1 #LyX 2.1 created this file. For more info see http://www.lyx.org/
7 % DO NOT ALTER THIS PREAMBLE!!!
9 % This preamble is designed to ensure that the file prints
10 % out as advertised. If you mess with this preamble,
11 % parts of this document may not print out as expected. If you
12 % have problems LaTeXing this file, please contact
13 % the documentation team
14 % email: lyx-docs@lists.lyx.org
20 % set fonts for nicer pdf view
21 \IfFileExists{lmodern.sty}
22 {\usepackage{lmodern}}{}
24 \fi % end if pdflatex is used
26 % solves the following problem:
27 % If the dection number consits of too many numerals the section heading
28 % will be printed in the TOC without a space between it and the section number.
29 % As solution more space between the number and the heading is inserted:
30 \renewcommand{\l@subsection}{\@dottedtocline{2}{1.5em}{2.8em}}
31 \renewcommand{\l@subsubsection}{\@dottedtocline{3}{4.3em}{3.6em}}
33 % increase link area for cross-references and autoname them,
34 \AtBeginDocument{\renewcommand{\ref}[1]{\mbox{\autoref{#1}}}}
35 \@ifundefined{extrasenglish}{\usepackage[english]{babel}}{}
36 \addto\extrasenglish{%
37 \renewcommand*{\equationautorefname}[1]{}%
38 \renewcommand{\sectionautorefname}{sec.\negthinspace}%
39 \renewcommand{\subsectionautorefname}{sec.\negthinspace}%
40 \renewcommand{\subsubsectionautorefname}{sec.\negthinspace}%
43 % don't load packages twice
44 % see first footnote in sec. 9.3
45 \@ifundefined{textcolor}{\usepackage{color}}{}
47 % the pages of the TOC are numbered roman
48 % and a PDF-bookmark for the TOC is added
50 \let\myTOC\tableofcontents
51 \renewcommand{\tableofcontents}{%
53 \pdfbookmark[1]{\contentsname}{}
56 \pagenumbering{arabic}}
58 % insert additional vertical space of 1.5 mm between footnotes,
60 \renewcommand{\footnote}[1]{\myFoot{#1\vspace{1.5mm}}}
62 % provides caption formatting
63 \setkomafont{captionlabel}{\bfseries}
65 % enables calculation of values
68 % for multiple columns used in sec. 24.7
74 % for the Fourier transformation symbol
77 % define a color, used in sec.9.3
78 \definecolor{darkgreen}{cmyk}{0.5, 0, 1, 0.5}
80 % declare operators (see sec. 10.4 and sec. 15.2)
81 \DeclareMathOperator*{\Lozenge}{\blacklozenge}
82 \DeclareMathOperator{\sgn}{sgn}
84 % example definitions for sec. 20.1
85 \newcommand{\gr}{\Longrightarrow}
86 \newcommand{\us}[1]{\underline{#1}}
87 \newcommand{\fb}[3]{\framebox#1#2{$#3$}}
88 \newcommand{\cb}[3][white]{\fcolorbox{#2}{#1}{$#3$}}
89 \newcommand{\fracS}[3][]{\genfrac{}{}{#1}{}{#2}{#3}}
91 % example macro from sec. 19.4
92 %\def\tagform@#1{\maketag@@@{|#1|}}
95 % ------------------------------------
96 % used to check for needed LaTeX packages
99 % check for package undertilde
100 % used for the command \utilde
101 \newboolean{undertilde}
102 \IfFileExists{undertilde.sty}
103 {\usepackage{undertilde}
104 \setboolean{undertilde}{true}}
105 {\setboolean{undertilde}{false}}
107 % check for package eurosym
108 % used for the Euro symbol
110 \IfFileExists{eurosym.sty}
111 {\usepackage[gennarrow]{eurosym}
112 \setboolean{eurosym}{true}}
113 {\setboolean{eurosym}{false}}
115 % check for package braket
116 % used for physical vectors
118 \IfFileExists{braket.sty}
120 \setboolean{braket}{true}}
121 {\setboolean{braket}{false}}
123 % check for package cancel
125 \IfFileExists{cancel.sty}
127 \setboolean{cancel}{true}}
128 {\setboolean{cancel}{false}}
130 % check for package upgreek
132 \IfFileExists{upgreek.sty}
133 {\usepackage{upgreek}
134 \setboolean{upgreek}{true}}
135 {\setboolean{upgreek}{false}}
137 \options bibliography=totoc,index=totoc,BCOR7.5mm,titlepage,captions=tableheading
138 \use_default_options false
139 \maintain_unincluded_children false
141 \language_package default
146 \font_typewriter default
148 \font_default_family default
149 \use_non_tex_fonts false
155 \default_output_format default
157 \bibtex_command default
158 \index_command default
162 \pdf_title "LyX's Math Manual"
163 \pdf_author "LyX Team, Uwe Stöhr"
164 \pdf_subject "LyX-documentation about math"
165 \pdf_keywords "LyX, Mathed"
167 \pdf_bookmarksnumbered true
168 \pdf_bookmarksopen true
169 \pdf_bookmarksopenlevel 1
170 \pdf_breaklinks false
174 \pdf_pdfusetitle false
175 \pdf_quoted_options "linkcolor=black, citecolor=black, urlcolor=blue, filecolor=blue, pdfpagelayout=OneColumn, pdfnewwindow=true, pdfstartview=XYZ, plainpages=false"
178 \use_package amsmath 2
179 \use_package amssymb 2
180 \use_package cancel 0
182 \use_package mathdots 1
183 \use_package mathtools 1
184 \use_package mhchem 1
185 \use_package stackrel 0
186 \use_package stmaryrd 0
187 \use_package undertilde 0
189 \cite_engine_type default
193 \paperorientation portrait
197 \notefontcolor #0000ff
204 \paragraph_separation skip
206 \quotes_language english
209 \paperpagestyle plain
213 \tracking_changes false
214 \output_changes false
217 \html_be_strict false
223 LyX's detailed Math manual
231 \begin_layout Plain Layout
233 If you have comments or error corrections, please send them to the LyX Documenta
237 \begin_inset CommandInset href
239 name "lyx-docs@lists.lyx.org"
240 target "lyx-docs@lists.lyx.org?subject=LyX's Math manual"
251 \begin_inset Note Note
254 \begin_layout Plain Layout
261 \begin_inset Newline newline
265 \begin_inset Newline newline
273 \begin_layout Standard
274 \begin_inset CommandInset toc
275 LatexCommand tableofcontents
282 \begin_layout Standard
283 \begin_inset Note Note
286 \begin_layout Plain Layout
287 To export this document to PDF, PS or DVI the LaTeX-packages
289 braket, cancel, eurosym, mathdots, mathtools, mhchem, undertilde
296 If they are not installed the document can be exported anyway but the sections
297 where the packages are required will not appear in the output.
302 ; if it is not installed, this file cannot be exported.
305 \begin_layout Plain Layout
306 The latest PDF-version of this document can be found here:
307 \begin_inset Newline newline
312 http://wiki.lyx.org/LyX/DocumentationDevelopment#Math
320 \begin_layout Standard
321 \begin_inset Newpage newpage
327 \begin_layout Section
331 \begin_layout Standard
332 This document explains LyX's math features and is furthermore a collection
333 of LaTeX-commands used for mathematical characters and constructs.
334 The explanations are designed for the usage of commands.
335 It is therefore required that you have read the section
346 \begin_layout Standard
347 Most of the characters and many constructs explained in this manual are
348 also accessible via the menu
352 \SpecialChar \menuseparator
368 But everybody who has to write lots of formulas will notice that it is
369 much faster to use commands instead of the math toolbar.
370 Therefore this manual is focused on commands but also mentions the correspondin
371 g toolbar buttons when available.
374 \begin_layout Standard
375 If not specially mentioned the commands are only available within formulas.
376 To be able to use all commands explained in this document, the option
380 must be checked in the document settings (menu
382 Document\SpecialChar \menuseparator
383 Settings\SpecialChar \menuseparator
394 \begin_layout Plain Layout
397 Use AMS math package automatically
403 \begin_layout Plain Layout
412 -math when math constructs are found that are supported by LyX.
420 \begin_layout Standard
421 This document doesn't list all
425 \begin_layout Plain Layout
438 \begin_layout Plain Layout
443 \begin_layout Plain Layout
452 -math commands is in the file
455 \begin_inset CommandInset href
458 target "ftp://ftp.ams.org/pub/tex/doc/amstex/amsguide.pdf"
464 , which is part of every LaTeX standard installation.
469 for lucidity reasons.
472 \begin_layout Section
476 \begin_layout Standard
477 To create an inline formula
478 \begin_inset Index idx
481 \begin_layout Plain Layout
487 that is embedded into a text line, use one of the shortcuts
493 or the toolbar button
500 \begin_inset Newline newline
503 To create a display style formula
504 \begin_inset Index idx
507 \begin_layout Plain Layout
508 Formula ! display style
513 which will appear bigger, has a different format, and will be in a separate
514 paragraph, use one of these shortcuts:
523 \begin_layout Standard
524 To change a display style formula to an inline formula, set the cursor into
525 the formula and use one of the shortcuts
533 Edit\SpecialChar \menuseparator
534 Math\SpecialChar \menuseparator
538 The same way is used to change an inline formula to a display style formula.
541 \begin_layout Standard
542 To display parts of an inline formula in the size of a display style formula,
550 \begin_inset Index idx
553 \begin_layout Plain Layout
562 Then a new blue box appears in which the desired formula part is inserted.
565 \begin_layout Standard
566 Only inline formulas are allowed inside tables.
569 \begin_layout Standard
574 can be turned on in the menu
576 View\SpecialChar \menuseparator
580 When you click there on
581 \begin_inset Quotes eld
585 \begin_inset Quotes erd
588 the toolbar will be shown permanently at the bottom; this state is visualized
593 menu with a checkmark.
594 When you click in this state again on
595 \begin_inset Quotes eld
599 \begin_inset Quotes erd
610 is only shown when the cursor is within a formula; this state is visualized
611 by the renaming of the menu entry from
612 \begin_inset Quotes eld
616 \begin_inset Quotes erd
620 \begin_inset Quotes eld
628 \begin_inset Quotes erd
634 \begin_layout Standard
636 \begin_inset Index idx
639 \begin_layout Plain Layout
645 is invoked by pressing the toolbar button
653 Insert\SpecialChar \menuseparator
658 \begin_layout Plain Layout
674 \begin_inset Note Note
677 \begin_layout Plain Layout
678 In LyX there are three
679 \begin_inset Quotes eld
683 \begin_inset Quotes erd
686 that appear in the output with sub- and superscript letters: TeX, LaTeX
690 \begin_layout Plain Layout
691 To avoid that these names are recognized as proper names, a TeX-brace pair
700 \begin_layout Standard
701 To change the LaTeX-preamble
702 \begin_inset Index idx
705 \begin_layout Plain Layout
713 Document\SpecialChar \menuseparator
714 Settings\SpecialChar \menuseparator
719 \begin_layout Plain Layout
735 \begin_layout Standard
736 To edit matrices, case differentiations and multiline formulas subsequently,
739 Edit\SpecialChar \menuseparator
744 Edit\SpecialChar \menuseparator
746 \begin_inset space \thinspace{}
750 \begin_inset space \thinspace{}
760 When lines and columns are swapped via the menu, the column or line where
761 the cursor is in is exchanged with the column to the right or the line
763 Is the cursor in the last column or row, the exchange is done with the
764 column to the left or the line above.
767 \begin_layout Standard
768 To write text in formulas
772 \begin_layout Plain Layout
773 For multiline formulas the command
780 \begin_inset CommandInset ref
782 reference "sub:Text-in-multiline"
796 \begin_inset Index idx
799 \begin_layout Plain Layout
806 \begin_inset Index idx
809 \begin_layout Plain Layout
816 This mode is invoked with the shortcut
822 or by the insertion of the command
829 \begin_inset Index idx
832 \begin_layout Plain Layout
841 The text appears black in LyX and can therefore be distinguished from the
842 other formula parts which appear blue.
843 In the output mathematical text is set upright, in contrary to other formula
847 \begin_layout Subsection*
851 \begin_layout Standard
852 Most of the LaTeX-commands for math constructs have the following scheme:
855 \begin_layout Standard
871 \begin_layout Standard
872 A command always starts with a backslash
873 \begin_inset Quotes gld
883 \begin_inset Quotes grd
887 To omit optional arguments, also omit the associated brackets.
888 The braces around the required arguments are named in this document as
890 \begin_inset Index idx
893 \begin_layout Plain Layout
900 If you add in a formula a left brace to a command name, LyX automatically
902 In all other cases TeX-braces are created in formulas with the command
910 TeX-braces appear red in LyX, in contrary to normal braces which appear
912 In TeX-mode no command is needed to get TeX-braces.
913 TeX-braces don't appear in the output.
916 \begin_layout Standard
917 When commands without arguments, like commands for symbols are entered in
918 TeX-mode, a space character must
922 be behind the command to end it.
923 This space doesn't appear in the output.
924 When the space should appear in the output, the space must be followed
925 by a protected space in normal text.
928 \begin_layout Standard
929 A protected space is inserted with
932 arg "command-alternatives space-insert protected ; math-space"
938 \begin_layout Subsection*
939 \begin_inset Newpage newpage
945 \begin_layout Itemize
947 \begin_inset space \textvisiblespace{}
950 denotes a space character to be input.
953 \begin_layout Itemize
955 \begin_inset Formula $\to$
958 denotes the usage of the corresponding arrow key on the keyboard.
963 key can often be used instead of
964 \begin_inset Formula $\to$
968 \begin_inset Formula $\downarrow$
976 \begin_inset Formula $\leftarrow$
980 \begin_inset Formula $\uparrow$
986 \begin_layout Subsection*
990 \begin_layout Standard
992 \begin_inset Float table
998 \begin_layout Plain Layout
1000 \begin_inset Caption Standard
1002 \begin_layout Plain Layout
1003 \begin_inset CommandInset label
1005 name "tab:Available-units"
1017 \begin_layout Plain Layout
1019 \begin_inset Tabular
1020 <lyxtabular version="3" rows="13" columns="2">
1021 <features rotate="0" tabularvalignment="middle">
1022 <column alignment="center" valignment="top">
1023 <column alignment="center" valignment="top">
1025 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
1028 \begin_layout Plain Layout
1034 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
1037 \begin_layout Plain Layout
1045 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
1048 \begin_layout Plain Layout
1054 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
1057 \begin_layout Plain Layout
1065 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
1068 \begin_layout Plain Layout
1074 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
1077 \begin_layout Plain Layout
1085 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
1088 \begin_layout Plain Layout
1094 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
1097 \begin_layout Plain Layout
1099 \begin_inset space \thinspace{}
1103 \begin_inset space \thinspace{}
1113 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
1116 \begin_layout Plain Layout
1122 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
1125 \begin_layout Plain Layout
1127 \begin_inset space \thinspace{}
1131 \begin_inset space \thinspace{}
1141 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
1144 \begin_layout Plain Layout
1150 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
1153 \begin_layout Plain Layout
1155 \begin_inset space \thinspace{}
1159 \begin_inset space \thinspace{}
1169 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
1172 \begin_layout Plain Layout
1178 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
1181 \begin_layout Plain Layout
1183 \begin_inset space \thinspace{}
1187 \begin_inset space \thinspace{}
1197 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
1200 \begin_layout Plain Layout
1206 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
1209 \begin_layout Plain Layout
1211 \begin_inset space \thinspace{}
1215 \begin_inset space \thinspace{}
1225 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
1228 \begin_layout Plain Layout
1234 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
1237 \begin_layout Plain Layout
1239 \begin_inset space \thinspace{}
1243 \begin_inset Formula $\approx$
1247 \begin_inset space \thinspace{}
1257 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
1260 \begin_layout Plain Layout
1266 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
1269 \begin_layout Plain Layout
1271 \begin_inset space \thinspace{}
1275 \begin_inset space \thinspace{}
1285 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
1288 \begin_layout Plain Layout
1294 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
1297 \begin_layout Plain Layout
1301 \begin_inset Quotes eld
1307 \begin_inset Quotes erd
1317 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
1320 \begin_layout Plain Layout
1326 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
1329 \begin_layout Plain Layout
1331 \begin_inset Quotes eld
1339 \begin_inset Quotes erd
1349 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
1352 \begin_layout Plain Layout
1358 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
1361 \begin_layout Plain Layout
1363 \begin_inset space \thinspace{}
1367 \begin_inset Formula $\nicefrac{1}{18}$
1371 \begin_inset space \thinspace{}
1392 \begin_layout Standard
1393 \begin_inset Newpage newpage
1399 \begin_layout Section
1403 \begin_layout Subsection
1405 \begin_inset Index idx
1408 \begin_layout Plain Layout
1415 \begin_inset Index idx
1418 \begin_layout Plain Layout
1425 \begin_inset Index idx
1428 \begin_layout Plain Layout
1433 \begin_layout Plain Layout
1444 \begin_layout Plain Layout
1457 \begin_inset Index idx
1460 \begin_layout Plain Layout
1465 \begin_layout Plain Layout
1476 \begin_layout Plain Layout
1491 \begin_layout Standard
1492 Indices are created with an underscore
1493 \begin_inset Quotes eld
1497 \begin_inset Quotes erd
1500 or via the math toolbar button
1503 arg "math-subscript"
1506 , exponents with a caret
1507 \begin_inset Quotes eld
1511 \begin_inset Quotes erd
1514 or via the math toolbar button
1517 arg "math-superscript"
1523 \begin_layout Standard
1525 \begin_inset Tabular
1526 <lyxtabular version="3" rows="4" columns="2">
1527 <features rotate="0" tabularvalignment="middle">
1528 <column alignment="center" valignment="top" width="0pt">
1529 <column alignment="center" valignment="top" width="0pt">
1531 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
1534 \begin_layout Plain Layout
1540 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
1543 \begin_layout Plain Layout
1545 \begin_inset Note Note
1548 \begin_layout Plain Layout
1555 is only used as spacer.
