1 #LyX 2.1 created this file. For more info see http://www.lyx.org/
7 % DO NOT ALTER THIS PREAMBLE!!!
9 % This preamble is designed to ensure that the file prints
10 % out as advertised. If you mess with this preamble,
11 % parts of this document may not print out as expected. If you
12 % have problems LaTeXing this file, please contact
13 % the documentation team
14 % email: lyx-docs@lists.lyx.org
20 % set fonts for nicer pdf view
21 \IfFileExists{lmodern.sty}
22 {\usepackage{lmodern}}{}
24 \fi % end if pdflatex is used
26 % solves the following problem:
27 % If the dection number consits of too many numerals the section heading
28 % will be printed in the TOC without a space between it and the section number.
29 % As solution more space between the number and the heading is inserted:
30 \renewcommand{\l@subsection}{\@dottedtocline{2}{1.5em}{2.8em}}
31 \renewcommand{\l@subsubsection}{\@dottedtocline{3}{4.3em}{3.6em}}
33 % increase link area for cross-references and autoname them,
34 \AtBeginDocument{\renewcommand{\ref}[1]{\mbox{\autoref{#1}}}}
35 \@ifundefined{extrasenglish}{\usepackage[english]{babel}}{}
36 \addto\extrasenglish{%
37 \renewcommand*{\equationautorefname}[1]{}%
38 \renewcommand{\sectionautorefname}{sec.\negthinspace}%
39 \renewcommand{\subsectionautorefname}{sec.\negthinspace}%
40 \renewcommand{\subsubsectionautorefname}{sec.\negthinspace}%
43 % don't load packages twice
44 % see first footnote in sec. 9.3
45 \@ifundefined{textcolor}{\usepackage{color}}{}
47 % the pages of the TOC are numbered roman
48 % and a PDF-bookmark for the TOC is added
50 \let\myTOC\tableofcontents
51 \renewcommand{\tableofcontents}{%
53 \pdfbookmark[1]{\contentsname}{}
56 \pagenumbering{arabic}}
58 % insert additional vertical space of 1.5 mm between footnotes,
60 \renewcommand{\footnote}[1]{\myFoot{#1\vspace{1.5mm}}}
62 % provides caption formatting
63 \setkomafont{captionlabel}{\bfseries}
65 % enables calculation of values
68 % for multiple columns used in sec. 24.7
74 % for the Fourier transformation symbol
77 % define a color, used in sec.9.3
78 \definecolor{darkgreen}{cmyk}{0.5, 0, 1, 0.5}
80 % declare operators (see sec. 10.4 and sec. 15.2)
81 \DeclareMathOperator*{\Lozenge}{\blacklozenge}
82 \DeclareMathOperator{\sgn}{sgn}
84 % example definitions for sec. 20.1
85 \newcommand{\gr}{\Longrightarrow}
86 \newcommand{\us}[1]{\underline{#1}}
87 \newcommand{\fb}[3]{\framebox#1#2{$#3$}}
88 \newcommand{\cb}[3][white]{\fcolorbox{#2}{#1}{$#3$}}
89 \newcommand{\fracS}[3][]{\genfrac{}{}{#1}{}{#2}{#3}}
91 % example macro from sec. 19.4
92 %\def\tagform@#1{\maketag@@@{|#1|}}
95 % ------------------------------------
96 % used to check for needed LaTeX packages
99 % check for package undertilde
100 % used for the command \utilde
101 \newboolean{undertilde}
102 \IfFileExists{undertilde.sty}
103 {\usepackage{undertilde}
104 \setboolean{undertilde}{true}}
105 {\setboolean{undertilde}{false}}
107 % check for package eurosym
108 % used for the Euro symbol
110 \IfFileExists{eurosym.sty}
111 {\usepackage[gennarrow]{eurosym}
112 \setboolean{eurosym}{true}}
113 {\setboolean{eurosym}{false}}
115 % check for package braket
116 % used for physical vectors
118 \IfFileExists{braket.sty}
120 \setboolean{braket}{true}}
121 {\setboolean{braket}{false}}
123 % check for package cancel
125 \IfFileExists{cancel.sty}
127 \setboolean{cancel}{true}}
128 {\setboolean{cancel}{false}}
130 % check for package upgreek
132 \IfFileExists{upgreek.sty}
133 {\usepackage{upgreek}
134 \setboolean{upgreek}{true}}
135 {\setboolean{upgreek}{false}}
137 \options bibliography=totoc,index=totoc,BCOR7.5mm,titlepage,captions=tableheading
138 \use_default_options false
139 \maintain_unincluded_children false
141 \language_package default
146 \font_typewriter default
148 \font_default_family default
149 \use_non_tex_fonts false
155 \default_output_format default
157 \bibtex_command default
158 \index_command default
162 \pdf_title "LyX's Math Manual"
163 \pdf_author "LyX Team, Uwe Stöhr"
164 \pdf_subject "LyX-documentation about math"
165 \pdf_keywords "LyX, Mathed"
167 \pdf_bookmarksnumbered true
168 \pdf_bookmarksopen true
169 \pdf_bookmarksopenlevel 1
170 \pdf_breaklinks false
174 \pdf_pdfusetitle false
175 \pdf_quoted_options "linkcolor=black, citecolor=black, urlcolor=blue, filecolor=blue, pdfpagelayout=OneColumn, pdfnewwindow=true, pdfstartview=XYZ, plainpages=false"
178 \use_package amsmath 2
179 \use_package amssymb 2
180 \use_package cancel 0
182 \use_package mathdots 1
183 \use_package mathtools 1
184 \use_package mhchem 1
185 \use_package stackrel 0
186 \use_package stmaryrd 0
187 \use_package undertilde 0
189 \cite_engine_type default
193 \paperorientation portrait
197 \notefontcolor #0000ff
204 \paragraph_separation skip
206 \quotes_language english
209 \paperpagestyle plain
213 \tracking_changes false
214 \output_changes false
217 \html_be_strict false
223 LyX's detailed Math manual
231 \begin_layout Plain Layout
233 If you have comments or error corrections, please send them to the LyX Documenta
237 \begin_inset CommandInset href
239 name "lyx-docs@lists.lyx.org"
240 target "lyx-docs@lists.lyx.org?subject=LyX's Math manual"
251 \begin_inset Note Note
254 \begin_layout Plain Layout
261 \begin_inset Newline newline
265 \begin_inset Newline newline
273 \begin_layout Standard
274 \begin_inset CommandInset toc
275 LatexCommand tableofcontents
282 \begin_layout Standard
283 \begin_inset Note Note
286 \begin_layout Plain Layout
287 To export this document to PDF, PS or DVI the LaTeX-packages
289 braket, cancel, eurosym, mathdots, mathtools, mhchem, undertilde
296 If they are not installed the document can be exported anyway but the sections
297 where the packages are required will not appear in the output.
302 ; if it is not installed, this file cannot be exported.
305 \begin_layout Plain Layout
306 The latest PDF-version of this document can be found here:
307 \begin_inset Newline newline
312 http://wiki.lyx.org/LyX/DocumentationDevelopment#Math
320 \begin_layout Standard
321 \begin_inset Newpage newpage
327 \begin_layout Section
331 \begin_layout Standard
332 This document explains LyX's math features and is furthermore a collection
333 of LaTeX-commands used for mathematical characters and constructs.
334 The explanations are designed for the usage of commands.
335 It is therefore required that you have read the section
346 \begin_layout Standard
347 Most of the characters and many constructs explained in this manual are
348 also accessible via the menu
352 \SpecialChar \menuseparator
368 But everybody who has to write lots of formulas will notice that it is
369 much faster to use commands instead of the math toolbar.
370 Therefore this manual is focused on commands but also mentions the correspondin
371 g toolbar buttons when available.
374 \begin_layout Standard
375 If not specially mentioned the commands are only available within formulas.
376 To be able to use all commands explained in this document, the option
380 must be checked in the document settings (menu
382 Document\SpecialChar \menuseparator
383 Settings\SpecialChar \menuseparator
394 \begin_layout Plain Layout
397 Use AMS math package automatically
403 \begin_layout Plain Layout
412 -math when math constructs are found that are supported by LyX.
420 \begin_layout Standard
421 This document doesn't list all
425 \begin_layout Plain Layout
438 \begin_layout Plain Layout
443 \begin_layout Plain Layout
452 -math commands is in the file
455 \begin_inset CommandInset href
458 target "ftp://ftp.ams.org/pub/tex/doc/amstex/amsguide.pdf"
464 , which is part of every LaTeX standard installation.
469 for lucidity reasons.
472 \begin_layout Section
476 \begin_layout Standard
477 To create an inline formula
478 \begin_inset Index idx
481 \begin_layout Plain Layout
487 that is embedded into a text line, use one of the shortcuts
493 or the toolbar button
500 \begin_inset Newline newline
503 To create a display style formula
504 \begin_inset Index idx
507 \begin_layout Plain Layout
508 Formula ! display style
513 which will appear bigger, has a different format, and will be in a separate
514 paragraph, use one of these shortcuts:
523 \begin_layout Standard
524 To change a display style formula to an inline formula, set the cursor into
525 the formula and use one of the shortcuts
533 Edit\SpecialChar \menuseparator
534 Math\SpecialChar \menuseparator
538 The same way is used to change an inline formula to a display style formula.
541 \begin_layout Standard
542 To display parts of an inline formula in the size of a display style formula,
550 \begin_inset Index idx
553 \begin_layout Plain Layout
562 Then a new blue box appears in which the desired formula part is inserted.
565 \begin_layout Standard
566 Only inline formulas are allowed inside tables.
569 \begin_layout Standard
574 can be turned on in the menu
576 View\SpecialChar \menuseparator
580 When you click there on
581 \begin_inset Quotes eld
585 \begin_inset Quotes erd
588 the toolbar will be shown permanently at the bottom; this state is visualized
593 menu with a checkmark.
594 When you click in this state again on
595 \begin_inset Quotes eld
599 \begin_inset Quotes erd
610 is only shown when the cursor is within a formula; this state is visualized
611 by the renaming of the menu entry from
612 \begin_inset Quotes eld
616 \begin_inset Quotes erd
620 \begin_inset Quotes eld
628 \begin_inset Quotes erd
634 \begin_layout Standard
636 \begin_inset Index idx
639 \begin_layout Plain Layout
645 is invoked by pressing the toolbar button
653 Insert\SpecialChar \menuseparator
658 \begin_layout Plain Layout
674 \begin_inset Note Note
677 \begin_layout Plain Layout
678 In LyX there are three
679 \begin_inset Quotes eld
683 \begin_inset Quotes erd
686 that appear in the output with sub- and superscript letters: TeX, LaTeX
690 \begin_layout Plain Layout
691 To avoid that these names are recognized as proper names, a TeX-brace pair
700 \begin_layout Standard
701 To change the LaTeX-preamble
702 \begin_inset Index idx
705 \begin_layout Plain Layout
713 Document\SpecialChar \menuseparator
714 Settings\SpecialChar \menuseparator
719 \begin_layout Plain Layout
735 \begin_layout Standard
736 To edit matrices, case differentiations and multiline formulas subsequently,
739 Edit\SpecialChar \menuseparator
744 Edit\SpecialChar \menuseparator
746 \begin_inset space \thinspace{}
750 \begin_inset space \thinspace{}
760 When lines and columns are swapped via the menu, the column or line where
761 the cursor is in is exchanged with the column to the right or the line
763 Is the cursor in the last column or row, the exchange is done with the
764 column to the left or the line above.
767 \begin_layout Standard
768 To write text in formulas
772 \begin_layout Plain Layout
773 For multiline formulas the command
780 \begin_inset CommandInset ref
782 reference "sub:Text-in-multiline"
796 \begin_inset Index idx
799 \begin_layout Plain Layout
806 \begin_inset Index idx
809 \begin_layout Plain Layout
816 This mode is invoked with the shortcut
822 or by the insertion of the command
829 \begin_inset Index idx
832 \begin_layout Plain Layout
841 The text appears black in LyX and can therefore be distinguished from the
842 other formula parts which appear blue.
843 In the output mathematical text is set upright, in contrary to other formula
847 \begin_layout Subsection*
851 \begin_layout Standard
852 Most of the LaTeX-commands for math constructs have the following scheme:
855 \begin_layout Standard
871 \begin_layout Standard
872 A command always starts with a backslash
873 \begin_inset Quotes gld
883 \begin_inset Quotes grd
887 To omit optional arguments, also omit the associated brackets.
888 The braces around the required arguments are named in this document as
890 \begin_inset Index idx
893 \begin_layout Plain Layout
900 If you add in a formula a left brace to a command name, LyX automatically
902 In all other cases TeX-braces are created in formulas with the command
910 TeX-braces appear red in LyX, in contrary to normal braces which appear
912 In TeX-mode no command is needed to get TeX-braces.
913 TeX-braces don't appear in the output.
916 \begin_layout Standard
917 When commands without arguments, like commands for symbols are entered in
918 TeX-mode, a space character must
922 be behind the command to end it.
923 This space doesn't appear in the output.
924 When the space should appear in the output, the space must be followed
925 by a protected space in normal text.
928 \begin_layout Standard
929 A protected space is inserted with
932 arg "command-alternatives space-insert protected ; math-space"
938 \begin_layout Subsection*
939 \begin_inset Newpage newpage
945 \begin_layout Itemize
947 \begin_inset space \textvisiblespace{}
950 denotes a space character to be input.
953 \begin_layout Itemize
955 \begin_inset Formula $\to$
958 denotes the usage of the corresponding arrow key on the keyboard.
963 key can often be used instead of
964 \begin_inset Formula $\to$
968 \begin_inset Formula $\downarrow$
976 \begin_inset Formula $\leftarrow$
980 \begin_inset Formula $\uparrow$
986 \begin_layout Subsection*
990 \begin_layout Standard
992 \begin_inset Float table
998 \begin_layout Plain Layout
1000 \begin_inset Caption Standard
1002 \begin_layout Plain Layout
1003 \begin_inset CommandInset label
1005 name "tab:Available-units"
1017 \begin_layout Plain Layout
1019 \begin_inset Tabular
1020 <lyxtabular version="3" rows="13" columns="2">
1021 <features rotate="0" tabularvalignment="middle">
1022 <column alignment="center" valignment="top">
1023 <column alignment="center" valignment="top">
1025 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
1028 \begin_layout Plain Layout
1034 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
1037 \begin_layout Plain Layout
1045 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
1048 \begin_layout Plain Layout
1054 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
1057 \begin_layout Plain Layout
1065 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
1068 \begin_layout Plain Layout
1074 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
1077 \begin_layout Plain Layout
1085 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
1088 \begin_layout Plain Layout
1094 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
1097 \begin_layout Plain Layout
1099 \begin_inset space \thinspace{}
1103 \begin_inset space \thinspace{}
1113 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
1116 \begin_layout Plain Layout
1122 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
1125 \begin_layout Plain Layout
1127 \begin_inset space \thinspace{}
1131 \begin_inset space \thinspace{}
1141 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
1144 \begin_layout Plain Layout
1150 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
1153 \begin_layout Plain Layout
1155 \begin_inset space \thinspace{}
1159 \begin_inset space \thinspace{}
1169 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
1172 \begin_layout Plain Layout
1178 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
1181 \begin_layout Plain Layout
1183 \begin_inset space \thinspace{}
1187 \begin_inset space \thinspace{}
1197 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
1200 \begin_layout Plain Layout
1206 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
1209 \begin_layout Plain Layout
1211 \begin_inset space \thinspace{}
1215 \begin_inset space \thinspace{}
1225 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
1228 \begin_layout Plain Layout
1234 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
1237 \begin_layout Plain Layout
1239 \begin_inset space \thinspace{}
1243 \begin_inset Formula $\approx$
1247 \begin_inset space \thinspace{}
1257 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
1260 \begin_layout Plain Layout
1266 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
1269 \begin_layout Plain Layout
1271 \begin_inset space \thinspace{}
1275 \begin_inset space \thinspace{}
1285 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
1288 \begin_layout Plain Layout
1294 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
1297 \begin_layout Plain Layout
1301 \begin_inset Quotes eld
1307 \begin_inset Quotes erd
1317 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
1320 \begin_layout Plain Layout
1326 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
1329 \begin_layout Plain Layout
1331 \begin_inset Quotes eld
1339 \begin_inset Quotes erd
1349 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
1352 \begin_layout Plain Layout
1358 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
1361 \begin_layout Plain Layout
1363 \begin_inset space \thinspace{}
1367 \begin_inset Formula $\nicefrac{1}{18}$
1371 \begin_inset space \thinspace{}
1392 \begin_layout Standard
1393 \begin_inset Newpage newpage
1399 \begin_layout Section
1403 \begin_layout Subsection
1405 \begin_inset Index idx
1408 \begin_layout Plain Layout
1415 \begin_inset Index idx
1418 \begin_layout Plain Layout
1425 \begin_inset Index idx
1428 \begin_layout Plain Layout
1433 \begin_layout Plain Layout
1444 \begin_layout Plain Layout
1457 \begin_inset Index idx
1460 \begin_layout Plain Layout
1465 \begin_layout Plain Layout
1476 \begin_layout Plain Layout
1491 \begin_layout Standard
1492 Indices are created with an underscore
1493 \begin_inset Quotes eld
1497 \begin_inset Quotes erd
1500 or via the math toolbar button
1503 arg "math-subscript"
1506 , exponents with a caret
1507 \begin_inset Quotes eld
1511 \begin_inset Quotes erd
1514 or via the math toolbar button
1517 arg "math-superscript"
1523 \begin_layout Standard
1525 \begin_inset Tabular
1526 <lyxtabular version="3" rows="4" columns="2">
1527 <features rotate="0" tabularvalignment="middle">
1528 <column alignment="center" valignment="top" width="0pt">
1529 <column alignment="center" valignment="top" width="0pt">
1531 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
1534 \begin_layout Plain Layout
1540 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
1543 \begin_layout Plain Layout
1545 \begin_inset Note Note
1548 \begin_layout Plain Layout
1555 is only used as spacer.
1567 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
1570 \begin_layout Plain Layout
1576 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
1579 \begin_layout Plain Layout
1580 \begin_inset Formula $B_{V}$
1590 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
1593 \begin_layout Plain Layout
1599 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
1602 \begin_layout Plain Layout
1603 \begin_inset Formula $\raisebox{5mm}{}B^{V}$
1613 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
1616 \begin_layout Plain Layout
1618 \begin_inset space \textvisiblespace{}
1626 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
1629 \begin_layout Plain Layout
1630 \begin_inset Formula $\raisebox{5mm}{}B^{A}$
1646 \begin_layout Standard
1647 As the caret is in some languages an accent, vowels will be accentuated
1648 in this case and not set as exponents
1652 \begin_layout Plain Layout
1653 Depending on the used keyboard settings this can also happen for characters
1660 To get exponents in this case, press
1664 after the caret as in the last example.
1667 \begin_layout Subsection
1669 \begin_inset CommandInset label
1671 name "sub:Fractions"
1676 \begin_inset Index idx
1679 \begin_layout Plain Layout
1688 \begin_layout Standard
1689 Fractions are generated with the command
1696 \begin_inset Index idx
1699 \begin_layout Plain Layout
1707 or via the math toolbar button
1710 arg "math-insert \\frac"
1714 The font size is adjusted automatically, depending on whether the fraction
1715 is in an inline or display style formula.
1716 With the math toolbar button
1719 arg "math-insert \\frac-square"
1722 you can select different fraction types.
1725 \begin_layout Standard
1733 \begin_inset Index idx
1736 \begin_layout Plain Layout
1744 a fraction can be created that always has the size of a display style formula.
1752 \begin_inset Index idx
1755 \begin_layout Plain Layout
1763 the fraction appears always with the size of an inline formula.
1767 \begin_layout Standard
1768 A line with the fraction
1769 \begin_inset Formula $\frac{1}{2}$
1772 that was created with the command
1781 \begin_layout Standard
1782 A line with the fraction
1783 \begin_inset Formula $\dfrac{1}{2}$
1786 that was created with the command
1795 \begin_layout Standard
1797 \begin_inset Tabular
1798 <lyxtabular version="3" rows="4" columns="2">
1799 <features rotate="0" tabularvalignment="middle">
1800 <column alignment="center" valignment="top" width="0pt">
1801 <column alignment="center" valignment="top" width="0pt">
1803 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
1806 \begin_layout Plain Layout
1812 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
1815 \begin_layout Plain Layout
1817 \begin_inset Note Note
1820 \begin_layout Plain Layout
1827 is only used as spacer.
1839 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
1842 \begin_layout Plain Layout
1846 \begin_inset space \textvisiblespace{}
1850 \begin_inset Formula $\downarrow$
1858 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
1861 \begin_layout Plain Layout
1862 \begin_inset Formula $\raisebox{4.5mm}{}\frac{A}{B}\raisebox{-2.5mm}{}$
1872 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
1875 \begin_layout Plain Layout
1879 \begin_inset space \textvisiblespace{}
1883 \begin_inset Formula $\downarrow$
1891 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
1894 \begin_layout Plain Layout
1895 \begin_inset Formula $\raisebox{7mm}{}\dfrac{A}{B}\raisebox{-4mm}{}$
1905 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
1908 \begin_layout Plain Layout
1912 \begin_inset space \textvisiblespace{}
1918 \begin_inset space \textvisiblespace{}
1922 \begin_inset Formula $\downarrow$
1926 \begin_inset Formula $\downarrow\downarrow$
1934 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
1937 \begin_layout Plain Layout
1938 \begin_inset Formula $\raisebox{8mm}{}\dfrac{e^{\frac{1}{2}}}{3}\raisebox{-4mm}{}$
1954 \begin_layout Standard
1955 \begin_inset VSpace bigskip
1959 \begin_inset Newpage newpage
1962 For nested fractions the command
1969 \begin_inset Index idx
1972 \begin_layout Plain Layout
1982 \begin_inset VSpace -3mm
1988 \begin_layout Standard
1989 \begin_inset Formula
1991 \textrm{created with \textbf{\textbackslash frac}} & & \textrm{created with \textbf{\textbackslash cfrac}}\\
1992 \frac{A}{B+\frac{C+\frac{E}{F}}{D}} & & \cfrac{A}{B+\cfrac{C+\cfrac{E}{F}}{D}}
2000 \begin_layout Standard
2001 The command for the example above is:
2004 \begin_layout Standard
2010 \begin_inset space \textvisiblespace{}
2014 \begin_inset Formula $\downarrow$
2020 \begin_inset space \textvisiblespace{}
2026 \begin_inset space \textvisiblespace{}
2030 \begin_inset Formula $\downarrow$
2034 \begin_inset Formula $\downarrow$
2040 \begin_layout Standard
2041 \begin_inset VSpace medskip
2047 \begin_layout Standard
2054 sets the fraction always in the size of a displayed formula, also when
2055 it is part of another fraction.
2058 \begin_layout Standard
2059 It is possible to specify the alignment of the numerator.
2066 is used to left align it, the command
2079 centers the numerator.
2080 These fractions demonstrate the different alignments:
2083 \begin_layout Standard
2086 \begin_inset Formula
2088 \cfrac[l]{A}{B+C}\,,\,\cfrac{A}{B+C}\,,\,\cfrac[r]{A}{B+C}
2096 \begin_layout Standard
2097 \begin_inset Note Greyedout
2100 \begin_layout Plain Layout
2117 are no real LaTeX commands but represent the command
2121 cfrac[alignment]{numerator}{denominator}
2124 Therefore you cannot use them in TeX code.
2132 \begin_layout Standard
2133 \begin_inset VSpace medskip
2136 It is often advantageous to combine
2149 \begin_inset Formula
2151 \cfrac{A}{B+\cfrac{C+\frac{E}{F}}{D}}
2159 \begin_layout Standard
2160 For inline fractions with a sloped fraction stroke you can use the command
2168 \begin_inset Index idx
2171 \begin_layout Plain Layout
2180 \begin_inset Formula $\nicefrac{5}{31}$
2190 \begin_inset Index idx
2193 \begin_layout Plain Layout
2202 \begin_inset Formula $\unitfrac{5}{31}$
2205 There is furthermore the command
2211 that offers to write a fraction in combination with a number:
2212 \begin_inset Formula $\unitfrac[2]{1}{3}$
2218 \begin_layout Standard
2219 \begin_inset Note Greyedout
2222 \begin_layout Plain Layout
2233 is not a real LaTeX command but the command
2234 \begin_inset Newline newline
2241 unitfrac[number]{numerator}{denominator}
2244 Therefore you cannot use it in TeX code.
2252 \begin_layout Standard
2253 How to define own fractions where the fraction stroke can be changed, is
2255 \begin_inset CommandInset ref
2257 reference "sub:Self-defined-Fractions"
2264 \begin_layout Standard
2265 \begin_inset Newpage newpage
2271 \begin_layout Subsection
2273 \begin_inset Index idx
2276 \begin_layout Plain Layout
2285 \begin_layout Standard
2286 Square roots are created with
2293 \begin_inset Index idx
2296 \begin_layout Plain Layout
2304 or the math toolbar button
2307 arg "math-insert \\sqrt"
2310 , all other roots with the command
2317 \begin_inset Index idx
2320 \begin_layout Plain Layout
2328 or with the math toolbar button
2331 arg "math-insert \\root"
2337 \begin_layout Standard
2339 \begin_inset Tabular
2340 <lyxtabular version="3" rows="3" columns="2">
2341 <features rotate="0" tabularvalignment="middle">
2342 <column alignment="center" valignment="top" width="0pt">
2343 <column alignment="center" valignment="top" width="0pt">
2345 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
2348 \begin_layout Plain Layout
2354 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
2357 \begin_layout Plain Layout
2359 \begin_inset Note Note
2362 \begin_layout Plain Layout
2369 is only used as spacer.
2381 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
2384 \begin_layout Plain Layout
2388 \begin_inset space \textvisiblespace{}
2396 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
2399 \begin_layout Plain Layout
2400 \begin_inset Formula $\raisebox{4.5mm}{}\sqrt{A-B}$
2410 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
2413 \begin_layout Plain Layout
2417 \begin_inset space \textvisiblespace{}
2421 \begin_inset Formula $\downarrow$
2429 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
2432 \begin_layout Plain Layout
2433 \begin_inset Formula $\raisebox{4.5mm}{}\sqrt[3]{A-B}$
2449 \begin_layout Standard
2450 A square root can also be created with
2456 when the root index field is left empty.
2459 \begin_layout Standard
2460 With certain indices the distance to the root is too small, like in this
2462 \begin_inset Formula $\sqrt[\beta]{B}$
2466 \begin_inset Newline newline
2470 \begin_inset Formula $\beta$
2474 To avoid this, the commands
2481 \begin_inset Index idx
2484 \begin_layout Plain Layout
2499 \begin_inset Index idx
2502 \begin_layout Plain Layout
2510 are used with the following scheme:
2513 \begin_layout Standard
2527 \begin_layout Standard
2528 Distance is the number of Big Points (unit bp;
2529 \begin_inset Formula $\mathrm{72\, bp=1\, inch}$
2532 ), that the index should be moved to the left or top, resp..
2533 The commands are written to the index.
2534 This way the command
2535 \begin_inset Newline newline
2545 \begin_inset Formula $\to$
2551 \begin_inset Formula $\to$
2557 \begin_inset space \textvisiblespace{}
2561 \begin_inset Formula $\to$
2565 \begin_inset Newline newline
2570 produces a correct typeset formula:
2571 \begin_inset Formula $\sqrt[\leftroot{-1}\uproot{2}\beta]{B}$
2577 \begin_layout Subsection
2578 Binomial Coefficients
2579 \begin_inset Index idx
2582 \begin_layout Plain Layout
2583 Binomial coefficients
2591 \begin_layout Standard
2592 Binomial coefficients are inserted with the command
2599 \begin_inset Index idx
2602 \begin_layout Plain Layout
2610 or with the submenu of the math toolbar button
2613 arg "math-insert \\frac-square"
2629 there are the commands
2636 \begin_inset Index idx
2639 \begin_layout Plain Layout
2654 \begin_inset Index idx
2657 \begin_layout Plain Layout
2666 For other brackets around binomial coeficients there are the commands
2673 \begin_inset Index idx
2676 \begin_layout Plain Layout
2691 \begin_inset Index idx
2694 \begin_layout Plain Layout
2705 \begin_layout Standard
2707 \begin_inset Tabular
2708 <lyxtabular version="3" rows="6" columns="2">
2709 <features rotate="0" tabularvalignment="middle">
2710 <column alignment="center" valignment="top" width="0pt">
2711 <column alignment="center" valignment="top" width="0pt">
2713 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
2716 \begin_layout Plain Layout
2722 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
2725 \begin_layout Plain Layout
2727 \begin_inset Note Note
2730 \begin_layout Plain Layout
2737 is only used as spacer.
2749 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
2752 \begin_layout Plain Layout
2756 \begin_inset space \textvisiblespace{}
2760 \begin_inset Formula $\downarrow$
2768 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
2771 \begin_layout Plain Layout
2772 \begin_inset Formula $\raisebox{5mm}{}\binom{A}{B}\raisebox{-2.5mm}{}$
2782 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
2785 \begin_layout Plain Layout
2789 \begin_inset space \textvisiblespace{}
2793 \begin_inset Formula $\downarrow$
2801 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
2804 \begin_layout Plain Layout
2805 \begin_inset Formula $\raisebox{5mm}{}\dbinom{A}{B}\raisebox{-2.5mm}{}$
2815 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
2818 \begin_layout Plain Layout
2822 \begin_inset space \textvisiblespace{}
2826 \begin_inset Formula $\downarrow$
2834 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
2837 \begin_layout Plain Layout
2838 \begin_inset Formula $\raisebox{5mm}{}\tbinom{A}{B}\raisebox{-2.5mm}{}$
2848 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
2851 \begin_layout Plain Layout
2855 \begin_inset space \textvisiblespace{}
2859 \begin_inset Formula $\downarrow$
2867 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
2870 \begin_layout Plain Layout
2871 \begin_inset Formula $\raisebox{5mm}{}{A \brack B}\raisebox{-2.5mm}{}$
2881 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
2884 \begin_layout Plain Layout
2888 \begin_inset space \textvisiblespace{}
2892 \begin_inset Formula $\downarrow$
2900 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
2903 \begin_layout Plain Layout
2904 \begin_inset Formula $\raisebox{5mm}{}{A \brace B}\raisebox{-2.5mm}{}$
2920 \begin_layout Subsection
2921 Case Differentiations
2922 \begin_inset Index idx
2925 \begin_layout Plain Layout
2926 Case differentiations
2934 \begin_layout Standard
2936 \begin_inset Tabular
2937 <lyxtabular version="3" rows="3" columns="2">
2938 <features rotate="0" tabularvalignment="middle">
2939 <column alignment="center" valignment="top" width="0pt">
2940 <column alignment="center" valignment="top" width="0pt">
2942 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
2945 \begin_layout Plain Layout
2951 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
2954 \begin_layout Plain Layout
2962 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
2965 \begin_layout Plain Layout
2969 \begin_inset space \textvisiblespace{}
2973 \begin_inset Formula $\to$
2977 \begin_inset Index idx
2980 \begin_layout Plain Layout
2993 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
2996 \begin_layout Plain Layout
2997 \begin_inset Formula $\begin{cases}
3008 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
3011 \begin_layout Plain Layout
3015 \begin_inset space \textvisiblespace{}
3021 arg "newline-insert newline"
3029 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
3032 \begin_layout Plain Layout
3033 \begin_inset Formula $\begin{cases}
3034 A & \textrm{for }x>0\\
3035 B & \textrm{for }x=0
3052 \begin_layout Standard
3059 or pressing the math toolbar button
3062 arg "math-insert \\cases"
3065 you can create new lines with the shortcut
3068 arg "newline-insert newline"
3071 or the table toolbar button
3074 arg "inset-modify tabular append-row"
3080 \begin_layout Standard
3087 is also available via the menu
3089 Insert\SpecialChar \menuseparator
3090 Math\SpecialChar \menuseparator
3096 \begin_layout Subsection
3098 \begin_inset Index idx
3101 \begin_layout Plain Layout
3110 \begin_layout Standard
3118 \begin_inset Index idx
3121 \begin_layout Plain Layout
3129 every character can be displayed canceled.
3130 The characters are quasi accentuated by a slash.
3133 \begin_layout Standard
3135 \begin_inset Tabular
3136 <lyxtabular version="3" rows="4" columns="2">
3137 <features rotate="0" tabularvalignment="middle">
3138 <column alignment="center" valignment="top" width="0pt">
3139 <column alignment="center" valignment="top" width="0pt">
3141 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
3144 \begin_layout Plain Layout
3150 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
3153 \begin_layout Plain Layout
3161 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
3164 \begin_layout Plain Layout
3172 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
3175 \begin_layout Plain Layout
3176 \begin_inset Formula $\not=$
3186 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
3189 \begin_layout Plain Layout
3199 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
3202 \begin_layout Plain Layout
3203 \begin_inset Formula $\not\le$
3213 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
3216 \begin_layout Plain Layout
3226 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
3229 \begin_layout Plain Layout
3230 \begin_inset Formula $\not\parallel$
3246 \begin_layout Standard
3247 The last example shows that not all negations look good.
3248 Therefore there are special commands for some negations (see
3249 \begin_inset CommandInset ref
3251 reference "sub:Mathematical-Symbols"
3256 \begin_inset CommandInset ref
3258 reference "sec:Relations"
3265 \begin_layout Subsection
3267 \begin_inset CommandInset label
3269 name "sub:Placeholders"
3274 \begin_inset Index idx
3277 \begin_layout Plain Layout
3284 \begin_inset Index idx
3287 \begin_layout Plain Layout
3288 Chemical characters ! Isotopes
3294 \begin_inset Index idx
3297 \begin_layout Plain Layout
3302 \begin_layout Plain Layout
3313 \begin_layout Plain Layout
3328 \begin_layout Standard
3330 \begin_inset space \thinspace{}
3334 \begin_inset space \space{}
3341 \begin_layout Plain Layout
3342 Typesetting isotopes and chemical symbols is described in
3343 \begin_inset CommandInset ref
3345 reference "sub:Chemical-Symbols-and"
3354 the following problem occurs:
3357 \begin_layout Standard
3359 \begin_inset Tabular
3360 <lyxtabular version="3" rows="2" columns="2">
3361 <features rotate="0" tabularvalignment="middle">
3362 <column alignment="center" valignment="top" width="0pt">
3363 <column alignment="center" valignment="top" width="0pt">
3365 <cell alignment="center" valignment="top" usebox="none">
3368 \begin_layout Plain Layout
3369 Indices created with sub- and superscripts:
3374 <cell alignment="center" valignment="top" usebox="none">
3377 \begin_layout Plain Layout
3378 \begin_inset Formula $_{9}^{19}\mathrm{F}\raisebox{-3mm}{}$
3388 <cell alignment="center" valignment="top" usebox="none">
3391 \begin_layout Plain Layout
3397 <cell alignment="center" valignment="top" usebox="none">
3400 \begin_layout Plain Layout
3401 \begin_inset Formula $_{\phantom{1}9}^{19}\mathrm{F}$
3415 \begin_inset Note Note
3418 \begin_layout Plain Layout
3425 is only used as spacer.
3433 \begin_layout Standard
3434 The shorter index is by default placed below or above the first character
3435 of the longer index.
3436 To avoid this there is the command
3443 \begin_inset Index idx
3446 \begin_layout Plain Layout
3454 or the math toolbar button
3455 \begin_inset space \thinspace{}
3462 \begin_layout Plain Layout
3463 can be found in the submenu of the toolbar button
3466 arg "math-insert \\space"
3475 \begin_inset Graphics
3476 filename ../images/math/phantom.png
3481 that creates one or more phantom characters.
3488 a small blue box appears that is superposed with two red arrows.
3489 The arrows indicate that the complete width and height of the box content
3490 will be created as placeholder.
3491 Phantom characters are accordingly placeholders with the size of the characters.
3494 \begin_layout Standard
3496 \begin_inset Tabular
3497 <lyxtabular version="3" rows="4" columns="2">
3498 <features rotate="0" tabularvalignment="middle">
3499 <column alignment="center" valignment="top">
3500 <column alignment="center" valignment="top">
3502 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
3505 \begin_layout Plain Layout
3511 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
3514 \begin_layout Plain Layout
3516 \begin_inset Note Note
3519 \begin_layout Plain Layout
3526 is only used as spacer.
3538 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
3541 \begin_layout Plain Layout
3543 \begin_inset space \textvisiblespace{}
3549 \begin_inset space \textvisiblespace{}
3553 \begin_inset Formula $\to$
3557 \begin_inset space \textvisiblespace{}
3565 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
3568 \begin_layout Plain Layout
3569 \begin_inset Formula $\raisebox{4.5mm}{}{}_{\phantom{1}9}^{19}\mathrm{F}\raisebox{-2.5mm}{}$
3579 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
3582 \begin_layout Plain Layout
3584 \begin_inset space \textvisiblespace{}
3590 \begin_inset space \textvisiblespace{}
3594 \begin_inset Formula $\to$
3598 \begin_inset space \textvisiblespace{}
3606 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
3609 \begin_layout Plain Layout
3610 \begin_inset Formula $\raisebox{4.5mm}{}{}_{\phantom{23}9}^{235}\mathrm{F}\raisebox{-2.5mm}{}$
3620 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
3623 \begin_layout Plain Layout
3627 \begin_inset space \textvisiblespace{}
3633 \begin_inset space \textvisiblespace{}
3637 \begin_inset Formula $\to$
3641 \begin_inset space \textvisiblespace{}
3649 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
3652 \begin_layout Plain Layout
3653 \begin_inset Formula $\raisebox{4.5mm}{}\Lambda_{MMt}^{\phantom{ii}t}\raisebox{-2.5mm}{}$
3669 \begin_layout Standard
3670 Furthermore there are the commands
3677 \begin_inset Index idx
3680 \begin_layout Plain Layout
3689 \begin_inset space ~
3693 \begin_inset Graphics
3694 filename ../images/math/vphantom.png
3706 \begin_inset Index idx
3709 \begin_layout Plain Layout
3718 \begin_inset space ~
3722 \begin_inset Graphics
3723 filename ../images/math/hphantom.png
3735 creates only space for the maximal height of the characters in the box
3736 but not for its width.
3743 creates only space for the width of the box content.
3744 Therefore the boxes of both commands have only one red arrow.
3747 \begin_layout Standard
3748 For example the command
3753 \begin_inset space \textvisiblespace{}
3760 creates space for the height of the integral sign,
3764 \begin_layout Plain Layout
3771 creates an integral sign, see
3772 \begin_inset CommandInset ref
3774 reference "sub:Big-Operators"
3783 because this is the larger character.
3784 An example application is in
3785 \begin_inset CommandInset ref
3787 reference "sub:Multiline-Brackets"
3794 \begin_layout Standard
3795 Placeholders can also be used for text when they are inserted via the menu
3798 Insert\SpecialChar \menuseparator
3799 Formatting\SpecialChar \menuseparator
3805 \begin_layout Standard
3807 \begin_inset Newline newline
3811 \begin_inset Phantom Phantom
3814 \begin_layout Plain Layout
3823 \begin_layout Subsection
3825 \begin_inset Index idx
3828 \begin_layout Plain Layout
3835 \begin_inset Index idx
3838 \begin_layout Plain Layout
3839 Formula ! underlined
3847 \begin_layout Standard
3849 \begin_inset Tabular
3850 <lyxtabular version="3" rows="4" columns="2">
3851 <features rotate="0" tabularvalignment="middle">
3852 <column alignment="center" valignment="top" width="0pt">
3853 <column alignment="center" valignment="top" width="0pt">
3855 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
3858 \begin_layout Plain Layout
3864 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
3867 \begin_layout Plain Layout
3869 \begin_inset Note Note
3872 \begin_layout Plain Layout
3879 is only used as spacer.
3891 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
3894 \begin_layout Plain Layout
3898 \begin_inset space \textvisiblespace{}
3902 \begin_inset Index idx
3905 \begin_layout Plain Layout
3918 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
3921 \begin_layout Plain Layout
3922 \begin_inset Formula $\raisebox{5mm}{}\overline{A+B}$
3932 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
3935 \begin_layout Plain Layout
3939 \begin_inset space \textvisiblespace{}
3943 \begin_inset Index idx
3946 \begin_layout Plain Layout
3959 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
3962 \begin_layout Plain Layout
3963 \begin_inset Formula $\underline{A+B}\raisebox{-2.5mm}{}$
3973 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
3976 \begin_layout Plain Layout
3980 \begin_inset space \textvisiblespace{}
3986 \begin_inset space \textvisiblespace{}
3994 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
3997 \begin_layout Plain Layout
3998 \begin_inset Formula $\raisebox{5mm}{}\overline{\underline{A+B}}\raisebox{-2.5mm}{}$
4014 \begin_layout Standard
4015 In the last example it doesn't matter if first
4030 \begin_layout Standard
4031 To double underline use
4040 \begin_layout Standard
4041 It is possible to place up to 6 lines above or below characters.
4044 \begin_layout Standard
4045 \begin_inset VSpace bigskip
4048 Custom lines can be created using the command
4055 \begin_inset Index idx
4058 \begin_layout Plain Layout
4066 which has the following scheme:
4069 \begin_layout Standard
4074 rule[vertical offset]{length}{thickness}
4077 \begin_layout Standard
4078 The optional vertical offset shifts the line upwards (or downwards, when
4079 the value is negative).
