
28339 \begin_inset Formula
28341 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}\\
28342 \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}}\\
28343 =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}}
28352 \begin_layout Plain Layout
28363 The second line was left aligned using
28372 \begin_layout Subsection
28373 Multiline Formula Parts
28374 \begin_inset CommandInset label
28376 name "sub:Multiline-Formula-Parts"
28381 \begin_inset Index idx
28384 \begin_layout Plain Layout
28385 Formula ! multiline ! formula parts
28393 \begin_layout Standard
28394 To display only parts of a formula with multiple lines, one of the following
28395 environments is used:
28412 They can be inserted via the menu
28414 Insert\SpecialChar \menuseparator
28417 or by using the commands described in this section.
28420 \begin_layout Standard
28421 The first three have the same properties as the corresponding multiline
28422 formula environments, but it is possible to set further formula parts beside
28425 \begin_inset Formula
28427 \left.\begin{aligned}\Delta x\Delta p & \ge\frac{\hbar}{2}\\
28428 \Delta E\Delta t & \ge\frac{\hbar}{2}
28430 \right\} \textrm{Uncertainty relations}
28438 \begin_layout Standard
28439 To get this formula, a displayed formula is created where the command
28446 \begin_inset Index idx
28449 \begin_layout Plain Layout
28458 A purple box appears around the blue formula box where now columns and
28459 lines can be added.
28460 Outside the multiline environment other formula parts can be set, like
28464 \begin_layout Standard
28465 The aligned environment is also suitable for long formulas whose lines are
28466 horizontally aligned.
28467 Using aligned in a displayed formula has the advantage that the formula
28468 number is vertically centered behind the lines.
28470 \begin_inset CommandInset ref
28472 reference "eq:shortlong"
28476 in the aligned environment:
28477 \begin_inset Formula
28479 \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}|}\\
28480 & -\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}|}
28489 \begin_layout Standard
28490 To use the environments
28509 \begin_inset Index idx
28512 \begin_layout Plain Layout
28527 \begin_inset Index idx
28530 \begin_layout Plain Layout
28545 \begin_inset Index idx
28548 \begin_layout Plain Layout
28556 are inserted, respectively.
28557 The split environment has the same properties as the aligned environment
28558 but it can only have two columns.
28561 \begin_layout Subsection
28562 Text in multiline Formulas
28563 \begin_inset CommandInset label
28565 name "sub:Text-in-multiline"
28570 \begin_inset Index idx
28573 \begin_layout Plain Layout
28580 \begin_inset Index idx
28583 \begin_layout Plain Layout
28584 Formula ! multiline ! text
28592 \begin_layout Standard
28593 In the Align environments, and the multline and gather environment, text
28594 can be inserted that will appear in a separate line and doesn't affect
28595 the column alignment.
28596 To do this, the command
28603 \begin_inset Index idx
28606 \begin_layout Plain Layout
28614 is used in the following scheme:
28617 \begin_layout Standard
28625 \begin_layout Standard
28626 The text should not be longer than a line because it cannot be hyphenated.
28627 As LyX doesn't yet support
28633 directly, the text is written as mathematical text.
28640 must hereby be at the beginning of a line and appears in the output above
28642 An example where the text was inserted at the beginning of the second line:
28643 \begin_inset Formula
28645 I & =a\sqrt{2}\int_{0}^{2\pi}\sqrt{1+\cos(\phi)}\;\mathrm{d}\phi\\
28646 \intertext{\text{integrand is symmetric to \ensuremath{\phi=\pi}, therefore}} & =2a\sqrt{2}\int_{0}^{\pi}\sqrt{1+\cos(\phi)}\;\mathrm{d}\phi
28654 \begin_layout Standard
28661 always creates some vertical space between the text and the formula lines.
28662 To avoid this space, set in the document settings under
28665 \begin_inset space ~
28675 \begin_inset Index idx
28678 \begin_layout Plain Layout
28679 Packages ! mathtools
28687 \begin_inset space ~
28693 Then you can use the command
28700 \begin_inset Index idx
28703 \begin_layout Plain Layout
28718 \begin_inset Newpage newpage
28724 \begin_layout Standard
28725 \begin_inset Formula
28727 I & =a\sqrt{2}\int_{0}^{2\pi}\sqrt{1+\cos(\phi)}\;\mathrm{d}\phi\\
28728 \shortintertext{\text{integrand is symmetric to \ensuremath{\phi=\pi}, therefore}} & =2a\sqrt{2}\int_{0}^{\pi}\sqrt{1+\cos(\phi)}\;\mathrm{d}\phi
28736 \begin_layout Section
28738 \begin_inset Index idx
28741 \begin_layout Plain Layout
28748 \begin_inset Index idx
28751 \begin_layout Plain Layout
28752 Formula ! numbering|see
28756 \begin_layout Plain Layout
28767 \begin_layout Plain Layout
28782 \begin_layout Subsection
28786 \begin_layout Standard
28787 Numbered formulas can be created with the menu
28789 Insert\SpecialChar \menuseparator
28790 Math\SpecialChar \menuseparator
28792 \begin_inset space ~
28800 \begin_inset space ~
28806 Existing formulas can be numbered with the menu
28808 Edit\SpecialChar \menuseparator
28809 Math\SpecialChar \menuseparator
28811 \begin_inset space ~
28819 arg "math-number-toggle"
28823 The formula number is displayed in LyX behind the formula as a number sign
28825 The number sign is replaced in the output by the formula number.
28828 \begin_layout Standard
28829 When numbering is turned on in multiline formulas, all lines will be numbered.
28830 But the numbering can be controlled with the menu
28832 Edit\SpecialChar \menuseparator
28833 Math\SpecialChar \menuseparator
28835 \begin_inset space ~
28839 \begin_inset space ~
28843 \begin_inset space ~
28851 arg "math-number-line-toggle"
28857 \begin_layout Standard
28858 Except for inline formulas, all formulas can be numbered with two different
28860 \begin_inset CommandInset ref
28862 reference "sec:Formula-Styles"
28869 \begin_layout Subsection
28871 \begin_inset Index idx
28874 \begin_layout Plain Layout
28875 Cross-references ! to formulas
28883 \begin_layout Standard
28884 All labeled formulas can be cross-referenced.
28885 A label is added by the menu
28887 Insert\SpecialChar \menuseparator
28890 or the toolbar button
28897 The cursor must hereby be inside a displayed formula.
28898 Alternatively you can right-click on the formula and choose
28903 A dialog pops up displaying the prefix
28908 The label is inserted there behind the prefix.
28909 The predefined prefix means
28910 \begin_inset Quotes eld
28914 \begin_inset Quotes erd
28917 and makes it easier to find labels in large documents because it marks
28918 it as formula label to divide it from e.
28919 \begin_inset space \thinspace{}
28923 \begin_inset space \space{}
28927 To change a label, the menu
28929 Insert\SpecialChar \menuseparator
28932 is used again or you right-click on a formula and then on
28939 \begin_layout Standard
28940 The name of the label is displayed in LyX within two parentheses behind
28942 A formula with a label is always numbered.
28945 \begin_layout Standard
28946 Cross-references are inserted via the menu
28948 Insert\SpecialChar \menuseparator
28951 or with the toolbar button
28954 arg "dialog-show-new-inset ref"
28958 A formula cross-reference appears in the output as formula number.
28959 When in the cross-reference dialog window the format
28963 is chosen, the cross-reference appears in the output as formula number
28965 \begin_inset Newline newline
28968 By right-clicking on a cross-reference in LyX, one jumps to the formula
28969 that is referenced.
28972 \begin_layout Standard
28973 Here are as examples cross-references to formulas of the following subsections:
28974 \begin_inset Note Note
28977 \begin_layout Plain Layout
28978 Note the different cross-reference types.
28986 \begin_layout Standard
28988 \begin_inset CommandInset ref
28995 \begin_inset CommandInset ref
29003 \begin_inset CommandInset ref
29009 ) big Latin letters are used for the numbering in contrary to (
29010 \begin_inset CommandInset ref
29019 \begin_layout Standard
29020 \begin_inset VSpace medskip
29023 When the argument of
29031 \begin_layout Plain Layout
29039 \begin_inset CommandInset ref
29041 reference "sub:User-defined-Numbering"
29052 contains a box like in
29053 \begin_inset CommandInset ref
29055 reference "sub:Paragraph-Boxes"
29059 , the formula cannot be referenced.
29062 \begin_layout Subsection
29064 \begin_inset Index idx
29067 \begin_layout Plain Layout
29068 Formula numbering ! subnumbering
29076 \begin_layout Standard
29077 With the help of the commands
29081 begin{subequations}
29089 formulas can be subnumbered.
29090 Both commands are inserted in TeX-mode.
29093 \begin_layout Standard
29095 \begin_inset Formula
29106 \begin_layout Plain Layout
29110 addtocounter{equation}{-1}
29119 \begin_layout Plain Layout
29123 begin{subequations}
29129 \begin_inset VSpace -5mm
29133 \begin_inset Formula
29141 \begin_inset Formula
29151 \begin_layout Standard
29155 \begin_layout Plain Layout
29167 \begin_layout Standard
29168 To create the example, the following is done:
29171 \begin_layout Enumerate
29172 first formula is inserted
29175 \begin_layout Enumerate
29180 addtocounter{equation}{-1}
29182 begin{subequations}
29183 \begin_inset Index idx
29186 \begin_layout Plain Layout
29195 \begin_inset Newline newline
29200 is inserted after the first formula
29203 \begin_layout Enumerate
29204 second formula is inserted
29207 \begin_layout Enumerate
29208 third formula is inserted
29211 \begin_layout Enumerate
29218 is inserted after the third formula
29221 \begin_layout Standard
29222 Every formula between the commands
29234 is subnumbered as a, b,
29235 \begin_inset Newline linebreak
29238 c, \SpecialChar \ldots{}
29239 For multiline formulas every line will be subnumbered.
29240 All subnumbered formulas are treated as
29245 But as every numbered formula increases the counter
29249 by one, the command
29255 is needed to decrease it.