1567 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
1570 \begin_layout Plain Layout
1576 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
1579 \begin_layout Plain Layout
1580 \begin_inset Formula $B_{V}$
1590 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
1593 \begin_layout Plain Layout
1599 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
1602 \begin_layout Plain Layout
1603 \begin_inset Formula $\raisebox{5mm}{}B^{V}$
1613 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
1616 \begin_layout Plain Layout
1618 \begin_inset space \textvisiblespace{}
1626 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
1629 \begin_layout Plain Layout
1630 \begin_inset Formula $\raisebox{5mm}{}B^{A}$
1646 \begin_layout Standard
1647 As the caret is in some languages an accent, vowels will be accentuated
1648 in this case and not set as exponents
1652 \begin_layout Plain Layout
1653 Depending on the used keyboard settings this can also happen for characters
1660 To get exponents in this case, press
1664 after the caret as in the last example.
1667 \begin_layout Subsection
1669 \begin_inset CommandInset label
1671 name "sub:Fractions"
1676 \begin_inset Index idx
1679 \begin_layout Plain Layout
1688 \begin_layout Standard
1689 Fractions are generated with the command
1696 \begin_inset Index idx
1699 \begin_layout Plain Layout
1707 or via the math toolbar button
1710 arg "math-insert \\frac"
1714 The font size is adjusted automatically, depending on whether the fraction
1715 is in an inline or display style formula.
1716 With the math toolbar button
1719 arg "math-insert \\frac-square"
1722 you can select different fraction types.
1725 \begin_layout Standard
1733 \begin_inset Index idx
1736 \begin_layout Plain Layout
1744 a fraction can be created that always has the size of a display style formula.
1752 \begin_inset Index idx
1755 \begin_layout Plain Layout
1763 the fraction appears always with the size of an inline formula.
1767 \begin_layout Standard
1768 A line with the fraction
1769 \begin_inset Formula $\frac{1}{2}$
1772 that was created with the command
1781 \begin_layout Standard
1782 A line with the fraction
1783 \begin_inset Formula $\dfrac{1}{2}$
1786 that was created with the command
1795 \begin_layout Standard
1797 \begin_inset Tabular
1798 <lyxtabular version="3" rows="4" columns="2">
1799 <features rotate="0" tabularvalignment="middle">
1800 <column alignment="center" valignment="top" width="0pt">
1801 <column alignment="center" valignment="top" width="0pt">
1803 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
1806 \begin_layout Plain Layout
1812 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
1815 \begin_layout Plain Layout
1817 \begin_inset Note Note
1820 \begin_layout Plain Layout
1827 is only used as spacer.
1839 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
1842 \begin_layout Plain Layout
1846 \begin_inset space \textvisiblespace{}
1850 \begin_inset Formula $\downarrow$
1858 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
1861 \begin_layout Plain Layout
1862 \begin_inset Formula $\raisebox{4.5mm}{}\frac{A}{B}\raisebox{-2.5mm}{}$
1872 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
1875 \begin_layout Plain Layout
1879 \begin_inset space \textvisiblespace{}
1883 \begin_inset Formula $\downarrow$
1891 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
1894 \begin_layout Plain Layout
1895 \begin_inset Formula $\raisebox{7mm}{}\dfrac{A}{B}\raisebox{-4mm}{}$
1905 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
1908 \begin_layout Plain Layout
1912 \begin_inset space \textvisiblespace{}
1918 \begin_inset space \textvisiblespace{}
1922 \begin_inset Formula $\downarrow$
1926 \begin_inset Formula $\downarrow\downarrow$
1934 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
1937 \begin_layout Plain Layout
1938 \begin_inset Formula $\raisebox{8mm}{}\dfrac{e^{\frac{1}{2}}}{3}\raisebox{-4mm}{}$
1954 \begin_layout Standard
1955 \begin_inset VSpace bigskip
1959 \begin_inset Newpage newpage
1962 For nested fractions the command
1969 \begin_inset Index idx
1972 \begin_layout Plain Layout
1982 \begin_inset VSpace -3mm
1988 \begin_layout Standard
1989 \begin_inset Formula
1991 \textrm{created with \textbf{\textbackslash frac}} & & \textrm{created with \textbf{\textbackslash cfrac}}\\
1992 \frac{A}{B+\frac{C+\frac{E}{F}}{D}} & & \cfrac{A}{B+\cfrac{C+\cfrac{E}{F}}{D}}
2000 \begin_layout Standard
2001 The command for the example above is:
2004 \begin_layout Standard
2010 \begin_inset space \textvisiblespace{}
2014 \begin_inset Formula $\downarrow$
2020 \begin_inset space \textvisiblespace{}
2026 \begin_inset space \textvisiblespace{}
2030 \begin_inset Formula $\downarrow$
2034 \begin_inset Formula $\downarrow$
2040 \begin_layout Standard
2041 \begin_inset VSpace medskip
2047 \begin_layout Standard
2054 sets the fraction always in the size of a displayed formula, also when
2055 it is part of another fraction.
2058 \begin_layout Standard
2059 It is possible to specify the alignment of the numerator.
2066 is used to left align it, the command
2079 centers the numerator.
2080 These fractions demonstrate the different alignments:
2083 \begin_layout Standard
2086 \begin_inset Formula
2088 \cfrac[l]{A}{B+C}\,,\,\cfrac{A}{B+C}\,,\,\cfrac[r]{A}{B+C}
2096 \begin_layout Standard
2097 \begin_inset Note Greyedout
2100 \begin_layout Plain Layout
2117 are no real LaTeX commands but represent the command
2121 cfrac[alignment]{numerator}{denominator}
2124 Therefore you cannot use them in TeX code.
2132 \begin_layout Standard
2133 \begin_inset VSpace medskip
2136 It is often advantageous to combine
2149 \begin_inset Formula
2151 \cfrac{A}{B+\cfrac{C+\frac{E}{F}}{D}}
2159 \begin_layout Standard
2160 For inline fractions with a sloped fraction stroke you can use the command
2168 \begin_inset Index idx
2171 \begin_layout Plain Layout
2180 \begin_inset Formula $\nicefrac{5}{31}$
2190 \begin_inset Index idx
2193 \begin_layout Plain Layout
2202 \begin_inset Formula $\unitfrac{5}{31}$
2205 There is furthermore the command
2211 that offers to write a fraction in combination with a number:
2212 \begin_inset Formula $\unitfrac[2]{1}{3}$
2218 \begin_layout Standard
2219 \begin_inset Note Greyedout
2222 \begin_layout Plain Layout
2233 is not a real LaTeX command but the command
2234 \begin_inset Newline newline
2241 unitfrac[number]{numerator}{denominator}
2244 Therefore you cannot use it in TeX code.
2252 \begin_layout Standard
2253 How to define own fractions where the fraction stroke can be changed, is
2255 \begin_inset CommandInset ref
2257 reference "sub:Self-defined-Fractions"
2264 \begin_layout Standard
2265 Multiline fractions are explained in
2266 \begin_inset CommandInset ref
2268 reference "sub:Multiline-Fractions"
2275 \begin_layout Subsection
2277 \begin_inset Index idx
2280 \begin_layout Plain Layout
2289 \begin_layout Standard
2290 Square roots are created with
2297 \begin_inset Index idx
2300 \begin_layout Plain Layout
2308 or the math toolbar button
2311 arg "math-insert \\sqrt"
2314 , all other roots with the command
2321 \begin_inset Index idx
2324 \begin_layout Plain Layout
2332 or with the math toolbar button
2335 arg "math-insert \\root"
2341 \begin_layout Standard
2343 \begin_inset Tabular
2344 <lyxtabular version="3" rows="3" columns="2">
2345 <features rotate="0" tabularvalignment="middle">
2346 <column alignment="center" valignment="top" width="0pt">
2347 <column alignment="center" valignment="top" width="0pt">
2349 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
2352 \begin_layout Plain Layout
2358 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
2361 \begin_layout Plain Layout
2363 \begin_inset Note Note
2366 \begin_layout Plain Layout
2373 is only used as spacer.
2385 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
2388 \begin_layout Plain Layout
2392 \begin_inset space \textvisiblespace{}
2400 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
2403 \begin_layout Plain Layout
2404 \begin_inset Formula $\raisebox{4.5mm}{}\sqrt{A-B}$
2414 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
2417 \begin_layout Plain Layout
2421 \begin_inset space \textvisiblespace{}
2425 \begin_inset Formula $\downarrow$
2433 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
2436 \begin_layout Plain Layout
2437 \begin_inset Formula $\raisebox{4.5mm}{}\sqrt[3]{A-B}$
2453 \begin_layout Standard
2454 A square root can also be created with
2460 when the root index field is left empty.
2463 \begin_layout Standard
2464 With certain indices the distance to the root is too small, like in this
2466 \begin_inset Formula $\sqrt[\beta]{B}$
2470 \begin_inset Newline newline
2474 \begin_inset Formula $\beta$
2478 To avoid this, the commands
2485 \begin_inset Index idx
2488 \begin_layout Plain Layout
2503 \begin_inset Index idx
2506 \begin_layout Plain Layout
2514 are used with the following scheme:
2517 \begin_layout Standard
2531 \begin_layout Standard
2532 Distance is the number of Big Points (unit bp;
2533 \begin_inset Formula $\mathrm{72\, bp=1\, inch}$
2536 ), that the index should be moved to the left or top, resp..
2537 The commands are written to the index.
2538 This way the command
2539 \begin_inset Newline newline
2549 \begin_inset Formula $\to$
2555 \begin_inset Formula $\to$
2561 \begin_inset space \textvisiblespace{}
2565 \begin_inset Formula $\to$
2569 \begin_inset Newline newline
2574 produces a correct typeset formula:
2575 \begin_inset Formula $\sqrt[\leftroot{-1}\uproot{2}\beta]{B}$
2581 \begin_layout Subsection
2582 Binomial Coefficients
2583 \begin_inset Index idx
2586 \begin_layout Plain Layout
2587 Binomial coefficients
2595 \begin_layout Standard
2596 Binomial coefficients are inserted with the command
2603 \begin_inset Index idx
2606 \begin_layout Plain Layout
2614 or with the submenu of the math toolbar button
2617 arg "math-insert \\frac-square"
2633 there are the commands
2640 \begin_inset Index idx
2643 \begin_layout Plain Layout
2658 \begin_inset Index idx
2661 \begin_layout Plain Layout
2670 For other brackets around binomial coeficients there are the commands
2677 \begin_inset Index idx
2680 \begin_layout Plain Layout
2695 \begin_inset Index idx
2698 \begin_layout Plain Layout
2709 \begin_layout Standard
2711 \begin_inset Tabular
2712 <lyxtabular version="3" rows="6" columns="2">
2713 <features rotate="0" tabularvalignment="middle">
2714 <column alignment="center" valignment="top" width="0pt">
2715 <column alignment="center" valignment="top" width="0pt">
2717 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
2720 \begin_layout Plain Layout
2726 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
2729 \begin_layout Plain Layout
2731 \begin_inset Note Note
2734 \begin_layout Plain Layout
2741 is only used as spacer.
2753 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
2756 \begin_layout Plain Layout
2760 \begin_inset space \textvisiblespace{}
2764 \begin_inset Formula $\downarrow$
2772 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
2775 \begin_layout Plain Layout
2776 \begin_inset Formula $\raisebox{5mm}{}\binom{A}{B}\raisebox{-2.5mm}{}$
2786 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
2789 \begin_layout Plain Layout
2793 \begin_inset space \textvisiblespace{}
2797 \begin_inset Formula $\downarrow$
2805 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
2808 \begin_layout Plain Layout
2809 \begin_inset Formula $\raisebox{5mm}{}\dbinom{A}{B}\raisebox{-2.5mm}{}$
2819 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
2822 \begin_layout Plain Layout
2826 \begin_inset space \textvisiblespace{}
2830 \begin_inset Formula $\downarrow$
2838 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
2841 \begin_layout Plain Layout
2842 \begin_inset Formula $\raisebox{5mm}{}\tbinom{A}{B}\raisebox{-2.5mm}{}$
2852 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
2855 \begin_layout Plain Layout
2859 \begin_inset space \textvisiblespace{}
2863 \begin_inset Formula $\downarrow$
2871 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
2874 \begin_layout Plain Layout
2875 \begin_inset Formula $\raisebox{5mm}{}{A \brack B}\raisebox{-2.5mm}{}$
2885 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
2888 \begin_layout Plain Layout
2892 \begin_inset space \textvisiblespace{}
2896 \begin_inset Formula $\downarrow$
2904 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
2907 \begin_layout Plain Layout
2908 \begin_inset Formula $\raisebox{5mm}{}{A \brace B}\raisebox{-2.5mm}{}$
2924 \begin_layout Subsection
2925 Case Differentiations
2926 \begin_inset Index idx
2929 \begin_layout Plain Layout
2930 Case differentiations
2938 \begin_layout Standard
2940 \begin_inset Tabular
2941 <lyxtabular version="3" rows="3" columns="2">
2942 <features rotate="0" tabularvalignment="middle">
2943 <column alignment="center" valignment="top" width="0pt">
2944 <column alignment="center" valignment="top" width="0pt">
2946 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
2949 \begin_layout Plain Layout
2955 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
2958 \begin_layout Plain Layout
2966 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
2969 \begin_layout Plain Layout
2973 \begin_inset space \textvisiblespace{}
2977 \begin_inset Formula $\to$
2981 \begin_inset Index idx
2984 \begin_layout Plain Layout
2997 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
3000 \begin_layout Plain Layout
3001 \begin_inset Formula $\begin{cases}
3012 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
3015 \begin_layout Plain Layout
3019 \begin_inset space \textvisiblespace{}
3025 arg "newline-insert newline"
3033 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
3036 \begin_layout Plain Layout
3037 \begin_inset Formula $\begin{cases}
3038 A & \textrm{for }x>0\\
3039 B & \textrm{for }x=0
3056 \begin_layout Standard
3063 or pressing the math toolbar button
3066 arg "math-insert \\cases"
3069 you can create new lines with the shortcut
3072 arg "newline-insert newline"
3075 or the table toolbar button
3078 arg "inset-modify tabular append-row"
3084 \begin_layout Standard
3091 is also available via the menu
3093 Insert\SpecialChar \menuseparator
3094 Math\SpecialChar \menuseparator
3100 \begin_layout Subsection
3102 \begin_inset Index idx
3105 \begin_layout Plain Layout
3114 \begin_layout Standard
3122 \begin_inset Index idx
3125 \begin_layout Plain Layout
3133 every character can be displayed canceled.
