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 Multiline fractions are explained in
2266 \begin_inset CommandInset ref
2268 reference "sub:Multiline-Fractions"
2275 \begin_layout Subsection
2277 \begin_inset Index idx
2280 \begin_layout Plain Layout
2289 \begin_layout Standard
2290 Square roots are created with
2297 \begin_inset Index idx
2300 \begin_layout Plain Layout
2308 or the math toolbar button
2311 arg "math-insert \\sqrt"
2314 , all other roots with the command
2321 \begin_inset Index idx
2324 \begin_layout Plain Layout
2332 or with the math toolbar button
2335 arg "math-insert \\root"
2341 \begin_layout Standard
2343 \begin_inset Tabular
2344 <lyxtabular version="3" rows="3" columns="2">
2345 <features rotate="0" tabularvalignment="middle">
2346 <column alignment="center" valignment="top" width="0pt">
2347 <column alignment="center" valignment="top" width="0pt">
2349 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
2352 \begin_layout Plain Layout
2358 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
2361 \begin_layout Plain Layout
2363 \begin_inset Note Note
2366 \begin_layout Plain Layout
2373 is only used as spacer.
2385 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
2388 \begin_layout Plain Layout
2392 \begin_inset space \textvisiblespace{}
2400 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
2403 \begin_layout Plain Layout
2404 \begin_inset Formula $\raisebox{4.5mm}{}\sqrt{A-B}$
2414 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
2417 \begin_layout Plain Layout
2421 \begin_inset space \textvisiblespace{}
2425 \begin_inset Formula $\downarrow$
2433 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
2436 \begin_layout Plain Layout
2437 \begin_inset Formula $\raisebox{4.5mm}{}\sqrt[3]{A-B}$
2453 \begin_layout Standard
2454 A square root can also be created with
2460 when the root index field is left empty.
2463 \begin_layout Standard
2464 With certain indices the distance to the root is too small, like in this
2466 \begin_inset Formula $\sqrt[\beta]{B}$
2470 \begin_inset Newline newline
2474 \begin_inset Formula $\beta$
2478 To avoid this, the commands
2485 \begin_inset Index idx
2488 \begin_layout Plain Layout
2503 \begin_inset Index idx
2506 \begin_layout Plain Layout
2514 are used with the following scheme:
2517 \begin_layout Standard
2531 \begin_layout Standard
2532 Distance is the number of Big Points (unit bp;
2533 \begin_inset Formula $\mathrm{72\, bp=1\, inch}$
2536 ), that the index should be moved to the left or top, resp..
2537 The commands are written to the index.
2538 This way the command
2539 \begin_inset Newline newline
2549 \begin_inset Formula $\to$
2555 \begin_inset Formula $\to$
2561 \begin_inset space \textvisiblespace{}
2565 \begin_inset Formula $\to$
2569 \begin_inset Newline newline
2574 produces a correct typeset formula:
2575 \begin_inset Formula $\sqrt[\leftroot{-1}\uproot{2}\beta]{B}$
2581 \begin_layout Subsection
2582 Binomial Coefficients
2583 \begin_inset Index idx
2586 \begin_layout Plain Layout
2587 Binomial coefficients
2595 \begin_layout Standard
2596 Binomial coefficients are inserted with the command
2603 \begin_inset Index idx
2606 \begin_layout Plain Layout
2614 or with the submenu of the math toolbar button
2617 arg "math-insert \\frac-square"
2633 there are the commands
2640 \begin_inset Index idx
2643 \begin_layout Plain Layout
2658 \begin_inset Index idx
2661 \begin_layout Plain Layout
2670 For other brackets around binomial coeficients there are the commands
2677 \begin_inset Index idx
2680 \begin_layout Plain Layout
2695 \begin_inset Index idx
2698 \begin_layout Plain Layout
2709 \begin_layout Standard
2711 \begin_inset Tabular
2712 <lyxtabular version="3" rows="6" columns="2">
2713 <features rotate="0" tabularvalignment="middle">
2714 <column alignment="center" valignment="top" width="0pt">
2715 <column alignment="center" valignment="top" width="0pt">
2717 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
2720 \begin_layout Plain Layout
2726 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
2729 \begin_layout Plain Layout
2731 \begin_inset Note Note
2734 \begin_layout Plain Layout
2741 is only used as spacer.
2753 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
2756 \begin_layout Plain Layout
2760 \begin_inset space \textvisiblespace{}
2764 \begin_inset Formula $\downarrow$
2772 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
2775 \begin_layout Plain Layout
2776 \begin_inset Formula $\raisebox{5mm}{}\binom{A}{B}\raisebox{-2.5mm}{}$
2786 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
2789 \begin_layout Plain Layout
2793 \begin_inset space \textvisiblespace{}
2797 \begin_inset Formula $\downarrow$
2805 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
2808 \begin_layout Plain Layout
2809 \begin_inset Formula $\raisebox{5mm}{}\dbinom{A}{B}\raisebox{-2.5mm}{}$
2819 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
2822 \begin_layout Plain Layout
2826 \begin_inset space \textvisiblespace{}
2830 \begin_inset Formula $\downarrow$
2838 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
2841 \begin_layout Plain Layout
2842 \begin_inset Formula $\raisebox{5mm}{}\tbinom{A}{B}\raisebox{-2.5mm}{}$
2852 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
2855 \begin_layout Plain Layout
2859 \begin_inset space \textvisiblespace{}
2863 \begin_inset Formula $\downarrow$
2871 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
2874 \begin_layout Plain Layout
2875 \begin_inset Formula $\raisebox{5mm}{}{A \brack B}\raisebox{-2.5mm}{}$
2885 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
2888 \begin_layout Plain Layout
2892 \begin_inset space \textvisiblespace{}
2896 \begin_inset Formula $\downarrow$
2904 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
2907 \begin_layout Plain Layout
2908 \begin_inset Formula $\raisebox{5mm}{}{A \brace B}\raisebox{-2.5mm}{}$
2924 \begin_layout Subsection
2925 Case Differentiations
2926 \begin_inset Index idx
2929 \begin_layout Plain Layout
2930 Case differentiations
2938 \begin_layout Standard
2940 \begin_inset Tabular
2941 <lyxtabular version="3" rows="3" columns="2">
2942 <features rotate="0" tabularvalignment="middle">
2943 <column alignment="center" valignment="top" width="0pt">
2944 <column alignment="center" valignment="top" width="0pt">
2946 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
2949 \begin_layout Plain Layout
2955 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
2958 \begin_layout Plain Layout
2966 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
2969 \begin_layout Plain Layout
2973 \begin_inset space \textvisiblespace{}
2977 \begin_inset Formula $\to$
2981 \begin_inset Index idx
2984 \begin_layout Plain Layout
2997 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
3000 \begin_layout Plain Layout
3001 \begin_inset Formula $\begin{cases}
3012 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
3015 \begin_layout Plain Layout
3019 \begin_inset space \textvisiblespace{}
3025 arg "newline-insert newline"
3033 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
3036 \begin_layout Plain Layout
3037 \begin_inset Formula $\begin{cases}
3038 A & \textrm{for }x>0\\
3039 B & \textrm{for }x=0
3056 \begin_layout Standard
3063 or pressing the math toolbar button
3066 arg "math-insert \\cases"
3069 you can create new lines with the shortcut
3072 arg "newline-insert newline"
3075 or the table toolbar button
3078 arg "inset-modify tabular append-row"
3084 \begin_layout Standard
3091 is also available via the menu
3093 Insert\SpecialChar \menuseparator
3094 Math\SpecialChar \menuseparator
3100 \begin_layout Subsection
3102 \begin_inset Index idx
3105 \begin_layout Plain Layout
3114 \begin_layout Standard
3122 \begin_inset Index idx
3125 \begin_layout Plain Layout
3133 every character can be displayed canceled.
3134 The characters are quasi accentuated by a slash.
3137 \begin_layout Standard
3139 \begin_inset Tabular
3140 <lyxtabular version="3" rows="4" columns="2">
3141 <features rotate="0" tabularvalignment="middle">
3142 <column alignment="center" valignment="top" width="0pt">
3143 <column alignment="center" valignment="top" width="0pt">
3145 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
3148 \begin_layout Plain Layout
3154 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
3157 \begin_layout Plain Layout
3165 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
3168 \begin_layout Plain Layout
3176 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
3179 \begin_layout Plain Layout
3180 \begin_inset Formula $\not=$
3190 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
3193 \begin_layout Plain Layout
3203 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
3206 \begin_layout Plain Layout
3207 \begin_inset Formula $\not\le$
3217 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
3220 \begin_layout Plain Layout
3230 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
3233 \begin_layout Plain Layout
3234 \begin_inset Formula $\not\parallel$
3250 \begin_layout Standard
3251 The last example shows that not all negations look good.
3252 Therefore there are special commands for some negations (see
3253 \begin_inset CommandInset ref
3255 reference "sub:Mathematical-Symbols"
3260 \begin_inset CommandInset ref
3262 reference "sec:Relations"
3269 \begin_layout Subsection
3271 \begin_inset CommandInset label
3273 name "sub:Placeholders"
3278 \begin_inset Index idx
3281 \begin_layout Plain Layout
3288 \begin_inset Index idx
3291 \begin_layout Plain Layout
3292 Chemical characters ! Isotopes
3298 \begin_inset Index idx
3301 \begin_layout Plain Layout
3306 \begin_layout Plain Layout
3317 \begin_layout Plain Layout
3332 \begin_layout Standard
3334 \begin_inset space \thinspace{}
3338 \begin_inset space \space{}
3345 \begin_layout Plain Layout
3346 Typesetting isotopes and chemical symbols is described in
3347 \begin_inset CommandInset ref
3349 reference "sub:Chemical-Symbols-and"
3358 the following problem occurs:
3361 \begin_layout Standard
3363 \begin_inset Tabular
3364 <lyxtabular version="3" rows="2" columns="2">
3365 <features rotate="0" tabularvalignment="middle">
3366 <column alignment="center" valignment="top" width="0pt">
3367 <column alignment="center" valignment="top" width="0pt">
3369 <cell alignment="center" valignment="top" usebox="none">
3372 \begin_layout Plain Layout
3373 Indices created with sub- and superscripts:
3378 <cell alignment="center" valignment="top" usebox="none">
3381 \begin_layout Plain Layout
3382 \begin_inset Formula $_{9}^{19}\mathrm{F}\raisebox{-3mm}{}$
3392 <cell alignment="center" valignment="top" usebox="none">
3395 \begin_layout Plain Layout
3401 <cell alignment="center" valignment="top" usebox="none">
3404 \begin_layout Plain Layout
3405 \begin_inset Formula $_{\phantom{1}9}^{19}\mathrm{F}$
3419 \begin_inset Note Note
3422 \begin_layout Plain Layout
3429 is only used as spacer.
3437 \begin_layout Standard
3438 The shorter index is by default placed below or above the first character
3439 of the longer index.
3440 To avoid this there is the command
3447 \begin_inset Index idx
3450 \begin_layout Plain Layout
3458 or the math toolbar button
3459 \begin_inset space \thinspace{}
3466 \begin_layout Plain Layout
3467 can be found in the submenu of the toolbar button
3470 arg "math-insert \\space"
3479 \begin_inset Graphics
3480 filename ../images/math/phantom.png
3485 that creates one or more phantom characters.
3492 a small blue box appears that is superposed with two red arrows.
3493 The arrows indicate that the complete width and height of the box content
3494 will be created as placeholder.
3495 Phantom characters are accordingly placeholders with the size of the characters.
3498 \begin_layout Standard
3500 \begin_inset Tabular
3501 <lyxtabular version="3" rows="4" columns="2">
3502 <features rotate="0" tabularvalignment="middle">
3503 <column alignment="center" valignment="top">
3504 <column alignment="center" valignment="top">
3506 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
3509 \begin_layout Plain Layout
3515 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
3518 \begin_layout Plain Layout
3520 \begin_inset Note Note
3523 \begin_layout Plain Layout
3530 is only used as spacer.
3542 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
3545 \begin_layout Plain Layout
3547 \begin_inset space \textvisiblespace{}
3553 \begin_inset space \textvisiblespace{}
3557 \begin_inset Formula $\to$
3561 \begin_inset space \textvisiblespace{}
3569 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
3572 \begin_layout Plain Layout
3573 \begin_inset Formula $\raisebox{4.5mm}{}{}_{\phantom{1}9}^{19}\mathrm{F}\raisebox{-2.5mm}{}$
3583 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
3586 \begin_layout Plain Layout
3588 \begin_inset space \textvisiblespace{}
3594 \begin_inset space \textvisiblespace{}
3598 \begin_inset Formula $\to$
3602 \begin_inset space \textvisiblespace{}
3610 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
3613 \begin_layout Plain Layout
3614 \begin_inset Formula $\raisebox{4.5mm}{}{}_{\phantom{23}9}^{235}\mathrm{F}\raisebox{-2.5mm}{}$
3624 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
3627 \begin_layout Plain Layout
3631 \begin_inset space \textvisiblespace{}
3637 \begin_inset space \textvisiblespace{}
3641 \begin_inset Formula $\to$
3645 \begin_inset space \textvisiblespace{}
3653 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
3656 \begin_layout Plain Layout
3657 \begin_inset Formula $\raisebox{4.5mm}{}\Lambda_{MMt}^{\phantom{ii}t}\raisebox{-2.5mm}{}$
3673 \begin_layout Standard
3674 Furthermore there are the commands
3681 \begin_inset Index idx
3684 \begin_layout Plain Layout
3693 \begin_inset space ~
3697 \begin_inset Graphics
3698 filename ../images/math/vphantom.png
3710 \begin_inset Index idx
3713 \begin_layout Plain Layout
3722 \begin_inset space ~
3726 \begin_inset Graphics
3727 filename ../images/math/hphantom.png
3739 creates only space for the maximal height of the characters in the box
3740 but not for its width.
3747 creates only space for the width of the box content.
3748 Therefore the boxes of both commands have only one red arrow.
3751 \begin_layout Standard
3752 For example the command
3757 \begin_inset space \textvisiblespace{}
3764 creates space for the height of the integral sign,
3768 \begin_layout Plain Layout
3775 creates an integral sign, see
3776 \begin_inset CommandInset ref
3778 reference "sub:Big-Operators"
3787 because this is the larger character.
3788 An example application is in
3789 \begin_inset CommandInset ref
3791 reference "sub:Multiline-Brackets"
3798 \begin_layout Standard
3799 Placeholders can also be used for text when they are inserted via the menu
3802 Insert\SpecialChar \menuseparator
3803 Formatting\SpecialChar \menuseparator
3809 \begin_layout Standard
3811 \begin_inset Newline newline
3815 \begin_inset Phantom Phantom
3818 \begin_layout Plain Layout
3827 \begin_layout Subsection
3829 \begin_inset Index idx
3832 \begin_layout Plain Layout
3839 \begin_inset Index idx
3842 \begin_layout Plain Layout
3843 Formula ! underlined
3851 \begin_layout Standard
3853 \begin_inset Tabular
3854 <lyxtabular version="3" rows="4" columns="2">
3855 <features rotate="0" tabularvalignment="middle">
3856 <column alignment="center" valignment="top" width="0pt">
3857 <column alignment="center" valignment="top" width="0pt">
3859 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
3862 \begin_layout Plain Layout
3868 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
3871 \begin_layout Plain Layout
3873 \begin_inset Note Note
3876 \begin_layout Plain Layout
3883 is only used as spacer.
3895 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
3898 \begin_layout Plain Layout
3902 \begin_inset space \textvisiblespace{}
3906 \begin_inset Index idx
3909 \begin_layout Plain Layout
3922 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
3925 \begin_layout Plain Layout
3926 \begin_inset Formula $\raisebox{5mm}{}\overline{A+B}$
3936 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
3939 \begin_layout Plain Layout
3943 \begin_inset space \textvisiblespace{}
3947 \begin_inset Index idx
3950 \begin_layout Plain Layout
3963 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
3966 \begin_layout Plain Layout
3967 \begin_inset Formula $\underline{A+B}\raisebox{-2.5mm}{}$
3977 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
3980 \begin_layout Plain Layout
3984 \begin_inset space \textvisiblespace{}
3990 \begin_inset space \textvisiblespace{}
3998 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
4001 \begin_layout Plain Layout
4002 \begin_inset Formula $\raisebox{5mm}{}\overline{\underline{A+B}}\raisebox{-2.5mm}{}$
4018 \begin_layout Standard
4019 In the last example it doesn't matter if first
4034 \begin_layout Standard
4035 To double underline use
4044 \begin_layout Standard
4045 It is possible to place up to 6 lines above or below characters.
4048 \begin_layout Standard
4049 \begin_inset VSpace bigskip
4052 Custom lines can be created using the command
4059 \begin_inset Index idx
4062 \begin_layout Plain Layout
4070 which has the following scheme:
4073 \begin_layout Standard
4078 rule[vertical offset]{length}{thickness}
4081 \begin_layout Standard
4082 The optional vertical offset shifts the line upwards (or downwards, when
4083 the value is negative).
4085 \begin_inset CommandInset ref
4087 reference "tab:Available-units"
4091 can be used for the values.
4092 Here are two example lines created with the commands
4093 \begin_inset Newline newline
4100 rule[-2ex]{3cm}{2pt}
4111 \begin_layout Standard
4113 \begin_inset Formula $\rule[-2ex]{3cm}{2pt}\rule{2cm}{1pt}$
4119 \begin_layout Standard
4126 can also be used for text when a line is inserted via the menu
4128 Insert\SpecialChar \menuseparator
4129 Formatting\SpecialChar \menuseparator
4131 \begin_inset space ~
4139 \begin_layout Standard
4141 \begin_inset CommandInset line
4152 \begin_layout Subsection
4154 \begin_inset CommandInset label
4161 \begin_inset Index idx
4164 \begin_layout Plain Layout
4173 \begin_layout Standard
4174 There are different types of ellipses available.
4178 \begin_layout Plain Layout
4179 In the math toolbar in the submenu of the button
4182 arg "math-insert \\ldots"
4190 For listings dots at the baseline are used (
4197 \begin_inset Index idx
4200 \begin_layout Plain Layout
4208 ), while for operations dots are needed that are on the same height as the
4216 \begin_inset Index idx
4219 \begin_layout Plain Layout
4228 When using the command
4235 \begin_inset Index idx
4238 \begin_layout Plain Layout
4246 , LaTeX decides on the basis of the next character what type is used.
4249 \begin_layout Standard
4251 \begin_inset Tabular
4252 <lyxtabular version="3" rows="9" columns="2">
4253 <features rotate="0" tabularvalignment="middle">
4254 <column alignment="center" valignment="top" width="0pt">
4255 <column alignment="center" valignment="top" width="0pt">
4257 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
4260 \begin_layout Plain Layout
4266 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
4269 \begin_layout Plain Layout
4277 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
4280 \begin_layout Plain Layout
4282 \begin_inset space \textvisiblespace{}
4288 \begin_inset space \textvisiblespace{}
4296 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
4299 \begin_layout Plain Layout
4300 \begin_inset Formula $A_{1},\dots,A_{n}$
4310 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
4313 \begin_layout Plain Layout
4315 \begin_inset space \textvisiblespace{}
4321 \begin_inset space \textvisiblespace{}
4329 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
4332 \begin_layout Plain Layout
4333 \begin_inset Formula $A_{1}+\dots+A_{n}$
4343 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
4346 \begin_layout Plain Layout
4348 \begin_inset space \textvisiblespace{}
4354 \begin_inset space \textvisiblespace{}
4362 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
4365 \begin_layout Plain Layout
4366 \begin_inset Formula $A_{1},\ldots,A_{n}$
4376 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
4379 \begin_layout Plain Layout
4381 \begin_inset space \textvisiblespace{}
4387 \begin_inset space \textvisiblespace{}
4395 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
4398 \begin_layout Plain Layout
4399 \begin_inset Formula $A_{1}+\cdots+A_{n}$
4409 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
4412 \begin_layout Plain Layout
4420 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
4423 \begin_layout Plain Layout
4424 \begin_inset Formula $\vdots$
4434 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
4437 \begin_layout Plain Layout
4445 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
4448 \begin_layout Plain Layout
4449 \begin_inset Formula $\ddots$
4459 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
4462 \begin_layout Plain Layout
4470 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
4473 \begin_layout Plain Layout
4474 \begin_inset Formula $\iddots$
4484 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
4487 \begin_layout Plain Layout
4489 \begin_inset space \thinspace{}
4492 matrix with the different dots
4497 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
4500 \begin_layout Plain Layout
4501 \begin_inset Formula $\begin{array}{ccc}
4502 A_{11} & \cdots & A_{1m}\\
4503 \vdots & \ddots & \vdots\\
4504 A_{n1} & \cdots & A_{nm}
4521 \begin_layout Standard
4522 The ellipses available in menu
4524 Insert\SpecialChar \menuseparator
4526 \begin_inset space ~
4540 \begin_layout Standard
4541 \begin_inset VSpace medskip
4550 , one of the options
4552 Use mathdots package (automatically)
4554 must be set in the document settings under
4557 \begin_inset space ~
4563 \begin_inset Newline newline
4568 Use mathdots package
4570 will improve the appearance of all dots in the documents if their font
4571 style or size is not the default.
4574 \begin_layout Standard
4575 \begin_inset VSpace medskip
4578 Specially for matrices there are ellipses that span over several columns.
4579 They are created with the command
4586 \begin_inset Index idx
4589 \begin_layout Plain Layout
4597 , that has the following scheme:
4600 \begin_layout Standard
4605 hdotsfor[distance]{number of columns}
4608 \begin_layout Standard
4609 The number of columns specifies how many columns should be spanned.
4610 Distance is a factor for the distance between the dots.
4613 \begin_layout Standard
4614 In the following matrix the command
4620 was inserted in the first box of the second line, to get an ellipsis with
4621 a dot distance twice as long as with the command
4628 \begin_inset Formula
4630 \left(\begin{array}{cccc}
4639 Note that the matrix fields that should be spanned must be empty, otherwise
4640 you get LaTeX-errors.
4643 \begin_layout Standard
4644 \begin_inset VSpace bigskip
4647 Furthermore you can fill with the command
4654 \begin_inset Index idx
4657 \begin_layout Plain Layout
4665 the rest of a line with dots.
4666 The effect of these commands is the same as with
4673 \begin_inset CommandInset ref
4675 reference "sub:Variable-Space"
4682 \begin_layout Standard
4683 For example the command
4688 \begin_inset space \textvisiblespace{}
4696 \begin_layout Standard
4697 \begin_inset Formula $A\dotfill B$
4703 \begin_layout Standard
4710 there is for a line the command
4717 \begin_inset Index idx
4720 \begin_layout Plain Layout
4731 \begin_layout Standard
4732 \begin_inset Formula $A\hrulefill B$
4738 \begin_layout Standard
4739 To use the commands for text, they have to be inserted in TeX-mode.
4742 \begin_layout Section
4744 \begin_inset CommandInset label
4751 \begin_inset Index idx
4754 \begin_layout Plain Layout
4763 \begin_layout Standard
4764 Matrices can be inserted via the math toolbar button
4767 arg "dialog-show mathmatrix"
4772 Insert\SpecialChar \menuseparator
4773 Math\SpecialChar \menuseparator
4777 In the matrix dialog you can specify the number of columns and rows, the
4778 alignment and the decoration.
4779 The vertical alignment is only of importance for matrices in inline formulas:
4782 \begin_layout Standard
4783 The first matrix is top
4784 \begin_inset Formula $\begin{array}[t]{cccc}
4792 \begin_inset Formula $\begin{array}{cccc}
4799 and the third bottom
4800 \begin_inset Formula $\begin{array}[b]{cccc}
4810 \begin_layout Standard
4811 The horizontal alignment specifies how the column entries should be aligned.
4812 It is set by entering a letter for every column.
4817 denotes left aligned,
4826 To create for example a 4
4831 \begin_inset space ~
4834 matrix where the first column is left aligned, the second and third are
4835 centered and the last one is right aligned, one enters for the horizontal
4841 Normally in a matrix all columns are centered, therefore the default for
4849 \begin_layout Standard
4850 Horizontal alignment:
4853 \begin_layout Standard
4859 \begin_inset Formula $\begin{array}{lll}
4871 \begin_inset Formula $\begin{array}{ccc}
4883 \begin_inset Formula $\begin{array}{rrr}
4893 \begin_layout Standard
4894 To add or delete rows and columns subsequently, the math toolbar buttons
4898 arg "inset-modify tabular append-row"
4904 arg "inset-modify tabular delete-row"
4908 \begin_inset space \thinspace{}
4913 Edit\SpecialChar \menuseparator
4917 New rows can also be created with
4920 arg "newline-insert newline"
4926 \begin_layout Standard
4927 \begin_inset VSpace bigskip
4934 adds parentheses in the selected style around the matrix.
4935 Alternatively, parentheses can can either be created with the commands
4943 \begin_inset Index idx
4946 \begin_layout Plain Layout
4961 \begin_inset Index idx
4964 \begin_layout Plain Layout
4975 \begin_inset space ~
4981 \begin_inset CommandInset ref
4983 reference "sub:Automatic-Bracket-Size"
4987 , or by using the following commands:
4988 \begin_inset VSpace medskip
4994 \begin_layout Standard
4995 \begin_inset space \hfill{}
4999 \begin_inset Tabular
5000 <lyxtabular version="3" rows="4" columns="2">
5001 <features rotate="0" tabularvalignment="middle">
5002 <column alignment="center" valignment="top">
5003 <column alignment="center" valignment="top">
5005 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
5008 \begin_layout Plain Layout
5014 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
5017 \begin_layout Plain Layout
5019 \begin_inset Note Note
5022 \begin_layout Plain Layout
5029 is only used as spacer.
5041 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
5044 \begin_layout Plain Layout
5048 \begin_inset space \textvisiblespace{}
5056 \begin_inset space \thinspace{}
5064 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
5067 \begin_layout Plain Layout
5068 \begin_inset Formula $\raisebox{7.5mm}{}\begin{bmatrix}\begin{array}{cc}
5069 0 & \textrm{-}\mathrm{i}\\
5071 \end{array}\end{bmatrix}\raisebox{-5.3mm}{}$
5081 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
5084 \begin_layout Plain Layout
5088 \begin_inset space \textvisiblespace{}
5096 \begin_inset space \thinspace{}
5104 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
5107 \begin_layout Plain Layout
5108 \begin_inset Formula $\raisebox{7.5mm}{}\begin{Bmatrix}\begin{array}{cc}
5109 0 & \textrm{-}\mathrm{i}\\
5111 \end{array}\end{Bmatrix}\raisebox{-5.3mm}{}$
5121 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
5124 \begin_layout Plain Layout
5128 \begin_inset space \textvisiblespace{}
5136 \begin_inset space \thinspace{}
5144 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
5147 \begin_layout Plain Layout
5148 \begin_inset Formula $\raisebox{7.5mm}{}\begin{pmatrix}\begin{array}{cc}
5149 0 & \textrm{-}\mathrm{i}\\
5151 \end{array}\end{pmatrix}\raisebox{-5.3mm}{}$
5165 \begin_inset space \hfill{}
5169 \begin_inset Tabular
5170 <lyxtabular version="3" rows="4" columns="2">
5171 <features rotate="0" tabularvalignment="middle">
5172 <column alignment="center" valignment="top">
5173 <column alignment="center" valignment="top">
5175 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
5178 \begin_layout Plain Layout
5184 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
5187 \begin_layout Plain Layout
5195 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
5198 \begin_layout Plain Layout
5202 \begin_inset space \textvisiblespace{}
5210 \begin_inset space \thinspace{}
5218 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
5221 \begin_layout Plain Layout
5222 \begin_inset Formula $\raisebox{7.5mm}{}\begin{vmatrix}\begin{array}{cc}
5223 0 & \textrm{-}\mathrm{i}\\
5225 \end{array}\end{vmatrix}\raisebox{-5.3mm}{}$
5235 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
5238 \begin_layout Plain Layout
5242 \begin_inset space \textvisiblespace{}
5250 \begin_inset space \thinspace{}
5258 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
5261 \begin_layout Plain Layout
5262 \begin_inset Formula $\raisebox{7.5mm}{}\begin{Vmatrix}\begin{array}{cc}
5263 0 & \textrm{-}\mathrm{i}\\
5265 \end{array}\end{Vmatrix}\raisebox{-5.3mm}{}$
5275 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
5278 \begin_layout Plain Layout
5282 \begin_inset space \textvisiblespace{}
5290 \begin_inset space \thinspace{}
5298 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
5301 \begin_layout Plain Layout
5302 \begin_inset Formula $\raisebox{7.5mm}{}\begin{matrix}\begin{array}{cc}
5303 0 & \textrm{-}\mathrm{i}\\
5305 \end{array}\end{matrix}\raisebox{-5.3mm}{}$
5319 \begin_inset space \hfill{}
5325 \begin_layout Standard
5326 \begin_inset VSpace medskip
5330 \begin_inset space \thinspace{}
5334 \begin_inset space \space{}
5343 is inserted, a blue box appears between two vertical lines where the matrix
5345 \begin_inset Newline newline
5348 Note that decorated matrices ignore the vertical alignment.
5351 \begin_layout Standard
5352 \begin_inset VSpace bigskip
5355 As all multiline formulas are matrices, the length
5362 \begin_inset Index idx
5365 \begin_layout Plain Layout
5373 that is described in
5374 \begin_inset CommandInset ref
5376 reference "sub:Column-Separation"
5380 can also be used to change the column separation of matrices.
5383 \begin_layout Standard
5384 To change the row separation, the command
5391 \begin_inset Index idx
5394 \begin_layout Plain Layout
5403 It is used as follows:
5406 \begin_layout Standard
5413 arraystretch}{stretch factor}
5414 \begin_inset Index idx
5417 \begin_layout Plain Layout
5428 \begin_layout Standard
5435 assigns the stretch factor to the predefined command
5443 \begin_inset space \thinspace{}
5447 \begin_inset space \space{}
5450 the row separation, use the factor 2.
5451 This is then used for all following matrices.
5452 To go back to the original separation, assign the factor 1 to
5461 \begin_layout Standard
5462 To set matrices into a text line, the command
5469 \begin_inset Index idx
5472 \begin_layout Plain Layout
5481 When it is inserted a blue box with two dashed lines appears.
5482 In this box the matrix is inserted.
5485 \begin_layout Standard
5487 \begin_inset Formula $\left(\begin{smallmatrix}A & B\\
5489 \end{smallmatrix}\right)$
5495 \begin_layout Section
5496 Brackets and Delimiters
5497 \begin_inset Index idx
5500 \begin_layout Plain Layout
5507 \begin_inset Index idx
5510 \begin_layout Plain Layout
5519 \begin_layout Subsection
5520 Vertical Brackets and Delimiters
5521 \begin_inset Index idx
5524 \begin_layout Plain Layout
5533 \begin_layout Standard
5534 \begin_inset space \hfill{}
5538 \begin_inset Tabular
5539 <lyxtabular version="3" rows="9" columns="2">
5540 <features rotate="0" tabularvalignment="middle">
5541 <column alignment="center" valignment="top" width="0pt">
5542 <column alignment="center" valignment="top" width="0pt">
5544 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
5547 \begin_layout Plain Layout
5553 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
5556 \begin_layout Plain Layout
5564 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
5567 \begin_layout Plain Layout
5573 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
5576 \begin_layout Plain Layout
5577 \begin_inset Formula $($
5587 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
5590 \begin_layout Plain Layout
5596 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
5599 \begin_layout Plain Layout
5600 \begin_inset Formula $\{$
5610 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
5613 \begin_layout Plain Layout
5619 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
5622 \begin_layout Plain Layout
5623 \begin_inset Formula $[$
5633 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
5636 \begin_layout Plain Layout
5644 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
5647 \begin_layout Plain Layout
5648 \begin_inset Formula $\langle$
5658 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
5661 \begin_layout Plain Layout
5669 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
5672 \begin_layout Plain Layout
5673 \begin_inset Formula $\lceil$
5683 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
5686 \begin_layout Plain Layout
5694 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
5697 \begin_layout Plain Layout
5698 \begin_inset Formula $\lfloor$
5708 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
5711 \begin_layout Plain Layout
5717 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
5720 \begin_layout Plain Layout
5721 \begin_inset Formula $/$
5731 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
5734 \begin_layout Plain Layout
5740 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
5743 \begin_layout Plain Layout
5744 \begin_inset Formula $|$
5758 \begin_inset space \hfill{}
5762 \begin_inset Tabular
5763 <lyxtabular version="3" rows="9" columns="2">
5764 <features rotate="0" tabularvalignment="middle">
5765 <column alignment="center" valignment="top" width="0pt">
5766 <column alignment="center" valignment="top" width="0pt">
5768 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
5771 \begin_layout Plain Layout
5777 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
5780 \begin_layout Plain Layout
5788 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
5791 \begin_layout Plain Layout
5797 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
5800 \begin_layout Plain Layout
5801 \begin_inset Formula $)$
5811 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
5814 \begin_layout Plain Layout
5820 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
5823 \begin_layout Plain Layout
5824 \begin_inset Formula $\}$
5834 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
5837 \begin_layout Plain Layout
5843 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
5846 \begin_layout Plain Layout
5847 \begin_inset Formula $]$
5857 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
5860 \begin_layout Plain Layout
5868 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
5871 \begin_layout Plain Layout
5872 \begin_inset Formula $\rangle$
5882 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
5885 \begin_layout Plain Layout
5893 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
5896 \begin_layout Plain Layout
5897 \begin_inset Formula $\rceil$
5907 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
5910 \begin_layout Plain Layout
5918 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
5921 \begin_layout Plain Layout
5922 \begin_inset Formula $\rfloor$
5932 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
5935 \begin_layout Plain Layout
5945 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
5948 \begin_layout Plain Layout
5949 \begin_inset Formula $\backslash$
5959 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
5962 \begin_layout Plain Layout
5970 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
5973 \begin_layout Plain Layout
5974 \begin_inset Formula $\|$
5988 \begin_inset space \hfill{}
5994 \begin_layout Standard
5997 \begin_inset Note Greyedout
6000 \begin_layout Plain Layout
6005 In TeX-mode the command
6012 \begin_inset Index idx
6015 \begin_layout Plain Layout
6023 must be used for the backslash, because the command
6031 produces a line break there.
6039 \begin_layout Standard
6040 For all characters listed above the size can be adjusted with the commands
6041 described in the following two subsections.
6042 When using these commands, the characters < and > can directly be used
6043 instead of the commands
6058 \begin_layout Subsubsection
6060 \begin_inset CommandInset label
6062 name "sub:Manual-Bracket-Size"
6067 \begin_inset Index idx
6070 \begin_layout Plain Layout
6071 Bracket size ! manual
6079 \begin_layout Standard
6080 The bracket size can be specified manually by the LaTeX-commands
6087 \begin_inset Index idx
6090 \begin_layout Plain Layout
6123 denotes the smallest and
6129 the largest bracket size.
6132 \begin_layout Standard
6133 These commands are used to emphasize levels of brackets:
6136 \begin_layout Standard
6138 \begin_inset Tabular
6139 <lyxtabular version="3" rows="2" columns="2">
6140 <features rotate="0" tabularvalignment="middle">
6141 <column alignment="center" valignment="top" width="0pt">
6142 <column alignment="center" valignment="top" width="0pt">
6144 <cell alignment="center" valignment="top" usebox="none">
6147 \begin_layout Plain Layout
6148 all brackets in the same size:
6153 <cell alignment="center" valignment="top" usebox="none">
6156 \begin_layout Plain Layout
6157 \begin_inset Formula $((A+B)(A-B))^{C}\raisebox{-4mm}{}$
6167 <cell alignment="center" valignment="top" usebox="none">
6170 \begin_layout Plain Layout
6176 <cell alignment="center" valignment="top" usebox="none">
6179 \begin_layout Plain Layout
6180 \begin_inset Formula $\Big((A+B)(A-B)\Big)^{C}$
6194 \begin_inset Note Note
6197 \begin_layout Plain Layout
6204 is only used as spacer.
6212 \begin_layout Standard
6213 For the second formula the command
6220 \begin_inset space \textvisiblespace{}
6228 \begin_layout Standard
6229 Here is an overview about all bracket sizes:
6232 \begin_layout Standard
6249 \begin_inset space \textvisiblespace{}
6257 \begin_inset space \textvisiblespace{}
6261 \begin_inset space \textvisiblespace{}
6271 \begin_layout Standard
6273 \begin_inset Formula $\Bigg(\exp\bigg<\Big[\big\{\ln(3x)\big\}^{2}\sin(x)\Big]^{A}\bigg>\Bigg)^{0,5}$
6279 \begin_layout Standard
6286 -commands there is the variant
6293 \begin_inset Index idx
6296 \begin_layout Plain Layout
6304 that adds a bit more space between the bracket and its content, and the
6318 \begin_inset Index idx
6321 \begin_layout Plain Layout
6331 , that don't add additional space.