29256 Otherwise the formulas
29257 \begin_inset CommandInset ref
29264 \begin_inset CommandInset ref
29271 \begin_inset CommandInset ref
29277 would be numbered as
29278 \begin_inset CommandInset ref
29285 \begin_inset CommandInset ref
29292 \begin_inset CommandInset ref
29301 \begin_layout Standard
29302 By inserting the commands in TeX-mode, a space is created between the first
29305 \begin_inset space \thinspace{}
29308 mm vertical space is inserted after the command
29312 begin{subequations}
29315 When the formula style
29321 \begin_layout Plain Layout
29323 \begin_inset CommandInset ref
29325 reference "sec:Formula-Styles"
29337 \begin_inset space \thinspace{}
29340 mm space is inserted instead.
29343 \begin_layout Standard
29344 Here is an example for a multiline formula where the numbering was turned
29345 off for the second line:
29349 \begin_layout Plain Layout
29353 begin{subequations}
29359 \begin_inset Formula
29361 A & = & (B-Z)^{2}=(B-Z)(B-Z)\label{eq:d}\\
29362 & = & B^{2}-ZB-BZ+Z^{2}\nonumber \\
29363 & = & B^{2}-2BZ+Z^{2}\label{eq:f}
29372 \begin_layout Plain Layout
29384 \begin_layout Subsection
29385 User-defined Numbering
29386 \begin_inset CommandInset label
29388 name "sub:User-defined-Numbering"
29393 \begin_inset Index idx
29396 \begin_layout Plain Layout
29397 Formula numbering ! user-defined
29405 \begin_layout Standard
29406 \begin_inset Index idx
29409 \begin_layout Plain Layout
29410 Formula numbering ! self-defined delimiters
29415 With the standard numbering parentheses are set around the formula number.
29416 To replace the parentheses for example by vertical bars, the following
29417 line is added to the LaTeX-preamble:
29420 \begin_layout Standard
29432 \begin_inset Note Note
29435 \begin_layout Plain Layout
29436 This macro is already declared in the LaTeX-preamble for testing.
29437 To activate it, remove the percent sign at the beginning.
29445 \begin_layout Standard
29446 To use other characters, the vertical bars besides the
29450 are replaced by one ore more characters.
29451 To get only the formula number the vertical bars are omitted.
29454 \begin_layout Standard
29455 \begin_inset VSpace bigskip
29458 When there should be an expression of your choice instead of the consecutive
29459 formula number in parentheses behind the formula, the command
29466 \begin_inset Index idx
29469 \begin_layout Plain Layout
29478 \begin_inset Formula
29480 A+B=C\tag{something}\label{eq:tag}
29485 In this example the command
29490 \begin_inset space \textvisiblespace{}
29495 was inserted in the formula.
29498 \begin_layout Standard
29504 \begin_inset space \textvisiblespace{}
29509 is inserted instead, the star prevents the parentheses around the expression:
29510 \begin_inset Formula
29512 A+B=C\tag*{something}
29520 \begin_layout Standard
29521 \begin_inset VSpace bigskip
29524 To restart the formula numbering with new document parts or sections, the
29525 following command is used:
29528 \begin_layout Standard
29533 @addtoreset{equation}{part}
29536 \begin_inset Index idx
29539 \begin_layout Plain Layout
29544 \begin_layout Plain Layout
29555 \begin_layout Plain Layout
29568 \begin_layout Plain Layout
29579 \begin_layout Plain Layout
29592 \begin_inset Newline newline
29596 \begin_inset Newline newline
29603 @addtoreset{equation}{section}
29606 \begin_layout Standard
29607 To be able to use these commands in TeX-mode, the
29608 \begin_inset Quotes eld
29612 \begin_inset Quotes erd
29615 character has to be made
29616 \begin_inset Quotes eld
29620 \begin_inset Quotes erd
29623 for LaTeX using the command
29637 So the command sequence in TeX-mode is:
29640 \begin_layout Standard
29646 \begin_inset Newline newline
29651 @addtoreset{equation}{section}
29652 \begin_inset Newline newline
29660 \begin_layout Standard
29661 In the LaTeX-preamble
29673 can be omitted as they are automatically internally inserted by LyX.
29676 \begin_layout Standard
29691 \begin_layout Plain Layout
29696 is part of the LaTeX-package
29701 \begin_inset Index idx
29704 \begin_layout Plain Layout
29705 Packages ! carlisle
29710 that is part of every LaTeX standard installation.
29716 \begin_inset Index idx
29719 \begin_layout Plain Layout
29720 Packages ! remreset
29725 has to be loaded in the LaTeX-preamble with the line
29728 \begin_layout Standard
29733 usepackage{remreset}
29736 \begin_layout Standard
29744 \begin_inset Index idx
29747 \begin_layout Plain Layout
29752 \begin_layout Plain Layout
29763 \begin_layout Plain Layout
29776 \begin_layout Plain Layout
29787 \begin_layout Plain Layout
29799 can be used with the same scheme as
29808 \begin_layout Standard
29809 \begin_inset VSpace bigskip
29812 Sometimes formulas should be numbered in the following form:
29815 \begin_layout Standard
29818 (section number.formula number)
29821 \begin_layout Standard
29822 The formula number should start with every section with
29823 \begin_inset Quotes eld
29827 \begin_inset Quotes erd
29833 \begin_layout Standard
29834 For this case there is the command
29841 \begin_inset Index idx
29844 \begin_layout Plain Layout
29852 , which is used with the following scheme:
29855 \begin_layout Standard
29860 numberwithin{counter}{sectioning}
29863 \begin_layout Standard
29864 Counter denotes what kind of numbering is affected, sectioning denotes what
29865 number is before the dot.
29868 \begin_layout Standard
29869 Thus in our case the following LaTeX-preamble or TeX code line is used:
29872 \begin_layout Standard
29877 numberwithin{equation}{section}
29880 \begin_layout Standard
29881 This is the result:
29885 \begin_layout Plain Layout
29889 numberwithin{equation}{section}
29895 \begin_inset Formula
29905 \begin_layout Standard
29907 \begin_inset space \thinspace{}
29911 \begin_inset space \space{}
29914 tables so that the number of the part is the sectioning,
29915 \begin_inset Newline newline
29922 numberwithin{table}{part}
29927 \begin_layout Standard
29928 To go back to the standard numbering or to prevent this kind of numbering
29929 when it is defined by the document class, the following command is inserted
29930 as TeX code or to the LaTeX-preamble:
29933 \begin_layout Standard
29943 \begin_inset Index idx
29946 \begin_layout Plain Layout
29960 \begin_layout Plain Layout
29976 \begin_inset Newline newline
29984 \begin_inset Newline newline
29996 \begin_layout Standard
30003 uses internally the command
30009 , described above, that also needs to be reverted.
30013 \begin_layout Plain Layout
30020 \begin_layout Plain Layout
30024 @removefromreset{equation}{section}
30027 \begin_layout Plain Layout
30039 \begin_layout Subsection
30040 Numbering with Roman Numbers and Letters
30041 \begin_inset Index idx
30044 \begin_layout Plain Layout
30045 Formula numbering ! with letters
30051 \begin_inset Index idx
30054 \begin_layout Plain Layout
30055 Formula numbering ! with Roman numbers
30063 \begin_layout Standard
30064 Formulas can also be numbered with Roman numbers and Latin letters.
30065 To number for example with small Roman numbers, the command
30068 \begin_layout Standard
30080 \begin_layout Standard
30081 is inserted before the formula in TeX-mode.
30089 \begin_inset Index idx
30092 \begin_layout Plain Layout
30100 redefines the predefined command
30116 \begin_layout Plain Layout
30123 has the same scheme like the command
30129 that is described in
30130 \begin_inset CommandInset ref
30132 reference "sub:The-Command-newcommand"
30145 is the formula counter.
30152 is used as prefix for a counter, the value of the counter is output as
30154 When a formula is numbered, LaTeX sets internally the command
30160 behind the formula.
30166 \begin_inset Index idx
30169 \begin_layout Plain Layout
30179 outputs the counter as small Roman number.
30182 \begin_layout Standard
30183 All formulas behind the command
30193 are now numbered Roman.
30194 To switch to numbering with big Roman numbers, the command is inserted
30208 \begin_inset Index idx
30211 \begin_layout Plain Layout
30223 \begin_inset Quotes eld
30227 \begin_inset Quotes erd
30230 with small Latin letters there is the command
30237 \begin_inset Index idx
30240 \begin_layout Plain Layout
30248 , for big ones there is the command
30255 \begin_inset Index idx
30258 \begin_layout Plain Layout
30271 \begin_layout Standard
30272 \begin_inset Note Greyedout
30275 \begin_layout Plain Layout
30282 \begin_inset space ~
30285 formulas can be numbered with Latin letters in one document.
30293 \begin_layout Standard
30297 \begin_layout Plain Layout
30313 \begin_layout Standard
30314 \begin_inset Formula
30316 A=\textrm{small roman}
30325 \begin_layout Plain Layout
30339 \begin_inset Formula
30341 B=\textrm{big Roman}\label{eq:Rom}
30350 \begin_layout Plain Layout
30364 \begin_inset Formula
30366 C=\textrm{small Latin}
30375 \begin_layout Plain Layout
30389 \begin_inset Formula
30391 D=\textrm{big Latin}\label{eq:Lat}
30399 \begin_layout Standard
30400 To switch back to the default numbering, insert the command:
30403 \begin_layout Standard
30413 \begin_inset Index idx
30416 \begin_layout Plain Layout
30427 \begin_layout Standard
30431 \begin_layout Plain Layout
30445 \begin_inset Formula
30455 \begin_layout Standard
30456 \begin_inset VSpace medskip
30459 As you see, formulas are numbered serially independent from the numbering
30461 When then numbering should start with
30462 \begin_inset Quotes eld
30466 \begin_inset Quotes erd
30469 when the style is changed, new equation counters have to be defined.