3134 The characters are quasi accentuated by a slash.
3137 \begin_layout Standard
3139 \begin_inset Tabular
3140 <lyxtabular version="3" rows="4" columns="2">
3141 <features rotate="0" tabularvalignment="middle">
3142 <column alignment="center" valignment="top" width="0pt">
3143 <column alignment="center" valignment="top" width="0pt">
3145 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
3148 \begin_layout Plain Layout
3154 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
3157 \begin_layout Plain Layout
3165 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
3168 \begin_layout Plain Layout
3176 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
3179 \begin_layout Plain Layout
3180 \begin_inset Formula $\not=$
3190 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
3193 \begin_layout Plain Layout
3203 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
3206 \begin_layout Plain Layout
3207 \begin_inset Formula $\not\le$
3217 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
3220 \begin_layout Plain Layout
3230 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
3233 \begin_layout Plain Layout
3234 \begin_inset Formula $\not\parallel$
3250 \begin_layout Standard
3251 The last example shows that not all negations look good.
3252 Therefore there are special commands for some negations (see
3253 \begin_inset CommandInset ref
3255 reference "sub:Mathematical-Symbols"
3260 \begin_inset CommandInset ref
3262 reference "sec:Relations"
3269 \begin_layout Subsection
3271 \begin_inset CommandInset label
3273 name "sub:Placeholders"
3278 \begin_inset Index idx
3281 \begin_layout Plain Layout
3288 \begin_inset Index idx
3291 \begin_layout Plain Layout
3292 Chemical characters ! Isotopes
3298 \begin_inset Index idx
3301 \begin_layout Plain Layout
3306 \begin_layout Plain Layout
3317 \begin_layout Plain Layout
3332 \begin_layout Standard
3334 \begin_inset space \thinspace{}
3338 \begin_inset space \space{}
3345 \begin_layout Plain Layout
3346 Typesetting isotopes and chemical symbols is described in
3347 \begin_inset CommandInset ref
3349 reference "sub:Chemical-Symbols-and"
3358 the following problem occurs:
3361 \begin_layout Standard
3363 \begin_inset Tabular
3364 <lyxtabular version="3" rows="2" columns="2">
3365 <features rotate="0" tabularvalignment="middle">
3366 <column alignment="center" valignment="top" width="0pt">
3367 <column alignment="center" valignment="top" width="0pt">
3369 <cell alignment="center" valignment="top" usebox="none">
3372 \begin_layout Plain Layout
3373 Indices created with sub- and superscripts:
3378 <cell alignment="center" valignment="top" usebox="none">
3381 \begin_layout Plain Layout
3382 \begin_inset Formula $_{9}^{19}\mathrm{F}\raisebox{-3mm}{}$
3392 <cell alignment="center" valignment="top" usebox="none">
3395 \begin_layout Plain Layout
3401 <cell alignment="center" valignment="top" usebox="none">
3404 \begin_layout Plain Layout
3405 \begin_inset Formula $_{\phantom{1}9}^{19}\mathrm{F}$
3419 \begin_inset Note Note
3422 \begin_layout Plain Layout
3429 is only used as spacer.
3437 \begin_layout Standard
3438 The shorter index is by default placed below or above the first character
3439 of the longer index.
3440 To avoid this there is the command
3447 \begin_inset Index idx
3450 \begin_layout Plain Layout
3458 or the math toolbar button
3459 \begin_inset space \thinspace{}
3466 \begin_layout Plain Layout
3467 can be found in the submenu of the toolbar button
3470 arg "math-insert \\space"
3479 \begin_inset Graphics
3480 filename ../images/math/phantom.png
3485 that creates one or more phantom characters.
3492 a small blue box appears that is superposed with two red arrows.
3493 The arrows indicate that the complete width and height of the box content
3494 will be created as placeholder.
3495 Phantom characters are accordingly placeholders with the size of the characters.
3498 \begin_layout Standard
3500 \begin_inset Tabular
3501 <lyxtabular version="3" rows="4" columns="2">
3502 <features rotate="0" tabularvalignment="middle">
3503 <column alignment="center" valignment="top">
3504 <column alignment="center" valignment="top">
3506 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
3509 \begin_layout Plain Layout
3515 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
3518 \begin_layout Plain Layout
3520 \begin_inset Note Note
3523 \begin_layout Plain Layout
3530 is only used as spacer.
3542 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
3545 \begin_layout Plain Layout
3547 \begin_inset space \textvisiblespace{}
3553 \begin_inset space \textvisiblespace{}
3557 \begin_inset Formula $\to$
3561 \begin_inset space \textvisiblespace{}
3569 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
3572 \begin_layout Plain Layout
3573 \begin_inset Formula $\raisebox{4.5mm}{}{}_{\phantom{1}9}^{19}\mathrm{F}\raisebox{-2.5mm}{}$
3583 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
3586 \begin_layout Plain Layout
3588 \begin_inset space \textvisiblespace{}
3594 \begin_inset space \textvisiblespace{}
3598 \begin_inset Formula $\to$
3602 \begin_inset space \textvisiblespace{}
3610 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
3613 \begin_layout Plain Layout
3614 \begin_inset Formula $\raisebox{4.5mm}{}{}_{\phantom{23}9}^{235}\mathrm{F}\raisebox{-2.5mm}{}$
3624 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
3627 \begin_layout Plain Layout
3631 \begin_inset space \textvisiblespace{}
3637 \begin_inset space \textvisiblespace{}
3641 \begin_inset Formula $\to$
3645 \begin_inset space \textvisiblespace{}
3653 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
3656 \begin_layout Plain Layout
3657 \begin_inset Formula $\raisebox{4.5mm}{}\Lambda_{MMt}^{\phantom{ii}t}\raisebox{-2.5mm}{}$
3673 \begin_layout Standard
3674 Furthermore there are the commands
3681 \begin_inset Index idx
3684 \begin_layout Plain Layout
3693 \begin_inset space ~
3697 \begin_inset Graphics
3698 filename ../images/math/vphantom.png
3710 \begin_inset Index idx
3713 \begin_layout Plain Layout
3722 \begin_inset space ~
3726 \begin_inset Graphics
3727 filename ../images/math/hphantom.png
3739 creates only space for the maximal height of the characters in the box
3740 but not for its width.
3747 creates only space for the width of the box content.
3748 Therefore the boxes of both commands have only one red arrow.
3751 \begin_layout Standard
3752 For example the command
3757 \begin_inset space \textvisiblespace{}
3764 creates space for the height of the integral sign,
3768 \begin_layout Plain Layout
3775 creates an integral sign, see
3776 \begin_inset CommandInset ref
3778 reference "sub:Big-Operators"
3787 because this is the larger character.
3788 An example application is in
3789 \begin_inset CommandInset ref
3791 reference "sub:Multiline-Brackets"
3798 \begin_layout Standard
3799 Placeholders can also be used for text when they are inserted via the menu
3802 Insert\SpecialChar \menuseparator
3803 Formatting\SpecialChar \menuseparator
3809 \begin_layout Standard
3811 \begin_inset Newline newline
3815 \begin_inset Phantom Phantom
3818 \begin_layout Plain Layout
3827 \begin_layout Subsection
3829 \begin_inset Index idx
3832 \begin_layout Plain Layout
3839 \begin_inset Index idx
3842 \begin_layout Plain Layout
3843 Formula ! underlined
3851 \begin_layout Standard
3853 \begin_inset Tabular
3854 <lyxtabular version="3" rows="4" columns="2">
3855 <features rotate="0" tabularvalignment="middle">
3856 <column alignment="center" valignment="top" width="0pt">
3857 <column alignment="center" valignment="top" width="0pt">
3859 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
3862 \begin_layout Plain Layout
3868 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
3871 \begin_layout Plain Layout
3873 \begin_inset Note Note
3876 \begin_layout Plain Layout
3883 is only used as spacer.
3895 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
3898 \begin_layout Plain Layout
3902 \begin_inset space \textvisiblespace{}
3906 \begin_inset Index idx
3909 \begin_layout Plain Layout
3922 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
3925 \begin_layout Plain Layout
3926 \begin_inset Formula $\raisebox{5mm}{}\overline{A+B}$
3936 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
3939 \begin_layout Plain Layout
3943 \begin_inset space \textvisiblespace{}
3947 \begin_inset Index idx
3950 \begin_layout Plain Layout
3963 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
3966 \begin_layout Plain Layout
3967 \begin_inset Formula $\underline{A+B}\raisebox{-2.5mm}{}$
3977 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
3980 \begin_layout Plain Layout
3984 \begin_inset space \textvisiblespace{}
3990 \begin_inset space \textvisiblespace{}
3998 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
4001 \begin_layout Plain Layout
4002 \begin_inset Formula $\raisebox{5mm}{}\overline{\underline{A+B}}\raisebox{-2.5mm}{}$
4018 \begin_layout Standard
4019 In the last example it doesn't matter if first
4034 \begin_layout Standard
4035 To double underline use
4044 \begin_layout Standard
4045 It is possible to place up to 6 lines above or below characters.
4048 \begin_layout Standard
4049 \begin_inset VSpace bigskip
4052 Custom lines can be created using the command
4059 \begin_inset Index idx
4062 \begin_layout Plain Layout
4070 which has the following scheme:
4073 \begin_layout Standard
4078 rule[vertical offset]{length}{thickness}
4081 \begin_layout Standard
4082 The optional vertical offset shifts the line upwards (or downwards, when
4083 the value is negative).
4085 \begin_inset CommandInset ref
4087 reference "tab:Available-units"
4091 can be used for the values.
4092 Here are two example lines created with the commands
4093 \begin_inset Newline newline
4100 rule[-2ex]{3cm}{2pt}
4111 \begin_layout Standard
4113 \begin_inset Formula $\rule[-2ex]{3cm}{2pt}\rule{2cm}{1pt}$
4119 \begin_layout Standard
4126 can also be used for text when a line is inserted via the menu
4128 Insert\SpecialChar \menuseparator
4129 Formatting\SpecialChar \menuseparator
4131 \begin_inset space ~
4139 \begin_layout Standard
4141 \begin_inset CommandInset line
4152 \begin_layout Subsection
4154 \begin_inset CommandInset label
4161 \begin_inset Index idx
4164 \begin_layout Plain Layout
4173 \begin_layout Standard
4174 There are different types of ellipses available.
4178 \begin_layout Plain Layout
4179 In the math toolbar in the submenu of the button
4182 arg "math-insert \\ldots"
4190 For listings dots at the baseline are used (
4197 \begin_inset Index idx
4200 \begin_layout Plain Layout
4208 ), while for operations dots are needed that are on the same height as the
4216 \begin_inset Index idx
4219 \begin_layout Plain Layout
4228 When using the command
4235 \begin_inset Index idx
4238 \begin_layout Plain Layout
4246 , LaTeX decides on the basis of the next character what type is used.
4249 \begin_layout Standard
4251 \begin_inset Tabular
4252 <lyxtabular version="3" rows="9" columns="2">
4253 <features rotate="0" tabularvalignment="middle">
4254 <column alignment="center" valignment="top" width="0pt">
4255 <column alignment="center" valignment="top" width="0pt">
4257 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
4260 \begin_layout Plain Layout
4266 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
4269 \begin_layout Plain Layout
4277 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
4280 \begin_layout Plain Layout
4282 \begin_inset space \textvisiblespace{}
4288 \begin_inset space \textvisiblespace{}
4296 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
4299 \begin_layout Plain Layout
4300 \begin_inset Formula $A_{1},\dots,A_{n}$
4310 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
4313 \begin_layout Plain Layout
4315 \begin_inset space \textvisiblespace{}
4321 \begin_inset space \textvisiblespace{}
4329 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
4332 \begin_layout Plain Layout
4333 \begin_inset Formula $A_{1}+\dots+A_{n}$
4343 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
4346 \begin_layout Plain Layout
4348 \begin_inset space \textvisiblespace{}
4354 \begin_inset space \textvisiblespace{}
4362 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
4365 \begin_layout Plain Layout
4366 \begin_inset Formula $A_{1},\ldots,A_{n}$
4376 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
4379 \begin_layout Plain Layout
4381 \begin_inset space \textvisiblespace{}
4387 \begin_inset space \textvisiblespace{}
4395 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
4398 \begin_layout Plain Layout
4399 \begin_inset Formula $A_{1}+\cdots+A_{n}$
4409 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
4412 \begin_layout Plain Layout
4420 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
4423 \begin_layout Plain Layout
4424 \begin_inset Formula $\vdots$
4434 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
4437 \begin_layout Plain Layout
4445 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
4448 \begin_layout Plain Layout
4449 \begin_inset Formula $\ddots$
4459 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
4462 \begin_layout Plain Layout
4470 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
4473 \begin_layout Plain Layout
4474 \begin_inset Formula $\iddots$
4484 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
4487 \begin_layout Plain Layout
4489 \begin_inset space \thinspace{}
4492 matrix with the different dots
4497 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
4500 \begin_layout Plain Layout
4501 \begin_inset Formula $\begin{array}{ccc}
4502 A_{11} & \cdots & A_{1m}\\
4503 \vdots & \ddots & \vdots\\
4504 A_{n1} & \cdots & A_{nm}
4521 \begin_layout Standard
4522 The ellipses available in menu
4524 Insert\SpecialChar \menuseparator
4526 \begin_inset space ~
4540 \begin_layout Standard
4541 \begin_inset VSpace medskip
4550 , one of the options
4552 Use mathdots package (automatically)
4554 must be set in the document settings under
4557 \begin_inset space ~
4563 \begin_inset Newline newline
4568 Use mathdots package
4570 will improve the appearance of all dots in the documents if their font
4571 style or size is not the default.
4574 \begin_layout Standard
4575 \begin_inset VSpace medskip
4578 Specially for matrices there are ellipses that span over several columns.
4579 They are created with the command
4586 \begin_inset Index idx
4589 \begin_layout Plain Layout
4597 , that has the following scheme:
4600 \begin_layout Standard
4605 hdotsfor[distance]{number of columns}
4608 \begin_layout Standard
4609 The number of columns specifies how many columns should be spanned.
4610 Distance is a factor for the distance between the dots.
4613 \begin_layout Standard
4614 In the following matrix the command
4620 was inserted in the first box of the second line, to get an ellipsis with
4621 a dot distance twice as long as with the command
4628 \begin_inset Formula
4630 \left(\begin{array}{cccc}
4639 Note that the matrix fields that should be spanned must be empty, otherwise
4640 you get LaTeX-errors.
4643 \begin_layout Standard
4644 \begin_inset VSpace bigskip
4647 Furthermore you can fill with the command
4654 \begin_inset Index idx
4657 \begin_layout Plain Layout
4665 the rest of a line with dots.
4666 The effect of these commands is the same as with
4673 \begin_inset CommandInset ref
4675 reference "sub:Variable-Space"
4682 \begin_layout Standard
4683 For example the command
4688 \begin_inset space \textvisiblespace{}
4696 \begin_layout Standard
4697 \begin_inset Formula $A\dotfill B$
4703 \begin_layout Standard
4710 there is for a line the command
4717 \begin_inset Index idx
4720 \begin_layout Plain Layout
4731 \begin_layout Standard
4732 \begin_inset Formula $A\hrulefill B$
4738 \begin_layout Standard
4739 To use the commands for text, they have to be inserted in TeX-mode.
4742 \begin_layout Section
4744 \begin_inset CommandInset label
4751 \begin_inset Index idx
4754 \begin_layout Plain Layout
4763 \begin_layout Standard
4764 Matrices can be inserted via the math toolbar button
4767 arg "dialog-show mathmatrix"
4772 Insert\SpecialChar \menuseparator
4773 Math\SpecialChar \menuseparator
4777 In the matrix dialog you can specify the number of columns and rows, the
4778 alignment and the decoration.