4081 \begin_inset CommandInset ref
4083 reference "tab:Available-units"
4087 can be used for the values.
4088 Here are two example lines created with the commands
4089 \begin_inset Newline newline
4096 rule[-2ex]{3cm}{2pt}
4107 \begin_layout Standard
4109 \begin_inset Formula $\rule[-2ex]{3cm}{2pt}\rule{2cm}{1pt}$
4115 \begin_layout Standard
4122 can also be used for text when a line is inserted via the menu
4124 Insert\SpecialChar \menuseparator
4125 Formatting\SpecialChar \menuseparator
4127 \begin_inset space ~
4135 \begin_layout Standard
4137 \begin_inset CommandInset line
4148 \begin_layout Subsection
4150 \begin_inset CommandInset label
4157 \begin_inset Index idx
4160 \begin_layout Plain Layout
4169 \begin_layout Standard
4170 There are different types of ellipses available.
4174 \begin_layout Plain Layout
4175 In the math toolbar in the submenu of the button
4178 arg "math-insert \\ldots"
4186 For listings dots at the baseline are used (
4193 \begin_inset Index idx
4196 \begin_layout Plain Layout
4204 ), while for operations dots are needed that are on the same height as the
4212 \begin_inset Index idx
4215 \begin_layout Plain Layout
4224 When using the command
4231 \begin_inset Index idx
4234 \begin_layout Plain Layout
4242 , LaTeX decides on the basis of the next character what type is used.
4245 \begin_layout Standard
4247 \begin_inset Tabular
4248 <lyxtabular version="3" rows="9" columns="2">
4249 <features rotate="0" tabularvalignment="middle">
4250 <column alignment="center" valignment="top" width="0pt">
4251 <column alignment="center" valignment="top" width="0pt">
4253 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
4256 \begin_layout Plain Layout
4262 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
4265 \begin_layout Plain Layout
4273 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
4276 \begin_layout Plain Layout
4278 \begin_inset space \textvisiblespace{}
4284 \begin_inset space \textvisiblespace{}
4292 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
4295 \begin_layout Plain Layout
4296 \begin_inset Formula $A_{1},\dots,A_{n}$
4306 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
4309 \begin_layout Plain Layout
4311 \begin_inset space \textvisiblespace{}
4317 \begin_inset space \textvisiblespace{}
4325 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
4328 \begin_layout Plain Layout
4329 \begin_inset Formula $A_{1}+\dots+A_{n}$
4339 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
4342 \begin_layout Plain Layout
4344 \begin_inset space \textvisiblespace{}
4350 \begin_inset space \textvisiblespace{}
4358 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
4361 \begin_layout Plain Layout
4362 \begin_inset Formula $A_{1},\ldots,A_{n}$
4372 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
4375 \begin_layout Plain Layout
4377 \begin_inset space \textvisiblespace{}
4383 \begin_inset space \textvisiblespace{}
4391 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
4394 \begin_layout Plain Layout
4395 \begin_inset Formula $A_{1}+\cdots+A_{n}$
4405 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
4408 \begin_layout Plain Layout
4416 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
4419 \begin_layout Plain Layout
4420 \begin_inset Formula $\vdots$
4430 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
4433 \begin_layout Plain Layout
4441 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
4444 \begin_layout Plain Layout
4445 \begin_inset Formula $\ddots$
4455 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
4458 \begin_layout Plain Layout
4466 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
4469 \begin_layout Plain Layout
4470 \begin_inset Formula $\iddots$
4480 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
4483 \begin_layout Plain Layout
4485 \begin_inset space \thinspace{}
4488 matrix with the different dots
4493 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
4496 \begin_layout Plain Layout
4497 \begin_inset Formula $\begin{array}{ccc}
4498 A_{11} & \cdots & A_{1m}\\
4499 \vdots & \ddots & \vdots\\
4500 A_{n1} & \cdots & A_{nm}
4517 \begin_layout Standard
4518 The ellipses available in menu
4520 Insert\SpecialChar \menuseparator
4522 \begin_inset space ~
4536 \begin_layout Standard
4537 \begin_inset VSpace medskip
4546 , one of the options
4548 Use mathdots package (automatically)
4550 must be set in the document settings under
4553 \begin_inset space ~
4559 \begin_inset Newline newline
4564 Use mathdots package
4566 will improve the appearance of all dots in the documents if their font
4567 style or size is not the default.
4570 \begin_layout Standard
4571 \begin_inset VSpace medskip
4574 Specially for matrices there are ellipses that span over several columns.
4575 They are created with the command
4582 \begin_inset Index idx
4585 \begin_layout Plain Layout
4593 , that has the following scheme:
4596 \begin_layout Standard
4601 hdotsfor[distance]{number of columns}
4604 \begin_layout Standard
4605 The number of columns specifies how many columns should be spanned.
4606 Distance is a factor for the distance between the dots.
4609 \begin_layout Standard
4610 In the following matrix the command
4616 was inserted in the first box of the second line, to get an ellipsis with
4617 a dot distance twice as long as with the command
4624 \begin_inset Formula
4626 \left(\begin{array}{cccc}
4635 Note that the matrix fields that should be spanned must be empty, otherwise
4636 you get LaTeX-errors.
4639 \begin_layout Standard
4640 \begin_inset VSpace bigskip
4643 Furthermore you can fill with the command
4650 \begin_inset Index idx
4653 \begin_layout Plain Layout
4661 the rest of a line with dots.
4662 The effect of these commands is the same as with
4669 \begin_inset CommandInset ref
4671 reference "sub:Variable-Space"
4678 \begin_layout Standard
4679 For example the command
4684 \begin_inset space \textvisiblespace{}
4692 \begin_layout Standard
4693 \begin_inset Formula $A\dotfill B$
4699 \begin_layout Standard
4706 there is for a line the command
4713 \begin_inset Index idx
4716 \begin_layout Plain Layout
4727 \begin_layout Standard
4728 \begin_inset Formula $A\hrulefill B$
4734 \begin_layout Standard
4735 To use the commands for text, they have to be inserted in TeX-mode.
4738 \begin_layout Section
4740 \begin_inset CommandInset label
4747 \begin_inset Index idx
4750 \begin_layout Plain Layout
4759 \begin_layout Standard
4760 Matrices can be inserted via the math toolbar button
4763 arg "dialog-show mathmatrix"
4768 Insert\SpecialChar \menuseparator
4769 Math\SpecialChar \menuseparator
4773 In the matrix dialog you can specify the number of columns and rows, the
4774 alignment and the decoration.
4775 The vertical alignment is only of importance for matrices in inline formulas:
4778 \begin_layout Standard
4779 The first matrix is top
4780 \begin_inset Formula $\begin{array}[t]{cccc}
4788 \begin_inset Formula $\begin{array}{cccc}
4795 and the third bottom
4796 \begin_inset Formula $\begin{array}[b]{cccc}
4806 \begin_layout Standard
4807 The horizontal alignment specifies how the column entries should be aligned.
4808 It is set by entering a letter for every column.
4813 denotes left aligned,
4822 To create for example a 4
4827 \begin_inset space ~
4830 matrix where the first column is left aligned, the second and third are
4831 centered and the last one is right aligned, one enters for the horizontal
4837 Normally in a matrix all columns are centered, therefore the default for
4845 \begin_layout Standard
4846 Horizontal alignment:
4849 \begin_layout Standard
4855 \begin_inset Formula $\begin{array}{lll}
4867 \begin_inset Formula $\begin{array}{ccc}
4879 \begin_inset Formula $\begin{array}{rrr}
4889 \begin_layout Standard
4890 To add or delete rows and columns subsequently, the math toolbar buttons
4894 arg "inset-modify tabular append-row"
4900 arg "inset-modify tabular delete-row"
4904 \begin_inset space \thinspace{}
4909 Edit\SpecialChar \menuseparator
4913 New rows can also be created with
4916 arg "newline-insert newline"
4922 \begin_layout Standard
4923 \begin_inset VSpace bigskip
4930 adds parentheses in the selected style around the matrix.
4931 Alternatively, parentheses can can either be created with the commands
4939 \begin_inset Index idx
4942 \begin_layout Plain Layout
4957 \begin_inset Index idx
4960 \begin_layout Plain Layout
4971 \begin_inset space ~
4977 \begin_inset CommandInset ref
4979 reference "sub:Automatic-Bracket-Size"
4983 , or by using the following commands:
4984 \begin_inset VSpace medskip
4990 \begin_layout Standard
4991 \begin_inset space \hfill{}
4995 \begin_inset Tabular
4996 <lyxtabular version="3" rows="4" columns="2">
4997 <features rotate="0" tabularvalignment="middle">
4998 <column alignment="center" valignment="top">
4999 <column alignment="center" valignment="top">
5001 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
5004 \begin_layout Plain Layout
5010 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
5013 \begin_layout Plain Layout
5015 \begin_inset Note Note
5018 \begin_layout Plain Layout
5025 is only used as spacer.
5037 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
5040 \begin_layout Plain Layout
5044 \begin_inset space \textvisiblespace{}
5052 \begin_inset space \thinspace{}
5060 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
5063 \begin_layout Plain Layout
5064 \begin_inset Formula $\raisebox{7.5mm}{}\begin{bmatrix}\begin{array}{cc}
5065 0 & \textrm{-}\mathrm{i}\\
5067 \end{array}\end{bmatrix}\raisebox{-5.3mm}{}$
5077 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
5080 \begin_layout Plain Layout
5084 \begin_inset space \textvisiblespace{}
5092 \begin_inset space \thinspace{}
5100 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
5103 \begin_layout Plain Layout
5104 \begin_inset Formula $\raisebox{7.5mm}{}\begin{Bmatrix}\begin{array}{cc}
5105 0 & \textrm{-}\mathrm{i}\\
5107 \end{array}\end{Bmatrix}\raisebox{-5.3mm}{}$
5117 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
5120 \begin_layout Plain Layout
5124 \begin_inset space \textvisiblespace{}
5132 \begin_inset space \thinspace{}
5140 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
5143 \begin_layout Plain Layout
5144 \begin_inset Formula $\raisebox{7.5mm}{}\begin{pmatrix}\begin{array}{cc}
5145 0 & \textrm{-}\mathrm{i}\\
5147 \end{array}\end{pmatrix}\raisebox{-5.3mm}{}$
5161 \begin_inset space \hfill{}
5165 \begin_inset Tabular
5166 <lyxtabular version="3" rows="4" columns="2">
5167 <features rotate="0" tabularvalignment="middle">
5168 <column alignment="center" valignment="top">
5169 <column alignment="center" valignment="top">
5171 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
5174 \begin_layout Plain Layout
5180 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
5183 \begin_layout Plain Layout
5191 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
5194 \begin_layout Plain Layout
5198 \begin_inset space \textvisiblespace{}
5206 \begin_inset space \thinspace{}
5214 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
5217 \begin_layout Plain Layout
5218 \begin_inset Formula $\raisebox{7.5mm}{}\begin{vmatrix}\begin{array}{cc}
5219 0 & \textrm{-}\mathrm{i}\\
5221 \end{array}\end{vmatrix}\raisebox{-5.3mm}{}$
5231 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
5234 \begin_layout Plain Layout
5238 \begin_inset space \textvisiblespace{}
5246 \begin_inset space \thinspace{}
5254 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
5257 \begin_layout Plain Layout
5258 \begin_inset Formula $\raisebox{7.5mm}{}\begin{Vmatrix}\begin{array}{cc}
5259 0 & \textrm{-}\mathrm{i}\\
5261 \end{array}\end{Vmatrix}\raisebox{-5.3mm}{}$
5271 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
5274 \begin_layout Plain Layout
5278 \begin_inset space \textvisiblespace{}
5286 \begin_inset space \thinspace{}
5294 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
5297 \begin_layout Plain Layout
5298 \begin_inset Formula $\raisebox{7.5mm}{}\begin{matrix}\begin{array}{cc}
5299 0 & \textrm{-}\mathrm{i}\\
5301 \end{array}\end{matrix}\raisebox{-5.3mm}{}$
5315 \begin_inset space \hfill{}
5321 \begin_layout Standard
5322 \begin_inset VSpace medskip
5326 \begin_inset space \thinspace{}
5330 \begin_inset space \space{}
5339 is inserted, a blue box appears between two vertical lines where the matrix
5341 \begin_inset Newline newline
5344 Note that decorated matrices ignore the vertical alignment.
5347 \begin_layout Standard
5348 \begin_inset VSpace bigskip
5351 As all multiline formulas are matrices, the length
5358 \begin_inset Index idx
5361 \begin_layout Plain Layout
5369 that is described in
5370 \begin_inset CommandInset ref
5372 reference "sub:Column-Separation"
5376 can also be used to change the column separation of matrices.
5379 \begin_layout Standard
5380 To change the row separation, the command
5387 \begin_inset Index idx
5390 \begin_layout Plain Layout
5399 It is used as follows:
5402 \begin_layout Standard
5409 arraystretch}{stretch factor}
5410 \begin_inset Index idx
5413 \begin_layout Plain Layout
5424 \begin_layout Standard
5431 assigns the stretch factor to the predefined command
5439 \begin_inset space \thinspace{}
5443 \begin_inset space \space{}
5446 the row separation, use the factor 2.
5447 This is then used for all following matrices.
5448 To go back to the original separation, assign the factor 1 to
5457 \begin_layout Standard
5458 To set matrices into a text line, the command
5465 \begin_inset Index idx
5468 \begin_layout Plain Layout
5477 When it is inserted a blue box with two dashed lines appears.
5478 In this box the matrix is inserted.
5481 \begin_layout Standard
5483 \begin_inset Formula $\left(\begin{smallmatrix}A & B\\
5485 \end{smallmatrix}\right)$
5491 \begin_layout Section
5492 Brackets and Delimiters
5493 \begin_inset Index idx
5496 \begin_layout Plain Layout
5503 \begin_inset Index idx
5506 \begin_layout Plain Layout
5515 \begin_layout Subsection
5516 Vertical Brackets and Delimiters
5517 \begin_inset Index idx
5520 \begin_layout Plain Layout
5529 \begin_layout Standard
5530 \begin_inset space \hfill{}
5534 \begin_inset Tabular
5535 <lyxtabular version="3" rows="9" columns="2">
5536 <features rotate="0" tabularvalignment="middle">
5537 <column alignment="center" valignment="top" width="0pt">
5538 <column alignment="center" valignment="top" width="0pt">
5540 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
5543 \begin_layout Plain Layout
5549 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
5552 \begin_layout Plain Layout
5560 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
5563 \begin_layout Plain Layout
5569 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
5572 \begin_layout Plain Layout
5573 \begin_inset Formula $($
5583 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
5586 \begin_layout Plain Layout
5592 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
5595 \begin_layout Plain Layout
5596 \begin_inset Formula $\{$
5606 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
5609 \begin_layout Plain Layout
5615 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
5618 \begin_layout Plain Layout
5619 \begin_inset Formula $[$
5629 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
5632 \begin_layout Plain Layout
5640 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
5643 \begin_layout Plain Layout
5644 \begin_inset Formula $\langle$
5654 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
5657 \begin_layout Plain Layout
5665 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
5668 \begin_layout Plain Layout
5669 \begin_inset Formula $\lceil$
5679 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
5682 \begin_layout Plain Layout
5690 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
5693 \begin_layout Plain Layout
5694 \begin_inset Formula $\lfloor$
5704 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
5707 \begin_layout Plain Layout
5713 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
5716 \begin_layout Plain Layout
5717 \begin_inset Formula $/$
5727 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
5730 \begin_layout Plain Layout
5736 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
5739 \begin_layout Plain Layout
5740 \begin_inset Formula $|$
5754 \begin_inset space \hfill{}
5758 \begin_inset Tabular
5759 <lyxtabular version="3" rows="9" columns="2">
5760 <features rotate="0" tabularvalignment="middle">
5761 <column alignment="center" valignment="top" width="0pt">
5762 <column alignment="center" valignment="top" width="0pt">
5764 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
5767 \begin_layout Plain Layout
5773 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
5776 \begin_layout Plain Layout
5784 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
5787 \begin_layout Plain Layout
5793 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
5796 \begin_layout Plain Layout
5797 \begin_inset Formula $)$
5807 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
5810 \begin_layout Plain Layout
5816 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
5819 \begin_layout Plain Layout
5820 \begin_inset Formula $\}$
5830 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
5833 \begin_layout Plain Layout
5839 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
5842 \begin_layout Plain Layout
5843 \begin_inset Formula $]$
5853 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
5856 \begin_layout Plain Layout
5864 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
5867 \begin_layout Plain Layout
5868 \begin_inset Formula $\rangle$
5878 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
5881 \begin_layout Plain Layout
5889 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
5892 \begin_layout Plain Layout
5893 \begin_inset Formula $\rceil$
5903 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
5906 \begin_layout Plain Layout
5914 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
5917 \begin_layout Plain Layout
5918 \begin_inset Formula $\rfloor$
5928 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
5931 \begin_layout Plain Layout
5941 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
5944 \begin_layout Plain Layout
5945 \begin_inset Formula $\backslash$
5955 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
5958 \begin_layout Plain Layout
5966 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
5969 \begin_layout Plain Layout
5970 \begin_inset Formula $\|$
5984 \begin_inset space \hfill{}
5990 \begin_layout Standard
5993 \begin_inset Note Greyedout
5996 \begin_layout Plain Layout
6001 In TeX-mode the command
6008 \begin_inset Index idx
6011 \begin_layout Plain Layout
6019 must be used for the backslash, because the command
6027 produces a line break there.
6035 \begin_layout Standard
6036 For all characters listed above the size can be adjusted with the commands
6037 described in the following two subsections.
6038 When using these commands, the characters < and > can directly be used
6039 instead of the commands
6054 \begin_layout Subsubsection
6056 \begin_inset CommandInset label
6058 name "sub:Manual-Bracket-Size"
6063 \begin_inset Index idx
6066 \begin_layout Plain Layout
6067 Bracket size ! manual
6075 \begin_layout Standard
6076 The bracket size can be specified manually by the LaTeX-commands
6083 \begin_inset Index idx
6086 \begin_layout Plain Layout
6119 denotes the smallest and
6125 the largest bracket size.
6128 \begin_layout Standard
6129 These commands are used to emphasize levels of brackets:
6132 \begin_layout Standard
6134 \begin_inset Tabular
6135 <lyxtabular version="3" rows="2" columns="2">
6136 <features rotate="0" tabularvalignment="middle">
6137 <column alignment="center" valignment="top" width="0pt">
6138 <column alignment="center" valignment="top" width="0pt">
6140 <cell alignment="center" valignment="top" usebox="none">
6143 \begin_layout Plain Layout
6144 all brackets in the same size:
6149 <cell alignment="center" valignment="top" usebox="none">
6152 \begin_layout Plain Layout
6153 \begin_inset Formula $((A+B)(A-B))^{C}\raisebox{-4mm}{}$
6163 <cell alignment="center" valignment="top" usebox="none">
6166 \begin_layout Plain Layout
6172 <cell alignment="center" valignment="top" usebox="none">
6175 \begin_layout Plain Layout
6176 \begin_inset Formula $\Big((A+B)(A-B)\Big)^{C}$
6190 \begin_inset Note Note
6193 \begin_layout Plain Layout
6200 is only used as spacer.
6208 \begin_layout Standard
6209 For the second formula the command
6216 \begin_inset space \textvisiblespace{}
6224 \begin_layout Standard
6225 Here is an overview about all bracket sizes:
6228 \begin_layout Standard
6245 \begin_inset space \textvisiblespace{}
6253 \begin_inset space \textvisiblespace{}
6257 \begin_inset space \textvisiblespace{}
6267 \begin_layout Standard
6269 \begin_inset Formula $\Bigg(\exp\bigg<\Big[\big\{\ln(3x)\big\}^{2}\sin(x)\Big]^{A}\bigg>\Bigg)^{0,5}$
6275 \begin_layout Standard
6282 -commands there is the variant
6289 \begin_inset Index idx
6292 \begin_layout Plain Layout
6300 that adds a bit more space between the bracket and its content, and the
6314 \begin_inset Index idx
6317 \begin_layout Plain Layout
6327 , that don't add additional space.
6332 at the end of the command
6338 is for a left bracket; for a right bracket this will be replaced by an
6344 A left or right bracket can each be an opening or closing bracket.
6347 \begin_layout Standard
6348 In the following table is a comparison of the variants:
6351 \begin_layout Standard
6353 \begin_inset Tabular
6354 <lyxtabular version="3" rows="5" columns="2">
6355 <features rotate="0" tabularvalignment="middle">
6356 <column alignment="center" valignment="middle">
6357 <column alignment="center" valignment="middle">
6359 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
6362 \begin_layout Plain Layout
6368 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
6371 \begin_layout Plain Layout
6373 \begin_inset Note Note
6376 \begin_layout Plain Layout
6383 is only used as spacer.
6395 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
6398 \begin_layout Plain Layout
6408 \begin_inset space \textvisiblespace{}
6418 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
6421 \begin_layout Plain Layout
6422 \begin_inset Formula $\raisebox{5.5mm}{}\Bigm(\bigm(\ln(3x)\bigm)^{2}\Bigm)\raisebox{-3.25mm}{}$
6432 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
6435 \begin_layout Plain Layout
6445 \begin_inset space \textvisiblespace{}
6455 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
6458 \begin_layout Plain Layout
6459 \begin_inset Formula $\raisebox{5.5mm}{}\Big(\big(\ln(3x)\big)^{2}\Big)\raisebox{-3.25mm}{}$
6469 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
6472 \begin_layout Plain Layout
6482 \begin_inset space \textvisiblespace{}
6492 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
6495 \begin_layout Plain Layout
6496 \begin_inset Formula $\raisebox{5.5mm}{}\Bigl(\bigl(\ln(3x)\bigr)^{2}\Bigr)\raisebox{-3.25mm}{}$
6506 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
6509 \begin_layout Plain Layout
6521 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
6524 \begin_layout Plain Layout
6525 \begin_inset Formula $\raisebox{4.5mm}{}\bigl)\ln(3x)\bigr(\raisebox{-2mm}{}$
6541 \begin_layout Subsubsection
6542 Automatic Bracket Size
6543 \begin_inset CommandInset label
6545 name "sub:Automatic-Bracket-Size"
6550 \begin_inset Index idx
6553 \begin_layout Plain Layout
6554 Bracket size ! automatic
6562 \begin_layout Standard
6563 Brackets with variable size can be inserted with the commands
6570 \begin_inset Index idx
6573 \begin_layout Plain Layout
6588 \begin_inset Index idx
6591 \begin_layout Plain Layout
6599 or via the math toolbar button
6602 arg "dialog-show mathdelimiter"
6618 the wanted bracket must be inserted.
6619 The bracket size will then automatically be calculated for the output.
6622 \begin_layout Standard
6624 normal bracket: The command
6631 \begin_inset space \textvisiblespace{}
6635 \begin_inset Formula $\downarrow$
6639 \begin_inset space \textvisiblespace{}
6645 \begin_inset Formula
6655 \begin_layout Standard
6657 multiline bracket: The command
6666 \begin_inset space \textvisiblespace{}
6670 \begin_inset Formula $\downarrow$
6674 \begin_inset space \textvisiblespace{}
6682 \begin_inset Formula
6684 \ln\left(\frac{A}{C}\right)
6692 \begin_layout Standard
6708 \begin_inset space ~
6714 This has the advantage that you can see in LyX immediately the real bracket
6715 size and that the matching right bracket will be created too.
6716 \begin_inset Newline newline
6719 The command for the last example would then be:
6730 \begin_inset space \textvisiblespace{}
6734 \begin_inset Formula $\downarrow$
6740 \begin_layout Standard
6741 To omit a left or right bracket, a dot is inserted for the omitted bracket.
6742 For example the command
6749 \begin_inset space \textvisiblespace{}
6753 \begin_inset Formula $\downarrow$
6757 \begin_inset space \textvisiblespace{}
6767 \begin_inset Formula
6769 \left.\frac{A}{B}\right\}
6788 will be converted by LyX to brackets in the right size when the document
6789 is reloaded and an omitted bracket will appear as dashed line.
6792 \begin_layout Standard
6793 \begin_inset VSpace bigskip
6796 Because all popular LaTeX-Distributions use eTeX, an extension to LaTeX,
6804 \begin_inset Index idx
6807 \begin_layout Plain Layout
6815 is additionally available for all brackets and limits.
6816 With this command the height of the following character is adapted to the
6817 one of the surrounding brackets, what is e.
6818 \begin_inset space \thinspace{}
6822 \begin_inset space \space{}
6825 needed for physical vectors:
6826 \begin_inset Formula
6828 \left\langle \phi\:\middle|\: J=\frac{3}{2}\,,\, M_{J}\right\rangle
6833 For physical vectors there is a special LaTeX-package, described in
6834 \begin_inset CommandInset ref
6836 reference "sub:Physical-Vectors"
6843 \begin_layout Subsection
6845 \begin_inset Index idx
6848 \begin_layout Plain Layout
6849 Brackets ! horizontal
6857 \begin_layout Standard
6859 \begin_inset Tabular
6860 <lyxtabular version="3" rows="4" columns="2">
6861 <features rotate="0" tabularvalignment="middle">
6862 <column alignment="center" valignment="top" width="0pt">
6863 <column alignment="center" valignment="top" width="0pt">
6865 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
6868 \begin_layout Plain Layout
6870 \begin_inset Note Note
6873 \begin_layout Plain Layout
6880 is only used as spacer.
6890 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
6893 \begin_layout Plain Layout
6901 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
6904 \begin_layout Plain Layout
6908 \begin_layout Plain Layout
6920 \begin_inset space \textvisiblespace{}
6924 \begin_inset space \textvisiblespace{}
6931 \begin_layout Plain Layout
6939 \begin_inset Index idx
6942 \begin_layout Plain Layout
6955 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
6958 \begin_layout Plain Layout
6959 \begin_inset Formula $\overbrace{A+B}^{3}$
6969 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
6972 \begin_layout Plain Layout
6976 \begin_layout Plain Layout
6988 \begin_inset space \textvisiblespace{}
6992 \begin_inset space \textvisiblespace{}
6999 \begin_layout Plain Layout
7007 \begin_inset Index idx
7010 \begin_layout Plain Layout
7023 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
7026 \begin_layout Plain Layout
7027 \begin_inset Formula $\underbrace{A+B}_{5}$
7037 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
7040 \begin_layout Plain Layout
7044 \begin_inset space \textvisiblespace{}
7050 \begin_inset space \textvisiblespace{}
7054 \begin_inset space \textvisiblespace{}
7058 \begin_inset space \textvisiblespace{}
7062 \begin_inset space \textvisiblespace{}
7066 \begin_inset space \textvisiblespace{}
7070 \begin_inset space \textvisiblespace{}
7078 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
7081 \begin_layout Plain Layout
7082 \begin_inset Formula $\overbrace{\underbrace{A+B_{w}}_{7}}^{C}$
7098 \begin_layout Standard
7099 In the last example it doesn't matter if
7111 is inserted at first.
7114 \begin_layout Standard
7115 \begin_inset VSpace bigskip
7118 When brackets are needed that overlap each other, multiline formulas, as
7120 \begin_inset CommandInset ref
7122 reference "sec:Multiline-Formulas"
7127 \begin_inset Formula
7129 A & = & \underbrace{gggg+bbqq}_{r}+\: dddd\\
7130 & & \hphantom{gggg+\:}\underbrace{\hphantom{bbqq+dddd}}_{s}
7135 In the first row the formula is inserted together with the first brace.
7136 It is hereby important that the space command
7140 \begin_layout Plain Layout
7141 Space commands are explained in
7142 \begin_inset CommandInset ref
7144 reference "sub:Predefined-Space"
7159 is inserted before the first
7160 \begin_inset Formula $d$
7163 , because the brace that ends behind the
7164 \begin_inset Formula $q$
7167 prevents that the following
7168 \begin_inset Quotes eld
7172 \begin_inset Quotes erd
7175 is surrounded by space.
7179 \begin_layout Plain Layout
7180 because a bracket is not handled as a character, see
7181 \begin_inset CommandInset ref
7183 reference "sub:Binary-Operators"
7192 In the second row the second brace is inserted.
7193 As it should begin before the
7194 \begin_inset Formula $b$
7209 \begin_layout Plain Layout
7217 \begin_inset CommandInset ref
7219 reference "sub:Placeholders"
7228 This space is needed because the
7229 \begin_inset Quotes eld
7233 \begin_inset Quotes erd
7236 is also surrounded by space in the formula.
7237 The brace is placed under the command
7246 \begin_layout Standard
7247 It gets more complicated when brackets overlap each other, like in the following
7252 \begin_layout Plain Layout
7264 \begin_inset Formula
7266 & & \hphantom{gggg+\:}\overbrace{\hphantom{bbqq+dddd}}^{s}\\
7267 A & = & \underbrace{gggg+bbqq}_{r}+\: dddd
7276 \begin_layout Plain Layout
7287 The first formula row is the same as the second row of the previous example,
7288 with the difference that the brace is above.
7289 The second row contains the formula together with the second brace.
7290 To avoid that there is space between the upper brace in the first row and
7291 the formula, the row spacing needs to be reduced.
7292 This is not easily possible due to a bug in LyX
7296 \begin_layout Plain Layout
7297 \begin_inset CommandInset href
7299 name "LyX-bug #1505"
7300 target "http://www.lyx.org/trac/ticket/1505"
7310 As a solution for the problem, the global formula row separation
7317 \begin_inset Index idx
7320 \begin_layout Plain Layout
7328 must be changed to -6
7329 \begin_inset space \thinspace{}
7332 pt before the formula with the command
7347 is set back after the formula to the standard value of 3
7348 \begin_inset space \thinspace{}
7351 pt using the same command.
7352 More about the row separation in formulas is explained in
7353 \begin_inset CommandInset ref
7355 reference "sub:Line-Separation"
7362 \begin_layout Section
7364 \begin_inset Index idx
7367 \begin_layout Plain Layout
7376 \begin_layout Standard
7377 Arrows can be inserted via the math toolbar button
7380 arg "math-insert \\leftarrow"
7383 or the commands listed in the following subsections.
7386 \begin_layout Subsection
7388 \begin_inset Index idx
7391 \begin_layout Plain Layout
7400 \begin_layout Standard
7401 \begin_inset space \hfill{}
7405 \begin_inset Tabular
7406 <lyxtabular version="3" rows="8" columns="2">
7407 <features rotate="0" tabularvalignment="middle">
7408 <column alignment="center" valignment="top" width="0pt">
7409 <column alignment="center" valignment="top" width="0pt">
7411 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
7414 \begin_layout Plain Layout
7420 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
7423 \begin_layout Plain Layout
7431 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
7434 \begin_layout Plain Layout
7442 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
7445 \begin_layout Plain Layout
7446 \begin_inset Formula $\gets$
7456 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
7459 \begin_layout Plain Layout
7467 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
7470 \begin_layout Plain Layout
7471 \begin_inset Formula $\Leftarrow$
7481 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
7484 \begin_layout Plain Layout
7492 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
7495 \begin_layout Plain Layout
7496 \begin_inset Formula $\longleftarrow$
7506 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
7509 \begin_layout Plain Layout
7517 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
7520 \begin_layout Plain Layout
7521 \begin_inset Formula $\Longleftarrow$
7531 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
7534 \begin_layout Plain Layout
7542 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
7545 \begin_layout Plain Layout
7546 \begin_inset Formula $\leftharpoonup$
7556 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
7559 \begin_layout Plain Layout
7567 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
7570 \begin_layout Plain Layout
7571 \begin_inset Formula $\leftharpoondown$
7581 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
7584 \begin_layout Plain Layout
7592 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
7595 \begin_layout Plain Layout
7596 \begin_inset Formula $\hookleftarrow$
7610 \begin_inset space \hfill{}
7614 \begin_inset Tabular
7615 <lyxtabular version="3" rows="8" columns="2">
7616 <features rotate="0" tabularvalignment="middle">
7617 <column alignment="center" valignment="top" width="0pt">
7618 <column alignment="center" valignment="top" width="0pt">
7620 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
7623 \begin_layout Plain Layout
7629 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
7632 \begin_layout Plain Layout
7640 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
7643 \begin_layout Plain Layout
7651 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
7654 \begin_layout Plain Layout
7655 \begin_inset Formula $\to$
7665 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
7668 \begin_layout Plain Layout
7676 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
7679 \begin_layout Plain Layout
7680 \begin_inset Formula $\Rightarrow$
7690 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
7693 \begin_layout Plain Layout
7701 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
7704 \begin_layout Plain Layout
7705 \begin_inset Formula $\longrightarrow$
7715 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
7718 \begin_layout Plain Layout
7726 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
7729 \begin_layout Plain Layout
7730 \begin_inset Formula $\Longrightarrow$
7740 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
7743 \begin_layout Plain Layout
7751 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
7754 \begin_layout Plain Layout
7755 \begin_inset Formula $\rightharpoonup$
7765 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
7768 \begin_layout Plain Layout
7776 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
7779 \begin_layout Plain Layout
7780 \begin_inset Formula $\rightharpoondown$
7790 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
7793 \begin_layout Plain Layout
7801 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
7804 \begin_layout Plain Layout
7805 \begin_inset Formula $\hookrightarrow$
7819 \begin_inset space \hfill{}
7825 \begin_layout Standard
7826 \begin_inset space \hfill{}
7830 \begin_inset Tabular
7831 <lyxtabular version="3" rows="6" columns="2">
7832 <features rotate="0" tabularvalignment="middle">
7833 <column alignment="center" valignment="top" width="0pt">
7834 <column alignment="center" valignment="top" width="0pt">
7836 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
7839 \begin_layout Plain Layout
7845 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
7848 \begin_layout Plain Layout
7856 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
7859 \begin_layout Plain Layout
7867 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
7870 \begin_layout Plain Layout
7871 \begin_inset Formula $\leftrightarrow$
7881 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
7884 \begin_layout Plain Layout
7892 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
7895 \begin_layout Plain Layout
7896 \begin_inset Formula $\Leftrightarrow$
7906 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
7909 \begin_layout Plain Layout
7917 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
7920 \begin_layout Plain Layout
7921 \begin_inset Formula $\longleftrightarrow$
7931 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
7934 \begin_layout Plain Layout
7942 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
7945 \begin_layout Plain Layout
7946 \begin_inset Formula $\Longleftrightarrow$
7956 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
7959 \begin_layout Plain Layout
7967 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
7970 \begin_layout Plain Layout
7971 \begin_inset Formula $\rightleftharpoons$
7985 \begin_inset space \hspace{}
7990 \begin_inset space \hfill{}
7994 \begin_inset Tabular
7995 <lyxtabular version="3" rows="5" columns="2">
7996 <features rotate="0" tabularvalignment="middle">
7997 <column alignment="center" valignment="top" width="0pt">
7998 <column alignment="center" valignment="top" width="0pt">
8000 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
8003 \begin_layout Plain Layout
8009 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
8012 \begin_layout Plain Layout
8020 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
8023 \begin_layout Plain Layout
8031 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
8034 \begin_layout Plain Layout
8035 \begin_inset Formula $\mapsto$
8045 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
8048 \begin_layout Plain Layout
8056 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
8059 \begin_layout Plain Layout
8060 \begin_inset Formula $\longmapsto$
8070 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
8073 \begin_layout Plain Layout
8081 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
8084 \begin_layout Plain Layout
8085 \begin_inset Formula $\leadsto$
8095 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
8098 \begin_layout Plain Layout
8106 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
8109 \begin_layout Plain Layout
8110 \begin_inset Formula $\dasharrow$
8124 \begin_inset space \hfill{}
8130 \begin_layout Standard
8131 \begin_inset VSpace medskip
8134 Arrows used as accents like e.
8135 \begin_inset space \thinspace{}
8139 \begin_inset space \space{}
8142 vector arrows are listed in
8143 \begin_inset CommandInset ref
8145 reference "sec:Accents"
8152 \begin_layout Standard
8153 \begin_inset VSpace bigskip
8156 Furthermore there are the labeled arrows
8157 \begin_inset Index idx
8160 \begin_layout Plain Layout
8173 \begin_inset Index idx
8176 \begin_layout Plain Layout
8191 \begin_inset Index idx
8194 \begin_layout Plain Layout
8201 \begin_layout Plain Layout
8216 When inserting one of these commands in a formula, an arrow with two blue
8217 boxes appear where the label can be inserted.
8218 The length of the arrow adapts to the label width.
8221 \begin_layout Standard
8223 \begin_inset Tabular
8224 <lyxtabular version="3" rows="3" columns="2">
8225 <features rotate="0" tabularvalignment="middle">
8226 <column alignment="center" valignment="top" width="0pt">
8227 <column alignment="center" valignment="top" width="0pt">
8229 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
8232 \begin_layout Plain Layout
8238 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
8241 \begin_layout Plain Layout
8243 \begin_inset Note Note
8246 \begin_layout Plain Layout
8253 is only used as spacer.
8265 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
8268 \begin_layout Plain Layout
8272 \begin_inset space \textvisiblespace{}
8276 \begin_inset Formula $\downarrow$
8280 \begin_inset Formula $\to$
8288 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
8291 \begin_layout Plain Layout
8292 \begin_inset Formula $\raisebox{5mm}{}F(a)\xleftarrow[x>0]{x=a}F(x)\raisebox{-4mm}{}$
8302 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
8305 \begin_layout Plain Layout
8309 \begin_inset space \textvisiblespace{}
8313 \begin_inset Formula $\downarrow$
8317 \begin_inset Formula $\to$
8325 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
8328 \begin_layout Plain Layout
8329 \begin_inset Formula $\raisebox{5mm}{}F(x)\xrightarrow[x>0]{x=a}F(a)\raisebox{-4mm}{}$
8345 \begin_layout Subsection
8346 Vertical and diagonal Arrows
8347 \begin_inset Index idx
8350 \begin_layout Plain Layout
8357 \begin_inset Index idx
8360 \begin_layout Plain Layout
8369 \begin_layout Standard
8370 \begin_inset space \hfill{}
8374 \begin_inset Tabular
8375 <lyxtabular version="3" rows="7" columns="2">
8376 <features rotate="0" tabularvalignment="middle">
8377 <column alignment="center" valignment="top" width="0pt">
8378 <column alignment="center" valignment="top" width="0pt">
8380 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
8383 \begin_layout Plain Layout
8389 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
8392 \begin_layout Plain Layout
8400 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
8403 \begin_layout Plain Layout
8411 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
8414 \begin_layout Plain Layout
8415 \begin_inset Formula $\uparrow$
8425 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
8428 \begin_layout Plain Layout
8436 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
8439 \begin_layout Plain Layout
8440 \begin_inset Formula $\Uparrow$
8450 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
8453 \begin_layout Plain Layout
8461 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
8464 \begin_layout Plain Layout
8465 \begin_inset Formula $\updownarrow$
8475 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
8478 \begin_layout Plain Layout
8486 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
8489 \begin_layout Plain Layout
8490 \begin_inset Formula $\Updownarrow$
8500 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
8503 \begin_layout Plain Layout
8511 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
8514 \begin_layout Plain Layout
8515 \begin_inset Formula $\Downarrow$
8525 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
8528 \begin_layout Plain Layout
8536 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
8539 \begin_layout Plain Layout
8540 \begin_inset Formula $\downarrow$
8554 \begin_inset space \hfill{}
8558 \begin_inset Tabular
8559 <lyxtabular version="3" rows="5" columns="2">
8560 <features rotate="0" tabularvalignment="middle">
8561 <column alignment="center" valignment="top" width="0pt">
8562 <column alignment="center" valignment="top" width="0pt">
8564 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
8567 \begin_layout Plain Layout
8573 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
8576 \begin_layout Plain Layout
8584 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
8587 \begin_layout Plain Layout
8595 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
8598 \begin_layout Plain Layout
8599 \begin_inset Formula $\nearrow$
8609 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
8612 \begin_layout Plain Layout
8620 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
8623 \begin_layout Plain Layout
8624 \begin_inset Formula $\searrow$
8634 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
8637 \begin_layout Plain Layout
8645 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
8648 \begin_layout Plain Layout
8649 \begin_inset Formula $\swarrow$
8659 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
8662 \begin_layout Plain Layout
8670 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
8673 \begin_layout Plain Layout
8674 \begin_inset Formula $\nwarrow$
8688 \begin_inset space \hfill{}
8694 \begin_layout Standard
8695 \begin_inset VSpace medskip
8698 Vertical arrows can be used also as delimiters together with the commands
8700 \begin_inset CommandInset ref
8702 reference "sub:Manual-Bracket-Size"
8707 \begin_inset CommandInset ref
8709 reference "sub:Automatic-Bracket-Size"
8716 \begin_layout Section
8718 \begin_inset CommandInset label
8725 \begin_inset Index idx
8728 \begin_layout Plain Layout
8737 \begin_layout Standard
8738 Accents can be inserted via the math toolbar button
8741 arg "math-insert \\hat"
8744 or the commands listed in the following subsections.