30470 A description about this can be found in the file
30471 \begin_inset CommandInset href
30473 name "Formula-numbering.lyx"
30474 target "run:Formula-numbering.lyx"
30481 \begin_layout Standard
30482 \begin_inset Newpage newpage
30488 \begin_layout Section
30489 Chemical Symbols and Equations
30490 \begin_inset CommandInset label
30492 name "sub:Chemical-Symbols-and"
30497 \begin_inset Index idx
30500 \begin_layout Plain Layout
30501 Chemical characters ! Symbols
30507 \begin_inset Index idx
30510 \begin_layout Plain Layout
30517 \begin_inset Index idx
30520 \begin_layout Plain Layout
30529 \begin_layout Standard
30530 An example text from chemistry:
30533 \begin_layout Quote
30535 \begin_inset Formula $\mathrm{SO_{4}^{2-}}$
30538 -ion reacts with two
30539 \begin_inset Formula $\mathrm{Na^{+}}$
30542 -ions to sodium sulfate
30543 \begin_inset Formula $\left(\mathrm{Na_{2}SO_{4}}\right)$
30547 The chemical equation for this is:
30548 \begin_inset Formula
30550 \mathrm{2\, Na^{+}+SO_{4}^{2-}\longrightarrow Na_{2}SO_{4}}\label{eq:chem-reaction}
30558 \begin_layout Standard
30559 This chemical equation can directly be created as formula.
30560 To avoid that the symbols appear italic, everything is highlighted and
30561 changed by the shortcut
30567 to the upright font style.
30571 \begin_layout Plain Layout
30577 \begin_inset CommandInset ref
30579 reference "sub:Font-Styles"
30591 \begin_layout Standard
30592 A more convenient way to typeset chemical formulas is to use the command
30600 \begin_inset Index idx
30603 \begin_layout Plain Layout
30611 that is available when the LaTeX-package
30616 \begin_inset Index idx
30619 \begin_layout Plain Layout
30632 to a formula a new blue box appears where chemical formulas can be inserted
30633 in an intuitive way.
30636 \begin_layout Standard
30638 \begin_inset Tabular
30639 <lyxtabular version="3" rows="9" columns="2">
30640 <features rotate="0" tabularvalignment="middle">
30641 <column alignment="center" valignment="top">
30642 <column alignment="center" valignment="top">
30644 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
30647 \begin_layout Plain Layout
30653 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
30656 \begin_layout Plain Layout
30658 \begin_inset Note Note
30661 \begin_layout Plain Layout
30668 is only used as spacer.
30680 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
30683 \begin_layout Plain Layout
30687 \begin_inset space \textvisiblespace{}
30695 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
30698 \begin_layout Plain Layout
30699 \begin_inset Formula $\raisebox{4.5mm}{}\ce{H2CO3}\raisebox{-2mm}{}$
30709 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
30712 \begin_layout Plain Layout
30716 \begin_inset space \textvisiblespace{}
30724 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
30727 \begin_layout Plain Layout
30728 \begin_inset Formula $\raisebox{5mm}{}\ce{SO4^{2-}}\raisebox{-2mm}{}$
30738 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
30741 \begin_layout Plain Layout
30745 \begin_inset space \textvisiblespace{}
30753 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
30756 \begin_layout Plain Layout
30757 \begin_inset Formula $\raisebox{4.5mm}{}\ce{(NH4)2S}\raisebox{-2mm}{}$
30767 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
30770 \begin_layout Plain Layout
30774 \begin_inset space \textvisiblespace{}
30782 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
30785 \begin_layout Plain Layout
30786 \begin_inset Formula $\raisebox{4.5mm}{}\ce{KCr(SO4)2.12H2O}\raisebox{-2mm}{}$
30796 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
30799 \begin_layout Plain Layout
30803 \begin_inset space \textvisiblespace{}
30809 \begin_inset space \textvisiblespace{}
30815 \begin_inset space \textvisiblespace{}
30823 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
30826 \begin_layout Plain Layout
30827 \begin_inset Formula $\raisebox{4.5mm}{}\ce{A-B\dbond C\tbond D}\raisebox{-2mm}{}$
30837 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
30840 \begin_layout Plain Layout
30844 \begin_inset space \textvisiblespace{}
30848 \begin_inset Formula $\downarrow$
30852 \begin_inset Formula $\to$
30860 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
30863 \begin_layout Plain Layout
30864 \begin_inset Formula $\raisebox{5mm}{}\ce{_{90}^{227}Th+}\raisebox{-2mm}{}$
30874 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
30877 \begin_layout Plain Layout
30881 \begin_inset space \textvisiblespace{}
30885 \begin_inset space \textvisiblespace{}
30889 \begin_inset space \textvisiblespace{}
30893 \begin_inset space \textvisiblespace{}
30897 \begin_inset space \textvisiblespace{}
30905 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
30908 \begin_layout Plain Layout
30909 \begin_inset Formula $\raisebox{4.5mm}{}\ce{CO2 + C <=> 2CO}\raisebox{-2mm}{}$
30919 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
30922 \begin_layout Plain Layout
30926 \begin_inset space \textvisiblespace{}
30930 \begin_inset space \textvisiblespace{}
30934 \begin_inset space \textvisiblespace{}
30938 \begin_inset space \textvisiblespace{}
30946 \begin_inset space \textvisiblespace{}
30954 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
30957 \begin_layout Plain Layout
30958 \begin_inset Formula $\raisebox{5mm}{}\ce{CO2 + C ->[\alpha][\beta] 2CO}\raisebox{-4mm}{}$
30974 \begin_layout Standard
30975 \begin_inset Note Greyedout
30978 \begin_layout Plain Layout
30984 Inserting a formula to a
30990 box will lead to LaTeX errors due to a LyX bug.
30996 \begin_layout Plain Layout
30997 \begin_inset CommandInset href
30999 name "LyX-bug #8566"
31000 target "http://www.lyx.org/trac/ticket/8566"
31011 In this case TeX code has to be used like for
31025 \begin_layout Plain Layout
31046 \begin_layout Standard
31047 \begin_inset Note Greyedout
31050 \begin_layout Plain Layout
31056 It is not possible in LyX to use the character ^ to get an up-arrow as
31062 One instead uses a negative thin space followed by the command
31069 \begin_inset Formula $\ce{Fe + 2H+ -> Fe^{2+} + H2\negthinspace\uparrow}$
31080 \begin_layout Standard
31087 the command for equation
31088 \begin_inset space ~
31092 \begin_inset CommandInset ref
31094 reference "eq:chem-reaction"
31099 \begin_inset Newline newline
31107 \begin_inset space \textvisiblespace{}
31111 \begin_inset space \textvisiblespace{}
31115 \begin_inset space \textvisiblespace{}
31119 \begin_inset space \textvisiblespace{}
31123 \begin_inset space \textvisiblespace{}
31127 \begin_inset space \textvisiblespace{}
31133 \begin_layout Standard
31134 To create multiline chemical equations first a multiline formula is created
31136 \begin_inset CommandInset ref
31138 reference "sec:Multiline-Formulas"
31143 Afterwards the command
31149 is used in every small blue box of the formula.
31151 \begin_inset CommandInset ref
31153 reference "eq:TEOS-reaction-1"
31158 \begin_inset CommandInset ref
31160 reference "eq:TEOS-reaction-2"
31164 are an example of a multi-stage chemical reaction where every equation
31165 has its own number.
31166 \begin_inset Formula
31168 \ce{TEOS + 4O} & \ce{->} & \ce{Si(OH)4 + 4C2H4O}\label{eq:TEOS-reaction-1}\\
31169 \ce{Si(OH)4} & \ce{->} & \ce{SiO2 + 2H2O}\label{eq:TEOS-reaction-2}
31177 \begin_layout Standard
31188 package provides the command
31195 \begin_inset Index idx
31198 \begin_layout Plain Layout
31206 that has to be used for special cases.
31207 For more information about
31213 and more examples have a look at the documentation of
31218 \begin_inset CommandInset citation
31227 \begin_layout Section
31231 \begin_layout Standard
31232 LyX supports two types of commutative diagrams:
31240 that are explained in the following.
31243 \begin_layout Subsection
31245 \begin_inset Index idx
31248 \begin_layout Plain Layout
31257 \begin_layout Standard
31258 Diagrams of this type visualize relations by vertical and horizontal lines
31260 \begin_inset Formula
31262 \begin{CD}A@>>>B@>>>C\\
31273 \begin_layout Standard
31274 To get them, the command
31279 \begin_inset Index idx
31282 \begin_layout Plain Layout
31292 is inserted to a formula.
31293 A blue box appears with two dashed lines where further commands can be
31298 arg "newline-insert newline"
31301 a new line is created.
31302 Horizontal relations are inserted in odd, vertical in even formula lines.
31305 \begin_layout Standard
31306 To create the relations there are the following commands:
31309 \begin_layout Itemize
31314 creates a left arrow,
31325 \begin_layout Itemize
31330 creates an up arrow,
31338 a vertical equal sign
31341 \begin_layout Itemize
31347 is a placeholder for non-existent relations
31350 \begin_layout Standard
31351 All arrows can be labeled as follows:
31354 \begin_layout Itemize
31355 If text inserted between the first and second < or >, resp., it is placed
31357 When it is inserted between the second and third one, it appears under
31361 \begin_layout Itemize
31362 When text for vertical arrows is inserted between the first and second A
31363 or V, resp., it is placed left beside the arrow.