6336 at the end of the command
6342 is for a left bracket; for a right bracket this will be replaced by an
6348 A left or right bracket can each be an opening or closing bracket.
6351 \begin_layout Standard
6352 In the following table is a comparison of the variants:
6355 \begin_layout Standard
6357 \begin_inset Tabular
6358 <lyxtabular version="3" rows="5" columns="2">
6359 <features rotate="0" tabularvalignment="middle">
6360 <column alignment="center" valignment="middle">
6361 <column alignment="center" valignment="middle">
6363 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
6366 \begin_layout Plain Layout
6372 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
6375 \begin_layout Plain Layout
6377 \begin_inset Note Note
6380 \begin_layout Plain Layout
6387 is only used as spacer.
6399 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
6402 \begin_layout Plain Layout
6412 \begin_inset space \textvisiblespace{}
6422 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
6425 \begin_layout Plain Layout
6426 \begin_inset Formula $\raisebox{5.5mm}{}\Bigm(\bigm(\ln(3x)\bigm)^{2}\Bigm)\raisebox{-3.25mm}{}$
6436 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
6439 \begin_layout Plain Layout
6449 \begin_inset space \textvisiblespace{}
6459 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
6462 \begin_layout Plain Layout
6463 \begin_inset Formula $\raisebox{5.5mm}{}\Big(\big(\ln(3x)\big)^{2}\Big)\raisebox{-3.25mm}{}$
6473 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
6476 \begin_layout Plain Layout
6486 \begin_inset space \textvisiblespace{}
6496 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
6499 \begin_layout Plain Layout
6500 \begin_inset Formula $\raisebox{5.5mm}{}\Bigl(\bigl(\ln(3x)\bigr)^{2}\Bigr)\raisebox{-3.25mm}{}$
6510 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
6513 \begin_layout Plain Layout
6525 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
6528 \begin_layout Plain Layout
6529 \begin_inset Formula $\raisebox{4.5mm}{}\bigl)\ln(3x)\bigr(\raisebox{-2mm}{}$
6545 \begin_layout Subsubsection
6546 Automatic Bracket Size
6547 \begin_inset CommandInset label
6549 name "sub:Automatic-Bracket-Size"
6554 \begin_inset Index idx
6557 \begin_layout Plain Layout
6558 Bracket size ! automatic
6566 \begin_layout Standard
6567 Brackets with variable size can be inserted with the commands
6574 \begin_inset Index idx
6577 \begin_layout Plain Layout
6592 \begin_inset Index idx
6595 \begin_layout Plain Layout
6603 or via the math toolbar button
6606 arg "dialog-show mathdelimiter"
6622 the wanted bracket must be inserted.
6623 The bracket size will then automatically be calculated for the output.
6626 \begin_layout Standard
6628 normal bracket: The command
6635 \begin_inset space \textvisiblespace{}
6639 \begin_inset Formula $\downarrow$
6643 \begin_inset space \textvisiblespace{}
6649 \begin_inset Formula
6659 \begin_layout Standard
6661 multiline bracket: The command
6670 \begin_inset space \textvisiblespace{}
6674 \begin_inset Formula $\downarrow$
6678 \begin_inset space \textvisiblespace{}
6686 \begin_inset Formula
6688 \ln\left(\frac{A}{C}\right)
6696 \begin_layout Standard
6712 \begin_inset space ~
6718 This has the advantage that you can see in LyX immediately the real bracket
6719 size and that the matching right bracket will be created too.
6720 \begin_inset Newline newline
6723 The command for the last example would then be:
6734 \begin_inset space \textvisiblespace{}
6738 \begin_inset Formula $\downarrow$
6744 \begin_layout Standard
6745 To omit a left or right bracket, a dot is inserted for the omitted bracket.
6746 For example the command
6753 \begin_inset space \textvisiblespace{}
6757 \begin_inset Formula $\downarrow$
6761 \begin_inset space \textvisiblespace{}
6771 \begin_inset Formula
6773 \left.\frac{A}{B}\right\}
6792 will be converted by LyX to brackets in the right size when the document
6793 is reloaded and an omitted bracket will appear as dashed line.
6796 \begin_layout Standard
6797 \begin_inset VSpace bigskip
6800 Because all popular LaTeX-Distributions use eTeX, an extension to LaTeX,
6808 \begin_inset Index idx
6811 \begin_layout Plain Layout
6819 is additionally available for all brackets and limits.
6820 With this command the height of the following character is adapted to the
6821 one of the surrounding brackets, what is e.
6822 \begin_inset space \thinspace{}
6826 \begin_inset space \space{}
6829 needed for physical vectors:
6830 \begin_inset Formula
6832 \left\langle \phi\:\middle|\: J=\frac{3}{2}\,,\, M_{J}\right\rangle
6837 For physical vectors there is a special LaTeX-package, described in
6838 \begin_inset CommandInset ref
6840 reference "sub:Physical-Vectors"
6847 \begin_layout Subsection
6849 \begin_inset Index idx
6852 \begin_layout Plain Layout
6853 Brackets ! horizontal
6861 \begin_layout Standard
6863 \begin_inset Tabular
6864 <lyxtabular version="3" rows="4" columns="2">
6865 <features rotate="0" tabularvalignment="middle">
6866 <column alignment="center" valignment="top" width="0pt">
6867 <column alignment="center" valignment="top" width="0pt">
6869 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
6872 \begin_layout Plain Layout
6874 \begin_inset Note Note
6877 \begin_layout Plain Layout
6884 is only used as spacer.
6894 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
6897 \begin_layout Plain Layout
6905 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
6908 \begin_layout Plain Layout
6912 \begin_layout Plain Layout
6924 \begin_inset space \textvisiblespace{}
6928 \begin_inset space \textvisiblespace{}
6935 \begin_layout Plain Layout
6943 \begin_inset Index idx
6946 \begin_layout Plain Layout
6959 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
6962 \begin_layout Plain Layout
6963 \begin_inset Formula $\overbrace{A+B}^{3}$
6973 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
6976 \begin_layout Plain Layout
6980 \begin_layout Plain Layout
6992 \begin_inset space \textvisiblespace{}
6996 \begin_inset space \textvisiblespace{}
7003 \begin_layout Plain Layout
7011 \begin_inset Index idx
7014 \begin_layout Plain Layout
7027 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
7030 \begin_layout Plain Layout
7031 \begin_inset Formula $\underbrace{A+B}_{5}$
7041 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
7044 \begin_layout Plain Layout
7048 \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{}
7074 \begin_inset space \textvisiblespace{}
7082 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
7085 \begin_layout Plain Layout
7086 \begin_inset Formula $\overbrace{\underbrace{A+B_{w}}_{7}}^{C}$
7102 \begin_layout Standard
7103 In the last example it doesn't matter if
7115 is inserted at first.
7118 \begin_layout Standard
7119 \begin_inset VSpace bigskip
7122 When brackets are needed that overlap each other, multiline formulas, as
7124 \begin_inset CommandInset ref
7126 reference "sec:Multiline-Formulas"
7131 \begin_inset Formula
7133 A & = & \underbrace{gggg+bbqq}_{r}+\: dddd\\
7134 & & \hphantom{gggg+\:}\underbrace{\hphantom{bbqq+dddd}}_{s}
7139 In the first row the formula is inserted together with the first brace.
7140 It is hereby important that the space command
7144 \begin_layout Plain Layout
7145 Space commands are explained in
7146 \begin_inset CommandInset ref
7148 reference "sub:Predefined-Space"
7163 is inserted before the first
7164 \begin_inset Formula $d$
7167 , because the brace that ends behind the
7168 \begin_inset Formula $q$
7171 prevents that the following
7172 \begin_inset Quotes eld
7176 \begin_inset Quotes erd
7179 is surrounded by space.
7183 \begin_layout Plain Layout
7184 because a bracket is not handled as a character, see
7185 \begin_inset CommandInset ref
7187 reference "sub:Binary-Operators"
7196 In the second row the second brace is inserted.
7197 As it should begin before the
7198 \begin_inset Formula $b$
7213 \begin_layout Plain Layout
7221 \begin_inset CommandInset ref
7223 reference "sub:Placeholders"
7232 This space is needed because the
7233 \begin_inset Quotes eld
7237 \begin_inset Quotes erd
7240 is also surrounded by space in the formula.
7241 The brace is placed under the command
7250 \begin_layout Standard
7251 It gets more complicated when brackets overlap each other, like in the following
7256 \begin_layout Plain Layout
7268 \begin_inset Formula
7270 & & \hphantom{gggg+\:}\overbrace{\hphantom{bbqq+dddd}}^{s}\\
7271 A & = & \underbrace{gggg+bbqq}_{r}+\: dddd
7280 \begin_layout Plain Layout
7291 The first formula row is the same as the second row of the previous example,
7292 with the difference that the brace is above.
7293 The second row contains the formula together with the second brace.
7294 To avoid that there is space between the upper brace in the first row and
7295 the formula, the row spacing needs to be reduced.
7296 This is not easily possible due to a bug in LyX
7300 \begin_layout Plain Layout
7301 \begin_inset CommandInset href
7303 name "LyX-bug #1505"
7304 target "http://www.lyx.org/trac/ticket/1505"
7314 As a solution for the problem, the global formula row separation
7321 \begin_inset Index idx
7324 \begin_layout Plain Layout
7332 must be changed to -6
7333 \begin_inset space \thinspace{}
7336 pt before the formula with the command
7351 is set back after the formula to the standard value of 3
7352 \begin_inset space \thinspace{}
7355 pt using the same command.
7356 More about the row separation in formulas is explained in
7357 \begin_inset CommandInset ref
7359 reference "sub:Line-Separation"
7366 \begin_layout Section
7368 \begin_inset Index idx
7371 \begin_layout Plain Layout
7380 \begin_layout Standard
7381 Arrows can be inserted via the math toolbar button
7384 arg "math-insert \\leftarrow"
7387 or the commands listed in the following subsections.
7390 \begin_layout Subsection
7392 \begin_inset Index idx
7395 \begin_layout Plain Layout
7404 \begin_layout Standard
7405 \begin_inset space \hfill{}
7409 \begin_inset Tabular
7410 <lyxtabular version="3" rows="8" columns="2">
7411 <features rotate="0" tabularvalignment="middle">
7412 <column alignment="center" valignment="top" width="0pt">
7413 <column alignment="center" valignment="top" width="0pt">
7415 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
7418 \begin_layout Plain Layout
7424 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
7427 \begin_layout Plain Layout
7435 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
7438 \begin_layout Plain Layout
7446 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
7449 \begin_layout Plain Layout
7450 \begin_inset Formula $\gets$
7460 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
7463 \begin_layout Plain Layout
7471 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
7474 \begin_layout Plain Layout
7475 \begin_inset Formula $\Leftarrow$
7485 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
7488 \begin_layout Plain Layout
7496 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
7499 \begin_layout Plain Layout
7500 \begin_inset Formula $\longleftarrow$
7510 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
7513 \begin_layout Plain Layout
7521 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
7524 \begin_layout Plain Layout
7525 \begin_inset Formula $\Longleftarrow$
7535 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
7538 \begin_layout Plain Layout
7546 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
7549 \begin_layout Plain Layout
7550 \begin_inset Formula $\leftharpoonup$
7560 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
7563 \begin_layout Plain Layout
7571 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
7574 \begin_layout Plain Layout
7575 \begin_inset Formula $\leftharpoondown$
7585 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
7588 \begin_layout Plain Layout
7596 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
7599 \begin_layout Plain Layout
7600 \begin_inset Formula $\hookleftarrow$
7614 \begin_inset space \hfill{}
7618 \begin_inset Tabular
7619 <lyxtabular version="3" rows="8" columns="2">
7620 <features rotate="0" tabularvalignment="middle">
7621 <column alignment="center" valignment="top" width="0pt">
7622 <column alignment="center" valignment="top" width="0pt">
7624 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
7627 \begin_layout Plain Layout
7633 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
7636 \begin_layout Plain Layout
7644 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
7647 \begin_layout Plain Layout
7655 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
7658 \begin_layout Plain Layout
7659 \begin_inset Formula $\to$
7669 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
7672 \begin_layout Plain Layout
7680 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
7683 \begin_layout Plain Layout
7684 \begin_inset Formula $\Rightarrow$
7694 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
7697 \begin_layout Plain Layout
7705 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
7708 \begin_layout Plain Layout
7709 \begin_inset Formula $\longrightarrow$
7719 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
7722 \begin_layout Plain Layout
7730 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
7733 \begin_layout Plain Layout
7734 \begin_inset Formula $\Longrightarrow$
7744 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
7747 \begin_layout Plain Layout
7755 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
7758 \begin_layout Plain Layout
7759 \begin_inset Formula $\rightharpoonup$
7769 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
7772 \begin_layout Plain Layout
7780 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
7783 \begin_layout Plain Layout
7784 \begin_inset Formula $\rightharpoondown$
7794 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
7797 \begin_layout Plain Layout
7805 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
7808 \begin_layout Plain Layout
7809 \begin_inset Formula $\hookrightarrow$
7823 \begin_inset space \hfill{}
7829 \begin_layout Standard
7830 \begin_inset space \hfill{}
7834 \begin_inset Tabular
7835 <lyxtabular version="3" rows="6" columns="2">
7836 <features rotate="0" tabularvalignment="middle">
7837 <column alignment="center" valignment="top" width="0pt">
7838 <column alignment="center" valignment="top" width="0pt">
7840 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
7843 \begin_layout Plain Layout
7849 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
7852 \begin_layout Plain Layout
7860 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
7863 \begin_layout Plain Layout
7871 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
7874 \begin_layout Plain Layout
7875 \begin_inset Formula $\leftrightarrow$
7885 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
7888 \begin_layout Plain Layout
7896 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
7899 \begin_layout Plain Layout
7900 \begin_inset Formula $\Leftrightarrow$
7910 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
7913 \begin_layout Plain Layout
7921 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
7924 \begin_layout Plain Layout
7925 \begin_inset Formula $\longleftrightarrow$
7935 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
7938 \begin_layout Plain Layout
7946 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
7949 \begin_layout Plain Layout
7950 \begin_inset Formula $\Longleftrightarrow$
7960 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
7963 \begin_layout Plain Layout
7971 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
7974 \begin_layout Plain Layout
7975 \begin_inset Formula $\rightleftharpoons$
7989 \begin_inset space \hspace{}
7994 \begin_inset space \hfill{}
7998 \begin_inset Tabular
7999 <lyxtabular version="3" rows="5" columns="2">
8000 <features rotate="0" tabularvalignment="middle">
8001 <column alignment="center" valignment="top" width="0pt">
8002 <column alignment="center" valignment="top" width="0pt">
8004 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
8007 \begin_layout Plain Layout
8013 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
8016 \begin_layout Plain Layout
8024 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
8027 \begin_layout Plain Layout
8035 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
8038 \begin_layout Plain Layout
8039 \begin_inset Formula $\mapsto$
8049 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
8052 \begin_layout Plain Layout
8060 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
8063 \begin_layout Plain Layout
8064 \begin_inset Formula $\longmapsto$
8074 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
8077 \begin_layout Plain Layout
8085 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
8088 \begin_layout Plain Layout
8089 \begin_inset Formula $\leadsto$
8099 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
8102 \begin_layout Plain Layout
8110 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
8113 \begin_layout Plain Layout
8114 \begin_inset Formula $\dasharrow$
8128 \begin_inset space \hfill{}
8134 \begin_layout Standard
8135 \begin_inset VSpace medskip
8138 Arrows used as accents like e.
8139 \begin_inset space \thinspace{}
8143 \begin_inset space \space{}
8146 vector arrows are listed in
8147 \begin_inset CommandInset ref
8149 reference "sec:Accents"
8156 \begin_layout Standard
8157 \begin_inset VSpace bigskip
8160 Furthermore there are the labeled arrows
8161 \begin_inset Index idx
8164 \begin_layout Plain Layout
8177 \begin_inset Index idx
8180 \begin_layout Plain Layout
8195 \begin_inset Index idx
8198 \begin_layout Plain Layout
8205 \begin_layout Plain Layout
8220 When inserting one of these commands in a formula, an arrow with two blue
8221 boxes appear where the label can be inserted.
8222 The length of the arrow adapts to the label width.
8225 \begin_layout Standard
8227 \begin_inset Tabular
8228 <lyxtabular version="3" rows="3" columns="2">
8229 <features rotate="0" tabularvalignment="middle">
8230 <column alignment="center" valignment="top" width="0pt">
8231 <column alignment="center" valignment="top" width="0pt">
8233 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
8236 \begin_layout Plain Layout
8242 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
8245 \begin_layout Plain Layout
8247 \begin_inset Note Note
8250 \begin_layout Plain Layout
8257 is only used as spacer.
8269 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
8272 \begin_layout Plain Layout
8276 \begin_inset space \textvisiblespace{}
8280 \begin_inset Formula $\downarrow$
8284 \begin_inset Formula $\to$
8292 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
8295 \begin_layout Plain Layout
8296 \begin_inset Formula $\raisebox{5mm}{}F(a)\xleftarrow[x>0]{x=a}F(x)\raisebox{-4mm}{}$
8306 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
8309 \begin_layout Plain Layout
8313 \begin_inset space \textvisiblespace{}
8317 \begin_inset Formula $\downarrow$
8321 \begin_inset Formula $\to$
8329 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
8332 \begin_layout Plain Layout
8333 \begin_inset Formula $\raisebox{5mm}{}F(x)\xrightarrow[x>0]{x=a}F(a)\raisebox{-4mm}{}$
8349 \begin_layout Subsection
8350 Vertical and diagonal Arrows
8351 \begin_inset Index idx
8354 \begin_layout Plain Layout
8361 \begin_inset Index idx
8364 \begin_layout Plain Layout
8373 \begin_layout Standard
8374 \begin_inset space \hfill{}
8378 \begin_inset Tabular
8379 <lyxtabular version="3" rows="7" columns="2">
8380 <features rotate="0" tabularvalignment="middle">
8381 <column alignment="center" valignment="top" width="0pt">
8382 <column alignment="center" valignment="top" width="0pt">
8384 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
8387 \begin_layout Plain Layout
8393 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
8396 \begin_layout Plain Layout
8404 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
8407 \begin_layout Plain Layout
8415 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
8418 \begin_layout Plain Layout
8419 \begin_inset Formula $\uparrow$
8429 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
8432 \begin_layout Plain Layout
8440 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
8443 \begin_layout Plain Layout
8444 \begin_inset Formula $\Uparrow$
8454 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
8457 \begin_layout Plain Layout
8465 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
8468 \begin_layout Plain Layout
8469 \begin_inset Formula $\updownarrow$
8479 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
8482 \begin_layout Plain Layout
8490 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
8493 \begin_layout Plain Layout
8494 \begin_inset Formula $\Updownarrow$
8504 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
8507 \begin_layout Plain Layout
8515 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
8518 \begin_layout Plain Layout
8519 \begin_inset Formula $\Downarrow$
8529 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
8532 \begin_layout Plain Layout
8540 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
8543 \begin_layout Plain Layout
8544 \begin_inset Formula $\downarrow$
8558 \begin_inset space \hfill{}
8562 \begin_inset Tabular
8563 <lyxtabular version="3" rows="5" columns="2">
8564 <features rotate="0" tabularvalignment="middle">
8565 <column alignment="center" valignment="top" width="0pt">
8566 <column alignment="center" valignment="top" width="0pt">
8568 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
8571 \begin_layout Plain Layout
8577 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
8580 \begin_layout Plain Layout
8588 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
8591 \begin_layout Plain Layout
8599 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
8602 \begin_layout Plain Layout
8603 \begin_inset Formula $\nearrow$
8613 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
8616 \begin_layout Plain Layout
8624 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
8627 \begin_layout Plain Layout
8628 \begin_inset Formula $\searrow$
8638 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
8641 \begin_layout Plain Layout
8649 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
8652 \begin_layout Plain Layout
8653 \begin_inset Formula $\swarrow$
8663 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
8666 \begin_layout Plain Layout
8674 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
8677 \begin_layout Plain Layout
8678 \begin_inset Formula $\nwarrow$
8692 \begin_inset space \hfill{}
8698 \begin_layout Standard
8699 \begin_inset VSpace medskip
8702 Vertical arrows can be used also as delimiters together with the commands
8704 \begin_inset CommandInset ref
8706 reference "sub:Manual-Bracket-Size"
8711 \begin_inset CommandInset ref
8713 reference "sub:Automatic-Bracket-Size"
8720 \begin_layout Section
8722 \begin_inset CommandInset label
8729 \begin_inset Index idx
8732 \begin_layout Plain Layout
8741 \begin_layout Standard
8742 Accents can be inserted via the math toolbar button
8745 arg "math-insert \\hat"
8748 or the commands listed in the following subsections.
8751 \begin_layout Subsection
8752 Accents for one Character
8756 \begin_layout Plain Layout
8769 \begin_layout Plain Layout
8771 \begin_inset CommandInset ref
8773 reference "sub:Accents-in-Text"
8786 \begin_layout Plain Layout
8794 \begin_inset Note Note
8797 \begin_layout Plain Layout
8804 is used to avoid that the footnote appears in the PDF-bookmark.
8807 \begin_layout Plain Layout
8815 \begin_inset CommandInset ref
8817 reference "sub:Formulas-in-Section"
8827 \begin_inset CommandInset label
8829 name "sub:Accents-for-one"
8834 \begin_inset Index idx
8837 \begin_layout Plain Layout
8838 Accents ! for one character
8846 \begin_layout Standard
8847 \begin_inset space \hfill{}
8851 \begin_inset Tabular
8852 <lyxtabular version="3" rows="8" columns="2">
8853 <features rotate="0" tabularvalignment="middle">
8854 <column alignment="center" valignment="top" width="0pt">
8855 <column alignment="center" valignment="top" width="0pt">
8857 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
8860 \begin_layout Plain Layout
8866 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
8869 \begin_layout Plain Layout
8871 \begin_inset Note Note
8874 \begin_layout Plain Layout
8881 is only used as spacer.
8893 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
8896 \begin_layout Plain Layout
8900 \begin_inset space \textvisiblespace{}
8908 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
8911 \begin_layout Plain Layout
8912 \begin_inset Formula $\raisebox{5mm}{}\dot{A}$
8922 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
8925 \begin_layout Plain Layout
8929 \begin_inset space \textvisiblespace{}
8937 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
8940 \begin_layout Plain Layout
8941 \begin_inset Formula $\raisebox{5mm}{}\ddot{A}$
8951 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
8954 \begin_layout Plain Layout
8958 \begin_inset space \textvisiblespace{}
8966 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
8969 \begin_layout Plain Layout
8970 \begin_inset Formula $\raisebox{5mm}{}\dddot{A}$
8980 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
8983 \begin_layout Plain Layout
8987 \begin_inset space \textvisiblespace{}
8995 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
8998 \begin_layout Plain Layout
8999 \begin_inset Formula $\raisebox{5mm}{}\ddddot{A}$
9009 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
9012 \begin_layout Plain Layout
9016 \begin_inset space \textvisiblespace{}
9020 \begin_inset Index idx
9023 \begin_layout Plain Layout
9034 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
9037 \begin_layout Plain Layout
9038 \begin_inset Formula $\raisebox{5mm}{}\vec{A}$
9048 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
9051 \begin_layout Plain Layout
9055 \begin_inset space \textvisiblespace{}
9063 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
9066 \begin_layout Plain Layout
9067 \begin_inset Formula $\raisebox{5mm}{}\bar{A}$
9077 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
9080 \begin_layout Plain Layout
9084 \begin_inset space \textvisiblespace{}
9092 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
9095 \begin_layout Plain Layout
9096 \begin_inset Formula $\raisebox{5mm}{}\mathring{A}$
9110 \begin_inset space \hfill{}
9114 \begin_inset Tabular
9115 <lyxtabular version="3" rows="7" columns="2">
9116 <features rotate="0" tabularvalignment="middle">
9117 <column alignment="center" valignment="top" width="0pt">
9118 <column alignment="center" valignment="top" width="0pt">
9120 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
9123 \begin_layout Plain Layout
9129 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
9132 \begin_layout Plain Layout
9140 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
9143 \begin_layout Plain Layout
9147 \begin_inset space \textvisiblespace{}
9155 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
9158 \begin_layout Plain Layout
9159 \begin_inset Formula $\raisebox{5mm}{}\tilde{A}$
9169 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
9172 \begin_layout Plain Layout
9176 \begin_inset space \textvisiblespace{}
9184 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
9187 \begin_layout Plain Layout
9188 \begin_inset Formula $\raisebox{5mm}{}\hat{A}$
9198 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
9201 \begin_layout Plain Layout
9205 \begin_inset space \textvisiblespace{}
9213 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
9216 \begin_layout Plain Layout
9217 \begin_inset Formula $\raisebox{5mm}{}\check{A}$
9227 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
9230 \begin_layout Plain Layout
9234 \begin_inset space \textvisiblespace{}
9242 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
9245 \begin_layout Plain Layout
9246 \begin_inset Formula $\raisebox{5mm}{}\acute{A}$
9256 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
9259 \begin_layout Plain Layout
9263 \begin_inset space \textvisiblespace{}
9271 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
9274 \begin_layout Plain Layout
9275 \begin_inset Formula $\raisebox{5mm}{}\grave{A}$
9285 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
9288 \begin_layout Plain Layout
9292 \begin_inset space \textvisiblespace{}
9300 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
9303 \begin_layout Plain Layout
9304 \begin_inset Formula $\raisebox{5mm}{}\breve{A}$
9318 \begin_inset space \hfill{}
9324 \begin_layout Standard
9325 \begin_inset VSpace bigskip
9331 \begin_layout Standard
9332 You can directly insert accents like é to formulas.
9333 LyX will transform them to the corresponding accent command.
9335 \begin_inset Index idx
9338 \begin_layout Plain Layout
9344 it is better to insert a quotation mark before the vowel.
9345 These two characters are then treated by LaTeX as
9349 character when the formula part with the umlaut is marked as German.
9357 \begin_inset Quotes eld
9361 \begin_inset Quotes erd
9364 umlauts are created as demonstrated in the following example:
9367 \begin_layout Standard
9368 \begin_inset VSpace -2mm
9374 \begin_layout Standard
9376 \begin_inset Tabular
9377 <lyxtabular version="3" rows="3" columns="2">
9378 <features rotate="0" tabularvalignment="middle">
9379 <column alignment="center" valignment="top">
9380 <column alignment="center" valignment="top">
9382 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
9385 \begin_layout Plain Layout
9391 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
9394 \begin_layout Plain Layout
9396 \begin_inset Note Note
9399 \begin_layout Plain Layout
9407 \begin_inset space \thinspace{}
9410 pt space are only used as spacer.
9422 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
9425 \begin_layout Plain Layout
9428 \begin_inset Quotes grd
9436 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
9439 \begin_layout Plain Layout
9440 \begin_inset space \hspace{}
9447 \begin_inset Formula $"i$
9457 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
9460 \begin_layout Plain Layout
9464 \begin_inset space \textvisiblespace{}
9472 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
9475 \begin_layout Plain Layout
9476 \begin_inset Formula $\raisebox{5mm}{}\ddot{i}$
9492 \begin_layout Standard
9493 Another advantage to
9499 is that umlauts can directly be converted to mathematical text because
9500 the accent commands above are
9506 in mathematical text
9509 To convert an accented character to mathematical text, only the character
9510 under the accent may be converted.
9511 This applies also for all other conversions, e.
9512 \begin_inset space \thinspace{}
9516 \begin_inset space \space{}
9522 \begin_layout Standard
9523 In mathematical text, umlauts and other accented characters can directly
9527 \begin_layout Standard
9528 \begin_inset VSpace bigskip
9534 \begin_layout Standard
9535 LyX also supports a tilde under the character if the LaTeX-package
9540 \begin_inset Index idx
9543 \begin_layout Plain Layout
9544 Packages ! undertilde
9549 is installed on your system:
9552 \begin_layout Standard
9556 \begin_layout Plain Layout
9566 \begin_inset Note Note
9569 \begin_layout Plain Layout
9570 The following table will only be displayed when the LaTeX-package
9582 \begin_layout Standard
9585 \begin_inset Tabular
9586 <lyxtabular version="3" rows="2" columns="2">
9587 <features rotate="0" tabularvalignment="middle">
9588 <column alignment="center" valignment="top" width="0pt">
9589 <column alignment="center" valignment="top" width="0pt">
9591 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
9594 \begin_layout Plain Layout
9600 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
9603 \begin_layout Plain Layout
9611 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
9614 \begin_layout Plain Layout
9618 \begin_inset space \textvisiblespace{}
9626 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
9629 \begin_layout Plain Layout
9630 \begin_inset Formula $\raisebox{5mm}{}\utilde{A}$
9646 \begin_layout Standard
9650 \begin_layout Plain Layout
9660 \begin_inset Note Note
9663 \begin_layout Plain Layout
9664 The following will be displayed when the LaTeX-package
9676 \begin_layout Standard
9677 You need to install the LaTeX-package
9681 to see the rest of this subsection in the output.
9684 \begin_layout Standard
9688 \begin_layout Plain Layout
9700 \begin_layout Subsection
9701 Accents for several Characters
9702 \begin_inset Index idx
9705 \begin_layout Plain Layout
9706 Accents ! for several characters
9714 \begin_layout Standard
9715 \begin_inset space \hfill{}
9719 \begin_inset Tabular
9720 <lyxtabular version="3" rows="5" columns="2">
9721 <features rotate="0" tabularvalignment="middle">
9722 <column alignment="center" valignment="top" width="0pt">
9723 <column alignment="center" valignment="top" width="0pt">
9725 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
9728 \begin_layout Plain Layout
9734 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
9737 \begin_layout Plain Layout
9739 \begin_inset Note Note
9742 \begin_layout Plain Layout
9749 is only used as spacer.
9761 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
9764 \begin_layout Plain Layout
9768 \begin_inset space \textvisiblespace{}
9776 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
9779 \begin_layout Plain Layout
9780 \begin_inset Formula $\raisebox{6mm}{}\overleftarrow{A=B}\raisebox{-2mm}{}$
9790 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
9793 \begin_layout Plain Layout
9797 \begin_inset space \textvisiblespace{}
9805 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
9808 \begin_layout Plain Layout
9809 \begin_inset Formula $\raisebox{5mm}{}\underleftarrow{A=B}\raisebox{-3mm}{}$
9819 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
9822 \begin_layout Plain Layout
9826 \begin_inset space \textvisiblespace{}
9834 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
9837 \begin_layout Plain Layout
9838 \begin_inset Formula $\raisebox{6mm}{}\overleftrightarrow{A=B}\raisebox{-2mm}{}$
9848 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
9851 \begin_layout Plain Layout
9855 \begin_inset space \textvisiblespace{}
9863 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
9866 \begin_layout Plain Layout
9867 \begin_inset Formula $\raisebox{5mm}{}\underleftrightarrow{A=B}\raisebox{-3mm}{}$
9881 \begin_inset space \hfill{}
9885 \begin_inset Tabular
9886 <lyxtabular version="3" rows="5" columns="2">
9887 <features rotate="0" tabularvalignment="middle">
9888 <column alignment="center" valignment="top" width="0pt">
9889 <column alignment="center" valignment="top" width="0pt">
9891 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
9894 \begin_layout Plain Layout
9900 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
9903 \begin_layout Plain Layout
9911 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
9914 \begin_layout Plain Layout
9918 \begin_inset space \textvisiblespace{}
9926 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
9929 \begin_layout Plain Layout
9930 \begin_inset Formula $\raisebox{6mm}{}\overrightarrow{A=B}\raisebox{-2mm}{}$
9940 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
9943 \begin_layout Plain Layout
9947 \begin_inset space \textvisiblespace{}
9955 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
9958 \begin_layout Plain Layout
9959 \begin_inset Formula $\raisebox{5mm}{}\underrightarrow{A=B}\raisebox{-3mm}{}$
9969 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
9972 \begin_layout Plain Layout
9976 \begin_inset space \textvisiblespace{}
9984 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
9987 \begin_layout Plain Layout
9988 \begin_inset Formula $\raisebox{6mm}{}\widetilde{A=B}\raisebox{-2mm}{}$
9998 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
10001 \begin_layout Plain Layout
10005 \begin_inset space \textvisiblespace{}
10013 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
10016 \begin_layout Plain Layout
10017 \begin_inset Formula $\raisebox{6mm}{}\widehat{A=B}\raisebox{-2mm}{}$
10031 \begin_inset space \hfill{}
10037 \begin_layout Standard
10038 \begin_inset VSpace medskip
10041 With these commands as many characters as you like can be accented.
10054 will only be set in the output with a length of three characters, as shown
10055 in the following example:
10056 \begin_inset Formula
10058 \widetilde{A+B=C-D}
10066 \begin_layout Standard
10074 \begin_inset Index idx
10077 \begin_layout Plain Layout
10092 \begin_inset Index idx
10095 \begin_layout Plain Layout
10103 described in the previous subsection it is also possible to accent several
10110 \begin_inset space \textvisiblespace{}
10114 \begin_inset Formula $\downarrow$
10120 \begin_inset Formula
10122 \underset{***}{A=B}
10130 \begin_layout Standard
10131 \begin_inset Newpage newpage
10137 \begin_layout Section
10139 \begin_inset CommandInset label
10146 \begin_inset Index idx
10149 \begin_layout Plain Layout
10158 \begin_layout Subsection
10160 \begin_inset CommandInset label
10162 name "sub:Predefined-Space"
10167 \begin_inset Index idx
10170 \begin_layout Plain Layout
10171 Space ! horizontal ! predefined
10179 \begin_layout Standard
10180 Sometimes it is necessary to insert horizontal space into a formula.
10181 This is done by inserting a protected space (shortcut
10184 arg "command-alternatives space-insert protected ; math-space"
10189 \begin_inset Quotes eld
10195 \begin_inset space \textvisiblespace{}
10201 \begin_inset Quotes erd
10204 appears and by pressing
10208 several times one can select one of eight different space sizes.
10209 The spaces can also be inserted using the math toolbar button
10212 arg "math-insert \\space"
10215 or special commands.
10216 Independent from the inserted command, one can select the size again by
10224 \begin_layout Standard
10227 \begin_inset Tabular
10228 <lyxtabular version="3" rows="6" columns="3">
10229 <features rotate="0" tabularvalignment="middle">
10230 <column alignment="center" valignment="top">
10231 <column alignment="center" valignment="top" width="15col%">
10232 <column alignment="center" valignment="top">
10234 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
10237 \begin_layout Plain Layout
10243 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
10246 \begin_layout Plain Layout
10256 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
10259 \begin_layout Plain Layout
10267 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
10270 \begin_layout Plain Layout
10278 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
10281 \begin_layout Plain Layout
10287 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
10290 \begin_layout Plain Layout
10291 \begin_inset Formula $A\, B$
10301 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
10304 \begin_layout Plain Layout
10312 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
10315 \begin_layout Plain Layout
10321 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
10324 \begin_layout Plain Layout
10325 \begin_inset Formula $A\: B$
10335 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
10338 \begin_layout Plain Layout
10346 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
10349 \begin_layout Plain Layout
10355 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
10358 \begin_layout Plain Layout
10359 \begin_inset Formula $A\; B$
10369 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
10372 \begin_layout Plain Layout
10380 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
10383 \begin_layout Plain Layout
10389 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
10392 \begin_layout Plain Layout
10393 \begin_inset Formula $A\quad B$
10403 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
10406 \begin_layout Plain Layout
10414 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
10417 \begin_layout Plain Layout
10423 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
10426 \begin_layout Plain Layout
10427 \begin_inset Formula $A\qquad B$
10441 \begin_inset space \hfill{}
10445 \begin_inset Tabular
10446 <lyxtabular version="3" rows="6" columns="3">
10447 <features rotate="0" tabularvalignment="middle">
10448 <column alignment="center" valignment="top">
10449 <column alignment="center" valignment="top" width="15col%">
10450 <column alignment="center" valignment="top">
10452 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
10455 \begin_layout Plain Layout
10461 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
10464 \begin_layout Plain Layout
10474 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
10477 \begin_layout Plain Layout
10485 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
10488 \begin_layout Plain Layout
10496 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
10499 \begin_layout Plain Layout
10505 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
10508 \begin_layout Plain Layout
10509 \begin_inset Formula $A\hfill B$
10519 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
10522 \begin_layout Plain Layout
10530 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
10533 \begin_layout Plain Layout
10539 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
10542 \begin_layout Plain Layout
10543 \begin_inset Formula $A\hspace*{1em}B$
10553 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
10556 \begin_layout Plain Layout
10564 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
10567 \begin_layout Plain Layout
10573 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
10576 \begin_layout Plain Layout
10577 \begin_inset Formula $A\hspace{1em}B$
10587 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
10590 \begin_layout Plain Layout
10594 \begin_inset space \textvisiblespace{}
10602 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
10605 \begin_layout Plain Layout
10611 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
10614 \begin_layout Plain Layout
10615 \begin_inset Formula $A\ B$
10625 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
10628 \begin_layout Plain Layout
10636 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
10639 \begin_layout Plain Layout
10645 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
10648 \begin_layout Plain Layout
10649 \begin_inset Formula $A\! B$
10665 \begin_layout Standard
10667 \begin_inset space ~
10671 \begin_inset space \thinspace{}
10675 \begin_inset space \thinspace{}
10678 7 are variable spaces which are explained in
10679 \begin_inset CommandInset ref
10681 reference "sub:Variable-Space"
10687 \begin_inset space ~
10690 9 seems to produce no space.