8747 \begin_layout Subsection
8748 Accents for one Character
8752 \begin_layout Plain Layout
8765 \begin_layout Plain Layout
8767 \begin_inset CommandInset ref
8769 reference "sub:Accents-in-Text"
8782 \begin_layout Plain Layout
8790 \begin_inset Note Note
8793 \begin_layout Plain Layout
8800 is used to avoid that the footnote appears in the PDF-bookmark.
8803 \begin_layout Plain Layout
8811 \begin_inset CommandInset ref
8813 reference "sub:Formulas-in-Section"
8823 \begin_inset CommandInset label
8825 name "sub:Accents-for-one"
8830 \begin_inset Index idx
8833 \begin_layout Plain Layout
8834 Accents ! for one character
8842 \begin_layout Standard
8843 \begin_inset space \hfill{}
8847 \begin_inset Tabular
8848 <lyxtabular version="3" rows="8" columns="2">
8849 <features rotate="0" tabularvalignment="middle">
8850 <column alignment="center" valignment="top" width="0pt">
8851 <column alignment="center" valignment="top" width="0pt">
8853 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
8856 \begin_layout Plain Layout
8862 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
8865 \begin_layout Plain Layout
8867 \begin_inset Note Note
8870 \begin_layout Plain Layout
8877 is only used as spacer.
8889 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
8892 \begin_layout Plain Layout
8896 \begin_inset space \textvisiblespace{}
8904 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
8907 \begin_layout Plain Layout
8908 \begin_inset Formula $\raisebox{5mm}{}\dot{A}$
8918 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
8921 \begin_layout Plain Layout
8925 \begin_inset space \textvisiblespace{}
8933 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
8936 \begin_layout Plain Layout
8937 \begin_inset Formula $\raisebox{5mm}{}\ddot{A}$
8947 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
8950 \begin_layout Plain Layout
8954 \begin_inset space \textvisiblespace{}
8962 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
8965 \begin_layout Plain Layout
8966 \begin_inset Formula $\raisebox{5mm}{}\dddot{A}$
8976 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
8979 \begin_layout Plain Layout
8983 \begin_inset space \textvisiblespace{}
8991 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
8994 \begin_layout Plain Layout
8995 \begin_inset Formula $\raisebox{5mm}{}\ddddot{A}$
9005 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
9008 \begin_layout Plain Layout
9012 \begin_inset space \textvisiblespace{}
9016 \begin_inset Index idx
9019 \begin_layout Plain Layout
9030 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
9033 \begin_layout Plain Layout
9034 \begin_inset Formula $\raisebox{5mm}{}\vec{A}$
9044 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
9047 \begin_layout Plain Layout
9051 \begin_inset space \textvisiblespace{}
9059 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
9062 \begin_layout Plain Layout
9063 \begin_inset Formula $\raisebox{5mm}{}\bar{A}$
9073 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
9076 \begin_layout Plain Layout
9080 \begin_inset space \textvisiblespace{}
9088 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
9091 \begin_layout Plain Layout
9092 \begin_inset Formula $\raisebox{5mm}{}\mathring{A}$
9106 \begin_inset space \hfill{}
9110 \begin_inset Tabular
9111 <lyxtabular version="3" rows="7" columns="2">
9112 <features rotate="0" tabularvalignment="middle">
9113 <column alignment="center" valignment="top" width="0pt">
9114 <column alignment="center" valignment="top" width="0pt">
9116 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
9119 \begin_layout Plain Layout
9125 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
9128 \begin_layout Plain Layout
9136 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
9139 \begin_layout Plain Layout
9143 \begin_inset space \textvisiblespace{}
9151 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
9154 \begin_layout Plain Layout
9155 \begin_inset Formula $\raisebox{5mm}{}\tilde{A}$
9165 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
9168 \begin_layout Plain Layout
9172 \begin_inset space \textvisiblespace{}
9180 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
9183 \begin_layout Plain Layout
9184 \begin_inset Formula $\raisebox{5mm}{}\hat{A}$
9194 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
9197 \begin_layout Plain Layout
9201 \begin_inset space \textvisiblespace{}
9209 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
9212 \begin_layout Plain Layout
9213 \begin_inset Formula $\raisebox{5mm}{}\check{A}$
9223 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
9226 \begin_layout Plain Layout
9230 \begin_inset space \textvisiblespace{}
9238 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
9241 \begin_layout Plain Layout
9242 \begin_inset Formula $\raisebox{5mm}{}\acute{A}$
9252 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
9255 \begin_layout Plain Layout
9259 \begin_inset space \textvisiblespace{}
9267 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
9270 \begin_layout Plain Layout
9271 \begin_inset Formula $\raisebox{5mm}{}\grave{A}$
9281 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
9284 \begin_layout Plain Layout
9288 \begin_inset space \textvisiblespace{}
9296 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
9299 \begin_layout Plain Layout
9300 \begin_inset Formula $\raisebox{5mm}{}\breve{A}$
9314 \begin_inset space \hfill{}
9320 \begin_layout Standard
9321 \begin_inset VSpace bigskip
9327 \begin_layout Standard
9328 You can directly insert accents like é to formulas.
9329 LyX will transform them to the corresponding accent command.
9331 \begin_inset Index idx
9334 \begin_layout Plain Layout
9340 it is better to insert a quotation mark before the vowel.
9341 These two characters are then treated by LaTeX as
9345 character when the formula part with the umlaut is marked as German.
9353 \begin_inset Quotes eld
9357 \begin_inset Quotes erd
9360 umlauts are created as demonstrated in the following example:
9363 \begin_layout Standard
9364 \begin_inset VSpace -2mm
9370 \begin_layout Standard
9372 \begin_inset Tabular
9373 <lyxtabular version="3" rows="3" columns="2">
9374 <features rotate="0" tabularvalignment="middle">
9375 <column alignment="center" valignment="top">
9376 <column alignment="center" valignment="top">
9378 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
9381 \begin_layout Plain Layout
9387 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
9390 \begin_layout Plain Layout
9392 \begin_inset Note Note
9395 \begin_layout Plain Layout
9403 \begin_inset space \thinspace{}
9406 pt space are only used as spacer.
9418 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
9421 \begin_layout Plain Layout
9424 \begin_inset Quotes grd
9432 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
9435 \begin_layout Plain Layout
9436 \begin_inset space \hspace{}
9443 \begin_inset Formula $"i$
9453 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
9456 \begin_layout Plain Layout
9460 \begin_inset space \textvisiblespace{}
9468 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
9471 \begin_layout Plain Layout
9472 \begin_inset Formula $\raisebox{5mm}{}\ddot{i}$
9488 \begin_layout Standard
9489 Another advantage to
9495 is that umlauts can directly be converted to mathematical text because
9496 the accent commands above are
9502 in mathematical text
9505 To convert an accented character to mathematical text, only the character
9506 under the accent may be converted.
9507 This applies also for all other conversions, e.
9508 \begin_inset space \thinspace{}
9512 \begin_inset space \space{}
9518 \begin_layout Standard
9519 In mathematical text, umlauts and other accented characters can directly
9523 \begin_layout Standard
9524 \begin_inset VSpace bigskip
9530 \begin_layout Standard
9531 LyX also supports a tilde under the character if the LaTeX-package
9536 \begin_inset Index idx
9539 \begin_layout Plain Layout
9540 Packages ! undertilde
9545 is installed on your system:
9548 \begin_layout Standard
9552 \begin_layout Plain Layout
9562 \begin_inset Note Note
9565 \begin_layout Plain Layout
9566 The following table will only be displayed when the LaTeX-package
9578 \begin_layout Standard
9581 \begin_inset Tabular
9582 <lyxtabular version="3" rows="2" columns="2">
9583 <features rotate="0" tabularvalignment="middle">
9584 <column alignment="center" valignment="top" width="0pt">
9585 <column alignment="center" valignment="top" width="0pt">
9587 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
9590 \begin_layout Plain Layout
9596 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
9599 \begin_layout Plain Layout
9607 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
9610 \begin_layout Plain Layout
9614 \begin_inset space \textvisiblespace{}
9622 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
9625 \begin_layout Plain Layout
9626 \begin_inset Formula $\raisebox{5mm}{}\utilde{A}$
9642 \begin_layout Standard
9646 \begin_layout Plain Layout
9656 \begin_inset Note Note
9659 \begin_layout Plain Layout
9660 The following will be displayed when the LaTeX-package
9672 \begin_layout Standard
9673 You need to install the LaTeX-package
9677 to see the rest of this subsection in the output.
9680 \begin_layout Standard
9684 \begin_layout Plain Layout
9696 \begin_layout Subsection
9697 Accents for several Characters
9698 \begin_inset Index idx
9701 \begin_layout Plain Layout
9702 Accents ! for several characters
9710 \begin_layout Standard
9711 \begin_inset space \hfill{}
9715 \begin_inset Tabular
9716 <lyxtabular version="3" rows="5" columns="2">
9717 <features rotate="0" tabularvalignment="middle">
9718 <column alignment="center" valignment="top" width="0pt">
9719 <column alignment="center" valignment="top" width="0pt">
9721 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
9724 \begin_layout Plain Layout
9730 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
9733 \begin_layout Plain Layout
9735 \begin_inset Note Note
9738 \begin_layout Plain Layout
9745 is only used as spacer.
9757 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
9760 \begin_layout Plain Layout
9764 \begin_inset space \textvisiblespace{}
9772 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
9775 \begin_layout Plain Layout
9776 \begin_inset Formula $\raisebox{6mm}{}\overleftarrow{A=B}\raisebox{-2mm}{}$
9786 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
9789 \begin_layout Plain Layout
9793 \begin_inset space \textvisiblespace{}
9801 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
9804 \begin_layout Plain Layout
9805 \begin_inset Formula $\raisebox{5mm}{}\underleftarrow{A=B}\raisebox{-3mm}{}$
9815 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
9818 \begin_layout Plain Layout
9822 \begin_inset space \textvisiblespace{}
9830 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
9833 \begin_layout Plain Layout
9834 \begin_inset Formula $\raisebox{6mm}{}\overleftrightarrow{A=B}\raisebox{-2mm}{}$
9844 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
9847 \begin_layout Plain Layout
9851 \begin_inset space \textvisiblespace{}
9859 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
9862 \begin_layout Plain Layout
9863 \begin_inset Formula $\raisebox{5mm}{}\underleftrightarrow{A=B}\raisebox{-3mm}{}$
9877 \begin_inset space \hfill{}
9881 \begin_inset Tabular
9882 <lyxtabular version="3" rows="5" columns="2">
9883 <features rotate="0" tabularvalignment="middle">
9884 <column alignment="center" valignment="top" width="0pt">
9885 <column alignment="center" valignment="top" width="0pt">
9887 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
9890 \begin_layout Plain Layout
9896 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
9899 \begin_layout Plain Layout
9907 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
9910 \begin_layout Plain Layout
9914 \begin_inset space \textvisiblespace{}
9922 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
9925 \begin_layout Plain Layout
9926 \begin_inset Formula $\raisebox{6mm}{}\overrightarrow{A=B}\raisebox{-2mm}{}$
9936 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
9939 \begin_layout Plain Layout
9943 \begin_inset space \textvisiblespace{}
9951 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
9954 \begin_layout Plain Layout
9955 \begin_inset Formula $\raisebox{5mm}{}\underrightarrow{A=B}\raisebox{-3mm}{}$
9965 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
9968 \begin_layout Plain Layout
9972 \begin_inset space \textvisiblespace{}
9980 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
9983 \begin_layout Plain Layout
9984 \begin_inset Formula $\raisebox{6mm}{}\widetilde{A=B}\raisebox{-2mm}{}$
9994 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
9997 \begin_layout Plain Layout
10001 \begin_inset space \textvisiblespace{}
10009 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
10012 \begin_layout Plain Layout
10013 \begin_inset Formula $\raisebox{6mm}{}\widehat{A=B}\raisebox{-2mm}{}$
10027 \begin_inset space \hfill{}
10033 \begin_layout Standard
10034 \begin_inset VSpace medskip
10037 With these commands as many characters as you like can be accented.
10050 will only be set in the output with a length of three characters, as shown
10051 in the following example:
10052 \begin_inset Formula
10054 \widetilde{A+B=C-D}
10062 \begin_layout Standard
10070 \begin_inset Index idx
10073 \begin_layout Plain Layout
10088 \begin_inset Index idx
10091 \begin_layout Plain Layout
10099 described in the previous subsection it is also possible to accent several
10106 \begin_inset space \textvisiblespace{}
10110 \begin_inset Formula $\downarrow$
10116 \begin_inset Formula
10118 \underset{***}{A=B}
10126 \begin_layout Standard
10127 \begin_inset Newpage newpage
10133 \begin_layout Section
10135 \begin_inset CommandInset label
10142 \begin_inset Index idx
10145 \begin_layout Plain Layout
10154 \begin_layout Subsection
10156 \begin_inset CommandInset label
10158 name "sub:Predefined-Space"
10163 \begin_inset Index idx
10166 \begin_layout Plain Layout
10167 Space ! horizontal ! predefined
10175 \begin_layout Standard
10176 Sometimes it is necessary to insert horizontal space into a formula.
10177 This is done by inserting a protected space (shortcut
10180 arg "command-alternatives space-insert protected ; math-space"
10185 \begin_inset Quotes eld
10191 \begin_inset space \textvisiblespace{}
10197 \begin_inset Quotes erd
10200 appears and by pressing
10204 several times one can select one of eight different space sizes.
10205 The spaces can also be inserted using the math toolbar button
10208 arg "math-insert \\space"
10211 or special commands.
10212 Independent from the inserted command, one can select the size again by
10220 \begin_layout Standard
10223 \begin_inset Tabular
10224 <lyxtabular version="3" rows="6" columns="3">
10225 <features rotate="0" tabularvalignment="middle">
10226 <column alignment="center" valignment="top">
10227 <column alignment="center" valignment="top" width="15col%">
10228 <column alignment="center" valignment="top">
10230 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
10233 \begin_layout Plain Layout
10239 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
10242 \begin_layout Plain Layout
10252 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
10255 \begin_layout Plain Layout
10263 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
10266 \begin_layout Plain Layout
10274 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
10277 \begin_layout Plain Layout
10283 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
10286 \begin_layout Plain Layout
10287 \begin_inset Formula $A\, B$
10297 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
10300 \begin_layout Plain Layout
10308 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
10311 \begin_layout Plain Layout
10317 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
10320 \begin_layout Plain Layout
10321 \begin_inset Formula $A\: B$
10331 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
10334 \begin_layout Plain Layout
10342 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
10345 \begin_layout Plain Layout
10351 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
10354 \begin_layout Plain Layout
10355 \begin_inset Formula $A\; B$
10365 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
10368 \begin_layout Plain Layout
10376 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
10379 \begin_layout Plain Layout
10385 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
10388 \begin_layout Plain Layout
10389 \begin_inset Formula $A\quad B$
10399 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
10402 \begin_layout Plain Layout
10410 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
10413 \begin_layout Plain Layout
10419 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
10422 \begin_layout Plain Layout
10423 \begin_inset Formula $A\qquad B$
10437 \begin_inset space \hfill{}
10441 \begin_inset Tabular
10442 <lyxtabular version="3" rows="6" columns="3">
10443 <features rotate="0" tabularvalignment="middle">
10444 <column alignment="center" valignment="top">
10445 <column alignment="center" valignment="top" width="15col%">
10446 <column alignment="center" valignment="top">
10448 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
10451 \begin_layout Plain Layout
10457 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
10460 \begin_layout Plain Layout
10470 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
10473 \begin_layout Plain Layout
10481 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
10484 \begin_layout Plain Layout
10492 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
10495 \begin_layout Plain Layout
10501 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
10504 \begin_layout Plain Layout
10505 \begin_inset Formula $A\hfill B$
10515 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
10518 \begin_layout Plain Layout
10526 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
10529 \begin_layout Plain Layout
10535 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
10538 \begin_layout Plain Layout
10539 \begin_inset Formula $A\hspace*{1em}B$
10549 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
10552 \begin_layout Plain Layout
10560 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
10563 \begin_layout Plain Layout
10569 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
10572 \begin_layout Plain Layout
10573 \begin_inset Formula $A\hspace{1em}B$
10583 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
10586 \begin_layout Plain Layout
10590 \begin_inset space \textvisiblespace{}
10598 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
10601 \begin_layout Plain Layout
10607 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
10610 \begin_layout Plain Layout
10611 \begin_inset Formula $A\ B$
10621 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
10624 \begin_layout Plain Layout
10632 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
10635 \begin_layout Plain Layout
10641 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
10644 \begin_layout Plain Layout
10645 \begin_inset Formula $A\! B$
10661 \begin_layout Standard
10663 \begin_inset space ~
10667 \begin_inset space \thinspace{}
10671 \begin_inset space \thinspace{}
10674 7 are variable spaces which are explained in
10675 \begin_inset CommandInset ref
10677 reference "sub:Variable-Space"
10683 \begin_inset space ~
10686 9 seems to produce no space.
10687 It is displayed red in LyX contrary to the other sizes, because it is a
10689 There are two more negative spaces:
10692 \begin_layout Standard
10694 \begin_inset Tabular
10695 <lyxtabular version="3" rows="3" columns="3">
10696 <features rotate="0" tabularvalignment="middle">
10697 <column alignment="center" valignment="middle" width="6.8cm">
10698 <column alignment="center" valignment="top" width="0pt">
10699 <column alignment="center" valignment="top" width="0pt">
10701 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
10704 \begin_layout Plain Layout
10710 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
10713 \begin_layout Plain Layout
10721 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
10724 \begin_layout Plain Layout
10734 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
10737 \begin_layout Plain Layout
10742 keystrokes after inserting the protected space
10747 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
10750 \begin_layout Plain Layout
10756 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
10759 \begin_layout Plain Layout
10767 <cell multicolumn="1" alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
10770 \begin_layout Plain Layout
10776 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
10779 \begin_layout Plain Layout
10780 \begin_inset Formula $A\negmedspace B$
10788 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
10791 \begin_layout Plain Layout
10792 \begin_inset Formula $A\negthickspace B$
10808 \begin_layout Standard
10809 Negative spaces can lead to characters overlapping each other.
10810 Thus they can be used to enforce ligatures, which are e.
10811 \begin_inset space \thinspace{}
10815 \begin_inset space \space{}
10818 useful for summation operators:
10821 \begin_layout Standard
10823 \begin_inset Tabular
10824 <lyxtabular version="3" rows="3" columns="2">
10825 <features rotate="0" tabularvalignment="middle">
10826 <column alignment="center" valignment="top">
10827 <column alignment="center" valignment="top">
10829 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
10832 \begin_layout Plain Layout
10838 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
10841 \begin_layout Plain Layout
10843 \begin_inset Note Note
10846 \begin_layout Plain Layout
10853 is only used as spacer.
10865 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
10868 \begin_layout Plain Layout
10874 \begin_inset space \textvisiblespace{}
10882 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
10885 \begin_layout Plain Layout
10886 \begin_inset Formula $\raisebox{4.5mm}{}\sum\sum f_{kl}\raisebox{-2.5mm}{}$
10896 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
10899 \begin_layout Plain Layout
10907 \begin_inset space \textvisiblespace{}
10915 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
10918 \begin_layout Plain Layout
10919 \begin_inset Formula $\raisebox{4.5mm}{}\sum\negmedspace\sum f_{kl}\raisebox{-2.5mm}{}$
10935 \begin_layout Standard
10937 \begin_inset VSpace medskip
10943 \begin_layout Standard
10945 Relations like for example equal signs, are always surrounded by space.
10946 To suppress this, the equal sign is placed into a TeX-brace.
10947 The following example demonstrates this:
10950 \begin_layout Standard
10952 \begin_inset Tabular
10953 <lyxtabular version="3" rows="2" columns="2">
10954 <features rotate="0" tabularvalignment="middle">
10955 <column alignment="center" valignment="top" width="0pt">
10956 <column alignment="center" valignment="top" width="0pt">
10958 <cell alignment="center" valignment="top" usebox="none">
10961 \begin_layout Plain Layout
10967 <cell alignment="center" valignment="top" usebox="none">
10970 \begin_layout Plain Layout
10971 \begin_inset Formula $A=B$
10981 <cell alignment="center" valignment="top" usebox="none">
10984 \begin_layout Plain Layout
10985 \begin_inset Note Note
10988 \begin_layout Plain Layout
10995 is only used as spacer.
11001 \begin_inset Formula $\raisebox{5mm}{}$
11004 equation without space
11009 <cell multicolumn="1" alignment="center" valignment="top" usebox="none">
11012 \begin_layout Plain Layout
11013 \begin_inset Formula $A{=}B$
11029 \begin_layout Standard
11031 The command for the last formula is:
11036 \begin_inset Formula $\to$
11042 \begin_layout Standard
11043 \begin_inset VSpace bigskip
11049 \begin_layout Standard
11050 Spaces are needed for physical units, because the space between the value
11051 and the unit is the smallest one and not a normal space.
11052 For units in text, the smallest space is inserted via the menu
11054 Insert\SpecialChar \menuseparator
11055 Formatting\SpecialChar \menuseparator
11057 \begin_inset space ~
11065 arg "space-insert thin"
11071 \begin_layout Standard
11072 An example to visualize the difference:
11075 \begin_layout Standard
11076 \begin_inset Tabular
11077 <lyxtabular version="3" rows="2" columns="2">
11078 <features rotate="0" tabularvalignment="middle">
11079 <column alignment="left" valignment="top">
11080 <column alignment="left" valignment="top">
11082 <cell alignment="center" valignment="top" usebox="none">
11085 \begin_layout Plain Layout
11087 \begin_inset Formula $\cdot$
11095 <cell alignment="center" valignment="top" usebox="none">
11098 \begin_layout Plain Layout
11099 space between value and unit
11106 <cell alignment="center" valignment="top" usebox="none">
11109 \begin_layout Plain Layout
11111 \begin_inset space \thinspace{}
11115 \begin_inset Formula $\cdot$
11123 <cell alignment="center" valignment="top" usebox="none">
11126 \begin_layout Plain Layout
11127 smallest space between value and unit
11140 \begin_layout Subsection
11145 \begin_layout Plain Layout
11158 \begin_layout Plain Layout
11159 for vertical space in formulas see
11160 \begin_inset CommandInset ref
11162 reference "sub:Line-Separation"
11175 \begin_layout Plain Layout
11183 \begin_inset Note Note
11186 \begin_layout Plain Layout
11189 texorpdfstring is used to avoid that the footnote appears in the PDF-bookmark.
11192 \begin_layout Plain Layout
11195 texorpdfstring is in section
11196 \begin_inset CommandInset ref
11198 reference "sub:Formulas-in-Section"
11208 \begin_inset CommandInset label
11210 name "sub:Variable-Space"
11215 \begin_inset Index idx
11218 \begin_layout Plain Layout
11219 Space ! horizontal ! variable
11227 \begin_layout Standard
11228 Space with a defined length can be inserted with the command
11235 \begin_inset Index idx
11238 \begin_layout Plain Layout
11248 \begin_inset Quotes eld
11254 \begin_inset space \textvisiblespace{}
11260 \begin_inset Quotes erd
11264 The length can be specified by left-clicking on the
11265 \begin_inset Quotes eld
11271 \begin_inset space \textvisiblespace{}
11277 \begin_inset Quotes erd
11281 The length may also be negative.
11282 When a space would be the first character in a line it would be omitted.
11283 To force its output use the command
11295 or left-click on the
11296 \begin_inset Quotes eld
11302 \begin_inset space \textvisiblespace{}
11308 \begin_inset Quotes erd
11311 and check the option
11316 \begin_inset Newline newline
11319 To insert as much space as is available, the command
11326 \begin_inset Index idx
11329 \begin_layout Plain Layout
11340 \begin_layout Standard
11341 \begin_inset VSpace -1mm
11347 \begin_layout Standard
11349 \begin_inset Tabular
11350 <lyxtabular version="3" rows="4" columns="2">
11351 <features rotate="0" tabularvalignment="middle">
11352 <column alignment="center" valignment="top">
11353 <column alignment="center" valignment="top">
11355 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
11358 \begin_layout Plain Layout
11366 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
11369 \begin_layout Plain Layout
11377 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
11380 \begin_layout Plain Layout
11384 \begin_inset space \textvisiblespace{}
11390 \begin_inset space \thinspace{}
11398 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
11401 \begin_layout Plain Layout
11402 \begin_inset Formula $A=B\hspace{3cm}A\not=C$
11412 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
11415 \begin_layout Plain Layout
11419 \begin_inset space \textvisiblespace{}
11425 \begin_inset space \thinspace{}
11433 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
11436 \begin_layout Plain Layout
11437 \begin_inset Formula $A\hspace{-1mm}A\not=A$
11447 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
11450 \begin_layout Plain Layout
11454 \begin_inset space \textvisiblespace{}
11462 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
11465 \begin_layout Plain Layout
11466 \begin_inset Formula $A=A\hfill B=B$
11482 \begin_layout Standard
11483 In the last example the available space is given by the longest column entry
11485 In an inline formula the space depends on the length of the line in which
11493 Thus, when the line uses the full width, no space will be created.
11500 only has an effect on displayed formulas when the formula style
11505 (Formula styles are explained in
11506 \begin_inset CommandInset ref
11508 reference "sec:Formula-Styles"
11515 \begin_layout Standard
11522 , there are the commands
11534 that fill the space with a pattern, see
11535 \begin_inset CommandInset ref
11537 reference "sub:Ellipses"
11544 \begin_layout Standard
11545 For text, variable space can be inserted via the menu
11547 Insert\SpecialChar \menuseparator
11548 Formatting\SpecialChar \menuseparator
11550 \begin_inset space ~
11558 \begin_layout Standard
11559 This is a line with
11560 \begin_inset space \hspace{}
11565 \begin_inset space \thinspace{}
11571 \begin_layout Standard
11572 This is a line with
11573 \begin_inset space \hfill{}
11579 \begin_layout Subsection
11580 Space besides inline Formulas
11581 \begin_inset Index idx
11584 \begin_layout Plain Layout
11585 Space ! besides inline formulas
11593 \begin_layout Standard
11594 The space that surrounds inline formulas can be adjusted with the length
11602 \begin_inset Index idx
11605 \begin_layout Plain Layout
11614 The value of a length is set with the command
11621 \begin_inset Index idx
11624 \begin_layout Plain Layout
11632 which has the following scheme:
11635 \begin_layout Standard
11640 setlength{length name}{value}
11643 \begin_layout Standard
11651 \begin_inset space \thinspace{}
11657 \begin_layout Standard
11667 \begin_layout Standard
11668 is inserted in TeX-mode.
11670 \begin_inset space \thinspace{}
11673 mm space will now be set around all inline formulas:
11677 \begin_layout Plain Layout
11691 \begin_layout Standard
11692 This is a line with an inline formula
11693 \begin_inset Formula $A=B$
11697 \begin_inset space \thinspace{}
11700 mm surrounding space.
11704 \begin_layout Plain Layout
11718 \begin_layout Standard
11719 To return to the predefined value,
11725 is set to the value 0
11726 \begin_inset space \thinspace{}
11732 \begin_layout Section
11734 \begin_inset Index idx
11737 \begin_layout Plain Layout
11744 \begin_inset Index idx
11747 \begin_layout Plain Layout
11752 \begin_layout Plain Layout
11763 \begin_layout Plain Layout
11778 \begin_layout Standard
11779 Boxes for text are described in chapter
11786 \begin_inset space ~
11794 \begin_layout Subsection
11796 \begin_inset CommandInset label
11798 name "sub:Boxes-with-Frame"
11803 \begin_inset Index idx
11806 \begin_layout Plain Layout
11815 \begin_layout Standard
11816 It is possible to frame a formula or part of one with the commands
11823 \begin_inset Index idx
11826 \begin_layout Plain Layout
11841 \begin_inset Index idx
11844 \begin_layout Plain Layout
11855 \begin_layout Standard
11856 When one of these commands is inserted in a formula, a blue box appears
11857 within a frame to enter formula parts.
11864 an additional formula has to be created by
11868 within this box, because the box content will otherwise be treated as mathemati
11876 is used, a new formula is automatically created inside the frame.
11879 \begin_layout Standard
11886 is not suitable to frame displayed formulas because the formula will always
11887 be set in the size of the text.
11894 is in contrary not suitable to frame inline formulas, because the formula
11895 will always be set in the size of a displayed formula.
11898 \begin_layout Standard
11912 \begin_inset Index idx
11915 \begin_layout Plain Layout
11923 where additionally the frame width and the alignment can be specified.
11930 is used in the following scheme:
11933 \begin_layout Standard
11938 framebox[frame width][position]{box content}
11941 \begin_layout Standard
11942 The position can either be
11959 right aligns the formula in the box.
11960 When no position is given, the formula will be centered.
11961 \begin_inset Newline newline
11964 If no width is given, also no position can be given.
11965 In this case the frame width is adjusted to the box content like for
11974 \begin_layout Standard
11981 is inserted, a box appears containing three blue boxes.
11982 The first two boxes are surrounded by brackets and denote the two optional
11984 The third box is for formula parts like for
11993 \begin_layout Standard
11994 \begin_inset Newpage newpage
12000 \begin_layout Standard
12002 \begin_inset Tabular
12003 <lyxtabular version="3" rows="5" columns="2">
12004 <features rotate="0" tabularvalignment="middle">
12005 <column alignment="center" valignment="top">
12006 <column alignment="center" valignment="top">
12008 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
12011 \begin_layout Plain Layout
12017 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
12020 \begin_layout Plain Layout
12022 \begin_inset Note Note
12025 \begin_layout Plain Layout
12032 is only used as spacer.
12044 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
12047 \begin_layout Plain Layout
12051 \begin_inset space \textvisiblespace{}
12061 \begin_inset space \textvisiblespace{}
12069 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
12072 \begin_layout Plain Layout
12073 \begin_inset Formula $\raisebox{6mm}{}\fbox{\ensuremath{\int A=B}}\raisebox{-4mm}{}$
12083 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
12086 \begin_layout Plain Layout
12090 \begin_inset space \textvisiblespace{}
12096 \begin_inset space \textvisiblespace{}
12104 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
12107 \begin_layout Plain Layout
12108 \begin_inset Formula $\raisebox{8.5mm}{}\boxed{\int A=B}\raisebox{-6.5mm}{}$
12118 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
12121 \begin_layout Plain Layout
12125 \begin_inset space \textvisiblespace{}
12133 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
12136 \begin_layout Plain Layout
12137 \begin_inset Formula $\raisebox{6mm}{}A+\fbox{B}\raisebox{-3mm}{}$
12147 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
12150 \begin_layout Plain Layout
12154 \begin_inset space \textvisiblespace{}
12158 \begin_inset Formula $\to$
12162 \begin_inset Formula $\to$
12172 \begin_inset space \textvisiblespace{}
12176 \begin_inset Formula $\downarrow$
12184 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
12187 \begin_layout Plain Layout
12188 \begin_inset Formula $\raisebox{6mm}{}$
12192 \begin_inset Formula $\framebox[20mm][]{\ensuremath{\frac{A}{B}}}$
12196 \begin_inset Formula $\raisebox{-4mm}{}$
12212 \begin_layout Standard
12213 The frame thickness can also be adjusted.
12214 To do this the following commands have to be inserted in TeX-mode before
12218 \begin_layout Standard
12228 \begin_inset Quotes eld
12232 \begin_inset Quotes erd
12246 \begin_inset Quotes eld
12250 \begin_inset Quotes erd
12256 \begin_layout Standard
12257 \begin_inset Quotes eld
12261 \begin_inset Quotes erd
12264 specifies the minimal distance between the frame and the first character
12266 An example for this is the following framed formula:
12270 \begin_layout Plain Layout
12282 \begin_inset Formula
12289 Before this formula the commands
12292 \begin_layout Standard
12314 \begin_layout Standard
12315 were inserted in TeX-mode.
12316 The given values are used for all following boxes.
12319 \begin_layout Standard
12320 To return to the standard frame size, the command
12323 \begin_layout Standard
12348 \begin_layout Plain Layout
12362 \begin_layout Standard
12363 is inserted in TeX-mode before the next formula.
12366 \begin_layout Subsection
12367 Boxes without Frame
12368 \begin_inset CommandInset label
12370 name "sub:Boxes-without-Frame"
12375 \begin_inset Index idx
12378 \begin_layout Plain Layout
12379 Boxes ! without frame
12387 \begin_layout Standard
12388 For boxes without a frame there are the following box commands:
12395 \begin_inset Index idx
12398 \begin_layout Plain Layout
12413 \begin_inset Index idx
12416 \begin_layout Plain Layout
12431 \begin_inset Index idx
12434 \begin_layout Plain Layout
12445 \begin_layout Standard
12452 a box can be super- or subscripted.
12453 But in contrary to normal super- and subscripting, the characters in the
12454 box keep their font size.
12461 is used in the following scheme:
12464 \begin_layout Standard
12469 raisebox{height}{box content}
12472 \begin_layout Standard
12473 When the box should contain a formula, an extra formula is needed like for
12484 \begin_inset Note Greyedout
12487 \begin_layout Plain Layout
12498 this extra formula is created by pressing
12502 twice instead of once because LyX doesn't yet support
12516 \begin_layout Standard
12518 \begin_inset Tabular
12519 <lyxtabular version="3" rows="4" columns="2">
12520 <features rotate="0" tabularvalignment="middle">
12521 <column alignment="center" valignment="top">
12522 <column alignment="center" valignment="top">
12524 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
12527 \begin_layout Plain Layout
12533 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
12536 \begin_layout Plain Layout
12544 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
12547 \begin_layout Plain Layout
12551 \begin_inset Formula $\to$
12557 \begin_inset Formula $\to$
12565 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
12568 \begin_layout Plain Layout
12569 \begin_inset Formula $H\raisebox{2mm}{al}lo$
12579 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
12582 \begin_layout Plain Layout
12586 \begin_inset Formula $\to$
12592 \begin_inset Formula $\to$
12600 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
12603 \begin_layout Plain Layout
12604 \begin_inset Formula $H\raisebox{-2mm}{al}lo$
12614 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
12617 \begin_layout Plain Layout
12621 \begin_inset Formula $\to$
12637 \begin_inset space \textvisiblespace{}
12645 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
12648 \begin_layout Plain Layout
12649 \begin_inset Formula $A=\raisebox{-2mm}{\mbox{\ensuremath{\sqrt{B}}}}$
12665 \begin_layout Standard
12690 , with the difference that there is no frame.
12693 \begin_layout Subsection
12695 \begin_inset CommandInset label
12697 name "sub:Colored-Boxes"
12702 \begin_inset Index idx
12705 \begin_layout Plain Layout
12714 \begin_layout Standard
12715 To be able to use all commands explained in this section, the LaTeX-package
12724 \begin_layout Plain Layout
12729 is part of every LaTeX standard installation.
12735 \begin_inset Index idx
12738 \begin_layout Plain Layout
12744 has to be loaded in the LaTeX-preamble with the line
12748 \begin_layout Plain Layout
12749 When text is colored somewhere in the document with a predefined color,
12750 LyX loads the LaTeX-package
12755 Thus it is possible that the package is loaded twice, but this does not
12762 \begin_inset Note Note
12765 \begin_layout Plain Layout
12766 To avoid that the package is loaded twice, a macro was inserted to the LaTeX-pre
12775 \begin_layout Standard
12783 \begin_layout Standard
12784 \begin_inset VSpace medskip
12787 To color boxes, the command
12794 \begin_inset Index idx
12797 \begin_layout Plain Layout
12805 is used in the following scheme:
12808 \begin_layout Standard
12813 colorbox{color}{box content}
12816 \begin_layout Standard
12817 The box content can also be a box and a
12823 can also be part of another box (see the 2nd and 3rd example).
12824 When the box should contain a formula, an extra formula has to be created,
12825 the same way as for
12835 \begin_layout Plain Layout
12836 This also applies for the command
12850 \begin_layout Standard
12851 One of the following predefined colors can be chosen:
12854 \begin_layout Standard
12888 \begin_layout Standard
12890 \begin_inset Tabular
12891 <lyxtabular version="3" rows="4" columns="2">
12892 <features rotate="0" tabularvalignment="middle">
12893 <column alignment="center" valignment="top">
12894 <column alignment="center" valignment="top">
12896 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
12899 \begin_layout Plain Layout
12905 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
12908 \begin_layout Plain Layout
12910 \begin_inset Note Note
12913 \begin_layout Plain Layout
12920 is only used as spacer.
12932 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
12935 \begin_layout Plain Layout
12939 \begin_inset Formula $\to$
12949 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
12952 \begin_layout Plain Layout
12953 \begin_inset Formula $\raisebox{6mm}{}\colorbox{yellow}{A=B}\raisebox{-3mm}{}$
12963 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
12966 \begin_layout Plain Layout
12970 \begin_inset Formula $\to$
12978 \begin_inset space \textvisiblespace{}
12986 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
12989 \begin_layout Plain Layout
12990 \begin_inset Formula $\raisebox{6mm}{}\colorbox{green}{\fbox{A=B}}\raisebox{-3mm}{}$
13000 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
13003 \begin_layout Plain Layout
13007 \begin_inset space \textvisiblespace{}
13013 \begin_inset Formula $\to$
13029 \begin_inset space \textvisiblespace{}
13037 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
13040 \begin_layout Plain Layout
13041 \begin_inset Formula $\raisebox{7mm}{}\fbox{\colorbox{green}{\mbox{\ensuremath{\int C=D}}}}\raisebox{-5mm}{}$
13057 \begin_layout Standard
13064 only colors the box but not the characters in the box.
13065 To color all characters, the whole formula is highlighted and the desired
13066 color is chosen in the
13069 \begin_inset space ~
13075 The dialog can be called with the toolbar button
13078 arg "dialog-show character"
13083 Edit\SpecialChar \menuseparator
13085 \begin_inset space ~
13088 Style\SpecialChar \menuseparator
13092 The formula number then has the same color as the formula.
13093 When the formula number should get another color than the formula characters,
13094 the color must be changed within the formula.
13097 \begin_layout Standard
13101 \begin_layout Standard
13104 \begin_inset Formula
13106 \int A=B\label{eq:red}
13114 \begin_inset Formula
13116 \textcolor{red}{\int A=B}\label{eq:redgreen}
13124 \begin_layout Standard
13126 \begin_inset CommandInset ref
13132 is completely colored red.
13133 \begin_inset Newline newline
13137 \begin_inset CommandInset ref
13139 reference "eq:redgreen"
13143 was first completely colored green to set the color for the formula number.
13144 Subsequently the formula characters were colored red.
13147 \begin_layout Standard
13148 \begin_inset VSpace bigskip
13151 To color the frame different than the rest of the box, the command
13158 \begin_inset Index idx
13161 \begin_layout Plain Layout
13169 is used in the following scheme:
13172 \begin_layout Standard
13177 fcolorbox{frame color}{color}{box content}
13180 \begin_layout Standard
13187 is an extension of the command
13194 The frame width is set, like for
13217 \begin_layout Plain Layout
13229 \begin_inset Formula
13231 \fcolorbox{cyan}{magenta}{A=B}
13240 \begin_layout Plain Layout
13254 \begin_layout Standard
13255 This formula was created with the command
13256 \begin_inset Newline newline
13264 \begin_inset Formula $\to$
13270 \begin_inset Formula $\to$
13280 \begin_layout Standard
13281 \begin_inset VSpace bigskip
13284 To use other colors than the predefined ones, they have to be defined first.
13287 \begin_layout Standard
13288 One can for example define the color
13289 \begin_inset Quotes eld
13297 \begin_inset Quotes erd
13300 with the LaTeX-preamble line:
13303 \begin_layout Standard
13308 definecolor{darkgreen}{cmyk}{0.5,
13323 \begin_inset Index idx
13326 \begin_layout Plain Layout
13337 \begin_layout Standard
13342 is the color space that denotes the colors
13359 The four comma separated numbers are the portion factor for the corresponding
13360 colors of the color space.
13361 The factors can be in the range of 0
13362 \begin_inset space \thinspace{}
13366 \begin_inset space \thinspace{}
13374 also the color space
13378 can be used for definitions.
13395 , so that there are in this case three portion factors for the corresponding
13397 Furthermore there is the color space
13401 with one portion factor for the gray value.