31364 When it is inserted between the second and third one, it appears right
31366 If the text contains an A or V, these letters must be set into a TeX-brace.
31369 \begin_layout Standard
31370 As example a diagram with all possible relations:
31373 \begin_layout Standard
31374 \begin_inset Formula
31376 \begin{CD}A@>j>>B@>>k>C@=F\\
31387 \begin_layout Standard
31388 The command for this is:
31389 \begin_inset Newline newline
31397 \begin_inset space \textvisiblespace{}
31400 A@>j>>B@>>k>C@=F Ctrl+Return
31401 \begin_inset Newline newline
31405 \begin_inset Phantom HPhantom
31408 \begin_layout Plain Layout
31414 \begin_inset space \textvisiblespace{}
31427 \begin_inset Formula $\to$
31433 \begin_inset Newline newline
31437 \begin_inset Phantom HPhantom
31440 \begin_layout Plain Layout
31446 \begin_inset space \textvisiblespace{}
31457 \begin_layout Subsection
31459 \begin_inset Index idx
31462 \begin_layout Plain Layout
31463 Diagrams ! xymatrix
31471 \begin_layout Standard
31472 To be able to use xymatrices, the LaTeX-package
31477 A xymatrix is created by inserting the command
31484 Then you are able to add new matrix columns and rows like for normal matrices,
31486 \begin_inset CommandInset ref
31488 reference "sec:Matrices"
31495 \begin_layout Standard
31496 In contrary to amscd diagrams, xymatrices supports diagonal and curved arrows,
31498 All possibilities to create commutative diagrams and decorations are explained
31503 that you find in the menu
31505 Help\SpecialChar \menuseparator
31507 \begin_inset space ~
31515 \begin_layout Subsection
31521 \begin_inset Index idx
31524 \begin_layout Plain Layout
31533 \begin_layout Standard
31538 -diagrams, the LaTeX-package
31547 -diagram is created by inserting the command
31554 Then you are able to add new matrix columns and rows like for normal matrices,
31556 \begin_inset CommandInset ref
31558 reference "sec:Matrices"
31565 \begin_layout Standard
31566 Examples how to create
31570 diagrams in LyX is given in the
31572 Feynman-diagram manual
31574 that you find in the menu
31576 Help\SpecialChar \menuseparator
31578 \begin_inset space ~
31586 \begin_layout Standard
31587 \begin_inset Newpage newpage
31593 \begin_layout Section
31594 User-defined Commands
31595 \begin_inset Index idx
31598 \begin_layout Plain Layout
31599 User-defined commands
31607 \begin_layout Standard
31608 \begin_inset Note Greyedout
31611 \begin_layout Plain Layout
31616 The names of user-defined commands and macros may only consist of Latin
31625 \begin_layout Subsection
31629 \begin_inset CommandInset label
31631 name "sub:The-Command-newcommand"
31636 \begin_inset Index idx
31639 \begin_layout Plain Layout
31640 User-defined commands !
31648 \begin_inset Index idx
31651 \begin_layout Plain Layout
31662 \begin_layout Standard
31663 Many LaTeX-commands are too long to be used frequently.
31664 But it is possible to define with the command
31670 new shorter commands.
31673 \begin_layout Standard
31674 The command scheme of
31683 \begin_layout Standard
31688 newcommand{new command name}[number of arguments][optional
31693 \begin_inset Newline newline
31697 \begin_inset Phantom HPhantom
31700 \begin_layout Plain Layout
31710 {command definition}
31713 \begin_layout Standard
31714 \begin_inset Note Greyedout
31717 \begin_layout Plain Layout
31722 Assure that the name of the new command is not already used in your document
31723 or by LaTeX-packages that you use.
31724 When you for example define the command
31736 , you get an error message because
31742 is already defined as command for
31743 \begin_inset Quotes eld
31747 \begin_inset Formula $\le$
31751 \begin_inset Quotes erd
31762 \begin_layout Standard
31763 The number of arguments is an integer in the range 0
31764 \begin_inset space \thinspace{}
31768 \begin_inset space \thinspace{}
31771 9 and specifies how many arguments the new command should have.
31772 With the optional value a value for an optional argument can be predefined.
31773 When this is done, the
31781 rgument of the new command is automatically an optional one.
31784 \begin_layout Standard
31785 Here are some examples:
31788 \begin_layout Itemize
31789 To define the command
31801 , the LaTeX-preamble line is:
31802 \begin_inset VSpace medskip
31806 \begin_inset Newline newline
31820 \begin_layout Itemize
31821 To define the command
31833 , the argument (that should be underlined) must be taken into account.
31834 For this the preamble line is:
31835 \begin_inset VSpace medskip
31839 \begin_inset Newline newline
31853 \begin_inset VSpace medskip
31857 \begin_inset Newline newline
31864 acts as argument placeholder, the
31868 behind it denotes that it is the placeholder for the first argument.
31871 \begin_layout Itemize
31879 \begin_inset space \thinspace{}
31883 \begin_inset space \space{}
31893 \begin_inset VSpace medskip
31897 \begin_inset Newline newline
31908 framebox#1#2{$#3$}}
31911 \begin_inset VSpace medskip
31915 \begin_inset Newline newline
31918 The two Dollar signs creates the extra formula needed for
31925 \begin_inset CommandInset ref
31927 reference "sub:Boxes-with-Frame"
31934 \begin_layout Itemize
31935 To create a new command for
31941 where the color for the box need not be specified, the argument for the
31942 color is defined optional:
31943 \begin_inset VSpace medskip
31947 \begin_inset Newline newline
31958 fcolorbox{#2}{#1}{$#3$}}
31961 \begin_inset VSpace medskip
31965 \begin_inset Newline newline
31968 When the color is not specified when using
31974 , the predefined color
31981 \begin_layout Standard
31982 A test of the new defined commands:
31985 \begin_layout Standard
31987 \begin_inset Tabular
31988 <lyxtabular version="3" rows="6" columns="2">
31989 <features rotate="0" tabularvalignment="middle">
31990 <column alignment="center" valignment="top">
31991 <column alignment="center" valignment="top">
31993 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
31996 \begin_layout Plain Layout
32002 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
32005 \begin_layout Plain Layout
32007 \begin_inset Note Note
32010 \begin_layout Plain Layout
32017 is only used as spacer.
32029 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
32032 \begin_layout Plain Layout
32036 \begin_inset space \textvisiblespace{}
32044 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
32047 \begin_layout Plain Layout
32048 \begin_inset Formula $A\gr B$
32058 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
32061 \begin_layout Plain Layout
32069 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
32072 \begin_layout Plain Layout
32073 \begin_inset Formula $\raisebox{4.5mm}{}\us{ABcd}\raisebox{-2mm}{}$
32083 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
32086 \begin_layout Plain Layout
32090 \begin_inset Formula $\to$
32096 \begin_inset Formula $\to$
32104 \begin_inset space \textvisiblespace{}
32112 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
32115 \begin_layout Plain Layout
32116 \begin_inset Formula $\raisebox{6mm}{}\fb{[2cm]}{}{\int A=B}\raisebox{-4mm}{}$
32126 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
32129 \begin_layout Plain Layout
32133 \begin_inset Formula $\to$
32141 \begin_inset space \textvisiblespace{}
32149 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
32152 \begin_layout Plain Layout
32153 \begin_inset Formula $\raisebox{6mm}{}\cb{red}{\int A=B}\raisebox{-4mm}{}$
32163 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
32166 \begin_layout Plain Layout
32172 \begin_inset Formula $\to$
32180 \begin_inset space \textvisiblespace{}
32188 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
32191 \begin_layout Plain Layout
32192 \begin_inset Formula $\raisebox{6mm}{}\cb[green]{red}{\int A=B}\raisebox{-4mm}{}$
32208 \begin_layout Subsection
32210 \begin_inset Index idx
32213 \begin_layout Plain Layout
32214 User-defined commands! Math macros
32220 \begin_inset Index idx
32223 \begin_layout Plain Layout
32232 \begin_layout Standard
32233 User-defined commands are especially convenient for complex expressions.
32234 When you are for example dealing with a document that has quadratic equations,
32235 the same solution type occurs several times.
32236 The general form of a quadratic equation is
32237 \begin_inset Formula
32239 0=\lambda^{2}+p\lambda+q
32244 The general form of the solution is
32245 \begin_inset Formula
32247 \lambda_{1,2}=-\frac{p}{2}\pm\sqrt{\frac{p²}{4}-q}
32255 \begin_layout Standard
32256 To define a command for the solution formula where only the three parameters
32258 \begin_inset Formula $\lambda$
32262 \begin_inset Formula $p$
32266 \begin_inset Formula $q$
32269 need to be specified and the index of
32270 \begin_inset Formula $\lambda$
32273 can be given optionally, the LaTeX-preamble line is
32274 \begin_inset Newline newline
32290 \begin_inset Newline newline
32294 \begin_inset Phantom HPhantom
32297 \begin_layout Plain Layout
32311 frac{#3^{2}}{4}-#4}}
32314 \begin_layout Standard
32315 To create with this the solution formula, the command
32316 \begin_inset Newline newline
32326 \begin_inset Formula $\to$
32332 \begin_inset Formula $\to$
32339 is inserted to a formula
32344 \begin_layout Standard
32345 The definition of the new command is unintuitive because one has to know
32346 the schemes of all used LaTeX commands, e.
32347 \begin_inset space \thinspace{}
32351 \begin_inset space \space{}
32354 that a fraction is inserted in LaTeX as
32358 frac{numerator}{denominator}
32361 Furthermore one can easily forget a brace in the definition and cannot
32362 see in LyX what the new command is doing.
32363 To avoid these problems LyX offers the possibility to use math macros instead
32373 \begin_layout Standard
32374 A math macro is created by using the menu
32376 Insert\SpecialChar \menuseparator
32377 Math\SpecialChar \menuseparator
32380 or the toolbar button
32383 arg "math-macro newmacroname_newcommand"
32387 The math macro toolbar appears together with the following box where the
32389 \begin_inset Newline newline
32393 \begin_inset space \hspace*{\fill}
32397 \begin_inset Graphics
32398 filename clipart/macrobox.png
32403 \begin_inset space \hspace*{\fill}
32407 \begin_inset Newline newline
32411 \begin_inset FormulaMacro
32412 \newcommand{\qG}[4][1,\,2]{#2_{#1}=-\frac{#3}{2}\pm\sqrt{\frac{#3^{2}}{4}-#4}}
32417 newmacroname is the default name of the macro that should be changed to
32418 something sensible.
32419 The wanted formula is inserted in the first blue box.
32420 An argument placeholder is inserted with the command
32427 \begin_inset space \thinspace{}
32431 \begin_inset space \space{}
32440 or by using the macro toolbar button
32443 arg "math-macro-add-param"
32447 Argument placeholders are displayed red.
32449 \begin_inset space ~
32452 arguments are possible.
32453 Optional arguments are created with the toolbar button
32456 arg "math-macro-add-optional-param"
32460 The first non-optional argument can be transformed to an optional one with
32464 arg "math-macro-make-optional"
32468 In the second blue box the appearance of the macro in LyX can be defined.
32469 Normally you want to see it as it is defined, so the box is kept empty.
32470 But when you have created a macro that needs lot of space on the screen,
32471 you can insert in the box for example
32472 \begin_inset Newline newline
32502 \begin_inset Newline newline
32507 For the macro only the arguments with the macro name in front of them will
32508 then be displayed in LyX, leading to a better overview.