10691 It is displayed red in LyX contrary to the other sizes, because it is a
10693 There are two more negative spaces:
10696 \begin_layout Standard
10698 \begin_inset Tabular
10699 <lyxtabular version="3" rows="3" columns="3">
10700 <features rotate="0" tabularvalignment="middle">
10701 <column alignment="center" valignment="middle" width="6.8cm">
10702 <column alignment="center" valignment="top" width="0pt">
10703 <column alignment="center" valignment="top" width="0pt">
10705 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
10708 \begin_layout Plain Layout
10714 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
10717 \begin_layout Plain Layout
10725 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
10728 \begin_layout Plain Layout
10738 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
10741 \begin_layout Plain Layout
10746 keystrokes after inserting the protected space
10751 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
10754 \begin_layout Plain Layout
10760 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
10763 \begin_layout Plain Layout
10771 <cell multicolumn="1" alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
10774 \begin_layout Plain Layout
10780 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
10783 \begin_layout Plain Layout
10784 \begin_inset Formula $A\negmedspace B$
10792 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
10795 \begin_layout Plain Layout
10796 \begin_inset Formula $A\negthickspace B$
10812 \begin_layout Standard
10813 Negative spaces can lead to characters overlapping each other.
10814 Thus they can be used to enforce ligatures, which are e.
10815 \begin_inset space \thinspace{}
10819 \begin_inset space \space{}
10822 useful for summation operators:
10825 \begin_layout Standard
10827 \begin_inset Tabular
10828 <lyxtabular version="3" rows="3" columns="2">
10829 <features rotate="0" tabularvalignment="middle">
10830 <column alignment="center" valignment="top">
10831 <column alignment="center" valignment="top">
10833 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
10836 \begin_layout Plain Layout
10842 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
10845 \begin_layout Plain Layout
10847 \begin_inset Note Note
10850 \begin_layout Plain Layout
10857 is only used as spacer.
10869 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
10872 \begin_layout Plain Layout
10878 \begin_inset space \textvisiblespace{}
10886 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
10889 \begin_layout Plain Layout
10890 \begin_inset Formula $\raisebox{4.5mm}{}\sum\sum f_{kl}\raisebox{-2.5mm}{}$
10900 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
10903 \begin_layout Plain Layout
10911 \begin_inset space \textvisiblespace{}
10919 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
10922 \begin_layout Plain Layout
10923 \begin_inset Formula $\raisebox{4.5mm}{}\sum\negmedspace\sum f_{kl}\raisebox{-2.5mm}{}$
10939 \begin_layout Standard
10941 \begin_inset VSpace medskip
10947 \begin_layout Standard
10949 Relations like for example equal signs, are always surrounded by space.
10950 To suppress this, the equal sign is placed into a TeX-brace.
10951 The following example demonstrates this:
10954 \begin_layout Standard
10956 \begin_inset Tabular
10957 <lyxtabular version="3" rows="2" columns="2">
10958 <features rotate="0" tabularvalignment="middle">
10959 <column alignment="center" valignment="top" width="0pt">
10960 <column alignment="center" valignment="top" width="0pt">
10962 <cell alignment="center" valignment="top" usebox="none">
10965 \begin_layout Plain Layout
10971 <cell alignment="center" valignment="top" usebox="none">
10974 \begin_layout Plain Layout
10975 \begin_inset Formula $A=B$
10985 <cell alignment="center" valignment="top" usebox="none">
10988 \begin_layout Plain Layout
10989 \begin_inset Note Note
10992 \begin_layout Plain Layout
10999 is only used as spacer.
11005 \begin_inset Formula $\raisebox{5mm}{}$
11008 equation without space
11013 <cell multicolumn="1" alignment="center" valignment="top" usebox="none">
11016 \begin_layout Plain Layout
11017 \begin_inset Formula $A{=}B$
11033 \begin_layout Standard
11035 The command for the last formula is:
11040 \begin_inset Formula $\to$
11046 \begin_layout Standard
11047 \begin_inset VSpace bigskip
11053 \begin_layout Standard
11054 Spaces are needed for physical units, because the space between the value
11055 and the unit is the smallest one and not a normal space.
11056 For units in text, the smallest space is inserted via the menu
11058 Insert\SpecialChar \menuseparator
11059 Formatting\SpecialChar \menuseparator
11061 \begin_inset space ~
11069 arg "space-insert thin"
11075 \begin_layout Standard
11076 An example to visualize the difference:
11079 \begin_layout Standard
11080 \begin_inset Tabular
11081 <lyxtabular version="3" rows="2" columns="2">
11082 <features rotate="0" tabularvalignment="middle">
11083 <column alignment="left" valignment="top">
11084 <column alignment="left" valignment="top">
11086 <cell alignment="center" valignment="top" usebox="none">
11089 \begin_layout Plain Layout
11091 \begin_inset Formula $\cdot$
11099 <cell alignment="center" valignment="top" usebox="none">
11102 \begin_layout Plain Layout
11103 space between value and unit
11110 <cell alignment="center" valignment="top" usebox="none">
11113 \begin_layout Plain Layout
11115 \begin_inset space \thinspace{}
11119 \begin_inset Formula $\cdot$
11127 <cell alignment="center" valignment="top" usebox="none">
11130 \begin_layout Plain Layout
11131 smallest space between value and unit
11144 \begin_layout Subsection
11149 \begin_layout Plain Layout
11162 \begin_layout Plain Layout
11163 for vertical space in formulas see
11164 \begin_inset CommandInset ref
11166 reference "sub:Line-Separation"
11179 \begin_layout Plain Layout
11187 \begin_inset Note Note
11190 \begin_layout Plain Layout
11193 texorpdfstring is used to avoid that the footnote appears in the PDF-bookmark.
11196 \begin_layout Plain Layout
11199 texorpdfstring is in section
11200 \begin_inset CommandInset ref
11202 reference "sub:Formulas-in-Section"
11212 \begin_inset CommandInset label
11214 name "sub:Variable-Space"
11219 \begin_inset Index idx
11222 \begin_layout Plain Layout
11223 Space ! horizontal ! variable
11231 \begin_layout Standard
11232 Space with a defined length can be inserted with the command
11239 \begin_inset Index idx
11242 \begin_layout Plain Layout
11252 \begin_inset Quotes eld
11258 \begin_inset space \textvisiblespace{}
11264 \begin_inset Quotes erd
11268 The length can be specified by left-clicking on the
11269 \begin_inset Quotes eld
11275 \begin_inset space \textvisiblespace{}
11281 \begin_inset Quotes erd
11285 The length may also be negative.
11286 When a space would be the first character in a line it would be omitted.
11287 To force its output use the command
11299 or left-click on the
11300 \begin_inset Quotes eld
11306 \begin_inset space \textvisiblespace{}
11312 \begin_inset Quotes erd
11315 and check the option
11320 \begin_inset Newline newline
11323 To insert as much space as is available, the command
11330 \begin_inset Index idx
11333 \begin_layout Plain Layout
11344 \begin_layout Standard
11345 \begin_inset VSpace -1mm
11351 \begin_layout Standard
11353 \begin_inset Tabular
11354 <lyxtabular version="3" rows="4" columns="2">
11355 <features rotate="0" tabularvalignment="middle">
11356 <column alignment="center" valignment="top">
11357 <column alignment="center" valignment="top">
11359 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
11362 \begin_layout Plain Layout
11370 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
11373 \begin_layout Plain Layout
11381 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
11384 \begin_layout Plain Layout
11388 \begin_inset space \textvisiblespace{}
11394 \begin_inset space \thinspace{}
11402 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
11405 \begin_layout Plain Layout
11406 \begin_inset Formula $A=B\hspace{3cm}A\not=C$
11416 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
11419 \begin_layout Plain Layout
11423 \begin_inset space \textvisiblespace{}
11429 \begin_inset space \thinspace{}
11437 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
11440 \begin_layout Plain Layout
11441 \begin_inset Formula $A\hspace{-1mm}A\not=A$
11451 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
11454 \begin_layout Plain Layout
11458 \begin_inset space \textvisiblespace{}
11466 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
11469 \begin_layout Plain Layout
11470 \begin_inset Formula $A=A\hfill B=B$
11486 \begin_layout Standard
11487 In the last example the available space is given by the longest column entry
11489 In an inline formula the space depends on the length of the line in which
11497 Thus, when the line uses the full width, no space will be created.
11504 only has an effect on displayed formulas when the formula style
11509 (Formula styles are explained in
11510 \begin_inset CommandInset ref
11512 reference "sec:Formula-Styles"
11519 \begin_layout Standard
11526 , there are the commands
11538 that fill the space with a pattern, see
11539 \begin_inset CommandInset ref
11541 reference "sub:Ellipses"
11548 \begin_layout Standard
11549 For text, variable space can be inserted via the menu
11551 Insert\SpecialChar \menuseparator
11552 Formatting\SpecialChar \menuseparator
11554 \begin_inset space ~
11562 \begin_layout Standard
11563 This is a line with
11564 \begin_inset space \hspace{}
11569 \begin_inset space \thinspace{}
11575 \begin_layout Standard
11576 This is a line with
11577 \begin_inset space \hfill{}
11583 \begin_layout Subsection
11584 Space besides inline Formulas
11585 \begin_inset Index idx
11588 \begin_layout Plain Layout
11589 Space ! besides inline formulas
11597 \begin_layout Standard
11598 The space that surrounds inline formulas can be adjusted with the length
11606 \begin_inset Index idx
11609 \begin_layout Plain Layout
11618 The value of a length is set with the command
11625 \begin_inset Index idx
11628 \begin_layout Plain Layout
11636 which has the following scheme:
11639 \begin_layout Standard
11644 setlength{length name}{value}
11647 \begin_layout Standard
11655 \begin_inset space \thinspace{}
11661 \begin_layout Standard
11671 \begin_layout Standard
11672 is inserted in TeX-mode.
11674 \begin_inset space \thinspace{}
11677 mm space will now be set around all inline formulas:
11681 \begin_layout Plain Layout
11695 \begin_layout Standard
11696 This is a line with an inline formula
11697 \begin_inset Formula $A=B$
11701 \begin_inset space \thinspace{}
11704 mm surrounding space.
11708 \begin_layout Plain Layout
11722 \begin_layout Standard
11723 To return to the predefined value,
11729 is set to the value 0
11730 \begin_inset space \thinspace{}
11736 \begin_layout Section
11738 \begin_inset Index idx
11741 \begin_layout Plain Layout
11748 \begin_inset Index idx
11751 \begin_layout Plain Layout
11756 \begin_layout Plain Layout
11767 \begin_layout Plain Layout
11782 \begin_layout Standard
11783 Boxes for text are described in chapter
11790 \begin_inset space ~
11798 \begin_layout Subsection
11800 \begin_inset CommandInset label
11802 name "sub:Boxes-with-Frame"
11807 \begin_inset Index idx
11810 \begin_layout Plain Layout
11819 \begin_layout Standard
11820 It is possible to frame a formula or part of one with the commands
11827 \begin_inset Index idx
11830 \begin_layout Plain Layout
11845 \begin_inset Index idx
11848 \begin_layout Plain Layout
11859 \begin_layout Standard
11860 When one of these commands is inserted in a formula, a blue box appears
11861 within a frame to enter formula parts.
11868 an additional formula has to be created by
11872 within this box, because the box content will otherwise be treated as mathemati
11880 is used, a new formula is automatically created inside the frame.
11883 \begin_layout Standard
11890 is not suitable to frame displayed formulas because the formula will always
11891 be set in the size of the text.
11898 is in contrary not suitable to frame inline formulas, because the formula
11899 will always be set in the size of a displayed formula.
11902 \begin_layout Standard
11916 \begin_inset Index idx
11919 \begin_layout Plain Layout
11927 where additionally the frame width and the alignment can be specified.
11934 is used in the following scheme:
11937 \begin_layout Standard
11942 framebox[frame width][position]{box content}
11945 \begin_layout Standard
11946 The position can either be
11963 right aligns the formula in the box.
11964 When no position is given, the formula will be centered.
11965 \begin_inset Newline newline
11968 If no width is given, also no position can be given.
11969 In this case the frame width is adjusted to the box content like for
11978 \begin_layout Standard
11985 is inserted, a box appears containing three blue boxes.
11986 The first two boxes are surrounded by brackets and denote the two optional
11988 The third box is for formula parts like for
11997 \begin_layout Standard
11998 \begin_inset Newpage newpage
12004 \begin_layout Standard
12006 \begin_inset Tabular
12007 <lyxtabular version="3" rows="5" columns="2">
12008 <features rotate="0" tabularvalignment="middle">
12009 <column alignment="center" valignment="top">
12010 <column alignment="center" valignment="top">
12012 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
12015 \begin_layout Plain Layout
12021 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
12024 \begin_layout Plain Layout
12026 \begin_inset Note Note
12029 \begin_layout Plain Layout
12036 is only used as spacer.
12048 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
12051 \begin_layout Plain Layout
12055 \begin_inset space \textvisiblespace{}
12065 \begin_inset space \textvisiblespace{}
12073 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
12076 \begin_layout Plain Layout
12077 \begin_inset Formula $\raisebox{6mm}{}\fbox{\ensuremath{\int A=B}}\raisebox{-4mm}{}$
12087 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
12090 \begin_layout Plain Layout
12094 \begin_inset space \textvisiblespace{}
12100 \begin_inset space \textvisiblespace{}
12108 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
12111 \begin_layout Plain Layout
12112 \begin_inset Formula $\raisebox{8.5mm}{}\boxed{\int A=B}\raisebox{-6.5mm}{}$
12122 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
12125 \begin_layout Plain Layout
12129 \begin_inset space \textvisiblespace{}
12137 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
12140 \begin_layout Plain Layout
12141 \begin_inset Formula $\raisebox{6mm}{}A+\fbox{B}\raisebox{-3mm}{}$
12151 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
12154 \begin_layout Plain Layout
12158 \begin_inset space \textvisiblespace{}
12162 \begin_inset Formula $\to$
12166 \begin_inset Formula $\to$
12176 \begin_inset space \textvisiblespace{}
12180 \begin_inset Formula $\downarrow$
12188 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
12191 \begin_layout Plain Layout
12192 \begin_inset Formula $\raisebox{6mm}{}$
12196 \begin_inset Formula $\framebox[20mm][]{\ensuremath{\frac{A}{B}}}$
12200 \begin_inset Formula $\raisebox{-4mm}{}$
12216 \begin_layout Standard
12217 The frame thickness can also be adjusted.
12218 To do this the following commands have to be inserted in TeX-mode before
12222 \begin_layout Standard
12232 \begin_inset Quotes eld
12236 \begin_inset Quotes erd
12250 \begin_inset Quotes eld
12254 \begin_inset Quotes erd
12260 \begin_layout Standard
12261 \begin_inset Quotes eld
12265 \begin_inset Quotes erd
12268 specifies the minimal distance between the frame and the first character
12270 An example for this is the following framed formula:
12274 \begin_layout Plain Layout
12286 \begin_inset Formula
12293 Before this formula the commands
12296 \begin_layout Standard
12318 \begin_layout Standard
12319 were inserted in TeX-mode.
12320 The given values are used for all following boxes.
12323 \begin_layout Standard
12324 To return to the standard frame size, the command
12327 \begin_layout Standard
12352 \begin_layout Plain Layout
12366 \begin_layout Standard
12367 is inserted in TeX-mode before the next formula.
12370 \begin_layout Subsection
12371 Boxes without Frame
12372 \begin_inset CommandInset label
12374 name "sub:Boxes-without-Frame"
12379 \begin_inset Index idx
12382 \begin_layout Plain Layout
12383 Boxes ! without frame
12391 \begin_layout Standard
12392 For boxes without a frame there are the following box commands:
12399 \begin_inset Index idx
12402 \begin_layout Plain Layout
12417 \begin_inset Index idx
12420 \begin_layout Plain Layout
12435 \begin_inset Index idx
12438 \begin_layout Plain Layout
12449 \begin_layout Standard
12456 a box can be super- or subscripted.
12457 But in contrary to normal super- and subscripting, the characters in the
12458 box keep their font size.
12465 is used in the following scheme:
12468 \begin_layout Standard
12473 raisebox{height}{box content}
12476 \begin_layout Standard
12477 When the box should contain a formula, an extra formula is needed like for
12488 \begin_inset Note Greyedout
12491 \begin_layout Plain Layout
12502 this extra formula is created by pressing
12506 twice instead of once because LyX doesn't yet support
12520 \begin_layout Standard
12522 \begin_inset Tabular
12523 <lyxtabular version="3" rows="4" columns="2">
12524 <features rotate="0" tabularvalignment="middle">
12525 <column alignment="center" valignment="top">
12526 <column alignment="center" valignment="top">
12528 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
12531 \begin_layout Plain Layout
12537 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
12540 \begin_layout Plain Layout
12548 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
12551 \begin_layout Plain Layout
12555 \begin_inset Formula $\to$
12561 \begin_inset Formula $\to$
12569 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
12572 \begin_layout Plain Layout
12573 \begin_inset Formula $H\raisebox{2mm}{al}lo$
12583 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
12586 \begin_layout Plain Layout
12590 \begin_inset Formula $\to$
12596 \begin_inset Formula $\to$
12604 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
12607 \begin_layout Plain Layout
12608 \begin_inset Formula $H\raisebox{-2mm}{al}lo$
12618 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
12621 \begin_layout Plain Layout
12625 \begin_inset Formula $\to$
12641 \begin_inset space \textvisiblespace{}
12649 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
12652 \begin_layout Plain Layout
12653 \begin_inset Formula $A=\raisebox{-2mm}{\mbox{\ensuremath{\sqrt{B}}}}$
12669 \begin_layout Standard
12694 , with the difference that there is no frame.
12697 \begin_layout Subsection
12699 \begin_inset CommandInset label
12701 name "sub:Colored-Boxes"
12706 \begin_inset Index idx
12709 \begin_layout Plain Layout
12718 \begin_layout Standard
12719 To be able to use all commands explained in this section, the LaTeX-package
12728 \begin_layout Plain Layout
12733 is part of every LaTeX standard installation.
12739 \begin_inset Index idx
12742 \begin_layout Plain Layout
12748 has to be loaded in the LaTeX-preamble with the line
12752 \begin_layout Plain Layout
12753 When text is colored somewhere in the document with a predefined color,
12754 LyX loads the LaTeX-package
12759 Thus it is possible that the package is loaded twice, but this does not
12766 \begin_inset Note Note
12769 \begin_layout Plain Layout
12770 To avoid that the package is loaded twice, a macro was inserted to the LaTeX-pre
12779 \begin_layout Standard
12787 \begin_layout Standard
12788 \begin_inset VSpace medskip
12791 To color boxes, the command
12798 \begin_inset Index idx
12801 \begin_layout Plain Layout
12809 is used in the following scheme:
12812 \begin_layout Standard
12817 colorbox{color}{box content}
12820 \begin_layout Standard
12821 The box content can also be a box and a
12827 can also be part of another box (see the 2nd and 3rd example).
12828 When the box should contain a formula, an extra formula has to be created,
12829 the same way as for
12839 \begin_layout Plain Layout
12840 This also applies for the command
12854 \begin_layout Standard
12855 One of the following predefined colors can be chosen:
12858 \begin_layout Standard
12892 \begin_layout Standard
12894 \begin_inset Tabular
12895 <lyxtabular version="3" rows="4" columns="2">
12896 <features rotate="0" tabularvalignment="middle">
12897 <column alignment="center" valignment="top">
12898 <column alignment="center" valignment="top">
12900 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
12903 \begin_layout Plain Layout
12909 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
12912 \begin_layout Plain Layout
12914 \begin_inset Note Note
12917 \begin_layout Plain Layout
12924 is only used as spacer.
12936 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
12939 \begin_layout Plain Layout
12943 \begin_inset Formula $\to$
12953 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
12956 \begin_layout Plain Layout
12957 \begin_inset Formula $\raisebox{6mm}{}\colorbox{yellow}{A=B}\raisebox{-3mm}{}$
12967 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
12970 \begin_layout Plain Layout
12974 \begin_inset Formula $\to$
12982 \begin_inset space \textvisiblespace{}
12990 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
12993 \begin_layout Plain Layout
12994 \begin_inset Formula $\raisebox{6mm}{}\colorbox{green}{\fbox{A=B}}\raisebox{-3mm}{}$
13004 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
13007 \begin_layout Plain Layout
13011 \begin_inset space \textvisiblespace{}
13017 \begin_inset Formula $\to$
13033 \begin_inset space \textvisiblespace{}
13041 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
13044 \begin_layout Plain Layout
13045 \begin_inset Formula $\raisebox{7mm}{}\fbox{\colorbox{green}{\mbox{\ensuremath{\int C=D}}}}\raisebox{-5mm}{}$
13061 \begin_layout Standard
13068 only colors the box but not the characters in the box.
13069 To color all characters, the whole formula is highlighted and the desired
13070 color is chosen in the
13073 \begin_inset space ~
13079 The dialog can be called with the toolbar button
13082 arg "dialog-show character"
13087 Edit\SpecialChar \menuseparator
13089 \begin_inset space ~
13092 Style\SpecialChar \menuseparator
13096 The formula number then has the same color as the formula.
13097 When the formula number should get another color than the formula characters,
13098 the color must be changed within the formula.
13101 \begin_layout Standard
13105 \begin_layout Standard
13108 \begin_inset Formula
13110 \int A=B\label{eq:red}
13118 \begin_inset Formula
13120 \textcolor{red}{\int A=B}\label{eq:redgreen}
13128 \begin_layout Standard
13130 \begin_inset CommandInset ref
13136 is completely colored red.
13137 \begin_inset Newline newline
13141 \begin_inset CommandInset ref
13143 reference "eq:redgreen"
13147 was first completely colored green to set the color for the formula number.
13148 Subsequently the formula characters were colored red.
13151 \begin_layout Standard
13152 \begin_inset VSpace bigskip
13155 To color the frame different than the rest of the box, the command
13162 \begin_inset Index idx
13165 \begin_layout Plain Layout
13173 is used in the following scheme:
13176 \begin_layout Standard
13181 fcolorbox{frame color}{color}{box content}
13184 \begin_layout Standard
13191 is an extension of the command
13198 The frame width is set, like for
13221 \begin_layout Plain Layout
13233 \begin_inset Formula
13235 \fcolorbox{cyan}{magenta}{A=B}
13244 \begin_layout Plain Layout
13258 \begin_layout Standard
13259 This formula was created with the command
13260 \begin_inset Newline newline
13268 \begin_inset Formula $\to$
13274 \begin_inset Formula $\to$
13284 \begin_layout Standard
13285 \begin_inset VSpace bigskip
13288 To use other colors than the predefined ones, they have to be defined first.
13291 \begin_layout Standard
13292 One can for example define the color
13293 \begin_inset Quotes eld
13301 \begin_inset Quotes erd
13304 with the LaTeX-preamble line:
13307 \begin_layout Standard
13312 definecolor{darkgreen}{cmyk}{0.5,
13327 \begin_inset Index idx
13330 \begin_layout Plain Layout
13341 \begin_layout Standard
13346 is the color space that denotes the colors
13363 The four comma separated numbers are the portion factor for the corresponding
13364 colors of the color space.
13365 The factors can be in the range of 0
13366 \begin_inset space \thinspace{}
13370 \begin_inset space \thinspace{}
13378 also the color space
13382 can be used for definitions.
13399 , so that there are in this case three portion factors for the corresponding
13401 Furthermore there is the color space
13405 with one portion factor for the gray value.
13408 \begin_layout Standard
13409 As example a framed box with the new defined color
13413 where the characters have been colored
13418 \begin_inset Formula
13420 \colorbox{darkgreen}{\color{yellow}\boxed{\int A\,\mathrm{d}x=\frac{\sqrt[5]{B}}{\ln\left(\frac{1}{3}\right)}}}
13428 \begin_layout Standard
13429 Self-defined colors can also be used for text with the help of the command
13437 \begin_inset Index idx
13440 \begin_layout Plain Layout
13449 \begin_layout Standard
13453 \begin_layout Plain Layout
13457 textcolor{darkgreen}{
13463 \begin_inset Quotes eld
13467 \begin_inset Quotes erd
13474 \begin_layout Plain Layout
13484 \begin_layout Standard
13492 \begin_inset Index idx
13495 \begin_layout Plain Layout
13503 is used in the scheme
13507 textcolor{color}{characters to color}
13512 \begin_layout Subsection
13514 \begin_inset CommandInset label
13516 name "sub:Paragraph-Boxes"
13521 \begin_inset Index idx
13524 \begin_layout Plain Layout
13525 Boxes ! as paragraph
13533 \begin_layout Standard
13534 A box that can contain several lines and paragraphs, a so-called paragraph
13535 box (parbox), can be created with the menu
13537 Insert\SpecialChar \menuseparator
13540 or the toolbar button
13549 \begin_layout Standard
13550 The following example shows a framed parbox in a line:
13553 \begin_layout Standard
13554 \begin_inset VSpace medskip
13558 \begin_inset Box Boxed
13568 height_special "totalheight"
13571 \begin_layout Plain Layout
13572 This is a paragraph box.
13574 \begin_inset space \thinspace{}
13577 cm long and can also contain formulas:
13578 \begin_inset Formula $\int A\,\mathrm{d}s=C$
13589 \begin_layout Standard
13590 \begin_inset VSpace medskip
13596 \begin_layout Standard
13597 Such a box is created by right-clicking on the gray box inset.
13598 A dialog pops up showing the box properties.
13612 \begin_inset space \thinspace{}
13617 Vertical Box Alignment
13622 \begin_layout Standard
13623 \begin_inset VSpace medskip
13626 In LaTeX a parbox is created with the command
13633 \begin_inset Index idx
13636 \begin_layout Plain Layout
13644 which has the following scheme:
13647 \begin_layout Standard
13652 parbox[position]{width}{box content}
13655 \begin_layout Standard
13670 \begin_inset Quotes eld
13674 \begin_inset Quotes erd
13677 means that the box is aligned within the surrounding text with its last
13684 \begin_inset Quotes eld
13688 \begin_inset Quotes erd
13691 this is done with the first line.
13692 When no position is given, the box will be vertically centered, see section
13700 \begin_inset space ~
13705 manual for examples.
13708 \begin_layout Standard
13709 \begin_inset VSpace bigskip
13712 To frame formulas completely, including the formula number, the formula
13713 must be set into a parbox.
13714 To do this, the command
13728 is inserted in TeX-mode before the formula.
13736 \begin_inset Index idx
13739 \begin_layout Plain Layout
13747 is hereby the line width set for the document.
13748 Because the frame is outside the parbox, 2
13749 \begin_inset space \thinspace{}
13752 times the frame separation and the frame thickness must be subtracted from
13754 As this is not automatically done by LyX due to a bug
13758 \begin_layout Plain Layout
13759 \begin_inset CommandInset href
13761 name "LyX-bug #4483"
13762 target "http://www.lyx.org/trac/ticket/4483"
13771 , TeX-mode has to be used.
13772 To be able to multiply and subtract in arguments, the LaTeX-package
13780 \begin_layout Plain Layout
13785 is part of every LaTeX standard installation.
13791 \begin_inset Index idx
13794 \begin_layout Plain Layout
13800 must be loaded in the LaTeX-preamble with the line
13803 \begin_layout Standard
13811 \begin_layout Standard
13812 Behind the formula both boxes are closed by entering
13817 Here is an example:
13821 \begin_layout Plain Layout
13835 \begin_layout Standard
13839 \begin_layout Plain Layout
13857 \begin_inset Formula
13859 \int A\,\mathrm{d}x=\frac{\sqrt[5]{B}}{\ln\left(\frac{1}{3}\right)}
13868 \begin_layout Plain Layout
13879 \begin_layout Plain Layout
13893 \begin_layout Standard
13894 \begin_inset VSpace medskip
13897 As a parbox is used as the argument of
13903 , there is in this case no difference between
13918 \begin_layout Standard
13919 \begin_inset VSpace bigskip
13922 Paragraph boxes are very useful to comment formulas directly.
13929 is used in combination with the command
13943 \begin_inset CommandInset ref
13945 reference "sub:User-defined-Numbering"
13952 \begin_layout Standard
13953 An example of a formula commented with
13962 \begin_layout Standard
13966 \begin_layout Plain Layout
13979 This is a description.
13980 It is distinctly separated from the formula and multiline.
13984 \begin_layout Plain Layout
13996 \begin_layout Standard
13997 Such a formula must be inserted completely in TeX-mode because LyX does
13998 not yet support the command
14005 The formula is created with the following command sequence:
14008 \begin_layout Standard
14021 is inserted in TeX-mode.
14025 \begin_layout Plain Layout
14026 When the formula style
14038 can also be replaced by
14045 (formula styles see
14046 \begin_inset CommandInset ref
14048 reference "sec:Formula-Styles"
14057 Then the description follows as normal text and finally
14063 is inserted in TeX-mode.
14076 hereby create a displayed formula.
14079 \begin_layout Standard
14086 can be seen in this example that was
14087 \begin_inset Quotes eld
14091 \begin_inset Quotes erd
14094 using the mathematical textmode:
14095 \begin_inset Formula
14097 5x-7b=3b\textrm{This is a description. It is not separated from the formula ...}
14105 \begin_layout Section
14107 \begin_inset Index idx
14110 \begin_layout Plain Layout
14119 \begin_layout Subsection
14121 \begin_inset CommandInset label
14123 name "sub:Big-Operators"
14128 \begin_inset Index idx
14131 \begin_layout Plain Layout
14138 \begin_inset Index idx
14141 \begin_layout Plain Layout
14148 \begin_inset Index idx
14151 \begin_layout Plain Layout
14160 \begin_layout Standard
14161 To be able to use all integral operators listed here, the option
14163 Use esint package automatically
14165 must be set in the document settings under
14168 \begin_inset space ~
14176 \begin_layout Standard
14177 \begin_inset space \hfill{}
14181 \begin_inset Tabular
14182 <lyxtabular version="3" rows="11" columns="2">
14183 <features rotate="0" tabularvalignment="middle">
14184 <column alignment="center" valignment="top" width="0pt">
14185 <column alignment="center" valignment="top" width="0pt">
14187 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
14190 \begin_layout Plain Layout
14196 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
14199 \begin_layout Plain Layout
14207 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
14210 \begin_layout Plain Layout
14214 \begin_inset Index idx
14217 \begin_layout Plain Layout
14230 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
14233 \begin_layout Plain Layout
14234 \begin_inset Formula $\int$
14244 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
14247 \begin_layout Plain Layout
14255 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
14258 \begin_layout Plain Layout
14259 \begin_inset Formula $\oint$
14269 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
14272 \begin_layout Plain Layout
14280 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
14283 \begin_layout Plain Layout
14284 \begin_inset Formula $\ointctrclockwise$
14294 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
14297 \begin_layout Plain Layout
14305 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
14308 \begin_layout Plain Layout
14309 \begin_inset Formula $\ointclockwise$
14319 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
14322 \begin_layout Plain Layout
14330 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
14333 \begin_layout Plain Layout
14334 \begin_inset Formula $\sqint$
14344 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
14347 \begin_layout Plain Layout
14355 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
14358 \begin_layout Plain Layout
14360 \begin_inset Formula $\fint$
14370 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
14373 \begin_layout Plain Layout
14381 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
14384 \begin_layout Plain Layout
14386 \begin_inset Formula $\landupint$
14396 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
14399 \begin_layout Plain Layout
14407 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
14410 \begin_layout Plain Layout
14412 \begin_inset Formula $\landdownint$
14422 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
14425 \begin_layout Plain Layout
14433 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
14436 \begin_layout Plain Layout
14437 \begin_inset Formula $\bigcap$
14447 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
14450 \begin_layout Plain Layout
14458 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
14461 \begin_layout Plain Layout
14462 \begin_inset Formula $\bigcup$
14476 \begin_inset space \hfill{}
14480 \begin_inset Tabular
14481 <lyxtabular version="3" rows="11" columns="2">
14482 <features rotate="0" tabularvalignment="middle">
14483 <column alignment="center" valignment="top" width="0pt">
14484 <column alignment="center" valignment="top" width="0pt">
14486 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
14489 \begin_layout Plain Layout
14495 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
14498 \begin_layout Plain Layout
14506 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
14509 \begin_layout Plain Layout
14513 \begin_inset Index idx
14516 \begin_layout Plain Layout
14529 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
14532 \begin_layout Plain Layout
14533 \begin_inset Formula $\sum$
14543 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
14546 \begin_layout Plain Layout
14550 \begin_inset Index idx
14553 \begin_layout Plain Layout
14560 \begin_layout Plain Layout
14579 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
14582 \begin_layout Plain Layout
14583 \begin_inset Formula $\prod$
14593 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
14596 \begin_layout Plain Layout
14604 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
14607 \begin_layout Plain Layout
14608 \begin_inset Formula $\coprod$
14618 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
14621 \begin_layout Plain Layout
14629 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
14632 \begin_layout Plain Layout
14633 \begin_inset Formula $\bigodot$
14643 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
14646 \begin_layout Plain Layout
14654 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
14657 \begin_layout Plain Layout
14658 \begin_inset Formula $\bigotimes$
14668 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
14671 \begin_layout Plain Layout
14679 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
14682 \begin_layout Plain Layout
14683 \begin_inset Formula $\bigoplus$
14693 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
14696 \begin_layout Plain Layout
14704 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
14707 \begin_layout Plain Layout
14708 \begin_inset Formula $\bigwedge$
14718 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
14721 \begin_layout Plain Layout
14729 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
14732 \begin_layout Plain Layout
14733 \begin_inset Formula $\bigvee$
14743 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
14746 \begin_layout Plain Layout
14754 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
14757 \begin_layout Plain Layout
14758 \begin_inset Formula $\bigsqcup$
14768 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
14771 \begin_layout Plain Layout
14779 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
14782 \begin_layout Plain Layout
14783 \begin_inset Formula $\biguplus$
14797 \begin_inset space \hfill{}
14803 \begin_layout Standard
14804 All big operators can also be inserted via the math toolbar button
14807 arg "math-insert \\intop"
14813 \begin_layout Standard
14814 The operators are called big because they are bigger than the sometimes
14815 equal looking binary operators.
14816 All big operators can have limits as described in the next subsection.
14819 \begin_layout Standard
14820 For all integral operators there is a second version available, ending in
14838 These operators are different from
14845 \begin_inset space \space{}
14848 in the style the operator limits are displayed, see
14849 \begin_inset CommandInset ref
14851 reference "sub:Operator-Limits"
14859 \begin_layout Subsubsection*
14860 Advice for Integrals
14863 \begin_layout Standard
14868 in an integral is an operator, that therefore has to be set upright.
14869 This is done by highlighting the
14873 and using the keyboard shortcut
14883 \begin_layout Plain Layout
14889 \begin_inset CommandInset ref
14891 reference "sub:Font-Styles"
14901 Finally the smallest space is inserted before the
14905 , as this is usual for operators.
14909 \begin_layout Standard
14911 \begin_inset Formula $\int A(x)dx$
14915 \begin_inset Newline newline
14919 \begin_inset Phantom HPhantom
14922 \begin_layout Plain Layout
14929 \begin_inset Formula $\int A(x)\,\mathrm{d}x$
14935 \begin_layout Standard
14936 For multiple integrals there are the following commands:
14937 \begin_inset VSpace medskip
14943 \begin_layout Standard
14944 \begin_inset space \hfill{}
14948 \begin_inset Tabular
14949 <lyxtabular version="3" rows="4" columns="2">
14950 <features rotate="0" tabularvalignment="middle">
14951 <column alignment="center" valignment="top">
14952 <column alignment="center" valignment="top">
14954 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
14957 \begin_layout Plain Layout
14963 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
14966 \begin_layout Plain Layout
14968 \begin_inset Note Note
14971 \begin_layout Plain Layout
14978 is only used as spacer.
14990 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
14993 \begin_layout Plain Layout
15001 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
15004 \begin_layout Plain Layout
15005 \begin_inset Formula $\raisebox{4.5mm}{}\iint\raisebox{-2.5mm}{}$
15015 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
15018 \begin_layout Plain Layout
15026 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
15029 \begin_layout Plain Layout
15030 \begin_inset Formula $\raisebox{4.5mm}{}\oiint\raisebox{-2.5mm}{}$
15040 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
15043 \begin_layout Plain Layout
15051 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
15054 \begin_layout Plain Layout
15055 \begin_inset Formula $\raisebox{4.5mm}{}\sqiint\raisebox{-2.5mm}{}$
15069 \begin_inset space \hfill{}
15073 \begin_inset Tabular
15074 <lyxtabular version="3" rows="4" columns="2">
15075 <features rotate="0" tabularvalignment="middle">
15076 <column alignment="center" valignment="top">
15077 <column alignment="center" valignment="top">
15079 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
15082 \begin_layout Plain Layout
15088 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
15091 \begin_layout Plain Layout
15099 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
15102 \begin_layout Plain Layout
15110 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
15113 \begin_layout Plain Layout
15114 \begin_inset Formula $\raisebox{4.5mm}{}\iiint\raisebox{-2.5mm}{}$
15124 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
15127 \begin_layout Plain Layout
15135 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
15138 \begin_layout Plain Layout
15139 \begin_inset Formula $\raisebox{4.5mm}{}\iiiint\raisebox{-2.5mm}{}$
15149 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
15152 \begin_layout Plain Layout
15160 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
15163 \begin_layout Plain Layout
15164 \begin_inset Formula $\raisebox{4.5mm}{}\dotsint\raisebox{-2.5mm}{}$
15178 \begin_inset space \hfill{}
15184 \begin_layout Standard
15185 \begin_inset Newpage newpage
15191 \begin_layout Subsection
15193 \begin_inset CommandInset label
15195 name "sub:Operator-Limits"
15200 \begin_inset Index idx
15203 \begin_layout Plain Layout
15212 \begin_layout Standard
15213 Limits are created by super- and subscripts:
15216 \begin_layout Standard
15218 \begin_inset Tabular
15219 <lyxtabular version="3" rows="2" columns="2">
15220 <features rotate="0" tabularvalignment="middle">
15221 <column alignment="center" valignment="top" width="0pt">
15222 <column alignment="center" valignment="top" width="0pt">
15224 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
15227 \begin_layout Plain Layout
15233 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
15236 \begin_layout Plain Layout
15238 \begin_inset Note Note
15241 \begin_layout Plain Layout
15248 is only used as spacer.