13404 \begin_layout Standard
13405 As example a framed box with the new defined color
13409 where the characters have been colored
13414 \begin_inset Formula
13416 \colorbox{darkgreen}{\color{yellow}\boxed{\int A\,\mathrm{d}x=\frac{\sqrt[5]{B}}{\ln\left(\frac{1}{3}\right)}}}
13424 \begin_layout Standard
13425 Self-defined colors can also be used for text with the help of the command
13433 \begin_inset Index idx
13436 \begin_layout Plain Layout
13445 \begin_layout Standard
13449 \begin_layout Plain Layout
13453 textcolor{darkgreen}{
13459 \begin_inset Quotes eld
13463 \begin_inset Quotes erd
13470 \begin_layout Plain Layout
13480 \begin_layout Standard
13488 \begin_inset Index idx
13491 \begin_layout Plain Layout
13499 is used in the scheme
13503 textcolor{color}{characters to color}
13508 \begin_layout Subsection
13510 \begin_inset CommandInset label
13512 name "sub:Paragraph-Boxes"
13517 \begin_inset Index idx
13520 \begin_layout Plain Layout
13521 Boxes ! as paragraph
13529 \begin_layout Standard
13530 A box that can contain several lines and paragraphs, a so-called paragraph
13531 box (parbox), can be created with the menu
13533 Insert\SpecialChar \menuseparator
13536 or the toolbar button
13545 \begin_layout Standard
13546 The following example shows a framed parbox in a line:
13549 \begin_layout Standard
13550 \begin_inset VSpace medskip
13554 \begin_inset Box Boxed
13564 height_special "totalheight"
13567 \begin_layout Plain Layout
13568 This is a paragraph box.
13570 \begin_inset space \thinspace{}
13573 cm long and can also contain formulas:
13574 \begin_inset Formula $\int A\,\mathrm{d}s=C$
13585 \begin_layout Standard
13586 \begin_inset VSpace medskip
13592 \begin_layout Standard
13593 Such a box is created by right-clicking on the gray box inset.
13594 A dialog pops up showing the box properties.
13608 \begin_inset space \thinspace{}
13613 Vertical Box Alignment
13618 \begin_layout Standard
13619 \begin_inset VSpace medskip
13622 In LaTeX a parbox is created with the command
13629 \begin_inset Index idx
13632 \begin_layout Plain Layout
13640 which has the following scheme:
13643 \begin_layout Standard
13648 parbox[position]{width}{box content}
13651 \begin_layout Standard
13666 \begin_inset Quotes eld
13670 \begin_inset Quotes erd
13673 means that the box is aligned within the surrounding text with its last
13680 \begin_inset Quotes eld
13684 \begin_inset Quotes erd
13687 this is done with the first line.
13688 When no position is given, the box will be vertically centered, see section
13696 \begin_inset space ~
13701 manual for examples.
13704 \begin_layout Standard
13705 \begin_inset VSpace bigskip
13708 To frame formulas completely, including the formula number, the formula
13709 must be set into a parbox.
13710 To do this, the command
13724 is inserted in TeX-mode before the formula.
13732 \begin_inset Index idx
13735 \begin_layout Plain Layout
13743 is hereby the line width set for the document.
13744 Because the frame is outside the parbox, 2
13745 \begin_inset space \thinspace{}
13748 times the frame separation and the frame thickness must be subtracted from
13750 As this is not automatically done by LyX due to a bug
13754 \begin_layout Plain Layout
13755 \begin_inset CommandInset href
13757 name "LyX-bug #4483"
13758 target "http://www.lyx.org/trac/ticket/4483"
13767 , TeX-mode has to be used.
13768 To be able to multiply and subtract in arguments, the LaTeX-package
13776 \begin_layout Plain Layout
13781 is part of every LaTeX standard installation.
13787 \begin_inset Index idx
13790 \begin_layout Plain Layout
13796 must be loaded in the LaTeX-preamble with the line
13799 \begin_layout Standard
13807 \begin_layout Standard
13808 Behind the formula both boxes are closed by entering
13813 Here is an example:
13817 \begin_layout Plain Layout
13831 \begin_layout Standard
13835 \begin_layout Plain Layout
13853 \begin_inset Formula
13855 \int A\,\mathrm{d}x=\frac{\sqrt[5]{B}}{\ln\left(\frac{1}{3}\right)}
13864 \begin_layout Plain Layout
13875 \begin_layout Plain Layout
13889 \begin_layout Standard
13890 \begin_inset VSpace medskip
13893 As a parbox is used as the argument of
13899 , there is in this case no difference between
13914 \begin_layout Standard
13915 \begin_inset VSpace bigskip
13918 Paragraph boxes are very useful to comment formulas directly.
13925 is used in combination with the command
13939 \begin_inset CommandInset ref
13941 reference "sub:User-defined-Numbering"
13948 \begin_layout Standard
13949 An example of a formula commented with
13958 \begin_layout Standard
13962 \begin_layout Plain Layout
13975 This is a description.
13976 It is distinctly separated from the formula and multiline.
13980 \begin_layout Plain Layout
13992 \begin_layout Standard
13993 Such a formula must be inserted completely in TeX-mode because LyX does
13994 not yet support the command
14001 The formula is created with the following command sequence:
14004 \begin_layout Standard
14017 is inserted in TeX-mode.
14021 \begin_layout Plain Layout
14022 When the formula style
14034 can also be replaced by
14041 (formula styles see
14042 \begin_inset CommandInset ref
14044 reference "sec:Formula-Styles"
14053 Then the description follows as normal text and finally
14059 is inserted in TeX-mode.
14072 hereby create a displayed formula.
14075 \begin_layout Standard
14082 can be seen in this example that was
14083 \begin_inset Quotes eld
14087 \begin_inset Quotes erd
14090 using the mathematical textmode:
14091 \begin_inset Formula
14093 5x-7b=3b\textrm{This is a description. It is not separated from the formula ...}
14101 \begin_layout Section
14103 \begin_inset Index idx
14106 \begin_layout Plain Layout
14115 \begin_layout Subsection
14117 \begin_inset CommandInset label
14119 name "sub:Big-Operators"
14124 \begin_inset Index idx
14127 \begin_layout Plain Layout
14134 \begin_inset Index idx
14137 \begin_layout Plain Layout
14144 \begin_inset Index idx
14147 \begin_layout Plain Layout
14156 \begin_layout Standard
14157 To be able to use all integral operators listed here, the option
14159 Use esint package automatically
14161 must be set in the document settings under
14164 \begin_inset space ~
14172 \begin_layout Standard
14173 \begin_inset space \hfill{}
14177 \begin_inset Tabular
14178 <lyxtabular version="3" rows="11" columns="2">
14179 <features rotate="0" tabularvalignment="middle">
14180 <column alignment="center" valignment="top" width="0pt">
14181 <column alignment="center" valignment="top" width="0pt">
14183 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
14186 \begin_layout Plain Layout
14192 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
14195 \begin_layout Plain Layout
14203 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
14206 \begin_layout Plain Layout
14210 \begin_inset Index idx
14213 \begin_layout Plain Layout
14226 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
14229 \begin_layout Plain Layout
14230 \begin_inset Formula $\int$
14240 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
14243 \begin_layout Plain Layout
14251 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
14254 \begin_layout Plain Layout
14255 \begin_inset Formula $\oint$
14265 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
14268 \begin_layout Plain Layout
14276 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
14279 \begin_layout Plain Layout
14280 \begin_inset Formula $\ointctrclockwise$
14290 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
14293 \begin_layout Plain Layout
14301 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
14304 \begin_layout Plain Layout
14305 \begin_inset Formula $\ointclockwise$
14315 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
14318 \begin_layout Plain Layout
14326 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
14329 \begin_layout Plain Layout
14330 \begin_inset Formula $\sqint$
14340 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
14343 \begin_layout Plain Layout
14351 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
14354 \begin_layout Plain Layout
14356 \begin_inset Formula $\fint$
14366 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
14369 \begin_layout Plain Layout
14377 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
14380 \begin_layout Plain Layout
14382 \begin_inset Formula $\landupint$
14392 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
14395 \begin_layout Plain Layout
14403 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
14406 \begin_layout Plain Layout
14408 \begin_inset Formula $\landdownint$
14418 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
14421 \begin_layout Plain Layout
14429 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
14432 \begin_layout Plain Layout
14433 \begin_inset Formula $\bigcap$
14443 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
14446 \begin_layout Plain Layout
14454 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
14457 \begin_layout Plain Layout
14458 \begin_inset Formula $\bigcup$
14472 \begin_inset space \hfill{}
14476 \begin_inset Tabular
14477 <lyxtabular version="3" rows="11" columns="2">
14478 <features rotate="0" tabularvalignment="middle">
14479 <column alignment="center" valignment="top" width="0pt">
14480 <column alignment="center" valignment="top" width="0pt">
14482 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
14485 \begin_layout Plain Layout
14491 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
14494 \begin_layout Plain Layout
14502 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
14505 \begin_layout Plain Layout
14509 \begin_inset Index idx
14512 \begin_layout Plain Layout
14525 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
14528 \begin_layout Plain Layout
14529 \begin_inset Formula $\sum$
14539 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
14542 \begin_layout Plain Layout
14546 \begin_inset Index idx
14549 \begin_layout Plain Layout
14556 \begin_layout Plain Layout
14575 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
14578 \begin_layout Plain Layout
14579 \begin_inset Formula $\prod$
14589 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
14592 \begin_layout Plain Layout
14600 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
14603 \begin_layout Plain Layout
14604 \begin_inset Formula $\coprod$
14614 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
14617 \begin_layout Plain Layout
14625 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
14628 \begin_layout Plain Layout
14629 \begin_inset Formula $\bigodot$
14639 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
14642 \begin_layout Plain Layout
14650 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
14653 \begin_layout Plain Layout
14654 \begin_inset Formula $\bigotimes$
14664 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
14667 \begin_layout Plain Layout
14675 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
14678 \begin_layout Plain Layout
14679 \begin_inset Formula $\bigoplus$
14689 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
14692 \begin_layout Plain Layout
14700 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
14703 \begin_layout Plain Layout
14704 \begin_inset Formula $\bigwedge$
14714 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
14717 \begin_layout Plain Layout
14725 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
14728 \begin_layout Plain Layout
14729 \begin_inset Formula $\bigvee$
14739 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
14742 \begin_layout Plain Layout
14750 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
14753 \begin_layout Plain Layout
14754 \begin_inset Formula $\bigsqcup$
14764 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
14767 \begin_layout Plain Layout
14775 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
14778 \begin_layout Plain Layout
14779 \begin_inset Formula $\biguplus$
14793 \begin_inset space \hfill{}
14799 \begin_layout Standard
14800 All big operators can also be inserted via the math toolbar button
14803 arg "math-insert \\intop"
14809 \begin_layout Standard
14810 The operators are called big because they are bigger than the sometimes
14811 equal looking binary operators.
14812 All big operators can have limits as described in the next subsection.
14815 \begin_layout Standard
14816 For all integral operators there is a second version available, ending in
14834 These operators are different from
14841 \begin_inset space \space{}
14844 in the style the operator limits are displayed, see
14845 \begin_inset CommandInset ref
14847 reference "sub:Operator-Limits"
14855 \begin_layout Subsubsection*
14856 Advice for Integrals
14859 \begin_layout Standard
14864 in an integral is an operator, that therefore has to be set upright.
14865 This is done by highlighting the
14869 and using the keyboard shortcut
14879 \begin_layout Plain Layout
14885 \begin_inset CommandInset ref
14887 reference "sub:Font-Styles"
14897 Finally the smallest space is inserted before the
14901 , as this is usual for operators.
14905 \begin_layout Standard
14907 \begin_inset Formula $\int A(x)dx$
14911 \begin_inset Newline newline
14915 \begin_inset Phantom HPhantom
14918 \begin_layout Plain Layout
14925 \begin_inset Formula $\int A(x)\,\mathrm{d}x$
14931 \begin_layout Standard
14932 For multiple integrals there are the following commands:
14933 \begin_inset VSpace medskip
14939 \begin_layout Standard
14940 \begin_inset space \hfill{}
14944 \begin_inset Tabular
14945 <lyxtabular version="3" rows="4" columns="2">
14946 <features rotate="0" tabularvalignment="middle">
14947 <column alignment="center" valignment="top">
14948 <column alignment="center" valignment="top">
14950 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
14953 \begin_layout Plain Layout
14959 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
14962 \begin_layout Plain Layout
14964 \begin_inset Note Note
14967 \begin_layout Plain Layout
14974 is only used as spacer.
14986 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
14989 \begin_layout Plain Layout
14997 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
15000 \begin_layout Plain Layout
15001 \begin_inset Formula $\raisebox{4.5mm}{}\iint\raisebox{-2.5mm}{}$
15011 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
15014 \begin_layout Plain Layout
15022 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
15025 \begin_layout Plain Layout
15026 \begin_inset Formula $\raisebox{4.5mm}{}\oiint\raisebox{-2.5mm}{}$
15036 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
15039 \begin_layout Plain Layout
15047 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
15050 \begin_layout Plain Layout
15051 \begin_inset Formula $\raisebox{4.5mm}{}\sqiint\raisebox{-2.5mm}{}$
15065 \begin_inset space \hfill{}
15069 \begin_inset Tabular
15070 <lyxtabular version="3" rows="4" columns="2">
15071 <features rotate="0" tabularvalignment="middle">
15072 <column alignment="center" valignment="top">
15073 <column alignment="center" valignment="top">
15075 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
15078 \begin_layout Plain Layout
15084 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
15087 \begin_layout Plain Layout
15095 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
15098 \begin_layout Plain Layout
15106 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
15109 \begin_layout Plain Layout
15110 \begin_inset Formula $\raisebox{4.5mm}{}\iiint\raisebox{-2.5mm}{}$
15120 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
15123 \begin_layout Plain Layout
15131 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
15134 \begin_layout Plain Layout
15135 \begin_inset Formula $\raisebox{4.5mm}{}\iiiint\raisebox{-2.5mm}{}$
15145 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
15148 \begin_layout Plain Layout
15156 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
15159 \begin_layout Plain Layout
15160 \begin_inset Formula $\raisebox{4.5mm}{}\dotsint\raisebox{-2.5mm}{}$
15174 \begin_inset space \hfill{}
15180 \begin_layout Standard
15181 \begin_inset Newpage newpage
15187 \begin_layout Subsection
15189 \begin_inset CommandInset label
15191 name "sub:Operator-Limits"
15196 \begin_inset Index idx
15199 \begin_layout Plain Layout
15208 \begin_layout Standard
15209 Limits are created by super- and subscripts:
15212 \begin_layout Standard
15214 \begin_inset Tabular
15215 <lyxtabular version="3" rows="2" columns="2">
15216 <features rotate="0" tabularvalignment="middle">
15217 <column alignment="center" valignment="top" width="0pt">
15218 <column alignment="center" valignment="top" width="0pt">
15220 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
15223 \begin_layout Plain Layout
15229 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
15232 \begin_layout Plain Layout
15234 \begin_inset Note Note
15237 \begin_layout Plain Layout
15244 is only used as spacer.
15256 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
15259 \begin_layout Plain Layout
15265 \begin_inset space \textvisiblespace{}
15269 \begin_inset Formula $\to$
15273 \begin_inset Formula $\to$
15281 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
15284 \begin_layout Plain Layout
15285 \begin_inset Formula $\raisebox{5mm}{}\prod_{0}^{\infty}A(x)\raisebox{-2.5mm}{}$
15301 \begin_layout Standard
15302 Limits of inline formulas are set right beside the operator.
15303 Limits in displayed formulas are set above or below the operator, except
15304 for integral limits.
15307 \begin_layout Standard
15308 To force that the limits are set beside the operator, the cursor is set
15309 directly behind the operator and the limits type is changed with the menu
15312 Edit\SpecialChar \menuseparator
15313 Math\SpecialChar \menuseparator
15332 \begin_layout Standard
15333 The default limits type is this:
15334 \begin_inset Formula
15336 \sum_{x=0}^{\infty}\frac{1}{x^{2}}
15341 This is how it looks when the limits type was changed to
15348 \begin_inset Formula
15350 \sum\nolimits _{x=0}^{\infty}\frac{1}{x^{2}}
15355 For integrals, except those ending with
15371 etc., the limits are by default set beside the operator.
15372 But for multiple integrals the limits are often set below the operator.
15373 In the following example the limits type was therefore set to
15377 and so set below the integrals:
15378 \begin_inset Formula
15380 \iiint\limits _{V}X\,\mathrm{d}V=U\label{eq:VolInt}
15388 \begin_layout Standard
15389 \begin_inset VSpace medskip
15392 To specify conditions for limits, the commands
15399 \begin_inset Index idx
15402 \begin_layout Plain Layout
15417 \begin_inset Index idx
15420 \begin_layout Plain Layout
15429 To create for example this expression
15430 \begin_inset Formula
15432 \sum_{\begin{subarray}{c}
15436 \end{subarray}}^{n}k^{-2}\label{eq:substack}
15444 \begin_layout Standard
15445 the following has to be done:
15446 \begin_inset Newline newline
15458 \begin_inset space \textvisiblespace{}
15464 One is now in a blue box under the summation operator and insert there
15470 \begin_inset space \textvisiblespace{}
15476 The blue box is now within a purple box and now several lines can be written
15478 A new line is created by inserting a line break (
15481 arg "newline-insert newline"
15486 \begin_inset Newline newline
15491 0<k<1000 Ctrl+Return
15492 \begin_inset Newline newline
15497 is typed in, a new box appears below for the new line.
15500 \begin_layout Standard
15501 The alignment of the lines can be changed to left aligned with the
15511 Edit\SpecialChar \menuseparator
15515 To get right alignment,
15520 \begin_inset space \textvisiblespace{}
15525 is inserted at the beginning of the line.
15528 \begin_layout Standard
15541 with the difference that the lines are always centered.
15544 \begin_layout Standard
15545 \begin_inset VSpace bigskip
15549 \begin_inset CommandInset ref
15551 reference "eq:substack"
15555 there can be too much space beside an operator, because the characters
15556 following the operator are set beside the limits.
15557 To avoid this the command
15564 \begin_inset Index idx
15567 \begin_layout Plain Layout
15576 It sets the width of its content to 0
15577 \begin_inset space \thinspace{}
15581 \begin_inset Newline newline
15585 \begin_inset CommandInset ref
15587 reference "eq:substack"
15591 , one uses the command
15594 \begin_layout Standard
15604 \begin_inset space \textvisiblespace{}
15607 0<k<1000 Ctrl+Return
15610 \begin_layout Standard
15611 to create the lower limit.
15612 The summand is now directly behind the summation operator:
15613 \begin_inset Formula
15615 \sum_{\mathclap{\substack{0<k<1000\\
15627 \begin_layout Standard
15628 \begin_inset VSpace bigskip
15634 \begin_layout Standard
15635 When several consecutive operators have limits the typesetting of the limits
15636 looks often imperfect in the output, see this example:
15637 \begin_inset Formula
15639 \text{a)}\lim_{n\to\infty}\max_{p\ge n}\quad\text{b)}\lim_{n\to\infty}\max_{p^{2}\ge n}\quad\text{c)}\lim_{n\to\infty}\sup_{p^{2}\ge nK}\quad\text{d)}\limsup_{n\to\infty}\max_{p\ge n}
15644 To improve the typesetting set in the document settings under
15647 \begin_inset space ~
15657 \begin_inset Index idx
15660 \begin_layout Plain Layout
15661 Packages ! mathtools
15669 \begin_inset space ~
15675 Then insert into your formula the command
15682 \begin_inset Index idx
15685 \begin_layout Plain Layout
15693 directly before the first operator.
15694 The example will then look like this:
15695 \begin_inset Formula
15697 \text{a)}\adjustlimits\lim_{n\to\infty}\max_{p\ge n}\quad\text{b)}\adjustlimits\lim_{n\to\infty}\max_{p^{2}\ge n}\quad\text{c)}\adjustlimits\lim_{n\to\infty}\sup_{p^{2}\ge nK}\quad\text{d)}\adjustlimits\limsup_{n\to\infty}\max_{p\ge n}
15705 \begin_layout Standard
15706 \begin_inset VSpace bigskip
15709 How to use one limit for several operators is described in
15710 \begin_inset CommandInset ref
15712 reference "sub:Self-defined-Operators"
15719 \begin_layout Subsection
15720 Decoration for Operators
15721 \begin_inset Index idx
15724 \begin_layout Plain Layout
15725 Operators ! Decoration
15733 \begin_layout Standard
15741 \begin_inset Index idx
15744 \begin_layout Plain Layout
15759 \begin_inset Index idx
15762 \begin_layout Plain Layout
15770 characters can be placed above or below an operator, respectively.
15778 \begin_inset Index idx
15781 \begin_layout Plain Layout
15789 characters can be set before and behind a big operator.
15792 \begin_layout Standard
15794 \begin_inset space ~
15806 \begin_layout Itemize
15813 is used to set characters at the corners of the operator
15816 \begin_layout Itemize
15823 is used to set characters before and/or behind the operator (this variant
15824 represents LaTeX's original
15833 \begin_layout Itemize
15840 is used to set characters at the left corners and/or behind the operator
15843 \begin_layout Itemize
15850 is used to set characters at the right corners and/or before the operator
15853 \begin_layout Standard
15854 For example the command
15859 \begin_inset space \textvisiblespace{}
15865 \begin_inset space \textvisiblespace{}
15869 \begin_inset Formula $\to$
15873 \begin_inset Formula $\to$
15877 \begin_inset space \textvisiblespace{}
15887 \begin_inset Formula
15889 \sideset{}{'}\sum_{k=1}^{n}
15897 \begin_layout Standard
15898 \begin_inset Note Greyedout
15901 \begin_layout Plain Layout
15908 can only be used to decorate big operators, binary operators are not allowed.
15916 \begin_layout Standard
15929 can also be used to decorate symbols and characters.
15930 For example, the command
15935 \begin_inset space \textvisiblespace{}
15941 \begin_inset space \textvisiblespace{}
15947 \begin_inset Formula $\uparrow$
15955 \begin_inset Formula
15957 \overset{a}{\maltese}
15965 \begin_layout Subsection
15967 \begin_inset CommandInset label
15969 name "sub:Binary-Operators"
15974 \begin_inset Index idx
15977 \begin_layout Plain Layout
15986 \begin_layout Standard
15987 Binary operators are surrounded by space when there is a character before
15989 \begin_inset VSpace medskip
15995 \begin_layout Standard
15996 \begin_inset space \hfill{}
16000 \begin_inset Tabular
16001 <lyxtabular version="3" rows="13" columns="2">
16002 <features rotate="0" tabularvalignment="middle">
16003 <column alignment="center" valignment="top" width="0pt">
16004 <column alignment="center" valignment="top" width="0pt">
16006 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
16009 \begin_layout Plain Layout
16011 \begin_inset Note Note
16014 \begin_layout Plain Layout
16021 is only used as spacer.
16031 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
16034 \begin_layout Plain Layout
16042 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
16045 \begin_layout Plain Layout
16051 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
16054 \begin_layout Plain Layout
16055 \begin_inset Formula $+$
16065 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
16068 \begin_layout Plain Layout
16074 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
16077 \begin_layout Plain Layout
16078 \begin_inset Formula $-$
16088 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
16091 \begin_layout Plain Layout
16099 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
16102 \begin_layout Plain Layout
16103 \begin_inset Formula $\pm$
16113 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
16116 \begin_layout Plain Layout
16124 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
16127 \begin_layout Plain Layout
16128 \begin_inset Formula $\mp$
16138 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
16141 \begin_layout Plain Layout
16149 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
16152 \begin_layout Plain Layout
16153 \begin_inset Formula $\cdot$
16163 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
16166 \begin_layout Plain Layout
16174 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
16177 \begin_layout Plain Layout
16178 \begin_inset Formula $\times$
16188 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
16191 \begin_layout Plain Layout
16199 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
16202 \begin_layout Plain Layout
16203 \begin_inset Formula $\div$
16213 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
16216 \begin_layout Plain Layout
16220 \begin_layout Plain Layout
16233 \begin_layout Plain Layout
16245 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
16248 \begin_layout Plain Layout
16249 \begin_inset Formula $*$
16259 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
16262 \begin_layout Plain Layout
16270 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
16273 \begin_layout Plain Layout
16274 \begin_inset Formula $\star$
16284 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
16287 \begin_layout Plain Layout
16295 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
16298 \begin_layout Plain Layout
16299 \begin_inset Formula $\circ$
16309 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
16312 \begin_layout Plain Layout
16320 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
16323 \begin_layout Plain Layout
16324 \begin_inset Formula $\diamond$
16334 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
16337 \begin_layout Plain Layout
16345 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
16348 \begin_layout Plain Layout
16349 \begin_inset Formula $\bullet$
16363 \begin_inset space \hfill{}
16367 \begin_inset Tabular
16368 <lyxtabular version="3" rows="13" columns="2">
16369 <features rotate="0" tabularvalignment="middle">
16370 <column alignment="center" valignment="top" width="0pt">
16371 <column alignment="center" valignment="top" width="0pt">
16373 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
16376 \begin_layout Plain Layout
16382 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
16385 \begin_layout Plain Layout
16393 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
16396 \begin_layout Plain Layout
16404 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
16407 \begin_layout Plain Layout
16408 \begin_inset Formula $\nabla$
16418 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
16421 \begin_layout Plain Layout
16429 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
16432 \begin_layout Plain Layout
16433 \begin_inset Formula $\bigtriangledown$
16443 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
16446 \begin_layout Plain Layout
16454 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
16457 \begin_layout Plain Layout
16458 \begin_inset Formula $\bigtriangleup$
16468 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
16471 \begin_layout Plain Layout
16479 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
16482 \begin_layout Plain Layout
16483 \begin_inset Formula $\Box$
16493 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
16496 \begin_layout Plain Layout
16504 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
16507 \begin_layout Plain Layout
16508 \begin_inset Formula $\cap$
16518 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
16521 \begin_layout Plain Layout
16529 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
16532 \begin_layout Plain Layout
16533 \begin_inset Formula $\cup$
16543 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
16546 \begin_layout Plain Layout
16554 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
16557 \begin_layout Plain Layout
16558 \begin_inset Formula $\dagger$
16568 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
16571 \begin_layout Plain Layout
16579 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
16582 \begin_layout Plain Layout
16583 \begin_inset Formula $\ddagger$
16593 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
16596 \begin_layout Plain Layout
16604 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
16607 \begin_layout Plain Layout
16608 \begin_inset Formula $\wr$
16618 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
16621 \begin_layout Plain Layout
16629 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
16632 \begin_layout Plain Layout
16633 \begin_inset Formula $\bigcirc$
16643 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
16646 \begin_layout Plain Layout
16654 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
16657 \begin_layout Plain Layout
16658 \begin_inset Formula $\wedge$
16668 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
16671 \begin_layout Plain Layout
16679 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
16682 \begin_layout Plain Layout
16683 \begin_inset Formula $\vee$
16697 \begin_inset space \hfill{}
16701 \begin_inset Tabular
16702 <lyxtabular version="3" rows="13" columns="2">
16703 <features rotate="0" tabularvalignment="middle">
16704 <column alignment="center" valignment="top" width="0pt">
16705 <column alignment="center" valignment="top" width="0pt">
16707 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
16710 \begin_layout Plain Layout
16716 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
16719 \begin_layout Plain Layout
16727 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
16730 \begin_layout Plain Layout
16738 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
16741 \begin_layout Plain Layout
16742 \begin_inset Formula $\oplus$
16752 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
16755 \begin_layout Plain Layout
16763 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
16766 \begin_layout Plain Layout
16767 \begin_inset Formula $\ominus$
16777 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
16780 \begin_layout Plain Layout
16788 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
16791 \begin_layout Plain Layout
16792 \begin_inset Formula $\otimes$
16802 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
16805 \begin_layout Plain Layout
16813 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
16816 \begin_layout Plain Layout
16817 \begin_inset Formula $\oslash$
16827 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
16830 \begin_layout Plain Layout
16838 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
16841 \begin_layout Plain Layout
16842 \begin_inset Formula $\odot$
16852 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
16855 \begin_layout Plain Layout
16863 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
16866 \begin_layout Plain Layout
16867 \begin_inset Formula $\amalg$
16877 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
16880 \begin_layout Plain Layout
16888 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
16891 \begin_layout Plain Layout
16892 \begin_inset Formula $\uplus$
16902 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
16905 \begin_layout Plain Layout
16913 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
16916 \begin_layout Plain Layout
16917 \begin_inset Formula $\setminus$
16927 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
16930 \begin_layout Plain Layout
16938 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
16941 \begin_layout Plain Layout
16942 \begin_inset Formula $\sqcap$
16952 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
16955 \begin_layout Plain Layout
16963 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
16966 \begin_layout Plain Layout
16967 \begin_inset Formula $\sqcup$
16977 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
16980 \begin_layout Plain Layout
16988 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
16991 \begin_layout Plain Layout
16992 \begin_inset Formula $\triangleleft$
17002 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
17005 \begin_layout Plain Layout
17013 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
17016 \begin_layout Plain Layout
17017 \begin_inset Formula $\triangleright$
17031 \begin_inset space \hfill{}
17037 \begin_layout Standard
17038 All binary operators can also be inserted via the math toolbar button
17041 arg "math-insert \\pm"
17047 \begin_layout Standard
17048 To typeset the Laplace operator also
17065 \begin_inset Formula $\nabla^{2}$
17068 ) can be used instead of
17077 \begin_layout Standard
17084 Insert\SpecialChar \menuseparator
17096 \begin_layout Subsection
17097 Self-defined Operators
17098 \begin_inset CommandInset label
17100 name "sub:Self-defined-Operators"
17105 \begin_inset Index idx
17108 \begin_layout Plain Layout
17109 Operators ! self-defined
17117 \begin_layout Standard
17118 With the help of the command
17122 DeclareMathOperator
17125 \begin_inset Index idx
17128 \begin_layout Plain Layout
17133 DeclareMathOperator
17138 custom operators can be defined in the LaTeX-preamble.
17139 Its command scheme is:
17142 \begin_layout Standard
17147 DeclareMathOperator{new command}{display}
17150 \begin_layout Standard
17151 Display can be characters or symbols that define how the operator looks
17153 To define a big operator a * is set behind the command.
17154 All self-defined big operators can have limits as described in
17155 \begin_inset CommandInset ref
17157 reference "sub:Operator-Limits"
17164 \begin_layout Standard
17165 For example the LaTeX-preamble line
17168 \begin_layout Standard
17173 DeclareMathOperator*{
17180 \begin_layout Standard
17181 defines the command
17187 , that inserts a big operator consisting of the lozenge symbol from
17188 \begin_inset CommandInset ref
17190 reference "sub:Miscellaneous-Symbols"
17195 \begin_inset Formula
17197 \Lozenge_{n=1}^{\infty}
17202 The command for this formula is:
17213 \begin_inset Formula $\to$
17219 \begin_layout Standard
17220 \begin_inset VSpace bigskip
17223 When self-defined operators are not used several times in the document,
17224 they can also be defined with the commands
17231 \begin_inset Index idx
17234 \begin_layout Plain Layout
17249 \begin_inset Index idx
17252 \begin_layout Plain Layout
17260 , which have the following scheme:
17263 \begin_layout Standard
17277 \begin_layout Standard
17284 defines big operators,
17293 \begin_layout Standard
17301 \begin_inset space \thinspace{}
17305 \begin_inset space \space{}
17308 be used to use one limit for several operators:
17311 \begin_layout Standard
17312 \begin_inset Formula
17314 \mathop{\sum\negmedspace\sum}_{i,j=1}^{N}
17322 \begin_layout Standard
17323 The command for the formula above is:
17324 \begin_inset Newline newline
17340 \begin_inset space \textvisiblespace{}
17346 \begin_inset Formula $\to$
17352 \begin_inset space \textvisiblespace{}
17360 \begin_layout Section
17362 \begin_inset Index idx
17365 \begin_layout Plain Layout
17374 \begin_layout Subsection
17376 \begin_inset CommandInset label
17378 name "sub:Font-Styles"
17383 \begin_inset Index idx
17386 \begin_layout Plain Layout
17395 \begin_layout Standard
17396 Latin letters in formulas can be set in one of the following font styles:
17397 \begin_inset VSpace -2mm
17403 \begin_layout Standard
17405 \begin_inset Tabular
17406 <lyxtabular version="3" rows="7" columns="3">
17407 <features rotate="0" tabularvalignment="middle">
17408 <column alignment="center" valignment="top">
17409 <column alignment="center" valignment="top">
17410 <column alignment="center" valignment="top">
17412 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
17415 \begin_layout Plain Layout
17421 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
17424 \begin_layout Plain Layout
17430 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
17433 \begin_layout Plain Layout
17441 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
17444 \begin_layout Plain Layout
17450 \begin_inset space \textvisiblespace{}
17460 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
17463 \begin_layout Plain Layout
17464 \begin_inset Formula $\mathbb{ABC}$
17472 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
17475 \begin_layout Plain Layout
17488 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
17491 \begin_layout Plain Layout
17497 \begin_inset space \textvisiblespace{}
17507 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
17510 \begin_layout Plain Layout
17511 \begin_inset Formula $\mathbf{AbC}$
17519 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
17522 \begin_layout Plain Layout
17535 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
17538 \begin_layout Plain Layout
17544 \begin_inset space \textvisiblespace{}
17554 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
17557 \begin_layout Plain Layout
17558 \begin_inset Formula $\boldsymbol{AbC}$
17566 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
17569 \begin_layout Plain Layout
17572 arg "font-boldsymbol"
17582 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
17585 \begin_layout Plain Layout
17591 \begin_inset space \textvisiblespace{}
17601 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
17604 \begin_layout Plain Layout
17605 \begin_inset Formula $\mathcal{ABC}$
17613 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
17616 \begin_layout Plain Layout
17629 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
17632 \begin_layout Plain Layout
17638 \begin_inset space \textvisiblespace{}
17648 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
17651 \begin_layout Plain Layout
17652 \begin_inset Formula $\mathfrak{AbC}$
17660 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
17663 \begin_layout Plain Layout
17671 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
17674 \begin_layout Plain Layout
17680 \begin_inset space \textvisiblespace{}
17690 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
17693 \begin_layout Plain Layout
17694 \begin_inset Formula $\mathscr{AbC}$
17702 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
17705 \begin_layout Plain Layout
17719 \begin_layout Standard
17721 \begin_inset Tabular
17722 <lyxtabular version="3" rows="5" columns="3">
17723 <features rotate="0" tabularvalignment="middle">
17724 <column alignment="center" valignment="top">
17725 <column alignment="center" valignment="top">
17726 <column alignment="center" valignment="top">
17728 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
17731 \begin_layout Plain Layout
17737 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
17740 \begin_layout Plain Layout
17746 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
17749 \begin_layout Plain Layout
17757 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
17760 \begin_layout Plain Layout
17766 \begin_inset space \textvisiblespace{}
17776 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
17779 \begin_layout Plain Layout
17780 \begin_inset Formula $\mathit{AbC}$
17788 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
17791 \begin_layout Plain Layout
17799 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
17802 \begin_layout Plain Layout
17808 \begin_inset space \textvisiblespace{}
17818 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
17821 \begin_layout Plain Layout
17822 \begin_inset Formula $\mathrm{AbC}$
17830 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
17833 \begin_layout Plain Layout
17846 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
17849 \begin_layout Plain Layout
17855 \begin_inset space \textvisiblespace{}
17865 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
17868 \begin_layout Plain Layout
17869 \begin_inset Formula $\mathsf{AbC}$
17877 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
17880 \begin_layout Plain Layout
17893 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
17896 \begin_layout Plain Layout
17902 \begin_inset space \textvisiblespace{}
17912 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
17915 \begin_layout Plain Layout
17916 \begin_inset Formula $\mathtt{AbC}$
17924 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
17927 \begin_layout Plain Layout
17930 arg "font-typewriter"
17946 \begin_layout Standard
17947 \begin_inset Note Greyedout
17950 \begin_layout Plain Layout
17967 can only be used for big letters.
17975 \begin_layout Standard
17976 Predefined is the style
17985 \begin_layout Standard
17986 The style commands work also for letters in mathematical constructs:
17987 \begin_inset Formula
17989 \mathfrak{A=\frac{b}{C}}
17997 \begin_layout Standard
17998 Characters in mathematical text don't appear in a math font style but in
17999 the text font style
18006 That their style can't be set correctly via the text style dialog is a
18011 \begin_layout Plain Layout
18012 \begin_inset CommandInset href
18014 name "LyX-bug #4629"
18015 target "http://www.lyx.org/trac/ticket/4629"
18027 \begin_layout Standard
18028 Instead of the style commands the dialog
18030 Edit\SpecialChar \menuseparator
18031 Math\SpecialChar \menuseparator
18034 or the toolbar button
18037 arg "math-insert \\font"
18043 \begin_layout Subsection
18045 \begin_inset CommandInset label
18047 name "sub:Bold-Formulas"
18052 \begin_inset Index idx
18055 \begin_layout Plain Layout
18064 \begin_layout Standard
18065 To make a complete formula bold, the command
18071 from the previous subsection cannot be used, because it doesn't work for
18072 small Greek letters.
18073 Furthermore it prints Latin letters always upright, like in the following
18077 \begin_layout Standard
18078 \begin_inset Formula
18080 \mathbf{\int_{n}^{2}f(\theta)=\Gamma}\qquad\textrm{equation with \textbackslash mathbf}
18088 \begin_layout Standard
18089 To display the formula correctly, the command
18096 \begin_inset Formula
18098 \boldsymbol{\int_{n}^{2}f(\theta)=\Gamma\qquad\textrm{equation with \textbackslash boldsymbol}}
18103 It is also possible to set the formula in a
18105 boldmath environment
18108 This environment is created by inserting the command
18115 \begin_inset Index idx
18118 \begin_layout Plain Layout
18127 To end the environment, the command
18134 \begin_inset Index idx
18137 \begin_layout Plain Layout
18145 is inserted in TeX-mode.
18149 \begin_layout Plain Layout
18159 \begin_inset Formula
18161 \int_{n}^{2}f(\theta)=\Gamma\qquad\textrm{equation in a boldmath environment}
18170 \begin_layout Plain Layout
18182 \begin_layout Subsection
18184 \begin_inset Index idx
18187 \begin_layout Plain Layout
18196 \begin_layout Standard
18197 Formulas can be colored like normal text: Highlight a formula or a formula
18203 Here is a formula in magenta:
18204 \begin_inset Formula
18206 {\color{magenta}\int A\,\mathrm{d}x=\frac{\sqrt[5]{B}}{\ln\left(\frac{1}{3}\right)}}
18214 \begin_layout Standard
18215 You can also define your own colors as described in
18216 \begin_inset CommandInset ref
18218 reference "sub:Colored-Boxes"
18223 They can be used with the TeX code command
18230 \begin_inset Index idx
18233 \begin_layout Plain Layout
18244 \begin_layout Standard
18249 textcolor{color}{characters or formula}
18252 \begin_layout Standard
18253 The following example was colored completely dark green and partly red:
18256 \begin_layout Standard
18260 \begin_layout Plain Layout
18264 textcolor{darkgreen}{
18270 \begin_inset Formula
18272 \int A\,\mathrm{d}x=\frac{{\color{red}\sqrt[5]{B}}}{\ln\left(\frac{1}{3}\right)}
18281 \begin_layout Plain Layout
18291 \begin_layout Standard
18292 Due to a bug in LyX only complete formulas can be colored with self-defined
18297 \begin_layout Plain Layout
18298 \begin_inset CommandInset href
18300 name "LyX-bug #5269"
18301 target "http://www.lyx.org/trac/ticket/5269"
18313 \begin_layout Subsection
18315 \begin_inset CommandInset label
18317 name "sub:Font-Sizes"
18322 \begin_inset Index idx
18325 \begin_layout Plain Layout
18334 \begin_layout Standard
18335 For characters in formulas there are, analog to characters in text, the
18336 following size commands:
18339 \begin_layout Standard
18383 \begin_inset Newline newline
18405 \begin_layout Standard
18406 The size produced by the commands depends on the document font size, which
18407 corresponds to the command
18414 The other commands produce smaller or larger sizes than
18421 The font size can however not exceed a certain value.
18422 Is for example the document font size 12
18423 \begin_inset space \thinspace{}
18432 switches to the same size as
18442 \begin_layout Standard
18443 A size command is inserted in TeX-mode before the formula and sets the size
18444 for all following formula and text characters.
18445 To switch back to the initial size, the command
18451 is inserted behind the formula in TeX-mode.
18454 \begin_layout Standard
18455 Within a formula the size can be changed using the following size commands:
18458 \begin_layout Standard
18461 \begin_inset Tabular
18462 <lyxtabular version="3" rows="5" columns="2">
18463 <features rotate="0" tabularvalignment="middle">
18464 <column alignment="center" valignment="top">
18465 <column alignment="center" valignment="top">
18467 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
18470 \begin_layout Plain Layout
18476 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
18479 \begin_layout Plain Layout
18481 \begin_inset Note Note
18484 \begin_layout Plain Layout
18491 is only used as spacer.