4779 The vertical alignment is only of importance for matrices in inline formulas:
4782 \begin_layout Standard
4783 The first matrix is top
4784 \begin_inset Formula $\begin{array}[t]{cccc}
4792 \begin_inset Formula $\begin{array}{cccc}
4799 and the third bottom
4800 \begin_inset Formula $\begin{array}[b]{cccc}
4810 \begin_layout Standard
4811 The horizontal alignment specifies how the column entries should be aligned.
4812 It is set by entering a letter for every column.
4817 denotes left aligned,
4826 To create for example a 4
4831 \begin_inset space ~
4834 matrix where the first column is left aligned, the second and third are
4835 centered and the last one is right aligned, one enters for the horizontal
4841 Normally in a matrix all columns are centered, therefore the default for
4849 \begin_layout Standard
4850 Horizontal alignment:
4853 \begin_layout Standard
4859 \begin_inset Formula $\begin{array}{lll}
4871 \begin_inset Formula $\begin{array}{ccc}
4883 \begin_inset Formula $\begin{array}{rrr}
4893 \begin_layout Standard
4894 To add or delete rows and columns subsequently, the math toolbar buttons
4898 arg "inset-modify tabular append-row"
4904 arg "inset-modify tabular delete-row"
4908 \begin_inset space \thinspace{}
4913 Edit\SpecialChar \menuseparator
4917 New rows can also be created with
4920 arg "newline-insert newline"
4926 \begin_layout Standard
4927 \begin_inset VSpace bigskip
4934 adds parentheses in the selected style around the matrix.
4935 Alternatively, parentheses can can either be created with the commands
4943 \begin_inset Index idx
4946 \begin_layout Plain Layout
4961 \begin_inset Index idx
4964 \begin_layout Plain Layout
4975 \begin_inset space ~
4981 \begin_inset CommandInset ref
4983 reference "sub:Automatic-Bracket-Size"
4987 , or by using the following commands:
4988 \begin_inset VSpace medskip
4994 \begin_layout Standard
4995 \begin_inset space \hfill{}
4999 \begin_inset Tabular
5000 <lyxtabular version="3" rows="4" columns="2">
5001 <features rotate="0" tabularvalignment="middle">
5002 <column alignment="center" valignment="top">
5003 <column alignment="center" valignment="top">
5005 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
5008 \begin_layout Plain Layout
5014 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
5017 \begin_layout Plain Layout
5019 \begin_inset Note Note
5022 \begin_layout Plain Layout
5029 is only used as spacer.
5041 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
5044 \begin_layout Plain Layout
5048 \begin_inset space \textvisiblespace{}
5056 \begin_inset space \thinspace{}
5064 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
5067 \begin_layout Plain Layout
5068 \begin_inset Formula $\raisebox{7.5mm}{}\begin{bmatrix}\begin{array}{cc}
5069 0 & \textrm{-}\mathrm{i}\\
5071 \end{array}\end{bmatrix}\raisebox{-5.3mm}{}$
5081 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
5084 \begin_layout Plain Layout
5088 \begin_inset space \textvisiblespace{}
5096 \begin_inset space \thinspace{}
5104 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
5107 \begin_layout Plain Layout
5108 \begin_inset Formula $\raisebox{7.5mm}{}\begin{Bmatrix}\begin{array}{cc}
5109 0 & \textrm{-}\mathrm{i}\\
5111 \end{array}\end{Bmatrix}\raisebox{-5.3mm}{}$
5121 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
5124 \begin_layout Plain Layout
5128 \begin_inset space \textvisiblespace{}
5136 \begin_inset space \thinspace{}
5144 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
5147 \begin_layout Plain Layout
5148 \begin_inset Formula $\raisebox{7.5mm}{}\begin{pmatrix}\begin{array}{cc}
5149 0 & \textrm{-}\mathrm{i}\\
5151 \end{array}\end{pmatrix}\raisebox{-5.3mm}{}$
5165 \begin_inset space \hfill{}
5169 \begin_inset Tabular
5170 <lyxtabular version="3" rows="4" columns="2">
5171 <features rotate="0" tabularvalignment="middle">
5172 <column alignment="center" valignment="top">
5173 <column alignment="center" valignment="top">
5175 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
5178 \begin_layout Plain Layout
5184 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
5187 \begin_layout Plain Layout
5195 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
5198 \begin_layout Plain Layout
5202 \begin_inset space \textvisiblespace{}
5210 \begin_inset space \thinspace{}
5218 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
5221 \begin_layout Plain Layout
5222 \begin_inset Formula $\raisebox{7.5mm}{}\begin{vmatrix}\begin{array}{cc}
5223 0 & \textrm{-}\mathrm{i}\\
5225 \end{array}\end{vmatrix}\raisebox{-5.3mm}{}$
5235 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
5238 \begin_layout Plain Layout
5242 \begin_inset space \textvisiblespace{}
5250 \begin_inset space \thinspace{}
5258 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
5261 \begin_layout Plain Layout
5262 \begin_inset Formula $\raisebox{7.5mm}{}\begin{Vmatrix}\begin{array}{cc}
5263 0 & \textrm{-}\mathrm{i}\\
5265 \end{array}\end{Vmatrix}\raisebox{-5.3mm}{}$
5275 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
5278 \begin_layout Plain Layout
5282 \begin_inset space \textvisiblespace{}
5290 \begin_inset space \thinspace{}
5298 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
5301 \begin_layout Plain Layout
5302 \begin_inset Formula $\raisebox{7.5mm}{}\begin{matrix}\begin{array}{cc}
5303 0 & \textrm{-}\mathrm{i}\\
5305 \end{array}\end{matrix}\raisebox{-5.3mm}{}$
5319 \begin_inset space \hfill{}
5325 \begin_layout Standard
5326 \begin_inset VSpace medskip
5330 \begin_inset space \thinspace{}
5334 \begin_inset space \space{}
5343 is inserted, a blue box appears between two vertical lines where the matrix
5345 \begin_inset Newline newline
5348 Note that decorated matrices ignore the vertical alignment.
5351 \begin_layout Standard
5352 \begin_inset VSpace bigskip
5355 As all multiline formulas are matrices, the length
5362 \begin_inset Index idx
5365 \begin_layout Plain Layout
5373 that is described in
5374 \begin_inset CommandInset ref
5376 reference "sub:Column-Separation"
5380 can also be used to change the column separation of matrices.
5383 \begin_layout Standard
5384 To change the row separation, the command
5391 \begin_inset Index idx
5394 \begin_layout Plain Layout
5403 It is used as follows:
5406 \begin_layout Standard
5413 arraystretch}{stretch factor}
5414 \begin_inset Index idx
5417 \begin_layout Plain Layout
5428 \begin_layout Standard
5435 assigns the stretch factor to the predefined command
5443 \begin_inset space \thinspace{}
5447 \begin_inset space \space{}
5450 the row separation, use the factor 2.
5451 This is then used for all following matrices.
5452 To go back to the original separation, assign the factor 1 to
5461 \begin_layout Standard
5462 To set matrices into a text line, the command
5469 \begin_inset Index idx
5472 \begin_layout Plain Layout
5481 When it is inserted a blue box with two dashed lines appears.
5482 In this box the matrix is inserted.
5485 \begin_layout Standard
5487 \begin_inset Formula $\left(\begin{smallmatrix}A & B\\
5489 \end{smallmatrix}\right)$
5495 \begin_layout Section
5496 Brackets and Delimiters
5497 \begin_inset Index idx
5500 \begin_layout Plain Layout
5507 \begin_inset Index idx
5510 \begin_layout Plain Layout
5519 \begin_layout Subsection
5520 Vertical Brackets and Delimiters
5521 \begin_inset Index idx
5524 \begin_layout Plain Layout
5533 \begin_layout Standard
5534 \begin_inset space \hfill{}
5538 \begin_inset Tabular
5539 <lyxtabular version="3" rows="9" columns="2">
5540 <features rotate="0" tabularvalignment="middle">
5541 <column alignment="center" valignment="top" width="0pt">
5542 <column alignment="center" valignment="top" width="0pt">
5544 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
5547 \begin_layout Plain Layout
5553 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
5556 \begin_layout Plain Layout
5564 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
5567 \begin_layout Plain Layout
5573 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
5576 \begin_layout Plain Layout
5577 \begin_inset Formula $($
5587 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
5590 \begin_layout Plain Layout
5596 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
5599 \begin_layout Plain Layout
5600 \begin_inset Formula $\{$
5610 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
5613 \begin_layout Plain Layout
5619 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
5622 \begin_layout Plain Layout
5623 \begin_inset Formula $[$
5633 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
5636 \begin_layout Plain Layout
5644 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
5647 \begin_layout Plain Layout
5648 \begin_inset Formula $\langle$
5658 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
5661 \begin_layout Plain Layout
5669 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
5672 \begin_layout Plain Layout
5673 \begin_inset Formula $\lceil$
5683 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
5686 \begin_layout Plain Layout
5694 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
5697 \begin_layout Plain Layout
5698 \begin_inset Formula $\lfloor$
5708 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
5711 \begin_layout Plain Layout
5717 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
5720 \begin_layout Plain Layout
5721 \begin_inset Formula $/$
5731 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
5734 \begin_layout Plain Layout
5740 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
5743 \begin_layout Plain Layout
5744 \begin_inset Formula $|$
5758 \begin_inset space \hfill{}
5762 \begin_inset Tabular
5763 <lyxtabular version="3" rows="9" columns="2">
5764 <features rotate="0" tabularvalignment="middle">
5765 <column alignment="center" valignment="top" width="0pt">
5766 <column alignment="center" valignment="top" width="0pt">
5768 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
5771 \begin_layout Plain Layout
5777 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
5780 \begin_layout Plain Layout
5788 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
5791 \begin_layout Plain Layout
5797 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
5800 \begin_layout Plain Layout
5801 \begin_inset Formula $)$
5811 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
5814 \begin_layout Plain Layout
5820 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
5823 \begin_layout Plain Layout
5824 \begin_inset Formula $\}$
5834 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
5837 \begin_layout Plain Layout
5843 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
5846 \begin_layout Plain Layout
5847 \begin_inset Formula $]$
5857 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
5860 \begin_layout Plain Layout
5868 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
5871 \begin_layout Plain Layout
5872 \begin_inset Formula $\rangle$
5882 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
5885 \begin_layout Plain Layout
5893 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
5896 \begin_layout Plain Layout
5897 \begin_inset Formula $\rceil$
5907 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
5910 \begin_layout Plain Layout
5918 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
5921 \begin_layout Plain Layout
5922 \begin_inset Formula $\rfloor$
5932 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
5935 \begin_layout Plain Layout
5945 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
5948 \begin_layout Plain Layout
5949 \begin_inset Formula $\backslash$
5959 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
5962 \begin_layout Plain Layout
5970 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
5973 \begin_layout Plain Layout
5974 \begin_inset Formula $\|$
5988 \begin_inset space \hfill{}
5994 \begin_layout Standard
5997 \begin_inset Note Greyedout
6000 \begin_layout Plain Layout
6005 In TeX-mode the command
6012 \begin_inset Index idx
6015 \begin_layout Plain Layout
6023 must be used for the backslash, because the command
6031 produces a line break there.
6039 \begin_layout Standard
6040 For all characters listed above the size can be adjusted with the commands
6041 described in the following two subsections.
6042 When using these commands, the characters < and > can directly be used
6043 instead of the commands
6058 \begin_layout Subsubsection
6060 \begin_inset CommandInset label
6062 name "sub:Manual-Bracket-Size"
6067 \begin_inset Index idx
6070 \begin_layout Plain Layout
6071 Bracket size ! manual
6079 \begin_layout Standard
6080 The bracket size can be specified manually by the LaTeX-commands
6087 \begin_inset Index idx
6090 \begin_layout Plain Layout
6123 denotes the smallest and
6129 the largest bracket size.
6132 \begin_layout Standard
6133 These commands are used to emphasize levels of brackets:
6136 \begin_layout Standard
6138 \begin_inset Tabular
6139 <lyxtabular version="3" rows="2" columns="2">
6140 <features rotate="0" tabularvalignment="middle">
6141 <column alignment="center" valignment="top" width="0pt">
6142 <column alignment="center" valignment="top" width="0pt">
6144 <cell alignment="center" valignment="top" usebox="none">
6147 \begin_layout Plain Layout
6148 all brackets in the same size:
6153 <cell alignment="center" valignment="top" usebox="none">
6156 \begin_layout Plain Layout
6157 \begin_inset Formula $((A+B)(A-B))^{C}\raisebox{-4mm}{}$
6167 <cell alignment="center" valignment="top" usebox="none">
6170 \begin_layout Plain Layout
6176 <cell alignment="center" valignment="top" usebox="none">
6179 \begin_layout Plain Layout
6180 \begin_inset Formula $\Big((A+B)(A-B)\Big)^{C}$
6194 \begin_inset Note Note
6197 \begin_layout Plain Layout
6204 is only used as spacer.
6212 \begin_layout Standard
6213 For the second formula the command
6220 \begin_inset space \textvisiblespace{}
6228 \begin_layout Standard
6229 Here is an overview about all bracket sizes:
6232 \begin_layout Standard
6249 \begin_inset space \textvisiblespace{}
6257 \begin_inset space \textvisiblespace{}
6261 \begin_inset space \textvisiblespace{}
6271 \begin_layout Standard
6273 \begin_inset Formula $\Bigg(\exp\bigg<\Big[\big\{\ln(3x)\big\}^{2}\sin(x)\Big]^{A}\bigg>\Bigg)^{0,5}$
6279 \begin_layout Standard
6286 -commands there is the variant
6293 \begin_inset Index idx
6296 \begin_layout Plain Layout
6304 that adds a bit more space between the bracket and its content, and the
6318 \begin_inset Index idx
6321 \begin_layout Plain Layout
6331 , that don't add additional space.
6336 at the end of the command
6342 is for a left bracket; for a right bracket this will be replaced by an
6348 A left or right bracket can each be an opening or closing bracket.
6351 \begin_layout Standard
6352 In the following table is a comparison of the variants:
6355 \begin_layout Standard
6357 \begin_inset Tabular
6358 <lyxtabular version="3" rows="5" columns="2">
6359 <features rotate="0" tabularvalignment="middle">
6360 <column alignment="center" valignment="middle">
6361 <column alignment="center" valignment="middle">
6363 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
6366 \begin_layout Plain Layout
6372 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
6375 \begin_layout Plain Layout
6377 \begin_inset Note Note
6380 \begin_layout Plain Layout
6387 is only used as spacer.
6399 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
6402 \begin_layout Plain Layout
6412 \begin_inset space \textvisiblespace{}
6422 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
6425 \begin_layout Plain Layout
6426 \begin_inset Formula $\raisebox{5.5mm}{}\Bigm(\bigm(\ln(3x)\bigm)^{2}\Bigm)\raisebox{-3.25mm}{}$
6436 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
6439 \begin_layout Plain Layout
6449 \begin_inset space \textvisiblespace{}
6459 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
6462 \begin_layout Plain Layout
6463 \begin_inset Formula $\raisebox{5.5mm}{}\Big(\big(\ln(3x)\big)^{2}\Big)\raisebox{-3.25mm}{}$
6473 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
6476 \begin_layout Plain Layout
6486 \begin_inset space \textvisiblespace{}
6496 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
6499 \begin_layout Plain Layout
6500 \begin_inset Formula $\raisebox{5.5mm}{}\Bigl(\bigl(\ln(3x)\bigr)^{2}\Bigr)\raisebox{-3.25mm}{}$
6510 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
6513 \begin_layout Plain Layout
6525 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
6528 \begin_layout Plain Layout
6529 \begin_inset Formula $\raisebox{4.5mm}{}\bigl)\ln(3x)\bigr(\raisebox{-2mm}{}$
6545 \begin_layout Subsubsection
6546 Automatic Bracket Size
6547 \begin_inset CommandInset label
6549 name "sub:Automatic-Bracket-Size"
6554 \begin_inset Index idx
6557 \begin_layout Plain Layout
6558 Bracket size ! automatic
6566 \begin_layout Standard
6567 Brackets with variable size can be inserted with the commands
6574 \begin_inset Index idx
6577 \begin_layout Plain Layout
6592 \begin_inset Index idx
6595 \begin_layout Plain Layout
6603 or via the math toolbar button
6606 arg "dialog-show mathdelimiter"
6622 the wanted bracket must be inserted.