15260 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
15263 \begin_layout Plain Layout
15269 \begin_inset space \textvisiblespace{}
15273 \begin_inset Formula $\to$
15277 \begin_inset Formula $\to$
15285 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
15288 \begin_layout Plain Layout
15289 \begin_inset Formula $\raisebox{5mm}{}\prod_{0}^{\infty}A(x)\raisebox{-2.5mm}{}$
15305 \begin_layout Standard
15306 Limits of inline formulas are set right beside the operator.
15307 Limits in displayed formulas are set above or below the operator, except
15308 for integral limits.
15311 \begin_layout Standard
15312 To force that the limits are set beside the operator, the cursor is set
15313 directly behind the operator and the limits type is changed with the menu
15316 Edit\SpecialChar \menuseparator
15317 Math\SpecialChar \menuseparator
15336 \begin_layout Standard
15337 The default limits type is this:
15338 \begin_inset Formula
15340 \sum_{x=0}^{\infty}\frac{1}{x^{2}}
15345 This is how it looks when the limits type was changed to
15352 \begin_inset Formula
15354 \sum\nolimits _{x=0}^{\infty}\frac{1}{x^{2}}
15359 For integrals, except those ending with
15375 etc., the limits are by default set beside the operator.
15376 But for multiple integrals the limits are often set below the operator.
15377 In the following example the limits type was therefore set to
15381 and so set below the integrals:
15382 \begin_inset Formula
15384 \iiint\limits _{V}X\,\mathrm{d}V=U\label{eq:VolInt}
15392 \begin_layout Standard
15393 \begin_inset VSpace medskip
15396 To specify conditions for limits, the commands
15403 \begin_inset Index idx
15406 \begin_layout Plain Layout
15421 \begin_inset Index idx
15424 \begin_layout Plain Layout
15433 To create for example this expression
15434 \begin_inset Formula
15436 \sum_{\begin{subarray}{c}
15440 \end{subarray}}^{n}k^{-2}\label{eq:substack}
15448 \begin_layout Standard
15449 the following has to be done:
15450 \begin_inset Newline newline
15462 \begin_inset space \textvisiblespace{}
15468 One is now in a blue box under the summation operator and insert there
15474 \begin_inset space \textvisiblespace{}
15480 The blue box is now within a purple box and now several lines can be written
15482 A new line is created by inserting a line break (
15485 arg "newline-insert newline"
15490 \begin_inset Newline newline
15495 0<k<1000 Ctrl+Return
15496 \begin_inset Newline newline
15501 is typed in, a new box appears below for the new line.
15504 \begin_layout Standard
15505 The alignment of the lines can be changed to left aligned with the
15515 Edit\SpecialChar \menuseparator
15519 To get right alignment,
15524 \begin_inset space \textvisiblespace{}
15529 is inserted at the beginning of the line.
15532 \begin_layout Standard
15545 with the difference that the lines are always centered.
15548 \begin_layout Standard
15549 \begin_inset VSpace bigskip
15553 \begin_inset CommandInset ref
15555 reference "eq:substack"
15559 there can be too much space beside an operator, because the characters
15560 following the operator are set beside the limits.
15561 To avoid this the command
15568 \begin_inset Index idx
15571 \begin_layout Plain Layout
15580 It sets the width of its content to 0
15581 \begin_inset space \thinspace{}
15585 \begin_inset Newline newline
15589 \begin_inset CommandInset ref
15591 reference "eq:substack"
15595 , one uses the command
15598 \begin_layout Standard
15608 \begin_inset space \textvisiblespace{}
15611 0<k<1000 Ctrl+Return
15614 \begin_layout Standard
15615 to create the lower limit.
15616 The summand is now directly behind the summation operator:
15617 \begin_inset Formula
15619 \sum_{\mathclap{\substack{0<k<1000\\
15631 \begin_layout Standard
15632 \begin_inset VSpace bigskip
15638 \begin_layout Standard
15639 When several consecutive operators have limits the typesetting of the limits
15640 looks often imperfect in the output, see this example:
15641 \begin_inset Formula
15643 \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}
15648 To improve the typesetting set in the document settings under
15651 \begin_inset space ~
15661 \begin_inset Index idx
15664 \begin_layout Plain Layout
15665 Packages ! mathtools
15673 \begin_inset space ~
15679 Then insert into your formula the command
15686 \begin_inset Index idx
15689 \begin_layout Plain Layout
15697 directly before the first operator.
15698 The example will then look like this:
15699 \begin_inset Formula
15701 \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}
15709 \begin_layout Standard
15710 \begin_inset VSpace bigskip
15713 How to use one limit for several operators is described in
15714 \begin_inset CommandInset ref
15716 reference "sub:Self-defined-Operators"
15723 \begin_layout Subsection
15724 Decoration for Operators
15725 \begin_inset Index idx
15728 \begin_layout Plain Layout
15729 Operators ! Decoration
15737 \begin_layout Standard
15745 \begin_inset Index idx
15748 \begin_layout Plain Layout
15763 \begin_inset Index idx
15766 \begin_layout Plain Layout
15774 characters can be placed above or below an operator, respectively.
15782 \begin_inset Index idx
15785 \begin_layout Plain Layout
15793 characters can be set before and behind a big operator.
15796 \begin_layout Standard
15798 \begin_inset space ~
15810 \begin_layout Itemize
15817 is used to set characters at the corners of the operator
15820 \begin_layout Itemize
15827 is used to set characters before and/or behind the operator (this variant
15828 represents LaTeX's original
15837 \begin_layout Itemize
15844 is used to set characters at the left corners and/or behind the operator
15847 \begin_layout Itemize
15854 is used to set characters at the right corners and/or before the operator
15857 \begin_layout Standard
15858 For example the command
15863 \begin_inset space \textvisiblespace{}
15869 \begin_inset space \textvisiblespace{}
15873 \begin_inset Formula $\to$
15877 \begin_inset Formula $\to$
15881 \begin_inset space \textvisiblespace{}
15891 \begin_inset Formula
15893 \sideset{}{'}\sum_{k=1}^{n}
15901 \begin_layout Standard
15902 \begin_inset Note Greyedout
15905 \begin_layout Plain Layout
15912 can only be used to decorate big operators, binary operators are not allowed.
15920 \begin_layout Standard
15933 can also be used to decorate symbols and characters.
15934 For example, the command
15939 \begin_inset space \textvisiblespace{}
15945 \begin_inset space \textvisiblespace{}
15951 \begin_inset Formula $\uparrow$
15959 \begin_inset Formula
15961 \overset{a}{\maltese}
15969 \begin_layout Subsection
15971 \begin_inset CommandInset label
15973 name "sub:Binary-Operators"
15978 \begin_inset Index idx
15981 \begin_layout Plain Layout
15990 \begin_layout Standard
15991 Binary operators are surrounded by space when there is a character before
15993 \begin_inset VSpace medskip
15999 \begin_layout Standard
16000 \begin_inset space \hfill{}
16004 \begin_inset Tabular
16005 <lyxtabular version="3" rows="13" columns="2">
16006 <features rotate="0" tabularvalignment="middle">
16007 <column alignment="center" valignment="top" width="0pt">
16008 <column alignment="center" valignment="top" width="0pt">
16010 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
16013 \begin_layout Plain Layout
16015 \begin_inset Note Note
16018 \begin_layout Plain Layout
16025 is only used as spacer.
16035 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
16038 \begin_layout Plain Layout
16046 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
16049 \begin_layout Plain Layout
16055 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
16058 \begin_layout Plain Layout
16059 \begin_inset Formula $+$
16069 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
16072 \begin_layout Plain Layout
16078 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
16081 \begin_layout Plain Layout
16082 \begin_inset Formula $-$
16092 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
16095 \begin_layout Plain Layout
16103 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
16106 \begin_layout Plain Layout
16107 \begin_inset Formula $\pm$
16117 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
16120 \begin_layout Plain Layout
16128 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
16131 \begin_layout Plain Layout
16132 \begin_inset Formula $\mp$
16142 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
16145 \begin_layout Plain Layout
16153 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
16156 \begin_layout Plain Layout
16157 \begin_inset Formula $\cdot$
16167 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
16170 \begin_layout Plain Layout
16178 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
16181 \begin_layout Plain Layout
16182 \begin_inset Formula $\times$
16192 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
16195 \begin_layout Plain Layout
16203 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
16206 \begin_layout Plain Layout
16207 \begin_inset Formula $\div$
16217 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
16220 \begin_layout Plain Layout
16224 \begin_layout Plain Layout
16237 \begin_layout Plain Layout
16249 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
16252 \begin_layout Plain Layout
16253 \begin_inset Formula $*$
16263 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
16266 \begin_layout Plain Layout
16274 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
16277 \begin_layout Plain Layout
16278 \begin_inset Formula $\star$
16288 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
16291 \begin_layout Plain Layout
16299 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
16302 \begin_layout Plain Layout
16303 \begin_inset Formula $\circ$
16313 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
16316 \begin_layout Plain Layout
16324 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
16327 \begin_layout Plain Layout
16328 \begin_inset Formula $\diamond$
16338 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
16341 \begin_layout Plain Layout
16349 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
16352 \begin_layout Plain Layout
16353 \begin_inset Formula $\bullet$
16367 \begin_inset space \hfill{}
16371 \begin_inset Tabular
16372 <lyxtabular version="3" rows="13" columns="2">
16373 <features rotate="0" tabularvalignment="middle">
16374 <column alignment="center" valignment="top" width="0pt">
16375 <column alignment="center" valignment="top" width="0pt">
16377 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
16380 \begin_layout Plain Layout
16386 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
16389 \begin_layout Plain Layout
16397 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
16400 \begin_layout Plain Layout
16408 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
16411 \begin_layout Plain Layout
16412 \begin_inset Formula $\nabla$
16422 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
16425 \begin_layout Plain Layout
16433 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
16436 \begin_layout Plain Layout
16437 \begin_inset Formula $\bigtriangledown$
16447 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
16450 \begin_layout Plain Layout
16458 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
16461 \begin_layout Plain Layout
16462 \begin_inset Formula $\bigtriangleup$
16472 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
16475 \begin_layout Plain Layout
16483 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
16486 \begin_layout Plain Layout
16487 \begin_inset Formula $\Box$
16497 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
16500 \begin_layout Plain Layout
16508 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
16511 \begin_layout Plain Layout
16512 \begin_inset Formula $\cap$
16522 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
16525 \begin_layout Plain Layout
16533 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
16536 \begin_layout Plain Layout
16537 \begin_inset Formula $\cup$
16547 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
16550 \begin_layout Plain Layout
16558 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
16561 \begin_layout Plain Layout
16562 \begin_inset Formula $\dagger$
16572 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
16575 \begin_layout Plain Layout
16583 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
16586 \begin_layout Plain Layout
16587 \begin_inset Formula $\ddagger$
16597 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
16600 \begin_layout Plain Layout
16608 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
16611 \begin_layout Plain Layout
16612 \begin_inset Formula $\wr$
16622 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
16625 \begin_layout Plain Layout
16633 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
16636 \begin_layout Plain Layout
16637 \begin_inset Formula $\bigcirc$
16647 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
16650 \begin_layout Plain Layout
16658 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
16661 \begin_layout Plain Layout
16662 \begin_inset Formula $\wedge$
16672 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
16675 \begin_layout Plain Layout
16683 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
16686 \begin_layout Plain Layout
16687 \begin_inset Formula $\vee$
16701 \begin_inset space \hfill{}
16705 \begin_inset Tabular
16706 <lyxtabular version="3" rows="13" columns="2">
16707 <features rotate="0" tabularvalignment="middle">
16708 <column alignment="center" valignment="top" width="0pt">
16709 <column alignment="center" valignment="top" width="0pt">
16711 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
16714 \begin_layout Plain Layout
16720 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
16723 \begin_layout Plain Layout
16731 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
16734 \begin_layout Plain Layout
16742 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
16745 \begin_layout Plain Layout
16746 \begin_inset Formula $\oplus$
16756 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
16759 \begin_layout Plain Layout
16767 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
16770 \begin_layout Plain Layout
16771 \begin_inset Formula $\ominus$
16781 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
16784 \begin_layout Plain Layout
16792 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
16795 \begin_layout Plain Layout
16796 \begin_inset Formula $\otimes$
16806 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
16809 \begin_layout Plain Layout
16817 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
16820 \begin_layout Plain Layout
16821 \begin_inset Formula $\oslash$
16831 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
16834 \begin_layout Plain Layout
16842 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
16845 \begin_layout Plain Layout
16846 \begin_inset Formula $\odot$
16856 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
16859 \begin_layout Plain Layout
16867 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
16870 \begin_layout Plain Layout
16871 \begin_inset Formula $\amalg$
16881 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
16884 \begin_layout Plain Layout
16892 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
16895 \begin_layout Plain Layout
16896 \begin_inset Formula $\uplus$
16906 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
16909 \begin_layout Plain Layout
16917 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
16920 \begin_layout Plain Layout
16921 \begin_inset Formula $\setminus$
16931 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
16934 \begin_layout Plain Layout
16942 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
16945 \begin_layout Plain Layout
16946 \begin_inset Formula $\sqcap$
16956 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
16959 \begin_layout Plain Layout
16967 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
16970 \begin_layout Plain Layout
16971 \begin_inset Formula $\sqcup$
16981 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
16984 \begin_layout Plain Layout
16992 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
16995 \begin_layout Plain Layout
16996 \begin_inset Formula $\triangleleft$
17006 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
17009 \begin_layout Plain Layout
17017 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
17020 \begin_layout Plain Layout
17021 \begin_inset Formula $\triangleright$
17035 \begin_inset space \hfill{}
17041 \begin_layout Standard
17042 All binary operators can also be inserted via the math toolbar button
17045 arg "math-insert \\pm"
17051 \begin_layout Standard
17052 To typeset the Laplace operator also
17069 \begin_inset Formula $\nabla^{2}$
17072 ) can be used instead of
17081 \begin_layout Standard
17088 Insert\SpecialChar \menuseparator
17100 \begin_layout Subsection
17101 Self-defined Operators
17102 \begin_inset CommandInset label
17104 name "sub:Self-defined-Operators"
17109 \begin_inset Index idx
17112 \begin_layout Plain Layout
17113 Operators ! self-defined
17121 \begin_layout Standard
17122 With the help of the command
17126 DeclareMathOperator
17129 \begin_inset Index idx
17132 \begin_layout Plain Layout
17137 DeclareMathOperator
17142 custom operators can be defined in the LaTeX-preamble.
17143 Its command scheme is:
17146 \begin_layout Standard
17151 DeclareMathOperator{new command}{display}
17154 \begin_layout Standard
17155 Display can be characters or symbols that define how the operator looks
17157 To define a big operator a * is set behind the command.
17158 All self-defined big operators can have limits as described in
17159 \begin_inset CommandInset ref
17161 reference "sub:Operator-Limits"
17168 \begin_layout Standard
17169 For example the LaTeX-preamble line
17172 \begin_layout Standard
17177 DeclareMathOperator*{
17184 \begin_layout Standard
17185 defines the command
17191 , that inserts a big operator consisting of the lozenge symbol from
17192 \begin_inset CommandInset ref
17194 reference "sub:Miscellaneous-Symbols"
17199 \begin_inset Formula
17201 \Lozenge_{n=1}^{\infty}
17206 The command for this formula is:
17217 \begin_inset Formula $\to$
17223 \begin_layout Standard
17224 \begin_inset VSpace bigskip
17227 When self-defined operators are not used several times in the document,
17228 they can also be defined with the commands
17235 \begin_inset Index idx
17238 \begin_layout Plain Layout
17253 \begin_inset Index idx
17256 \begin_layout Plain Layout
17264 , which have the following scheme:
17267 \begin_layout Standard
17281 \begin_layout Standard
17288 defines big operators,
17297 \begin_layout Standard
17305 \begin_inset space \thinspace{}
17309 \begin_inset space \space{}
17312 be used to use one limit for several operators:
17315 \begin_layout Standard
17316 \begin_inset Formula
17318 \mathop{\sum\negmedspace\sum}_{i,j=1}^{N}
17326 \begin_layout Standard
17327 The command for the formula above is:
17328 \begin_inset Newline newline
17344 \begin_inset space \textvisiblespace{}
17350 \begin_inset Formula $\to$
17356 \begin_inset space \textvisiblespace{}
17364 \begin_layout Section
17366 \begin_inset Index idx
17369 \begin_layout Plain Layout
17378 \begin_layout Subsection
17380 \begin_inset CommandInset label
17382 name "sub:Font-Styles"
17387 \begin_inset Index idx
17390 \begin_layout Plain Layout
17399 \begin_layout Standard
17400 Latin letters in formulas can be set in one of the following font styles:
17401 \begin_inset VSpace -2mm
17407 \begin_layout Standard
17409 \begin_inset Tabular
17410 <lyxtabular version="3" rows="7" columns="3">
17411 <features rotate="0" tabularvalignment="middle">
17412 <column alignment="center" valignment="top">
17413 <column alignment="center" valignment="top">
17414 <column alignment="center" valignment="top">
17416 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
17419 \begin_layout Plain Layout
17425 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
17428 \begin_layout Plain Layout
17434 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
17437 \begin_layout Plain Layout
17445 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
17448 \begin_layout Plain Layout
17454 \begin_inset space \textvisiblespace{}
17464 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
17467 \begin_layout Plain Layout
17468 \begin_inset Formula $\mathbb{ABC}$
17476 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
17479 \begin_layout Plain Layout
17492 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
17495 \begin_layout Plain Layout
17501 \begin_inset space \textvisiblespace{}
17511 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
17514 \begin_layout Plain Layout
17515 \begin_inset Formula $\mathbf{AbC}$
17523 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
17526 \begin_layout Plain Layout
17539 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
17542 \begin_layout Plain Layout
17548 \begin_inset space \textvisiblespace{}
17558 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
17561 \begin_layout Plain Layout
17562 \begin_inset Formula $\boldsymbol{AbC}$
17570 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
17573 \begin_layout Plain Layout
17576 arg "font-boldsymbol"
17586 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
17589 \begin_layout Plain Layout
17595 \begin_inset space \textvisiblespace{}
17605 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
17608 \begin_layout Plain Layout
17609 \begin_inset Formula $\mathcal{ABC}$
17617 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
17620 \begin_layout Plain Layout
17633 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
17636 \begin_layout Plain Layout
17642 \begin_inset space \textvisiblespace{}
17652 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
17655 \begin_layout Plain Layout
17656 \begin_inset Formula $\mathfrak{AbC}$
17664 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
17667 \begin_layout Plain Layout
17675 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
17678 \begin_layout Plain Layout
17684 \begin_inset space \textvisiblespace{}
17694 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
17697 \begin_layout Plain Layout
17698 \begin_inset Formula $\mathscr{AbC}$
17706 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
17709 \begin_layout Plain Layout
17723 \begin_layout Standard
17725 \begin_inset Tabular
17726 <lyxtabular version="3" rows="5" columns="3">
17727 <features rotate="0" tabularvalignment="middle">
17728 <column alignment="center" valignment="top">
17729 <column alignment="center" valignment="top">
17730 <column alignment="center" valignment="top">
17732 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
17735 \begin_layout Plain Layout
17741 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
17744 \begin_layout Plain Layout
17750 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
17753 \begin_layout Plain Layout
17761 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
17764 \begin_layout Plain Layout
17770 \begin_inset space \textvisiblespace{}
17780 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
17783 \begin_layout Plain Layout
17784 \begin_inset Formula $\mathit{AbC}$
17792 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
17795 \begin_layout Plain Layout
17803 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
17806 \begin_layout Plain Layout
17812 \begin_inset space \textvisiblespace{}
17822 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
17825 \begin_layout Plain Layout
17826 \begin_inset Formula $\mathrm{AbC}$
17834 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
17837 \begin_layout Plain Layout
17850 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
17853 \begin_layout Plain Layout
17859 \begin_inset space \textvisiblespace{}
17869 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
17872 \begin_layout Plain Layout
17873 \begin_inset Formula $\mathsf{AbC}$
17881 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
17884 \begin_layout Plain Layout
17897 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
17900 \begin_layout Plain Layout
17906 \begin_inset space \textvisiblespace{}
17916 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
17919 \begin_layout Plain Layout
17920 \begin_inset Formula $\mathtt{AbC}$
17928 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
17931 \begin_layout Plain Layout
17934 arg "font-typewriter"
17950 \begin_layout Standard
17951 \begin_inset Note Greyedout
17954 \begin_layout Plain Layout
17971 can only be used for big letters.
17979 \begin_layout Standard
17980 Predefined is the style
17989 \begin_layout Standard
17990 The style commands work also for letters in mathematical constructs:
17991 \begin_inset Formula
17993 \mathfrak{A=\frac{b}{C}}
18001 \begin_layout Standard
18002 Characters in mathematical text don't appear in a math font style but in
18003 the text font style
18010 That their style can't be set correctly via the text style dialog is a
18015 \begin_layout Plain Layout
18016 \begin_inset CommandInset href
18018 name "LyX-bug #4629"
18019 target "http://www.lyx.org/trac/ticket/4629"
18031 \begin_layout Standard
18032 Instead of the style commands the dialog
18034 Edit\SpecialChar \menuseparator
18035 Math\SpecialChar \menuseparator
18038 or the toolbar button
18041 arg "math-insert \\font"
18047 \begin_layout Subsection
18049 \begin_inset CommandInset label
18051 name "sub:Bold-Formulas"
18056 \begin_inset Index idx
18059 \begin_layout Plain Layout
18068 \begin_layout Standard
18069 To make a complete formula bold, the command
18075 from the previous subsection cannot be used, because it doesn't work for
18076 small Greek letters.
18077 Furthermore it prints Latin letters always upright, like in the following
18081 \begin_layout Standard
18082 \begin_inset Formula
18084 \mathbf{\int_{n}^{2}f(\theta)=\Gamma}\qquad\textrm{equation with \textbackslash mathbf}
18092 \begin_layout Standard
18093 To display the formula correctly, the command
18100 \begin_inset Formula
18102 \boldsymbol{\int_{n}^{2}f(\theta)=\Gamma\qquad\textrm{equation with \textbackslash boldsymbol}}
18107 It is also possible to set the formula in a
18109 boldmath environment
18112 This environment is created by inserting the command
18119 \begin_inset Index idx
18122 \begin_layout Plain Layout
18131 To end the environment, the command
18138 \begin_inset Index idx
18141 \begin_layout Plain Layout
18149 is inserted in TeX-mode.
18153 \begin_layout Plain Layout
18163 \begin_inset Formula
18165 \int_{n}^{2}f(\theta)=\Gamma\qquad\textrm{equation in a boldmath environment}
18174 \begin_layout Plain Layout
18186 \begin_layout Subsection
18188 \begin_inset Index idx
18191 \begin_layout Plain Layout
18200 \begin_layout Standard
18201 Formulas can be colored like normal text: Highlight a formula or a formula
18207 Here is a formula in magenta:
18208 \begin_inset Formula
18210 {\color{magenta}\int A\,\mathrm{d}x=\frac{\sqrt[5]{B}}{\ln\left(\frac{1}{3}\right)}}
18218 \begin_layout Standard
18219 You can also define your own colors as described in
18220 \begin_inset CommandInset ref
18222 reference "sub:Colored-Boxes"
18227 They can be used with the TeX code command
18234 \begin_inset Index idx
18237 \begin_layout Plain Layout
18248 \begin_layout Standard
18253 textcolor{color}{characters or formula}
18256 \begin_layout Standard
18257 The following example was colored completely dark green and partly red:
18260 \begin_layout Standard
18264 \begin_layout Plain Layout
18268 textcolor{darkgreen}{
18274 \begin_inset Formula
18276 \int A\,\mathrm{d}x=\frac{{\color{red}\sqrt[5]{B}}}{\ln\left(\frac{1}{3}\right)}
18285 \begin_layout Plain Layout
18295 \begin_layout Standard
18296 Due to a bug in LyX only complete formulas can be colored with self-defined
18301 \begin_layout Plain Layout
18302 \begin_inset CommandInset href
18304 name "LyX-bug #5269"
18305 target "http://www.lyx.org/trac/ticket/5269"
18317 \begin_layout Subsection
18319 \begin_inset CommandInset label
18321 name "sub:Font-Sizes"
18326 \begin_inset Index idx
18329 \begin_layout Plain Layout
18338 \begin_layout Standard
18339 For characters in formulas there are, analog to characters in text, the
18340 following size commands:
18343 \begin_layout Standard
18387 \begin_inset Newline newline
18409 \begin_layout Standard
18410 The size produced by the commands depends on the document font size, which
18411 corresponds to the command
18418 The other commands produce smaller or larger sizes than
18425 The font size can however not exceed a certain value.
18426 Is for example the document font size 12
18427 \begin_inset space \thinspace{}
18436 switches to the same size as
18446 \begin_layout Standard
18447 A size command is inserted in TeX-mode before the formula and sets the size
18448 for all following formula and text characters.
18449 To switch back to the initial size, the command
18455 is inserted behind the formula in TeX-mode.
18458 \begin_layout Standard
18459 Within a formula the size can be changed using the following size commands
18460 or the toolbar button
18463 arg "math-insert \\style"
18469 \begin_layout Standard
18472 \begin_inset Tabular
18473 <lyxtabular version="3" rows="5" columns="2">
18474 <features rotate="0" tabularvalignment="middle">
18475 <column alignment="center" valignment="top">
18476 <column alignment="center" valignment="top">
18478 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
18481 \begin_layout Plain Layout
18487 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
18490 \begin_layout Plain Layout
18492 \begin_inset Note Note
18495 \begin_layout Plain Layout
18502 is only used as spacer.
18514 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
18517 \begin_layout Plain Layout
18521 \begin_inset Index idx
18524 \begin_layout Plain Layout
18537 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
18540 \begin_layout Plain Layout
18541 \begin_inset Formula $\raisebox{6.5mm}{}{\displaystyle E_{\mathrm{pot_{1}}}=\frac{K}{l+\frac{m}{n_{2}}}}\raisebox{-5.5mm}{}$
18551 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
18554 \begin_layout Plain Layout
18562 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
18565 \begin_layout Plain Layout
18566 \begin_inset Formula $\raisebox{4.5mm}{}{\textstyle E_{\mathrm{pot_{1}}}=\frac{K}{l+\frac{m}{n_{2}}}}\raisebox{-4mm}{}$
18576 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
18579 \begin_layout Plain Layout
18587 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
18590 \begin_layout Plain Layout
18591 \begin_inset Formula $\raisebox{4.5mm}{}{\scriptstyle E_{\mathrm{pot_{1}}}=\frac{K}{l+\frac{m}{n_{2}}}}\raisebox{-3.5mm}{}$
18601 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
18604 \begin_layout Plain Layout
18612 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
18615 \begin_layout Plain Layout
18616 \begin_inset Formula $\raisebox{4.5mm}{}{\scriptscriptstyle E_{\mathrm{pot_{1}}}=\frac{K}{l+\frac{m}{n_{2}}}}\raisebox{-3.5mm}{}$
18632 \begin_layout Standard
18633 After entering these commands, a blue box appears in which the formula parts
18637 \begin_layout Standard
18638 There is a further method to change the font size, that though only works
18639 for symbols or letters in mathematical text.
18640 To use it, one of the above text size commands is inserted in mathematical
18642 All following characters until the end of the mathematical text or until
18643 another size command will have the selected size.
18645 \begin_inset VSpace -2mm
18651 \begin_layout Standard
18655 \begin_layout Plain Layout
18665 \begin_inset Formula
18667 A=\frac{B}{c}\cdot\maltese
18673 \begin_inset Formula
18675 \maltese A\textrm{\Large\maltese\textit{A}}\textrm{\tiny\maltese\textit{A}}
18684 \begin_layout Plain Layout
18696 \begin_layout Standard
18697 \begin_inset VSpace medskip
18700 Before both formulas the command
18707 The command for the second formula is:
18708 \begin_inset Newline newline
18716 \begin_inset space \textvisiblespace{}
18722 \begin_inset space \textvisiblespace{}
18728 \begin_inset space \textvisiblespace{}
18734 \begin_inset space \textvisiblespace{}
18738 \begin_inset Formula $\to$
18742 \begin_inset Formula $\to$
18746 \begin_inset Newline newline
18750 \begin_inset space \hspace*{}
18761 \begin_inset space \textvisiblespace{}
18767 \begin_inset space \textvisiblespace{}
18773 \begin_inset space \textvisiblespace{}
18779 \begin_layout Standard
18780 If a symbol cannot be displayed in different sizes, it will always be displayed
18781 in the default size.
18784 \begin_layout Section
18786 \begin_inset Index idx
18789 \begin_layout Plain Layout
18798 \begin_layout Standard
18799 Greek letters can also be inserted via the toolbar button
18802 arg "math-insert \\alpha"
18806 All international typesetting norms purport that Greek letters in math
18807 have to be typeset italic/slanted.
18808 In some languages, like French or Russian, they are nevertheless sometimes
18812 \begin_layout Subsection
18814 \begin_inset Index idx
18817 \begin_layout Plain Layout
18818 Greek letters ! small
18826 \begin_layout Standard
18827 \begin_inset space \hfill{}
18831 \begin_inset Tabular
18832 <lyxtabular version="3" rows="11" columns="2">
18833 <features rotate="0" tabularvalignment="middle">
18834 <column alignment="center" valignment="top" width="0pt">
18835 <column alignment="center" valignment="top" width="0pt">
18837 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
18840 \begin_layout Plain Layout
18846 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
18849 \begin_layout Plain Layout
18857 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
18860 \begin_layout Plain Layout
18868 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
18871 \begin_layout Plain Layout
18872 \begin_inset Formula $\alpha$
18882 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
18885 \begin_layout Plain Layout
18893 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
18896 \begin_layout Plain Layout
18897 \begin_inset Formula $\beta$
18907 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
18910 \begin_layout Plain Layout
18918 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
18921 \begin_layout Plain Layout
18922 \begin_inset Formula $\gamma$
18932 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
18935 \begin_layout Plain Layout
18943 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
18946 \begin_layout Plain Layout
18947 \begin_inset Formula $\delta$
18957 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
18960 \begin_layout Plain Layout
18968 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
18971 \begin_layout Plain Layout
18972 \begin_inset Formula $\epsilon$
18982 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
18985 \begin_layout Plain Layout
18993 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
18996 \begin_layout Plain Layout
18997 \begin_inset Formula $\varepsilon$
19007 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
19010 \begin_layout Plain Layout
19018 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
19021 \begin_layout Plain Layout
19022 \begin_inset Formula $\zeta$
19032 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
19035 \begin_layout Plain Layout
19043 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
19046 \begin_layout Plain Layout
19047 \begin_inset Formula $\eta$
19057 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
19060 \begin_layout Plain Layout
19068 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
19071 \begin_layout Plain Layout
19072 \begin_inset Formula $\theta$
19082 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
19085 \begin_layout Plain Layout
19093 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
19096 \begin_layout Plain Layout
19097 \begin_inset Formula $\vartheta$
19111 \begin_inset space \hfill{}
19115 \begin_inset Tabular
19116 <lyxtabular version="3" rows="12" columns="2">
19117 <features rotate="0" tabularvalignment="middle">
19118 <column alignment="center" valignment="top" width="0pt">
19119 <column alignment="center" valignment="top" width="0pt">
19121 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
19124 \begin_layout Plain Layout
19130 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
19133 \begin_layout Plain Layout
19141 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
19144 \begin_layout Plain Layout
19152 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
19155 \begin_layout Plain Layout
19156 \begin_inset Formula $\iota$
19166 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
19169 \begin_layout Plain Layout
19177 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
19180 \begin_layout Plain Layout
19181 \begin_inset Formula $\kappa$
19191 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
19194 \begin_layout Plain Layout
19202 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
19205 \begin_layout Plain Layout
19206 \begin_inset Formula $\varkappa$
19216 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
19219 \begin_layout Plain Layout
19227 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
19230 \begin_layout Plain Layout
19231 \begin_inset Formula $\lambda$
19241 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
19244 \begin_layout Plain Layout
19252 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
19255 \begin_layout Plain Layout
19256 \begin_inset Formula $\mu$
19266 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
19269 \begin_layout Plain Layout
19277 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
19280 \begin_layout Plain Layout
19281 \begin_inset Formula $\nu$
19291 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
19294 \begin_layout Plain Layout
19302 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
19305 \begin_layout Plain Layout
19306 \begin_inset Formula $\xi$
19316 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
19319 \begin_layout Plain Layout
19325 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
19328 \begin_layout Plain Layout
19329 \begin_inset Formula $o$
19339 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
19342 \begin_layout Plain Layout
19350 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
19353 \begin_layout Plain Layout
19354 \begin_inset Formula $\pi$
19364 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
19367 \begin_layout Plain Layout
19375 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
19378 \begin_layout Plain Layout
19379 \begin_inset Formula $\varpi$
19389 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
19392 \begin_layout Plain Layout
19400 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
19403 \begin_layout Plain Layout
19404 \begin_inset Formula $\rho$
19418 \begin_inset space \hfill{}
19422 \begin_inset Tabular
19423 <lyxtabular version="3" rows="11" columns="2">
19424 <features rotate="0" tabularvalignment="middle">
19425 <column alignment="center" valignment="top" width="0pt">
19426 <column alignment="center" valignment="top" width="0pt">
19428 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
19431 \begin_layout Plain Layout
19437 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
19440 \begin_layout Plain Layout
19448 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
19451 \begin_layout Plain Layout
19459 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
19462 \begin_layout Plain Layout
19463 \begin_inset Formula $\varrho$
19473 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
19476 \begin_layout Plain Layout
19484 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
19487 \begin_layout Plain Layout
19488 \begin_inset Formula $\sigma$
19498 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
19501 \begin_layout Plain Layout
19509 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
19512 \begin_layout Plain Layout
19513 \begin_inset Formula $\varsigma$
19523 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
19526 \begin_layout Plain Layout
19534 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
19537 \begin_layout Plain Layout
19538 \begin_inset Formula $\tau$
19548 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
19551 \begin_layout Plain Layout
19559 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
19562 \begin_layout Plain Layout
19563 \begin_inset Formula $\upsilon$
19573 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
19576 \begin_layout Plain Layout
19584 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
19587 \begin_layout Plain Layout
19588 \begin_inset Formula $\phi$
19598 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
19601 \begin_layout Plain Layout
19609 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
19612 \begin_layout Plain Layout
19613 \begin_inset Formula $\varphi$
19623 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
19626 \begin_layout Plain Layout
19634 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
19637 \begin_layout Plain Layout
19638 \begin_inset Formula $\chi$
19648 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
19651 \begin_layout Plain Layout
19659 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
19662 \begin_layout Plain Layout
19663 \begin_inset Formula $\psi$
19673 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
19676 \begin_layout Plain Layout
19684 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
19687 \begin_layout Plain Layout
19688 \begin_inset Formula $\omega$
19702 \begin_inset space \hfill{}
19708 \begin_layout Standard
19709 \begin_inset VSpace medskip
19715 \begin_layout Standard
19716 How to create special upright Greek letters is explained in
19717 \begin_inset CommandInset ref
19719 reference "sub:Upright-small-Greek"
19726 \begin_layout Subsection
19728 \begin_inset Index idx
19731 \begin_layout Plain Layout
19732 Greek letters ! big
19740 \begin_layout Standard
19741 \begin_inset space \hfill{}
19745 \begin_inset Tabular
19746 <lyxtabular version="3" rows="7" columns="2">
19747 <features rotate="0" tabularvalignment="middle">
19748 <column alignment="center" valignment="top" width="0pt">
19749 <column alignment="center" valignment="top" width="0pt">
19751 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
19754 \begin_layout Plain Layout
19760 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
19763 \begin_layout Plain Layout
19771 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
19774 \begin_layout Plain Layout
19782 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
19785 \begin_layout Plain Layout
19786 \begin_inset Formula $\Gamma$
19796 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
19799 \begin_layout Plain Layout
19807 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
19810 \begin_layout Plain Layout
19811 \begin_inset Formula $\Delta$
19821 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
19824 \begin_layout Plain Layout
19832 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
19835 \begin_layout Plain Layout
19836 \begin_inset Formula $\Theta$
19846 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
19849 \begin_layout Plain Layout
19857 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
19860 \begin_layout Plain Layout
19861 \begin_inset Formula $\Lambda$
19871 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
19874 \begin_layout Plain Layout
19882 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
19885 \begin_layout Plain Layout
19886 \begin_inset Formula $\Xi$
19896 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
19899 \begin_layout Plain Layout
19907 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
19910 \begin_layout Plain Layout
19911 \begin_inset Formula $\Pi$
19925 \begin_inset space \hfill{}
19929 \begin_inset Tabular
19930 <lyxtabular version="3" rows="6" columns="2">
19931 <features rotate="0" tabularvalignment="middle">
19932 <column alignment="center" valignment="top" width="0pt">
19933 <column alignment="center" valignment="top" width="0pt">
19935 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
19938 \begin_layout Plain Layout
19944 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
19947 \begin_layout Plain Layout
19955 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
19958 \begin_layout Plain Layout
19966 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
19969 \begin_layout Plain Layout
19970 \begin_inset Formula $\Sigma$
19980 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
19983 \begin_layout Plain Layout
19991 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
19994 \begin_layout Plain Layout
19995 \begin_inset Formula $\Upsilon$
20005 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
20008 \begin_layout Plain Layout
20016 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
20019 \begin_layout Plain Layout
20020 \begin_inset Formula $\Phi$
20030 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
20033 \begin_layout Plain Layout
20041 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
20044 \begin_layout Plain Layout
20045 \begin_inset Formula $\Psi$
20055 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
20058 \begin_layout Plain Layout
20066 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
20069 \begin_layout Plain Layout
20070 \begin_inset Formula $\Omega$
20084 \begin_inset space \hfill{}
20090 \begin_layout Standard
20091 \begin_inset VSpace medskip
20094 That the big Greek letters appear upright is caused by a design bug when
20096 To get correct italic big letters, begin every command with
20101 For example the command
20108 \begin_inset Formula $\varGamma$
20112 Another way is to load the package
20120 \begin_layout Plain Layout
20125 is part of the LaTeX-package
20130 \begin_inset Index idx
20133 \begin_layout Plain Layout
20138 \begin_layout Plain Layout
20158 \begin_inset Index idx
20161 \begin_layout Plain Layout
20167 with the LaTeX-preamble line
20170 \begin_layout Standard
20175 usepackage{fixmath}
20178 \begin_layout Standard
20179 Then all big Greek letters in a document will automatically be typeset italic.
20182 \begin_layout Subsection
20184 \begin_inset Index idx
20187 \begin_layout Plain Layout
20188 Greek letters ! bold
20196 \begin_layout Standard
20197 Greek letters cannot be set with different font styles like Latin letters.
20198 They can only be made bold with the command
20205 \begin_inset Index idx
20208 \begin_layout Plain Layout
20219 \begin_layout Standard
20221 \begin_inset Tabular
20222 <lyxtabular version="3" rows="3" columns="2">
20223 <features rotate="0" tabularvalignment="middle">
20224 <column alignment="center" valignment="top">
20225 <column alignment="center" valignment="top">
20227 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
20230 \begin_layout Plain Layout
20236 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
20239 \begin_layout Plain Layout
20247 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
20250 \begin_layout Plain Layout
20262 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
20265 \begin_layout Plain Layout
20266 \begin_inset Formula $\Upsilon\boldsymbol{\Upsilon}$
20276 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
20279 \begin_layout Plain Layout
20291 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
20294 \begin_layout Plain Layout
20295 \begin_inset Formula $\theta\boldsymbol{\theta}$
20311 \begin_layout Section
20316 \begin_layout Plain Layout
20329 \begin_layout Plain Layout
20330 A list with all symbols of most of the LaTeX-packages can be found in
20331 \begin_inset CommandInset citation
20346 \begin_layout Plain Layout
20354 \begin_inset Note Note
20357 \begin_layout Plain Layout
20360 texorpdfstring is used to avoid that the footnote appears in the PDF-bookmark.