18503 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
18506 \begin_layout Plain Layout
18510 \begin_inset Index idx
18513 \begin_layout Plain Layout
18526 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
18529 \begin_layout Plain Layout
18530 \begin_inset Formula $\raisebox{6.5mm}{}{\displaystyle E_{\mathrm{pot_{1}}}=\frac{K}{l+\frac{m}{n_{2}}}}\raisebox{-5.5mm}{}$
18540 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
18543 \begin_layout Plain Layout
18551 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
18554 \begin_layout Plain Layout
18555 \begin_inset Formula $\raisebox{4.5mm}{}{\textstyle E_{\mathrm{pot_{1}}}=\frac{K}{l+\frac{m}{n_{2}}}}\raisebox{-4mm}{}$
18565 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
18568 \begin_layout Plain Layout
18576 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
18579 \begin_layout Plain Layout
18580 \begin_inset Formula $\raisebox{4.5mm}{}{\scriptstyle E_{\mathrm{pot_{1}}}=\frac{K}{l+\frac{m}{n_{2}}}}\raisebox{-3.5mm}{}$
18590 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
18593 \begin_layout Plain Layout
18601 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
18604 \begin_layout Plain Layout
18605 \begin_inset Formula $\raisebox{4.5mm}{}{\scriptscriptstyle E_{\mathrm{pot_{1}}}=\frac{K}{l+\frac{m}{n_{2}}}}\raisebox{-3.5mm}{}$
18621 \begin_layout Standard
18622 After entering these commands, a blue box appears in which the formula parts
18626 \begin_layout Standard
18627 There is a further method to change the font size, that though only works
18628 for symbols or letters in mathematical text.
18629 To use it, one of the above text size commands is inserted in mathematical
18631 All following characters until the end of the mathematical text or until
18632 another size command will have the selected size.
18634 \begin_inset VSpace -2mm
18640 \begin_layout Standard
18644 \begin_layout Plain Layout
18654 \begin_inset Formula
18656 A=\frac{B}{c}\cdot\maltese
18662 \begin_inset Formula
18664 \maltese A\textrm{\Large\maltese\textit{A}}\textrm{\tiny\maltese\textit{A}}
18673 \begin_layout Plain Layout
18685 \begin_layout Standard
18686 \begin_inset VSpace medskip
18689 Before both formulas the command
18696 The command for the second formula is:
18697 \begin_inset Newline newline
18705 \begin_inset space \textvisiblespace{}
18711 \begin_inset space \textvisiblespace{}
18717 \begin_inset space \textvisiblespace{}
18723 \begin_inset space \textvisiblespace{}
18727 \begin_inset Formula $\to$
18731 \begin_inset Formula $\to$
18735 \begin_inset Newline newline
18739 \begin_inset space \hspace*{}
18750 \begin_inset space \textvisiblespace{}
18756 \begin_inset space \textvisiblespace{}
18762 \begin_inset space \textvisiblespace{}
18768 \begin_layout Standard
18769 If a symbol cannot be displayed in different sizes, it will always be displayed
18770 in the default size.
18773 \begin_layout Section
18775 \begin_inset Index idx
18778 \begin_layout Plain Layout
18787 \begin_layout Standard
18788 Greek letters can also be inserted via the toolbar button
18791 arg "math-insert \\alpha"
18795 All international typesetting norms purport that Greek letters in math
18796 have to be typeset italic/slanted.
18797 In some languages, like French or Russian, they are nevertheless sometimes
18801 \begin_layout Subsection
18803 \begin_inset Index idx
18806 \begin_layout Plain Layout
18807 Greek letters ! small
18815 \begin_layout Standard
18816 \begin_inset space \hfill{}
18820 \begin_inset Tabular
18821 <lyxtabular version="3" rows="11" columns="2">
18822 <features rotate="0" tabularvalignment="middle">
18823 <column alignment="center" valignment="top" width="0pt">
18824 <column alignment="center" valignment="top" width="0pt">
18826 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
18829 \begin_layout Plain Layout
18835 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
18838 \begin_layout Plain Layout
18846 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
18849 \begin_layout Plain Layout
18857 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
18860 \begin_layout Plain Layout
18861 \begin_inset Formula $\alpha$
18871 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
18874 \begin_layout Plain Layout
18882 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
18885 \begin_layout Plain Layout
18886 \begin_inset Formula $\beta$
18896 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
18899 \begin_layout Plain Layout
18907 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
18910 \begin_layout Plain Layout
18911 \begin_inset Formula $\gamma$
18921 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
18924 \begin_layout Plain Layout
18932 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
18935 \begin_layout Plain Layout
18936 \begin_inset Formula $\delta$
18946 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
18949 \begin_layout Plain Layout
18957 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
18960 \begin_layout Plain Layout
18961 \begin_inset Formula $\epsilon$
18971 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
18974 \begin_layout Plain Layout
18982 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
18985 \begin_layout Plain Layout
18986 \begin_inset Formula $\varepsilon$
18996 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
18999 \begin_layout Plain Layout
19007 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
19010 \begin_layout Plain Layout
19011 \begin_inset Formula $\zeta$
19021 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
19024 \begin_layout Plain Layout
19032 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
19035 \begin_layout Plain Layout
19036 \begin_inset Formula $\eta$
19046 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
19049 \begin_layout Plain Layout
19057 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
19060 \begin_layout Plain Layout
19061 \begin_inset Formula $\theta$
19071 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
19074 \begin_layout Plain Layout
19082 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
19085 \begin_layout Plain Layout
19086 \begin_inset Formula $\vartheta$
19100 \begin_inset space \hfill{}
19104 \begin_inset Tabular
19105 <lyxtabular version="3" rows="12" columns="2">
19106 <features rotate="0" tabularvalignment="middle">
19107 <column alignment="center" valignment="top" width="0pt">
19108 <column alignment="center" valignment="top" width="0pt">
19110 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
19113 \begin_layout Plain Layout
19119 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
19122 \begin_layout Plain Layout
19130 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
19133 \begin_layout Plain Layout
19141 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
19144 \begin_layout Plain Layout
19145 \begin_inset Formula $\iota$
19155 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
19158 \begin_layout Plain Layout
19166 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
19169 \begin_layout Plain Layout
19170 \begin_inset Formula $\kappa$
19180 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
19183 \begin_layout Plain Layout
19191 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
19194 \begin_layout Plain Layout
19195 \begin_inset Formula $\varkappa$
19205 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
19208 \begin_layout Plain Layout
19216 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
19219 \begin_layout Plain Layout
19220 \begin_inset Formula $\lambda$
19230 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
19233 \begin_layout Plain Layout
19241 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
19244 \begin_layout Plain Layout
19245 \begin_inset Formula $\mu$
19255 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
19258 \begin_layout Plain Layout
19266 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
19269 \begin_layout Plain Layout
19270 \begin_inset Formula $\nu$
19280 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
19283 \begin_layout Plain Layout
19291 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
19294 \begin_layout Plain Layout
19295 \begin_inset Formula $\xi$
19305 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
19308 \begin_layout Plain Layout
19314 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
19317 \begin_layout Plain Layout
19318 \begin_inset Formula $o$
19328 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
19331 \begin_layout Plain Layout
19339 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
19342 \begin_layout Plain Layout
19343 \begin_inset Formula $\pi$
19353 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
19356 \begin_layout Plain Layout
19364 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
19367 \begin_layout Plain Layout
19368 \begin_inset Formula $\varpi$
19378 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
19381 \begin_layout Plain Layout
19389 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
19392 \begin_layout Plain Layout
19393 \begin_inset Formula $\rho$
19407 \begin_inset space \hfill{}
19411 \begin_inset Tabular
19412 <lyxtabular version="3" rows="11" columns="2">
19413 <features rotate="0" tabularvalignment="middle">
19414 <column alignment="center" valignment="top" width="0pt">
19415 <column alignment="center" valignment="top" width="0pt">
19417 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
19420 \begin_layout Plain Layout
19426 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
19429 \begin_layout Plain Layout
19437 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
19440 \begin_layout Plain Layout
19448 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
19451 \begin_layout Plain Layout
19452 \begin_inset Formula $\varrho$
19462 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
19465 \begin_layout Plain Layout
19473 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
19476 \begin_layout Plain Layout
19477 \begin_inset Formula $\sigma$
19487 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
19490 \begin_layout Plain Layout
19498 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
19501 \begin_layout Plain Layout
19502 \begin_inset Formula $\varsigma$
19512 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
19515 \begin_layout Plain Layout
19523 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
19526 \begin_layout Plain Layout
19527 \begin_inset Formula $\tau$
19537 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
19540 \begin_layout Plain Layout
19548 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
19551 \begin_layout Plain Layout
19552 \begin_inset Formula $\upsilon$
19562 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
19565 \begin_layout Plain Layout
19573 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
19576 \begin_layout Plain Layout
19577 \begin_inset Formula $\phi$
19587 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
19590 \begin_layout Plain Layout
19598 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
19601 \begin_layout Plain Layout
19602 \begin_inset Formula $\varphi$
19612 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
19615 \begin_layout Plain Layout
19623 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
19626 \begin_layout Plain Layout
19627 \begin_inset Formula $\chi$
19637 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
19640 \begin_layout Plain Layout
19648 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
19651 \begin_layout Plain Layout
19652 \begin_inset Formula $\psi$
19662 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
19665 \begin_layout Plain Layout
19673 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
19676 \begin_layout Plain Layout
19677 \begin_inset Formula $\omega$
19691 \begin_inset space \hfill{}
19697 \begin_layout Standard
19698 \begin_inset VSpace medskip
19704 \begin_layout Standard
19705 How to create special upright Greek letters is explained in
19706 \begin_inset CommandInset ref
19708 reference "sub:Upright-small-Greek"
19715 \begin_layout Subsection
19717 \begin_inset Index idx
19720 \begin_layout Plain Layout
19721 Greek letters ! big
19729 \begin_layout Standard
19730 \begin_inset space \hfill{}
19734 \begin_inset Tabular
19735 <lyxtabular version="3" rows="7" columns="2">
19736 <features rotate="0" tabularvalignment="middle">
19737 <column alignment="center" valignment="top" width="0pt">
19738 <column alignment="center" valignment="top" width="0pt">
19740 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
19743 \begin_layout Plain Layout
19749 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
19752 \begin_layout Plain Layout
19760 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
19763 \begin_layout Plain Layout
19771 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
19774 \begin_layout Plain Layout
19775 \begin_inset Formula $\Gamma$
19785 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
19788 \begin_layout Plain Layout
19796 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
19799 \begin_layout Plain Layout
19800 \begin_inset Formula $\Delta$
19810 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
19813 \begin_layout Plain Layout
19821 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
19824 \begin_layout Plain Layout
19825 \begin_inset Formula $\Theta$
19835 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
19838 \begin_layout Plain Layout
19846 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
19849 \begin_layout Plain Layout
19850 \begin_inset Formula $\Lambda$
19860 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
19863 \begin_layout Plain Layout
19871 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
19874 \begin_layout Plain Layout
19875 \begin_inset Formula $\Xi$
19885 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
19888 \begin_layout Plain Layout
19896 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
19899 \begin_layout Plain Layout
19900 \begin_inset Formula $\Pi$
19914 \begin_inset space \hfill{}
19918 \begin_inset Tabular
19919 <lyxtabular version="3" rows="6" columns="2">
19920 <features rotate="0" tabularvalignment="middle">
19921 <column alignment="center" valignment="top" width="0pt">
19922 <column alignment="center" valignment="top" width="0pt">
19924 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
19927 \begin_layout Plain Layout
19933 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
19936 \begin_layout Plain Layout
19944 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
19947 \begin_layout Plain Layout
19955 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
19958 \begin_layout Plain Layout
19959 \begin_inset Formula $\Sigma$
19969 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
19972 \begin_layout Plain Layout
19980 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
19983 \begin_layout Plain Layout
19984 \begin_inset Formula $\Upsilon$
19994 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
19997 \begin_layout Plain Layout
20005 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
20008 \begin_layout Plain Layout
20009 \begin_inset Formula $\Phi$
20019 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
20022 \begin_layout Plain Layout
20030 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
20033 \begin_layout Plain Layout
20034 \begin_inset Formula $\Psi$
20044 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
20047 \begin_layout Plain Layout
20055 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
20058 \begin_layout Plain Layout
20059 \begin_inset Formula $\Omega$
20073 \begin_inset space \hfill{}
20079 \begin_layout Standard
20080 \begin_inset VSpace medskip
20083 That the big Greek letters appear upright is caused by a design bug when
20085 To get correct italic big letters, begin every command with
20090 For example the command
20097 \begin_inset Formula $\varGamma$
20101 Another way is to load the package
20109 \begin_layout Plain Layout
20114 is part of the LaTeX-package
20119 \begin_inset Index idx
20122 \begin_layout Plain Layout
20127 \begin_layout Plain Layout
20147 \begin_inset Index idx
20150 \begin_layout Plain Layout
20156 with the LaTeX-preamble line
20159 \begin_layout Standard
20164 usepackage{fixmath}
20167 \begin_layout Standard
20168 Then all big Greek letters in a document will automatically be typeset italic.
20171 \begin_layout Subsection
20173 \begin_inset Index idx
20176 \begin_layout Plain Layout
20177 Greek letters ! bold
20185 \begin_layout Standard
20186 Greek letters cannot be set with different font styles like Latin letters.
20187 They can only be made bold with the command
20194 \begin_inset Index idx
20197 \begin_layout Plain Layout
20208 \begin_layout Standard
20210 \begin_inset Tabular
20211 <lyxtabular version="3" rows="3" columns="2">
20212 <features rotate="0" tabularvalignment="middle">
20213 <column alignment="center" valignment="top">
20214 <column alignment="center" valignment="top">
20216 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
20219 \begin_layout Plain Layout
20225 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
20228 \begin_layout Plain Layout
20236 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
20239 \begin_layout Plain Layout
20251 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
20254 \begin_layout Plain Layout
20255 \begin_inset Formula $\Upsilon\boldsymbol{\Upsilon}$
20265 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
20268 \begin_layout Plain Layout
20280 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
20283 \begin_layout Plain Layout
20284 \begin_inset Formula $\theta\boldsymbol{\theta}$
20300 \begin_layout Section
20305 \begin_layout Plain Layout
20318 \begin_layout Plain Layout
20319 A list with all symbols of most of the LaTeX-packages can be found in
20320 \begin_inset CommandInset citation
20335 \begin_layout Plain Layout
20343 \begin_inset Note Note
20346 \begin_layout Plain Layout
20349 texorpdfstring is used to avoid that the footnote appears in the PDF-bookmark.
20352 \begin_layout Plain Layout
20355 texorpdfstring is in section
20356 \begin_inset CommandInset ref
20358 reference "sub:Formulas-in-Section"
20368 \begin_inset Index idx
20371 \begin_layout Plain Layout
20380 \begin_layout Standard
20381 Many of the symbols listed in this section can also be inserted via the
20385 arg "math-insert \\nabla"
20391 arg "math-insert \\digamma"
20397 \begin_layout Subsection
20398 Mathematical Symbols
20399 \begin_inset CommandInset label
20401 name "sub:Mathematical-Symbols"
20406 \begin_inset Index idx
20409 \begin_layout Plain Layout
20410 Symbols ! mathematical
20418 \begin_layout Standard
20419 \begin_inset space \hfill{}
20423 \begin_inset Tabular
20424 <lyxtabular version="3" rows="10" columns="2">
20425 <features rotate="0" tabularvalignment="middle">
20426 <column alignment="center" valignment="top" width="0pt">
20427 <column alignment="center" valignment="top" width="0pt">
20429 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
20432 \begin_layout Plain Layout
20438 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
20441 \begin_layout Plain Layout
20449 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
20452 \begin_layout Plain Layout
20460 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
20463 \begin_layout Plain Layout
20464 \begin_inset Formula $\neg$
20474 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
20477 \begin_layout Plain Layout
20485 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
20488 \begin_layout Plain Layout
20489 \begin_inset Formula $\Im$
20499 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
20502 \begin_layout Plain Layout
20510 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
20513 \begin_layout Plain Layout
20514 \begin_inset Formula $\Re$
20524 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
20527 \begin_layout Plain Layout
20535 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
20538 \begin_layout Plain Layout
20539 \begin_inset Formula $\aleph$
20549 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
20552 \begin_layout Plain Layout
20560 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
20563 \begin_layout Plain Layout
20564 \begin_inset Formula $\partial$
20574 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
20577 \begin_layout Plain Layout
20585 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
20588 \begin_layout Plain Layout
20589 \begin_inset Formula $\infty$
20599 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
20602 \begin_layout Plain Layout
20610 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
20613 \begin_layout Plain Layout
20614 \begin_inset Formula $\wp$
20624 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
20627 \begin_layout Plain Layout
20635 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
20638 \begin_layout Plain Layout
20639 \begin_inset Formula $\imath$
20649 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
20652 \begin_layout Plain Layout
20660 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
20663 \begin_layout Plain Layout
20664 \begin_inset Formula $\jmath$
20678 \begin_inset space \hfill{}
20682 \begin_inset Tabular
20683 <lyxtabular version="3" rows="10" columns="2">
20684 <features rotate="0" tabularvalignment="middle">
20685 <column alignment="center" valignment="top" width="0pt">
20686 <column alignment="center" valignment="top" width="0pt">
20688 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
20691 \begin_layout Plain Layout
20697 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
20700 \begin_layout Plain Layout
20702 \begin_inset Note Note
20705 \begin_layout Plain Layout
20712 is only used as spacer.
20724 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
20727 \begin_layout Plain Layout
20735 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
20738 \begin_layout Plain Layout
20739 \begin_inset Formula $\forall$
20749 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
20752 \begin_layout Plain Layout
20760 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
20763 \begin_layout Plain Layout
20764 \begin_inset Formula $\exists$
20774 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
20777 \begin_layout Plain Layout
20785 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
20788 \begin_layout Plain Layout
20789 \begin_inset Formula $\nexists$
20799 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
20802 \begin_layout Plain Layout
20810 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
20813 \begin_layout Plain Layout
20814 \begin_inset Formula $\emptyset$
20824 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
20827 \begin_layout Plain Layout
20835 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
20838 \begin_layout Plain Layout
20839 \begin_inset Formula $\varnothing$
20849 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
20852 \begin_layout Plain Layout
20860 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
20863 \begin_layout Plain Layout
20864 \begin_inset Formula $\dag$
20874 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
20877 \begin_layout Plain Layout
20885 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
20888 \begin_layout Plain Layout
20889 \begin_inset Formula $\ddag$
20899 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
20902 \begin_layout Plain Layout
20910 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
20913 \begin_layout Plain Layout
20917 \begin_layout Plain Layout
20927 \begin_inset Formula $\complement$
20934 \begin_layout Plain Layout
20948 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
20951 \begin_layout Plain Layout
20959 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
20962 \begin_layout Plain Layout
20963 \begin_inset Formula $\Bbbk$
20977 \begin_inset space \hfill{}
20981 \begin_inset Tabular
20982 <lyxtabular version="3" rows="10" columns="2">
20983 <features rotate="0" tabularvalignment="middle">
20984 <column alignment="center" valignment="top" width="0pt">
20985 <column alignment="center" valignment="top" width="0pt">
20987 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
20990 \begin_layout Plain Layout
20996 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
20999 \begin_layout Plain Layout
21007 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
21010 \begin_layout Plain Layout
21018 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
21021 \begin_layout Plain Layout
21022 \begin_inset Formula $\prime$
21032 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
21035 \begin_layout Plain Layout
21043 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
21046 \begin_layout Plain Layout
21047 \begin_inset Formula $\backprime$
21057 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
21060 \begin_layout Plain Layout
21068 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
21071 \begin_layout Plain Layout
21072 \begin_inset Formula $\mho$
21082 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
21085 \begin_layout Plain Layout
21093 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
21096 \begin_layout Plain Layout
21097 \begin_inset Formula $\triangle$
21107 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
21110 \begin_layout Plain Layout
21118 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
21121 \begin_layout Plain Layout
21122 \begin_inset Formula $\angle$
21132 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
21135 \begin_layout Plain Layout
21143 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
21146 \begin_layout Plain Layout
21147 \begin_inset Formula $\measuredangle$
21157 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
21160 \begin_layout Plain Layout
21168 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
21171 \begin_layout Plain Layout
21172 \begin_inset Formula $\sphericalangle$
21182 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
21185 \begin_layout Plain Layout
21193 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
21196 \begin_layout Plain Layout
21197 \begin_inset Formula $\top$
21207 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
21210 \begin_layout Plain Layout
21218 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
21221 \begin_layout Plain Layout
21222 \begin_inset Formula $\bot$
21236 \begin_inset space \hfill{}
21242 \begin_layout Subsection
21243 Miscellaneous Symbols
21244 \begin_inset CommandInset label
21246 name "sub:Miscellaneous-Symbols"
21251 \begin_inset Index idx
21254 \begin_layout Plain Layout
21255 Symbols ! miscellaneous
21263 \begin_layout Standard
21266 \begin_inset Tabular
21267 <lyxtabular version="3" rows="10" columns="2">
21268 <features rotate="0" tabularvalignment="middle">
21269 <column alignment="center" valignment="top" width="0pt">
21270 <column alignment="center" valignment="top" width="0pt">
21272 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
21275 \begin_layout Plain Layout
21281 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
21284 \begin_layout Plain Layout
21292 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
21295 \begin_layout Plain Layout
21303 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
21306 \begin_layout Plain Layout
21307 \begin_inset Formula $\flat$
21317 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
21320 \begin_layout Plain Layout
21328 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
21331 \begin_layout Plain Layout
21332 \begin_inset Formula $\natural$
21342 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
21345 \begin_layout Plain Layout
21353 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
21356 \begin_layout Plain Layout
21357 \begin_inset Formula $\sharp$
21367 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
21370 \begin_layout Plain Layout
21378 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
21381 \begin_layout Plain Layout
21382 \begin_inset Formula $\surd$
21392 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
21395 \begin_layout Plain Layout
21403 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
21406 \begin_layout Plain Layout
21407 \begin_inset Formula $\checkmark$
21417 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
21420 \begin_layout Plain Layout
21428 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
21431 \begin_layout Plain Layout
21432 \begin_inset Formula $\yen$
21442 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
21445 \begin_layout Plain Layout
21453 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
21456 \begin_layout Plain Layout
21457 \begin_inset Formula $\pounds$
21467 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
21470 \begin_layout Plain Layout
21476 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
21479 \begin_layout Plain Layout
21480 \begin_inset Formula $\$$
21490 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
21493 \begin_layout Plain Layout
21499 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
21502 \begin_layout Plain Layout
21503 \begin_inset Formula $§$
21517 \begin_inset Tabular
21518 <lyxtabular version="3" rows="10" columns="2">
21519 <features rotate="0" tabularvalignment="middle">
21520 <column alignment="center" valignment="top">
21521 <column alignment="center" valignment="top">
21523 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
21526 \begin_layout Plain Layout
21532 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
21535 \begin_layout Plain Layout
21543 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
21546 \begin_layout Plain Layout
21554 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
21557 \begin_layout Plain Layout
21558 \begin_inset Formula $\hbar$
21568 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
21571 \begin_layout Plain Layout
21579 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
21582 \begin_layout Plain Layout
21583 \begin_inset Formula $\hslash$
21593 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
21596 \begin_layout Plain Layout
21604 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
21607 \begin_layout Plain Layout
21608 \begin_inset Formula $\clubsuit$
21618 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
21621 \begin_layout Plain Layout
21629 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
21632 \begin_layout Plain Layout
21633 \begin_inset Formula $\spadesuit$
21643 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
21646 \begin_layout Plain Layout
21654 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
21657 \begin_layout Plain Layout
21658 \begin_inset Formula $\bigstar$
21668 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
21671 \begin_layout Plain Layout
21679 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
21682 \begin_layout Plain Layout
21683 \begin_inset Formula $\blacklozenge$
21693 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
21696 \begin_layout Plain Layout
21704 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
21707 \begin_layout Plain Layout
21708 \begin_inset Formula $\blacktriangle$
21718 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
21721 \begin_layout Plain Layout
21729 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
21732 \begin_layout Plain Layout
21733 \begin_inset Formula $\blacktriangledown$
21743 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
21746 \begin_layout Plain Layout
21754 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
21757 \begin_layout Plain Layout
21758 \begin_inset Formula $\bullet$
21772 \begin_inset Tabular
21773 <lyxtabular version="3" rows="10" columns="2">
21774 <features rotate="0" tabularvalignment="middle">
21775 <column alignment="center" valignment="top" width="0pt">
21776 <column alignment="center" valignment="top" width="0pt">
21778 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
21781 \begin_layout Plain Layout
21787 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
21790 \begin_layout Plain Layout
21798 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
21801 \begin_layout Plain Layout
21809 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
21812 \begin_layout Plain Layout
21813 \begin_inset Formula $\diamondsuit$
21823 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
21826 \begin_layout Plain Layout
21834 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
21837 \begin_layout Plain Layout
21838 \begin_inset Formula $\Diamond$
21848 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
21851 \begin_layout Plain Layout
21859 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
21862 \begin_layout Plain Layout
21863 \begin_inset Formula $\heartsuit$
21873 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
21876 \begin_layout Plain Layout
21884 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
21887 \begin_layout Plain Layout
21888 \begin_inset Formula $\P$
21898 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
21901 \begin_layout Plain Layout
21909 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
21912 \begin_layout Plain Layout
21913 \begin_inset Formula $\copyright$
21923 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
21926 \begin_layout Plain Layout
21934 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
21937 \begin_layout Plain Layout
21938 \begin_inset Formula $\circledR$
21948 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
21951 \begin_layout Plain Layout
21959 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
21962 \begin_layout Plain Layout
21963 \begin_inset Formula $\maltese$
21973 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
21976 \begin_layout Plain Layout
21984 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
21987 \begin_layout Plain Layout
21988 \begin_inset Formula $\diagup$
21998 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
22001 \begin_layout Plain Layout
22009 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
22012 \begin_layout Plain Layout
22013 \begin_inset Formula $\diagdown$
22029 \begin_layout Standard
22030 \begin_inset VSpace medskip
22036 \begin_layout Standard
22037 Some symbols can be displayed in different sizes, see
22038 \begin_inset CommandInset ref
22040 reference "sub:Font-Sizes"
22047 \begin_layout Subsection
22049 \begin_inset Index idx
22052 \begin_layout Plain Layout
22053 Symbols ! Euro-symbol
22059 \begin_inset Index idx
22062 \begin_layout Plain Layout
22069 \begin_layout Plain Layout
22086 \begin_layout Standard
22087 To use the Euro symbol in formulas, the LaTeX-package
22092 \begin_inset Index idx
22095 \begin_layout Plain Layout
22101 must be installed and loaded with the LaTeX-preamble line
22104 \begin_layout Standard
22109 usepackage[gennarrow]{eurosym}
22112 \begin_layout Standard
22113 The Euro symbol can now be inserted with the command
22120 \begin_inset Index idx
22123 \begin_layout Plain Layout
22134 \begin_layout Standard
22135 The Euro symbol can directly be inserted with the € key in mathematical
22136 text, without having
22151 can also be inserted in TeX-mode.
22152 The official currency symbol can then be inserted with the command
22159 \begin_inset Index idx
22162 \begin_layout Plain Layout
22170 , that is only available in TeX-mode.
22173 \begin_layout Standard
22177 \begin_layout Plain Layout
22187 \begin_inset Note Note
22190 \begin_layout Plain Layout
22191 The following table will only be displayed when the LaTeX-package
22203 \begin_layout Standard
22204 An overview about the different Euro symbols:
22207 \begin_layout Standard
22209 \begin_inset Tabular
22210 <lyxtabular version="3" rows="4" columns="3">
22211 <features rotate="0" tabularvalignment="middle">
22212 <column alignment="center" valignment="top" width="0pt">
22213 <column alignment="center" valignment="top" width="0pt">
22214 <column alignment="center" valignment="top" width="0pt">
22216 <cell multicolumn="1" alignment="center" valignment="top" bottomline="true" usebox="none">
22219 \begin_layout Plain Layout
22225 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
22228 \begin_layout Plain Layout
22234 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
22237 \begin_layout Plain Layout
22245 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
22248 \begin_layout Plain Layout
22254 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
22257 \begin_layout Plain Layout
22265 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
22268 \begin_layout Plain Layout
22269 \begin_inset Formula $\euro$
22279 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
22282 \begin_layout Plain Layout
22288 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
22291 \begin_layout Plain Layout
22297 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
22300 \begin_layout Plain Layout
22301 \begin_inset Formula $\mbox{€}$
22311 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
22314 \begin_layout Plain Layout
22320 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
22323 \begin_layout Plain Layout
22331 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
22334 \begin_layout Plain Layout
22338 \begin_layout Plain Layout
22360 \begin_layout Standard
22364 \begin_layout Plain Layout
22374 \begin_inset Note Note
22377 \begin_layout Plain Layout
22378 The following will be displayed when the LaTeX-package
22390 \begin_layout Standard
22391 You need to install the LaTeX-package
22395 to see the rest of this subsection in the output.
22398 \begin_layout Standard
22402 \begin_layout Plain Layout
22414 \begin_layout Section
22416 \begin_inset CommandInset label
22418 name "sec:Relations"
22423 \begin_inset Index idx
22426 \begin_layout Plain Layout
22433 \begin_inset Index idx
22436 \begin_layout Plain Layout
22441 \begin_layout Plain Layout
22452 \begin_layout Plain Layout
22467 \begin_layout Standard
22468 All following relations can also be inserted via the toolbar button
22471 arg "math-insert \\leq"
22477 \begin_layout Standard
22478 \begin_inset space \hfill{}
22482 \begin_inset Tabular
22483 <lyxtabular version="3" rows="17" columns="2">
22484 <features rotate="0" tabularvalignment="middle">
22485 <column alignment="center" valignment="top" width="0pt">
22486 <column alignment="center" valignment="top" width="0pt">
22488 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
22491 \begin_layout Plain Layout
22497 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
22500 \begin_layout Plain Layout
22508 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
22511 \begin_layout Plain Layout
22517 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
22520 \begin_layout Plain Layout
22521 \begin_inset Formula $<$
22531 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
22534 \begin_layout Plain Layout
22542 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
22545 \begin_layout Plain Layout
22546 \begin_inset Formula $\le$
22556 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
22559 \begin_layout Plain Layout
22567 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
22570 \begin_layout Plain Layout
22571 \begin_inset Formula $\ll$
22581 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
22584 \begin_layout Plain Layout
22592 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
22595 \begin_layout Plain Layout
22596 \begin_inset Formula $\prec$
22606 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
22609 \begin_layout Plain Layout
22617 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
22620 \begin_layout Plain Layout
22621 \begin_inset Formula $\preceq$
22631 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
22634 \begin_layout Plain Layout
22642 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
22645 \begin_layout Plain Layout
22646 \begin_inset Formula $\subset$
22656 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
22659 \begin_layout Plain Layout
22667 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
22670 \begin_layout Plain Layout
22671 \begin_inset Formula $\subseteq$
22681 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
22684 \begin_layout Plain Layout
22692 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
22695 \begin_layout Plain Layout
22696 \begin_inset Formula $\sqsubseteq$
22706 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
22709 \begin_layout Plain Layout
22717 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
22720 \begin_layout Plain Layout
22721 \begin_inset Formula $\in$
22731 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
22734 \begin_layout Plain Layout
22742 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
22745 \begin_layout Plain Layout
22746 \begin_inset Formula $\vdash$
22756 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
22759 \begin_layout Plain Layout
22767 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
22770 \begin_layout Plain Layout
22771 \begin_inset Formula $\smile$
22781 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
22784 \begin_layout Plain Layout
22792 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
22795 \begin_layout Plain Layout
22796 \begin_inset Formula $\lhd$
22806 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
22809 \begin_layout Plain Layout
22817 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
22820 \begin_layout Plain Layout
22821 \begin_inset Formula $\unlhd$
22831 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
22834 \begin_layout Plain Layout
22842 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
22845 \begin_layout Plain Layout
22846 \begin_inset Formula $\gtrless$
22856 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
22859 \begin_layout Plain Layout
22867 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
22870 \begin_layout Plain Layout
22871 \begin_inset Formula $\mid$
22881 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
22884 \begin_layout Plain Layout
22892 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
22895 \begin_layout Plain Layout
22896 \begin_inset Formula $\nmid$
22910 \begin_inset space \hfill{}
22914 \begin_inset Tabular
22915 <lyxtabular version="3" rows="17" columns="2">
22916 <features rotate="0" tabularvalignment="middle">
22917 <column alignment="center" valignment="top" width="0pt">
22918 <column alignment="center" valignment="top" width="0pt">
22920 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
22923 \begin_layout Plain Layout
22929 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
22932 \begin_layout Plain Layout
22940 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
22943 \begin_layout Plain Layout
22949 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
22952 \begin_layout Plain Layout
22953 \begin_inset Formula $=$
22963 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
22966 \begin_layout Plain Layout
22974 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
22977 \begin_layout Plain Layout
22978 \begin_inset Formula $\not=$
22988 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
22991 \begin_layout Plain Layout
22999 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
23002 \begin_layout Plain Layout
23003 \begin_inset Formula $\equiv$
23013 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
23016 \begin_layout Plain Layout
23024 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
23027 \begin_layout Plain Layout
23028 \begin_inset Formula $\sim$
23038 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
23041 \begin_layout Plain Layout
23049 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
23052 \begin_layout Plain Layout
23053 \begin_inset Formula $\simeq$
23063 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
23066 \begin_layout Plain Layout
23074 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
23077 \begin_layout Plain Layout
23078 \begin_inset Formula $\approx$
23088 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
23091 \begin_layout Plain Layout
23099 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
23102 \begin_layout Plain Layout
23103 \begin_inset Formula $\cong$
23113 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
23116 \begin_layout Plain Layout
23124 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
23127 \begin_layout Plain Layout
23128 \begin_inset Formula $\bowtie$
23138 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
23141 \begin_layout Plain Layout
23149 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
23152 \begin_layout Plain Layout
23153 \begin_inset Formula $\notin$
23163 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
23166 \begin_layout Plain Layout
23174 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
23177 \begin_layout Plain Layout
23178 \begin_inset Formula $\perp$
23188 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
23191 \begin_layout Plain Layout
23199 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
23202 \begin_layout Plain Layout
23203 \begin_inset Formula $\propto$
23213 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
23216 \begin_layout Plain Layout
23224 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
23227 \begin_layout Plain Layout
23228 \begin_inset Formula $\asymp$
23238 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
23241 \begin_layout Plain Layout
23249 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
23252 \begin_layout Plain Layout
23253 \begin_inset Formula $\doteq$
23263 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
23266 \begin_layout Plain Layout
23274 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
23277 \begin_layout Plain Layout
23278 \begin_inset Formula $\circeq$
23288 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
23291 \begin_layout Plain Layout
23299 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
23302 \begin_layout Plain Layout
23303 \begin_inset Formula $\models$
23313 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
23316 \begin_layout Plain Layout
23324 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
23327 \begin_layout Plain Layout
23328 \begin_inset Formula $\widehat{=}$
23342 \begin_inset space \hfill{}
23346 \begin_inset Tabular
23347 <lyxtabular version="3" rows="17" columns="2">
23348 <features rotate="0" tabularvalignment="middle">
23349 <column alignment="center" valignment="top" width="0pt">
23350 <column alignment="center" valignment="top" width="0pt">
23352 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
23355 \begin_layout Plain Layout
23361 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
23364 \begin_layout Plain Layout
23372 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
23375 \begin_layout Plain Layout
23381 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
23384 \begin_layout Plain Layout
23385 \begin_inset Formula $>$
23395 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
23398 \begin_layout Plain Layout
23406 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
23409 \begin_layout Plain Layout
23410 \begin_inset Formula $\ge$
23420 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
23423 \begin_layout Plain Layout
23431 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
23434 \begin_layout Plain Layout
23435 \begin_inset Formula $\gg$
23445 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
23448 \begin_layout Plain Layout
23456 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
23459 \begin_layout Plain Layout
23460 \begin_inset Formula $\succ$
23470 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
23473 \begin_layout Plain Layout
23481 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
23484 \begin_layout Plain Layout
23485 \begin_inset Formula $\succeq$
23495 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
23498 \begin_layout Plain Layout
23506 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
23509 \begin_layout Plain Layout
23510 \begin_inset Formula $\supset$
23520 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
23523 \begin_layout Plain Layout
23531 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
23534 \begin_layout Plain Layout
23535 \begin_inset Formula $\supseteq$
23545 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
23548 \begin_layout Plain Layout
23556 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
23559 \begin_layout Plain Layout
23560 \begin_inset Formula $\sqsupseteq$
23570 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
23573 \begin_layout Plain Layout
23581 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
23584 \begin_layout Plain Layout
23585 \begin_inset Formula $\ni$
23595 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
23598 \begin_layout Plain Layout
23606 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
23609 \begin_layout Plain Layout
23610 \begin_inset Formula $\dashv$
23620 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
23623 \begin_layout Plain Layout
23631 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
23634 \begin_layout Plain Layout
23635 \begin_inset Formula $\frown$
23645 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
23648 \begin_layout Plain Layout
23656 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
23659 \begin_layout Plain Layout
23660 \begin_inset Formula $\rhd$
23670 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
23673 \begin_layout Plain Layout
23681 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
23684 \begin_layout Plain Layout
23685 \begin_inset Formula $\unrhd$
23695 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
23698 \begin_layout Plain Layout
23706 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
23709 \begin_layout Plain Layout
23710 \begin_inset Formula $\lessgtr$
23720 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
23723 \begin_layout Plain Layout
23731 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
23734 \begin_layout Plain Layout
23735 \begin_inset Formula $\parallel$
23745 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
23748 \begin_layout Plain Layout
23756 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
23759 \begin_layout Plain Layout
23760 \begin_inset Formula $\nparallel$
23774 \begin_inset space \hfill{}
23780 \begin_layout Standard
23781 \begin_inset VSpace medskip
23796 are bigger than the equal looking operators
23811 \begin_layout Standard
23812 LyX supports also many special relations.
23813 Use the toolbar button
23816 arg "math-insert \\leqq"
23819 to see a list of these relations.
23822 \begin_layout Standard
23823 Relations are, in contrary to symbols, always surrounded by space.
23826 \begin_layout Standard
23827 Relations with labels can be created with the command
23834 \begin_inset Index idx
23837 \begin_layout Plain Layout
23848 \begin_layout Standard
23850 \begin_inset Tabular
23851 <lyxtabular version="3" rows="2" columns="2">
23852 <features rotate="0" tabularvalignment="middle">
23853 <column alignment="center" valignment="top">
23854 <column alignment="center" valignment="top">
23856 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
23859 \begin_layout Plain Layout
23865 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
23868 \begin_layout Plain Layout
23870 \begin_inset Note Note
23873 \begin_layout Plain Layout
23880 is only used as spacer.