6623 The bracket size will then automatically be calculated for the output.
6626 \begin_layout Standard
6628 normal bracket: The command
6635 \begin_inset space \textvisiblespace{}
6639 \begin_inset Formula $\downarrow$
6643 \begin_inset space \textvisiblespace{}
6649 \begin_inset Formula
6659 \begin_layout Standard
6661 multiline bracket: The command
6670 \begin_inset space \textvisiblespace{}
6674 \begin_inset Formula $\downarrow$
6678 \begin_inset space \textvisiblespace{}
6686 \begin_inset Formula
6688 \ln\left(\frac{A}{C}\right)
6696 \begin_layout Standard
6712 \begin_inset space ~
6718 This has the advantage that you can see in LyX immediately the real bracket
6719 size and that the matching right bracket will be created too.
6720 \begin_inset Newline newline
6723 The command for the last example would then be:
6734 \begin_inset space \textvisiblespace{}
6738 \begin_inset Formula $\downarrow$
6744 \begin_layout Standard
6745 To omit a left or right bracket, a dot is inserted for the omitted bracket.
6746 For example the command
6753 \begin_inset space \textvisiblespace{}
6757 \begin_inset Formula $\downarrow$
6761 \begin_inset space \textvisiblespace{}
6771 \begin_inset Formula
6773 \left.\frac{A}{B}\right\}
6792 will be converted by LyX to brackets in the right size when the document
6793 is reloaded and an omitted bracket will appear as dashed line.
6796 \begin_layout Standard
6797 \begin_inset VSpace bigskip
6800 Because all popular LaTeX-Distributions use eTeX, an extension to LaTeX,
6808 \begin_inset Index idx
6811 \begin_layout Plain Layout
6819 is additionally available for all brackets and limits.
6820 With this command the height of the following character is adapted to the
6821 one of the surrounding brackets, what is e.
6822 \begin_inset space \thinspace{}
6826 \begin_inset space \space{}
6829 needed for physical vectors:
6830 \begin_inset Formula
6832 \left\langle \phi\:\middle|\: J=\frac{3}{2}\,,\, M_{J}\right\rangle
6837 For physical vectors there is a special LaTeX-package, described in
6838 \begin_inset CommandInset ref
6840 reference "sub:Physical-Vectors"
6847 \begin_layout Subsection
6849 \begin_inset Index idx
6852 \begin_layout Plain Layout
6853 Brackets ! horizontal
6861 \begin_layout Standard
6863 \begin_inset Tabular
6864 <lyxtabular version="3" rows="4" columns="2">
6865 <features rotate="0" tabularvalignment="middle">
6866 <column alignment="center" valignment="top" width="0pt">
6867 <column alignment="center" valignment="top" width="0pt">
6869 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
6872 \begin_layout Plain Layout
6874 \begin_inset Note Note
6877 \begin_layout Plain Layout
6884 is only used as spacer.
6894 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
6897 \begin_layout Plain Layout
6905 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
6908 \begin_layout Plain Layout
6912 \begin_layout Plain Layout
6924 \begin_inset space \textvisiblespace{}
6928 \begin_inset space \textvisiblespace{}
6935 \begin_layout Plain Layout
6943 \begin_inset Index idx
6946 \begin_layout Plain Layout
6959 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
6962 \begin_layout Plain Layout
6963 \begin_inset Formula $\overbrace{A+B}^{3}$
6973 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
6976 \begin_layout Plain Layout
6980 \begin_layout Plain Layout
6992 \begin_inset space \textvisiblespace{}
6996 \begin_inset space \textvisiblespace{}
7003 \begin_layout Plain Layout
7011 \begin_inset Index idx
7014 \begin_layout Plain Layout
7027 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
7030 \begin_layout Plain Layout
7031 \begin_inset Formula $\underbrace{A+B}_{5}$
7041 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
7044 \begin_layout Plain Layout
7048 \begin_inset space \textvisiblespace{}
7054 \begin_inset space \textvisiblespace{}
7058 \begin_inset space \textvisiblespace{}
7062 \begin_inset space \textvisiblespace{}
7066 \begin_inset space \textvisiblespace{}
7070 \begin_inset space \textvisiblespace{}
7074 \begin_inset space \textvisiblespace{}
7082 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
7085 \begin_layout Plain Layout
7086 \begin_inset Formula $\overbrace{\underbrace{A+B_{w}}_{7}}^{C}$
7102 \begin_layout Standard
7103 In the last example it doesn't matter if
7115 is inserted at first.
7118 \begin_layout Standard
7119 \begin_inset VSpace medskip
7125 \begin_layout Standard
7126 If you set in the document settings under
7129 \begin_inset space ~
7139 \begin_inset Index idx
7142 \begin_layout Plain Layout
7143 Packages ! mathtools
7151 \begin_inset space ~
7156 , you have access to square backets:
7159 \begin_layout Standard
7161 \begin_inset Tabular
7162 <lyxtabular version="3" rows="4" columns="2">
7163 <features rotate="0" tabularvalignment="middle">
7164 <column alignment="center" valignment="top" width="0pt">
7165 <column alignment="center" valignment="top" width="0pt">
7167 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
7170 \begin_layout Plain Layout
7172 \begin_inset Note Note
7175 \begin_layout Plain Layout
7182 is only used as spacer.
7192 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
7195 \begin_layout Plain Layout
7203 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
7206 \begin_layout Plain Layout
7210 \begin_layout Plain Layout
7246 \begin_inset space \textvisiblespace{}
7253 \begin_layout Plain Layout
7261 \begin_inset Index idx
7264 \begin_layout Plain Layout
7277 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
7280 \begin_layout Plain Layout
7281 \begin_inset Formula $\overbracket{A+B}^{3}$
7291 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
7294 \begin_layout Plain Layout
7298 \begin_layout Plain Layout
7334 \begin_inset space \textvisiblespace{}
7341 \begin_layout Plain Layout
7349 \begin_inset Index idx
7352 \begin_layout Plain Layout
7377 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
7380 \begin_layout Plain Layout
7381 \begin_inset Formula $\underbracket{A+B}_{5}$
7391 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
7394 \begin_layout Plain Layout
7400 \begin_inset space \textvisiblespace{}
7404 \begin_inset space \textvisiblespace{}
7408 \begin_inset space \textvisiblespace{}
7412 \begin_inset space \textvisiblespace{}
7416 \begin_inset space \textvisiblespace{}
7424 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
7427 \begin_layout Plain Layout
7428 \begin_inset Formula $\overbracket{\underbracket{A+B_{w}}_{7}}^{C}$
7444 \begin_layout Standard
7457 you can change the thickness of the bracket's stroke by specifying the
7458 desired thickness in square brackets behind the command:
7461 \begin_layout Standard
7463 \begin_inset Tabular
7464 <lyxtabular version="3" rows="3" columns="2">
7465 <features rotate="0" tabularvalignment="middle">
7466 <column alignment="center" valignment="top" width="0pt">
7467 <column alignment="center" valignment="top" width="0pt">
7469 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
7472 \begin_layout Plain Layout
7474 \begin_inset Note Note
7477 \begin_layout Plain Layout
7484 is only used as spacer.
7494 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
7497 \begin_layout Plain Layout
7505 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
7508 \begin_layout Plain Layout
7512 \begin_layout Plain Layout
7550 \begin_inset space \textvisiblespace{}
7557 \begin_layout Plain Layout
7569 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
7572 \begin_layout Plain Layout
7573 \begin_inset Formula $\overbracket[3pt]{A+B}^{3}$
7583 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
7586 \begin_layout Plain Layout
7590 \begin_layout Plain Layout
7628 \begin_inset space \textvisiblespace{}
7635 \begin_layout Plain Layout
7647 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
7650 \begin_layout Plain Layout
7651 \begin_inset Formula $\underbracket[1pt]{A+B}_{5}$
7667 \begin_layout Standard
7668 \begin_inset VSpace bigskip
7671 When brackets should overlap each other, multiline formulas, as described
7673 \begin_inset CommandInset ref
7675 reference "sec:Multiline-Formulas"
7680 \begin_inset Formula
7682 A & = & \underbrace{gggg+bbqq}_{r}+\: dddd\\
7683 & & \hphantom{gggg+\:}\underbrace{\hphantom{bbqq+dddd}}_{s}
7688 In the first row the formula is inserted together with the first brace.
7689 It is hereby important that the space command
7693 \begin_layout Plain Layout
7694 Space commands are explained in
7695 \begin_inset CommandInset ref
7697 reference "sub:Predefined-Space"
7712 is inserted before the first
7713 \begin_inset Formula $d$
7716 , because the brace that ends behind the
7717 \begin_inset Formula $q$
7720 prevents that the following
7721 \begin_inset Quotes eld
7725 \begin_inset Quotes erd
7728 is surrounded by space.
7732 \begin_layout Plain Layout
7733 because a bracket is not handled as a character, see
7734 \begin_inset CommandInset ref
7736 reference "sub:Binary-Operators"
7745 In the second row the second brace is inserted.
7746 As it should begin before the
7747 \begin_inset Formula $b$
7762 \begin_layout Plain Layout
7770 \begin_inset CommandInset ref
7772 reference "sub:Placeholders"
7781 This space is needed because the
7782 \begin_inset Quotes eld
7786 \begin_inset Quotes erd
7789 is also surrounded by space in the formula.
7790 The brace is placed under the command
7799 \begin_layout Standard
7800 It gets more complicated when brackets overlap each other above and under
7801 the formula, like in the following example:
7805 \begin_layout Plain Layout
7817 \begin_inset Formula
7819 & & \hphantom{gggg+\:}\overbrace{\hphantom{bbqq+dddd}}^{s}\\
7820 A & = & \underbrace{gggg+bbqq}_{r}+\: dddd
7829 \begin_layout Plain Layout
7840 The first formula row is the same as the second row of the previous example,
7841 with the difference that the brace is above.
7842 The second row contains the formula together with the second brace.
7843 To avoid that there is space between the upper brace in the first row and
7844 the formula, the row spacing needs to be reduced.
7845 This is not easily possible due to a bug in LyX
7849 \begin_layout Plain Layout
7850 \begin_inset CommandInset href
7852 name "LyX-bug #1505"
7853 target "http://www.lyx.org/trac/ticket/1505"
7863 As a solution for the problem, the global formula row separation
7870 \begin_inset Index idx
7873 \begin_layout Plain Layout
7881 must be changed to -6
7882 \begin_inset space \thinspace{}
7885 pt before the formula with the command
7900 is set back after the formula to the standard value of 3
7901 \begin_inset space \thinspace{}
7904 pt using the same command.
7905 More about the row separation in formulas is explained in
7906 \begin_inset CommandInset ref
7908 reference "sub:Line-Separation"
7915 \begin_layout Section
7917 \begin_inset Index idx
7920 \begin_layout Plain Layout
7929 \begin_layout Standard
7930 Arrows can be inserted via the math toolbar button
7933 arg "math-insert \\leftarrow"
7936 or the commands listed in the following subsections.
7939 \begin_layout Subsection
7941 \begin_inset Index idx
7944 \begin_layout Plain Layout
7953 \begin_layout Standard
7954 \begin_inset space \hfill{}
7958 \begin_inset Tabular
7959 <lyxtabular version="3" rows="8" columns="2">
7960 <features rotate="0" tabularvalignment="middle">
7961 <column alignment="center" valignment="top" width="0pt">
7962 <column alignment="center" valignment="top" width="0pt">
7964 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
7967 \begin_layout Plain Layout
7973 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
7976 \begin_layout Plain Layout
7984 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
7987 \begin_layout Plain Layout
7995 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
7998 \begin_layout Plain Layout
7999 \begin_inset Formula $\gets$
8009 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
8012 \begin_layout Plain Layout
8020 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
8023 \begin_layout Plain Layout
8024 \begin_inset Formula $\Leftarrow$
8034 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
8037 \begin_layout Plain Layout
8045 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
8048 \begin_layout Plain Layout
8049 \begin_inset Formula $\longleftarrow$
8059 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
8062 \begin_layout Plain Layout
8070 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
8073 \begin_layout Plain Layout
8074 \begin_inset Formula $\Longleftarrow$
8084 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
8087 \begin_layout Plain Layout
8095 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
8098 \begin_layout Plain Layout
8099 \begin_inset Formula $\leftharpoonup$
8109 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
8112 \begin_layout Plain Layout
8120 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
8123 \begin_layout Plain Layout
8124 \begin_inset Formula $\leftharpoondown$
8134 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
8137 \begin_layout Plain Layout
8145 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
8148 \begin_layout Plain Layout
8149 \begin_inset Formula $\hookleftarrow$
8163 \begin_inset space \hfill{}
8167 \begin_inset Tabular
8168 <lyxtabular version="3" rows="8" columns="2">
8169 <features rotate="0" tabularvalignment="middle">
8170 <column alignment="center" valignment="top" width="0pt">
8171 <column alignment="center" valignment="top" width="0pt">
8173 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
8176 \begin_layout Plain Layout
8182 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
8185 \begin_layout Plain Layout
8193 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
8196 \begin_layout Plain Layout
8204 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
8207 \begin_layout Plain Layout
8208 \begin_inset Formula $\to$
8218 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
8221 \begin_layout Plain Layout
8229 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
8232 \begin_layout Plain Layout
8233 \begin_inset Formula $\Rightarrow$
8243 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
8246 \begin_layout Plain Layout
8254 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
8257 \begin_layout Plain Layout
8258 \begin_inset Formula $\longrightarrow$
8268 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
8271 \begin_layout Plain Layout
8279 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
8282 \begin_layout Plain Layout
8283 \begin_inset Formula $\Longrightarrow$
8293 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
8296 \begin_layout Plain Layout
8304 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
8307 \begin_layout Plain Layout
8308 \begin_inset Formula $\rightharpoonup$
8318 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
8321 \begin_layout Plain Layout
8329 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
8332 \begin_layout Plain Layout
8333 \begin_inset Formula $\rightharpoondown$
8343 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
8346 \begin_layout Plain Layout
8354 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
8357 \begin_layout Plain Layout
8358 \begin_inset Formula $\hookrightarrow$
8372 \begin_inset space \hfill{}
8378 \begin_layout Standard
8379 \begin_inset space \hfill{}
8383 \begin_inset Tabular
8384 <lyxtabular version="3" rows="6" columns="2">
8385 <features rotate="0" tabularvalignment="middle">
8386 <column alignment="center" valignment="top" width="0pt">
8387 <column alignment="center" valignment="top" width="0pt">
8389 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
8392 \begin_layout Plain Layout
8398 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
8401 \begin_layout Plain Layout
8409 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
8412 \begin_layout Plain Layout
8420 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
8423 \begin_layout Plain Layout
8424 \begin_inset Formula $\leftrightarrow$
8434 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
8437 \begin_layout Plain Layout
8445 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
8448 \begin_layout Plain Layout
8449 \begin_inset Formula $\Leftrightarrow$
8459 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
8462 \begin_layout Plain Layout
8470 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
8473 \begin_layout Plain Layout
8474 \begin_inset Formula $\longleftrightarrow$
8484 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
8487 \begin_layout Plain Layout
8495 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
8498 \begin_layout Plain Layout
8499 \begin_inset Formula $\Longleftrightarrow$
8509 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
8512 \begin_layout Plain Layout
8520 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
8523 \begin_layout Plain Layout
8524 \begin_inset Formula $\rightleftharpoons$
8538 \begin_inset space \hspace{}
8543 \begin_inset space \hfill{}
8547 \begin_inset Tabular
8548 <lyxtabular version="3" rows="5" columns="2">
8549 <features rotate="0" tabularvalignment="middle">
8550 <column alignment="center" valignment="top" width="0pt">
8551 <column alignment="center" valignment="top" width="0pt">
8553 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
8556 \begin_layout Plain Layout
8562 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
8565 \begin_layout Plain Layout
8573 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
8576 \begin_layout Plain Layout
8584 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
8587 \begin_layout Plain Layout
8588 \begin_inset Formula $\mapsto$
8598 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
8601 \begin_layout Plain Layout
8609 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
8612 \begin_layout Plain Layout
8613 \begin_inset Formula $\longmapsto$
8623 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
8626 \begin_layout Plain Layout
8634 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
8637 \begin_layout Plain Layout
8638 \begin_inset Formula $\leadsto$
8648 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
8651 \begin_layout Plain Layout
8659 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
8662 \begin_layout Plain Layout
8663 \begin_inset Formula $\dasharrow$
8677 \begin_inset space \hfill{}
8683 \begin_layout Standard
8684 \begin_inset VSpace medskip
8687 Arrows used as accents like e.
8688 \begin_inset space \thinspace{}
8692 \begin_inset space \space{}
8695 vector arrows are listed in
8696 \begin_inset CommandInset ref
8698 reference "sec:Accents"
8705 \begin_layout Standard
8706 \begin_inset VSpace bigskip
8709 Furthermore there are the labeled arrows
8710 \begin_inset Index idx
8713 \begin_layout Plain Layout
8726 \begin_inset Index idx
8729 \begin_layout Plain Layout
8744 \begin_inset Index idx
8747 \begin_layout Plain Layout
8754 \begin_layout Plain Layout
8769 When inserting one of these commands in a formula, an arrow with two blue
8770 boxes appear where the label can be inserted.