32509 The formula appears in the output as defined in the first box.
32510 \begin_inset Newline newline
32513 The appearance of macros in formulas can furthermore be changed for single
32514 macros by setting the cursor in the macro and using the menu
32516 View\SpecialChar \menuseparator
32518 \begin_inset space ~
32522 \begin_inset space ~
32530 \begin_layout Standard
32531 To use a macro, the macro name is inserted as command to a formula, in our
32539 Our macro looks in LyX like this:
32540 \begin_inset Newline newline
32544 \begin_inset space \hspace*{\fill}
32548 \begin_inset Graphics
32549 filename clipart/macrouse.png
32554 \begin_inset space \hspace*{\fill}
32558 \begin_inset Newline newline
32561 Here is our macro example with the arguments
32562 \begin_inset Formula $x$
32566 \begin_inset Formula $\ln(x)$
32570 \begin_inset Formula $B$
32576 \begin_layout Standard
32577 \begin_inset Formula
32587 \begin_layout Standard
32588 LyX offers in the menu
32590 Tools\SpecialChar \menuseparator
32591 Preferences\SpecialChar \menuseparator
32592 Editing\SpecialChar \menuseparator
32595 different styles to edit macros.
32596 To find the style that suits you the most, choose a style and set the cursor
32597 in a macro formula to see the difference.
32600 \begin_layout Standard
32601 A math macro is transformed internally to a
32607 command when exporting the document.
32614 command is not placed in the LaTeX-preamble, therefore macros can only
32615 be used in formulas that are in the document below the macro definition
32619 \begin_layout Standard
32620 Math macros can also be directly created from a
32627 When writing for example the command
32630 \begin_inset Newline newline
32639 xleftarrow[#2]{#1}}
32640 \begin_inset Newline newline
32645 in LyX as normal text, highlighting it completely and using then the shortcut
32650 , the command will be transformed to a math macro.
32651 Using this method you need to be careful that the
32657 command is typed correctly, otherwise you get a faulty macro leading to
32661 \begin_layout Standard
32662 Math macros currently have the problem that further formulas in macro definition
32663 s are handled wrongly.
32664 Therefore the example
32671 \begin_inset CommandInset ref
32673 reference "sub:The-Command-newcommand"
32677 cannot be created as macro.
32680 \begin_layout Standard
32681 When the cursor is in a macro definition box, you will see the macro toolbar
32685 \begin_layout Standard
32686 \begin_inset VSpace defskip
32692 \begin_layout Standard
32693 \begin_inset Graphics
32694 filename clipart/MacroToolbar.png
32699 \begin_inset Index idx
32702 \begin_layout Plain Layout
32711 \begin_layout Standard
32712 \begin_inset VSpace defskip
32718 \begin_layout Standard
32719 The macro toolbar contains from left to right the following buttons:
32722 \begin_layout Standard
32723 \begin_inset VSpace defskip
32729 \begin_layout Standard
32730 \begin_inset Tabular
32731 <lyxtabular version="3" rows="9" columns="2">
32732 <features rotate="0" islongtable="true" longtabularalignment="center">
32733 <column alignment="left" valignment="top">
32734 <column alignment="left" valignment="top" width="85col%">
32735 <row interlinespace="2.5mm">
32736 <cell alignment="center" valignment="top" usebox="none">
32739 \begin_layout Plain Layout
32742 arg "math-macro-remove-param"
32750 <cell alignment="center" valignment="top" usebox="none">
32753 \begin_layout Plain Layout
32756 Edit\SpecialChar \menuseparator
32757 Math\SpecialChar \menuseparator
32759 \begin_inset space ~
32762 Definition\SpecialChar \menuseparator
32763 Remove Last Argument
32769 <row interlinespace="2.5mm">
32770 <cell alignment="center" valignment="top" usebox="none">
32773 \begin_layout Plain Layout
32776 arg "math-macro-add-param"
32784 <cell alignment="center" valignment="top" usebox="none">
32787 \begin_layout Plain Layout
32790 Edit\SpecialChar \menuseparator
32791 Math\SpecialChar \menuseparator
32793 \begin_inset space ~
32796 Definition\SpecialChar \menuseparator
32803 <row interlinespace="2.5mm">
32804 <cell alignment="center" valignment="top" usebox="none">
32807 \begin_layout Plain Layout
32810 arg "math-macro-make-optional"
32818 <cell alignment="center" valignment="top" usebox="none">
32821 \begin_layout Plain Layout
32824 Edit\SpecialChar \menuseparator
32825 Math\SpecialChar \menuseparator
32827 \begin_inset space ~
32830 Definition\SpecialChar \menuseparator
32831 Transform First Non-Optional to
32832 \begin_inset Newline newline
32836 \begin_inset Phantom HPhantom
32839 \begin_layout Plain Layout
32842 Edit\SpecialChar \menuseparator
32843 Math\SpecialChar \menuseparator
32845 \begin_inset space ~
32848 Definition\SpecialChar \menuseparator
32860 <row interlinespace="2.5mm">
32861 <cell alignment="center" valignment="top" usebox="none">
32864 \begin_layout Plain Layout
32867 arg "math-macro-make-nonoptional"
32875 <cell alignment="center" valignment="top" usebox="none">
32878 \begin_layout Plain Layout
32881 Edit\SpecialChar \menuseparator
32882 Math\SpecialChar \menuseparator
32884 \begin_inset space ~
32887 Definition\SpecialChar \menuseparator
32888 Transform Last Optional to
32889 \begin_inset Newline newline
32893 \begin_inset Phantom HPhantom
32896 \begin_layout Plain Layout
32899 Edit\SpecialChar \menuseparator
32900 Math\SpecialChar \menuseparator
32902 \begin_inset space ~
32905 Definition\SpecialChar \menuseparator
32911 Non-Optional Argument
32917 <row interlinespace="2.5mm">
32918 <cell alignment="center" valignment="top" usebox="none">
32921 \begin_layout Plain Layout
32924 arg "math-macro-remove-optional-param"
32932 <cell alignment="center" valignment="top" usebox="none">
32935 \begin_layout Plain Layout
32938 Edit\SpecialChar \menuseparator
32939 Math\SpecialChar \menuseparator
32941 \begin_inset space ~
32944 Definition\SpecialChar \menuseparator
32945 Remove Optional Argument
32951 <row interlinespace="2.5mm">
32952 <cell alignment="center" valignment="top" usebox="none">
32955 \begin_layout Plain Layout
32958 arg "math-macro-add-optional-param"
32966 <cell alignment="center" valignment="top" usebox="none">
32969 \begin_layout Plain Layout
32972 Edit\SpecialChar \menuseparator
32973 Math\SpecialChar \menuseparator
32975 \begin_inset space ~
32978 Definition\SpecialChar \menuseparator
32979 Insert Optional Argument
32985 <row interlinespace="2.5mm">
32986 <cell alignment="center" valignment="top" usebox="none">
32989 \begin_layout Plain Layout
32992 arg "math-macro-remove-greedy-param"
33000 <cell alignment="center" valignment="top" usebox="none">
33003 \begin_layout Plain Layout
33006 Edit\SpecialChar \menuseparator
33007 Math\SpecialChar \menuseparator
33009 \begin_inset space ~
33012 Definition\SpecialChar \menuseparator
33013 Remove Last Argument
33014 \begin_inset Newline newline
33018 \begin_inset Phantom HPhantom
33021 \begin_layout Plain Layout
33024 Edit\SpecialChar \menuseparator
33025 Math\SpecialChar \menuseparator
33027 \begin_inset space ~
33030 Definition\SpecialChar \menuseparator
33036 Spitting Out To The Right
33042 <row interlinespace="2.5mm">
33043 <cell alignment="center" valignment="top" usebox="none">
33046 \begin_layout Plain Layout
33049 arg "math-macro-append-greedy-param"
33057 <cell alignment="center" valignment="top" usebox="none">
33060 \begin_layout Plain Layout
33063 Edit\SpecialChar \menuseparator
33064 Math\SpecialChar \menuseparator
33066 \begin_inset space ~
33069 Definition\SpecialChar \menuseparator
33071 \begin_inset Newline newline
33075 \begin_inset Phantom HPhantom
33078 \begin_layout Plain Layout
33081 Edit\SpecialChar \menuseparator
33082 Math\SpecialChar \menuseparator
33084 \begin_inset space ~
33087 Definition\SpecialChar \menuseparator
33093 Eating From The Right
33099 <row interlinespace="2.5mm">
33100 <cell alignment="center" valignment="top" usebox="none">
33103 \begin_layout Plain Layout
33106 arg "math-macro-add-greedy-optional-param"
33114 <cell alignment="center" valignment="top" usebox="none">
33117 \begin_layout Plain Layout
33120 Edit\SpecialChar \menuseparator
33121 Math\SpecialChar \menuseparator
33123 \begin_inset space ~
33126 Definition\SpecialChar \menuseparator
33127 Append Optional Argument
33128 \begin_inset Newline newline
33132 \begin_inset Phantom HPhantom
33135 \begin_layout Plain Layout
33138 Edit\SpecialChar \menuseparator
33139 Math\SpecialChar \menuseparator
33141 \begin_inset space ~
33144 Definition\SpecialChar \menuseparator
33150 Eating From The Right
33163 \begin_layout Section
33164 Computer Algebra Systems
33167 \begin_layout Standard
33168 LyX offers the exchange between mathematical expressions written in LyX's
33169 math editor and external applications or user defined scripts.
33170 Currently supported applications are
33187 Note that the set of supported mathematical constructs is limited only
33188 to very simple cases.
33191 \begin_layout Subsection
33195 \begin_layout Standard
33196 Write some expression in a formula, go to the
33198 Edit\SpecialChar \menuseparator
33199 Math\SpecialChar \menuseparator
33200 Use Computer Algebra System
33202 menu and choose the application you have installed on the computer.