23892 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
23895 \begin_layout Plain Layout
23899 \begin_inset space \textvisiblespace{}
23907 \begin_inset space \textvisiblespace{}
23911 \begin_inset Formula $\downarrow$
23917 \begin_inset space \textvisiblespace{}
23921 \begin_inset space \textvisiblespace{}
23929 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
23932 \begin_layout Plain Layout
23933 \begin_inset Formula $\raisebox{5mm}{}A(r)\stackrel{r\to\infty}{\approx}B$
23949 \begin_layout Section
23953 \begin_layout Subsection
23954 Predefined Functions
23955 \begin_inset CommandInset label
23957 name "sub:Predefined-Functions"
23962 \begin_inset Index idx
23965 \begin_layout Plain Layout
23966 Functions ! predefined
23974 \begin_layout Standard
23975 In general, variables are set
23979 in mathematical expressions, but not function names, because
23980 \begin_inset Formula $sin$
23983 could be misunderstood as
23984 \begin_inset Formula $s\cdot i\cdot n$
23988 Therefore there are predefined functionswhich are additionally a bit separated
23990 They are inserted as commands starting with a backslash before their name.
23993 \begin_layout Standard
23995 \begin_inset Tabular
23996 <lyxtabular version="3" rows="2" columns="4">
23997 <features rotate="0" tabularvalignment="middle">
23998 <column alignment="center" valignment="top" width="0pt">
23999 <column alignment="center" valignment="top" width="0pt">
24000 <column alignment="center" valignment="top" width="0pt">
24001 <column alignment="center" valignment="top" width="0pt">
24003 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
24006 \begin_layout Plain Layout
24012 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
24015 \begin_layout Plain Layout
24021 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
24024 \begin_layout Plain Layout
24030 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
24033 \begin_layout Plain Layout
24041 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
24044 \begin_layout Plain Layout
24050 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
24053 \begin_layout Plain Layout
24054 \begin_inset Formula $Asin(x)+B$
24062 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
24065 \begin_layout Plain Layout
24073 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
24076 \begin_layout Plain Layout
24077 \begin_inset Formula $A\sin(x)+B$
24093 \begin_layout Standard
24094 The following functions are predefined:
24097 \begin_layout Standard
24098 \begin_inset VSpace -2mm
24104 \begin_layout Standard
24106 \begin_inset Tabular
24107 <lyxtabular version="3" rows="9" columns="4">
24108 <features rotate="0" tabularvalignment="middle">
24109 <column alignment="center" valignment="top" width="0pt">
24110 <column alignment="center" valignment="top" width="0pt">
24111 <column alignment="center" valignment="top" width="0pt">
24112 <column alignment="center" valignment="top" width="0pt">
24114 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
24117 \begin_layout Plain Layout
24123 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
24126 \begin_layout Plain Layout
24132 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
24135 \begin_layout Plain Layout
24141 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
24144 \begin_layout Plain Layout
24152 <cell alignment="center" valignment="top" topline="true" leftline="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" rightline="true" usebox="none">
24188 \begin_layout Plain Layout
24198 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
24201 \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" rightline="true" usebox="none">
24234 \begin_layout Plain Layout
24244 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
24247 \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" rightline="true" usebox="none">
24280 \begin_layout Plain Layout
24290 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
24293 \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" rightline="true" usebox="none">
24326 \begin_layout Plain Layout
24336 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
24339 \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" rightline="true" usebox="none">
24372 \begin_layout Plain Layout
24382 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
24385 \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" rightline="true" usebox="none">
24418 \begin_layout Plain Layout
24428 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
24431 \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" rightline="true" usebox="none">
24464 \begin_layout Plain Layout
24474 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
24477 \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" rightline="true" usebox="none">
24510 \begin_layout Plain Layout
24526 \begin_layout Standard
24527 They can also be inserted with the math toolbar button
24528 \begin_inset Graphics
24529 filename ../images/math/functions.png
24537 \begin_layout Subsection
24538 Self-defined Functions
24539 \begin_inset Index idx
24542 \begin_layout Plain Layout
24543 Functions ! self-defined
24551 \begin_layout Standard
24552 To use a function that is not predefined, like for example the sign function
24553 sgn(x), there are two possibilities:
24556 \begin_layout Itemize
24557 Define the function by inserting the following line to the LaTeX-preamble
24561 \begin_layout Plain Layout
24566 DeclareMathOperator
24569 \begin_inset CommandInset ref
24571 reference "sub:Self-defined-Operators"
24581 \begin_inset Newline newline
24585 \begin_inset VSpace -3mm
24589 \begin_inset Newline newline
24596 DeclareMathOperator{
24601 \begin_inset Index idx
24604 \begin_layout Plain Layout
24609 DeclareMathOperator
24615 \begin_inset Newline newline
24619 \begin_inset VSpace -2mm
24623 \begin_inset Newline newline
24626 Now the new defined function can be called with the command
24635 \begin_layout Itemize
24636 Write the formula as usual, mark the formula name, in our example the letters
24641 , and change it to mathematical text.
24642 Finally, a space is inserted between prefactor and function.
24645 \begin_layout Standard
24646 The result is the same with both methods as with a predefined function
24650 \begin_layout Plain Layout
24651 In LyX self-defined functions are displayed red, predefined ones black.
24659 \begin_layout Standard
24661 \begin_inset Tabular
24662 <lyxtabular version="3" rows="3" columns="2">
24663 <features rotate="0" tabularvalignment="middle">
24664 <column alignment="center" valignment="top" width="0pt">
24665 <column alignment="center" valignment="top" width="0pt">
24667 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
24670 \begin_layout Plain Layout
24676 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
24679 \begin_layout Plain Layout
24687 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
24690 \begin_layout Plain Layout
24698 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
24701 \begin_layout Plain Layout
24702 \begin_inset Formula $A\sgn(x)+B$
24712 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
24715 \begin_layout Plain Layout
24719 \begin_inset Formula $\underbrace{\textrm{sgn}}_{\textrm{Alt+M}\,\textrm{M}}$
24727 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
24730 \begin_layout Plain Layout
24731 \begin_inset Formula $A\,\textrm{sgn}(x)+B$
24747 \begin_layout Standard
24748 The first method is more suitable when the self-defined function should
24749 be used several times.
24752 \begin_layout Subsection
24754 \begin_inset Index idx
24757 \begin_layout Plain Layout
24766 \begin_layout Standard
24767 For limits, in addition to the commands
24774 \begin_inset Index idx
24777 \begin_layout Plain Layout
24797 the following functions are defined:
24800 \begin_layout Standard
24802 \begin_inset Tabular
24803 <lyxtabular version="3" rows="5" columns="2">
24804 <features rotate="0" tabularvalignment="middle">
24805 <column alignment="center" valignment="top">
24806 <column alignment="center" valignment="top">
24808 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
24811 \begin_layout Plain Layout
24817 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
24820 \begin_layout Plain Layout
24822 \begin_inset Note Note
24825 \begin_layout Plain Layout
24832 is only used as spacer.
24844 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
24847 \begin_layout Plain Layout
24855 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
24858 \begin_layout Plain Layout
24859 \begin_inset Formula $\varliminf$
24869 <cell alignment="center" valignment="top" leftline="true" usebox="none">
24872 \begin_layout Plain Layout
24880 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
24883 \begin_layout Plain Layout
24884 \begin_inset Formula $\varlimsup$
24894 <cell alignment="center" valignment="top" leftline="true" usebox="none">
24897 \begin_layout Plain Layout
24905 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
24908 \begin_layout Plain Layout
24909 \begin_inset Formula $\varprojlim$
24919 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
24922 \begin_layout Plain Layout
24930 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
24933 \begin_layout Plain Layout
24934 \begin_inset Formula $\varinjlim$
24938 \begin_inset Formula $\raisebox{-2.5mm}{}$
24954 \begin_layout Standard
24955 \begin_inset VSpace medskip
24958 The limit is created by inserting a subscript.
24959 It is set right beside the function in an inline formula:
24962 \begin_layout Standard
24964 \begin_inset Tabular
24965 <lyxtabular version="3" rows="2" columns="2">
24966 <features rotate="0" tabularvalignment="middle">
24967 <column alignment="center" valignment="top" width="0pt">
24968 <column alignment="center" valignment="top" width="0pt">
24970 <cell alignment="center" valignment="top" usebox="none">
24973 \begin_layout Plain Layout
24979 <cell alignment="center" valignment="top" usebox="none">
24982 \begin_layout Plain Layout
24983 \begin_inset space \hspace{}
24988 \begin_inset Note Note
24991 \begin_layout Plain Layout
24998 are used here as spacer.
25010 <cell alignment="center" valignment="top" usebox="none">
25013 \begin_layout Plain Layout
25019 \begin_inset space \textvisiblespace{}
25023 \begin_inset space \textvisiblespace{}
25031 <cell alignment="center" valignment="top" usebox="none">
25034 \begin_layout Plain Layout
25035 \begin_inset Formula $\hspace{1cm}\raisebox{5mm}{}\lim_{x\to A}x=B$
25051 \begin_layout Standard
25052 In a displayed formula the limit is set below the formula, as usual:
25053 \begin_inset Formula
25063 \begin_layout Standard
25064 \begin_inset VSpace medskip
25070 \begin_layout Standard
25071 How to adjust the typesetting of the limits see
25072 \begin_inset CommandInset ref
25074 reference "sub:Operator-Limits"
25081 \begin_layout Subsection
25083 \begin_inset Index idx
25086 \begin_layout Plain Layout
25087 Functions ! modulo-
25095 \begin_layout Standard
25096 The modulo-function is special, because it exists in four variants.
25097 The variants in a displayed formula are:
25098 \begin_inset Formula
25100 \underline{\textrm{Command}\raisebox{-0.9mm}{}} & & \underline{\textrm{Result}}\\
25101 \mathrm{a\backslash mod\textrm{␣}b} & & a\mod b\\
25102 \mathrm{a\backslash pmod\textrm{␣}b} & & a\pmod b\\
25103 \mathrm{a\backslash bmod\textrm{␣}b} & & a\bmod b\\
25104 \mathrm{a\backslash pod\textrm{␣}b} & & a\pod b
25112 \begin_layout Standard
25113 In an inline formula less space is set before the function names for all
25115 By default the modulo-functions take only the first following character
25117 To use more than one character, one has to put them into TeX-braces:
25118 \begin_inset Formula
25120 \underline{\textrm{Command}\raisebox{-0.9mm}{}} & & \underline{\textrm{Result}}\\
25121 \mathrm{a\backslash pod\textrm{␣}bcd} & & a\pod bcd\\
25122 \mathrm{a\backslash pod\backslash\{bc\to d} & & a\pod{bc}d
25130 \begin_layout Section
25132 \begin_inset Index idx
25135 \begin_layout Plain Layout
25144 \begin_layout Subsection
25145 Special Characters in Mathematical Text
25148 \begin_layout Standard
25149 The following commands can only be used in mathematical text or in TeX-mode:
25152 \begin_layout Standard
25153 \begin_inset space \hfill{}
25157 \begin_inset Tabular
25158 <lyxtabular version="3" rows="8" columns="2">
25159 <features rotate="0" tabularvalignment="middle">
25160 <column alignment="block" valignment="top">
25161 <column alignment="block" valignment="top">
25163 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
25166 \begin_layout Plain Layout
25172 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
25175 \begin_layout Plain Layout
25183 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
25186 \begin_layout Plain Layout
25194 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
25197 \begin_layout Plain Layout
25198 \begin_inset Formula $\textrm{œ}$
25208 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
25211 \begin_layout Plain Layout
25219 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
25222 \begin_layout Plain Layout
25223 \begin_inset Formula $\textrm{Œ}$
25233 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
25236 \begin_layout Plain Layout
25244 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
25247 \begin_layout Plain Layout
25248 \begin_inset Formula $\textrm{æ}$
25258 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
25261 \begin_layout Plain Layout
25269 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
25272 \begin_layout Plain Layout
25273 \begin_inset Formula $\textrm{Æ}$
25283 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
25286 \begin_layout Plain Layout
25294 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
25297 \begin_layout Plain Layout
25298 \begin_inset Formula $\textrm{\aa}$
25308 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
25311 \begin_layout Plain Layout
25315 \begin_inset Index idx
25318 \begin_layout Plain Layout
25325 \begin_layout Plain Layout
25346 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
25349 \begin_layout Plain Layout
25350 \begin_inset Formula $\textrm{Å}$
25360 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
25363 \begin_layout Plain Layout
25371 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
25374 \begin_layout Plain Layout
25375 \begin_inset Formula $\textrm{ı}$
25389 \begin_inset space \hfill{}
25393 \begin_inset Tabular
25394 <lyxtabular version="3" rows="8" columns="2">
25395 <features rotate="0" tabularvalignment="middle">
25396 <column alignment="block" valignment="top">
25397 <column alignment="center" valignment="top">
25399 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
25402 \begin_layout Plain Layout
25404 \begin_inset Note Note
25407 \begin_layout Plain Layout
25409 \begin_inset space \thinspace{}
25412 mm is used for separation, because otherwise the output will be ¡ and ¿
25423 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
25426 \begin_layout Plain Layout
25434 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
25437 \begin_layout Plain Layout
25445 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
25448 \begin_layout Plain Layout
25449 \begin_inset Formula $\textrm{ø}$
25459 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
25462 \begin_layout Plain Layout
25470 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
25473 \begin_layout Plain Layout
25474 \begin_inset Formula $\textrm{Ø}$
25484 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
25487 \begin_layout Plain Layout
25495 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
25498 \begin_layout Plain Layout
25499 \begin_inset Formula $\textrm{ł}$
25509 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
25512 \begin_layout Plain Layout
25520 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
25523 \begin_layout Plain Layout
25524 \begin_inset Formula $\textrm{Ł}$
25534 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
25537 \begin_layout Plain Layout
25539 \begin_inset space \hspace{}
25544 \begin_inset space \textvisiblespace{}
25552 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
25555 \begin_layout Plain Layout
25556 \begin_inset Formula $\textrm{!`}$
25566 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
25569 \begin_layout Plain Layout
25571 \begin_inset space \hspace{}
25576 \begin_inset space \textvisiblespace{}
25584 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
25587 \begin_layout Plain Layout
25588 \begin_inset Formula $\textrm{?`}$
25598 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
25601 \begin_layout Plain Layout
25609 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
25612 \begin_layout Plain Layout
25613 \begin_inset Formula $\textrm{ȷ}$
25627 \begin_inset space \hfill{}
25633 \begin_layout Standard
25635 \begin_inset Formula $\textrm{\textrm{Å}}$
25639 \begin_inset Formula $\textrm{\textrm{Ø}}$
25642 can also be inserted via the math toolbar button
25643 \begin_inset Graphics
25644 filename ../images/math/digamma.png
25652 \begin_layout Standard
25653 An exception are the commands
25656 \begin_inset space \hspace{}
25665 \begin_inset space \hspace{}
25671 , because they can be inserted in LyX directly to text.
25674 \begin_layout Subsection
25676 \begin_inset CommandInset label
25678 name "sub:Accents-in-Text"
25683 \begin_inset Index idx
25686 \begin_layout Plain Layout
25695 \begin_layout Standard
25696 With the following commands all letters can be accented.
25697 The commands must be inserted in TeX-mode.
25700 \begin_layout Standard
25701 \begin_inset space \hfill{}
25705 \begin_inset Tabular
25706 <lyxtabular version="3" rows="8" columns="2">
25707 <features rotate="0" tabularvalignment="middle">
25708 <column alignment="block" valignment="top">
25709 <column alignment="block" valignment="top">
25711 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
25714 \begin_layout Plain Layout
25720 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
25723 \begin_layout Plain Layout
25731 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
25734 \begin_layout Plain Layout
25738 \begin_inset Quotes grd
25746 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
25749 \begin_layout Plain Layout
25753 \begin_layout Plain Layout
25769 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
25772 \begin_layout Plain Layout
25780 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
25783 \begin_layout Plain Layout
25787 \begin_layout Plain Layout
25803 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
25806 \begin_layout Plain Layout
25810 \begin_inset space \textvisiblespace{}
25818 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
25821 \begin_layout Plain Layout
25825 \begin_layout Plain Layout
25841 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
25844 \begin_layout Plain Layout
25852 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
25855 \begin_layout Plain Layout
25859 \begin_layout Plain Layout
25875 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
25878 \begin_layout Plain Layout
25882 \begin_inset space \textvisiblespace{}
25890 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
25893 \begin_layout Plain Layout
25897 \begin_layout Plain Layout
25913 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
25916 \begin_layout Plain Layout
25920 \begin_inset space \textvisiblespace{}
25928 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
25931 \begin_layout Plain Layout
25935 \begin_layout Plain Layout
25951 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
25954 \begin_layout Plain Layout
25958 \begin_inset space \textvisiblespace{}
25966 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
25969 \begin_layout Plain Layout
25973 \begin_layout Plain Layout
25993 \begin_inset space \hfill{}
25997 \begin_inset Tabular
25998 <lyxtabular version="3" rows="8" columns="2">
25999 <features rotate="0" tabularvalignment="middle">
26000 <column alignment="block" valignment="top">
26001 <column alignment="center" valignment="top">
26003 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
26006 \begin_layout Plain Layout
26012 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
26015 \begin_layout Plain Layout
26023 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
26026 \begin_layout Plain Layout
26030 \begin_inset space \textvisiblespace{}
26038 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
26041 \begin_layout Plain Layout
26045 \begin_layout Plain Layout
26061 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
26064 \begin_layout Plain Layout
26072 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
26075 \begin_layout Plain Layout
26079 \begin_layout Plain Layout
26095 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
26098 \begin_layout Plain Layout
26102 \begin_inset Index idx
26105 \begin_layout Plain Layout
26116 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
26119 \begin_layout Plain Layout
26123 \begin_layout Plain Layout
26139 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
26142 \begin_layout Plain Layout
26150 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
26153 \begin_layout Plain Layout
26157 \begin_layout Plain Layout
26173 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
26176 \begin_layout Plain Layout
26180 \begin_inset space \textvisiblespace{}
26188 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
26191 \begin_layout Plain Layout
26195 \begin_layout Plain Layout
26211 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
26214 \begin_layout Plain Layout
26218 \begin_inset space \textvisiblespace{}
26226 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
26229 \begin_layout Plain Layout
26233 \begin_layout Plain Layout
26249 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
26252 \begin_layout Plain Layout
26256 \begin_inset space \textvisiblespace{}
26264 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
26267 \begin_layout Plain Layout
26271 \begin_layout Plain Layout
26291 \begin_inset space \hfill{}
26297 \begin_layout Standard
26298 \begin_inset VSpace medskip
26307 also two different characters can be accented.
26313 \begin_inset space \textvisiblespace{}
26322 \begin_layout Plain Layout
26334 \begin_layout Standard
26347 can in combination with vowels directly be inserted with the keyboard without
26349 The same applies for the tilde
26353 \begin_layout Plain Layout
26354 This only applies for keyboards where the tilde is defined as accent.
26363 in combination with
26378 \begin_layout Standard
26421 and accents that are inserted directly with the keyboard are also available
26422 in mathematical text.
26423 For the other accents there are special math commands to be used in formulas,
26425 \begin_inset CommandInset ref
26427 reference "sub:Accents-for-one"
26434 \begin_layout Standard
26435 \begin_inset VSpace bigskip
26438 Furthermore, with the command
26445 \begin_inset Index idx
26448 \begin_layout Plain Layout
26456 all numbers and letters can be set into a circle, quasi accented with a
26457 circle, similar to the copyright symbol.
26460 \begin_layout Standard
26462 \begin_inset Tabular
26463 <lyxtabular version="3" rows="3" columns="2">
26464 <features rotate="0" tabularvalignment="middle">
26465 <column alignment="center" valignment="top">
26466 <column alignment="center" valignment="top">
26468 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
26471 \begin_layout Plain Layout
26477 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
26480 \begin_layout Plain Layout
26482 \begin_inset Note Note
26485 \begin_layout Plain Layout
26492 is only used as spacer.
26504 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
26507 \begin_layout Plain Layout
26515 <cell multicolumn="1" alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
26518 \begin_layout Plain Layout
26522 \begin_layout Plain Layout
26538 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
26541 \begin_layout Plain Layout
26552 raisebox{-1.5pt}{W}}
26557 <cell multicolumn="1" alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
26560 \begin_layout Plain Layout
26561 \begin_inset Formula $\raisebox{4.5mm}{}$
26568 \begin_layout Plain Layout
26586 \begin_inset Formula $\raisebox{-2mm}{}$
26602 \begin_layout Standard
26603 One has to take care that the character fits in the circle.
26614 \begin_layout Plain Layout
26616 \begin_inset CommandInset ref
26618 reference "sub:Font-Sizes"
26627 specifies thereby the size of the circle.
26638 \begin_layout Plain Layout
26640 \begin_inset CommandInset ref
26642 reference "sub:Boxes-without-Frame"
26651 the character can be centered.
26654 \begin_layout Subsection
26656 \begin_inset Index idx
26659 \begin_layout Plain Layout
26668 \begin_layout Standard
26669 Old-style figures (also known as old-style numerals) are created with the
26677 \begin_inset Index idx
26680 \begin_layout Plain Layout
26689 The command can be used in formulas and in TeX-mode.
26690 The command scheme is:
26693 \begin_layout Standard
26698 oldstylenums{number}
26701 \begin_layout Standard
26706 oldstylenums{0123456789
26709 \begin_inset Formula $\oldstylenums{0123456789}$
26715 \begin_layout Section
26717 \begin_inset CommandInset label
26719 name "sec:Formula-Styles"
26724 \begin_inset Index idx
26727 \begin_layout Plain Layout
26736 \begin_layout Itemize
26737 There are two different alignment styles:
26741 \begin_layout Description
26742 Centered is the predefined standard
26745 \begin_layout Description
26746 Indented for this the option
26750 must be inserted in the menu
26752 Document\SpecialChar \menuseparator
26758 \begin_inset space ~
26764 \begin_layout Standard
26769 is used, the indentation can be adjusted with the length
26776 \begin_inset Index idx
26779 \begin_layout Plain Layout
26788 Should the distance be 15
26789 \begin_inset space \thinspace{}
26792 mm, the following command line is inserted in the LaTeX-preamble
26795 \begin_layout Standard
26805 \begin_layout Standard
26806 When no length is specified, the predefined value of 30
26807 \begin_inset space \thinspace{}
26814 \begin_layout Itemize
26815 And two different numbering styles:
26819 \begin_layout Description
26820 Right is the predefined standard
26823 \begin_layout Description
26824 Left for this the option
26828 must be inserted in the menu
26830 Document\SpecialChar \menuseparator
26836 \begin_inset space ~
26843 \begin_layout Standard
26852 can also be used together.
26853 In this case both options are inserted, separated by a comma.
26856 \begin_layout Standard
26857 The chosen styles are used for all displayed formulas of the document.
26858 When both, centered and indented formulas should be created in a document,
26864 The indented formulas are then set in a flalign environment, see
26865 \begin_inset CommandInset ref
26867 reference "sub:Flalign-Environment"
26874 \begin_layout Section
26876 \begin_inset CommandInset label
26878 name "sec:Multiline-Formulas"
26883 \begin_inset Index idx
26886 \begin_layout Plain Layout
26887 Formula ! multiline
26895 \begin_layout Subsection
26899 \begin_layout Standard
26900 In LyX multiline formulas are created by pressing
26905 arg "newline-insert newline"
26911 This creates either an
26913 eqnarray environment
26915 that is described in
26916 \begin_inset CommandInset ref
26918 reference "sub:Eqnarray-Environment"
26922 or, when the option
26924 Use AMS math package
26926 in the document settings is selected, an
26930 that is described in
26931 \begin_inset CommandInset ref
26933 reference "sub:Standard-align-Environment"
26938 The align environment is recommended because it provides in any case a
26939 typographically correct output.
26942 \begin_layout Standard
26943 There are other multiline formula environments that can be created via the
26946 Insert\SpecialChar \menuseparator
26950 These environments are described in the following sections.
26953 \begin_layout Standard
26954 In all multiline formula environments a new line is created by pressing
26958 arg "newline-insert newline"
26962 To add or delete lines, the math toolbar buttons
26963 \begin_inset Graphics
26964 filename ../images/tabular-feature_append-row.png
26970 \begin_inset Graphics
26971 filename ../images/tabular-feature_delete-row.png
26976 , respectively, or the menu
26978 Edit\SpecialChar \menuseparator
26984 \begin_layout Subsubsection
26986 \begin_inset CommandInset label
26988 name "sub:Line-Separation"
26993 \begin_inset Index idx
26996 \begin_layout Plain Layout
26997 Formula ! multiline ! Line separation
27005 \begin_layout Standard
27006 There is sometimes not enough space in multiline formulas between the lines:
27007 \begin_inset Formula
27009 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}\\
27010 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
27018 \begin_layout Standard
27019 In LaTeX additional line space is specified as optional argument of the
27021 This is not yet possible in LyX
27025 \begin_layout Plain Layout
27027 \begin_inset CommandInset href
27029 name "LyX-bug #1505"
27030 target "http://www.lyx.org/trac/ticket/1505"
27039 , therefore the whole formula must be inserted in TeX-mode.
27040 To add in our example space, the command
27048 is inserted at the end of the first line.
27053 \begin_layout Plain Layout
27060 \begin_layout Plain Layout
27062 B^{2}(B^{2}-2r_{g}^{2}+2x_{0}^{2}-2r_{k}^{2})+4x_{0}^{2}x^{2}+4x_{0}xD &
27065 textrm{-}4x^{2}B^{2}+4x_{0}xB^{2}
27072 \begin_layout Plain Layout
27076 left(B^{2}+x_{0}^{2}
27084 left(B^{2}-2r_{g}^{2}+2x_{0}^{2}-2r_{k}^{2}
27089 \begin_layout Plain Layout
27101 \begin_layout Standard
27102 \begin_inset VSpace bigskip
27105 To set the line separation for all lines in a formula, the length
27112 \begin_inset Index idx
27115 \begin_layout Plain Layout
27125 \begin_inset Formula $\mbox{line separation}=\mathrm{6\, pt+\backslash jot}$
27136 \begin_inset space \thinspace{}
27141 \begin_inset space \thinspace{}
27144 mm additional line separation as in the previous example, the command
27147 \begin_layout Standard
27157 \begin_layout Standard
27158 is inserted in TeX-mode before the formula.
27159 This requires that the LaTeX-package
27167 \begin_layout Plain Layout
27172 is part of every LaTeX standard installation.
27178 \begin_inset Index idx
27181 \begin_layout Plain Layout
27187 was loaded in LaTeX-preamble with the line
27190 \begin_layout Standard
27198 \begin_layout Standard
27203 \begin_layout Plain Layout
27215 \begin_inset Formula
27217 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}\\
27218 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
27226 \begin_layout Standard
27230 \begin_layout Plain Layout
27241 To get back to the predefined distance,
27247 is set to the value 3
27248 \begin_inset space \thinspace{}
27254 \begin_layout Subsubsection
27256 \begin_inset CommandInset label
27258 name "sub:Column-Separation"
27263 \begin_inset Index idx
27266 \begin_layout Plain Layout
27267 Formula ! multiline ! Column separation
27275 \begin_layout Standard
27276 Multiline formulas form a matrix.
27277 A formula in the eqnarray environment is for example a matrix with three
27279 By changing the column separation in this environment, the space beside
27280 the relation sign can be changed.
27283 \begin_layout Standard
27284 The column separation is specified with the length
27291 \begin_inset Index idx
27294 \begin_layout Plain Layout
27303 \begin_inset Newline newline
27306 column separation = 2
27307 \begin_inset space \thinspace{}
27317 \begin_inset Newline newline
27323 \begin_layout Standard
27333 \begin_layout Standard
27334 inserted in TeX-mode, sets for all following formulas a column separation
27336 \begin_inset space \thinspace{}
27340 To get back to the predefined distance,
27347 \begin_inset space \thinspace{}
27353 \begin_layout Standard
27355 \begin_inset space \thinspace{}
27358 cm column separation:
27362 \begin_layout Plain Layout
27374 \begin_inset Formula
27382 A formula with the predefined column separation for matrices of 10
27383 \begin_inset space \thinspace{}
27390 \begin_layout Plain Layout
27402 \begin_inset Formula
27413 \begin_layout Subsubsection
27415 \begin_inset Index idx
27418 \begin_layout Plain Layout
27427 \begin_layout Standard
27428 Long formulas can be typeset using these methods:
27431 \begin_layout Itemize
27432 When one side of the equation is much shorter than the line width, this
27433 one is chosen for the left side and the right side is typeset over two
27435 \begin_inset Formula
27437 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 \\
27438 & & -\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}
27443 The minus sign at the beginning of the second line does normally not appear
27444 as an operator because it is the first character of the line.
27445 Thus it would not be surrounded by space and could not be distinguished
27446 from the fraction bar.
27448 \begin_inset space \thinspace{}
27451 pt space was inserted behind the minus sign with the command
27461 \begin_layout Plain Layout
27469 \begin_inset CommandInset ref
27471 reference "sub:Variable-Space"
27481 \begin_inset Index idx
27484 \begin_layout Plain Layout
27495 \begin_layout Itemize
27496 When both sides of the equation are too long, the command
27503 \begin_inset Index idx
27506 \begin_layout Plain Layout
27515 It is inserted in the first column of the first line and causes all further
27516 insertions to overwrite the following columns:
27517 \begin_inset Formula
27519 \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 \\
27520 & & -\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 \\
27521 & & =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}
27526 After the insertion of
27532 , the cursor is in a purple box that is a bit shifted to the left from the
27534 In this the formula is inserted.
27535 \begin_inset Newline newline
27538 The content of the further lines is inserted to the second or another formula
27540 The greater the column number where it was inserted, the larger the indentation.
27541 \begin_inset VSpace medskip
27545 \begin_inset Newline newline
27549 \begin_inset Note Greyedout
27552 \begin_layout Plain Layout
27553 Note the following when using
27562 \begin_layout Itemize
27563 The formula doesn't use the full page width.
27565 \begin_inset space \thinspace{}
27569 \begin_inset space \space{}
27573 \begin_inset Formula $-B^{2}$
27576 is added to the first line in the above example, it would have been outside
27578 To better use the width, negative space can be inserted at the beginning
27582 \begin_layout Itemize
27583 Due to a bug in LyX the cursor cannot be set with the mouse into the first
27588 \begin_layout Plain Layout
27589 \begin_inset CommandInset href
27591 name "LyX-bug #1429"
27592 target "http://www.lyx.org/trac/ticket/1429"
27601 One can only set the cursor at the beginning of the line and move it with
27610 \begin_layout Itemize
27611 Other methods to set long formulas are offered by the environments described
27613 \begin_inset CommandInset ref
27615 reference "sub:Multline-Environment"
27620 \begin_inset CommandInset ref
27622 reference "sub:Multiline-Formula-Parts"
27629 \begin_layout Subsubsection
27631 \begin_inset CommandInset label
27633 name "sub:Multiline-Brackets"
27638 \begin_inset Index idx
27641 \begin_layout Plain Layout
27642 Brackets ! for multiline expressions
27650 \begin_layout Standard
27651 For brackets spanning multiple lines the following problem occurs:
27652 \begin_inset Formula
27654 A & = & \sin(x)\left[\prod_{R=1}^{\infty}\frac{1}{R}+\cdots\right.\\
27655 & & \left.\cdots+B-D\right]
27663 \begin_layout Standard
27664 The closing bracket is smaller than the opening bracket because brackets
27665 with variable size may not span multiple lines.
27668 \begin_layout Standard
27669 To set the bracket size for the second line correctly, the first line is
27677 \begin_inset Index idx
27680 \begin_layout Plain Layout
27688 and the second line with
27696 \begin_layout Plain Layout
27710 \begin_inset CommandInset ref
27712 reference "sub:Automatic-Bracket-Size"
27724 \begin_inset Index idx
27727 \begin_layout Plain Layout
27750 \begin_inset space \textvisiblespace{}
27760 \begin_inset space \textvisiblespace{}
27770 \begin_inset space \textvisiblespace{}
27776 \begin_inset Formula $\downarrow$
27782 \begin_inset Index idx
27785 \begin_layout Plain Layout
27793 is inserted, because the multiplication operator with its limits is the
27794 largest symbol in the first line and this should be the size for the bracket
27795 in the second line.
27798 \begin_layout Standard
27799 The result is this:
27800 \begin_inset Formula
27802 A & = & \sin(x)\left[\prod_{R=1}^{\infty}\frac{1}{R}+\cdots\right.\\
27803 & & \left.\vphantom{\prod_{R=1}^{\infty}}\cdots+B-D\right]
27811 \begin_layout Subsection
27815 \begin_layout Standard
27816 Align environments can be used for every kind of multiline formulas.
27817 They are especially useful to set several formulas side by side.
27820 \begin_layout Standard
27821 Align environments consist of columns.
27822 The odd columns are right aligned, the even ones left aligned.
27823 Every line in an Align environment can be numbered.
27826 \begin_layout Standard
27827 Align environments are created via the menu
27829 Insert\SpecialChar \menuseparator
27835 Edit\SpecialChar \menuseparator
27836 Math\SpecialChar \menuseparator
27837 Change Formula Type
27839 already existing formulas can be converted to Align environments.
27842 \begin_layout Standard
27843 To add or delete columns, the math toolbar buttons
27844 \begin_inset Graphics
27845 filename ../images/tabular-feature_append-column.png
27851 \begin_inset Graphics
27852 filename ../images/tabular-feature_delete-column.png
27857 , respectively, or the menu
27859 Edit\SpecialChar \menuseparator
27865 \begin_layout Subsubsection
27866 Standard align Environment
27867 \begin_inset CommandInset label
27869 name "sub:Standard-align-Environment"
27874 \begin_inset Index idx
27877 \begin_layout Plain Layout
27878 Formula ! multiline ! align environment
27886 \begin_layout Standard
27887 This Align environment is created by pressing
27890 arg "newline-insert newline"
27893 in a formula or by the menu
27895 Insert\SpecialChar \menuseparator
27896 Math\SpecialChar \menuseparator
27897 AMS align Environment
27902 \begin_layout Standard
27903 An example for two formulas set side by side, that are created with a four
27904 column align environment:
27905 \begin_inset Formula
27907 A & =\sin(B) & C & =D\\
27908 C & \ne A & B & \ne D
27913 As it can be seen, the formulas in this environment are placed so as if
27922 \begin_layout Plain Layout
27930 \begin_inset CommandInset ref
27932 reference "sub:Variable-Space"
27943 before the first and after every even column.
27944 When the formula style
27950 \begin_layout Plain Layout
27952 \begin_inset CommandInset ref
27954 reference "sec:Formula-Styles"
27965 is used, the formula is set without the
27971 before the first column.
27974 \begin_layout Subsubsection
27975 Alignat Environment
27976 \begin_inset Index idx
27979 \begin_layout Plain Layout
27980 Formula ! multiline ! alignat environment
27988 \begin_layout Standard
27989 The alignat environment has no predefined column separation.
27990 It can be inserted manually with the spaces that are described
27991 \begin_inset CommandInset ref
27993 reference "sub:Space"
28000 \begin_layout Standard
28001 The above example in the alignat environment where 1
28002 \begin_inset space \thinspace{}
28005 cm space was inserted at the beginning of the second formula:
28006 \begin_inset Formula
28007 \begin{alignat*}{2}
28008 A & =\sin(B) & \hspace{1cm}C & =D\\
28009 C & \ne A & B & \ne D
28014 Because the column separation can be set separately for every column, this
28015 environment is especially suitable to set three and more formulas side
28019 \begin_layout Subsubsection
28020 Flalign Environment
28021 \begin_inset CommandInset label
28023 name "sub:Flalign-Environment"
28028 \begin_inset Index idx
28031 \begin_layout Plain Layout
28032 Formula ! multiline ! flalign environment
28040 \begin_layout Standard
28041 In this environment the first two columns are always set as much as possible
28042 to the left and the last two ones to the right.
28044 \begin_inset Formula
28046 A & =1 & B & =2 & C & =3\\
28047 X & =\textrm{-}1 & Y & =\textrm{-}2 & Z & =4
28055 \begin_layout Standard
28056 By creating a flalign environment with an odd number of columns where an
28057 empty TeX-brace is inserted to the last column, several formulas in a document
28058 can be set to the left, although the formula style
28063 As example the indented formula
28064 \begin_inset CommandInset ref
28066 reference "eq:VolInt"
28071 \begin_inset Formula
28073 \hspace{30pt}\iiint\limits _{V}X\,\mathrm{d}V & =U & {}
28078 The first two columns contain the formula.
28079 To indent it as with the formula style
28084 \begin_inset space \thinspace{}
28087 pt space was inserted at the beginning of the first column.
28090 \begin_layout Subsection
28091 Eqnarray Environment
28092 \begin_inset CommandInset label
28094 name "sub:Eqnarray-Environment"
28099 \begin_inset Index idx
28102 \begin_layout Plain Layout
28103 Formula ! multiline ! eqnarray environment
28111 \begin_layout Standard
28112 When this environment has been created, three blue boxes appear.
28113 The content of the first box is right aligned, the content of the last
28115 The content of the middle box appears centered and a bit smaller, because
28116 it is designed to insert there only relation characters.
28117 \begin_inset Formula
28119 \frac{ABC}{D} & \frac{ABC}{D} & \frac{ABC}{D}\\
28129 \begin_layout Subsection
28131 \begin_inset Index idx
28134 \begin_layout Plain Layout
28135 Formula ! multiline ! gather environment
28143 \begin_layout Standard
28144 This environment consists of only one centered column.
28145 Every line can be numbered.
28146 \begin_inset Formula
28157 \begin_layout Subsection
28158 Multline Environment
28159 \begin_inset CommandInset label
28161 name "sub:Multline-Environment"
28166 \begin_inset Index idx
28169 \begin_layout Plain Layout
28170 Formula ! multiline ! multline environment
28178 \begin_layout Standard
28179 The multline environment consists, like the gather environment, of only
28181 But the first line is left aligned, the last one right aligned.
28182 All other lines are centered.
28183 Therefore this environment is suitable for long formulas.
28185 \begin_inset CommandInset ref
28187 reference "eq:lefteqn"
28191 in the multline environment:
28192 \begin_inset Formula
28194 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}\\
28195 -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}\\
28196 =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}}
28204 \begin_layout Standard
28205 In the output only the last (first) line of a multline environment appears
28206 numbered when the document numbering is right (left).
28210 \begin_layout Plain Layout
28211 numbering styles see
28212 \begin_inset CommandInset ref
28214 reference "sec:Formula-Styles"
28226 \begin_layout Standard
28234 \begin_inset Index idx
28237 \begin_layout Plain Layout
28252 \begin_inset Index idx
28255 \begin_layout Plain Layout
28263 a centered line can be right or left aligned, respectively.
28264 The commands are used as follows:
28267 \begin_layout Standard
28272 shoveright{line content}
28278 shoveleft{line content}
28281 \begin_layout Standard
28282 \begin_inset VSpace medskip
28292 \begin_inset Index idx
28295 \begin_layout Plain Layout
28303 specifies the distance of the first line from the left page margin.
28304 Predefined is the length 0
28305 \begin_inset space \thinspace{}
28311 \begin_layout Standard
28312 As example the above formula where the command
28315 \begin_layout Standard
28325 \begin_layout Standard
28326 was inserted in TeX-mode before:
28330 \begin_layout Plain Layout
28342 \begin_inset Formula
28344 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}\\
28345 \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}}\\
28346 =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}}
28355 \begin_layout Plain Layout
28366 The second line was left aligned using
28375 \begin_layout Subsection
28376 Multiline Formula Parts
28377 \begin_inset CommandInset label
28379 name "sub:Multiline-Formula-Parts"
28384 \begin_inset Index idx
28387 \begin_layout Plain Layout
28388 Formula ! multiline ! formula parts
28396 \begin_layout Standard
28397 To display only parts of a formula with multiple lines, one of the following
28398 environments is used:
28415 They can be inserted via the menu
28417 Insert\SpecialChar \menuseparator
28420 or by using the commands described in this section.
28423 \begin_layout Standard
28424 The first three have the same properties as the corresponding multiline
28425 formula environments, but it is possible to set further formula parts beside
28428 \begin_inset Formula
28430 \left.\begin{aligned}\Delta x\Delta p & \ge\frac{\hbar}{2}\\
28431 \Delta E\Delta t & \ge\frac{\hbar}{2}
28433 \right\} \textrm{Uncertainty relations}
28441 \begin_layout Standard
28442 To get this formula, a displayed formula is created where the command
28449 \begin_inset Index idx
28452 \begin_layout Plain Layout
28461 A purple box appears around the blue formula box where now columns and
28462 lines can be added.
28463 Outside the multiline environment other formula parts can be set, like
28467 \begin_layout Standard
28468 The aligned environment is also suitable for long formulas whose lines are
28469 horizontally aligned.
28470 Using aligned in a displayed formula has the advantage that the formula
28471 number is vertically centered behind the lines.
28473 \begin_inset CommandInset ref
28475 reference "eq:shortlong"
28479 in the aligned environment:
28480 \begin_inset Formula
28482 \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}|}\\
28483 & -\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}|}
28492 \begin_layout Standard
28493 To use the environments
28512 \begin_inset Index idx
28515 \begin_layout Plain Layout
28530 \begin_inset Index idx
28533 \begin_layout Plain Layout
28548 \begin_inset Index idx
28551 \begin_layout Plain Layout
28559 are inserted, respectively.
28560 The split environment has the same properties as the aligned environment
28561 but it can only have two columns.
28564 \begin_layout Subsection
28565 Text in multiline Formulas
28566 \begin_inset CommandInset label
28568 name "sub:Text-in-multiline"
28573 \begin_inset Index idx
28576 \begin_layout Plain Layout
28583 \begin_inset Index idx
28586 \begin_layout Plain Layout
28587 Formula ! multiline ! text
28595 \begin_layout Standard
28596 In the Align environments, and the multline and gather environment, text
28597 can be inserted that will appear in a separate line and doesn't affect
28598 the column alignment.
28599 To do this, the command
28606 \begin_inset Index idx
28609 \begin_layout Plain Layout
28617 is used in the following scheme:
28620 \begin_layout Standard
28628 \begin_layout Standard
28629 The text should not be longer than a line because it cannot be hyphenated.
28630 As LyX doesn't yet support
28636 directly, the text is written as mathematical text.