20363 \begin_layout Plain Layout
20366 texorpdfstring is in section
20367 \begin_inset CommandInset ref
20369 reference "sub:Formulas-in-Section"
20379 \begin_inset Index idx
20382 \begin_layout Plain Layout
20391 \begin_layout Standard
20392 Many of the symbols listed in this section can also be inserted via the
20396 arg "math-insert \\nabla"
20402 arg "math-insert \\digamma"
20408 \begin_layout Subsection
20409 Mathematical Symbols
20410 \begin_inset CommandInset label
20412 name "sub:Mathematical-Symbols"
20417 \begin_inset Index idx
20420 \begin_layout Plain Layout
20421 Symbols ! mathematical
20429 \begin_layout Standard
20430 \begin_inset space \hfill{}
20434 \begin_inset Tabular
20435 <lyxtabular version="3" rows="10" columns="2">
20436 <features rotate="0" tabularvalignment="middle">
20437 <column alignment="center" valignment="top" width="0pt">
20438 <column alignment="center" valignment="top" width="0pt">
20440 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
20443 \begin_layout Plain Layout
20449 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
20452 \begin_layout Plain Layout
20460 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
20463 \begin_layout Plain Layout
20471 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
20474 \begin_layout Plain Layout
20475 \begin_inset Formula $\neg$
20485 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
20488 \begin_layout Plain Layout
20496 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
20499 \begin_layout Plain Layout
20500 \begin_inset Formula $\Im$
20510 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
20513 \begin_layout Plain Layout
20521 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
20524 \begin_layout Plain Layout
20525 \begin_inset Formula $\Re$
20535 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
20538 \begin_layout Plain Layout
20546 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
20549 \begin_layout Plain Layout
20550 \begin_inset Formula $\aleph$
20560 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
20563 \begin_layout Plain Layout
20571 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
20574 \begin_layout Plain Layout
20575 \begin_inset Formula $\partial$
20585 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
20588 \begin_layout Plain Layout
20596 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
20599 \begin_layout Plain Layout
20600 \begin_inset Formula $\infty$
20610 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
20613 \begin_layout Plain Layout
20621 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
20624 \begin_layout Plain Layout
20625 \begin_inset Formula $\wp$
20635 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
20638 \begin_layout Plain Layout
20646 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
20649 \begin_layout Plain Layout
20650 \begin_inset Formula $\imath$
20660 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
20663 \begin_layout Plain Layout
20671 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
20674 \begin_layout Plain Layout
20675 \begin_inset Formula $\jmath$
20689 \begin_inset space \hfill{}
20693 \begin_inset Tabular
20694 <lyxtabular version="3" rows="10" columns="2">
20695 <features rotate="0" tabularvalignment="middle">
20696 <column alignment="center" valignment="top" width="0pt">
20697 <column alignment="center" valignment="top" width="0pt">
20699 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
20702 \begin_layout Plain Layout
20708 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
20711 \begin_layout Plain Layout
20713 \begin_inset Note Note
20716 \begin_layout Plain Layout
20723 is only used as spacer.
20735 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
20738 \begin_layout Plain Layout
20746 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
20749 \begin_layout Plain Layout
20750 \begin_inset Formula $\forall$
20760 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
20763 \begin_layout Plain Layout
20771 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
20774 \begin_layout Plain Layout
20775 \begin_inset Formula $\exists$
20785 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
20788 \begin_layout Plain Layout
20796 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
20799 \begin_layout Plain Layout
20800 \begin_inset Formula $\nexists$
20810 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
20813 \begin_layout Plain Layout
20821 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
20824 \begin_layout Plain Layout
20825 \begin_inset Formula $\emptyset$
20835 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
20838 \begin_layout Plain Layout
20846 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
20849 \begin_layout Plain Layout
20850 \begin_inset Formula $\varnothing$
20860 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
20863 \begin_layout Plain Layout
20871 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
20874 \begin_layout Plain Layout
20875 \begin_inset Formula $\dag$
20885 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
20888 \begin_layout Plain Layout
20896 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
20899 \begin_layout Plain Layout
20900 \begin_inset Formula $\ddag$
20910 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
20913 \begin_layout Plain Layout
20921 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
20924 \begin_layout Plain Layout
20928 \begin_layout Plain Layout
20938 \begin_inset Formula $\complement$
20945 \begin_layout Plain Layout
20959 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
20962 \begin_layout Plain Layout
20970 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
20973 \begin_layout Plain Layout
20974 \begin_inset Formula $\Bbbk$
20988 \begin_inset space \hfill{}
20992 \begin_inset Tabular
20993 <lyxtabular version="3" rows="10" columns="2">
20994 <features rotate="0" tabularvalignment="middle">
20995 <column alignment="center" valignment="top" width="0pt">
20996 <column alignment="center" valignment="top" width="0pt">
20998 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
21001 \begin_layout Plain Layout
21007 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
21010 \begin_layout Plain Layout
21018 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
21021 \begin_layout Plain Layout
21029 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
21032 \begin_layout Plain Layout
21033 \begin_inset Formula $\prime$
21043 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
21046 \begin_layout Plain Layout
21054 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
21057 \begin_layout Plain Layout
21058 \begin_inset Formula $\backprime$
21068 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
21071 \begin_layout Plain Layout
21079 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
21082 \begin_layout Plain Layout
21083 \begin_inset Formula $\mho$
21093 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
21096 \begin_layout Plain Layout
21104 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
21107 \begin_layout Plain Layout
21108 \begin_inset Formula $\triangle$
21118 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
21121 \begin_layout Plain Layout
21129 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
21132 \begin_layout Plain Layout
21133 \begin_inset Formula $\angle$
21143 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
21146 \begin_layout Plain Layout
21154 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
21157 \begin_layout Plain Layout
21158 \begin_inset Formula $\measuredangle$
21168 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
21171 \begin_layout Plain Layout
21179 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
21182 \begin_layout Plain Layout
21183 \begin_inset Formula $\sphericalangle$
21193 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
21196 \begin_layout Plain Layout
21204 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
21207 \begin_layout Plain Layout
21208 \begin_inset Formula $\top$
21218 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
21221 \begin_layout Plain Layout
21229 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
21232 \begin_layout Plain Layout
21233 \begin_inset Formula $\bot$
21247 \begin_inset space \hfill{}
21253 \begin_layout Subsection
21254 Miscellaneous Symbols
21255 \begin_inset CommandInset label
21257 name "sub:Miscellaneous-Symbols"
21262 \begin_inset Index idx
21265 \begin_layout Plain Layout
21266 Symbols ! miscellaneous
21274 \begin_layout Standard
21277 \begin_inset Tabular
21278 <lyxtabular version="3" rows="10" columns="2">
21279 <features rotate="0" tabularvalignment="middle">
21280 <column alignment="center" valignment="top" width="0pt">
21281 <column alignment="center" valignment="top" width="0pt">
21283 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
21286 \begin_layout Plain Layout
21292 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
21295 \begin_layout Plain Layout
21303 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
21306 \begin_layout Plain Layout
21314 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
21317 \begin_layout Plain Layout
21318 \begin_inset Formula $\flat$
21328 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
21331 \begin_layout Plain Layout
21339 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
21342 \begin_layout Plain Layout
21343 \begin_inset Formula $\natural$
21353 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
21356 \begin_layout Plain Layout
21364 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
21367 \begin_layout Plain Layout
21368 \begin_inset Formula $\sharp$
21378 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
21381 \begin_layout Plain Layout
21389 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
21392 \begin_layout Plain Layout
21393 \begin_inset Formula $\surd$
21403 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
21406 \begin_layout Plain Layout
21414 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
21417 \begin_layout Plain Layout
21418 \begin_inset Formula $\checkmark$
21428 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
21431 \begin_layout Plain Layout
21439 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
21442 \begin_layout Plain Layout
21443 \begin_inset Formula $\yen$
21453 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
21456 \begin_layout Plain Layout
21464 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
21467 \begin_layout Plain Layout
21468 \begin_inset Formula $\pounds$
21478 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
21481 \begin_layout Plain Layout
21487 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
21490 \begin_layout Plain Layout
21491 \begin_inset Formula $\$$
21501 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
21504 \begin_layout Plain Layout
21510 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
21513 \begin_layout Plain Layout
21514 \begin_inset Formula $§$
21528 \begin_inset Tabular
21529 <lyxtabular version="3" rows="10" columns="2">
21530 <features rotate="0" tabularvalignment="middle">
21531 <column alignment="center" valignment="top">
21532 <column alignment="center" valignment="top">
21534 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
21537 \begin_layout Plain Layout
21543 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
21546 \begin_layout Plain Layout
21554 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
21557 \begin_layout Plain Layout
21565 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
21568 \begin_layout Plain Layout
21569 \begin_inset Formula $\hbar$
21579 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
21582 \begin_layout Plain Layout
21590 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
21593 \begin_layout Plain Layout
21594 \begin_inset Formula $\hslash$
21604 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
21607 \begin_layout Plain Layout
21615 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
21618 \begin_layout Plain Layout
21619 \begin_inset Formula $\clubsuit$
21629 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
21632 \begin_layout Plain Layout
21640 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
21643 \begin_layout Plain Layout
21644 \begin_inset Formula $\spadesuit$
21654 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
21657 \begin_layout Plain Layout
21665 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
21668 \begin_layout Plain Layout
21669 \begin_inset Formula $\bigstar$
21679 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
21682 \begin_layout Plain Layout
21690 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
21693 \begin_layout Plain Layout
21694 \begin_inset Formula $\blacklozenge$
21704 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
21707 \begin_layout Plain Layout
21715 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
21718 \begin_layout Plain Layout
21719 \begin_inset Formula $\blacktriangle$
21729 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
21732 \begin_layout Plain Layout
21740 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
21743 \begin_layout Plain Layout
21744 \begin_inset Formula $\blacktriangledown$
21754 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
21757 \begin_layout Plain Layout
21765 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
21768 \begin_layout Plain Layout
21769 \begin_inset Formula $\bullet$
21783 \begin_inset Tabular
21784 <lyxtabular version="3" rows="10" columns="2">
21785 <features rotate="0" tabularvalignment="middle">
21786 <column alignment="center" valignment="top" width="0pt">
21787 <column alignment="center" valignment="top" width="0pt">
21789 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
21792 \begin_layout Plain Layout
21798 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
21801 \begin_layout Plain Layout
21809 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
21812 \begin_layout Plain Layout
21820 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
21823 \begin_layout Plain Layout
21824 \begin_inset Formula $\diamondsuit$
21834 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
21837 \begin_layout Plain Layout
21845 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
21848 \begin_layout Plain Layout
21849 \begin_inset Formula $\Diamond$
21859 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
21862 \begin_layout Plain Layout
21870 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
21873 \begin_layout Plain Layout
21874 \begin_inset Formula $\heartsuit$
21884 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
21887 \begin_layout Plain Layout
21895 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
21898 \begin_layout Plain Layout
21899 \begin_inset Formula $\P$
21909 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
21912 \begin_layout Plain Layout
21920 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
21923 \begin_layout Plain Layout
21924 \begin_inset Formula $\copyright$
21934 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
21937 \begin_layout Plain Layout
21945 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
21948 \begin_layout Plain Layout
21949 \begin_inset Formula $\circledR$
21959 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
21962 \begin_layout Plain Layout
21970 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
21973 \begin_layout Plain Layout
21974 \begin_inset Formula $\maltese$
21984 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
21987 \begin_layout Plain Layout
21995 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
21998 \begin_layout Plain Layout
21999 \begin_inset Formula $\diagup$
22009 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
22012 \begin_layout Plain Layout
22020 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
22023 \begin_layout Plain Layout
22024 \begin_inset Formula $\diagdown$
22040 \begin_layout Standard
22041 \begin_inset VSpace medskip
22047 \begin_layout Standard
22048 Some symbols can be displayed in different sizes, see
22049 \begin_inset CommandInset ref
22051 reference "sub:Font-Sizes"
22058 \begin_layout Subsection
22060 \begin_inset Index idx
22063 \begin_layout Plain Layout
22064 Symbols ! Euro-symbol
22070 \begin_inset Index idx
22073 \begin_layout Plain Layout
22080 \begin_layout Plain Layout
22097 \begin_layout Standard
22098 To use the Euro symbol in formulas, the LaTeX-package
22103 \begin_inset Index idx
22106 \begin_layout Plain Layout
22112 must be installed and loaded with the LaTeX-preamble line
22115 \begin_layout Standard
22120 usepackage[gennarrow]{eurosym}
22123 \begin_layout Standard
22124 The Euro symbol can now be inserted with the command
22131 \begin_inset Index idx
22134 \begin_layout Plain Layout
22145 \begin_layout Standard
22146 The Euro symbol can directly be inserted with the € key in mathematical
22147 text, without having
22162 can also be inserted in TeX-mode.
22163 The official currency symbol can then be inserted with the command
22170 \begin_inset Index idx
22173 \begin_layout Plain Layout
22181 , that is only available in TeX-mode.
22184 \begin_layout Standard
22188 \begin_layout Plain Layout
22198 \begin_inset Note Note
22201 \begin_layout Plain Layout
22202 The following table will only be displayed when the LaTeX-package
22214 \begin_layout Standard
22215 An overview about the different Euro symbols:
22218 \begin_layout Standard
22220 \begin_inset Tabular
22221 <lyxtabular version="3" rows="4" columns="3">
22222 <features rotate="0" tabularvalignment="middle">
22223 <column alignment="center" valignment="top" width="0pt">
22224 <column alignment="center" valignment="top" width="0pt">
22225 <column alignment="center" valignment="top" width="0pt">
22227 <cell multicolumn="1" alignment="center" valignment="top" bottomline="true" usebox="none">
22230 \begin_layout Plain Layout
22236 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
22239 \begin_layout Plain Layout
22245 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
22248 \begin_layout Plain Layout
22256 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
22259 \begin_layout Plain Layout
22265 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
22268 \begin_layout Plain Layout
22276 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
22279 \begin_layout Plain Layout
22280 \begin_inset Formula $\euro$
22290 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
22293 \begin_layout Plain Layout
22299 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
22302 \begin_layout Plain Layout
22308 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
22311 \begin_layout Plain Layout
22312 \begin_inset Formula $\mbox{€}$
22322 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
22325 \begin_layout Plain Layout
22331 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
22334 \begin_layout Plain Layout
22342 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
22345 \begin_layout Plain Layout
22349 \begin_layout Plain Layout
22371 \begin_layout Standard
22375 \begin_layout Plain Layout
22385 \begin_inset Note Note
22388 \begin_layout Plain Layout
22389 The following will be displayed when the LaTeX-package
22401 \begin_layout Standard
22402 You need to install the LaTeX-package
22406 to see the rest of this subsection in the output.
22409 \begin_layout Standard
22413 \begin_layout Plain Layout
22425 \begin_layout Section
22427 \begin_inset CommandInset label
22429 name "sec:Relations"
22434 \begin_inset Index idx
22437 \begin_layout Plain Layout
22444 \begin_inset Index idx
22447 \begin_layout Plain Layout
22452 \begin_layout Plain Layout
22463 \begin_layout Plain Layout
22478 \begin_layout Standard
22479 All following relations can also be inserted via the toolbar button
22482 arg "math-insert \\leq"
22488 \begin_layout Standard
22489 \begin_inset space \hfill{}
22493 \begin_inset Tabular
22494 <lyxtabular version="3" rows="17" columns="2">
22495 <features rotate="0" tabularvalignment="middle">
22496 <column alignment="center" valignment="top" width="0pt">
22497 <column alignment="center" valignment="top" width="0pt">
22499 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
22502 \begin_layout Plain Layout
22508 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
22511 \begin_layout Plain Layout
22519 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
22522 \begin_layout Plain Layout
22528 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
22531 \begin_layout Plain Layout
22532 \begin_inset Formula $<$
22542 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
22545 \begin_layout Plain Layout
22553 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
22556 \begin_layout Plain Layout
22557 \begin_inset Formula $\le$
22567 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
22570 \begin_layout Plain Layout
22578 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
22581 \begin_layout Plain Layout
22582 \begin_inset Formula $\ll$
22592 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
22595 \begin_layout Plain Layout
22603 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
22606 \begin_layout Plain Layout
22607 \begin_inset Formula $\prec$
22617 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
22620 \begin_layout Plain Layout
22628 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
22631 \begin_layout Plain Layout
22632 \begin_inset Formula $\preceq$
22642 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
22645 \begin_layout Plain Layout
22653 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
22656 \begin_layout Plain Layout
22657 \begin_inset Formula $\subset$
22667 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
22670 \begin_layout Plain Layout
22678 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
22681 \begin_layout Plain Layout
22682 \begin_inset Formula $\subseteq$
22692 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
22695 \begin_layout Plain Layout
22703 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
22706 \begin_layout Plain Layout
22707 \begin_inset Formula $\sqsubseteq$
22717 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
22720 \begin_layout Plain Layout
22728 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
22731 \begin_layout Plain Layout
22732 \begin_inset Formula $\in$
22742 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
22745 \begin_layout Plain Layout
22753 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
22756 \begin_layout Plain Layout
22757 \begin_inset Formula $\vdash$
22767 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
22770 \begin_layout Plain Layout
22778 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
22781 \begin_layout Plain Layout
22782 \begin_inset Formula $\smile$
22792 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
22795 \begin_layout Plain Layout
22803 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
22806 \begin_layout Plain Layout
22807 \begin_inset Formula $\lhd$
22817 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
22820 \begin_layout Plain Layout
22828 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
22831 \begin_layout Plain Layout
22832 \begin_inset Formula $\unlhd$
22842 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
22845 \begin_layout Plain Layout
22853 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
22856 \begin_layout Plain Layout
22857 \begin_inset Formula $\gtrless$
22867 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
22870 \begin_layout Plain Layout
22878 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
22881 \begin_layout Plain Layout
22882 \begin_inset Formula $\mid$
22892 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
22895 \begin_layout Plain Layout
22903 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
22906 \begin_layout Plain Layout
22907 \begin_inset Formula $\nmid$
22921 \begin_inset space \hfill{}
22925 \begin_inset Tabular
22926 <lyxtabular version="3" rows="17" columns="2">
22927 <features rotate="0" tabularvalignment="middle">
22928 <column alignment="center" valignment="top" width="0pt">
22929 <column alignment="center" valignment="top" width="0pt">
22931 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
22934 \begin_layout Plain Layout
22940 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
22943 \begin_layout Plain Layout
22951 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
22954 \begin_layout Plain Layout
22960 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
22963 \begin_layout Plain Layout
22964 \begin_inset Formula $=$
22974 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
22977 \begin_layout Plain Layout
22985 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
22988 \begin_layout Plain Layout
22989 \begin_inset Formula $\not=$
22999 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
23002 \begin_layout Plain Layout
23010 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
23013 \begin_layout Plain Layout
23014 \begin_inset Formula $\equiv$
23024 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
23027 \begin_layout Plain Layout
23035 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
23038 \begin_layout Plain Layout
23039 \begin_inset Formula $\sim$
23049 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
23052 \begin_layout Plain Layout
23060 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
23063 \begin_layout Plain Layout
23064 \begin_inset Formula $\simeq$
23074 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
23077 \begin_layout Plain Layout
23085 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
23088 \begin_layout Plain Layout
23089 \begin_inset Formula $\approx$
23099 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
23102 \begin_layout Plain Layout
23110 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
23113 \begin_layout Plain Layout
23114 \begin_inset Formula $\cong$
23124 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
23127 \begin_layout Plain Layout
23135 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
23138 \begin_layout Plain Layout
23139 \begin_inset Formula $\bowtie$
23149 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
23152 \begin_layout Plain Layout
23160 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
23163 \begin_layout Plain Layout
23164 \begin_inset Formula $\notin$
23174 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
23177 \begin_layout Plain Layout
23185 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
23188 \begin_layout Plain Layout
23189 \begin_inset Formula $\perp$
23199 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
23202 \begin_layout Plain Layout
23210 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
23213 \begin_layout Plain Layout
23214 \begin_inset Formula $\propto$
23224 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
23227 \begin_layout Plain Layout
23235 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
23238 \begin_layout Plain Layout
23239 \begin_inset Formula $\asymp$
23249 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
23252 \begin_layout Plain Layout
23260 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
23263 \begin_layout Plain Layout
23264 \begin_inset Formula $\doteq$
23274 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
23277 \begin_layout Plain Layout
23285 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
23288 \begin_layout Plain Layout
23289 \begin_inset Formula $\circeq$
23299 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
23302 \begin_layout Plain Layout
23310 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
23313 \begin_layout Plain Layout
23314 \begin_inset Formula $\models$
23324 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
23327 \begin_layout Plain Layout
23335 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
23338 \begin_layout Plain Layout
23339 \begin_inset Formula $\widehat{=}$
23353 \begin_inset space \hfill{}
23357 \begin_inset Tabular
23358 <lyxtabular version="3" rows="17" columns="2">
23359 <features rotate="0" tabularvalignment="middle">
23360 <column alignment="center" valignment="top" width="0pt">
23361 <column alignment="center" valignment="top" width="0pt">
23363 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
23366 \begin_layout Plain Layout
23372 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
23375 \begin_layout Plain Layout
23383 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
23386 \begin_layout Plain Layout
23392 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
23395 \begin_layout Plain Layout
23396 \begin_inset Formula $>$
23406 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
23409 \begin_layout Plain Layout
23417 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
23420 \begin_layout Plain Layout
23421 \begin_inset Formula $\ge$
23431 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
23434 \begin_layout Plain Layout
23442 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
23445 \begin_layout Plain Layout
23446 \begin_inset Formula $\gg$
23456 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
23459 \begin_layout Plain Layout
23467 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
23470 \begin_layout Plain Layout
23471 \begin_inset Formula $\succ$
23481 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
23484 \begin_layout Plain Layout
23492 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
23495 \begin_layout Plain Layout
23496 \begin_inset Formula $\succeq$
23506 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
23509 \begin_layout Plain Layout
23517 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
23520 \begin_layout Plain Layout
23521 \begin_inset Formula $\supset$
23531 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
23534 \begin_layout Plain Layout
23542 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
23545 \begin_layout Plain Layout
23546 \begin_inset Formula $\supseteq$
23556 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
23559 \begin_layout Plain Layout
23567 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
23570 \begin_layout Plain Layout
23571 \begin_inset Formula $\sqsupseteq$
23581 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
23584 \begin_layout Plain Layout
23592 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
23595 \begin_layout Plain Layout
23596 \begin_inset Formula $\ni$
23606 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
23609 \begin_layout Plain Layout
23617 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
23620 \begin_layout Plain Layout
23621 \begin_inset Formula $\dashv$
23631 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
23634 \begin_layout Plain Layout
23642 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
23645 \begin_layout Plain Layout
23646 \begin_inset Formula $\frown$
23656 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
23659 \begin_layout Plain Layout
23667 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
23670 \begin_layout Plain Layout
23671 \begin_inset Formula $\rhd$
23681 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
23684 \begin_layout Plain Layout
23692 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
23695 \begin_layout Plain Layout
23696 \begin_inset Formula $\unrhd$
23706 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
23709 \begin_layout Plain Layout
23717 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
23720 \begin_layout Plain Layout
23721 \begin_inset Formula $\lessgtr$
23731 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
23734 \begin_layout Plain Layout
23742 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
23745 \begin_layout Plain Layout
23746 \begin_inset Formula $\parallel$
23756 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
23759 \begin_layout Plain Layout
23767 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
23770 \begin_layout Plain Layout
23771 \begin_inset Formula $\nparallel$
23785 \begin_inset space \hfill{}
23791 \begin_layout Standard
23792 \begin_inset VSpace medskip
23807 are bigger than the equal looking operators
23822 \begin_layout Standard
23823 LyX supports also many special relations.
23824 Use the toolbar button
23827 arg "math-insert \\leqq"
23830 to see a list of these relations.
23833 \begin_layout Standard
23834 Relations are, in contrary to symbols, always surrounded by space.
23837 \begin_layout Standard
23838 Relations with labels can be created with the command
23845 \begin_inset Index idx
23848 \begin_layout Plain Layout
23859 \begin_layout Standard
23861 \begin_inset Tabular
23862 <lyxtabular version="3" rows="2" columns="2">
23863 <features rotate="0" tabularvalignment="middle">
23864 <column alignment="center" valignment="top">
23865 <column alignment="center" valignment="top">
23867 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
23870 \begin_layout Plain Layout
23876 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
23879 \begin_layout Plain Layout
23881 \begin_inset Note Note
23884 \begin_layout Plain Layout
23891 is only used as spacer.
23903 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
23906 \begin_layout Plain Layout
23910 \begin_inset space \textvisiblespace{}
23918 \begin_inset space \textvisiblespace{}
23922 \begin_inset Formula $\downarrow$
23928 \begin_inset space \textvisiblespace{}
23932 \begin_inset space \textvisiblespace{}
23940 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
23943 \begin_layout Plain Layout
23944 \begin_inset Formula $\raisebox{5mm}{}A(r)\stackrel{r\to\infty}{\approx}B$
23960 \begin_layout Section
23964 \begin_layout Subsection
23965 Predefined Functions
23966 \begin_inset CommandInset label
23968 name "sub:Predefined-Functions"
23973 \begin_inset Index idx
23976 \begin_layout Plain Layout
23977 Functions ! predefined
23985 \begin_layout Standard
23986 In general, variables are set
23990 in mathematical expressions, but not function names, because
23991 \begin_inset Formula $sin$
23994 could be misunderstood as
23995 \begin_inset Formula $s\cdot i\cdot n$
23999 Therefore there are predefined functionswhich are additionally a bit separated
24001 They are inserted as commands starting with a backslash before their name.
24004 \begin_layout Standard
24006 \begin_inset Tabular
24007 <lyxtabular version="3" rows="2" columns="4">
24008 <features rotate="0" tabularvalignment="middle">
24009 <column alignment="center" valignment="top" width="0pt">
24010 <column alignment="center" valignment="top" width="0pt">
24011 <column alignment="center" valignment="top" width="0pt">
24012 <column alignment="center" valignment="top" width="0pt">
24014 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
24017 \begin_layout Plain Layout
24023 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
24026 \begin_layout Plain Layout
24032 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
24035 \begin_layout Plain Layout
24041 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
24044 \begin_layout Plain Layout
24052 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
24055 \begin_layout Plain Layout
24061 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
24064 \begin_layout Plain Layout
24065 \begin_inset Formula $Asin(x)+B$
24073 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
24076 \begin_layout Plain Layout
24084 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
24087 \begin_layout Plain Layout
24088 \begin_inset Formula $A\sin(x)+B$
24104 \begin_layout Standard
24105 The following functions are predefined:
24108 \begin_layout Standard
24109 \begin_inset VSpace -2mm
24115 \begin_layout Standard
24117 \begin_inset Tabular
24118 <lyxtabular version="3" rows="9" columns="4">
24119 <features rotate="0" tabularvalignment="middle">
24120 <column alignment="center" valignment="top" width="0pt">
24121 <column alignment="center" valignment="top" width="0pt">
24122 <column alignment="center" valignment="top" width="0pt">
24123 <column alignment="center" valignment="top" width="0pt">
24125 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
24128 \begin_layout Plain Layout
24134 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
24137 \begin_layout Plain Layout
24143 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
24146 \begin_layout Plain Layout
24152 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
24155 \begin_layout Plain Layout
24163 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
24166 \begin_layout Plain Layout
24174 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
24177 \begin_layout Plain Layout
24185 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
24188 \begin_layout Plain Layout
24196 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
24199 \begin_layout Plain Layout
24209 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
24212 \begin_layout Plain Layout
24220 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
24223 \begin_layout Plain Layout
24231 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
24234 \begin_layout Plain Layout
24242 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
24245 \begin_layout Plain Layout
24255 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
24258 \begin_layout Plain Layout
24266 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
24269 \begin_layout Plain Layout
24277 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
24280 \begin_layout Plain Layout
24288 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
24291 \begin_layout Plain Layout
24301 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
24304 \begin_layout Plain Layout
24312 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
24315 \begin_layout Plain Layout
24323 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
24326 \begin_layout Plain Layout
24334 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
24337 \begin_layout Plain Layout
24347 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
24350 \begin_layout Plain Layout
24358 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
24361 \begin_layout Plain Layout
24369 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
24372 \begin_layout Plain Layout
24380 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
24383 \begin_layout Plain Layout
24393 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
24396 \begin_layout Plain Layout
24404 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
24407 \begin_layout Plain Layout
24415 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
24418 \begin_layout Plain Layout
24426 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
24429 \begin_layout Plain Layout
24439 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
24442 \begin_layout Plain Layout
24450 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
24453 \begin_layout Plain Layout
24461 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
24464 \begin_layout Plain Layout
24472 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
24475 \begin_layout Plain Layout
24485 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
24488 \begin_layout Plain Layout
24496 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
24499 \begin_layout Plain Layout
24507 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
24510 \begin_layout Plain Layout
24518 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
24521 \begin_layout Plain Layout
24537 \begin_layout Standard
24538 They can also be inserted with the math toolbar button
24541 arg "math-insert \\functions"
24547 \begin_layout Subsection
24548 Self-defined Functions
24549 \begin_inset Index idx
24552 \begin_layout Plain Layout
24553 Functions ! self-defined
24561 \begin_layout Standard
24562 To use a function that is not predefined, like for example the sign function
24563 sgn(x), there are two possibilities:
24566 \begin_layout Itemize
24567 Define the function by inserting the following line to the LaTeX-preamble
24571 \begin_layout Plain Layout
24576 DeclareMathOperator
24579 \begin_inset CommandInset ref
24581 reference "sub:Self-defined-Operators"
24591 \begin_inset Newline newline
24595 \begin_inset VSpace -3mm
24599 \begin_inset Newline newline
24606 DeclareMathOperator{
24611 \begin_inset Index idx
24614 \begin_layout Plain Layout
24619 DeclareMathOperator
24625 \begin_inset Newline newline
24629 \begin_inset VSpace -2mm
24633 \begin_inset Newline newline
24636 Now the new defined function can be called with the command
24645 \begin_layout Itemize
24646 Write the formula as usual, mark the formula name, in our example the letters
24651 , and change it to mathematical text.
24652 Finally, a space is inserted between prefactor and function.
24655 \begin_layout Standard
24656 The result is the same with both methods as with a predefined function
24660 \begin_layout Plain Layout
24661 In LyX self-defined functions are displayed red, predefined ones black.
24669 \begin_layout Standard
24671 \begin_inset Tabular
24672 <lyxtabular version="3" rows="3" columns="2">
24673 <features rotate="0" tabularvalignment="middle">
24674 <column alignment="center" valignment="top" width="0pt">
24675 <column alignment="center" valignment="top" width="0pt">
24677 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
24680 \begin_layout Plain Layout
24686 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
24689 \begin_layout Plain Layout
24697 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
24700 \begin_layout Plain Layout
24708 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
24711 \begin_layout Plain Layout
24712 \begin_inset Formula $A\sgn(x)+B$
24722 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
24725 \begin_layout Plain Layout
24729 \begin_inset Formula $\underbrace{\textrm{sgn}}_{\textrm{Alt+M}\,\textrm{M}}$
24737 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
24740 \begin_layout Plain Layout
24741 \begin_inset Formula $A\,\textrm{sgn}(x)+B$
24757 \begin_layout Standard
24758 The first method is more suitable when the self-defined function should
24759 be used several times.
24762 \begin_layout Subsection
24764 \begin_inset Index idx
24767 \begin_layout Plain Layout
24776 \begin_layout Standard
24777 For limits, in addition to the commands
24784 \begin_inset Index idx
24787 \begin_layout Plain Layout
24807 the following functions are defined:
24810 \begin_layout Standard
24812 \begin_inset Tabular
24813 <lyxtabular version="3" rows="5" columns="2">
24814 <features rotate="0" tabularvalignment="middle">
24815 <column alignment="center" valignment="top">
24816 <column alignment="center" valignment="top">
24818 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
24821 \begin_layout Plain Layout
24827 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
24830 \begin_layout Plain Layout
24832 \begin_inset Note Note
24835 \begin_layout Plain Layout
24842 is only used as spacer.
24854 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
24857 \begin_layout Plain Layout
24865 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
24868 \begin_layout Plain Layout
24869 \begin_inset Formula $\varliminf$
24879 <cell alignment="center" valignment="top" leftline="true" usebox="none">
24882 \begin_layout Plain Layout
24890 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
24893 \begin_layout Plain Layout
24894 \begin_inset Formula $\varlimsup$
24904 <cell alignment="center" valignment="top" leftline="true" usebox="none">
24907 \begin_layout Plain Layout
24915 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
24918 \begin_layout Plain Layout
24919 \begin_inset Formula $\varprojlim$
24929 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
24932 \begin_layout Plain Layout
24940 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
24943 \begin_layout Plain Layout
24944 \begin_inset Formula $\varinjlim$
24948 \begin_inset Formula $\raisebox{-2.5mm}{}$
24964 \begin_layout Standard
24965 \begin_inset VSpace medskip
24968 The limit is created by inserting a subscript.
24969 It is set right beside the function in an inline formula:
24972 \begin_layout Standard
24974 \begin_inset Tabular
24975 <lyxtabular version="3" rows="2" columns="2">
24976 <features rotate="0" tabularvalignment="middle">
24977 <column alignment="center" valignment="top" width="0pt">
24978 <column alignment="center" valignment="top" width="0pt">
24980 <cell alignment="center" valignment="top" usebox="none">
24983 \begin_layout Plain Layout
24989 <cell alignment="center" valignment="top" usebox="none">
24992 \begin_layout Plain Layout
24993 \begin_inset space \hspace{}
24998 \begin_inset Note Note
25001 \begin_layout Plain Layout
25008 are used here as spacer.