33203 After that the result of computation should show on the right side of the
33204 expression together with the
33205 \begin_inset Quotes eld
33209 \begin_inset Quotes erd
33215 \begin_layout Standard
33216 Here are few simple examples (with results from
33220 ) to show what kind of computations can be performed:
33223 \begin_layout Itemize
33224 \begin_inset Formula $\frac{37}{3}*2-\sum_{i=1}^{3}i^{i}=-\frac{22}{3}$
33230 \begin_layout Itemize
33231 \begin_inset Formula $\frac{37.0}{3}=12.33333333333333$
33237 \begin_layout Itemize
33238 \begin_inset Formula $\int_{1}^{2}\sin(x)dx=\cos1-\cos2$
33244 \begin_layout Itemize
33245 \begin_inset Formula $\det\left[\begin{array}{ccc}
33249 \end{array}\right]=-56$
33255 \begin_layout Itemize
33256 \begin_inset Formula $\lim_{x\rightarrow0}\left(\frac{\sin(x)}{x}\right)=1$
33262 \begin_layout Subsection
33266 \begin_layout Standard
33267 Currently there is no keyboard shortcut for calling the algebra applications.
33268 One can easily bind a shortcut to the
33272 LyX function (see the
33280 \begin_inset space \thinspace{}
33284 \begin_inset space \space{}
33291 key inside the math editor.
33296 one would use this shortcut definition command:
33299 \begin_layout Standard
33302 command-alternatives break-paragraph;math-extern maxima
33305 \begin_layout Section
33307 \begin_inset Index idx
33310 \begin_layout Plain Layout
33319 \begin_layout Subsection
33321 \begin_inset Index idx
33324 \begin_layout Plain Layout
33333 \begin_layout Standard
33334 Negative numbers often look ugly in formulas because the minus sign before
33335 the number is set with the same length as the minus operator sign.
33336 When writing the negative number in normal text, the minus sign appears
33340 \begin_layout Standard
33341 Thus, the problem disappears when converting the minus sign to mathematical
33345 \begin_layout Standard
33346 An example to visualize the problem:
33349 \begin_layout Standard
33351 \begin_inset Tabular
33352 <lyxtabular version="3" rows="3" columns="2">
33353 <features rotate="0" tabularvalignment="middle">
33354 <column alignment="right" valignment="top">
33355 <column alignment="left" valignment="top">
33357 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
33360 \begin_layout Plain Layout
33366 <cell alignment="center" valignment="top" topline="true" rightline="true" usebox="none">
33369 \begin_layout Plain Layout
33377 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
33380 \begin_layout Plain Layout
33386 <cell alignment="center" valignment="top" topline="true" bottomline="true" rightline="true" usebox="none">
33389 \begin_layout Plain Layout
33390 \begin_inset Formula $x=-2$
33400 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
33403 \begin_layout Plain Layout
33409 <cell alignment="center" valignment="top" topline="true" bottomline="true" rightline="true" usebox="none">
33412 \begin_layout Plain Layout
33413 \begin_inset Formula $x=\textrm{-}2$
33429 \begin_layout Subsection
33430 Comma as decimal Separator
33431 \begin_inset Index idx
33434 \begin_layout Plain Layout
33443 \begin_layout Standard
33444 In LaTeX a comma inside a formula is used, according to the English convention,
33445 as number group separator.
33446 So there will be space added behind all commas in formulas.
33449 \begin_layout Standard
33450 To avoid this, the comma is highlighted and changed to mathematical text
33460 \begin_layout Standard
33461 To use all formula commas in the document as decimal separator, the file
33470 \begin_layout Plain Layout
33475 is part of the LaTeX-package
33480 \begin_inset Index idx
33483 \begin_layout Plain Layout
33488 \begin_layout Plain Layout
33508 \begin_inset Index idx
33511 \begin_layout Plain Layout
33517 is loaded with the LaTeX-preamble line
33520 \begin_layout Standard
33528 \begin_layout Subsection
33530 \begin_inset CommandInset label
33532 name "sub:Physical-Vectors"
33537 \begin_inset Index idx
33540 \begin_layout Plain Layout
33549 \begin_layout Standard
33550 Predefined vectors are offered by the LaTeX-package
33555 \begin_inset Index idx
33558 \begin_layout Plain Layout
33564 that is loaded with the LaTeX-preamble line
33567 \begin_layout Standard
33575 \begin_layout Standard
33579 \begin_layout Plain Layout
33589 \begin_inset Note Note
33592 \begin_layout Plain Layout
33593 The following table will only be displayed when the LaTeX-package
33605 \begin_layout Standard
33606 The following commands are defined:
33609 \begin_layout Standard
33611 \begin_inset Tabular
33612 <lyxtabular version="3" rows="4" columns="2">
33613 <features rotate="0" tabularvalignment="middle">
33614 <column alignment="center" valignment="top">
33615 <column alignment="center" valignment="top">
33617 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
33620 \begin_layout Plain Layout
33626 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
33629 \begin_layout Plain Layout
33637 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
33640 \begin_layout Plain Layout
33650 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
33653 \begin_layout Plain Layout
33654 \begin_inset Formula $\Bra{\psi}$
33664 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
33667 \begin_layout Plain Layout
33677 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
33680 \begin_layout Plain Layout
33681 \begin_inset Formula $\Ket{\psi}$
33691 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
33694 \begin_layout Plain Layout
33706 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
33709 \begin_layout Plain Layout
33710 \begin_inset Formula $\Braket{\psi|\phi}$
33726 \begin_layout Standard
33733 assures that all vertical bars are set in the size of the surrounding brackets:
33734 \begin_inset Formula
33736 \Braket{\phi|J=\frac{3}{2}\,,\, M_{J}}
33745 \begin_layout Plain Layout
33755 \begin_inset Note Note
33758 \begin_layout Plain Layout
33759 The following will be displayed when the LaTeX-package
33771 \begin_layout Standard
33772 You need to install the LaTeX-package
33776 to see the rest of this subsection in the output.
33779 \begin_layout Standard
33783 \begin_layout Plain Layout
33795 \begin_layout Standard
33802 can also be achieved using the command
33808 , that is described in
33809 \begin_inset CommandInset ref
33811 reference "sub:Automatic-Bracket-Size"
33818 \begin_layout Subsection
33819 Self-defined Fractions
33820 \begin_inset CommandInset label
33822 name "sub:Self-defined-Fractions"
33827 \begin_inset Index idx
33830 \begin_layout Plain Layout
33831 Fractions ! self-defined
33839 \begin_layout Standard
33840 To define custom commands for fractions, the command
33847 \begin_inset Index idx
33850 \begin_layout Plain Layout
33857 \begin_layout Plain Layout
33871 is used in the following scheme:
33874 \begin_layout Standard
33887 bracket}{fraction bar thickness}{style}
33888 \begin_inset Newline newline
33892 \begin_inset Phantom HPhantom
33895 \begin_layout Plain Layout
33905 {numerator}{denominator}
33908 \begin_layout Standard
33909 The style is a number in the range of 0
33910 \begin_inset space \thinspace{}
33914 \begin_inset space \thinspace{}
33920 \begin_layout Standard
33922 \begin_inset Tabular
33923 <lyxtabular version="3" rows="5" columns="2">
33924 <features rotate="0" tabularvalignment="middle">
33925 <column alignment="center" valignment="top">
33926 <column alignment="center" valignment="top">
33928 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
33931 \begin_layout Plain Layout
33937 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
33940 \begin_layout Plain Layout
33948 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
33951 \begin_layout Plain Layout
33957 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
33960 \begin_layout Plain Layout
33961 display style formula
33968 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
33971 \begin_layout Plain Layout
33977 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
33980 \begin_layout Plain Layout
33988 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
33991 \begin_layout Plain Layout
33997 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
34000 \begin_layout Plain Layout
34008 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
34011 \begin_layout Plain Layout
34017 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
34020 \begin_layout Plain Layout
34034 \begin_layout Standard
34035 When no style is given, the size is adjusted to the surrounding environment
34036 like for the command
34045 \begin_layout Standard
34046 When no fraction bar thickness is given, the predefined value of 0.4
34047 \begin_inset space \thinspace{}
34053 \begin_layout Standard
34054 \begin_inset VSpace medskip
34057 For example, the commands
34070 \begin_inset CommandInset ref
34072 reference "sub:Fractions"
34076 are defined with the commands
34079 \begin_layout Standard
34088 genfrac{}{}{}{0}{#1}{#2}}
34091 \begin_layout Standard
34095 \begin_layout Standard
34104 genfrac{(}{)}{0pt}{1}{#1}{#2}}
34107 \begin_layout Standard
34108 \begin_inset VSpace medskip
34111 To define a fraction where the fraction bar thickness can be given as optional
34112 argument, the following line is inserted to the LaTeX-preamble:
34115 \begin_layout Standard
34124 genfrac{}{}{#1}{}{#2}{#3}}
34127 \begin_layout Standard
34129 \begin_inset Formula
34131 \text{Command} & & \mathrm{\backslash fracS[1mm]\backslash\{A\to\backslash\{B} & & \mathrm{\backslash fracS[5mm]\backslash\{A\to\backslash\{B}\\
34132 \text{Result} & & \fracS[1mm]{A}{B} & & \fracS[5mm]{A}{B}
34137 As one can see, the distance of the numerator and the denominator to the
34138 fraction bar is round about three times the bar thickness.
34141 \begin_layout Subsection
34143 \begin_inset Index idx
34146 \begin_layout Plain Layout
34155 \begin_layout Standard
34156 There are four ways to cancel formulas or parts of formulas:
34159 \begin_layout Standard
34163 \begin_layout Plain Layout
34173 \begin_inset Note Note
34176 \begin_layout Plain Layout
34177 The following table will only be displayed when the LaTeX-package
34189 \begin_layout Standard
34191 \begin_inset Tabular
34192 <lyxtabular version="3" rows="5" columns="2">
34193 <features rotate="0" tabularvalignment="middle">
34194 <column alignment="center" valignment="top">
34195 <column alignment="center" valignment="top">
34197 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
34200 \begin_layout Plain Layout
34206 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
34209 \begin_layout Plain Layout
34211 \begin_inset Note Note
34214 \begin_layout Plain Layout
34221 are used here as spacer.