28643 must hereby be at the beginning of a line and appears in the output above
28645 An example where the text was inserted at the beginning of the second line:
28646 \begin_inset Formula
28648 I & =a\sqrt{2}\int_{0}^{2\pi}\sqrt{1+\cos(\phi)}\;\mathrm{d}\phi\\
28649 \intertext{\text{integrand is symmetric to \ensuremath{\phi=\pi}, therefore}} & =2a\sqrt{2}\int_{0}^{\pi}\sqrt{1+\cos(\phi)}\;\mathrm{d}\phi
28657 \begin_layout Section
28659 \begin_inset Index idx
28662 \begin_layout Plain Layout
28669 \begin_inset Index idx
28672 \begin_layout Plain Layout
28673 Formula ! numbering|see
28677 \begin_layout Plain Layout
28688 \begin_layout Plain Layout
28703 \begin_layout Subsection
28707 \begin_layout Standard
28708 Numbered formulas can be created with the menu
28710 Insert\SpecialChar \menuseparator
28711 Math\SpecialChar \menuseparator
28713 \begin_inset space ~
28721 \begin_inset space ~
28727 Existing formulas can be numbered with the menu
28729 Edit\SpecialChar \menuseparator
28730 Math\SpecialChar \menuseparator
28732 \begin_inset space ~
28740 arg "math-number-toggle"
28744 The formula number is displayed in LyX behind the formula as a number sign
28746 The number sign is replaced in the output by the formula number.
28749 \begin_layout Standard
28750 When numbering is turned on in multiline formulas, all lines will be numbered.
28751 But the numbering can be controlled with the menu
28753 Edit\SpecialChar \menuseparator
28754 Math\SpecialChar \menuseparator
28756 \begin_inset space ~
28760 \begin_inset space ~
28764 \begin_inset space ~
28772 arg "math-number-line-toggle"
28778 \begin_layout Standard
28779 Except for inline formulas, all formulas can be numbered with two different
28781 \begin_inset CommandInset ref
28783 reference "sec:Formula-Styles"
28790 \begin_layout Subsection
28792 \begin_inset Index idx
28795 \begin_layout Plain Layout
28796 Cross-references ! to formulas
28804 \begin_layout Standard
28805 All labeled formulas can be cross-referenced.
28806 A label is added by the menu
28808 Insert\SpecialChar \menuseparator
28811 or the toolbar button
28812 \begin_inset Graphics
28813 filename ../images/label-insert.png
28819 The cursor must hereby be inside a displayed formula.
28820 Alternatively you can right-click on the formula and choose
28825 A dialog pops up displaying the prefix
28830 The label is inserted there behind the prefix.
28831 The predefined prefix means
28832 \begin_inset Quotes eld
28836 \begin_inset Quotes erd
28839 and makes it easier to find labels in large documents because it marks
28840 it as formula label to divide it from e.
28841 \begin_inset space \thinspace{}
28845 \begin_inset space \space{}
28849 To change a label, the menu
28851 Insert\SpecialChar \menuseparator
28854 is used again or you right-click on a formula and then on
28861 \begin_layout Standard
28862 The name of the label is displayed in LyX within two parentheses behind
28864 A formula with a label is always numbered.
28867 \begin_layout Standard
28868 Cross-references are inserted via the menu
28870 Insert\SpecialChar \menuseparator
28873 or with the toolbar button
28874 \begin_inset Graphics
28875 filename ../images/dialog-show-new-inset_ref.png
28881 A formula cross-reference appears in the output as formula number.
28882 When in the cross-reference dialog window the format
28886 is chosen, the cross-reference appears in the output as formula number
28888 \begin_inset Newline newline
28891 By right-clicking on a cross-reference in LyX, one jumps to the formula
28892 that is referenced.
28895 \begin_layout Standard
28896 Here are as examples cross-references to formulas of the following subsections:
28897 \begin_inset Note Note
28900 \begin_layout Plain Layout
28901 Note the different cross-reference types.
28909 \begin_layout Standard
28911 \begin_inset CommandInset ref
28918 \begin_inset CommandInset ref
28926 \begin_inset CommandInset ref
28932 ) big Latin letters are used for the numbering in contrary to (
28933 \begin_inset CommandInset ref
28942 \begin_layout Standard
28943 \begin_inset VSpace medskip
28946 When the argument of
28954 \begin_layout Plain Layout
28962 \begin_inset CommandInset ref
28964 reference "sub:User-defined-Numbering"
28975 contains a box like in
28976 \begin_inset CommandInset ref
28978 reference "sub:Paragraph-Boxes"
28982 , the formula cannot be referenced.
28985 \begin_layout Subsection
28987 \begin_inset Index idx
28990 \begin_layout Plain Layout
28991 Formula numbering ! subnumbering
28999 \begin_layout Standard
29000 With the help of the commands
29004 begin{subequations}
29012 formulas can be subnumbered.
29013 Both commands are inserted in TeX-mode.
29016 \begin_layout Standard
29018 \begin_inset Formula
29029 \begin_layout Plain Layout
29033 addtocounter{equation}{-1}
29042 \begin_layout Plain Layout
29046 begin{subequations}
29052 \begin_inset VSpace -5mm
29056 \begin_inset Formula
29064 \begin_inset Formula
29074 \begin_layout Standard
29078 \begin_layout Plain Layout
29090 \begin_layout Standard
29091 To create the example, the following is done:
29094 \begin_layout Enumerate
29095 first formula is inserted
29098 \begin_layout Enumerate
29103 addtocounter{equation}{-1}
29105 begin{subequations}
29106 \begin_inset Index idx
29109 \begin_layout Plain Layout
29118 \begin_inset Newline newline
29123 is inserted after the first formula
29126 \begin_layout Enumerate
29127 second formula is inserted
29130 \begin_layout Enumerate
29131 third formula is inserted
29134 \begin_layout Enumerate
29141 is inserted after the third formula
29144 \begin_layout Standard
29145 Every formula between the commands
29157 is subnumbered as a, b,
29158 \begin_inset Newline linebreak
29161 c, \SpecialChar \ldots{}
29162 For multiline formulas every line will be subnumbered.
29163 All subnumbered formulas are treated as
29168 But as every numbered formula increases the counter
29172 by one, the command
29178 is needed to decrease it.
29179 Otherwise the formulas
29180 \begin_inset CommandInset ref
29187 \begin_inset CommandInset ref
29194 \begin_inset CommandInset ref
29200 would be numbered as
29201 \begin_inset CommandInset ref
29208 \begin_inset CommandInset ref
29215 \begin_inset CommandInset ref
29224 \begin_layout Standard
29225 By inserting the commands in TeX-mode, a space is created between the first
29228 \begin_inset space \thinspace{}
29231 mm vertical space is inserted after the command
29235 begin{subequations}
29238 When the formula style
29244 \begin_layout Plain Layout
29246 \begin_inset CommandInset ref
29248 reference "sec:Formula-Styles"
29260 \begin_inset space \thinspace{}
29263 mm space is inserted instead.
29266 \begin_layout Standard
29267 Here is an example for a multiline formula where the numbering was turned
29268 off for the second line:
29272 \begin_layout Plain Layout
29276 begin{subequations}
29282 \begin_inset Formula
29284 A & = & (B-Z)^{2}=(B-Z)(B-Z)\label{eq:d}\\
29285 & = & B^{2}-ZB-BZ+Z^{2}\nonumber \\
29286 & = & B^{2}-2BZ+Z^{2}\label{eq:f}
29295 \begin_layout Plain Layout
29307 \begin_layout Subsection
29308 User-defined Numbering
29309 \begin_inset CommandInset label
29311 name "sub:User-defined-Numbering"
29316 \begin_inset Index idx
29319 \begin_layout Plain Layout
29320 Formula numbering ! user-defined
29328 \begin_layout Standard
29329 \begin_inset Index idx
29332 \begin_layout Plain Layout
29333 Formula numbering ! self-defined delimiters
29338 With the standard numbering parentheses are set around the formula number.
29339 To replace the parentheses for example by vertical bars, the following
29340 line is added to the LaTeX-preamble:
29343 \begin_layout Standard
29355 \begin_inset Note Note
29358 \begin_layout Plain Layout
29359 This macro is already declared in the LaTeX-preamble for testing.
29360 To activate it, remove the percent sign at the beginning.
29368 \begin_layout Standard
29369 To use other characters, the vertical bars besides the
29373 are replaced by one ore more characters.
29374 To get only the formula number the vertical bars are omitted.
29377 \begin_layout Standard
29378 \begin_inset VSpace bigskip
29381 When there should be an expression of your choice instead of the consecutive
29382 formula number in parentheses behind the formula, the command
29389 \begin_inset Index idx
29392 \begin_layout Plain Layout
29401 \begin_inset Formula
29403 A+B=C\tag{something}\label{eq:tag}
29408 In this example the command
29413 \begin_inset space \textvisiblespace{}
29418 was inserted in the formula.
29421 \begin_layout Standard
29427 \begin_inset space \textvisiblespace{}
29432 is inserted instead, the star prevents the parentheses around the expression:
29433 \begin_inset Formula
29435 A+B=C\tag*{something}
29443 \begin_layout Standard
29444 \begin_inset VSpace bigskip
29447 To restart the formula numbering with new document parts or sections, the
29448 following command is used:
29451 \begin_layout Standard
29456 @addtoreset{equation}{part}
29459 \begin_inset Index idx
29462 \begin_layout Plain Layout
29467 \begin_layout Plain Layout
29478 \begin_layout Plain Layout
29491 \begin_layout Plain Layout
29502 \begin_layout Plain Layout
29515 \begin_inset Newline newline
29519 \begin_inset Newline newline
29526 @addtoreset{equation}{section}
29529 \begin_layout Standard
29530 To be able to use these commands in TeX-mode, the
29531 \begin_inset Quotes eld
29535 \begin_inset Quotes erd
29538 character has to be made
29539 \begin_inset Quotes eld
29543 \begin_inset Quotes erd
29546 for LaTeX using the command
29560 So the command sequence in TeX-mode is:
29563 \begin_layout Standard
29569 \begin_inset Newline newline
29574 @addtoreset{equation}{section}
29575 \begin_inset Newline newline
29583 \begin_layout Standard
29584 In the LaTeX-preamble
29596 can be omitted as they are automatically internally inserted by LyX.
29599 \begin_layout Standard
29614 \begin_layout Plain Layout
29619 is part of the LaTeX-package
29624 \begin_inset Index idx
29627 \begin_layout Plain Layout
29628 Packages ! carlisle
29633 that is part of every LaTeX standard installation.
29639 \begin_inset Index idx
29642 \begin_layout Plain Layout
29643 Packages ! remreset
29648 has to be loaded in the LaTeX-preamble with the line
29651 \begin_layout Standard
29656 usepackage{remreset}
29659 \begin_layout Standard
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
29722 can be used with the same scheme as
29731 \begin_layout Standard
29732 \begin_inset VSpace bigskip
29735 Sometimes formulas should be numbered in the following form:
29738 \begin_layout Standard
29741 (section number.formula number)
29744 \begin_layout Standard
29745 The formula number should start with every section with
29746 \begin_inset Quotes eld
29750 \begin_inset Quotes erd
29756 \begin_layout Standard
29757 For this case there is the command
29764 \begin_inset Index idx
29767 \begin_layout Plain Layout
29775 , which is used with the following scheme:
29778 \begin_layout Standard
29783 numberwithin{counter}{sectioning}
29786 \begin_layout Standard
29787 Counter denotes what kind of numbering is affected, sectioning denotes what
29788 number is before the dot.
29791 \begin_layout Standard
29792 Thus in our case the following LaTeX-preamble or TeX code line is used:
29795 \begin_layout Standard
29800 numberwithin{equation}{section}
29803 \begin_layout Standard
29804 This is the result:
29808 \begin_layout Plain Layout
29812 numberwithin{equation}{section}
29818 \begin_inset Formula
29828 \begin_layout Standard
29830 \begin_inset space \thinspace{}
29834 \begin_inset space \space{}
29837 tables so that the number of the part is the sectioning,
29838 \begin_inset Newline newline
29845 numberwithin{table}{part}
29850 \begin_layout Standard
29851 To go back to the standard numbering or to prevent this kind of numbering
29852 when it is defined by the document class, the following command is inserted
29853 as TeX code or to the LaTeX-preamble:
29856 \begin_layout Standard
29866 \begin_inset Index idx
29869 \begin_layout Plain Layout
29883 \begin_layout Plain Layout
29899 \begin_inset Newline newline
29907 \begin_inset Newline newline
29919 \begin_layout Standard
29926 uses internally the command
29932 , described above, that also needs to be reverted.
29936 \begin_layout Plain Layout
29943 \begin_layout Plain Layout
29947 @removefromreset{equation}{section}
29950 \begin_layout Plain Layout
29962 \begin_layout Subsection
29963 Numbering with Roman Numbers and Letters
29964 \begin_inset Index idx
29967 \begin_layout Plain Layout
29968 Formula numbering ! with letters
29974 \begin_inset Index idx
29977 \begin_layout Plain Layout
29978 Formula numbering ! with Roman numbers
29986 \begin_layout Standard
29987 Formulas can also be numbered with Roman numbers and Latin letters.
29988 To number for example with small Roman numbers, the command
29991 \begin_layout Standard
30003 \begin_layout Standard
30004 is inserted before the formula in TeX-mode.
30012 \begin_inset Index idx
30015 \begin_layout Plain Layout
30023 redefines the predefined command
30039 \begin_layout Plain Layout
30046 has the same scheme like the command
30052 that is described in
30053 \begin_inset CommandInset ref
30055 reference "sub:The-Command-newcommand"
30068 is the formula counter.
30075 is used as prefix for a counter, the value of the counter is output as
30077 When a formula is numbered, LaTeX sets internally the command
30083 behind the formula.
30089 \begin_inset Index idx
30092 \begin_layout Plain Layout
30102 outputs the counter as small Roman number.
30105 \begin_layout Standard
30106 All formulas behind the command
30116 are now numbered Roman.
30117 To switch to numbering with big Roman numbers, the command is inserted
30131 \begin_inset Index idx
30134 \begin_layout Plain Layout
30146 \begin_inset Quotes eld
30150 \begin_inset Quotes erd
30153 with small Latin letters there is the command
30160 \begin_inset Index idx
30163 \begin_layout Plain Layout
30171 , for big ones there is the command
30178 \begin_inset Index idx
30181 \begin_layout Plain Layout
30194 \begin_layout Standard
30195 \begin_inset Note Greyedout
30198 \begin_layout Plain Layout
30205 \begin_inset space ~
30208 formulas can be numbered with Latin letters in one document.
30216 \begin_layout Standard
30220 \begin_layout Plain Layout
30236 \begin_layout Standard
30237 \begin_inset Formula
30239 A=\textrm{small roman}
30248 \begin_layout Plain Layout
30262 \begin_inset Formula
30264 B=\textrm{big Roman}\label{eq:Rom}
30273 \begin_layout Plain Layout
30287 \begin_inset Formula
30289 C=\textrm{small Latin}
30298 \begin_layout Plain Layout
30312 \begin_inset Formula
30314 D=\textrm{big Latin}\label{eq:Lat}
30322 \begin_layout Standard
30323 To switch back to the default numbering, insert the command:
30326 \begin_layout Standard
30336 \begin_inset Index idx
30339 \begin_layout Plain Layout
30350 \begin_layout Standard
30354 \begin_layout Plain Layout
30368 \begin_inset Formula
30378 \begin_layout Standard
30379 \begin_inset VSpace medskip
30382 As you see, formulas are numbered serially independent from the numbering
30384 When then numbering should start with
30385 \begin_inset Quotes eld
30389 \begin_inset Quotes erd
30392 when the style is changed, new equation counters have to be defined.
30393 A description about this can be found in the file
30394 \begin_inset CommandInset href
30396 name "Formula-numbering.lyx"
30397 target "run:Formula-numbering.lyx"
30404 \begin_layout Standard
30405 \begin_inset Newpage newpage
30411 \begin_layout Section
30412 Chemical Symbols and Equations
30413 \begin_inset CommandInset label
30415 name "sub:Chemical-Symbols-and"
30420 \begin_inset Index idx
30423 \begin_layout Plain Layout
30424 Chemical characters ! Symbols
30430 \begin_inset Index idx
30433 \begin_layout Plain Layout
30440 \begin_inset Index idx
30443 \begin_layout Plain Layout
30452 \begin_layout Standard
30453 An example text from chemistry:
30456 \begin_layout Quote
30458 \begin_inset Formula $\mathrm{SO_{4}^{2-}}$
30461 -ion reacts with two
30462 \begin_inset Formula $\mathrm{Na^{+}}$
30465 -ions to sodium sulfate
30466 \begin_inset Formula $\left(\mathrm{Na_{2}SO_{4}}\right)$
30470 The chemical equation for this is:
30471 \begin_inset Formula
30473 \mathrm{2\, Na^{+}+SO_{4}^{2-}\longrightarrow Na_{2}SO_{4}}\label{eq:chem-reaction}
30481 \begin_layout Standard
30482 This chemical equation can directly be created as formula.
30483 To avoid that the symbols appear italic, everything is highlighted and
30484 changed by the shortcut
30490 to the upright font style.
30494 \begin_layout Plain Layout
30500 \begin_inset CommandInset ref
30502 reference "sub:Font-Styles"
30514 \begin_layout Standard
30515 A more convenient way to typeset chemical formulas is to use the command
30523 \begin_inset Index idx
30526 \begin_layout Plain Layout
30534 that is available when the LaTeX-package
30539 \begin_inset Index idx
30542 \begin_layout Plain Layout
30555 to a formula a new blue box appears where chemical formulas can be inserted
30556 in an intuitive way.
30559 \begin_layout Standard
30561 \begin_inset Tabular
30562 <lyxtabular version="3" rows="9" columns="2">
30563 <features rotate="0" tabularvalignment="middle">
30564 <column alignment="center" valignment="top">
30565 <column alignment="center" valignment="top">
30567 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
30570 \begin_layout Plain Layout
30576 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
30579 \begin_layout Plain Layout
30581 \begin_inset Note Note
30584 \begin_layout Plain Layout
30591 is only used as spacer.
30603 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
30606 \begin_layout Plain Layout
30610 \begin_inset space \textvisiblespace{}
30618 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
30621 \begin_layout Plain Layout
30622 \begin_inset Formula $\raisebox{4.5mm}{}\ce{H2CO3}\raisebox{-2mm}{}$
30632 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
30635 \begin_layout Plain Layout
30639 \begin_inset space \textvisiblespace{}
30647 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
30650 \begin_layout Plain Layout
30651 \begin_inset Formula $\raisebox{5mm}{}\ce{SO4^{2-}}\raisebox{-2mm}{}$
30661 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
30664 \begin_layout Plain Layout
30668 \begin_inset space \textvisiblespace{}
30676 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
30679 \begin_layout Plain Layout
30680 \begin_inset Formula $\raisebox{4.5mm}{}\ce{(NH4)2S}\raisebox{-2mm}{}$
30690 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
30693 \begin_layout Plain Layout
30697 \begin_inset space \textvisiblespace{}
30705 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
30708 \begin_layout Plain Layout
30709 \begin_inset Formula $\raisebox{4.5mm}{}\ce{KCr(SO4)2.12H2O}\raisebox{-2mm}{}$
30719 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
30722 \begin_layout Plain Layout
30726 \begin_inset space \textvisiblespace{}
30732 \begin_inset space \textvisiblespace{}
30738 \begin_inset space \textvisiblespace{}
30746 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
30749 \begin_layout Plain Layout
30750 \begin_inset Formula $\raisebox{4.5mm}{}\ce{A-B\dbond C\tbond D}\raisebox{-2mm}{}$
30760 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
30763 \begin_layout Plain Layout
30767 \begin_inset space \textvisiblespace{}
30771 \begin_inset Formula $\downarrow$
30775 \begin_inset Formula $\to$
30783 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
30786 \begin_layout Plain Layout
30787 \begin_inset Formula $\raisebox{5mm}{}\ce{_{90}^{227}Th+}\raisebox{-2mm}{}$
30797 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
30800 \begin_layout Plain Layout
30804 \begin_inset space \textvisiblespace{}
30808 \begin_inset space \textvisiblespace{}
30812 \begin_inset space \textvisiblespace{}
30816 \begin_inset space \textvisiblespace{}
30820 \begin_inset space \textvisiblespace{}
30828 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
30831 \begin_layout Plain Layout
30832 \begin_inset Formula $\raisebox{4.5mm}{}\ce{CO2 + C <=> 2CO}\raisebox{-2mm}{}$
30842 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
30845 \begin_layout Plain Layout
30849 \begin_inset space \textvisiblespace{}
30853 \begin_inset space \textvisiblespace{}
30857 \begin_inset space \textvisiblespace{}
30861 \begin_inset space \textvisiblespace{}
30869 \begin_inset space \textvisiblespace{}
30877 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
30880 \begin_layout Plain Layout
30881 \begin_inset Formula $\raisebox{5mm}{}\ce{CO2 + C ->[\alpha][\beta] 2CO}\raisebox{-4mm}{}$
30897 \begin_layout Standard
30898 \begin_inset Note Greyedout
30901 \begin_layout Plain Layout
30907 Inserting a formula to a
30913 box will lead to LaTeX errors due to a LyX bug.
30919 \begin_layout Plain Layout
30920 \begin_inset CommandInset href
30922 name "LyX-bug #8566"
30923 target "http://www.lyx.org/trac/ticket/8566"
30934 In this case TeX code has to be used like for
30948 \begin_layout Plain Layout
30969 \begin_layout Standard
30970 \begin_inset Note Greyedout
30973 \begin_layout Plain Layout
30979 It is not possible in LyX to use the character ^ to get an up-arrow as
30985 One instead uses a negative thin space followed by the command
30992 \begin_inset Formula $\ce{Fe + 2H+ -> Fe^{2+} + H2\negthinspace\uparrow}$
31003 \begin_layout Standard
31010 the command for equation
31011 \begin_inset space ~
31015 \begin_inset CommandInset ref
31017 reference "eq:chem-reaction"
31022 \begin_inset Newline newline
31030 \begin_inset space \textvisiblespace{}
31034 \begin_inset space \textvisiblespace{}
31038 \begin_inset space \textvisiblespace{}
31042 \begin_inset space \textvisiblespace{}
31046 \begin_inset space \textvisiblespace{}
31050 \begin_inset space \textvisiblespace{}
31056 \begin_layout Standard
31057 To create multiline chemical equations first a multiline formula is created
31059 \begin_inset CommandInset ref
31061 reference "sec:Multiline-Formulas"
31066 Afterwards the command
31072 is used in every small blue box of the formula.
31074 \begin_inset CommandInset ref
31076 reference "eq:TEOS-reaction-1"
31081 \begin_inset CommandInset ref
31083 reference "eq:TEOS-reaction-2"
31087 are an example of a multi-stage chemical reaction where every equation
31088 has its own number.
31089 \begin_inset Formula
31091 \ce{TEOS + 4O} & \ce{->} & \ce{Si(OH)4 + 4C2H4O}\label{eq:TEOS-reaction-1}\\
31092 \ce{Si(OH)4} & \ce{->} & \ce{SiO2 + 2H2O}\label{eq:TEOS-reaction-2}
31100 \begin_layout Standard
31111 package provides the command
31118 \begin_inset Index idx
31121 \begin_layout Plain Layout
31129 that has to be used for special cases.
31130 For more information about
31136 and more examples have a look at the documentation of
31141 \begin_inset CommandInset citation
31150 \begin_layout Section
31154 \begin_layout Standard
31155 LyX supports two types of commutative diagrams:
31163 that are explained in the following.
31166 \begin_layout Subsection
31168 \begin_inset Index idx
31171 \begin_layout Plain Layout
31180 \begin_layout Standard
31181 Diagrams of this type visualize relations by vertical and horizontal lines
31183 \begin_inset Formula
31185 \begin{CD}A@>>>B@>>>C\\
31196 \begin_layout Standard
31197 To get them, the command
31202 \begin_inset Index idx
31205 \begin_layout Plain Layout
31215 is inserted to a formula.
31216 A blue box appears with two dashed lines where further commands can be
31221 arg "newline-insert newline"
31224 a new line is created.
31225 Horizontal relations are inserted in odd, vertical in even formula lines.
31228 \begin_layout Standard
31229 To create the relations there are the following commands:
31232 \begin_layout Itemize
31237 creates a left arrow,
31248 \begin_layout Itemize
31253 creates an up arrow,
31261 a vertical equal sign
31264 \begin_layout Itemize
31270 is a placeholder for non-existent relations
31273 \begin_layout Standard
31274 All arrows can be labeled as follows:
31277 \begin_layout Itemize
31278 If text inserted between the first and second < or >, resp., it is placed
31280 When it is inserted between the second and third one, it appears under
31284 \begin_layout Itemize
31285 When text for vertical arrows is inserted between the first and second A
31286 or V, resp., it is placed left beside the arrow.
31287 When it is inserted between the second and third one, it appears right
31289 If the text contains an A or V, these letters must be set into a TeX-brace.
31292 \begin_layout Standard
31293 As example a diagram with all possible relations:
31296 \begin_layout Standard
31297 \begin_inset Formula
31299 \begin{CD}A@>j>>B@>>k>C@=F\\
31310 \begin_layout Standard
31311 The command for this is:
31312 \begin_inset Newline newline
31320 \begin_inset space \textvisiblespace{}
31323 A@>j>>B@>>k>C@=F Ctrl+Return
31324 \begin_inset Newline newline
31328 \begin_inset Phantom HPhantom
31331 \begin_layout Plain Layout
31337 \begin_inset space \textvisiblespace{}
31350 \begin_inset Formula $\to$
31356 \begin_inset Newline newline
31360 \begin_inset Phantom HPhantom
31363 \begin_layout Plain Layout
31369 \begin_inset space \textvisiblespace{}
31380 \begin_layout Subsection
31382 \begin_inset Index idx
31385 \begin_layout Plain Layout
31386 Diagrams ! xymatrix
31394 \begin_layout Standard
31395 To be able to use xymatrices, the LaTeX-package
31400 A xymatrix is created by inserting the command
31407 Then you are able to add new matrix columns and rows like for normal matrices,
31409 \begin_inset CommandInset ref
31411 reference "sec:Matrices"
31418 \begin_layout Standard
31419 In contrary to amscd diagrams, xymatrices supports diagonal and curved arrows,
31421 All possibilities to create commutative diagrams and decorations are explained
31426 that you find in the menu
31428 Help\SpecialChar \menuseparator
31430 \begin_inset space ~
31438 \begin_layout Subsection
31444 \begin_inset Index idx
31447 \begin_layout Plain Layout
31456 \begin_layout Standard
31461 -diagrams, the LaTeX-package
31470 -diagram is created by inserting the command
31477 Then you are able to add new matrix columns and rows like for normal matrices,
31479 \begin_inset CommandInset ref
31481 reference "sec:Matrices"
31488 \begin_layout Standard
31489 Examples how to create
31493 diagrams in LyX is given in the
31495 Feynman-diagram manual
31497 that you find in the menu
31499 Help\SpecialChar \menuseparator
31501 \begin_inset space ~
31509 \begin_layout Standard
31510 \begin_inset Newpage newpage
31516 \begin_layout Section
31517 User-defined Commands
31518 \begin_inset Index idx
31521 \begin_layout Plain Layout
31522 User-defined commands
31530 \begin_layout Standard
31531 \begin_inset Note Greyedout
31534 \begin_layout Plain Layout
31539 The names of user-defined commands and macros may only consist of Latin
31548 \begin_layout Subsection
31552 \begin_inset CommandInset label
31554 name "sub:The-Command-newcommand"
31559 \begin_inset Index idx
31562 \begin_layout Plain Layout
31563 User-defined commands !
31571 \begin_inset Index idx
31574 \begin_layout Plain Layout
31585 \begin_layout Standard
31586 Many LaTeX-commands are too long to be used frequently.
31587 But it is possible to define with the command
31593 new shorter commands.
31596 \begin_layout Standard
31597 The command scheme of
31606 \begin_layout Standard
31611 newcommand{new command name}[number of arguments][optional
31616 \begin_inset Newline newline
31620 \begin_inset Phantom HPhantom
31623 \begin_layout Plain Layout
31633 {command definition}
31636 \begin_layout Standard
31637 \begin_inset Note Greyedout
31640 \begin_layout Plain Layout
31645 Assure that the name of the new command is not already used in your document
31646 or by LaTeX-packages that you use.
31647 When you for example define the command
31659 , you get an error message because
31665 is already defined as command for
31666 \begin_inset Quotes eld
31670 \begin_inset Formula $\le$
31674 \begin_inset Quotes erd
31685 \begin_layout Standard
31686 The number of arguments is an integer in the range 0
31687 \begin_inset space \thinspace{}
31691 \begin_inset space \thinspace{}
31694 9 and specifies how many arguments the new command should have.
31695 With the optional value a value for an optional argument can be predefined.
31696 When this is done, the
31704 rgument of the new command is automatically an optional one.
31707 \begin_layout Standard
31708 Here are some examples:
31711 \begin_layout Itemize
31712 To define the command
31724 , the LaTeX-preamble line is:
31725 \begin_inset VSpace medskip
31729 \begin_inset Newline newline
31743 \begin_layout Itemize
31744 To define the command
31756 , the argument (that should be underlined) must be taken into account.
31757 For this the preamble line is:
31758 \begin_inset VSpace medskip
31762 \begin_inset Newline newline
31776 \begin_inset VSpace medskip
31780 \begin_inset Newline newline
31787 acts as argument placeholder, the
31791 behind it denotes that it is the placeholder for the first argument.
31794 \begin_layout Itemize
31802 \begin_inset space \thinspace{}
31806 \begin_inset space \space{}
31816 \begin_inset VSpace medskip
31820 \begin_inset Newline newline
31831 framebox#1#2{$#3$}}
31834 \begin_inset VSpace medskip
31838 \begin_inset Newline newline
31841 The two Dollar signs creates the extra formula needed for
31848 \begin_inset CommandInset ref
31850 reference "sub:Boxes-with-Frame"
31857 \begin_layout Itemize
31858 To create a new command for
31864 where the color for the box need not be specified, the argument for the
31865 color is defined optional:
31866 \begin_inset VSpace medskip
31870 \begin_inset Newline newline
31881 fcolorbox{#2}{#1}{$#3$}}
31884 \begin_inset VSpace medskip
31888 \begin_inset Newline newline
31891 When the color is not specified when using
31897 , the predefined color
31904 \begin_layout Standard
31905 A test of the new defined commands:
31908 \begin_layout Standard
31910 \begin_inset Tabular
31911 <lyxtabular version="3" rows="6" columns="2">
31912 <features rotate="0" tabularvalignment="middle">
31913 <column alignment="center" valignment="top">
31914 <column alignment="center" valignment="top">
31916 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
31919 \begin_layout Plain Layout
31925 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
31928 \begin_layout Plain Layout
31930 \begin_inset Note Note
31933 \begin_layout Plain Layout
31940 is only used as spacer.
31952 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
31955 \begin_layout Plain Layout
31959 \begin_inset space \textvisiblespace{}
31967 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
31970 \begin_layout Plain Layout
31971 \begin_inset Formula $A\gr B$
31981 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
31984 \begin_layout Plain Layout
31992 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
31995 \begin_layout Plain Layout
31996 \begin_inset Formula $\raisebox{4.5mm}{}\us{ABcd}\raisebox{-2mm}{}$
32006 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
32009 \begin_layout Plain Layout
32013 \begin_inset Formula $\to$
32019 \begin_inset Formula $\to$
32027 \begin_inset space \textvisiblespace{}
32035 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
32038 \begin_layout Plain Layout
32039 \begin_inset Formula $\raisebox{6mm}{}\fb{[2cm]}{}{\int A=B}\raisebox{-4mm}{}$
32049 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
32052 \begin_layout Plain Layout
32056 \begin_inset Formula $\to$
32064 \begin_inset space \textvisiblespace{}
32072 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
32075 \begin_layout Plain Layout
32076 \begin_inset Formula $\raisebox{6mm}{}\cb{red}{\int A=B}\raisebox{-4mm}{}$
32086 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
32089 \begin_layout Plain Layout
32095 \begin_inset Formula $\to$
32103 \begin_inset space \textvisiblespace{}
32111 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
32114 \begin_layout Plain Layout
32115 \begin_inset Formula $\raisebox{6mm}{}\cb[green]{red}{\int A=B}\raisebox{-4mm}{}$
32131 \begin_layout Subsection
32133 \begin_inset Index idx
32136 \begin_layout Plain Layout
32137 User-defined commands! Math macros
32143 \begin_inset Index idx
32146 \begin_layout Plain Layout
32155 \begin_layout Standard
32156 User-defined commands are especially convenient for complex expressions.
32157 When you are for example dealing with a document that has quadratic equations,
32158 the same solution type occurs several times.
32159 The general form of a quadratic equation is
32160 \begin_inset Formula
32162 0=\lambda^{2}+p\lambda+q
32167 The general form of the solution is
32168 \begin_inset Formula
32170 \lambda_{1,2}=-\frac{p}{2}\pm\sqrt{\frac{p²}{4}-q}
32178 \begin_layout Standard
32179 To define a command for the solution formula where only the three parameters
32181 \begin_inset Formula $\lambda$
32185 \begin_inset Formula $p$
32189 \begin_inset Formula $q$
32192 need to be specified and the index of
32193 \begin_inset Formula $\lambda$
32196 can be given optionally, the LaTeX-preamble line is
32197 \begin_inset Newline newline
32213 \begin_inset Newline newline
32217 \begin_inset Phantom HPhantom
32220 \begin_layout Plain Layout
32234 frac{#3^{2}}{4}-#4}}
32237 \begin_layout Standard
32238 To create with this the solution formula, the command
32239 \begin_inset Newline newline
32249 \begin_inset Formula $\to$
32255 \begin_inset Formula $\to$
32262 is inserted to a formula
32267 \begin_layout Standard
32268 The definition of the new command is unintuitive because one has to know
32269 the schemes of all used LaTeX commands, e.
32270 \begin_inset space \thinspace{}
32274 \begin_inset space \space{}
32277 that a fraction is inserted in LaTeX as
32281 frac{numerator}{denominator}
32284 Furthermore one can easily forget a brace in the definition and cannot
32285 see in LyX what the new command is doing.
32286 To avoid these problems LyX offers the possibility to use math macros instead
32296 \begin_layout Standard
32297 A math macro is created by using the menu
32299 Insert\SpecialChar \menuseparator
32300 Math\SpecialChar \menuseparator
32303 or the toolbar button
32304 \begin_inset Graphics
32305 filename ../images/math-macro_newmacroname_newcommand.png
32311 The math macro toolbar appears together with the following box where the
32313 \begin_inset Newline newline
32317 \begin_inset space \hspace*{\fill}
32321 \begin_inset Graphics
32322 filename clipart/macrobox.png
32327 \begin_inset space \hspace*{\fill}
32331 \begin_inset Newline newline
32335 \begin_inset FormulaMacro
32336 \newcommand{\qG}[4][1,\,2]{#2_{#1}=-\frac{#3}{2}\pm\sqrt{\frac{#3^{2}}{4}-#4}}
32341 newmacroname is the default name of the macro that should be changed to
32342 something sensible.
32343 The wanted formula is inserted in the first blue box.
32344 An argument placeholder is inserted with the command
32351 \begin_inset space \thinspace{}
32355 \begin_inset space \space{}
32364 or by using the macro toolbar button
32365 \begin_inset Graphics
32366 filename ../images/math-macro-add-param.png
32372 Argument placeholders are displayed red.
32374 \begin_inset space ~
32377 arguments are possible.
32378 Optional arguments are created with the toolbar button
32379 \begin_inset Graphics
32380 filename ../images/math-macro-add-optional-param.png
32386 The first non-optional argument can be transformed to an optional one with
32388 \begin_inset Graphics
32389 filename ../images/math-macro-make-optional.png
32395 In the second blue box the appearance of the macro in LyX can be defined.
32396 Normally you want to see it as it is defined, so the box is kept empty.
32397 But when you have created a macro that needs lot of space on the screen,
32398 you can insert in the box for example
32399 \begin_inset Newline newline
32429 \begin_inset Newline newline
32434 For the macro only the arguments with the macro name in front of them will
32435 then be displayed in LyX, leading to a better overview.
32436 The formula appears in the output as defined in the first box.
32437 \begin_inset Newline newline
32440 The appearance of macros in formulas can furthermore be changed for single
32441 macros by setting the cursor in the macro and using the menu
32443 View\SpecialChar \menuseparator
32445 \begin_inset space ~
32449 \begin_inset space ~
32457 \begin_layout Standard
32458 To use a macro, the macro name is inserted as command to a formula, in our
32466 Our macro looks in LyX like this:
32467 \begin_inset Newline newline
32471 \begin_inset space \hspace*{\fill}
32475 \begin_inset Graphics
32476 filename clipart/macrouse.png
32481 \begin_inset space \hspace*{\fill}
32485 \begin_inset Newline newline
32488 Here is our macro example with the arguments
32489 \begin_inset Formula $x$
32493 \begin_inset Formula $\ln(x)$
32497 \begin_inset Formula $B$
32503 \begin_layout Standard
32504 \begin_inset Formula
32514 \begin_layout Standard
32515 LyX offers in the menu
32517 Tools\SpecialChar \menuseparator
32518 Preferences\SpecialChar \menuseparator
32519 Editing\SpecialChar \menuseparator
32522 different styles to edit macros.
32523 To find the style that suits you the most, choose a style and set the cursor
32524 in a macro formula to see the difference.
32527 \begin_layout Standard
32528 A math macro is transformed internally to a
32534 command when exporting the document.
32541 command is not placed in the LaTeX-preamble, therefore macros can only
32542 be used in formulas that are in the document below the macro definition
32546 \begin_layout Standard
32547 Math macros can also be directly created from a
32554 When writing for example the command
32557 \begin_inset Newline newline
32566 xleftarrow[#2]{#1}}
32567 \begin_inset Newline newline
32572 in LyX as normal text, highlighting it completely and using then the shortcut
32577 , the command will be transformed to a math macro.
32578 Using this method you need to be careful that the
32584 command is typed correctly, otherwise you get a faulty macro leading to
32588 \begin_layout Standard
32589 Math macros currently have the problem that further formulas in macro definition
32590 s are handled wrongly.
32591 Therefore the example
32598 \begin_inset CommandInset ref
32600 reference "sub:The-Command-newcommand"
32604 cannot be created as macro.