8771 The length of the arrow adapts to the label width.
8774 \begin_layout Standard
8776 \begin_inset Tabular
8777 <lyxtabular version="3" rows="3" columns="2">
8778 <features rotate="0" tabularvalignment="middle">
8779 <column alignment="center" valignment="top" width="0pt">
8780 <column alignment="center" valignment="top" width="0pt">
8782 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
8785 \begin_layout Plain Layout
8791 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
8794 \begin_layout Plain Layout
8796 \begin_inset Note Note
8799 \begin_layout Plain Layout
8806 is only used as spacer.
8818 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
8821 \begin_layout Plain Layout
8825 \begin_inset space \textvisiblespace{}
8829 \begin_inset Formula $\downarrow$
8833 \begin_inset Formula $\to$
8841 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
8844 \begin_layout Plain Layout
8845 \begin_inset Formula $\raisebox{5.5mm}{}F(a)\xleftarrow[x>0]{x=a}F(x)\raisebox{-4mm}{}$
8855 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
8858 \begin_layout Plain Layout
8862 \begin_inset space \textvisiblespace{}
8866 \begin_inset Formula $\downarrow$
8870 \begin_inset Formula $\to$
8878 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
8881 \begin_layout Plain Layout
8882 \begin_inset Formula $\raisebox{5.5mm}{}F(x)\xrightarrow[x>0]{x=a}F(a)\raisebox{-4mm}{}$
8898 \begin_layout Standard
8899 \begin_inset VSpace medskip
8905 \begin_layout Standard
8906 If you set in the document settings under
8909 \begin_inset space ~
8919 \begin_inset Index idx
8922 \begin_layout Plain Layout
8923 Packages ! mathtools
8931 \begin_inset space ~
8936 , you have access to the following labeled arrows:
8939 \begin_layout Standard
8940 \begin_inset Newpage newpage
8946 \begin_layout Standard
8948 \begin_inset space \hspace*{\fill}
8952 \begin_inset Tabular
8953 <lyxtabular version="3" rows="7" columns="2">
8954 <features rotate="0" tabularvalignment="middle">
8955 <column alignment="center" valignment="top" width="0pt">
8956 <column alignment="center" valignment="top" width="0pt">
8958 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
8961 \begin_layout Plain Layout
8967 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
8970 \begin_layout Plain Layout
8972 \begin_inset Note Note
8975 \begin_layout Plain Layout
8982 is only used as spacer.
8994 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
8997 \begin_layout Plain Layout
9017 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
9020 \begin_layout Plain Layout
9021 \begin_inset Formula $\raisebox{6mm}{}\xleftrightarrow[x=a]{x>0}\raisebox{-4mm}{}$
9031 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
9034 \begin_layout Plain Layout
9054 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
9057 \begin_layout Plain Layout
9058 \begin_inset Formula $\raisebox{6mm}{}\xLeftarrow[x=a]{x>0}\raisebox{-4mm}{}$
9068 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
9071 \begin_layout Plain Layout
9091 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
9094 \begin_layout Plain Layout
9095 \begin_inset Formula $\raisebox{6mm}{}\xRightarrow[x=a]{x>0}\raisebox{-4mm}{}$
9105 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
9108 \begin_layout Plain Layout
9128 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
9131 \begin_layout Plain Layout
9132 \begin_inset Formula $\raisebox{6mm}{}\xLeftrightarrow[x=a]{x>0}\raisebox{-4mm}{}$
9142 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
9145 \begin_layout Plain Layout
9165 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
9168 \begin_layout Plain Layout
9169 \begin_inset Formula $\raisebox{6mm}{}\xhookleftarrow[x=a]{x>0}\raisebox{-4mm}{}$
9179 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
9182 \begin_layout Plain Layout
9202 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
9205 \begin_layout Plain Layout
9206 \begin_inset Formula $\raisebox{6mm}{}\xhookrightarrow[x=a]{x>0}\raisebox{-4mm}{}$
9220 \begin_inset space \hspace*{\fill}
9224 \begin_inset Tabular
9225 <lyxtabular version="3" rows="7" columns="2">
9226 <features rotate="0" tabularvalignment="middle">
9227 <column alignment="center" valignment="top" width="0pt">
9228 <column alignment="center" valignment="top" width="0pt">
9230 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
9233 \begin_layout Plain Layout
9239 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
9242 \begin_layout Plain Layout
9244 \begin_inset Note Note
9247 \begin_layout Plain Layout
9254 is only used as spacer.
9266 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
9269 \begin_layout Plain Layout
9289 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
9292 \begin_layout Plain Layout
9293 \begin_inset Formula $\raisebox{6mm}{}\xleftharpoondown[x=a]{x>0}\raisebox{-4mm}{}$
9303 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
9306 \begin_layout Plain Layout
9326 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
9329 \begin_layout Plain Layout
9330 \begin_inset Formula $\raisebox{6mm}{}\xleftharpoonup[x=a]{x>0}\raisebox{-4mm}{}$
9340 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
9343 \begin_layout Plain Layout
9363 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
9366 \begin_layout Plain Layout
9367 \begin_inset Formula $\raisebox{6mm}{}\xrightharpoondown[x=a]{x>0}\raisebox{-4mm}{}$
9377 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
9380 \begin_layout Plain Layout
9400 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
9403 \begin_layout Plain Layout
9404 \begin_inset Formula $\raisebox{6mm}{}\xrightharpoonup[x=a]{x>0}\raisebox{-4mm}{}$
9414 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
9417 \begin_layout Plain Layout
9437 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
9440 \begin_layout Plain Layout
9441 \begin_inset Formula $\raisebox{6mm}{}\xleftrightharpoons[x=a]{x>0}\raisebox{-4mm}{}$
9451 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
9454 \begin_layout Plain Layout
9474 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
9477 \begin_layout Plain Layout
9478 \begin_inset Formula $\raisebox{6mm}{}\xrightleftharpoons[x=a]{x>0}\raisebox{-4mm}{}$
9492 \begin_inset space \hspace*{\fill}
9498 \begin_layout Standard
9499 The command scheme is for all these arrows:
9502 \begin_layout Standard
9504 \begin_inset Tabular
9505 <lyxtabular version="3" rows="2" columns="2">
9506 <features rotate="0" tabularvalignment="middle">
9507 <column alignment="center" valignment="top" width="0pt">
9508 <column alignment="center" valignment="top" width="0pt">
9510 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
9513 \begin_layout Plain Layout
9519 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
9522 \begin_layout Plain Layout
9524 \begin_inset Note Note
9527 \begin_layout Plain Layout
9534 is only used as spacer.
9546 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
9549 \begin_layout Plain Layout
9552 xleftrightarrow[x=a]
9555 \begin_inset Formula $\to$
9563 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
9566 \begin_layout Plain Layout
9567 \begin_inset Formula $\raisebox{6mm}{}F(a)\xleftrightarrow[x=a]{x>0}F(x)\raisebox{-4mm}{}$
9583 \begin_layout Subsection
9584 Vertical and diagonal Arrows
9585 \begin_inset Index idx
9588 \begin_layout Plain Layout
9595 \begin_inset Index idx
9598 \begin_layout Plain Layout
9607 \begin_layout Standard
9608 \begin_inset space \hfill{}
9612 \begin_inset Tabular
9613 <lyxtabular version="3" rows="7" columns="2">
9614 <features rotate="0" tabularvalignment="middle">
9615 <column alignment="center" valignment="top" width="0pt">
9616 <column alignment="center" valignment="top" width="0pt">
9618 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
9621 \begin_layout Plain Layout
9627 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
9630 \begin_layout Plain Layout
9638 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
9641 \begin_layout Plain Layout
9649 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
9652 \begin_layout Plain Layout
9653 \begin_inset Formula $\uparrow$
9663 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
9666 \begin_layout Plain Layout
9674 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
9677 \begin_layout Plain Layout
9678 \begin_inset Formula $\Uparrow$
9688 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
9691 \begin_layout Plain Layout
9699 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
9702 \begin_layout Plain Layout
9703 \begin_inset Formula $\updownarrow$
9713 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
9716 \begin_layout Plain Layout
9724 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
9727 \begin_layout Plain Layout
9728 \begin_inset Formula $\Updownarrow$
9738 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
9741 \begin_layout Plain Layout
9749 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
9752 \begin_layout Plain Layout
9753 \begin_inset Formula $\Downarrow$
9763 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
9766 \begin_layout Plain Layout
9774 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
9777 \begin_layout Plain Layout
9778 \begin_inset Formula $\downarrow$
9792 \begin_inset space \hfill{}
9796 \begin_inset Tabular
9797 <lyxtabular version="3" rows="5" columns="2">
9798 <features rotate="0" tabularvalignment="middle">
9799 <column alignment="center" valignment="top" width="0pt">
9800 <column alignment="center" valignment="top" width="0pt">
9802 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
9805 \begin_layout Plain Layout
9811 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
9814 \begin_layout Plain Layout
9822 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
9825 \begin_layout Plain Layout
9833 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
9836 \begin_layout Plain Layout
9837 \begin_inset Formula $\nearrow$
9847 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
9850 \begin_layout Plain Layout
9858 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
9861 \begin_layout Plain Layout
9862 \begin_inset Formula $\searrow$
9872 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
9875 \begin_layout Plain Layout
9883 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
9886 \begin_layout Plain Layout
9887 \begin_inset Formula $\swarrow$
9897 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
9900 \begin_layout Plain Layout
9908 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
9911 \begin_layout Plain Layout
9912 \begin_inset Formula $\nwarrow$
9926 \begin_inset space \hfill{}
9932 \begin_layout Standard
9933 \begin_inset VSpace medskip
9936 Vertical arrows can be used also as delimiters together with the commands
9938 \begin_inset CommandInset ref
9940 reference "sub:Manual-Bracket-Size"
9945 \begin_inset CommandInset ref
9947 reference "sub:Automatic-Bracket-Size"
9954 \begin_layout Section
9956 \begin_inset CommandInset label
9963 \begin_inset Index idx
9966 \begin_layout Plain Layout
9975 \begin_layout Standard
9976 Accents can be inserted via the math toolbar button
9979 arg "math-insert \\hat"
9982 or the commands listed in the following subsections.
9985 \begin_layout Subsection
9986 Accents for one Character
9990 \begin_layout Plain Layout
10003 \begin_layout Plain Layout
10004 accents in text see
10005 \begin_inset CommandInset ref
10007 reference "sub:Accents-in-Text"
10020 \begin_layout Plain Layout
10028 \begin_inset Note Note
10031 \begin_layout Plain Layout
10038 is used to avoid that the footnote appears in the PDF-bookmark.
10041 \begin_layout Plain Layout
10049 \begin_inset CommandInset ref
10051 reference "sub:Formulas-in-Section"
10061 \begin_inset CommandInset label
10063 name "sub:Accents-for-one"
10068 \begin_inset Index idx
10071 \begin_layout Plain Layout
10072 Accents ! for one character
10080 \begin_layout Standard
10081 \begin_inset space \hfill{}
10085 \begin_inset Tabular
10086 <lyxtabular version="3" rows="8" columns="2">
10087 <features rotate="0" tabularvalignment="middle">
10088 <column alignment="center" valignment="top" width="0pt">
10089 <column alignment="center" valignment="top" width="0pt">
10091 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
10094 \begin_layout Plain Layout
10100 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
10103 \begin_layout Plain Layout
10105 \begin_inset Note Note
10108 \begin_layout Plain Layout
10115 is only used as spacer.
10127 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
10130 \begin_layout Plain Layout
10134 \begin_inset space \textvisiblespace{}
10142 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
10145 \begin_layout Plain Layout
10146 \begin_inset Formula $\raisebox{5mm}{}\dot{A}$
10156 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
10159 \begin_layout Plain Layout
10163 \begin_inset space \textvisiblespace{}
10171 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
10174 \begin_layout Plain Layout
10175 \begin_inset Formula $\raisebox{5mm}{}\ddot{A}$
10185 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
10188 \begin_layout Plain Layout
10192 \begin_inset space \textvisiblespace{}
10200 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
10203 \begin_layout Plain Layout
10204 \begin_inset Formula $\raisebox{5mm}{}\dddot{A}$
10214 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
10217 \begin_layout Plain Layout
10221 \begin_inset space \textvisiblespace{}
10229 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
10232 \begin_layout Plain Layout
10233 \begin_inset Formula $\raisebox{5mm}{}\ddddot{A}$
10243 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
10246 \begin_layout Plain Layout
10250 \begin_inset space \textvisiblespace{}
10254 \begin_inset Index idx
10257 \begin_layout Plain Layout
10268 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
10271 \begin_layout Plain Layout
10272 \begin_inset Formula $\raisebox{5mm}{}\vec{A}$
10282 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
10285 \begin_layout Plain Layout
10289 \begin_inset space \textvisiblespace{}
10297 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
10300 \begin_layout Plain Layout
10301 \begin_inset Formula $\raisebox{5mm}{}\bar{A}$
10311 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
10314 \begin_layout Plain Layout
10318 \begin_inset space \textvisiblespace{}
10326 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
10329 \begin_layout Plain Layout
10330 \begin_inset Formula $\raisebox{5mm}{}\mathring{A}$
10344 \begin_inset space \hfill{}
10348 \begin_inset Tabular
10349 <lyxtabular version="3" rows="7" columns="2">
10350 <features rotate="0" tabularvalignment="middle">
10351 <column alignment="center" valignment="top" width="0pt">
10352 <column alignment="center" valignment="top" width="0pt">
10354 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
10357 \begin_layout Plain Layout
10363 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
10366 \begin_layout Plain Layout
10374 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
10377 \begin_layout Plain Layout
10381 \begin_inset space \textvisiblespace{}
10389 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
10392 \begin_layout Plain Layout
10393 \begin_inset Formula $\raisebox{5mm}{}\tilde{A}$
10403 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
10406 \begin_layout Plain Layout
10410 \begin_inset space \textvisiblespace{}
10418 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
10421 \begin_layout Plain Layout
10422 \begin_inset Formula $\raisebox{5mm}{}\hat{A}$
10432 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
10435 \begin_layout Plain Layout
10439 \begin_inset space \textvisiblespace{}
10447 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
10450 \begin_layout Plain Layout
10451 \begin_inset Formula $\raisebox{5mm}{}\check{A}$
10461 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
10464 \begin_layout Plain Layout
10468 \begin_inset space \textvisiblespace{}
10476 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
10479 \begin_layout Plain Layout
10480 \begin_inset Formula $\raisebox{5mm}{}\acute{A}$
10490 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
10493 \begin_layout Plain Layout
10497 \begin_inset space \textvisiblespace{}
10505 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
10508 \begin_layout Plain Layout
10509 \begin_inset Formula $\raisebox{5mm}{}\grave{A}$
10519 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
10522 \begin_layout Plain Layout
10526 \begin_inset space \textvisiblespace{}
10534 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
10537 \begin_layout Plain Layout
10538 \begin_inset Formula $\raisebox{5mm}{}\breve{A}$
10552 \begin_inset space \hfill{}
10558 \begin_layout Standard
10559 \begin_inset VSpace bigskip
10565 \begin_layout Standard
10566 You can directly insert accents like é to formulas.
10567 LyX will transform them to the corresponding accent command.
10569 \begin_inset Index idx
10572 \begin_layout Plain Layout
10578 it is better to insert a quotation mark before the vowel.
10579 These two characters are then treated by LaTeX as
10583 character when the formula part with the umlaut is marked as German.