25020 <cell alignment="center" valignment="top" usebox="none">
25023 \begin_layout Plain Layout
25029 \begin_inset space \textvisiblespace{}
25033 \begin_inset space \textvisiblespace{}
25041 <cell alignment="center" valignment="top" usebox="none">
25044 \begin_layout Plain Layout
25045 \begin_inset Formula $\hspace{1cm}\raisebox{5mm}{}\lim_{x\to A}x=B$
25061 \begin_layout Standard
25062 In a displayed formula the limit is set below the formula, as usual:
25063 \begin_inset Formula
25073 \begin_layout Standard
25074 \begin_inset VSpace medskip
25080 \begin_layout Standard
25081 How to adjust the typesetting of the limits see
25082 \begin_inset CommandInset ref
25084 reference "sub:Operator-Limits"
25091 \begin_layout Subsection
25093 \begin_inset Index idx
25096 \begin_layout Plain Layout
25097 Functions ! modulo-
25105 \begin_layout Standard
25106 The modulo-function is special, because it exists in four variants.
25107 The variants in a displayed formula are:
25108 \begin_inset Formula
25110 \underline{\textrm{Command}\raisebox{-0.9mm}{}} & & \underline{\textrm{Result}}\\
25111 \mathrm{a\backslash mod\textrm{␣}b} & & a\mod b\\
25112 \mathrm{a\backslash pmod\textrm{␣}b} & & a\pmod b\\
25113 \mathrm{a\backslash bmod\textrm{␣}b} & & a\bmod b\\
25114 \mathrm{a\backslash pod\textrm{␣}b} & & a\pod b
25122 \begin_layout Standard
25123 In an inline formula less space is set before the function names for all
25125 By default the modulo-functions take only the first following character
25127 To use more than one character, one has to put them into TeX-braces:
25128 \begin_inset Formula
25130 \underline{\textrm{Command}\raisebox{-0.9mm}{}} & & \underline{\textrm{Result}}\\
25131 \mathrm{a\backslash pod\textrm{␣}bcd} & & a\pod bcd\\
25132 \mathrm{a\backslash pod\backslash\{bc\to d} & & a\pod{bc}d
25140 \begin_layout Section
25142 \begin_inset Index idx
25145 \begin_layout Plain Layout
25154 \begin_layout Subsection
25155 Special Characters in Mathematical Text
25158 \begin_layout Standard
25159 The following commands can only be used in mathematical text or in TeX-mode:
25162 \begin_layout Standard
25163 \begin_inset space \hfill{}
25167 \begin_inset Tabular
25168 <lyxtabular version="3" rows="8" columns="2">
25169 <features rotate="0" tabularvalignment="middle">
25170 <column alignment="block" valignment="top">
25171 <column alignment="block" valignment="top">
25173 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
25176 \begin_layout Plain Layout
25182 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
25185 \begin_layout Plain Layout
25193 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
25196 \begin_layout Plain Layout
25204 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
25207 \begin_layout Plain Layout
25208 \begin_inset Formula $\textrm{œ}$
25218 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
25221 \begin_layout Plain Layout
25229 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
25232 \begin_layout Plain Layout
25233 \begin_inset Formula $\textrm{Œ}$
25243 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
25246 \begin_layout Plain Layout
25254 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
25257 \begin_layout Plain Layout
25258 \begin_inset Formula $\textrm{æ}$
25268 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
25271 \begin_layout Plain Layout
25279 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
25282 \begin_layout Plain Layout
25283 \begin_inset Formula $\textrm{Æ}$
25293 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
25296 \begin_layout Plain Layout
25304 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
25307 \begin_layout Plain Layout
25308 \begin_inset Formula $\textrm{\aa}$
25318 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
25321 \begin_layout Plain Layout
25325 \begin_inset Index idx
25328 \begin_layout Plain Layout
25335 \begin_layout Plain Layout
25356 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
25359 \begin_layout Plain Layout
25360 \begin_inset Formula $\textrm{Å}$
25370 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
25373 \begin_layout Plain Layout
25381 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
25384 \begin_layout Plain Layout
25385 \begin_inset Formula $\textrm{ı}$
25399 \begin_inset space \hfill{}
25403 \begin_inset Tabular
25404 <lyxtabular version="3" rows="8" columns="2">
25405 <features rotate="0" tabularvalignment="middle">
25406 <column alignment="block" valignment="top">
25407 <column alignment="center" valignment="top">
25409 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
25412 \begin_layout Plain Layout
25414 \begin_inset Note Note
25417 \begin_layout Plain Layout
25419 \begin_inset space \thinspace{}
25422 mm is used for separation, because otherwise the output will be ¡ and ¿
25433 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
25436 \begin_layout Plain Layout
25444 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
25447 \begin_layout Plain Layout
25455 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
25458 \begin_layout Plain Layout
25459 \begin_inset Formula $\textrm{ø}$
25469 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
25472 \begin_layout Plain Layout
25480 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
25483 \begin_layout Plain Layout
25484 \begin_inset Formula $\textrm{Ø}$
25494 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
25497 \begin_layout Plain Layout
25505 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
25508 \begin_layout Plain Layout
25509 \begin_inset Formula $\textrm{ł}$
25519 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
25522 \begin_layout Plain Layout
25530 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
25533 \begin_layout Plain Layout
25534 \begin_inset Formula $\textrm{Ł}$
25544 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
25547 \begin_layout Plain Layout
25549 \begin_inset space \hspace{}
25554 \begin_inset space \textvisiblespace{}
25562 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
25565 \begin_layout Plain Layout
25566 \begin_inset Formula $\textrm{!`}$
25576 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
25579 \begin_layout Plain Layout
25581 \begin_inset space \hspace{}
25586 \begin_inset space \textvisiblespace{}
25594 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
25597 \begin_layout Plain Layout
25598 \begin_inset Formula $\textrm{?`}$
25608 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
25611 \begin_layout Plain Layout
25619 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
25622 \begin_layout Plain Layout
25623 \begin_inset Formula $\textrm{ȷ}$
25637 \begin_inset space \hfill{}
25643 \begin_layout Standard
25645 \begin_inset Formula $\textrm{\textrm{Å}}$
25649 \begin_inset Formula $\textrm{\textrm{Ø}}$
25652 can also be inserted via the math toolbar button
25655 arg "math-insert \\digamma"
25661 \begin_layout Standard
25662 An exception are the commands
25665 \begin_inset space \hspace{}
25674 \begin_inset space \hspace{}
25680 , because they can be inserted in LyX directly to text.
25683 \begin_layout Subsection
25685 \begin_inset CommandInset label
25687 name "sub:Accents-in-Text"
25692 \begin_inset Index idx
25695 \begin_layout Plain Layout
25704 \begin_layout Standard
25705 With the following commands all letters can be accented.
25706 The commands must be inserted in TeX-mode.
25709 \begin_layout Standard
25710 \begin_inset space \hfill{}
25714 \begin_inset Tabular
25715 <lyxtabular version="3" rows="8" columns="2">
25716 <features rotate="0" tabularvalignment="middle">
25717 <column alignment="block" valignment="top">
25718 <column alignment="block" valignment="top">
25720 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
25723 \begin_layout Plain Layout
25729 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
25732 \begin_layout Plain Layout
25740 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
25743 \begin_layout Plain Layout
25747 \begin_inset Quotes grd
25755 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
25758 \begin_layout Plain Layout
25762 \begin_layout Plain Layout
25778 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
25781 \begin_layout Plain Layout
25789 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
25792 \begin_layout Plain Layout
25796 \begin_layout Plain Layout
25812 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
25815 \begin_layout Plain Layout
25819 \begin_inset space \textvisiblespace{}
25827 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
25830 \begin_layout Plain Layout
25834 \begin_layout Plain Layout
25850 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
25853 \begin_layout Plain Layout
25861 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
25864 \begin_layout Plain Layout
25868 \begin_layout Plain Layout
25884 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
25887 \begin_layout Plain Layout
25891 \begin_inset space \textvisiblespace{}
25899 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
25902 \begin_layout Plain Layout
25906 \begin_layout Plain Layout
25922 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
25925 \begin_layout Plain Layout
25929 \begin_inset space \textvisiblespace{}
25937 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
25940 \begin_layout Plain Layout
25944 \begin_layout Plain Layout
25960 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
25963 \begin_layout Plain Layout
25967 \begin_inset space \textvisiblespace{}
25975 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
25978 \begin_layout Plain Layout
25982 \begin_layout Plain Layout
26002 \begin_inset space \hfill{}
26006 \begin_inset Tabular
26007 <lyxtabular version="3" rows="8" columns="2">
26008 <features rotate="0" tabularvalignment="middle">
26009 <column alignment="block" valignment="top">
26010 <column alignment="center" valignment="top">
26012 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
26015 \begin_layout Plain Layout
26021 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
26024 \begin_layout Plain Layout
26032 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
26035 \begin_layout Plain Layout
26039 \begin_inset space \textvisiblespace{}
26047 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
26050 \begin_layout Plain Layout
26054 \begin_layout Plain Layout
26070 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
26073 \begin_layout Plain Layout
26081 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
26084 \begin_layout Plain Layout
26088 \begin_layout Plain Layout
26104 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
26107 \begin_layout Plain Layout
26111 \begin_inset Index idx
26114 \begin_layout Plain Layout
26125 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
26128 \begin_layout Plain Layout
26132 \begin_layout Plain Layout
26148 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
26151 \begin_layout Plain Layout
26159 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
26162 \begin_layout Plain Layout
26166 \begin_layout Plain Layout
26182 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
26185 \begin_layout Plain Layout
26189 \begin_inset space \textvisiblespace{}
26197 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
26200 \begin_layout Plain Layout
26204 \begin_layout Plain Layout
26220 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
26223 \begin_layout Plain Layout
26227 \begin_inset space \textvisiblespace{}
26235 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
26238 \begin_layout Plain Layout
26242 \begin_layout Plain Layout
26258 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
26261 \begin_layout Plain Layout
26265 \begin_inset space \textvisiblespace{}
26273 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
26276 \begin_layout Plain Layout
26280 \begin_layout Plain Layout
26300 \begin_inset space \hfill{}
26306 \begin_layout Standard
26307 \begin_inset VSpace medskip
26316 also two different characters can be accented.
26322 \begin_inset space \textvisiblespace{}
26331 \begin_layout Plain Layout
26343 \begin_layout Standard
26356 can in combination with vowels directly be inserted with the keyboard without
26358 The same applies for the tilde
26362 \begin_layout Plain Layout
26363 This only applies for keyboards where the tilde is defined as accent.
26372 in combination with
26387 \begin_layout Standard
26430 and accents that are inserted directly with the keyboard are also available
26431 in mathematical text.
26432 For the other accents there are special math commands to be used in formulas,
26434 \begin_inset CommandInset ref
26436 reference "sub:Accents-for-one"
26443 \begin_layout Standard
26444 \begin_inset VSpace bigskip
26447 Furthermore, with the command
26454 \begin_inset Index idx
26457 \begin_layout Plain Layout
26465 all numbers and letters can be set into a circle, quasi accented with a
26466 circle, similar to the copyright symbol.
26469 \begin_layout Standard
26471 \begin_inset Tabular
26472 <lyxtabular version="3" rows="3" columns="2">
26473 <features rotate="0" tabularvalignment="middle">
26474 <column alignment="center" valignment="top">
26475 <column alignment="center" valignment="top">
26477 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
26480 \begin_layout Plain Layout
26486 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
26489 \begin_layout Plain Layout
26491 \begin_inset Note Note
26494 \begin_layout Plain Layout
26501 is only used as spacer.
26513 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
26516 \begin_layout Plain Layout
26524 <cell multicolumn="1" alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
26527 \begin_layout Plain Layout
26531 \begin_layout Plain Layout
26547 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
26550 \begin_layout Plain Layout
26561 raisebox{-1.5pt}{W}}
26566 <cell multicolumn="1" alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
26569 \begin_layout Plain Layout
26570 \begin_inset Formula $\raisebox{4.5mm}{}$
26577 \begin_layout Plain Layout
26595 \begin_inset Formula $\raisebox{-2mm}{}$
26611 \begin_layout Standard
26612 One has to take care that the character fits in the circle.
26623 \begin_layout Plain Layout
26625 \begin_inset CommandInset ref
26627 reference "sub:Font-Sizes"
26636 specifies thereby the size of the circle.
26647 \begin_layout Plain Layout
26649 \begin_inset CommandInset ref
26651 reference "sub:Boxes-without-Frame"
26660 the character can be centered.
26663 \begin_layout Subsection
26665 \begin_inset Index idx
26668 \begin_layout Plain Layout
26677 \begin_layout Standard
26678 Old-style figures (also known as old-style numerals) are created with the
26686 \begin_inset Index idx
26689 \begin_layout Plain Layout
26698 The command can be used in formulas and in TeX-mode.
26699 The command scheme is:
26702 \begin_layout Standard
26707 oldstylenums{number}
26710 \begin_layout Standard
26715 oldstylenums{0123456789
26718 \begin_inset Formula $\oldstylenums{0123456789}$
26724 \begin_layout Section
26726 \begin_inset CommandInset label
26728 name "sec:Formula-Styles"
26733 \begin_inset Index idx
26736 \begin_layout Plain Layout
26745 \begin_layout Itemize
26746 There are two different alignment styles:
26750 \begin_layout Description
26751 Centered is the predefined standard
26754 \begin_layout Description
26755 Indented for this the option
26759 must be inserted in the menu
26761 Document\SpecialChar \menuseparator
26767 \begin_inset space ~
26773 \begin_layout Standard
26778 is used, the indentation can be adjusted with the length
26785 \begin_inset Index idx
26788 \begin_layout Plain Layout
26797 Should the distance be 15
26798 \begin_inset space \thinspace{}
26801 mm, the following command line is inserted in the LaTeX-preamble
26804 \begin_layout Standard
26814 \begin_layout Standard
26815 When no length is specified, the predefined value of 30
26816 \begin_inset space \thinspace{}
26823 \begin_layout Itemize
26824 And two different numbering styles:
26828 \begin_layout Description
26829 Right is the predefined standard
26832 \begin_layout Description
26833 Left for this the option
26837 must be inserted in the menu
26839 Document\SpecialChar \menuseparator
26845 \begin_inset space ~
26852 \begin_layout Standard
26861 can also be used together.
26862 In this case both options are inserted, separated by a comma.
26865 \begin_layout Standard
26866 The chosen styles are used for all displayed formulas of the document.
26867 When both, centered and indented formulas should be created in a document,
26873 The indented formulas are then set in a flalign environment, see
26874 \begin_inset CommandInset ref
26876 reference "sub:Flalign-Environment"
26883 \begin_layout Section
26885 \begin_inset CommandInset label
26887 name "sec:Multiline-Formulas"
26892 \begin_inset Index idx
26895 \begin_layout Plain Layout
26896 Formula ! multiline
26904 \begin_layout Subsection
26908 \begin_layout Standard
26909 In LyX multiline formulas are created by pressing
26912 arg "newline-insert newline"
26916 This creates either an
26918 eqnarray environment
26920 that is described in
26921 \begin_inset CommandInset ref
26923 reference "sub:Eqnarray-Environment"
26927 or, when the option
26929 Use AMS math package
26931 in the document settings is selected, an
26935 that is described in
26936 \begin_inset CommandInset ref
26938 reference "sub:Standard-align-Environment"
26943 The align environment is recommended because it provides in any case a
26944 typographically correct output.
26947 \begin_layout Standard
26948 There are other multiline formula environments that can be created via the
26951 Insert\SpecialChar \menuseparator
26955 These environments are described in the following sections.
26958 \begin_layout Standard
26959 In all multiline formula environments a new line is created by pressing
26963 arg "newline-insert newline"
26967 To add or delete lines, the math toolbar buttons
26970 arg "inset-modify tabular append-row"
26976 arg "inset-modify tabular delete-row"
26979 , respectively, or the menu
26981 Edit\SpecialChar \menuseparator
26987 \begin_layout Subsubsection
26989 \begin_inset CommandInset label
26991 name "sub:Line-Separation"
26996 \begin_inset Index idx
26999 \begin_layout Plain Layout
27000 Formula ! multiline ! Line separation
27008 \begin_layout Standard
27009 There is sometimes not enough space in multiline formulas between the lines:
27010 \begin_inset Formula
27012 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}\\
27013 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
27021 \begin_layout Standard
27022 In LaTeX additional line space is specified as optional argument of the
27024 This is not yet possible in LyX
27028 \begin_layout Plain Layout
27030 \begin_inset CommandInset href
27032 name "LyX-bug #1505"
27033 target "http://www.lyx.org/trac/ticket/1505"
27042 , therefore the whole formula must be inserted in TeX-mode.
27043 To add in our example space, the command
27051 is inserted at the end of the first line.
27056 \begin_layout Plain Layout
27063 \begin_layout Plain Layout
27065 B^{2}(B^{2}-2r_{g}^{2}+2x_{0}^{2}-2r_{k}^{2})+4x_{0}^{2}x^{2}+4x_{0}xD &
27068 textrm{-}4x^{2}B^{2}+4x_{0}xB^{2}
27075 \begin_layout Plain Layout
27079 left(B^{2}+x_{0}^{2}
27087 left(B^{2}-2r_{g}^{2}+2x_{0}^{2}-2r_{k}^{2}
27092 \begin_layout Plain Layout
27104 \begin_layout Standard
27105 \begin_inset VSpace bigskip
27108 To set the line separation for all lines in a formula, the length
27115 \begin_inset Index idx
27118 \begin_layout Plain Layout
27128 \begin_inset Formula $\mbox{line separation}=\mathrm{6\, pt+\backslash jot}$
27139 \begin_inset space \thinspace{}
27144 \begin_inset space \thinspace{}
27147 mm additional line separation as in the previous example, the command
27150 \begin_layout Standard
27160 \begin_layout Standard
27161 is inserted in TeX-mode before the formula.
27162 This requires that the LaTeX-package
27170 \begin_layout Plain Layout
27175 is part of every LaTeX standard installation.
27181 \begin_inset Index idx
27184 \begin_layout Plain Layout
27190 was loaded in LaTeX-preamble with the line
27193 \begin_layout Standard
27201 \begin_layout Standard
27206 \begin_layout Plain Layout
27218 \begin_inset Formula
27220 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}\\
27221 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
27229 \begin_layout Standard
27233 \begin_layout Plain Layout
27244 To get back to the predefined distance,
27250 is set to the value 3
27251 \begin_inset space \thinspace{}
27257 \begin_layout Subsubsection
27259 \begin_inset CommandInset label
27261 name "sub:Column-Separation"
27266 \begin_inset Index idx
27269 \begin_layout Plain Layout
27270 Formula ! multiline ! Column separation
27278 \begin_layout Standard
27279 Multiline formulas form a matrix.
27280 A formula in the eqnarray environment is for example a matrix with three
27282 By changing the column separation in this environment, the space beside
27283 the relation sign can be changed.
27286 \begin_layout Standard
27287 The column separation is specified with the length
27294 \begin_inset Index idx
27297 \begin_layout Plain Layout
27306 \begin_inset Newline newline
27309 column separation = 2
27310 \begin_inset space \thinspace{}
27320 \begin_inset Newline newline
27326 \begin_layout Standard
27336 \begin_layout Standard
27337 inserted in TeX-mode, sets for all following formulas a column separation
27339 \begin_inset space \thinspace{}
27343 To get back to the predefined distance,
27350 \begin_inset space \thinspace{}
27356 \begin_layout Standard
27358 \begin_inset space \thinspace{}
27361 cm column separation:
27365 \begin_layout Plain Layout
27377 \begin_inset Formula
27385 A formula with the predefined column separation for matrices of 10
27386 \begin_inset space \thinspace{}
27393 \begin_layout Plain Layout
27405 \begin_inset Formula
27416 \begin_layout Subsubsection
27418 \begin_inset Index idx
27421 \begin_layout Plain Layout
27430 \begin_layout Standard
27431 Long formulas can be typeset using these methods:
27434 \begin_layout Itemize
27435 When one side of the equation is much shorter than the line width, this
27436 one is chosen for the left side and the right side is typeset over two
27438 \begin_inset Formula
27440 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 \\
27441 & & -\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}
27446 The minus sign at the beginning of the second line does normally not appear
27447 as an operator because it is the first character of the line.
27448 Thus it would not be surrounded by space and could not be distinguished
27449 from the fraction bar.
27451 \begin_inset space \thinspace{}
27454 pt space was inserted behind the minus sign with the command
27464 \begin_layout Plain Layout
27472 \begin_inset CommandInset ref
27474 reference "sub:Variable-Space"
27484 \begin_inset Index idx
27487 \begin_layout Plain Layout
27498 \begin_layout Itemize
27499 When both sides of the equation are too long, the command
27506 \begin_inset Index idx
27509 \begin_layout Plain Layout
27518 It is inserted in the first column of the first line and causes all further
27519 insertions to overwrite the following columns:
27520 \begin_inset Formula
27522 \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 \\
27523 & & -\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 \\
27524 & & =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}
27529 After the insertion of
27535 , the cursor is in a purple box that is a bit shifted to the left from the
27537 In this the formula is inserted.
27538 \begin_inset Newline newline
27541 The content of the further lines is inserted to the second or another formula
27543 The greater the column number where it was inserted, the larger the indentation.
27544 \begin_inset VSpace medskip
27548 \begin_inset Newline newline
27552 \begin_inset Note Greyedout
27555 \begin_layout Plain Layout
27556 Note the following when using
27565 \begin_layout Itemize
27566 The formula doesn't use the full page width.
27568 \begin_inset space \thinspace{}
27572 \begin_inset space \space{}
27576 \begin_inset Formula $-B^{2}$
27579 is added to the first line in the above example, it would have been outside
27581 To better use the width, negative space can be inserted at the beginning
27585 \begin_layout Itemize
27586 Due to a bug in LyX the cursor cannot be set with the mouse into the first
27591 \begin_layout Plain Layout
27592 \begin_inset CommandInset href
27594 name "LyX-bug #1429"
27595 target "http://www.lyx.org/trac/ticket/1429"
27604 One can only set the cursor at the beginning of the line and move it with
27613 \begin_layout Itemize
27614 Other methods to set long formulas are offered by the environments described
27616 \begin_inset CommandInset ref
27618 reference "sub:Multline-Environment"
27623 \begin_inset CommandInset ref
27625 reference "sub:Multiline-Formula-Parts"
27632 \begin_layout Subsubsection
27633 Multiline Fractions
27634 \begin_inset CommandInset label
27636 name "sub:Multiline-Fractions"
27641 \begin_inset Index idx
27644 \begin_layout Plain Layout
27645 Fractions ! multiline
27653 \begin_layout Standard
27654 There are cases where the denominator and/or the numerator of a fraction
27655 is so long that the fraction does not fit into one line.
27656 It is then necessary to add a line break within the fraction.
27657 This can be done using the command
27664 \begin_inset Index idx
27667 \begin_layout Plain Layout
27676 To activate it, set in the document settings under
27679 \begin_inset space ~
27689 \begin_inset Index idx
27692 \begin_layout Plain Layout
27693 Packages ! mathtools
27701 \begin_inset space ~
27716 \begin_layout Standard
27721 splitfrac{first line}{second line}
27724 \begin_layout Standard
27725 and is used as denominator and/or numerator:
27728 \begin_layout Standard
27729 \begin_inset Formula
27731 a=\frac{\splitfrac{xy+xy+xy+xy+xy}{+wy+wy+wy+wy}}{z}\ne\frac{\splitdfrac{xy+\frac{xy}{z}+xy+xy+xy}{+xy+xy+xy+xy}}{z}
27736 The command for the first numerator above is:
27739 \begin_layout Standard
27745 \begin_inset space \textvisiblespace{}
27751 \begin_inset space \textvisiblespace{}
27759 \begin_layout Subsubsection
27761 \begin_inset CommandInset label
27763 name "sub:Multiline-Brackets"
27768 \begin_inset Index idx
27771 \begin_layout Plain Layout
27772 Brackets ! for multiline expressions
27780 \begin_layout Standard
27781 For brackets spanning multiple lines the following problem occurs:
27782 \begin_inset Formula
27784 A & = & \sin(x)\left[\prod_{R=1}^{\infty}\frac{1}{R}+\cdots\right.\\
27785 & & \left.\cdots+B-D\right]
27793 \begin_layout Standard
27794 The closing bracket is smaller than the opening bracket because brackets
27795 with variable size may not span multiple lines.
27798 \begin_layout Standard
27799 To set the bracket size for the second line correctly, the first line is
27807 \begin_inset Index idx
27810 \begin_layout Plain Layout
27818 and the second line with
27826 \begin_layout Plain Layout
27840 \begin_inset CommandInset ref
27842 reference "sub:Automatic-Bracket-Size"
27854 \begin_inset Index idx
27857 \begin_layout Plain Layout
27880 \begin_inset space \textvisiblespace{}
27890 \begin_inset space \textvisiblespace{}
27900 \begin_inset space \textvisiblespace{}
27906 \begin_inset Formula $\downarrow$
27912 \begin_inset Index idx
27915 \begin_layout Plain Layout
27923 is inserted, because the multiplication operator with its limits is the
27924 largest symbol in the first line and this should be the size for the bracket
27925 in the second line.
27928 \begin_layout Standard
27929 The result is this:
27930 \begin_inset Formula
27932 A & = & \sin(x)\left[\prod_{R=1}^{\infty}\frac{1}{R}+\cdots\right.\\
27933 & & \left.\vphantom{\prod_{R=1}^{\infty}}\cdots+B-D\right]
27941 \begin_layout Subsection
27945 \begin_layout Standard
27946 Align environments can be used for every kind of multiline formulas.
27947 They are especially useful to set several formulas side by side.
27950 \begin_layout Standard
27951 Align environments consist of columns.
27952 The odd columns are right aligned, the even ones left aligned.
27953 Every line in an Align environment can be numbered.
27956 \begin_layout Standard
27957 Align environments are created via the menu
27959 Insert\SpecialChar \menuseparator
27965 Edit\SpecialChar \menuseparator
27966 Math\SpecialChar \menuseparator
27967 Change Formula Type
27969 already existing formulas can be converted to Align environments.
27972 \begin_layout Standard
27973 To add or delete columns, the math toolbar buttons
27976 arg "inset-modify tabular append-column"
27982 arg "inset-modify tabular delete-column"
27985 , respectively, or the menu
27987 Edit\SpecialChar \menuseparator
27993 \begin_layout Subsubsection
27994 Standard align Environment
27995 \begin_inset CommandInset label
27997 name "sub:Standard-align-Environment"
28002 \begin_inset Index idx
28005 \begin_layout Plain Layout
28006 Formula ! multiline ! align environment
28014 \begin_layout Standard
28015 This Align environment is created by pressing
28018 arg "newline-insert newline"
28021 in a formula or by the menu
28023 Insert\SpecialChar \menuseparator
28024 Math\SpecialChar \menuseparator
28025 AMS align Environment
28030 \begin_layout Standard
28031 An example for two formulas set side by side, that are created with a four
28032 column align environment:
28033 \begin_inset Formula
28035 A & =\sin(B) & C & =D\\
28036 C & \ne A & B & \ne D
28041 As it can be seen, the formulas in this environment are placed so as if
28050 \begin_layout Plain Layout
28058 \begin_inset CommandInset ref
28060 reference "sub:Variable-Space"
28071 before the first and after every even column.
28072 When the formula style
28078 \begin_layout Plain Layout
28080 \begin_inset CommandInset ref
28082 reference "sec:Formula-Styles"
28093 is used, the formula is set without the
28099 before the first column.
28102 \begin_layout Subsubsection
28103 Alignat Environment
28104 \begin_inset Index idx
28107 \begin_layout Plain Layout
28108 Formula ! multiline ! alignat environment
28116 \begin_layout Standard
28117 The alignat environment has no predefined column separation.
28118 It can be inserted manually with the spaces that are described
28119 \begin_inset CommandInset ref
28121 reference "sub:Space"
28128 \begin_layout Standard
28129 The above example in the alignat environment where 1
28130 \begin_inset space \thinspace{}
28133 cm space was inserted at the beginning of the second formula:
28134 \begin_inset Formula
28135 \begin{alignat*}{2}
28136 A & =\sin(B) & \hspace{1cm}C & =D\\
28137 C & \ne A & B & \ne D
28142 Because the column separation can be set separately for every column, this
28143 environment is especially suitable to set three and more formulas side
28147 \begin_layout Subsubsection
28148 Flalign Environment
28149 \begin_inset CommandInset label
28151 name "sub:Flalign-Environment"
28156 \begin_inset Index idx
28159 \begin_layout Plain Layout
28160 Formula ! multiline ! flalign environment
28168 \begin_layout Standard
28169 In this environment the first two columns are always set as much as possible
28170 to the left and the last two ones to the right.
28172 \begin_inset Formula
28174 A & =1 & B & =2 & C & =3\\
28175 X & =\textrm{-}1 & Y & =\textrm{-}2 & Z & =4
28183 \begin_layout Standard
28184 By creating a flalign environment with an odd number of columns where an
28185 empty TeX-brace is inserted to the last column, several formulas in a document
28186 can be set to the left, although the formula style
28191 As example the indented formula
28192 \begin_inset CommandInset ref
28194 reference "eq:VolInt"
28199 \begin_inset Formula
28201 \hspace{30pt}\iiint\limits _{V}X\,\mathrm{d}V & =U & {}
28206 The first two columns contain the formula.
28207 To indent it as with the formula style
28212 \begin_inset space \thinspace{}
28215 pt space was inserted at the beginning of the first column.
28218 \begin_layout Subsection
28219 Eqnarray Environment
28220 \begin_inset CommandInset label
28222 name "sub:Eqnarray-Environment"
28227 \begin_inset Index idx
28230 \begin_layout Plain Layout
28231 Formula ! multiline ! eqnarray environment
28239 \begin_layout Standard
28240 When this environment has been created, three blue boxes appear.
28241 The content of the first box is right aligned, the content of the last
28243 The content of the middle box appears centered and a bit smaller, because
28244 it is designed to insert there only relation characters.
28245 \begin_inset Formula
28247 \frac{ABC}{D} & \frac{ABC}{D} & \frac{ABC}{D}\\
28257 \begin_layout Subsection
28259 \begin_inset Index idx
28262 \begin_layout Plain Layout
28263 Formula ! multiline ! gather environment
28271 \begin_layout Standard
28272 This environment consists of only one centered column.
28273 Every line can be numbered.
28274 \begin_inset Formula
28285 \begin_layout Subsection
28286 Multline Environment
28287 \begin_inset CommandInset label
28289 name "sub:Multline-Environment"
28294 \begin_inset Index idx
28297 \begin_layout Plain Layout
28298 Formula ! multiline ! multline environment
28306 \begin_layout Standard
28307 The multline environment consists, like the gather environment, of only
28309 But the first line is left aligned, the last one right aligned.
28310 All other lines are centered.
28311 Therefore this environment is suitable for long formulas.
28313 \begin_inset CommandInset ref
28315 reference "eq:lefteqn"
28319 in the multline environment:
28320 \begin_inset Formula
28322 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}\\
28323 -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}\\
28324 =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}}
28332 \begin_layout Standard
28333 In the output only the last (first) line of a multline environment appears
28334 numbered when the document numbering is right (left).
28338 \begin_layout Plain Layout
28339 numbering styles see
28340 \begin_inset CommandInset ref
28342 reference "sec:Formula-Styles"
28354 \begin_layout Standard
28362 \begin_inset Index idx
28365 \begin_layout Plain Layout
28380 \begin_inset Index idx
28383 \begin_layout Plain Layout
28391 a centered line can be right or left aligned, respectively.
28392 The commands are used as follows:
28395 \begin_layout Standard
28400 shoveright{line content}
28406 shoveleft{line content}
28409 \begin_layout Standard
28410 \begin_inset VSpace medskip
28420 \begin_inset Index idx
28423 \begin_layout Plain Layout
28431 specifies the distance of the first line from the left page margin.
28432 Predefined is the length 0
28433 \begin_inset space \thinspace{}
28439 \begin_layout Standard
28440 As example the above formula where the command
28443 \begin_layout Standard
28453 \begin_layout Standard
28454 was inserted in TeX-mode before:
28458 \begin_layout Plain Layout
28470 \begin_inset Formula
28472 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}\\
28473 \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}}\\
28474 =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}}
28483 \begin_layout Plain Layout
28494 The second line was left aligned using
28503 \begin_layout Subsection
28504 Multiline Formula Parts
28505 \begin_inset CommandInset label
28507 name "sub:Multiline-Formula-Parts"
28512 \begin_inset Index idx
28515 \begin_layout Plain Layout
28516 Formula ! multiline ! formula parts
28524 \begin_layout Standard
28525 To display only parts of a formula with multiple lines, one of the following
28526 environments is used:
28543 They can be inserted via the menu
28545 Insert\SpecialChar \menuseparator
28548 or by using the commands described in this section.
28551 \begin_layout Standard
28552 The first three have the same properties as the corresponding multiline
28553 formula environments, but it is possible to set further formula parts beside
28556 \begin_inset Formula
28558 \left.\begin{aligned}\Delta x\Delta p & \ge\frac{\hbar}{2}\\
28559 \Delta E\Delta t & \ge\frac{\hbar}{2}
28561 \right\} \textrm{Uncertainty relations}
28569 \begin_layout Standard
28570 To get this formula, a displayed formula is created where the command
28577 \begin_inset Index idx
28580 \begin_layout Plain Layout
28589 A purple box appears around the blue formula box where now columns and
28590 lines can be added.
28591 Outside the multiline environment other formula parts can be set, like
28595 \begin_layout Standard
28596 The aligned environment is also suitable for long formulas whose lines are
28597 horizontally aligned.
28598 Using aligned in a displayed formula has the advantage that the formula
28599 number is vertically centered behind the lines.
28601 \begin_inset CommandInset ref
28603 reference "eq:shortlong"
28607 in the aligned environment:
28608 \begin_inset Formula
28610 \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}|}\\
28611 & -\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}|}
28620 \begin_layout Standard
28621 To use the environments
28640 \begin_inset Index idx
28643 \begin_layout Plain Layout
28658 \begin_inset Index idx
28661 \begin_layout Plain Layout
28676 \begin_inset Index idx
28679 \begin_layout Plain Layout
28687 are inserted, respectively.
28688 The split environment has the same properties as the aligned environment
28689 but it can only have two columns.
28692 \begin_layout Subsection
28693 Text in multiline Formulas
28694 \begin_inset CommandInset label
28696 name "sub:Text-in-multiline"
28701 \begin_inset Index idx
28704 \begin_layout Plain Layout
28711 \begin_inset Index idx
28714 \begin_layout Plain Layout
28715 Formula ! multiline ! text
28723 \begin_layout Standard
28724 In the Align environments, and the multline and gather environment, text
28725 can be inserted that will appear in a separate line and doesn't affect
28726 the column alignment.
28727 To do this, the command
28734 \begin_inset Index idx
28737 \begin_layout Plain Layout
28745 is used in the following scheme:
28748 \begin_layout Standard
28756 \begin_layout Standard
28757 The text should not be longer than a line because it cannot be hyphenated.
28758 As LyX doesn't yet support
28764 directly, the text is written as mathematical text.
28771 must hereby be at the beginning of a line and appears in the output above
28773 An example where the text was inserted at the beginning of the second line:
28774 \begin_inset Formula
28776 I & =a\sqrt{2}\int_{0}^{2\pi}\sqrt{1+\cos(\phi)}\;\mathrm{d}\phi\\
28777 \intertext{\text{integrand is symmetric to \ensuremath{\phi=\pi}, therefore}} & =2a\sqrt{2}\int_{0}^{\pi}\sqrt{1+\cos(\phi)}\;\mathrm{d}\phi
28785 \begin_layout Standard
28792 always creates some vertical space between the text and the formula lines.