34233 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
34236 \begin_layout Plain Layout
34240 \begin_inset space \textvisiblespace{}
34246 \begin_inset space \textvisiblespace{}
34254 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
34257 \begin_layout Plain Layout
34258 \begin_inset Formula $\raisebox{4.5mm}{}\cancel{\int A=B}\raisebox{-2.5mm}{}$
34268 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
34271 \begin_layout Plain Layout
34275 \begin_inset space \textvisiblespace{}
34281 \begin_inset space \textvisiblespace{}
34289 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
34292 \begin_layout Plain Layout
34293 \begin_inset Formula $\raisebox{4.5mm}{}\bcancel{\int A=B}\raisebox{-2.5mm}{}$
34303 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
34306 \begin_layout Plain Layout
34310 \begin_inset space \textvisiblespace{}
34316 \begin_inset space \textvisiblespace{}
34324 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
34327 \begin_layout Plain Layout
34328 \begin_inset Formula $\raisebox{4.5mm}{}\xcancel{\int A=B}\raisebox{-2.5mm}{}$
34338 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
34341 \begin_layout Plain Layout
34345 \begin_inset space \textvisiblespace{}
34351 \begin_inset space \textvisiblespace{}
34355 \begin_inset Formula $\to$
34363 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
34366 \begin_layout Plain Layout
34367 \begin_inset Formula $\raisebox{7mm}{}\cancelto{1}{\int A=B}\raisebox{-2.5mm}{}\hspace{3mm}$
34383 \begin_layout Standard
34390 is especially suitable to visualize the reduction of fractions within formulas:
34391 \begin_inset Formula
34393 \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}}}
34401 \begin_layout Standard
34402 To change the size of
34409 \begin_inset Quotes eld
34413 \begin_inset Quotes erd
34416 value one can add the LaTeX-preamble line
34419 \begin_layout Standard
34424 PassOptionsToPackage{option}{cancel}
34427 \begin_layout Standard
34436 which leads to the same size as for the canceled value, or
34440 which makes is it a bit smaller than normal.
34443 \begin_layout Standard
34444 To color the cancellation bar one adds this command as TeX code:
34447 \begin_layout Standard
34459 \begin_layout Standard
34464 can be replaced by a color of your choice.
34467 \begin_layout Standard
34471 \begin_layout Plain Layout
34487 \begin_layout Standard
34488 \begin_inset Formula
34490 \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}}}
34498 \begin_layout Standard
34502 \begin_layout Plain Layout
34516 \begin_inset Note Note
34519 \begin_layout Plain Layout
34528 \begin_layout Standard
34529 For further customizations, see the documentation of the package
34534 \begin_inset CommandInset citation
34541 \begin_inset Index idx
34544 \begin_layout Plain Layout
34553 \begin_layout Standard
34557 \begin_layout Plain Layout
34567 \begin_inset Note Note
34570 \begin_layout Plain Layout
34571 The following will be displayed when the LaTeX-package
34583 \begin_layout Standard
34584 You need to install the LaTeX-package
34588 to see the rest of this subsection in the output.
34591 \begin_layout Standard
34595 \begin_layout Plain Layout
34607 \begin_layout Standard
34608 \begin_inset Newpage newpage
34614 \begin_layout Subsection
34615 Formulas in Section Headings
34616 \begin_inset CommandInset label
34618 name "sub:Formulas-in-Section"
34623 \begin_inset Index idx
34626 \begin_layout Plain Layout
34627 Formula ! in section headings
34635 \begin_layout Standard
34636 When formulas are used in section headings, the following has to be taken
34640 \begin_layout Standard
34641 \begin_inset Note Greyedout
34644 \begin_layout Plain Layout
34650 \begin_inset Index idx
34653 \begin_layout Plain Layout
34654 Packages ! hyperref
34659 support is enabled in the document settings dialog under
34662 \begin_inset space ~
34667 , PDF-bookmarks are created for every section heading in the table of contents.
34668 If a section heading contains formulas, they are incorrectly displayed
34669 in the bookmark text, because formulas in bookmarks infringe the PDF convention
34678 \begin_layout Standard
34679 Both problems can be solved by inserting at the end of the section heading
34680 a short title with the menu
34682 Insert\SpecialChar \menuseparator
34684 \begin_inset space ~
34690 Short titles are used as alternative for multiline section headings to
34691 keep the table of contents clearly arranged.
34692 Only the short title appears in the table of contents and therefore also
34693 in the PDF-bookmark.
34696 \begin_layout Standard
34697 When formulas should be used in the table of contents but
34701 is used, one can use the following command in TeX-mode:
34704 \begin_layout Standard
34709 texorpdfstring{part}{alternative}
34710 \begin_inset Index idx
34713 \begin_layout Plain Layout
34724 \begin_layout Standard
34725 Part is the part of the heading that shouldn't appear in the PDF-bookmark.
34726 This can be characters, formulas, footnotes, but also cross-references.
34727 The alternative is used instead of the part for the bookmark.
34730 \begin_layout Standard
34731 Here are two example headings:
34732 \begin_inset VSpace -3mm
34739 \begin_layout Plain Layout
34751 \begin_layout Subsubsection
34752 Heading without formula in table of contents
34753 \begin_inset Formula $\sqrt{-1}=\mathrm{i}$
34757 \begin_inset Argument 1
34760 \begin_layout Plain Layout
34761 Heading without formula in table of contents
34769 \begin_layout Subsubsection
34770 Heading with formula in table of contents
34774 \begin_layout Plain Layout
34784 \begin_inset Formula $\sqrt{-1}=\mathrm{i}$
34791 \begin_layout Plain Layout
34801 \begin_layout Standard
34805 \begin_layout Plain Layout
34814 In the first heading a short title was used, in the second one
34823 \begin_layout Standard
34824 To get the same formatting as for the other headings, the complete heading
34833 \begin_layout Plain Layout
34835 \begin_inset CommandInset ref
34837 reference "sub:Bold-Formulas"
34849 \begin_layout Subsection
34850 Formulas in multi-column Text
34851 \begin_inset Index idx
34854 \begin_layout Plain Layout
34855 Formula ! in multi-column text
34863 \begin_layout Standard
34864 Formulas in multi-column text are often too wide to fit into a column and
34865 thus need to be set over the whole page width.
34866 This is done by using the LaTeX-package
34874 \begin_layout Plain Layout
34879 is part of every LaTeX standard installation.
34885 \begin_inset Index idx
34888 \begin_layout Plain Layout
34889 Packages ! multicol
34894 , that is loaded with the LaTeX-preamble line
34897 \begin_layout Standard
34902 usepackage{multicol}
34905 \begin_layout Standard
34906 \begin_inset Note Greyedout
34909 \begin_layout Plain Layout
34910 Note that in this case the setting
34913 \begin_inset space ~
34920 Document\SpecialChar \menuseparator
34926 \begin_inset space ~
34946 \begin_layout Standard
34947 Before the multi-column text the command
34950 \begin_layout Standard
34955 begin{multicols}{column number}
34958 \begin_layout Standard
34959 is written in TeX-mode.
34960 The column number is a number in the range of 2
34961 \begin_inset space \thinspace{}
34965 \begin_inset space \thinspace{}
34969 Before the formula the multi-column text is ended by inserting the command
34972 \begin_layout Standard
34980 \begin_layout Standard
34984 \begin_layout Standard
34985 Due to the command some space is automatically added before the formula.
34987 \begin_inset space \thinspace{}
34990 mm vertical space is inserted before the formula.
34991 When the formula style
34997 \begin_layout Plain Layout
34999 \begin_inset CommandInset ref
35001 reference "sec:Formula-Styles"
35013 \begin_inset space \thinspace{}
35016 mm space is inserted instead.
35019 \begin_layout Standard
35020 As example a multi-column text with a displayed formula:
35023 \begin_layout Standard
35029 \begin_layout Plain Layout
35033 begin{multicols}{2}
35038 Das Spektrum wird fouriertransformiert.
35039 Die Fouriertransformation wird verwendet, um die überlagerten Signale (Netzwerk
35040 , Lösungsmittel) zu trennen.
35041 Nachdem wir die Phasenverschiebung bestimmen konnten, interessiert uns
35042 nun das Aussehen des Ausgangssignals.
35043 Im Experiment haben wir es mit sehr vielen Teilchen zu tun, so dass man
35044 über alle Phasen integrieren muss.
35046 \begin_inset Formula $S$
35049 unser normiertes Ausgangssignal und
35050 \begin_inset Formula $P$
35053 die Phasenverteilungsfunktion, so ergibt sich die Beziehung
35057 \begin_layout Plain Layout
35067 \begin_inset VSpace -6mm
35071 \begin_inset Formula
35073 S(t)=S_{0}(t)\int_{-\infty}^{\infty}P(\phi,t)\mathrm{e}^{\mathrm{i}\phi}\,\mathrm{d}\phi
35082 \begin_layout Plain Layout
35086 begin{multicols}{2}
35092 \begin_inset Formula $S_{0}$
35095 das Signal ohne Gradient ist und die Normierungsbedingung
35096 \begin_inset Formula $\int_{-\infty}^{\infty}P(\phi,t)\,\mathrm{d}\phi=1$
35100 Nun dürfen wir aber nicht den Relaxationsprozess außer Acht lassen.
35102 \begin_inset Formula $\nicefrac{\pi}{2}$
35106 \begin_inset space \thinspace{}
35109 -rf-Puls beginnt sich die Magnetisierung zu entfokussieren, wodurch sich
35110 das Signal zusätzlich abschwächt.