10591 \begin_inset Quotes eld
10595 \begin_inset Quotes erd
10598 umlauts are created as demonstrated in the following example:
10601 \begin_layout Standard
10602 \begin_inset VSpace -2mm
10608 \begin_layout Standard
10610 \begin_inset Tabular
10611 <lyxtabular version="3" rows="3" columns="2">
10612 <features rotate="0" tabularvalignment="middle">
10613 <column alignment="center" valignment="top">
10614 <column alignment="center" valignment="top">
10616 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
10619 \begin_layout Plain Layout
10625 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
10628 \begin_layout Plain Layout
10630 \begin_inset Note Note
10633 \begin_layout Plain Layout
10641 \begin_inset space \thinspace{}
10644 pt space are only used as spacer.
10656 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
10659 \begin_layout Plain Layout
10662 \begin_inset Quotes grd
10670 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
10673 \begin_layout Plain Layout
10674 \begin_inset space \hspace{}
10681 \begin_inset Formula $"i$
10691 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
10694 \begin_layout Plain Layout
10698 \begin_inset space \textvisiblespace{}
10706 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
10709 \begin_layout Plain Layout
10710 \begin_inset Formula $\raisebox{5mm}{}\ddot{i}$
10726 \begin_layout Standard
10727 Another advantage to
10733 is that umlauts can directly be converted to mathematical text because
10734 the accent commands above are
10740 in mathematical text
10743 To convert an accented character to mathematical text, only the character
10744 under the accent may be converted.
10745 This applies also for all other conversions, e.
10746 \begin_inset space \thinspace{}
10750 \begin_inset space \space{}
10756 \begin_layout Standard
10757 In mathematical text, umlauts and other accented characters can directly
10761 \begin_layout Standard
10762 \begin_inset VSpace bigskip
10768 \begin_layout Standard
10769 LyX also supports a tilde under the character if the LaTeX-package
10774 \begin_inset Index idx
10777 \begin_layout Plain Layout
10778 Packages ! undertilde
10783 is installed on your system:
10786 \begin_layout Standard
10790 \begin_layout Plain Layout
10800 \begin_inset Note Note
10803 \begin_layout Plain Layout
10804 The following table will only be displayed when the LaTeX-package
10816 \begin_layout Standard
10819 \begin_inset Tabular
10820 <lyxtabular version="3" rows="2" columns="2">
10821 <features rotate="0" tabularvalignment="middle">
10822 <column alignment="center" valignment="top" width="0pt">
10823 <column alignment="center" valignment="top" width="0pt">
10825 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
10828 \begin_layout Plain Layout
10834 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
10837 \begin_layout Plain Layout
10845 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
10848 \begin_layout Plain Layout
10852 \begin_inset space \textvisiblespace{}
10860 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
10863 \begin_layout Plain Layout
10864 \begin_inset Formula $\raisebox{5mm}{}\utilde{A}$
10880 \begin_layout Standard
10884 \begin_layout Plain Layout
10894 \begin_inset Note Note
10897 \begin_layout Plain Layout
10898 The following will be displayed when the LaTeX-package
10910 \begin_layout Standard
10911 You need to install the LaTeX-package
10915 to see the rest of this subsection in the output.
10918 \begin_layout Standard
10922 \begin_layout Plain Layout
10934 \begin_layout Standard
10935 \begin_inset Newpage newpage
10941 \begin_layout Subsection
10942 Accents for several Characters
10943 \begin_inset Index idx
10946 \begin_layout Plain Layout
10947 Accents ! for several characters
10955 \begin_layout Standard
10956 \begin_inset space \hfill{}
10960 \begin_inset Tabular
10961 <lyxtabular version="3" rows="5" columns="2">
10962 <features rotate="0" tabularvalignment="middle">
10963 <column alignment="center" valignment="top" width="0pt">
10964 <column alignment="center" valignment="top" width="0pt">
10966 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
10969 \begin_layout Plain Layout
10975 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
10978 \begin_layout Plain Layout
10980 \begin_inset Note Note
10983 \begin_layout Plain Layout
10990 is only used as spacer.
11002 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
11005 \begin_layout Plain Layout
11009 \begin_inset space \textvisiblespace{}
11017 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
11020 \begin_layout Plain Layout
11021 \begin_inset Formula $\raisebox{6mm}{}\overleftarrow{A=B}\raisebox{-2mm}{}$
11031 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
11034 \begin_layout Plain Layout
11038 \begin_inset space \textvisiblespace{}
11046 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
11049 \begin_layout Plain Layout
11050 \begin_inset Formula $\raisebox{5mm}{}\underleftarrow{A=B}\raisebox{-3mm}{}$
11060 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
11063 \begin_layout Plain Layout
11067 \begin_inset space \textvisiblespace{}
11075 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
11078 \begin_layout Plain Layout
11079 \begin_inset Formula $\raisebox{6mm}{}\overleftrightarrow{A=B}\raisebox{-2mm}{}$
11089 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
11092 \begin_layout Plain Layout
11095 underleftrightarrow
11096 \begin_inset space \textvisiblespace{}
11104 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
11107 \begin_layout Plain Layout
11108 \begin_inset Formula $\raisebox{5mm}{}\underleftrightarrow{A=B}\raisebox{-3mm}{}$
11122 \begin_inset space \hfill{}
11126 \begin_inset Tabular
11127 <lyxtabular version="3" rows="5" columns="2">
11128 <features rotate="0" tabularvalignment="middle">
11129 <column alignment="center" valignment="top" width="0pt">
11130 <column alignment="center" valignment="top" width="0pt">
11132 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
11135 \begin_layout Plain Layout
11141 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
11144 \begin_layout Plain Layout
11152 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
11155 \begin_layout Plain Layout
11159 \begin_inset space \textvisiblespace{}
11167 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
11170 \begin_layout Plain Layout
11171 \begin_inset Formula $\raisebox{6mm}{}\overrightarrow{A=B}\raisebox{-2mm}{}$
11181 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
11184 \begin_layout Plain Layout
11188 \begin_inset space \textvisiblespace{}
11196 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
11199 \begin_layout Plain Layout
11200 \begin_inset Formula $\raisebox{5mm}{}\underrightarrow{A=B}\raisebox{-3mm}{}$
11210 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
11213 \begin_layout Plain Layout
11217 \begin_inset space \textvisiblespace{}
11225 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
11228 \begin_layout Plain Layout
11229 \begin_inset Formula $\raisebox{6mm}{}\widetilde{A=B}\raisebox{-2mm}{}$
11239 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
11242 \begin_layout Plain Layout
11246 \begin_inset space \textvisiblespace{}
11254 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
11257 \begin_layout Plain Layout
11258 \begin_inset Formula $\raisebox{6mm}{}\widehat{A=B}\raisebox{-2mm}{}$
11272 \begin_inset space \hfill{}
11278 \begin_layout Standard
11279 \begin_inset VSpace medskip
11282 With these commands as many characters as you like can be accented.
11295 will only be set in the output with a length of three characters, as shown
11296 in the following example:
11297 \begin_inset Formula
11299 \widetilde{A+B=C-D}
11307 \begin_layout Standard
11315 \begin_inset Index idx
11318 \begin_layout Plain Layout
11333 \begin_inset Index idx
11336 \begin_layout Plain Layout
11344 described in the previous subsection it is also possible to accent several
11351 \begin_inset space \textvisiblespace{}
11355 \begin_inset Formula $\downarrow$
11361 \begin_inset Formula
11363 \underset{***}{A=B}
11371 \begin_layout Section
11373 \begin_inset CommandInset label
11380 \begin_inset Index idx
11383 \begin_layout Plain Layout
11392 \begin_layout Subsection
11394 \begin_inset CommandInset label
11396 name "sub:Predefined-Space"
11401 \begin_inset Index idx
11404 \begin_layout Plain Layout
11405 Space ! horizontal ! predefined
11413 \begin_layout Standard
11414 Sometimes it is necessary to insert horizontal space into a formula.
11415 This is done by inserting a protected space (shortcut
11418 arg "command-alternatives space-insert protected ; math-space"
11423 \begin_inset Quotes eld
11429 \begin_inset space \textvisiblespace{}
11435 \begin_inset Quotes erd
11438 appears and by pressing
11442 several times one can select one of eight different space sizes.
11443 The spaces can also be inserted using the math toolbar button
11446 arg "math-insert \\space"
11449 or special commands.
11450 Independent from the inserted command, one can select the size again by
11458 \begin_layout Standard
11461 \begin_inset Tabular
11462 <lyxtabular version="3" rows="6" columns="3">
11463 <features rotate="0" tabularvalignment="middle">
11464 <column alignment="center" valignment="top">
11465 <column alignment="center" valignment="top" width="15col%">
11466 <column alignment="center" valignment="top">
11468 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
11471 \begin_layout Plain Layout
11477 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
11480 \begin_layout Plain Layout
11490 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
11493 \begin_layout Plain Layout
11501 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
11504 \begin_layout Plain Layout
11512 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
11515 \begin_layout Plain Layout
11521 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
11524 \begin_layout Plain Layout
11525 \begin_inset Formula $A\, B$
11535 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
11538 \begin_layout Plain Layout
11546 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
11549 \begin_layout Plain Layout
11555 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
11558 \begin_layout Plain Layout
11559 \begin_inset Formula $A\: B$
11569 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
11572 \begin_layout Plain Layout
11580 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
11583 \begin_layout Plain Layout
11589 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
11592 \begin_layout Plain Layout
11593 \begin_inset Formula $A\; B$
11603 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
11606 \begin_layout Plain Layout
11614 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
11617 \begin_layout Plain Layout
11623 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
11626 \begin_layout Plain Layout
11627 \begin_inset Formula $A\quad B$
11637 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
11640 \begin_layout Plain Layout
11648 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
11651 \begin_layout Plain Layout
11657 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
11660 \begin_layout Plain Layout
11661 \begin_inset Formula $A\qquad B$
11675 \begin_inset space \hfill{}
11679 \begin_inset Tabular
11680 <lyxtabular version="3" rows="6" columns="3">
11681 <features rotate="0" tabularvalignment="middle">
11682 <column alignment="center" valignment="top">
11683 <column alignment="center" valignment="top" width="15col%">
11684 <column alignment="center" valignment="top">
11686 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
11689 \begin_layout Plain Layout
11695 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
11698 \begin_layout Plain Layout
11708 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
11711 \begin_layout Plain Layout
11719 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
11722 \begin_layout Plain Layout
11730 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
11733 \begin_layout Plain Layout
11739 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
11742 \begin_layout Plain Layout
11743 \begin_inset Formula $A\hfill B$
11753 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
11756 \begin_layout Plain Layout
11764 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
11767 \begin_layout Plain Layout
11773 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
11776 \begin_layout Plain Layout
11777 \begin_inset Formula $A\hspace*{1em}B$
11787 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
11790 \begin_layout Plain Layout
11798 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
11801 \begin_layout Plain Layout
11807 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
11810 \begin_layout Plain Layout
11811 \begin_inset Formula $A\hspace{1em}B$
11821 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
11824 \begin_layout Plain Layout
11828 \begin_inset space \textvisiblespace{}
11836 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
11839 \begin_layout Plain Layout
11845 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
11848 \begin_layout Plain Layout
11849 \begin_inset Formula $A\ B$
11859 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
11862 \begin_layout Plain Layout
11870 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
11873 \begin_layout Plain Layout
11879 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
11882 \begin_layout Plain Layout
11883 \begin_inset Formula $A\! B$
11899 \begin_layout Standard
11901 \begin_inset space ~
11905 \begin_inset space \thinspace{}
11909 \begin_inset space \thinspace{}
11912 7 are variable spaces which are explained in
11913 \begin_inset CommandInset ref
11915 reference "sub:Variable-Space"
11921 \begin_inset space ~
11924 9 seems to produce no space.
11925 It is displayed red in LyX contrary to the other sizes, because it is a
11927 There are two more negative spaces:
11930 \begin_layout Standard
11932 \begin_inset Tabular
11933 <lyxtabular version="3" rows="3" columns="3">
11934 <features rotate="0" tabularvalignment="middle">
11935 <column alignment="center" valignment="middle" width="6.8cm">
11936 <column alignment="center" valignment="top" width="0pt">
11937 <column alignment="center" valignment="top" width="0pt">
11939 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
11942 \begin_layout Plain Layout
11948 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
11951 \begin_layout Plain Layout
11959 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
11962 \begin_layout Plain Layout
11972 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
11975 \begin_layout Plain Layout
11980 keystrokes after inserting the protected space
11985 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
11988 \begin_layout Plain Layout
11994 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
11997 \begin_layout Plain Layout
12005 <cell multicolumn="1" alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
12008 \begin_layout Plain Layout
12014 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
12017 \begin_layout Plain Layout
12018 \begin_inset Formula $A\negmedspace B$
12026 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
12029 \begin_layout Plain Layout
12030 \begin_inset Formula $A\negthickspace B$
12046 \begin_layout Standard
12047 Negative spaces can lead to characters overlapping each other.
12048 Thus they can be used to enforce ligatures, which are e.
12049 \begin_inset space \thinspace{}
12053 \begin_inset space \space{}
12056 useful for summation operators:
12059 \begin_layout Standard
12061 \begin_inset Tabular
12062 <lyxtabular version="3" rows="3" columns="2">
12063 <features rotate="0" tabularvalignment="middle">
12064 <column alignment="center" valignment="top">
12065 <column alignment="center" valignment="top">
12067 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
12070 \begin_layout Plain Layout
12076 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
12079 \begin_layout Plain Layout
12081 \begin_inset Note Note
12084 \begin_layout Plain Layout
12091 is only used as spacer.
12103 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
12106 \begin_layout Plain Layout
12112 \begin_inset space \textvisiblespace{}
12120 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
12123 \begin_layout Plain Layout
12124 \begin_inset Formula $\raisebox{4.5mm}{}\sum\sum f_{kl}\raisebox{-2.5mm}{}$
12134 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
12137 \begin_layout Plain Layout
12145 \begin_inset space \textvisiblespace{}
12153 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
12156 \begin_layout Plain Layout
12157 \begin_inset Formula $\raisebox{4.5mm}{}\sum\negmedspace\sum f_{kl}\raisebox{-2.5mm}{}$
12173 \begin_layout Standard
12175 \begin_inset VSpace medskip
12181 \begin_layout Standard
12183 Relations like for example equal signs, are always surrounded by space.
12184 To suppress this, the equal sign is placed into a TeX-brace.
12185 The following example demonstrates this:
12188 \begin_layout Standard
12190 \begin_inset Tabular
12191 <lyxtabular version="3" rows="2" columns="2">
12192 <features rotate="0" tabularvalignment="middle">
12193 <column alignment="center" valignment="top" width="0pt">
12194 <column alignment="center" valignment="top" width="0pt">
12196 <cell alignment="center" valignment="top" usebox="none">
12199 \begin_layout Plain Layout
12205 <cell alignment="center" valignment="top" usebox="none">
12208 \begin_layout Plain Layout
12209 \begin_inset Formula $A=B$
12219 <cell alignment="center" valignment="top" usebox="none">
12222 \begin_layout Plain Layout
12223 \begin_inset Note Note
12226 \begin_layout Plain Layout
12233 is only used as spacer.
12239 \begin_inset Formula $\raisebox{5mm}{}$
12242 equation without space
12247 <cell multicolumn="1" alignment="center" valignment="top" usebox="none">
12250 \begin_layout Plain Layout
12251 \begin_inset Formula $A{=}B$
12267 \begin_layout Standard
12269 The command for the last formula is:
12274 \begin_inset Formula $\to$
12280 \begin_layout Standard
12281 \begin_inset VSpace bigskip
12287 \begin_layout Standard
12288 Spaces are needed for physical units, because the space between the value
12289 and the unit is the smallest one and not a normal space.