28793 To avoid this space, set in the document settings under
28796 \begin_inset space ~
28806 \begin_inset Index idx
28809 \begin_layout Plain Layout
28810 Packages ! mathtools
28818 \begin_inset space ~
28824 Then you can use the command
28831 \begin_inset Index idx
28834 \begin_layout Plain Layout
28849 \begin_inset Newpage newpage
28855 \begin_layout Standard
28856 \begin_inset Formula
28858 I & =a\sqrt{2}\int_{0}^{2\pi}\sqrt{1+\cos(\phi)}\;\mathrm{d}\phi\\
28859 \shortintertext{\text{integrand is symmetric to \ensuremath{\phi=\pi}, therefore}} & =2a\sqrt{2}\int_{0}^{\pi}\sqrt{1+\cos(\phi)}\;\mathrm{d}\phi
28867 \begin_layout Section
28869 \begin_inset Index idx
28872 \begin_layout Plain Layout
28879 \begin_inset Index idx
28882 \begin_layout Plain Layout
28883 Formula ! numbering|see
28887 \begin_layout Plain Layout
28898 \begin_layout Plain Layout
28913 \begin_layout Subsection
28917 \begin_layout Standard
28918 Numbered formulas can be created with the menu
28920 Insert\SpecialChar \menuseparator
28921 Math\SpecialChar \menuseparator
28923 \begin_inset space ~
28931 \begin_inset space ~
28937 Existing formulas can be numbered with the menu
28939 Edit\SpecialChar \menuseparator
28940 Math\SpecialChar \menuseparator
28942 \begin_inset space ~
28950 arg "math-number-toggle"
28954 The formula number is displayed in LyX behind the formula as a number sign
28956 The number sign is replaced in the output by the formula number.
28959 \begin_layout Standard
28960 When numbering is turned on in multiline formulas, all lines will be numbered.
28961 But the numbering can be controlled with the menu
28963 Edit\SpecialChar \menuseparator
28964 Math\SpecialChar \menuseparator
28966 \begin_inset space ~
28970 \begin_inset space ~
28974 \begin_inset space ~
28982 arg "math-number-line-toggle"
28988 \begin_layout Standard
28989 Except for inline formulas, all formulas can be numbered with two different
28991 \begin_inset CommandInset ref
28993 reference "sec:Formula-Styles"
29000 \begin_layout Subsection
29002 \begin_inset Index idx
29005 \begin_layout Plain Layout
29006 Cross-references ! to formulas
29014 \begin_layout Standard
29015 All labeled formulas can be cross-referenced.
29016 A label is added by the menu
29018 Insert\SpecialChar \menuseparator
29021 or the toolbar button
29028 The cursor must hereby be inside a displayed formula.
29029 Alternatively you can right-click on the formula and choose
29034 A dialog pops up displaying the prefix
29039 The label is inserted there behind the prefix.
29040 The predefined prefix means
29041 \begin_inset Quotes eld
29045 \begin_inset Quotes erd
29048 and makes it easier to find labels in large documents because it marks
29049 it as formula label to divide it from e.
29050 \begin_inset space \thinspace{}
29054 \begin_inset space \space{}
29058 To change a label, the menu
29060 Insert\SpecialChar \menuseparator
29063 is used again or you right-click on a formula and then on
29070 \begin_layout Standard
29071 The name of the label is displayed in LyX within two parentheses behind
29073 A formula with a label is always numbered.
29076 \begin_layout Standard
29077 Cross-references are inserted via the menu
29079 Insert\SpecialChar \menuseparator
29082 or with the toolbar button
29085 arg "dialog-show-new-inset ref"
29089 A formula cross-reference appears in the output as formula number.
29090 When in the cross-reference dialog window the format
29094 is chosen, the cross-reference appears in the output as formula number
29096 \begin_inset Newline newline
29099 By right-clicking on a cross-reference in LyX, one jumps to the formula
29100 that is referenced.
29103 \begin_layout Standard
29104 Here are as examples cross-references to formulas of the following subsections:
29105 \begin_inset Note Note
29108 \begin_layout Plain Layout
29109 Note the different cross-reference types.
29117 \begin_layout Standard
29119 \begin_inset CommandInset ref
29126 \begin_inset CommandInset ref
29134 \begin_inset CommandInset ref
29140 ) big Latin letters are used for the numbering in contrary to (
29141 \begin_inset CommandInset ref
29150 \begin_layout Standard
29151 \begin_inset VSpace medskip
29154 When the argument of
29162 \begin_layout Plain Layout
29170 \begin_inset CommandInset ref
29172 reference "sub:User-defined-Numbering"
29183 contains a box like in
29184 \begin_inset CommandInset ref
29186 reference "sub:Paragraph-Boxes"
29190 , the formula cannot be referenced.
29193 \begin_layout Subsection
29195 \begin_inset Index idx
29198 \begin_layout Plain Layout
29199 Formula numbering ! subnumbering
29207 \begin_layout Standard
29208 With the help of the commands
29212 begin{subequations}
29220 formulas can be subnumbered.
29221 Both commands are inserted in TeX-mode.
29224 \begin_layout Standard
29226 \begin_inset Formula
29237 \begin_layout Plain Layout
29241 addtocounter{equation}{-1}
29250 \begin_layout Plain Layout
29254 begin{subequations}
29260 \begin_inset VSpace -5mm
29264 \begin_inset Formula
29272 \begin_inset Formula
29282 \begin_layout Standard
29286 \begin_layout Plain Layout
29298 \begin_layout Standard
29299 To create the example, the following is done:
29302 \begin_layout Enumerate
29303 first formula is inserted
29306 \begin_layout Enumerate
29311 addtocounter{equation}{-1}
29313 begin{subequations}
29314 \begin_inset Index idx
29317 \begin_layout Plain Layout
29326 \begin_inset Newline newline
29331 is inserted after the first formula
29334 \begin_layout Enumerate
29335 second formula is inserted
29338 \begin_layout Enumerate
29339 third formula is inserted
29342 \begin_layout Enumerate
29349 is inserted after the third formula
29352 \begin_layout Standard
29353 Every formula between the commands
29365 is subnumbered as a, b,
29366 \begin_inset Newline linebreak
29369 c, \SpecialChar \ldots{}
29370 For multiline formulas every line will be subnumbered.
29371 All subnumbered formulas are treated as
29376 But as every numbered formula increases the counter
29380 by one, the command
29386 is needed to decrease it.
29387 Otherwise the formulas
29388 \begin_inset CommandInset ref
29395 \begin_inset CommandInset ref
29402 \begin_inset CommandInset ref
29408 would be numbered as
29409 \begin_inset CommandInset ref
29416 \begin_inset CommandInset ref
29423 \begin_inset CommandInset ref
29432 \begin_layout Standard
29433 By inserting the commands in TeX-mode, a space is created between the first
29436 \begin_inset space \thinspace{}
29439 mm vertical space is inserted after the command
29443 begin{subequations}
29446 When the formula style
29452 \begin_layout Plain Layout
29454 \begin_inset CommandInset ref
29456 reference "sec:Formula-Styles"
29468 \begin_inset space \thinspace{}
29471 mm space is inserted instead.
29474 \begin_layout Standard
29475 Here is an example for a multiline formula where the numbering was turned
29476 off for the second line:
29480 \begin_layout Plain Layout
29484 begin{subequations}
29490 \begin_inset Formula
29492 A & = & (B-Z)^{2}=(B-Z)(B-Z)\label{eq:d}\\
29493 & = & B^{2}-ZB-BZ+Z^{2}\nonumber \\
29494 & = & B^{2}-2BZ+Z^{2}\label{eq:f}
29503 \begin_layout Plain Layout
29515 \begin_layout Subsection
29516 User-defined Numbering
29517 \begin_inset CommandInset label
29519 name "sub:User-defined-Numbering"
29524 \begin_inset Index idx
29527 \begin_layout Plain Layout
29528 Formula numbering ! user-defined
29536 \begin_layout Standard
29537 \begin_inset Index idx
29540 \begin_layout Plain Layout
29541 Formula numbering ! self-defined delimiters
29546 With the standard numbering parentheses are set around the formula number.
29547 To replace the parentheses for example by vertical bars, the following
29548 line is added to the LaTeX-preamble:
29551 \begin_layout Standard
29563 \begin_inset Note Note
29566 \begin_layout Plain Layout
29567 This macro is already declared in the LaTeX-preamble for testing.
29568 To activate it, remove the percent sign at the beginning.
29576 \begin_layout Standard
29577 To use other characters, the vertical bars besides the
29581 are replaced by one ore more characters.
29582 To get only the formula number the vertical bars are omitted.
29585 \begin_layout Standard
29586 \begin_inset VSpace bigskip
29589 When there should be an expression of your choice instead of the consecutive
29590 formula number in parentheses behind the formula, the command
29597 \begin_inset Index idx
29600 \begin_layout Plain Layout
29609 \begin_inset Formula
29611 A+B=C\tag{something}\label{eq:tag}
29616 In this example the command
29621 \begin_inset space \textvisiblespace{}
29626 was inserted in the formula.
29629 \begin_layout Standard
29635 \begin_inset space \textvisiblespace{}
29640 is inserted instead, the star prevents the parentheses around the expression:
29641 \begin_inset Formula
29643 A+B=C\tag*{something}
29651 \begin_layout Standard
29652 \begin_inset VSpace bigskip
29655 To restart the formula numbering with new document parts or sections, the
29656 following command is used:
29659 \begin_layout Standard
29664 @addtoreset{equation}{part}
29667 \begin_inset Index idx
29670 \begin_layout Plain Layout
29675 \begin_layout Plain Layout
29686 \begin_layout Plain Layout
29699 \begin_layout Plain Layout
29710 \begin_layout Plain Layout
29723 \begin_inset Newline newline
29727 \begin_inset Newline newline
29734 @addtoreset{equation}{section}
29737 \begin_layout Standard
29738 To be able to use these commands in TeX-mode, the
29739 \begin_inset Quotes eld
29743 \begin_inset Quotes erd
29746 character has to be made
29747 \begin_inset Quotes eld
29751 \begin_inset Quotes erd
29754 for LaTeX using the command
29768 So the command sequence in TeX-mode is:
29771 \begin_layout Standard
29777 \begin_inset Newline newline
29782 @addtoreset{equation}{section}
29783 \begin_inset Newline newline
29791 \begin_layout Standard
29792 In the LaTeX-preamble
29804 can be omitted as they are automatically internally inserted by LyX.
29807 \begin_layout Standard
29822 \begin_layout Plain Layout
29827 is part of the LaTeX-package
29832 \begin_inset Index idx
29835 \begin_layout Plain Layout
29836 Packages ! carlisle
29841 that is part of every LaTeX standard installation.
29847 \begin_inset Index idx
29850 \begin_layout Plain Layout
29851 Packages ! remreset
29856 has to be loaded in the LaTeX-preamble with the line
29859 \begin_layout Standard
29864 usepackage{remreset}
29867 \begin_layout Standard
29875 \begin_inset Index idx
29878 \begin_layout Plain Layout
29883 \begin_layout Plain Layout
29894 \begin_layout Plain Layout
29907 \begin_layout Plain Layout
29918 \begin_layout Plain Layout
29930 can be used with the same scheme as
29939 \begin_layout Standard
29940 \begin_inset VSpace bigskip
29943 Sometimes formulas should be numbered in the following form:
29946 \begin_layout Standard
29949 (section number.formula number)
29952 \begin_layout Standard
29953 The formula number should start with every section with
29954 \begin_inset Quotes eld
29958 \begin_inset Quotes erd
29964 \begin_layout Standard
29965 For this case there is the command
29972 \begin_inset Index idx
29975 \begin_layout Plain Layout
29983 , which is used with the following scheme:
29986 \begin_layout Standard
29991 numberwithin{counter}{sectioning}
29994 \begin_layout Standard
29995 Counter denotes what kind of numbering is affected, sectioning denotes what
29996 number is before the dot.
29999 \begin_layout Standard
30000 Thus in our case the following LaTeX-preamble or TeX code line is used:
30003 \begin_layout Standard
30008 numberwithin{equation}{section}
30011 \begin_layout Standard
30012 This is the result:
30016 \begin_layout Plain Layout
30020 numberwithin{equation}{section}
30026 \begin_inset Formula
30036 \begin_layout Standard
30038 \begin_inset space \thinspace{}
30042 \begin_inset space \space{}
30045 tables so that the number of the part is the sectioning,
30046 \begin_inset Newline newline
30053 numberwithin{table}{part}
30058 \begin_layout Standard
30059 To go back to the standard numbering or to prevent this kind of numbering
30060 when it is defined by the document class, the following command is inserted
30061 as TeX code or to the LaTeX-preamble:
30064 \begin_layout Standard
30074 \begin_inset Index idx
30077 \begin_layout Plain Layout
30091 \begin_layout Plain Layout
30107 \begin_inset Newline newline
30115 \begin_inset Newline newline
30127 \begin_layout Standard
30134 uses internally the command
30140 , described above, that also needs to be reverted.
30144 \begin_layout Plain Layout
30151 \begin_layout Plain Layout
30155 @removefromreset{equation}{section}
30158 \begin_layout Plain Layout
30170 \begin_layout Subsection
30171 Numbering with Roman Numbers and Letters
30172 \begin_inset Index idx
30175 \begin_layout Plain Layout
30176 Formula numbering ! with letters
30182 \begin_inset Index idx
30185 \begin_layout Plain Layout
30186 Formula numbering ! with Roman numbers
30194 \begin_layout Standard
30195 Formulas can also be numbered with Roman numbers and Latin letters.
30196 To number for example with small Roman numbers, the command
30199 \begin_layout Standard
30211 \begin_layout Standard
30212 is inserted before the formula in TeX-mode.
30220 \begin_inset Index idx
30223 \begin_layout Plain Layout
30231 redefines the predefined command
30247 \begin_layout Plain Layout
30254 has the same scheme like the command
30260 that is described in
30261 \begin_inset CommandInset ref
30263 reference "sub:The-Command-newcommand"
30276 is the formula counter.
30283 is used as prefix for a counter, the value of the counter is output as
30285 When a formula is numbered, LaTeX sets internally the command
30291 behind the formula.
30297 \begin_inset Index idx
30300 \begin_layout Plain Layout
30310 outputs the counter as small Roman number.
30313 \begin_layout Standard
30314 All formulas behind the command
30324 are now numbered Roman.
30325 To switch to numbering with big Roman numbers, the command is inserted
30339 \begin_inset Index idx
30342 \begin_layout Plain Layout
30354 \begin_inset Quotes eld
30358 \begin_inset Quotes erd
30361 with small Latin letters there is the command
30368 \begin_inset Index idx
30371 \begin_layout Plain Layout
30379 , for big ones there is the command
30386 \begin_inset Index idx
30389 \begin_layout Plain Layout
30402 \begin_layout Standard
30403 \begin_inset Note Greyedout
30406 \begin_layout Plain Layout
30413 \begin_inset space ~
30416 formulas can be numbered with Latin letters in one document.
30424 \begin_layout Standard
30428 \begin_layout Plain Layout
30444 \begin_layout Standard
30445 \begin_inset Formula
30447 A=\textrm{small roman}
30456 \begin_layout Plain Layout
30470 \begin_inset Formula
30472 B=\textrm{big Roman}\label{eq:Rom}
30481 \begin_layout Plain Layout
30495 \begin_inset Formula
30497 C=\textrm{small Latin}
30506 \begin_layout Plain Layout
30520 \begin_inset Formula
30522 D=\textrm{big Latin}\label{eq:Lat}
30530 \begin_layout Standard
30531 To switch back to the default numbering, insert the command:
30534 \begin_layout Standard
30544 \begin_inset Index idx
30547 \begin_layout Plain Layout
30558 \begin_layout Standard
30562 \begin_layout Plain Layout
30576 \begin_inset Formula
30586 \begin_layout Standard
30587 \begin_inset VSpace medskip
30590 As you see, formulas are numbered serially independent from the numbering
30592 When then numbering should start with
30593 \begin_inset Quotes eld
30597 \begin_inset Quotes erd
30600 when the style is changed, new equation counters have to be defined.
30601 A description about this can be found in the file
30602 \begin_inset CommandInset href
30604 name "Formula-numbering.lyx"
30605 target "run:Formula-numbering.lyx"
30612 \begin_layout Standard
30613 \begin_inset Newpage newpage
30619 \begin_layout Section
30620 Chemical Symbols and Equations
30621 \begin_inset CommandInset label
30623 name "sub:Chemical-Symbols-and"
30628 \begin_inset Index idx
30631 \begin_layout Plain Layout
30632 Chemical characters ! Symbols
30638 \begin_inset Index idx
30641 \begin_layout Plain Layout
30648 \begin_inset Index idx
30651 \begin_layout Plain Layout
30660 \begin_layout Standard
30661 An example text from chemistry:
30664 \begin_layout Quote
30666 \begin_inset Formula $\mathrm{SO_{4}^{2-}}$
30669 -ion reacts with two
30670 \begin_inset Formula $\mathrm{Na^{+}}$
30673 -ions to sodium sulfate
30674 \begin_inset Formula $\left(\mathrm{Na_{2}SO_{4}}\right)$
30678 The chemical equation for this is:
30679 \begin_inset Formula
30681 \mathrm{2\, Na^{+}+SO_{4}^{2-}\longrightarrow Na_{2}SO_{4}}\label{eq:chem-reaction}
30689 \begin_layout Standard
30690 This chemical equation can directly be created as formula.
30691 To avoid that the symbols appear italic, everything is highlighted and
30692 changed by the shortcut
30698 to the upright font style.
30702 \begin_layout Plain Layout
30708 \begin_inset CommandInset ref
30710 reference "sub:Font-Styles"
30722 \begin_layout Standard
30723 A more convenient way to typeset chemical formulas is to use the command
30731 \begin_inset Index idx
30734 \begin_layout Plain Layout
30742 that is available when the LaTeX-package
30747 \begin_inset Index idx
30750 \begin_layout Plain Layout
30763 to a formula a new blue box appears where chemical formulas can be inserted
30764 in an intuitive way.
30767 \begin_layout Standard
30769 \begin_inset Tabular
30770 <lyxtabular version="3" rows="9" columns="2">
30771 <features rotate="0" tabularvalignment="middle">
30772 <column alignment="center" valignment="top">
30773 <column alignment="center" valignment="top">
30775 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
30778 \begin_layout Plain Layout
30784 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
30787 \begin_layout Plain Layout
30789 \begin_inset Note Note
30792 \begin_layout Plain Layout
30799 is only used as spacer.
30811 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
30814 \begin_layout Plain Layout
30818 \begin_inset space \textvisiblespace{}
30826 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
30829 \begin_layout Plain Layout
30830 \begin_inset Formula $\raisebox{4.5mm}{}\ce{H2CO3}\raisebox{-2mm}{}$
30840 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
30843 \begin_layout Plain Layout
30847 \begin_inset space \textvisiblespace{}
30855 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
30858 \begin_layout Plain Layout
30859 \begin_inset Formula $\raisebox{5mm}{}\ce{SO4^{2-}}\raisebox{-2mm}{}$
30869 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
30872 \begin_layout Plain Layout
30876 \begin_inset space \textvisiblespace{}
30884 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
30887 \begin_layout Plain Layout
30888 \begin_inset Formula $\raisebox{4.5mm}{}\ce{(NH4)2S}\raisebox{-2mm}{}$
30898 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
30901 \begin_layout Plain Layout
30905 \begin_inset space \textvisiblespace{}
30913 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
30916 \begin_layout Plain Layout
30917 \begin_inset Formula $\raisebox{4.5mm}{}\ce{KCr(SO4)2.12H2O}\raisebox{-2mm}{}$
30927 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
30930 \begin_layout Plain Layout
30934 \begin_inset space \textvisiblespace{}
30940 \begin_inset space \textvisiblespace{}
30946 \begin_inset space \textvisiblespace{}
30954 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
30957 \begin_layout Plain Layout
30958 \begin_inset Formula $\raisebox{4.5mm}{}\ce{A-B\dbond C\tbond D}\raisebox{-2mm}{}$
30968 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
30971 \begin_layout Plain Layout
30975 \begin_inset space \textvisiblespace{}
30979 \begin_inset Formula $\downarrow$
30983 \begin_inset Formula $\to$
30991 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
30994 \begin_layout Plain Layout
30995 \begin_inset Formula $\raisebox{5mm}{}\ce{_{90}^{227}Th+}\raisebox{-2mm}{}$
31005 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
31008 \begin_layout Plain Layout
31012 \begin_inset space \textvisiblespace{}
31016 \begin_inset space \textvisiblespace{}
31020 \begin_inset space \textvisiblespace{}
31024 \begin_inset space \textvisiblespace{}
31028 \begin_inset space \textvisiblespace{}
31036 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
31039 \begin_layout Plain Layout
31040 \begin_inset Formula $\raisebox{4.5mm}{}\ce{CO2 + C <=> 2CO}\raisebox{-2mm}{}$
31050 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
31053 \begin_layout Plain Layout
31057 \begin_inset space \textvisiblespace{}
31061 \begin_inset space \textvisiblespace{}
31065 \begin_inset space \textvisiblespace{}
31069 \begin_inset space \textvisiblespace{}
31077 \begin_inset space \textvisiblespace{}
31085 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
31088 \begin_layout Plain Layout
31089 \begin_inset Formula $\raisebox{5mm}{}\ce{CO2 + C ->[\alpha][\beta] 2CO}\raisebox{-4mm}{}$
31105 \begin_layout Standard
31106 \begin_inset Note Greyedout
31109 \begin_layout Plain Layout
31115 Inserting a formula to a
31121 box will lead to LaTeX errors due to a LyX bug.
31127 \begin_layout Plain Layout
31128 \begin_inset CommandInset href
31130 name "LyX-bug #8566"
31131 target "http://www.lyx.org/trac/ticket/8566"
31142 In this case TeX code has to be used like for
31156 \begin_layout Plain Layout
31177 \begin_layout Standard
31178 \begin_inset Note Greyedout
31181 \begin_layout Plain Layout
31187 It is not possible in LyX to use the character ^ to get an up-arrow as
31193 One instead uses a negative thin space followed by the command
31200 \begin_inset Formula $\ce{Fe + 2H+ -> Fe^{2+} + H2\negthinspace\uparrow}$
31211 \begin_layout Standard
31218 the command for equation
31219 \begin_inset space ~
31223 \begin_inset CommandInset ref
31225 reference "eq:chem-reaction"
31230 \begin_inset Newline newline
31238 \begin_inset space \textvisiblespace{}
31242 \begin_inset space \textvisiblespace{}
31246 \begin_inset space \textvisiblespace{}
31250 \begin_inset space \textvisiblespace{}
31254 \begin_inset space \textvisiblespace{}
31258 \begin_inset space \textvisiblespace{}
31264 \begin_layout Standard
31265 To create multiline chemical equations first a multiline formula is created
31267 \begin_inset CommandInset ref
31269 reference "sec:Multiline-Formulas"
31274 Afterwards the command
31280 is used in every small blue box of the formula.
31282 \begin_inset CommandInset ref
31284 reference "eq:TEOS-reaction-1"
31289 \begin_inset CommandInset ref
31291 reference "eq:TEOS-reaction-2"
31295 are an example of a multi-stage chemical reaction where every equation
31296 has its own number.
31297 \begin_inset Formula
31299 \ce{TEOS + 4O} & \ce{->} & \ce{Si(OH)4 + 4C2H4O}\label{eq:TEOS-reaction-1}\\
31300 \ce{Si(OH)4} & \ce{->} & \ce{SiO2 + 2H2O}\label{eq:TEOS-reaction-2}
31308 \begin_layout Standard
31319 package provides the command
31326 \begin_inset Index idx
31329 \begin_layout Plain Layout
31337 that has to be used for special cases.
31338 For more information about
31344 and more examples have a look at the documentation of
31349 \begin_inset CommandInset citation
31358 \begin_layout Section
31362 \begin_layout Standard
31363 LyX supports two types of commutative diagrams:
31371 that are explained in the following.
31374 \begin_layout Subsection
31376 \begin_inset Index idx
31379 \begin_layout Plain Layout
31388 \begin_layout Standard
31389 Diagrams of this type visualize relations by vertical and horizontal lines
31391 \begin_inset Formula
31393 \begin{CD}A@>>>B@>>>C\\
31404 \begin_layout Standard
31405 To get them, the command
31410 \begin_inset Index idx
31413 \begin_layout Plain Layout
31423 is inserted to a formula.
31424 A blue box appears with two dashed lines where further commands can be
31429 arg "newline-insert newline"
31432 a new line is created.
31433 Horizontal relations are inserted in odd, vertical in even formula lines.
31436 \begin_layout Standard
31437 To create the relations there are the following commands:
31440 \begin_layout Itemize
31445 creates a left arrow,
31456 \begin_layout Itemize
31461 creates an up arrow,
31469 a vertical equal sign
31472 \begin_layout Itemize
31478 is a placeholder for non-existent relations
31481 \begin_layout Standard
31482 All arrows can be labeled as follows:
31485 \begin_layout Itemize
31486 If text inserted between the first and second < or >, resp., it is placed
31488 When it is inserted between the second and third one, it appears under
31492 \begin_layout Itemize
31493 When text for vertical arrows is inserted between the first and second A
31494 or V, resp., it is placed left beside the arrow.
31495 When it is inserted between the second and third one, it appears right
31497 If the text contains an A or V, these letters must be set into a TeX-brace.
31500 \begin_layout Standard
31501 As example a diagram with all possible relations:
31504 \begin_layout Standard
31505 \begin_inset Formula
31507 \begin{CD}A@>j>>B@>>k>C@=F\\
31518 \begin_layout Standard
31519 The command for this is:
31520 \begin_inset Newline newline
31528 \begin_inset space \textvisiblespace{}
31531 A@>j>>B@>>k>C@=F Ctrl+Return
31532 \begin_inset Newline newline
31536 \begin_inset Phantom HPhantom
31539 \begin_layout Plain Layout
31545 \begin_inset space \textvisiblespace{}
31558 \begin_inset Formula $\to$
31564 \begin_inset Newline newline
31568 \begin_inset Phantom HPhantom
31571 \begin_layout Plain Layout
31577 \begin_inset space \textvisiblespace{}
31588 \begin_layout Subsection
31590 \begin_inset Index idx
31593 \begin_layout Plain Layout
31594 Diagrams ! xymatrix
31602 \begin_layout Standard
31603 To be able to use xymatrices, the LaTeX-package
31608 A xymatrix is created by inserting the command
31615 Then you are able to add new matrix columns and rows like for normal matrices,
31617 \begin_inset CommandInset ref
31619 reference "sec:Matrices"
31626 \begin_layout Standard
31627 In contrary to amscd diagrams, xymatrices supports diagonal and curved arrows,
31629 All possibilities to create commutative diagrams and decorations are explained
31634 that you find in the menu
31636 Help\SpecialChar \menuseparator
31638 \begin_inset space ~
31646 \begin_layout Subsection
31652 \begin_inset Index idx
31655 \begin_layout Plain Layout
31664 \begin_layout Standard
31669 -diagrams, the LaTeX-package
31678 -diagram is created by inserting the command
31685 Then you are able to add new matrix columns and rows like for normal matrices,
31687 \begin_inset CommandInset ref
31689 reference "sec:Matrices"
31696 \begin_layout Standard
31697 Examples how to create
31701 diagrams in LyX is given in the
31703 Feynman-diagram manual
31705 that you find in the menu
31707 Help\SpecialChar \menuseparator
31709 \begin_inset space ~
31717 \begin_layout Standard
31718 \begin_inset Newpage newpage
31724 \begin_layout Section
31725 User-defined Commands
31726 \begin_inset Index idx
31729 \begin_layout Plain Layout
31730 User-defined commands
31738 \begin_layout Standard
31739 \begin_inset Note Greyedout
31742 \begin_layout Plain Layout
31747 The names of user-defined commands and macros may only consist of Latin
31756 \begin_layout Subsection
31760 \begin_inset CommandInset label
31762 name "sub:The-Command-newcommand"
31767 \begin_inset Index idx
31770 \begin_layout Plain Layout
31771 User-defined commands !
31779 \begin_inset Index idx
31782 \begin_layout Plain Layout
31793 \begin_layout Standard
31794 Many LaTeX-commands are too long to be used frequently.
31795 But it is possible to define with the command
31801 new shorter commands.
31804 \begin_layout Standard
31805 The command scheme of
31814 \begin_layout Standard
31819 newcommand{new command name}[number of arguments][optional
31824 \begin_inset Newline newline
31828 \begin_inset Phantom HPhantom
31831 \begin_layout Plain Layout
31841 {command definition}
31844 \begin_layout Standard
31845 \begin_inset Note Greyedout
31848 \begin_layout Plain Layout
31853 Assure that the name of the new command is not already used in your document
31854 or by LaTeX-packages that you use.
31855 When you for example define the command
31867 , you get an error message because
31873 is already defined as command for
31874 \begin_inset Quotes eld
31878 \begin_inset Formula $\le$
31882 \begin_inset Quotes erd
31893 \begin_layout Standard
31894 The number of arguments is an integer in the range 0
31895 \begin_inset space \thinspace{}
31899 \begin_inset space \thinspace{}
31902 9 and specifies how many arguments the new command should have.
31903 With the optional value a value for an optional argument can be predefined.
31904 When this is done, the
31912 rgument of the new command is automatically an optional one.
31915 \begin_layout Standard
31916 Here are some examples:
31919 \begin_layout Itemize
31920 To define the command
31932 , the LaTeX-preamble line is:
31933 \begin_inset VSpace medskip
31937 \begin_inset Newline newline
31951 \begin_layout Itemize
31952 To define the command
31964 , the argument (that should be underlined) must be taken into account.
31965 For this the preamble line is:
31966 \begin_inset VSpace medskip
31970 \begin_inset Newline newline
31984 \begin_inset VSpace medskip
31988 \begin_inset Newline newline
31995 acts as argument placeholder, the
31999 behind it denotes that it is the placeholder for the first argument.
32002 \begin_layout Itemize
32010 \begin_inset space \thinspace{}
32014 \begin_inset space \space{}
32024 \begin_inset VSpace medskip
32028 \begin_inset Newline newline
32039 framebox#1#2{$#3$}}
32042 \begin_inset VSpace medskip
32046 \begin_inset Newline newline
32049 The two Dollar signs creates the extra formula needed for
32056 \begin_inset CommandInset ref
32058 reference "sub:Boxes-with-Frame"
32065 \begin_layout Itemize
32066 To create a new command for
32072 where the color for the box need not be specified, the argument for the
32073 color is defined optional:
32074 \begin_inset VSpace medskip
32078 \begin_inset Newline newline
32089 fcolorbox{#2}{#1}{$#3$}}
32092 \begin_inset VSpace medskip
32096 \begin_inset Newline newline
32099 When the color is not specified when using
32105 , the predefined color
32112 \begin_layout Standard
32113 A test of the new defined commands:
32116 \begin_layout Standard
32118 \begin_inset Tabular
32119 <lyxtabular version="3" rows="6" columns="2">
32120 <features rotate="0" tabularvalignment="middle">
32121 <column alignment="center" valignment="top">
32122 <column alignment="center" valignment="top">
32124 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
32127 \begin_layout Plain Layout
32133 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
32136 \begin_layout Plain Layout
32138 \begin_inset Note Note
32141 \begin_layout Plain Layout
32148 is only used as spacer.
32160 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
32163 \begin_layout Plain Layout
32167 \begin_inset space \textvisiblespace{}
32175 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
32178 \begin_layout Plain Layout
32179 \begin_inset Formula $A\gr B$
32189 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
32192 \begin_layout Plain Layout
32200 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
32203 \begin_layout Plain Layout
32204 \begin_inset Formula $\raisebox{4.5mm}{}\us{ABcd}\raisebox{-2mm}{}$
32214 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
32217 \begin_layout Plain Layout
32221 \begin_inset Formula $\to$
32227 \begin_inset Formula $\to$
32235 \begin_inset space \textvisiblespace{}
32243 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
32246 \begin_layout Plain Layout
32247 \begin_inset Formula $\raisebox{6mm}{}\fb{[2cm]}{}{\int A=B}\raisebox{-4mm}{}$
32257 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
32260 \begin_layout Plain Layout
32264 \begin_inset Formula $\to$
32272 \begin_inset space \textvisiblespace{}
32280 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
32283 \begin_layout Plain Layout
32284 \begin_inset Formula $\raisebox{6mm}{}\cb{red}{\int A=B}\raisebox{-4mm}{}$
32294 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
32297 \begin_layout Plain Layout
32303 \begin_inset Formula $\to$
32311 \begin_inset space \textvisiblespace{}
32319 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
32322 \begin_layout Plain Layout
32323 \begin_inset Formula $\raisebox{6mm}{}\cb[green]{red}{\int A=B}\raisebox{-4mm}{}$
32339 \begin_layout Subsection
32341 \begin_inset Index idx
32344 \begin_layout Plain Layout
32345 User-defined commands! Math macros
32351 \begin_inset Index idx
32354 \begin_layout Plain Layout
32363 \begin_layout Standard
32364 User-defined commands are especially convenient for complex expressions.
32365 When you are for example dealing with a document that has quadratic equations,
32366 the same solution type occurs several times.
32367 The general form of a quadratic equation is
32368 \begin_inset Formula
32370 0=\lambda^{2}+p\lambda+q
32375 The general form of the solution is
32376 \begin_inset Formula
32378 \lambda_{1,2}=-\frac{p}{2}\pm\sqrt{\frac{p²}{4}-q}
32386 \begin_layout Standard
32387 To define a command for the solution formula where only the three parameters
32389 \begin_inset Formula $\lambda$
32393 \begin_inset Formula $p$
32397 \begin_inset Formula $q$
32400 need to be specified and the index of
32401 \begin_inset Formula $\lambda$
32404 can be given optionally, the LaTeX-preamble line is
32405 \begin_inset Newline newline
32421 \begin_inset Newline newline
32425 \begin_inset Phantom HPhantom
32428 \begin_layout Plain Layout
32442 frac{#3^{2}}{4}-#4}}
32445 \begin_layout Standard
32446 To create with this the solution formula, the command
32447 \begin_inset Newline newline
32457 \begin_inset Formula $\to$
32463 \begin_inset Formula $\to$
32470 is inserted to a formula
32475 \begin_layout Standard
32476 The definition of the new command is unintuitive because one has to know
32477 the schemes of all used LaTeX commands, e.
32478 \begin_inset space \thinspace{}
32482 \begin_inset space \space{}
32485 that a fraction is inserted in LaTeX as
32489 frac{numerator}{denominator}
32492 Furthermore one can easily forget a brace in the definition and cannot
32493 see in LyX what the new command is doing.
32494 To avoid these problems LyX offers the possibility to use math macros instead
32504 \begin_layout Standard
32505 A math macro is created by using the menu
32507 Insert\SpecialChar \menuseparator
32508 Math\SpecialChar \menuseparator
32511 or the toolbar button
32514 arg "math-macro newmacroname_newcommand"
32518 The math macro toolbar appears together with the following box where the
32520 \begin_inset Newline newline
32524 \begin_inset space \hspace*{\fill}
32528 \begin_inset Graphics
32529 filename clipart/macrobox.png
32534 \begin_inset space \hspace*{\fill}
32538 \begin_inset Newline newline
32542 \begin_inset FormulaMacro
32543 \newcommand{\qG}[4][1,\,2]{#2_{#1}=-\frac{#3}{2}\pm\sqrt{\frac{#3^{2}}{4}-#4}}
32548 newmacroname is the default name of the macro that should be changed to
32549 something sensible.
32550 The wanted formula is inserted in the first blue box.
32551 An argument placeholder is inserted with the command
32558 \begin_inset space \thinspace{}
32562 \begin_inset space \space{}
32571 or by using the macro toolbar button
32574 arg "math-macro-add-param"
32578 Argument placeholders are displayed red.
32580 \begin_inset space ~
32583 arguments are possible.
32584 Optional arguments are created with the toolbar button
32587 arg "math-macro-add-optional-param"
32591 The first non-optional argument can be transformed to an optional one with
32595 arg "math-macro-make-optional"
32599 In the second blue box the appearance of the macro in LyX can be defined.
32600 Normally you want to see it as it is defined, so the box is kept empty.
32601 But when you have created a macro that needs lot of space on the screen,
32602 you can insert in the box for example
32603 \begin_inset Newline newline
32633 \begin_inset Newline newline
32638 For the macro only the arguments with the macro name in front of them will
32639 then be displayed in LyX, leading to a better overview.
32640 The formula appears in the output as defined in the first box.
32641 \begin_inset Newline newline
32644 The appearance of macros in formulas can furthermore be changed for single
32645 macros by setting the cursor in the macro and using the menu
32647 View\SpecialChar \menuseparator
32649 \begin_inset space ~
32653 \begin_inset space ~
32661 \begin_layout Standard
32662 To use a macro, the macro name is inserted as command to a formula, in our
32670 Our macro looks in LyX like this:
32671 \begin_inset Newline newline
32675 \begin_inset space \hspace*{\fill}
32679 \begin_inset Graphics
32680 filename clipart/macrouse.png
32685 \begin_inset space \hspace*{\fill}
32689 \begin_inset Newline newline
32692 Here is our macro example with the arguments
32693 \begin_inset Formula $x$
32697 \begin_inset Formula $\ln(x)$
32701 \begin_inset Formula $B$
32707 \begin_layout Standard
32708 \begin_inset Formula
32718 \begin_layout Standard
32719 LyX offers in the menu
32721 Tools\SpecialChar \menuseparator
32722 Preferences\SpecialChar \menuseparator
32723 Editing\SpecialChar \menuseparator
32726 different styles to edit macros.
32727 To find the style that suits you the most, choose a style and set the cursor
32728 in a macro formula to see the difference.
32731 \begin_layout Standard
32732 A math macro is transformed internally to a
32738 command when exporting the document.
32745 command is not placed in the LaTeX-preamble, therefore macros can only
32746 be used in formulas that are in the document below the macro definition
32750 \begin_layout Standard
32751 Math macros can also be directly created from a
32758 When writing for example the command
32761 \begin_inset Newline newline
32770 xleftarrow[#2]{#1}}
32771 \begin_inset Newline newline
32776 in LyX as normal text, highlighting it completely and using then the shortcut
32781 , the command will be transformed to a math macro.