35111 Diese Abschwächung verläuft exponentiell in Abhängigkeit der so genannten
35113 \begin_inset Formula $T_{2}$
35119 \begin_layout Standard
35125 \begin_layout Plain Layout
35137 \begin_layout Subsection
35138 Formulas with Description of Variables
35139 \begin_inset Index idx
35142 \begin_layout Plain Layout
35143 Formula ! with description of variables
35151 \begin_layout Standard
35152 To describe variables within a formula, like in formula
35153 \begin_inset CommandInset ref
35155 reference "eq:within"
35164 \begin_inset Formula $n$
35168 \begin_inset space ~
35171 matrix is used with left aligned columns for the
35172 \begin_inset Formula $n$
35179 \begin_layout Plain Layout
35181 \begin_inset CommandInset ref
35183 reference "sec:Matrices"
35192 To set the description in a smaller size, before the matrix e.
35193 \begin_inset space \thinspace{}
35197 \begin_inset space \space{}
35210 \begin_layout Plain Layout
35212 \begin_inset CommandInset ref
35214 reference "sub:Font-Sizes"
35226 \begin_layout Standard
35227 When the formula style
35233 \begin_layout Plain Layout
35235 \begin_inset CommandInset ref
35237 reference "sec:Formula-Styles"
35258 \begin_layout Plain Layout
35265 only works in formulas with the style
35270 \begin_inset CommandInset ref
35272 reference "sub:Variable-Space"
35281 is inserted before and after the matrix to have the same separation of
35282 the matrix from the equation and the side margin.
35285 \begin_layout Standard
35286 When the formula style
35290 is used, the method described in
35291 \begin_inset CommandInset ref
35293 reference "sub:Flalign-Environment"
35297 is used to indent formulas.
35299 \begin_inset CommandInset ref
35301 reference "eq:within"
35305 consists of five columns where in the first two columns contain the equation,
35306 the third the matrix and the last one an empty TeX-brace.
35307 \begin_inset Formula
35309 \hspace{30pt}F_{A} & =\rho·V·g & \footnotesize\begin{array}{ll}
35310 \rho & \textrm{density}\\
35311 V & \textrm{volume}\\
35312 g & \textrm{gravitational acceleration}
35313 \end{array} & & {}\label{eq:within}
35321 \begin_layout Subsection
35322 Upright small Greek Letters
35323 \begin_inset CommandInset label
35325 name "sub:Upright-small-Greek"
35330 \begin_inset Index idx
35333 \begin_layout Plain Layout
35334 Greek letters ! upright
35342 \begin_layout Standard
35343 Most of the math fonts only provide italic small Greek letters.
35344 But for symbols of elementary particles like pions and neutrinos, upright
35345 Greek letters are needed.
35354 \begin_layout Plain Layout
35359 is part of the LaTeX-package
35364 \begin_inset Index idx
35367 \begin_layout Plain Layout
35372 \begin_layout Plain Layout
35392 \begin_inset Index idx
35395 \begin_layout Plain Layout
35401 that is loaded with the LaTeX-preamble line
35404 \begin_layout Standard
35409 usepackage{upgreek}
35412 \begin_layout Standard
35418 \begin_layout Plain Layout
35428 \begin_inset Note Note
35431 \begin_layout Plain Layout
35432 The following table will only be displayed when the LaTeX-package
35441 They are created when the command for a small Greek letter is started with
35447 For example the command
35454 \begin_inset Formula $\uptau$
35460 \begin_layout Standard
35461 With these commands reactions of elementary particles can be typeset:
35462 \begin_inset Formula
35464 \uppi^{+}\to\upmu^{+}+\upnu_{\upmu}
35472 \begin_layout Standard
35473 The upright letters are more bold and wider than the italic ones.
35474 They should therefore not be used for units like
35475 \begin_inset Quotes eld
35479 \begin_inset Quotes erd
35485 \begin_layout Standard
35489 \begin_layout Plain Layout
35499 \begin_inset Note Note
35502 \begin_layout Plain Layout
35503 The following will be displayed when the LaTeX-package
35515 \begin_layout Standard
35516 You need to install the LaTeX-package
35520 to see the rest of this subsection in the output.
35523 \begin_layout Standard
35527 \begin_layout Plain Layout
35539 \begin_layout Subsection
35540 Text Characters in Formulas
35541 \begin_inset CommandInset label
35543 name "sub:Text-Characters-in"
35548 \begin_inset Index idx
35551 \begin_layout Plain Layout
35560 \begin_layout Standard
35561 In some cases you might want to insert text characters directly into formulas.
35562 When for example the centered dot · is often used in formulas like
35563 \begin_inset Formula $\nu=5·10^{5}\,\mathrm{Hz}$
35566 , one would have to insert the command
35576 \begin_layout Plain Layout
35578 \begin_inset CommandInset ref
35580 reference "sub:Binary-Operators"
35589 all the time, because this character is defined in all encodings as text
35591 But the encoding can be changed by this LaTeX-preamble line:
35594 \begin_layout Standard
35599 Declare Inputtext{183}{
35609 f\SpecialChar \textcompwordmark{}
35613 \begin_layout Standard
35614 The character encoding (menu
35616 Document\SpecialChar \menuseparator
35617 Settings\SpecialChar \menuseparator
35620 ) specifies what character appears when a keyboard key is pressed.
35621 When the key for the character '·' is pressed, internally the command
35628 But this command is not available in a formula so that you would get LaTeX-erro
35630 With the changed encoding the right command is chosen automatically, depending
35631 on if the character was inserted into a formula or not.
35634 \begin_layout Standard
35635 The encoding of several characters is saved in definition files.
35636 For example the encoding
35640 is defined in the file
35644 which is in the installation folder of LaTeX.
35645 Encodings should only be changed via the LaTeX-preamble and not in the
35647 Otherwise documents could not be edited by other LyX users working on other
35651 \begin_layout Standard
35652 \begin_inset VSpace medskip
35655 Besides the centered dot, in this document the degree sign ° is defined
35656 with the following LaTeX-preamble line so that it can be directly inserted
35660 \begin_layout Standard
35665 DeclareInputtext{176}{
35675 f\SpecialChar \textcompwordmark{}
35679 \begin_layout Standard
35680 \begin_inset Newpage newpage
35686 \begin_layout Section
35689 \begin_inset Index idx
35692 \begin_layout Plain Layout
35701 \begin_layout Standard
35702 This section is a summary of the most important typographic rules, listed
35707 \begin_layout Plain Layout
35708 This collection was partly taken from the German semi-official dictionary
35710 \begin_inset Quotes eld
35714 \begin_inset Quotes erd
35718 \begin_inset CommandInset citation
35724 that lists some of the ISO rules.
35725 More rules are listed in
35726 \begin_inset CommandInset citation
35740 \begin_layout Itemize
35749 \begin_layout Plain Layout
35750 done with font styles, see
35751 \begin_inset CommandInset ref
35753 reference "sub:Font-Styles"
35762 , no matter if they appear in italic text: 30
35763 \begin_inset space \thinspace{}
35767 \begin_inset Newline newline
35770 Between the value and the unit is the smallest space, see
35771 \begin_inset CommandInset ref
35773 reference "sub:Predefined-Space"
35778 \begin_inset Newline newline
35781 This convention is automatically fulfilled when the command
35788 When it is entered to a formula, two boxes appear.
35789 In the first one the value is inserted, in the second one the unit, and
35791 \begin_inset Formula $\unit[30]{km/h}$
35795 \begin_inset space \thinspace{}
35805 is not a real LaTeX command but the command
35811 , therefore you cannot use it in TeX code.
35814 \begin_layout Itemize
35815 Percent and perthousand signs are set like physical units:
35816 \begin_inset Newline newline
35820 \begin_inset space \thinspace{}
35826 \begin_layout Itemize
35827 The degree sign follows directly on the value: 15°, but not when it is used
35829 \begin_inset space \thinspace{}
35835 \begin_layout Itemize
35836 In numbers with more than four digits the smallest space is inserted before
35837 every third digit to group them:
35847 \begin_inset space \thinspace{}
35851 \begin_inset space \thinspace{}
35857 \begin_layout Itemize
35858 For dimensions like 120×90×40
35859 \begin_inset space \thinspace{}
35862 cm the multiplication sign
35863 \begin_inset Quotes eld
35867 \begin_inset Quotes erd
35871 It is available either via the command
35879 Insert\SpecialChar \menuseparator
35880 Special Character\SpecialChar \menuseparator
35886 \begin_layout Itemize
35887 Functions with names consisting of several letters are set upright to avoid
35889 \begin_inset CommandInset ref
35891 reference "sub:Predefined-Functions"
35898 \begin_layout Itemize
35899 Indices consisting of several letters, are set upright:
35900 \begin_inset Formula $E_{\mathrm{kin}}$
35904 \begin_inset Newline newline
35907 Components of matrices are set italic:
35908 \begin_inset Formula $\hat{H}_{kl}$
35914 \begin_layout Itemize
35915 The differentiation/integration operator 'd', the Euler's number 'e' and
35916 the imaginary unit 'i' should be set upright, to avoid mixing them up with
35920 \begin_layout Itemize
35921 The character that denotes a
35925 transformation is inserted either by the command
35930 \begin_inset space \textvisiblespace{}
35937 Insert\SpecialChar \menuseparator
35938 Special Character\SpecialChar \menuseparator
35939 Symbols\SpecialChar \menuseparator
35941 \begin_inset space ~
35947 \begin_inset Formula $\mathscr{F}$
35953 \begin_layout Standard
35954 \begin_inset Newpage newpage
35960 \begin_layout Section
35962 \begin_inset Index idx
35965 \begin_layout Plain Layout
35974 \begin_layout Standard
35975 Some characters and symbols can be created with several commands.
35976 Here is a list of the synonym commands:
35979 \begin_layout Standard
35980 \begin_inset VSpace bigskip
35984 \begin_inset space \hfill{}
35988 \begin_inset Tabular
35989 <lyxtabular version="3" rows="12" columns="2">
35990 <features rotate="0" tabularvalignment="middle">
35991 <column alignment="center" valignment="top" width="0pt">
35992 <column alignment="center" valignment="top" width="0pt">
35994 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
35997 \begin_layout Plain Layout
36003 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
36006 \begin_layout Plain Layout
36008 \begin_inset Note Note
36011 \begin_layout Plain Layout
36018 is only used as spacer.
36030 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
36033 \begin_layout Plain Layout
36041 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
36044 \begin_layout Plain Layout
36048 \begin_layout Plain Layout
36061 \begin_layout Plain Layout
36075 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
36078 \begin_layout Plain Layout
36086 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
36089 \begin_layout Plain Layout
36099 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
36102 \begin_layout Plain Layout
36110 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
36113 \begin_layout Plain Layout
36123 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
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36634 The LaTeX Companion
36637 Addison Wesley, 2004
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36859 Auflage, Duden 2001
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