32607 \begin_layout Standard
32608 When the cursor is in a macro definition box, you will see the macro toolbar
32612 \begin_layout Standard
32613 \begin_inset VSpace defskip
32619 \begin_layout Standard
32620 \begin_inset Graphics
32621 filename clipart/MacroToolbar.png
32626 \begin_inset Index idx
32629 \begin_layout Plain Layout
32638 \begin_layout Standard
32639 \begin_inset VSpace defskip
32645 \begin_layout Standard
32646 The macro toolbar contains from left to right the following buttons:
32649 \begin_layout Standard
32650 \begin_inset VSpace defskip
32656 \begin_layout Standard
32657 \begin_inset Tabular
32658 <lyxtabular version="3" rows="9" columns="2">
32659 <features rotate="0" islongtable="true" longtabularalignment="center">
32660 <column alignment="left" valignment="top">
32661 <column alignment="left" valignment="top" width="85col%">
32662 <row interlinespace="2.5mm">
32663 <cell alignment="center" valignment="top" usebox="none">
32666 \begin_layout Plain Layout
32667 \begin_inset Graphics
32668 filename ../images/math-macro-remove-param.png
32669 rotateOrigin center
32678 <cell alignment="center" valignment="top" usebox="none">
32681 \begin_layout Plain Layout
32684 Edit\SpecialChar \menuseparator
32685 Math\SpecialChar \menuseparator
32687 \begin_inset space ~
32690 Definition\SpecialChar \menuseparator
32691 Remove Last Argument
32697 <row interlinespace="2.5mm">
32698 <cell alignment="center" valignment="top" usebox="none">
32701 \begin_layout Plain Layout
32702 \begin_inset Graphics
32703 filename ../images/math-macro-add-param.png
32704 rotateOrigin center
32713 <cell alignment="center" valignment="top" usebox="none">
32716 \begin_layout Plain Layout
32719 Edit\SpecialChar \menuseparator
32720 Math\SpecialChar \menuseparator
32722 \begin_inset space ~
32725 Definition\SpecialChar \menuseparator
32732 <row interlinespace="2.5mm">
32733 <cell alignment="center" valignment="top" usebox="none">
32736 \begin_layout Plain Layout
32737 \begin_inset Graphics
32738 filename ../images/math-macro-make-optional.png
32739 rotateOrigin center
32748 <cell alignment="center" valignment="top" usebox="none">
32751 \begin_layout Plain Layout
32754 Edit\SpecialChar \menuseparator
32755 Math\SpecialChar \menuseparator
32757 \begin_inset space ~
32760 Definition\SpecialChar \menuseparator
32761 Make First Non-Optional into
32762 \begin_inset Newline newline
32766 \begin_inset Phantom HPhantom
32769 \begin_layout Plain Layout
32772 Edit\SpecialChar \menuseparator
32773 Math\SpecialChar \menuseparator
32775 \begin_inset space ~
32778 Definition\SpecialChar \menuseparator
32790 <row interlinespace="2.5mm">
32791 <cell alignment="center" valignment="top" usebox="none">
32794 \begin_layout Plain Layout
32795 \begin_inset Graphics
32796 filename ../images/math-macro-make-nonoptional.png
32797 rotateOrigin center
32806 <cell alignment="center" valignment="top" usebox="none">
32809 \begin_layout Plain Layout
32812 Edit\SpecialChar \menuseparator
32813 Math\SpecialChar \menuseparator
32815 \begin_inset space ~
32818 Definition\SpecialChar \menuseparator
32819 Make Last Optional into
32820 \begin_inset Newline newline
32824 \begin_inset Phantom HPhantom
32827 \begin_layout Plain Layout
32830 Edit\SpecialChar \menuseparator
32831 Math\SpecialChar \menuseparator
32833 \begin_inset space ~
32836 Definition\SpecialChar \menuseparator
32842 Non-Optional Argument
32848 <row interlinespace="2.5mm">
32849 <cell alignment="center" valignment="top" usebox="none">
32852 \begin_layout Plain Layout
32853 \begin_inset Graphics
32854 filename ../images/math-macro-remove-optional-param.png
32855 rotateOrigin center
32864 <cell alignment="center" valignment="top" usebox="none">
32867 \begin_layout Plain Layout
32870 Edit\SpecialChar \menuseparator
32871 Math\SpecialChar \menuseparator
32873 \begin_inset space ~
32876 Definition\SpecialChar \menuseparator
32877 Remove Optional Argument
32883 <row interlinespace="2.5mm">
32884 <cell alignment="center" valignment="top" usebox="none">
32887 \begin_layout Plain Layout
32888 \begin_inset Graphics
32889 filename ../images/math-macro-add-optional-param.png
32890 rotateOrigin center
32899 <cell alignment="center" valignment="top" usebox="none">
32902 \begin_layout Plain Layout
32905 Edit\SpecialChar \menuseparator
32906 Math\SpecialChar \menuseparator
32908 \begin_inset space ~
32911 Definition\SpecialChar \menuseparator
32912 Insert Optional Argument
32918 <row interlinespace="2.5mm">
32919 <cell alignment="center" valignment="top" usebox="none">
32922 \begin_layout Plain Layout
32923 \begin_inset Graphics
32924 filename ../images/math-macro-remove-greedy-param.png
32925 rotateOrigin center
32934 <cell alignment="center" valignment="top" usebox="none">
32937 \begin_layout Plain Layout
32940 Edit\SpecialChar \menuseparator
32941 Math\SpecialChar \menuseparator
32943 \begin_inset space ~
32946 Definition\SpecialChar \menuseparator
32947 Remove Last Argument
32948 \begin_inset Newline newline
32952 \begin_inset Phantom HPhantom
32955 \begin_layout Plain Layout
32958 Edit\SpecialChar \menuseparator
32959 Math\SpecialChar \menuseparator
32961 \begin_inset space ~
32964 Definition\SpecialChar \menuseparator
32970 Spitting Out To The Right
32976 <row interlinespace="2.5mm">
32977 <cell alignment="center" valignment="top" usebox="none">
32980 \begin_layout Plain Layout
32981 \begin_inset Graphics
32982 filename ../images/math-macro-append-greedy-param.png
32983 rotateOrigin center
32992 <cell alignment="center" valignment="top" usebox="none">
32995 \begin_layout Plain Layout
32998 Edit\SpecialChar \menuseparator
32999 Math\SpecialChar \menuseparator
33001 \begin_inset space ~
33004 Definition\SpecialChar \menuseparator
33006 \begin_inset Newline newline
33010 \begin_inset Phantom HPhantom
33013 \begin_layout Plain Layout
33016 Edit\SpecialChar \menuseparator
33017 Math\SpecialChar \menuseparator
33019 \begin_inset space ~
33022 Definition\SpecialChar \menuseparator
33028 Eating From The Right
33034 <row interlinespace="2.5mm">
33035 <cell alignment="center" valignment="top" usebox="none">
33038 \begin_layout Plain Layout
33039 \begin_inset Graphics
33040 filename ../images/math-macro-add-greedy-optional-param.png
33041 rotateOrigin center
33050 <cell alignment="center" valignment="top" usebox="none">
33053 \begin_layout Plain Layout
33056 Edit\SpecialChar \menuseparator
33057 Math\SpecialChar \menuseparator
33059 \begin_inset space ~
33062 Definition\SpecialChar \menuseparator
33063 Append Optional Argument
33064 \begin_inset Newline newline
33068 \begin_inset Phantom HPhantom
33071 \begin_layout Plain Layout
33074 Edit\SpecialChar \menuseparator
33075 Math\SpecialChar \menuseparator
33077 \begin_inset space ~
33080 Definition\SpecialChar \menuseparator
33086 Eating From The Right
33099 \begin_layout Section
33100 Computer Algebra Systems
33103 \begin_layout Standard
33104 LyX offers the exchange between mathematical expressions written in LyX's
33105 math editor and external applications or user defined scripts.
33106 Currently supported applications are
33123 Note that the set of supported mathematical constructs is limited only
33124 to very simple cases.
33127 \begin_layout Subsection
33131 \begin_layout Standard
33132 Write some expression in a formula, go to the
33134 Edit\SpecialChar \menuseparator
33135 Math\SpecialChar \menuseparator
33136 Use Computer Algebra System
33138 menu and choose the application you have installed on the computer.
33139 After that the result of computation should show on the right side of the
33140 expression together with the
33141 \begin_inset Quotes eld
33145 \begin_inset Quotes erd
33151 \begin_layout Standard
33152 Here are few simple examples (with results from
33156 ) to show what kind of computations can be performed:
33159 \begin_layout Itemize
33160 \begin_inset Formula $\frac{37}{3}*2-\sum_{i=1}^{3}i^{i}=-\frac{22}{3}$
33166 \begin_layout Itemize
33167 \begin_inset Formula $\frac{37.0}{3}=12.33333333333333$
33173 \begin_layout Itemize
33174 \begin_inset Formula $\int_{1}^{2}\sin(x)dx=\cos1-\cos2$
33180 \begin_layout Itemize
33181 \begin_inset Formula $\det\left[\begin{array}{ccc}
33185 \end{array}\right]=-56$
33191 \begin_layout Itemize
33192 \begin_inset Formula $\lim_{x\rightarrow0}\left(\frac{\sin(x)}{x}\right)=1$
33198 \begin_layout Subsection
33202 \begin_layout Standard
33203 Currently there is no keyboard shortcut for calling the algebra applications.
33204 One can easily bind a shortcut to the
33208 LyX function (see the
33216 \begin_inset space \thinspace{}
33220 \begin_inset space \space{}
33227 key inside the math editor.
33232 one would use this shortcut definition command:
33235 \begin_layout Standard
33238 command-alternatives break-paragraph;math-extern maxima
33241 \begin_layout Section
33243 \begin_inset Index idx
33246 \begin_layout Plain Layout
33255 \begin_layout Subsection
33257 \begin_inset Index idx
33260 \begin_layout Plain Layout
33269 \begin_layout Standard
33270 Negative numbers often look ugly in formulas because the minus sign before
33271 the number is set with the same length as the minus operator sign.
33272 When writing the negative number in normal text, the minus sign appears
33276 \begin_layout Standard
33277 Thus, the problem disappears when converting the minus sign to mathematical
33281 \begin_layout Standard
33282 An example to visualize the problem:
33285 \begin_layout Standard
33287 \begin_inset Tabular
33288 <lyxtabular version="3" rows="3" columns="2">
33289 <features rotate="0" tabularvalignment="middle">
33290 <column alignment="right" valignment="top">
33291 <column alignment="left" valignment="top">
33293 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
33296 \begin_layout Plain Layout
33302 <cell alignment="center" valignment="top" topline="true" rightline="true" usebox="none">
33305 \begin_layout Plain Layout
33313 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
33316 \begin_layout Plain Layout
33322 <cell alignment="center" valignment="top" topline="true" bottomline="true" rightline="true" usebox="none">
33325 \begin_layout Plain Layout
33326 \begin_inset Formula $x=-2$
33336 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
33339 \begin_layout Plain Layout
33345 <cell alignment="center" valignment="top" topline="true" bottomline="true" rightline="true" usebox="none">
33348 \begin_layout Plain Layout
33349 \begin_inset Formula $x=\textrm{-}2$
33365 \begin_layout Subsection
33366 Comma as decimal Separator
33367 \begin_inset Index idx
33370 \begin_layout Plain Layout
33379 \begin_layout Standard
33380 In LaTeX a comma inside a formula is used, according to the English convention,
33381 as number group separator.
33382 So there will be space added behind all commas in formulas.
33385 \begin_layout Standard
33386 To avoid this, the comma is highlighted and changed to mathematical text
33396 \begin_layout Standard
33397 To use all formula commas in the document as decimal separator, the file
33406 \begin_layout Plain Layout
33411 is part of the LaTeX-package
33416 \begin_inset Index idx
33419 \begin_layout Plain Layout
33424 \begin_layout Plain Layout
33444 \begin_inset Index idx
33447 \begin_layout Plain Layout
33453 is loaded with the LaTeX-preamble line
33456 \begin_layout Standard
33464 \begin_layout Subsection
33466 \begin_inset CommandInset label
33468 name "sub:Physical-Vectors"
33473 \begin_inset Index idx
33476 \begin_layout Plain Layout
33485 \begin_layout Standard
33486 Predefined vectors are offered by the LaTeX-package
33491 \begin_inset Index idx
33494 \begin_layout Plain Layout
33500 that is loaded with the LaTeX-preamble line
33503 \begin_layout Standard
33511 \begin_layout Standard
33515 \begin_layout Plain Layout
33525 \begin_inset Note Note
33528 \begin_layout Plain Layout
33529 The following table will only be displayed when the LaTeX-package
33541 \begin_layout Standard
33542 The following commands are defined:
33545 \begin_layout Standard
33547 \begin_inset Tabular
33548 <lyxtabular version="3" rows="4" columns="2">
33549 <features rotate="0" tabularvalignment="middle">
33550 <column alignment="center" valignment="top">
33551 <column alignment="center" valignment="top">
33553 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
33556 \begin_layout Plain Layout
33562 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
33565 \begin_layout Plain Layout
33573 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
33576 \begin_layout Plain Layout
33586 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
33589 \begin_layout Plain Layout
33590 \begin_inset Formula $\Bra{\psi}$
33600 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
33603 \begin_layout Plain Layout
33613 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
33616 \begin_layout Plain Layout
33617 \begin_inset Formula $\Ket{\psi}$
33627 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
33630 \begin_layout Plain Layout
33642 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
33645 \begin_layout Plain Layout
33646 \begin_inset Formula $\Braket{\psi|\phi}$
33662 \begin_layout Standard
33669 assures that all vertical bars are set in the size of the surrounding brackets:
33670 \begin_inset Formula
33672 \Braket{\phi|J=\frac{3}{2}\,,\, M_{J}}
33681 \begin_layout Plain Layout
33691 \begin_inset Note Note
33694 \begin_layout Plain Layout
33695 The following will be displayed when the LaTeX-package
33707 \begin_layout Standard
33708 You need to install the LaTeX-package
33712 to see the rest of this subsection in the output.
33715 \begin_layout Standard
33719 \begin_layout Plain Layout
33731 \begin_layout Standard
33738 can also be achieved using the command
33744 , that is described in
33745 \begin_inset CommandInset ref
33747 reference "sub:Automatic-Bracket-Size"
33754 \begin_layout Subsection
33755 Self-defined Fractions
33756 \begin_inset CommandInset label
33758 name "sub:Self-defined-Fractions"
33763 \begin_inset Index idx
33766 \begin_layout Plain Layout
33767 Fractions ! self-defined
33775 \begin_layout Standard
33776 To define custom commands for fractions, the command
33783 \begin_inset Index idx
33786 \begin_layout Plain Layout
33793 \begin_layout Plain Layout
33807 is used in the following scheme:
33810 \begin_layout Standard
33823 bracket}{fraction bar thickness}{style}
33824 \begin_inset Newline newline
33828 \begin_inset Phantom HPhantom
33831 \begin_layout Plain Layout
33841 {numerator}{denominator}
33844 \begin_layout Standard
33845 The style is a number in the range of 0
33846 \begin_inset space \thinspace{}
33850 \begin_inset space \thinspace{}
33856 \begin_layout Standard
33858 \begin_inset Tabular
33859 <lyxtabular version="3" rows="5" columns="2">
33860 <features rotate="0" tabularvalignment="middle">
33861 <column alignment="center" valignment="top">
33862 <column alignment="center" valignment="top">
33864 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
33867 \begin_layout Plain Layout
33873 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
33876 \begin_layout Plain Layout
33884 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
33887 \begin_layout Plain Layout
33893 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
33896 \begin_layout Plain Layout
33897 display style formula
33904 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
33907 \begin_layout Plain Layout
33913 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
33916 \begin_layout Plain Layout
33924 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
33927 \begin_layout Plain Layout
33933 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
33936 \begin_layout Plain Layout
33944 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
33947 \begin_layout Plain Layout
33953 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
33956 \begin_layout Plain Layout
33970 \begin_layout Standard
33971 When no style is given, the size is adjusted to the surrounding environment
33972 like for the command
33981 \begin_layout Standard
33982 When no fraction bar thickness is given, the predefined value of 0.4
33983 \begin_inset space \thinspace{}
33989 \begin_layout Standard
33990 \begin_inset VSpace medskip
33993 For example, the commands
34006 \begin_inset CommandInset ref
34008 reference "sub:Fractions"
34012 are defined with the commands
34015 \begin_layout Standard
34024 genfrac{}{}{}{0}{#1}{#2}}
34027 \begin_layout Standard
34031 \begin_layout Standard
34040 genfrac{(}{)}{0pt}{1}{#1}{#2}}
34043 \begin_layout Standard
34044 \begin_inset VSpace medskip
34047 To define a fraction where the fraction bar thickness can be given as optional
34048 argument, the following line is inserted to the LaTeX-preamble:
34051 \begin_layout Standard
34060 genfrac{}{}{#1}{}{#2}{#3}}
34063 \begin_layout Standard
34065 \begin_inset Formula
34067 \text{Command} & & \mathrm{\backslash fracS[1mm]\backslash\{A\to\backslash\{B} & & \mathrm{\backslash fracS[5mm]\backslash\{A\to\backslash\{B}\\
34068 \text{Result} & & \fracS[1mm]{A}{B} & & \fracS[5mm]{A}{B}
34073 As one can see, the distance of the numerator and the denominator to the
34074 fraction bar is round about three times the bar thickness.
34077 \begin_layout Subsection
34079 \begin_inset Index idx
34082 \begin_layout Plain Layout
34091 \begin_layout Standard
34092 There are four ways to cancel formulas or parts of formulas:
34095 \begin_layout Standard
34099 \begin_layout Plain Layout
34109 \begin_inset Note Note
34112 \begin_layout Plain Layout
34113 The following table will only be displayed when the LaTeX-package
34125 \begin_layout Standard
34127 \begin_inset Tabular
34128 <lyxtabular version="3" rows="5" columns="2">
34129 <features rotate="0" tabularvalignment="middle">
34130 <column alignment="center" valignment="top">
34131 <column alignment="center" valignment="top">
34133 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
34136 \begin_layout Plain Layout
34142 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
34145 \begin_layout Plain Layout
34147 \begin_inset Note Note
34150 \begin_layout Plain Layout
34157 are used here as spacer.
34169 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
34172 \begin_layout Plain Layout
34176 \begin_inset space \textvisiblespace{}
34182 \begin_inset space \textvisiblespace{}
34190 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
34193 \begin_layout Plain Layout
34194 \begin_inset Formula $\raisebox{4.5mm}{}\cancel{\int A=B}\raisebox{-2.5mm}{}$
34204 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
34207 \begin_layout Plain Layout
34211 \begin_inset space \textvisiblespace{}
34217 \begin_inset space \textvisiblespace{}
34225 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
34228 \begin_layout Plain Layout
34229 \begin_inset Formula $\raisebox{4.5mm}{}\bcancel{\int A=B}\raisebox{-2.5mm}{}$
34239 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
34242 \begin_layout Plain Layout
34246 \begin_inset space \textvisiblespace{}
34252 \begin_inset space \textvisiblespace{}
34260 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
34263 \begin_layout Plain Layout
34264 \begin_inset Formula $\raisebox{4.5mm}{}\xcancel{\int A=B}\raisebox{-2.5mm}{}$
34274 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
34277 \begin_layout Plain Layout
34281 \begin_inset space \textvisiblespace{}
34287 \begin_inset space \textvisiblespace{}
34291 \begin_inset Formula $\to$
34299 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
34302 \begin_layout Plain Layout
34303 \begin_inset Formula $\raisebox{7mm}{}\cancelto{1}{\int A=B}\raisebox{-2.5mm}{}\hspace{3mm}$
34319 \begin_layout Standard
34326 is especially suitable to visualize the reduction of fractions within formulas:
34327 \begin_inset Formula
34329 \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}}}
34337 \begin_layout Standard
34338 To change the size of
34345 \begin_inset Quotes eld
34349 \begin_inset Quotes erd
34352 value one can add the LaTeX-preamble line
34355 \begin_layout Standard
34360 PassOptionsToPackage{option}{cancel}
34363 \begin_layout Standard
34372 which leads to the same size as for the canceled value, or
34376 which makes is it a bit smaller than normal.
34379 \begin_layout Standard
34380 To color the cancellation bar one adds this command as TeX code:
34383 \begin_layout Standard
34395 \begin_layout Standard
34400 can be replaced by a color of your choice.
34403 \begin_layout Standard
34407 \begin_layout Plain Layout
34423 \begin_layout Standard
34424 \begin_inset Formula
34426 \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}}}
34434 \begin_layout Standard
34438 \begin_layout Plain Layout
34452 \begin_inset Note Note
34455 \begin_layout Plain Layout
34464 \begin_layout Standard
34465 For further customizations, see the documentation of the package
34470 \begin_inset CommandInset citation
34477 \begin_inset Index idx
34480 \begin_layout Plain Layout
34489 \begin_layout Standard
34493 \begin_layout Plain Layout
34503 \begin_inset Note Note
34506 \begin_layout Plain Layout
34507 The following will be displayed when the LaTeX-package
34519 \begin_layout Standard
34520 You need to install the LaTeX-package
34524 to see the rest of this subsection in the output.
34527 \begin_layout Standard
34531 \begin_layout Plain Layout
34543 \begin_layout Standard
34544 \begin_inset Newpage newpage
34550 \begin_layout Subsection
34551 Formulas in Section Headings
34552 \begin_inset CommandInset label
34554 name "sub:Formulas-in-Section"
34559 \begin_inset Index idx
34562 \begin_layout Plain Layout
34563 Formula ! in section headings
34571 \begin_layout Standard
34572 When formulas are used in section headings, the following has to be taken
34576 \begin_layout Standard
34577 \begin_inset Note Greyedout
34580 \begin_layout Plain Layout
34586 \begin_inset Index idx
34589 \begin_layout Plain Layout
34590 Packages ! hyperref
34595 support is enabled in the document settings dialog under
34598 \begin_inset space ~
34603 , PDF-bookmarks are created for every section heading in the table of contents.
34604 If a section heading contains formulas, they are incorrectly displayed
34605 in the bookmark text, because formulas in bookmarks infringe the PDF convention
34614 \begin_layout Standard
34615 Both problems can be solved by inserting at the end of the section heading
34616 a short title with the menu
34618 Insert\SpecialChar \menuseparator
34620 \begin_inset space ~
34626 Short titles are used as alternative for multiline section headings to
34627 keep the table of contents clearly arranged.
34628 Only the short title appears in the table of contents and therefore also
34629 in the PDF-bookmark.
34632 \begin_layout Standard
34633 When formulas should be used in the table of contents but
34637 is used, one can use the following command in TeX-mode:
34640 \begin_layout Standard
34645 texorpdfstring{part}{alternative}
34646 \begin_inset Index idx
34649 \begin_layout Plain Layout
34660 \begin_layout Standard
34661 Part is the part of the heading that shouldn't appear in the PDF-bookmark.
34662 This can be characters, formulas, footnotes, but also cross-references.
34663 The alternative is used instead of the part for the bookmark.
34666 \begin_layout Standard
34667 Here are two example headings:
34668 \begin_inset VSpace -3mm
34675 \begin_layout Plain Layout
34687 \begin_layout Subsubsection
34688 Heading without formula in table of contents
34689 \begin_inset Formula $\sqrt{-1}=\mathrm{i}$
34693 \begin_inset Argument 1
34696 \begin_layout Plain Layout
34697 Heading without formula in table of contents
34705 \begin_layout Subsubsection
34706 Heading with formula in table of contents
34710 \begin_layout Plain Layout
34720 \begin_inset Formula $\sqrt{-1}=\mathrm{i}$
34727 \begin_layout Plain Layout
34737 \begin_layout Standard
34741 \begin_layout Plain Layout
34750 In the first heading a short title was used, in the second one
34759 \begin_layout Standard
34760 To get the same formatting as for the other headings, the complete heading
34769 \begin_layout Plain Layout
34771 \begin_inset CommandInset ref
34773 reference "sub:Bold-Formulas"
34785 \begin_layout Subsection
34786 Formulas in multi-column Text
34787 \begin_inset Index idx
34790 \begin_layout Plain Layout
34791 Formula ! in multi-column text
34799 \begin_layout Standard
34800 Formulas in multi-column text are often too wide to fit into a column and
34801 thus need to be set over the whole page width.
34802 This is done by using the LaTeX-package
34810 \begin_layout Plain Layout
34815 is part of every LaTeX standard installation.
34821 \begin_inset Index idx
34824 \begin_layout Plain Layout
34825 Packages ! multicol
34830 , that is loaded with the LaTeX-preamble line
34833 \begin_layout Standard
34838 usepackage{multicol}
34841 \begin_layout Standard
34842 \begin_inset Note Greyedout
34845 \begin_layout Plain Layout
34846 Note that in this case the setting
34849 \begin_inset space ~
34856 Document\SpecialChar \menuseparator
34862 \begin_inset space ~
34882 \begin_layout Standard
34883 Before the multi-column text the command
34886 \begin_layout Standard
34891 begin{multicols}{column number}
34894 \begin_layout Standard
34895 is written in TeX-mode.
34896 The column number is a number in the range of 2
34897 \begin_inset space \thinspace{}
34901 \begin_inset space \thinspace{}
34905 Before the formula the multi-column text is ended by inserting the command
34908 \begin_layout Standard
34916 \begin_layout Standard
34920 \begin_layout Standard
34921 Due to the command some space is automatically added before the formula.
34923 \begin_inset space \thinspace{}
34926 mm vertical space is inserted before the formula.
34927 When the formula style
34933 \begin_layout Plain Layout
34935 \begin_inset CommandInset ref
34937 reference "sec:Formula-Styles"
34949 \begin_inset space \thinspace{}
34952 mm space is inserted instead.
34955 \begin_layout Standard
34956 As example a multi-column text with a displayed formula:
34959 \begin_layout Standard
34965 \begin_layout Plain Layout
34969 begin{multicols}{2}
34974 Das Spektrum wird fouriertransformiert.
34975 Die Fouriertransformation wird verwendet, um die überlagerten Signale (Netzwerk
34976 , Lösungsmittel) zu trennen.
34977 Nachdem wir die Phasenverschiebung bestimmen konnten, interessiert uns
34978 nun das Aussehen des Ausgangssignals.
34979 Im Experiment haben wir es mit sehr vielen Teilchen zu tun, so dass man
34980 über alle Phasen integrieren muss.
34982 \begin_inset Formula $S$
34985 unser normiertes Ausgangssignal und
34986 \begin_inset Formula $P$
34989 die Phasenverteilungsfunktion, so ergibt sich die Beziehung
34993 \begin_layout Plain Layout
35003 \begin_inset VSpace -6mm
35007 \begin_inset Formula
35009 S(t)=S_{0}(t)\int_{-\infty}^{\infty}P(\phi,t)\mathrm{e}^{\mathrm{i}\phi}\,\mathrm{d}\phi
35018 \begin_layout Plain Layout
35022 begin{multicols}{2}
35028 \begin_inset Formula $S_{0}$
35031 das Signal ohne Gradient ist und die Normierungsbedingung
35032 \begin_inset Formula $\int_{-\infty}^{\infty}P(\phi,t)\,\mathrm{d}\phi=1$
35036 Nun dürfen wir aber nicht den Relaxationsprozess außer Acht lassen.
35038 \begin_inset Formula $\nicefrac{\pi}{2}$
35042 \begin_inset space \thinspace{}
35045 -rf-Puls beginnt sich die Magnetisierung zu entfokussieren, wodurch sich
35046 das Signal zusätzlich abschwächt.
35047 Diese Abschwächung verläuft exponentiell in Abhängigkeit der so genannten
35049 \begin_inset Formula $T_{2}$
35055 \begin_layout Standard
35061 \begin_layout Plain Layout
35073 \begin_layout Subsection
35074 Formulas with Description of Variables
35075 \begin_inset Index idx
35078 \begin_layout Plain Layout
35079 Formula ! with description of variables
35087 \begin_layout Standard
35088 To describe variables within a formula, like in formula
35089 \begin_inset CommandInset ref
35091 reference "eq:within"
35100 \begin_inset Formula $n$
35104 \begin_inset space ~
35107 matrix is used with left aligned columns for the
35108 \begin_inset Formula $n$
35115 \begin_layout Plain Layout
35117 \begin_inset CommandInset ref
35119 reference "sec:Matrices"
35128 To set the description in a smaller size, before the matrix e.
35129 \begin_inset space \thinspace{}
35133 \begin_inset space \space{}
35146 \begin_layout Plain Layout
35148 \begin_inset CommandInset ref
35150 reference "sub:Font-Sizes"
35162 \begin_layout Standard
35163 When the formula style
35169 \begin_layout Plain Layout
35171 \begin_inset CommandInset ref
35173 reference "sec:Formula-Styles"
35194 \begin_layout Plain Layout
35201 only works in formulas with the style
35206 \begin_inset CommandInset ref
35208 reference "sub:Variable-Space"
35217 is inserted before and after the matrix to have the same separation of
35218 the matrix from the equation and the side margin.
35221 \begin_layout Standard
35222 When the formula style
35226 is used, the method described in
35227 \begin_inset CommandInset ref
35229 reference "sub:Flalign-Environment"
35233 is used to indent formulas.
35235 \begin_inset CommandInset ref
35237 reference "eq:within"
35241 consists of five columns where in the first two columns contain the equation,
35242 the third the matrix and the last one an empty TeX-brace.
35243 \begin_inset Formula
35245 \hspace{30pt}F_{A} & =\rho·V·g & \footnotesize\begin{array}{ll}
35246 \rho & \textrm{density}\\
35247 V & \textrm{volume}\\
35248 g & \textrm{gravitational acceleration}
35249 \end{array} & & {}\label{eq:within}
35257 \begin_layout Subsection
35258 Upright small Greek Letters
35259 \begin_inset CommandInset label
35261 name "sub:Upright-small-Greek"
35266 \begin_inset Index idx
35269 \begin_layout Plain Layout
35270 Greek letters ! upright
35278 \begin_layout Standard
35279 Most of the math fonts only provide italic small Greek letters.
35280 But for symbols of elementary particles like pions and neutrinos, upright
35281 Greek letters are needed.
35290 \begin_layout Plain Layout
35295 is part of the LaTeX-package
35300 \begin_inset Index idx
35303 \begin_layout Plain Layout
35308 \begin_layout Plain Layout
35328 \begin_inset Index idx
35331 \begin_layout Plain Layout
35337 that is loaded with the LaTeX-preamble line
35340 \begin_layout Standard
35345 usepackage{upgreek}
35348 \begin_layout Standard
35354 \begin_layout Plain Layout
35364 \begin_inset Note Note
35367 \begin_layout Plain Layout
35368 The following table will only be displayed when the LaTeX-package
35377 They are created when the command for a small Greek letter is started with
35383 For example the command
35390 \begin_inset Formula $\uptau$
35396 \begin_layout Standard
35397 With these commands reactions of elementary particles can be typeset:
35398 \begin_inset Formula
35400 \uppi^{+}\to\upmu^{+}+\upnu_{\upmu}
35408 \begin_layout Standard
35409 The upright letters are more bold and wider than the italic ones.
35410 They should therefore not be used for units like
35411 \begin_inset Quotes eld
35415 \begin_inset Quotes erd
35421 \begin_layout Standard
35425 \begin_layout Plain Layout
35435 \begin_inset Note Note
35438 \begin_layout Plain Layout
35439 The following will be displayed when the LaTeX-package
35451 \begin_layout Standard
35452 You need to install the LaTeX-package
35456 to see the rest of this subsection in the output.
35459 \begin_layout Standard
35463 \begin_layout Plain Layout
35475 \begin_layout Subsection
35476 Text Characters in Formulas
35477 \begin_inset CommandInset label
35479 name "sub:Text-Characters-in"
35484 \begin_inset Index idx
35487 \begin_layout Plain Layout
35496 \begin_layout Standard
35497 In some cases you might want to insert text characters directly into formulas.
35498 When for example the centered dot · is often used in formulas like
35499 \begin_inset Formula $\nu=5·10^{5}\,\mathrm{Hz}$
35502 , one would have to insert the command
35512 \begin_layout Plain Layout
35514 \begin_inset CommandInset ref
35516 reference "sub:Binary-Operators"
35525 all the time, because this character is defined in all encodings as text
35527 But the encoding can be changed by this LaTeX-preamble line:
35530 \begin_layout Standard
35535 Declare Inputtext{183}{
35545 f\SpecialChar \textcompwordmark{}
35549 \begin_layout Standard
35550 The character encoding (menu
35552 Document\SpecialChar \menuseparator
35553 Settings\SpecialChar \menuseparator
35556 ) specifies what character appears when a keyboard key is pressed.
35557 When the key for the character '·' is pressed, internally the command
35564 But this command is not available in a formula so that you would get LaTeX-erro
35566 With the changed encoding the right command is chosen automatically, depending
35567 on if the character was inserted into a formula or not.
35570 \begin_layout Standard
35571 The encoding of several characters is saved in definition files.
35572 For example the encoding
35576 is defined in the file
35580 which is in the installation folder of LaTeX.
35581 Encodings should only be changed via the LaTeX-preamble and not in the
35583 Otherwise documents could not be edited by other LyX users working on other
35587 \begin_layout Standard
35588 \begin_inset VSpace medskip
35591 Besides the centered dot, in this document the degree sign ° is defined
35592 with the following LaTeX-preamble line so that it can be directly inserted
35596 \begin_layout Standard
35601 DeclareInputtext{176}{
35611 f\SpecialChar \textcompwordmark{}
35615 \begin_layout Standard
35616 \begin_inset Newpage newpage
35622 \begin_layout Section
35625 \begin_inset Index idx
35628 \begin_layout Plain Layout
35637 \begin_layout Standard
35638 This section is a summary of the most important typographic rules, listed
35643 \begin_layout Plain Layout
35644 This collection was partly taken from the German semi-official dictionary
35646 \begin_inset Quotes eld
35650 \begin_inset Quotes erd
35654 \begin_inset CommandInset citation
35660 that lists some of the ISO rules.
35661 More rules are listed in
35662 \begin_inset CommandInset citation
35676 \begin_layout Itemize
35685 \begin_layout Plain Layout
35686 done with font styles, see
35687 \begin_inset CommandInset ref
35689 reference "sub:Font-Styles"
35698 , no matter if they appear in italic text: 30
35699 \begin_inset space \thinspace{}
35703 \begin_inset Newline newline
35706 Between the value and the unit is the smallest space, see
35707 \begin_inset CommandInset ref
35709 reference "sub:Predefined-Space"
35714 \begin_inset Newline newline
35717 This convention is automatically fulfilled when the command
35724 When it is entered to a formula, two boxes appear.
35725 In the first one the value is inserted, in the second one the unit, and
35727 \begin_inset Formula $\unit[30]{km/h}$
35731 \begin_inset space \thinspace{}
35741 is not a real LaTeX command but the command
35747 , therefore you cannot use it in TeX code.
35750 \begin_layout Itemize
35751 Percent and perthousand signs are set like physical units:
35752 \begin_inset Newline newline
35756 \begin_inset space \thinspace{}
35762 \begin_layout Itemize
35763 The degree sign follows directly on the value: 15°, but not when it is used
35765 \begin_inset space \thinspace{}
35771 \begin_layout Itemize
35772 In numbers with more than four digits the smallest space is inserted before
35773 every third digit to group them:
35783 \begin_inset space \thinspace{}
35787 \begin_inset space \thinspace{}
35793 \begin_layout Itemize
35794 For dimensions like 120×90×40
35795 \begin_inset space \thinspace{}
35798 cm the multiplication sign
35799 \begin_inset Quotes eld
35803 \begin_inset Quotes erd
35807 It is available either via the command
35815 Insert\SpecialChar \menuseparator
35816 Special Character\SpecialChar \menuseparator
35822 \begin_layout Itemize
35823 Functions with names consisting of several letters are set upright to avoid
35825 \begin_inset CommandInset ref
35827 reference "sub:Predefined-Functions"
35834 \begin_layout Itemize
35835 Indices consisting of several letters, are set upright:
35836 \begin_inset Formula $E_{\mathrm{kin}}$
35840 \begin_inset Newline newline
35843 Components of matrices are set italic:
35844 \begin_inset Formula $\hat{H}_{kl}$
35850 \begin_layout Itemize
35851 The differentiation/integration operator 'd', the Euler's number 'e' and
35852 the imaginary unit 'i' should be set upright, to avoid mixing them up with
35856 \begin_layout Itemize
35857 The character that denotes a
35861 transformation is inserted either by the command
35866 \begin_inset space \textvisiblespace{}
35873 Insert\SpecialChar \menuseparator
35874 Special Character\SpecialChar \menuseparator
35875 Symbols\SpecialChar \menuseparator
35877 \begin_inset space ~
35883 \begin_inset Formula $\mathscr{F}$
35889 \begin_layout Standard
35890 \begin_inset Newpage newpage
35896 \begin_layout Section
35898 \begin_inset Index idx
35901 \begin_layout Plain Layout
35910 \begin_layout Standard
35911 Some characters and symbols can be created with several commands.
35912 Here is a list of the synonym commands:
35915 \begin_layout Standard
35916 \begin_inset VSpace bigskip
35920 \begin_inset space \hfill{}
35924 \begin_inset Tabular
35925 <lyxtabular version="3" rows="12" columns="2">
35926 <features rotate="0" tabularvalignment="middle">
35927 <column alignment="center" valignment="top" width="0pt">
35928 <column alignment="center" valignment="top" width="0pt">
35930 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
35933 \begin_layout Plain Layout
35939 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
35942 \begin_layout Plain Layout
35944 \begin_inset Note Note
35947 \begin_layout Plain Layout
35954 is only used as spacer.
35966 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
35969 \begin_layout Plain Layout
35977 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
35980 \begin_layout Plain Layout
35984 \begin_layout Plain Layout
35997 \begin_layout Plain Layout
36011 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
36014 \begin_layout Plain Layout
36022 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
36025 \begin_layout Plain Layout
36035 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
36038 \begin_layout Plain Layout
36046 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
36049 \begin_layout Plain Layout
36059 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
36062 \begin_layout Plain Layout
36070 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
36073 \begin_layout Plain Layout
36081 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
36084 \begin_layout Plain Layout
36092 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
36095 \begin_layout Plain Layout
36103 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
36106 \begin_layout Plain Layout
36114 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
36117 \begin_layout Plain Layout
36127 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
36130 \begin_layout Plain Layout
36138 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
36141 \begin_layout Plain Layout
36151 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
36154 \begin_layout Plain Layout
36162 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
36165 \begin_layout Plain Layout
36175 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
36178 \begin_layout Plain Layout
36186 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
36189 \begin_layout Plain Layout
36199 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
36202 \begin_layout Plain Layout
36210 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
36213 \begin_layout Plain Layout
36221 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
36224 \begin_layout Plain Layout
36232 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
36235 \begin_layout Plain Layout
36247 \begin_inset space \hfill{}
36251 \begin_inset Tabular
36252 <lyxtabular version="3" rows="12" columns="2">
36253 <features rotate="0" tabularvalignment="middle">
36254 <column alignment="center" valignment="top" width="0pt">
36255 <column alignment="center" valignment="top" width="0pt">
36257 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
36260 \begin_layout Plain Layout
36266 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
36269 \begin_layout Plain Layout
36277 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
36280 \begin_layout Plain Layout
36288 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
36291 \begin_layout Plain Layout
36303 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
36306 \begin_layout Plain Layout
36314 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
36317 \begin_layout Plain Layout
36327 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
36330 \begin_layout Plain Layout
36338 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
36341 \begin_layout Plain Layout
36351 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
36354 \begin_layout Plain Layout
36362 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
36365 \begin_layout Plain Layout
36373 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
36376 \begin_layout Plain Layout
36384 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
36387 \begin_layout Plain Layout
36395 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
36398 \begin_layout Plain Layout
36406 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
36409 \begin_layout Plain Layout
36419 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
36422 \begin_layout Plain Layout
36430 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
36433 \begin_layout Plain Layout
36443 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
36446 \begin_layout Plain Layout
36454 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
36457 \begin_layout Plain Layout
36467 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
36470 \begin_layout Plain Layout
36478 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
36481 \begin_layout Plain Layout
36491 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
36494 \begin_layout Plain Layout
36502 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
36505 \begin_layout Plain Layout
36515 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
36518 \begin_layout Plain Layout
36526 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
36529 \begin_layout Plain Layout
36543 \begin_inset space \hfill{}
36549 \begin_layout Standard
36550 \begin_inset Newpage newpage
36556 \begin_layout Bibliography
36557 \begin_inset CommandInset bibitem
36558 LatexCommand bibitem
36570 The LaTeX Companion
36573 Addison Wesley, 2004
36576 \begin_layout Bibliography
36577 \begin_inset CommandInset bibitem
36578 LatexCommand bibitem
36584 \begin_inset CommandInset href
36587 target "ftp://ftp.dante.de/tex-archive/info/math/voss/mathmode/Mathmode.pdf"
36591 of LaTeX's math abilities
36594 \begin_layout Bibliography
36595 \begin_inset CommandInset bibitem
36596 LatexCommand bibitem
36602 \begin_inset CommandInset href
36605 target "http://mirrors.ctan.org/macros/latex/required/amslatex/math/amsldoc.pdf"
36613 \begin_layout Plain Layout
36625 \begin_layout Bibliography
36626 \begin_inset CommandInset bibitem
36627 LatexCommand bibitem
36633 \begin_inset CommandInset href
36636 target "ftp://ftp.dante.de/tex-archive/info/symbols/comprehensive/symbols-a4.pdf"
36640 of all symbols available with LaTeX-packages
36643 \begin_layout Bibliography
36644 \begin_inset CommandInset bibitem
36645 LatexCommand bibitem
36651 \begin_inset CommandInset href
36653 name "Documentation"
36654 target "http://mirrors.ctan.org/macros/latex/contrib/cancel/cancel.pdf"
36658 of the LaTeX-package
36663 \begin_inset Index idx
36666 \begin_layout Plain Layout
36675 \begin_layout Bibliography
36676 \begin_inset CommandInset bibitem
36677 LatexCommand bibitem
36683 \begin_inset CommandInset href
36685 name "Documentation"
36686 target "http://www.tug.org/applications/hyperref/ftp/doc/manual.pdf"
36690 of the LaTeX-package
36695 \begin_inset Index idx
36698 \begin_layout Plain Layout
36699 Packages ! hyperref
36707 \begin_layout Bibliography
36708 \begin_inset CommandInset bibitem
36709 LatexCommand bibitem
36715 \begin_inset CommandInset href
36717 name "Documentation"
36718 target "http://www.ctan.org/tex-archive/macros/latex/contrib/mhchem/mhchem.pdf"
36722 of the LaTeX-package
36727 \begin_inset Index idx
36730 \begin_layout Plain Layout
36739 \begin_layout Bibliography
36740 \begin_inset CommandInset bibitem
36741 LatexCommand bibitem
36747 \begin_inset CommandInset href
36750 target "http://www.tug.org/TUGboat/Articles/tb22-4/tb72perlS.pdf"
36761 \begin_inset CommandInset ref
36763 reference "sub:Operator-Limits"
36768 \begin_inset Index idx
36771 \begin_layout Plain Layout
36782 \begin_layout Bibliography
36783 \begin_inset CommandInset bibitem
36784 LatexCommand bibitem
36795 Auflage, Duden 2001
36798 \begin_layout Bibliography
36799 \begin_inset CommandInset bibitem
36800 LatexCommand bibitem
36806 \begin_inset CommandInset href
36809 target "http://physics.nist.gov/Document/checklist.pdf"
36813 for reviewing manuscripts
36816 \begin_layout Standard
36817 \begin_inset CommandInset index_print
36818 LatexCommand printindex