32782 Using this method you need to be careful that the
32788 command is typed correctly, otherwise you get a faulty macro leading to
32792 \begin_layout Standard
32793 Math macros currently have the problem that further formulas in macro definition
32794 s are handled wrongly.
32795 Therefore the example
32802 \begin_inset CommandInset ref
32804 reference "sub:The-Command-newcommand"
32808 cannot be created as macro.
32811 \begin_layout Standard
32812 When the cursor is in a macro definition box, you will see the macro toolbar
32816 \begin_layout Standard
32817 \begin_inset VSpace defskip
32823 \begin_layout Standard
32824 \begin_inset Graphics
32825 filename clipart/MacroToolbar.png
32830 \begin_inset Index idx
32833 \begin_layout Plain Layout
32842 \begin_layout Standard
32843 \begin_inset VSpace defskip
32849 \begin_layout Standard
32850 The macro toolbar contains from left to right the following buttons:
32853 \begin_layout Standard
32854 \begin_inset VSpace defskip
32860 \begin_layout Standard
32861 \begin_inset Tabular
32862 <lyxtabular version="3" rows="9" columns="2">
32863 <features rotate="0" islongtable="true" longtabularalignment="center">
32864 <column alignment="left" valignment="top">
32865 <column alignment="left" valignment="top" width="85col%">
32866 <row interlinespace="2.5mm">
32867 <cell alignment="center" valignment="top" usebox="none">
32870 \begin_layout Plain Layout
32873 arg "math-macro-remove-param"
32881 <cell alignment="center" valignment="top" usebox="none">
32884 \begin_layout Plain Layout
32887 Edit\SpecialChar \menuseparator
32888 Math\SpecialChar \menuseparator
32890 \begin_inset space ~
32893 Definition\SpecialChar \menuseparator
32894 Remove Last Argument
32900 <row interlinespace="2.5mm">
32901 <cell alignment="center" valignment="top" usebox="none">
32904 \begin_layout Plain Layout
32907 arg "math-macro-add-param"
32915 <cell alignment="center" valignment="top" usebox="none">
32918 \begin_layout Plain Layout
32921 Edit\SpecialChar \menuseparator
32922 Math\SpecialChar \menuseparator
32924 \begin_inset space ~
32927 Definition\SpecialChar \menuseparator
32934 <row interlinespace="2.5mm">
32935 <cell alignment="center" valignment="top" usebox="none">
32938 \begin_layout Plain Layout
32941 arg "math-macro-make-optional"
32949 <cell alignment="center" valignment="top" usebox="none">
32952 \begin_layout Plain Layout
32955 Edit\SpecialChar \menuseparator
32956 Math\SpecialChar \menuseparator
32958 \begin_inset space ~
32961 Definition\SpecialChar \menuseparator
32962 Transform First Non-Optional to
32963 \begin_inset Newline newline
32967 \begin_inset Phantom HPhantom
32970 \begin_layout Plain Layout
32973 Edit\SpecialChar \menuseparator
32974 Math\SpecialChar \menuseparator
32976 \begin_inset space ~
32979 Definition\SpecialChar \menuseparator
32991 <row interlinespace="2.5mm">
32992 <cell alignment="center" valignment="top" usebox="none">
32995 \begin_layout Plain Layout
32998 arg "math-macro-make-nonoptional"
33006 <cell alignment="center" valignment="top" usebox="none">
33009 \begin_layout Plain Layout
33012 Edit\SpecialChar \menuseparator
33013 Math\SpecialChar \menuseparator
33015 \begin_inset space ~
33018 Definition\SpecialChar \menuseparator
33019 Transform Last Optional to
33020 \begin_inset Newline newline
33024 \begin_inset Phantom HPhantom
33027 \begin_layout Plain Layout
33030 Edit\SpecialChar \menuseparator
33031 Math\SpecialChar \menuseparator
33033 \begin_inset space ~
33036 Definition\SpecialChar \menuseparator
33042 Non-Optional Argument
33048 <row interlinespace="2.5mm">
33049 <cell alignment="center" valignment="top" usebox="none">
33052 \begin_layout Plain Layout
33055 arg "math-macro-remove-optional-param"
33063 <cell alignment="center" valignment="top" usebox="none">
33066 \begin_layout Plain Layout
33069 Edit\SpecialChar \menuseparator
33070 Math\SpecialChar \menuseparator
33072 \begin_inset space ~
33075 Definition\SpecialChar \menuseparator
33076 Remove Optional Argument
33082 <row interlinespace="2.5mm">
33083 <cell alignment="center" valignment="top" usebox="none">
33086 \begin_layout Plain Layout
33089 arg "math-macro-add-optional-param"
33097 <cell alignment="center" valignment="top" usebox="none">
33100 \begin_layout Plain Layout
33103 Edit\SpecialChar \menuseparator
33104 Math\SpecialChar \menuseparator
33106 \begin_inset space ~
33109 Definition\SpecialChar \menuseparator
33110 Insert Optional Argument
33116 <row interlinespace="2.5mm">
33117 <cell alignment="center" valignment="top" usebox="none">
33120 \begin_layout Plain Layout
33123 arg "math-macro-remove-greedy-param"
33131 <cell alignment="center" valignment="top" usebox="none">
33134 \begin_layout Plain Layout
33137 Edit\SpecialChar \menuseparator
33138 Math\SpecialChar \menuseparator
33140 \begin_inset space ~
33143 Definition\SpecialChar \menuseparator
33144 Remove Last Argument
33145 \begin_inset Newline newline
33149 \begin_inset Phantom HPhantom
33152 \begin_layout Plain Layout
33155 Edit\SpecialChar \menuseparator
33156 Math\SpecialChar \menuseparator
33158 \begin_inset space ~
33161 Definition\SpecialChar \menuseparator
33167 Spitting Out To The Right
33173 <row interlinespace="2.5mm">
33174 <cell alignment="center" valignment="top" usebox="none">
33177 \begin_layout Plain Layout
33180 arg "math-macro-append-greedy-param"
33188 <cell alignment="center" valignment="top" usebox="none">
33191 \begin_layout Plain Layout
33194 Edit\SpecialChar \menuseparator
33195 Math\SpecialChar \menuseparator
33197 \begin_inset space ~
33200 Definition\SpecialChar \menuseparator
33202 \begin_inset Newline newline
33206 \begin_inset Phantom HPhantom
33209 \begin_layout Plain Layout
33212 Edit\SpecialChar \menuseparator
33213 Math\SpecialChar \menuseparator
33215 \begin_inset space ~
33218 Definition\SpecialChar \menuseparator
33224 Eating From The Right
33230 <row interlinespace="2.5mm">
33231 <cell alignment="center" valignment="top" usebox="none">
33234 \begin_layout Plain Layout
33237 arg "math-macro-add-greedy-optional-param"
33245 <cell alignment="center" valignment="top" usebox="none">
33248 \begin_layout Plain Layout
33251 Edit\SpecialChar \menuseparator
33252 Math\SpecialChar \menuseparator
33254 \begin_inset space ~
33257 Definition\SpecialChar \menuseparator
33258 Append Optional Argument
33259 \begin_inset Newline newline
33263 \begin_inset Phantom HPhantom
33266 \begin_layout Plain Layout
33269 Edit\SpecialChar \menuseparator
33270 Math\SpecialChar \menuseparator
33272 \begin_inset space ~
33275 Definition\SpecialChar \menuseparator
33281 Eating From The Right
33294 \begin_layout Section
33295 Computer Algebra Systems
33298 \begin_layout Standard
33299 LyX offers the exchange between mathematical expressions written in LyX's
33300 math editor and external applications or user defined scripts.
33301 Currently supported applications are
33318 Note that the set of supported mathematical constructs is limited only
33319 to very simple cases.
33322 \begin_layout Subsection
33326 \begin_layout Standard
33327 Write some expression in a formula, go to the
33329 Edit\SpecialChar \menuseparator
33330 Math\SpecialChar \menuseparator
33331 Use Computer Algebra System
33333 menu and choose the application you have installed on the computer.
33334 After that the result of computation should show on the right side of the
33335 expression together with the
33336 \begin_inset Quotes eld
33340 \begin_inset Quotes erd
33346 \begin_layout Standard
33347 Here are few simple examples (with results from
33351 ) to show what kind of computations can be performed:
33354 \begin_layout Itemize
33355 \begin_inset Formula $\frac{37}{3}*2-\sum_{i=1}^{3}i^{i}=-\frac{22}{3}$
33361 \begin_layout Itemize
33362 \begin_inset Formula $\frac{37.0}{3}=12.33333333333333$
33368 \begin_layout Itemize
33369 \begin_inset Formula $\int_{1}^{2}\sin(x)dx=\cos1-\cos2$
33375 \begin_layout Itemize
33376 \begin_inset Formula $\det\left[\begin{array}{ccc}
33380 \end{array}\right]=-56$
33386 \begin_layout Itemize
33387 \begin_inset Formula $\lim_{x\rightarrow0}\left(\frac{\sin(x)}{x}\right)=1$
33393 \begin_layout Subsection
33397 \begin_layout Standard
33398 Currently there is no keyboard shortcut for calling the algebra applications.
33399 One can easily bind a shortcut to the
33403 LyX function (see the
33411 \begin_inset space \thinspace{}
33415 \begin_inset space \space{}
33422 key inside the math editor.
33427 one would use this shortcut definition command:
33430 \begin_layout Standard
33433 command-alternatives break-paragraph;math-extern maxima
33436 \begin_layout Section
33438 \begin_inset Index idx
33441 \begin_layout Plain Layout
33450 \begin_layout Subsection
33452 \begin_inset Index idx
33455 \begin_layout Plain Layout
33464 \begin_layout Standard
33465 Negative numbers often look ugly in formulas because the minus sign before
33466 the number is set with the same length as the minus operator sign.
33467 When writing the negative number in normal text, the minus sign appears
33471 \begin_layout Standard
33472 Thus, the problem disappears when converting the minus sign to mathematical
33476 \begin_layout Standard
33477 An example to visualize the problem:
33480 \begin_layout Standard
33482 \begin_inset Tabular
33483 <lyxtabular version="3" rows="3" columns="2">
33484 <features rotate="0" tabularvalignment="middle">
33485 <column alignment="right" valignment="top">
33486 <column alignment="left" valignment="top">
33488 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
33491 \begin_layout Plain Layout
33497 <cell alignment="center" valignment="top" topline="true" rightline="true" usebox="none">
33500 \begin_layout Plain Layout
33508 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
33511 \begin_layout Plain Layout
33517 <cell alignment="center" valignment="top" topline="true" bottomline="true" rightline="true" usebox="none">
33520 \begin_layout Plain Layout
33521 \begin_inset Formula $x=-2$
33531 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
33534 \begin_layout Plain Layout
33540 <cell alignment="center" valignment="top" topline="true" bottomline="true" rightline="true" usebox="none">
33543 \begin_layout Plain Layout
33544 \begin_inset Formula $x=\textrm{-}2$
33560 \begin_layout Subsection
33561 Comma as decimal Separator
33562 \begin_inset Index idx
33565 \begin_layout Plain Layout
33574 \begin_layout Standard
33575 In LaTeX a comma inside a formula is used, according to the English convention,
33576 as number group separator.
33577 So there will be space added behind all commas in formulas.
33580 \begin_layout Standard
33581 To avoid this, the comma is highlighted and changed to mathematical text
33591 \begin_layout Standard
33592 To use all formula commas in the document as decimal separator, the file
33601 \begin_layout Plain Layout
33606 is part of the LaTeX-package
33611 \begin_inset Index idx
33614 \begin_layout Plain Layout
33619 \begin_layout Plain Layout
33639 \begin_inset Index idx
33642 \begin_layout Plain Layout
33648 is loaded with the LaTeX-preamble line
33651 \begin_layout Standard
33659 \begin_layout Subsection
33661 \begin_inset CommandInset label
33663 name "sub:Physical-Vectors"
33668 \begin_inset Index idx
33671 \begin_layout Plain Layout
33680 \begin_layout Standard
33681 Predefined vectors are offered by the LaTeX-package
33686 \begin_inset Index idx
33689 \begin_layout Plain Layout
33695 that is loaded with the LaTeX-preamble line
33698 \begin_layout Standard
33706 \begin_layout Standard
33710 \begin_layout Plain Layout
33720 \begin_inset Note Note
33723 \begin_layout Plain Layout
33724 The following table will only be displayed when the LaTeX-package
33736 \begin_layout Standard
33737 The following commands are defined:
33740 \begin_layout Standard
33742 \begin_inset Tabular
33743 <lyxtabular version="3" rows="4" columns="2">
33744 <features rotate="0" tabularvalignment="middle">
33745 <column alignment="center" valignment="top">
33746 <column alignment="center" valignment="top">
33748 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
33751 \begin_layout Plain Layout
33757 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
33760 \begin_layout Plain Layout
33768 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
33771 \begin_layout Plain Layout
33781 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
33784 \begin_layout Plain Layout
33785 \begin_inset Formula $\Bra{\psi}$
33795 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
33798 \begin_layout Plain Layout
33808 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
33811 \begin_layout Plain Layout
33812 \begin_inset Formula $\Ket{\psi}$
33822 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
33825 \begin_layout Plain Layout
33837 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
33840 \begin_layout Plain Layout
33841 \begin_inset Formula $\Braket{\psi|\phi}$
33857 \begin_layout Standard
33864 assures that all vertical bars are set in the size of the surrounding brackets:
33865 \begin_inset Formula
33867 \Braket{\phi|J=\frac{3}{2}\,,\, M_{J}}
33876 \begin_layout Plain Layout
33886 \begin_inset Note Note
33889 \begin_layout Plain Layout
33890 The following will be displayed when the LaTeX-package
33902 \begin_layout Standard
33903 You need to install the LaTeX-package
33907 to see the rest of this subsection in the output.
33910 \begin_layout Standard
33914 \begin_layout Plain Layout
33926 \begin_layout Standard
33933 can also be achieved using the command
33939 , that is described in
33940 \begin_inset CommandInset ref
33942 reference "sub:Automatic-Bracket-Size"
33949 \begin_layout Subsection
33950 Self-defined Fractions
33951 \begin_inset CommandInset label
33953 name "sub:Self-defined-Fractions"
33958 \begin_inset Index idx
33961 \begin_layout Plain Layout
33962 Fractions ! self-defined
33970 \begin_layout Standard
33971 To define custom commands for fractions, the command
33978 \begin_inset Index idx
33981 \begin_layout Plain Layout
33988 \begin_layout Plain Layout
34002 is used in the following scheme:
34005 \begin_layout Standard
34018 bracket}{fraction bar thickness}{style}
34019 \begin_inset Newline newline
34023 \begin_inset Phantom HPhantom
34026 \begin_layout Plain Layout
34036 {numerator}{denominator}
34039 \begin_layout Standard
34040 The style is a number in the range of 0
34041 \begin_inset space \thinspace{}
34045 \begin_inset space \thinspace{}
34051 \begin_layout Standard
34053 \begin_inset Tabular
34054 <lyxtabular version="3" rows="5" columns="2">
34055 <features rotate="0" tabularvalignment="middle">
34056 <column alignment="center" valignment="top">
34057 <column alignment="center" valignment="top">
34059 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
34062 \begin_layout Plain Layout
34068 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
34071 \begin_layout Plain Layout
34079 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
34082 \begin_layout Plain Layout
34088 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
34091 \begin_layout Plain Layout
34092 display style formula
34099 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
34102 \begin_layout Plain Layout
34108 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
34111 \begin_layout Plain Layout
34119 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
34122 \begin_layout Plain Layout
34128 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
34131 \begin_layout Plain Layout
34139 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
34142 \begin_layout Plain Layout
34148 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
34151 \begin_layout Plain Layout
34165 \begin_layout Standard
34166 When no style is given, the size is adjusted to the surrounding environment
34167 like for the command
34176 \begin_layout Standard
34177 When no fraction bar thickness is given, the predefined value of 0.4
34178 \begin_inset space \thinspace{}
34184 \begin_layout Standard
34185 \begin_inset VSpace medskip
34188 For example, the commands
34201 \begin_inset CommandInset ref
34203 reference "sub:Fractions"
34207 are defined with the commands
34210 \begin_layout Standard
34219 genfrac{}{}{}{0}{#1}{#2}}
34222 \begin_layout Standard
34226 \begin_layout Standard
34235 genfrac{(}{)}{0pt}{1}{#1}{#2}}
34238 \begin_layout Standard
34239 \begin_inset VSpace medskip
34242 To define a fraction where the fraction bar thickness can be given as optional
34243 argument, the following line is inserted to the LaTeX-preamble:
34246 \begin_layout Standard
34255 genfrac{}{}{#1}{}{#2}{#3}}
34258 \begin_layout Standard
34260 \begin_inset Formula
34262 \text{Command} & & \mathrm{\backslash fracS[1mm]\backslash\{A\to\backslash\{B} & & \mathrm{\backslash fracS[5mm]\backslash\{A\to\backslash\{B}\\
34263 \text{Result} & & \fracS[1mm]{A}{B} & & \fracS[5mm]{A}{B}
34268 As one can see, the distance of the numerator and the denominator to the
34269 fraction bar is round about three times the bar thickness.
34272 \begin_layout Subsection
34274 \begin_inset Index idx
34277 \begin_layout Plain Layout
34286 \begin_layout Standard
34287 There are four ways to cancel formulas or parts of formulas:
34290 \begin_layout Standard
34294 \begin_layout Plain Layout
34304 \begin_inset Note Note
34307 \begin_layout Plain Layout
34308 The following table will only be displayed when the LaTeX-package
34320 \begin_layout Standard
34322 \begin_inset Tabular
34323 <lyxtabular version="3" rows="5" columns="2">
34324 <features rotate="0" tabularvalignment="middle">
34325 <column alignment="center" valignment="top">
34326 <column alignment="center" valignment="top">
34328 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
34331 \begin_layout Plain Layout
34337 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
34340 \begin_layout Plain Layout
34342 \begin_inset Note Note
34345 \begin_layout Plain Layout
34352 are used here as spacer.
34364 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
34367 \begin_layout Plain Layout
34371 \begin_inset space \textvisiblespace{}
34377 \begin_inset space \textvisiblespace{}
34385 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
34388 \begin_layout Plain Layout
34389 \begin_inset Formula $\raisebox{4.5mm}{}\cancel{\int A=B}\raisebox{-2.5mm}{}$
34399 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
34402 \begin_layout Plain Layout
34406 \begin_inset space \textvisiblespace{}
34412 \begin_inset space \textvisiblespace{}
34420 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
34423 \begin_layout Plain Layout
34424 \begin_inset Formula $\raisebox{4.5mm}{}\bcancel{\int A=B}\raisebox{-2.5mm}{}$
34434 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
34437 \begin_layout Plain Layout
34441 \begin_inset space \textvisiblespace{}
34447 \begin_inset space \textvisiblespace{}
34455 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
34458 \begin_layout Plain Layout
34459 \begin_inset Formula $\raisebox{4.5mm}{}\xcancel{\int A=B}\raisebox{-2.5mm}{}$
34469 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
34472 \begin_layout Plain Layout
34476 \begin_inset space \textvisiblespace{}
34482 \begin_inset space \textvisiblespace{}
34486 \begin_inset Formula $\to$
34494 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
34497 \begin_layout Plain Layout
34498 \begin_inset Formula $\raisebox{7mm}{}\cancelto{1}{\int A=B}\raisebox{-2.5mm}{}\hspace{3mm}$
34514 \begin_layout Standard
34521 is especially suitable to visualize the reduction of fractions within formulas:
34522 \begin_inset Formula
34524 \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}}}
34532 \begin_layout Standard
34533 To change the size of
34540 \begin_inset Quotes eld
34544 \begin_inset Quotes erd
34547 value one can add the LaTeX-preamble line
34550 \begin_layout Standard
34555 PassOptionsToPackage{option}{cancel}
34558 \begin_layout Standard
34567 which leads to the same size as for the canceled value, or
34571 which makes is it a bit smaller than normal.
34574 \begin_layout Standard
34575 To color the cancellation bar one adds this command as TeX code:
34578 \begin_layout Standard
34590 \begin_layout Standard
34595 can be replaced by a color of your choice.
34598 \begin_layout Standard
34602 \begin_layout Plain Layout
34618 \begin_layout Standard
34619 \begin_inset Formula
34621 \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}}}
34629 \begin_layout Standard
34633 \begin_layout Plain Layout
34647 \begin_inset Note Note
34650 \begin_layout Plain Layout
34659 \begin_layout Standard
34660 For further customizations, see the documentation of the package
34665 \begin_inset CommandInset citation
34672 \begin_inset Index idx
34675 \begin_layout Plain Layout
34684 \begin_layout Standard
34688 \begin_layout Plain Layout
34698 \begin_inset Note Note
34701 \begin_layout Plain Layout
34702 The following will be displayed when the LaTeX-package
34714 \begin_layout Standard
34715 You need to install the LaTeX-package
34719 to see the rest of this subsection in the output.
34722 \begin_layout Standard
34726 \begin_layout Plain Layout
34738 \begin_layout Standard
34739 \begin_inset Newpage newpage
34745 \begin_layout Subsection
34746 Formulas in Section Headings
34747 \begin_inset CommandInset label
34749 name "sub:Formulas-in-Section"
34754 \begin_inset Index idx
34757 \begin_layout Plain Layout
34758 Formula ! in section headings
34766 \begin_layout Standard
34767 When formulas are used in section headings, the following has to be taken
34771 \begin_layout Standard
34772 \begin_inset Note Greyedout
34775 \begin_layout Plain Layout
34781 \begin_inset Index idx
34784 \begin_layout Plain Layout
34785 Packages ! hyperref
34790 support is enabled in the document settings dialog under
34793 \begin_inset space ~
34798 , PDF-bookmarks are created for every section heading in the table of contents.
34799 If a section heading contains formulas, they are incorrectly displayed
34800 in the bookmark text, because formulas in bookmarks infringe the PDF convention
34809 \begin_layout Standard
34810 Both problems can be solved by inserting at the end of the section heading
34811 a short title with the menu
34813 Insert\SpecialChar \menuseparator
34815 \begin_inset space ~
34821 Short titles are used as alternative for multiline section headings to
34822 keep the table of contents clearly arranged.
34823 Only the short title appears in the table of contents and therefore also
34824 in the PDF-bookmark.
34827 \begin_layout Standard
34828 When formulas should be used in the table of contents but
34832 is used, one can use the following command in TeX-mode:
34835 \begin_layout Standard
34840 texorpdfstring{part}{alternative}
34841 \begin_inset Index idx
34844 \begin_layout Plain Layout
34855 \begin_layout Standard
34856 Part is the part of the heading that shouldn't appear in the PDF-bookmark.
34857 This can be characters, formulas, footnotes, but also cross-references.
34858 The alternative is used instead of the part for the bookmark.
34861 \begin_layout Standard
34862 Here are two example headings:
34863 \begin_inset VSpace -3mm
34870 \begin_layout Plain Layout
34882 \begin_layout Subsubsection
34883 Heading without formula in table of contents
34884 \begin_inset Formula $\sqrt{-1}=\mathrm{i}$
34888 \begin_inset Argument 1
34891 \begin_layout Plain Layout
34892 Heading without formula in table of contents
34900 \begin_layout Subsubsection
34901 Heading with formula in table of contents
34905 \begin_layout Plain Layout
34915 \begin_inset Formula $\sqrt{-1}=\mathrm{i}$
34922 \begin_layout Plain Layout
34932 \begin_layout Standard
34936 \begin_layout Plain Layout
34945 In the first heading a short title was used, in the second one
34954 \begin_layout Standard
34955 To get the same formatting as for the other headings, the complete heading
34964 \begin_layout Plain Layout
34966 \begin_inset CommandInset ref
34968 reference "sub:Bold-Formulas"
34980 \begin_layout Subsection
34981 Formulas in multi-column Text
34982 \begin_inset Index idx
34985 \begin_layout Plain Layout
34986 Formula ! in multi-column text
34994 \begin_layout Standard
34995 Formulas in multi-column text are often too wide to fit into a column and
34996 thus need to be set over the whole page width.
34997 This is done by using the LaTeX-package
35005 \begin_layout Plain Layout
35010 is part of every LaTeX standard installation.
35016 \begin_inset Index idx
35019 \begin_layout Plain Layout
35020 Packages ! multicol
35025 , that is loaded with the LaTeX-preamble line
35028 \begin_layout Standard
35033 usepackage{multicol}
35036 \begin_layout Standard
35037 \begin_inset Note Greyedout
35040 \begin_layout Plain Layout
35041 Note that in this case the setting
35044 \begin_inset space ~
35051 Document\SpecialChar \menuseparator
35057 \begin_inset space ~
35077 \begin_layout Standard
35078 Before the multi-column text the command
35081 \begin_layout Standard
35086 begin{multicols}{column number}
35089 \begin_layout Standard
35090 is written in TeX-mode.
35091 The column number is a number in the range of 2
35092 \begin_inset space \thinspace{}
35096 \begin_inset space \thinspace{}
35100 Before the formula the multi-column text is ended by inserting the command
35103 \begin_layout Standard
35111 \begin_layout Standard
35115 \begin_layout Standard
35116 Due to the command some space is automatically added before the formula.
35118 \begin_inset space \thinspace{}
35121 mm vertical space is inserted before the formula.
35122 When the formula style
35128 \begin_layout Plain Layout
35130 \begin_inset CommandInset ref
35132 reference "sec:Formula-Styles"
35144 \begin_inset space \thinspace{}
35147 mm space is inserted instead.
35150 \begin_layout Standard
35151 As example a multi-column text with a displayed formula:
35154 \begin_layout Standard
35160 \begin_layout Plain Layout
35164 begin{multicols}{2}
35169 Das Spektrum wird fouriertransformiert.
35170 Die Fouriertransformation wird verwendet, um die überlagerten Signale (Netzwerk
35171 , Lösungsmittel) zu trennen.
35172 Nachdem wir die Phasenverschiebung bestimmen konnten, interessiert uns
35173 nun das Aussehen des Ausgangssignals.
35174 Im Experiment haben wir es mit sehr vielen Teilchen zu tun, so dass man
35175 über alle Phasen integrieren muss.
35177 \begin_inset Formula $S$
35180 unser normiertes Ausgangssignal und
35181 \begin_inset Formula $P$
35184 die Phasenverteilungsfunktion, so ergibt sich die Beziehung
35188 \begin_layout Plain Layout
35198 \begin_inset VSpace -6mm
35202 \begin_inset Formula
35204 S(t)=S_{0}(t)\int_{-\infty}^{\infty}P(\phi,t)\mathrm{e}^{\mathrm{i}\phi}\,\mathrm{d}\phi
35213 \begin_layout Plain Layout
35217 begin{multicols}{2}
35223 \begin_inset Formula $S_{0}$
35226 das Signal ohne Gradient ist und die Normierungsbedingung
35227 \begin_inset Formula $\int_{-\infty}^{\infty}P(\phi,t)\,\mathrm{d}\phi=1$
35231 Nun dürfen wir aber nicht den Relaxationsprozess außer Acht lassen.
35233 \begin_inset Formula $\nicefrac{\pi}{2}$
35237 \begin_inset space \thinspace{}
35240 -rf-Puls beginnt sich die Magnetisierung zu entfokussieren, wodurch sich
35241 das Signal zusätzlich abschwächt.
35242 Diese Abschwächung verläuft exponentiell in Abhängigkeit der so genannten
35244 \begin_inset Formula $T_{2}$
35250 \begin_layout Standard
35256 \begin_layout Plain Layout
35268 \begin_layout Subsection
35269 Formulas with Description of Variables
35270 \begin_inset Index idx
35273 \begin_layout Plain Layout
35274 Formula ! with description of variables
35282 \begin_layout Standard
35283 To describe variables within a formula, like in formula
35284 \begin_inset CommandInset ref
35286 reference "eq:within"
35295 \begin_inset Formula $n$
35299 \begin_inset space ~
35302 matrix is used with left aligned columns for the
35303 \begin_inset Formula $n$
35310 \begin_layout Plain Layout
35312 \begin_inset CommandInset ref
35314 reference "sec:Matrices"
35323 To set the description in a smaller size, before the matrix e.
35324 \begin_inset space \thinspace{}
35328 \begin_inset space \space{}
35341 \begin_layout Plain Layout
35343 \begin_inset CommandInset ref
35345 reference "sub:Font-Sizes"
35357 \begin_layout Standard
35358 When the formula style
35364 \begin_layout Plain Layout
35366 \begin_inset CommandInset ref
35368 reference "sec:Formula-Styles"
35389 \begin_layout Plain Layout
35396 only works in formulas with the style
35401 \begin_inset CommandInset ref
35403 reference "sub:Variable-Space"
35412 is inserted before and after the matrix to have the same separation of
35413 the matrix from the equation and the side margin.
35416 \begin_layout Standard
35417 When the formula style
35421 is used, the method described in
35422 \begin_inset CommandInset ref
35424 reference "sub:Flalign-Environment"
35428 is used to indent formulas.
35430 \begin_inset CommandInset ref
35432 reference "eq:within"
35436 consists of five columns where in the first two columns contain the equation,
35437 the third the matrix and the last one an empty TeX-brace.
35438 \begin_inset Formula
35440 \hspace{30pt}F_{A} & =\rho·V·g & \footnotesize\begin{array}{ll}
35441 \rho & \textrm{density}\\
35442 V & \textrm{volume}\\
35443 g & \textrm{gravitational acceleration}
35444 \end{array} & & {}\label{eq:within}
35452 \begin_layout Subsection
35453 Upright small Greek Letters
35454 \begin_inset CommandInset label
35456 name "sub:Upright-small-Greek"
35461 \begin_inset Index idx
35464 \begin_layout Plain Layout
35465 Greek letters ! upright
35473 \begin_layout Standard
35474 Most of the math fonts only provide italic small Greek letters.
35475 But for symbols of elementary particles like pions and neutrinos, upright
35476 Greek letters are needed.
35485 \begin_layout Plain Layout
35490 is part of the LaTeX-package
35495 \begin_inset Index idx
35498 \begin_layout Plain Layout
35503 \begin_layout Plain Layout
35523 \begin_inset Index idx
35526 \begin_layout Plain Layout
35532 that is loaded with the LaTeX-preamble line
35535 \begin_layout Standard
35540 usepackage{upgreek}
35543 \begin_layout Standard
35549 \begin_layout Plain Layout
35559 \begin_inset Note Note
35562 \begin_layout Plain Layout
35563 The following table will only be displayed when the LaTeX-package
35572 They are created when the command for a small Greek letter is started with
35578 For example the command
35585 \begin_inset Formula $\uptau$
35591 \begin_layout Standard
35592 With these commands reactions of elementary particles can be typeset:
35593 \begin_inset Formula
35595 \uppi^{+}\to\upmu^{+}+\upnu_{\upmu}
35603 \begin_layout Standard
35604 The upright letters are more bold and wider than the italic ones.
35605 They should therefore not be used for units like
35606 \begin_inset Quotes eld
35610 \begin_inset Quotes erd
35616 \begin_layout Standard
35620 \begin_layout Plain Layout
35630 \begin_inset Note Note
35633 \begin_layout Plain Layout
35634 The following will be displayed when the LaTeX-package
35646 \begin_layout Standard
35647 You need to install the LaTeX-package
35651 to see the rest of this subsection in the output.
35654 \begin_layout Standard
35658 \begin_layout Plain Layout
35670 \begin_layout Subsection
35671 Text Characters in Formulas
35672 \begin_inset CommandInset label
35674 name "sub:Text-Characters-in"
35679 \begin_inset Index idx
35682 \begin_layout Plain Layout
35691 \begin_layout Standard
35692 In some cases you might want to insert text characters directly into formulas.
35693 When for example the centered dot · is often used in formulas like
35694 \begin_inset Formula $\nu=5·10^{5}\,\mathrm{Hz}$
35697 , one would have to insert the command
35707 \begin_layout Plain Layout
35709 \begin_inset CommandInset ref
35711 reference "sub:Binary-Operators"
35720 all the time, because this character is defined in all encodings as text
35722 But the encoding can be changed by this LaTeX-preamble line:
35725 \begin_layout Standard
35730 Declare Inputtext{183}{
35740 f\SpecialChar \textcompwordmark{}
35744 \begin_layout Standard
35745 The character encoding (menu
35747 Document\SpecialChar \menuseparator
35748 Settings\SpecialChar \menuseparator
35751 ) specifies what character appears when a keyboard key is pressed.
35752 When the key for the character '·' is pressed, internally the command
35759 But this command is not available in a formula so that you would get LaTeX-erro
35761 With the changed encoding the right command is chosen automatically, depending
35762 on if the character was inserted into a formula or not.
35765 \begin_layout Standard
35766 The encoding of several characters is saved in definition files.
35767 For example the encoding
35771 is defined in the file
35775 which is in the installation folder of LaTeX.
35776 Encodings should only be changed via the LaTeX-preamble and not in the
35778 Otherwise documents could not be edited by other LyX users working on other
35782 \begin_layout Standard
35783 \begin_inset VSpace medskip
35786 Besides the centered dot, in this document the degree sign ° is defined
35787 with the following LaTeX-preamble line so that it can be directly inserted
35791 \begin_layout Standard
35796 DeclareInputtext{176}{
35806 f\SpecialChar \textcompwordmark{}
35810 \begin_layout Standard
35811 \begin_inset Newpage newpage
35817 \begin_layout Section
35820 \begin_inset Index idx
35823 \begin_layout Plain Layout
35832 \begin_layout Standard
35833 This section is a summary of the most important typographic rules, listed
35838 \begin_layout Plain Layout
35839 This collection was partly taken from the German semi-official dictionary
35841 \begin_inset Quotes eld
35845 \begin_inset Quotes erd
35849 \begin_inset CommandInset citation
35855 that lists some of the ISO rules.
35856 More rules are listed in
35857 \begin_inset CommandInset citation
35871 \begin_layout Itemize
35880 \begin_layout Plain Layout
35881 done with font styles, see
35882 \begin_inset CommandInset ref
35884 reference "sub:Font-Styles"
35893 , no matter if they appear in italic text: 30
35894 \begin_inset space \thinspace{}
35898 \begin_inset Newline newline
35901 Between the value and the unit is the smallest space, see
35902 \begin_inset CommandInset ref
35904 reference "sub:Predefined-Space"
35909 \begin_inset Newline newline
35912 This convention is automatically fulfilled when the command
35919 When it is entered to a formula, two boxes appear.
35920 In the first one the value is inserted, in the second one the unit, and
35922 \begin_inset Formula $\unit[30]{km/h}$
35926 \begin_inset space \thinspace{}
35936 is not a real LaTeX command but the command
35942 , therefore you cannot use it in TeX code.
35945 \begin_layout Itemize
35946 Percent and perthousand signs are set like physical units:
35947 \begin_inset Newline newline
35951 \begin_inset space \thinspace{}
35957 \begin_layout Itemize
35958 The degree sign follows directly on the value: 15°, but not when it is used
35960 \begin_inset space \thinspace{}
35966 \begin_layout Itemize
35967 In numbers with more than four digits the smallest space is inserted before
35968 every third digit to group them:
35978 \begin_inset space \thinspace{}
35982 \begin_inset space \thinspace{}
35988 \begin_layout Itemize
35989 For dimensions like 120×90×40
35990 \begin_inset space \thinspace{}
35993 cm the multiplication sign
35994 \begin_inset Quotes eld
35998 \begin_inset Quotes erd
36002 It is available either via the command
36010 Insert\SpecialChar \menuseparator
36011 Special Character\SpecialChar \menuseparator
36017 \begin_layout Itemize
36018 Functions with names consisting of several letters are set upright to avoid
36020 \begin_inset CommandInset ref
36022 reference "sub:Predefined-Functions"
36029 \begin_layout Itemize
36030 Indices consisting of several letters, are set upright:
36031 \begin_inset Formula $E_{\mathrm{kin}}$
36035 \begin_inset Newline newline
36038 Components of matrices are set italic:
36039 \begin_inset Formula $\hat{H}_{kl}$
36045 \begin_layout Itemize
36046 The differentiation/integration operator 'd', the Euler's number 'e' and
36047 the imaginary unit 'i' should be set upright, to avoid mixing them up with
36051 \begin_layout Itemize
36052 The character that denotes a
36056 transformation is inserted either by the command
36061 \begin_inset space \textvisiblespace{}
36068 Insert\SpecialChar \menuseparator
36069 Special Character\SpecialChar \menuseparator
36070 Symbols\SpecialChar \menuseparator
36072 \begin_inset space ~
36078 \begin_inset Formula $\mathscr{F}$
36084 \begin_layout Standard
36085 \begin_inset Newpage newpage
36091 \begin_layout Section
36093 \begin_inset Index idx
36096 \begin_layout Plain Layout
36105 \begin_layout Standard
36106 Some characters and symbols can be created with several commands.
36107 Here is a list of the synonym commands:
36110 \begin_layout Standard
36111 \begin_inset VSpace bigskip
36115 \begin_inset space \hfill{}
36119 \begin_inset Tabular
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36768 Addison Wesley, 2004
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