12290 For units in text, the smallest space is inserted via the menu
12292 Insert\SpecialChar \menuseparator
12293 Formatting\SpecialChar \menuseparator
12295 \begin_inset space ~
12303 arg "space-insert thin"
12309 \begin_layout Standard
12310 An example to visualize the difference:
12313 \begin_layout Standard
12314 \begin_inset Tabular
12315 <lyxtabular version="3" rows="2" columns="2">
12316 <features rotate="0" tabularvalignment="middle">
12317 <column alignment="left" valignment="top">
12318 <column alignment="left" valignment="top">
12320 <cell alignment="center" valignment="top" usebox="none">
12323 \begin_layout Plain Layout
12325 \begin_inset Formula $\cdot$
12333 <cell alignment="center" valignment="top" usebox="none">
12336 \begin_layout Plain Layout
12337 space between value and unit
12344 <cell alignment="center" valignment="top" usebox="none">
12347 \begin_layout Plain Layout
12349 \begin_inset space \thinspace{}
12353 \begin_inset Formula $\cdot$
12361 <cell alignment="center" valignment="top" usebox="none">
12364 \begin_layout Plain Layout
12365 smallest space between value and unit
12378 \begin_layout Subsection
12383 \begin_layout Plain Layout
12396 \begin_layout Plain Layout
12397 for vertical space in formulas see
12398 \begin_inset CommandInset ref
12400 reference "sub:Line-Separation"
12413 \begin_layout Plain Layout
12421 \begin_inset Note Note
12424 \begin_layout Plain Layout
12427 texorpdfstring is used to avoid that the footnote appears in the PDF-bookmark.
12430 \begin_layout Plain Layout
12433 texorpdfstring is in section
12434 \begin_inset CommandInset ref
12436 reference "sub:Formulas-in-Section"
12446 \begin_inset CommandInset label
12448 name "sub:Variable-Space"
12453 \begin_inset Index idx
12456 \begin_layout Plain Layout
12457 Space ! horizontal ! variable
12465 \begin_layout Standard
12466 Space with a defined length can be inserted with the command
12473 \begin_inset Index idx
12476 \begin_layout Plain Layout
12486 \begin_inset Quotes eld
12492 \begin_inset space \textvisiblespace{}
12498 \begin_inset Quotes erd
12502 The length can be specified by left-clicking on the
12503 \begin_inset Quotes eld
12509 \begin_inset space \textvisiblespace{}
12515 \begin_inset Quotes erd
12519 The length may also be negative.
12520 When a space would be the first character in a line it would be omitted.
12521 To force its output use the command
12533 or left-click on the
12534 \begin_inset Quotes eld
12540 \begin_inset space \textvisiblespace{}
12546 \begin_inset Quotes erd
12549 and check the option
12554 \begin_inset Newline newline
12557 To insert as much space as is available, the command
12564 \begin_inset Index idx
12567 \begin_layout Plain Layout
12578 \begin_layout Standard
12579 \begin_inset VSpace -1mm
12585 \begin_layout Standard
12587 \begin_inset Tabular
12588 <lyxtabular version="3" rows="4" columns="2">
12589 <features rotate="0" tabularvalignment="middle">
12590 <column alignment="center" valignment="top">
12591 <column alignment="center" valignment="top">
12593 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
12596 \begin_layout Plain Layout
12604 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
12607 \begin_layout Plain Layout
12615 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
12618 \begin_layout Plain Layout
12622 \begin_inset space \textvisiblespace{}
12628 \begin_inset space \thinspace{}
12636 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
12639 \begin_layout Plain Layout
12640 \begin_inset Formula $A=B\hspace{3cm}A\not=C$
12650 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
12653 \begin_layout Plain Layout
12657 \begin_inset space \textvisiblespace{}
12663 \begin_inset space \thinspace{}
12671 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
12674 \begin_layout Plain Layout
12675 \begin_inset Formula $A\hspace{-1mm}A\not=A$
12685 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
12688 \begin_layout Plain Layout
12692 \begin_inset space \textvisiblespace{}
12700 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
12703 \begin_layout Plain Layout
12704 \begin_inset Formula $A=A\hfill B=B$
12720 \begin_layout Standard
12721 In the last example the available space is given by the longest column entry
12723 In an inline formula the space depends on the length of the line in which
12731 Thus, when the line uses the full width, no space will be created.
12738 only has an effect on displayed formulas when the formula style
12743 (Formula styles are explained in
12744 \begin_inset CommandInset ref
12746 reference "sec:Formula-Styles"
12753 \begin_layout Standard
12760 , there are the commands
12772 that fill the space with a pattern, see
12773 \begin_inset CommandInset ref
12775 reference "sub:Ellipses"
12782 \begin_layout Standard
12783 For text, variable space can be inserted via the menu
12785 Insert\SpecialChar \menuseparator
12786 Formatting\SpecialChar \menuseparator
12788 \begin_inset space ~
12796 \begin_layout Standard
12797 This is a line with
12798 \begin_inset space \hspace{}
12803 \begin_inset space \thinspace{}
12809 \begin_layout Standard
12810 This is a line with
12811 \begin_inset space \hfill{}
12817 \begin_layout Subsection
12818 Space besides inline Formulas
12819 \begin_inset Index idx
12822 \begin_layout Plain Layout
12823 Space ! besides inline formulas
12831 \begin_layout Standard
12832 The space that surrounds inline formulas can be adjusted with the length
12840 \begin_inset Index idx
12843 \begin_layout Plain Layout
12852 The value of a length is set with the command
12859 \begin_inset Index idx
12862 \begin_layout Plain Layout
12870 which has the following scheme:
12873 \begin_layout Standard
12878 setlength{length name}{value}
12881 \begin_layout Standard
12889 \begin_inset space \thinspace{}
12895 \begin_layout Standard
12905 \begin_layout Standard
12906 is inserted in TeX-mode.
12908 \begin_inset space \thinspace{}
12911 mm space will now be set around all inline formulas:
12915 \begin_layout Plain Layout
12929 \begin_layout Standard
12930 This is a line with an inline formula
12931 \begin_inset Formula $A=B$
12935 \begin_inset space \thinspace{}
12938 mm surrounding space.
12942 \begin_layout Plain Layout
12956 \begin_layout Standard
12957 To return to the predefined value,
12963 is set to the value 0
12964 \begin_inset space \thinspace{}
12970 \begin_layout Section
12972 \begin_inset Index idx
12975 \begin_layout Plain Layout
12982 \begin_inset Index idx
12985 \begin_layout Plain Layout
12990 \begin_layout Plain Layout
13001 \begin_layout Plain Layout
13016 \begin_layout Standard
13017 Boxes for text are described in chapter
13024 \begin_inset space ~
13032 \begin_layout Subsection
13034 \begin_inset CommandInset label
13036 name "sub:Boxes-with-Frame"
13041 \begin_inset Index idx
13044 \begin_layout Plain Layout
13053 \begin_layout Standard
13054 It is possible to frame a formula or part of one with the commands
13061 \begin_inset Index idx
13064 \begin_layout Plain Layout
13079 \begin_inset Index idx
13082 \begin_layout Plain Layout
13093 \begin_layout Standard
13094 When one of these commands is inserted in a formula, a blue box appears
13095 within a frame to enter formula parts.
13102 an additional formula has to be created by
13106 within this box, because the box content will otherwise be treated as mathemati
13114 is used, a new formula is automatically created inside the frame.
13117 \begin_layout Standard
13124 is not suitable to frame displayed formulas because the formula will always
13125 be set in the size of the text.
13132 is in contrary not suitable to frame inline formulas, because the formula
13133 will always be set in the size of a displayed formula.
13136 \begin_layout Standard
13150 \begin_inset Index idx
13153 \begin_layout Plain Layout
13161 where additionally the frame width and the alignment can be specified.
13168 is used in the following scheme:
13171 \begin_layout Standard
13176 framebox[frame width][position]{box content}
13179 \begin_layout Standard
13180 The position can either be
13197 right aligns the formula in the box.
13198 When no position is given, the formula will be centered.
13199 \begin_inset Newline newline
13202 If no width is given, also no position can be given.
13203 In this case the frame width is adjusted to the box content like for
13212 \begin_layout Standard
13219 is inserted, a box appears containing three blue boxes.
13220 The first two boxes are surrounded by brackets and denote the two optional
13222 The third box is for formula parts like for
13231 \begin_layout Standard
13233 \begin_inset Tabular
13234 <lyxtabular version="3" rows="5" columns="2">
13235 <features rotate="0" tabularvalignment="middle">
13236 <column alignment="center" valignment="top">
13237 <column alignment="center" valignment="top">
13239 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
13242 \begin_layout Plain Layout
13248 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
13251 \begin_layout Plain Layout
13253 \begin_inset Note Note
13256 \begin_layout Plain Layout
13263 is only used as spacer.
13275 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
13278 \begin_layout Plain Layout
13282 \begin_inset space \textvisiblespace{}
13292 \begin_inset space \textvisiblespace{}
13300 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
13303 \begin_layout Plain Layout
13304 \begin_inset Formula $\raisebox{6mm}{}\fbox{\ensuremath{\int A=B}}\raisebox{-4mm}{}$
13314 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
13317 \begin_layout Plain Layout
13321 \begin_inset space \textvisiblespace{}
13327 \begin_inset space \textvisiblespace{}
13335 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
13338 \begin_layout Plain Layout
13339 \begin_inset Formula $\raisebox{8.5mm}{}\boxed{\int A=B}\raisebox{-6.5mm}{}$
13349 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
13352 \begin_layout Plain Layout
13356 \begin_inset space \textvisiblespace{}
13364 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
13367 \begin_layout Plain Layout
13368 \begin_inset Formula $\raisebox{6mm}{}A+\fbox{B}\raisebox{-3mm}{}$
13378 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
13381 \begin_layout Plain Layout
13385 \begin_inset space \textvisiblespace{}
13389 \begin_inset Formula $\to$
13393 \begin_inset Formula $\to$
13403 \begin_inset space \textvisiblespace{}
13407 \begin_inset Formula $\downarrow$
13415 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
13418 \begin_layout Plain Layout
13419 \begin_inset Formula $\raisebox{6mm}{}$
13423 \begin_inset Formula $\framebox[20mm][]{\ensuremath{\frac{A}{B}}}$
13427 \begin_inset Formula $\raisebox{-4mm}{}$
13443 \begin_layout Standard
13444 The frame thickness can also be adjusted.
13445 To do this the following commands have to be inserted in TeX-mode before
13449 \begin_layout Standard
13459 \begin_inset Quotes eld
13463 \begin_inset Quotes erd
13477 \begin_inset Quotes eld
13481 \begin_inset Quotes erd
13487 \begin_layout Standard
13488 \begin_inset Quotes eld
13492 \begin_inset Quotes erd
13495 specifies the minimal distance between the frame and the first character
13497 An example for this is the following framed formula:
13501 \begin_layout Plain Layout
13513 \begin_inset Formula
13520 Before this formula the commands
13523 \begin_layout Standard
13545 \begin_layout Standard
13546 were inserted in TeX-mode.
13547 The given values are used for all following boxes.
13550 \begin_layout Standard
13551 To return to the standard frame size, the command
13554 \begin_layout Standard
13579 \begin_layout Plain Layout
13593 \begin_layout Standard
13594 is inserted in TeX-mode before the next formula.
13597 \begin_layout Subsection
13598 Boxes without Frame
13599 \begin_inset CommandInset label
13601 name "sub:Boxes-without-Frame"
13606 \begin_inset Index idx
13609 \begin_layout Plain Layout
13610 Boxes ! without frame
13618 \begin_layout Standard
13619 For boxes without a frame there are the following box commands:
13626 \begin_inset Index idx
13629 \begin_layout Plain Layout
13644 \begin_inset Index idx
13647 \begin_layout Plain Layout
13662 \begin_inset Index idx
13665 \begin_layout Plain Layout
13676 \begin_layout Standard
13683 a box can be super- or subscripted.
13684 But in contrary to normal super- and subscripting, the characters in the
13685 box keep their font size.
13692 is used in the following scheme:
13695 \begin_layout Standard
13700 raisebox{height}{box content}
13703 \begin_layout Standard
13704 When the box should contain a formula, an extra formula is needed like for
13715 \begin_inset Note Greyedout
13718 \begin_layout Plain Layout
13729 this extra formula is created by pressing
13733 twice instead of once because LyX doesn't yet support
13747 \begin_layout Standard
13749 \begin_inset Tabular
13750 <lyxtabular version="3" rows="4" columns="2">
13751 <features rotate="0" tabularvalignment="middle">
13752 <column alignment="center" valignment="top">
13753 <column alignment="center" valignment="top">
13755 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
13758 \begin_layout Plain Layout
13764 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
13767 \begin_layout Plain Layout
13775 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
13778 \begin_layout Plain Layout
13782 \begin_inset Formula $\to$
13788 \begin_inset Formula $\to$
13796 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
13799 \begin_layout Plain Layout
13800 \begin_inset Formula $H\raisebox{2mm}{al}lo$
13810 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
13813 \begin_layout Plain Layout
13817 \begin_inset Formula $\to$
13823 \begin_inset Formula $\to$
13831 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
13834 \begin_layout Plain Layout
13835 \begin_inset Formula $H\raisebox{-2mm}{al}lo$
13845 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
13848 \begin_layout Plain Layout
13852 \begin_inset Formula $\to$
13868 \begin_inset space \textvisiblespace{}
13876 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
13879 \begin_layout Plain Layout
13880 \begin_inset Formula $A=\raisebox{-2mm}{\mbox{\ensuremath{\sqrt{B}}}}$
13896 \begin_layout Standard
13921 , with the difference that there is no frame.
13924 \begin_layout Subsection
13926 \begin_inset CommandInset label
13928 name "sub:Colored-Boxes"
13933 \begin_inset Index idx
13936 \begin_layout Plain Layout
13945 \begin_layout Standard
13946 To be able to use all commands explained in this section, the LaTeX-package
13955 \begin_layout Plain Layout
13960 is part of every LaTeX standard installation.
13966 \begin_inset Index idx
13969 \begin_layout Plain Layout
13975 has to be loaded in the LaTeX-preamble with the line
13979 \begin_layout Plain Layout
13980 When text is colored somewhere in the document with a predefined color,
13981 LyX loads the LaTeX-package
13986 Thus it is possible that the package is loaded twice, but this does not
13993 \begin_inset Note Note
13996 \begin_layout Plain Layout
13997 To avoid that the package is loaded twice, a macro was inserted to the LaTeX-pre
14006 \begin_layout Standard
14014 \begin_layout Standard
14015 \begin_inset VSpace medskip
14018 To color boxes, the command
14025 \begin_inset Index idx
14028 \begin_layout Plain Layout
14036 is used in the following scheme:
14039 \begin_layout Standard
14044 colorbox{color}{box content}
14047 \begin_layout Standard
14048 The box content can also be a box and a
14054 can also be part of another box (see the 2nd and 3rd example).
14055 When the box should contain a formula, an extra formula has to be created,
14056 the same way as for
14066 \begin_layout Plain Layout
14067 This also applies for the command
14081 \begin_layout Standard
14082 One of the following predefined colors can be chosen:
14085 \begin_layout Standard
14119 \begin_layout Standard
14121 \begin_inset Tabular
14122 <lyxtabular version="3" rows="4" columns="2">
14123 <features rotate="0" tabularvalignment="middle">
14124 <column alignment="center" valignment="top">
14125 <column alignment="center" valignment="top">
14127 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
14130 \begin_layout Plain Layout
14136 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
14139 \begin_layout Plain Layout
14141 \begin_inset Note Note
14144 \begin_layout Plain Layout
14151 is only used as spacer.
14163 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
14166 \begin_layout Plain Layout
14170 \begin_inset Formula $\to$
14180 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
14183 \begin_layout Plain Layout
14184 \begin_inset Formula $\raisebox{6mm}{}\colorbox{yellow}{A=B}\raisebox{-3mm}{}$
14194 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
14197 \begin_layout Plain Layout
14201 \begin_inset Formula $\to$
14209 \begin_inset space \textvisiblespace{}
14217 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
14220 \begin_layout Plain Layout
14221 \begin_inset Formula $\raisebox{6mm}{}\colorbox{green}{\fbox{A=B}}\raisebox{-3mm}{}$
14231 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
14234 \begin_layout Plain Layout
14238 \begin_inset space \textvisiblespace{}
14244 \begin_inset Formula $\to$
14260 \begin_inset space \textvisiblespace{}
14268 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
14271 \begin_layout Plain Layout
14272 \begin_inset Formula $\raisebox{7mm}{}\fbox{\colorbox{green}{\mbox{\ensuremath{\int C=D}}}}\raisebox{-5mm}{}$
14288 \begin_layout Standard
14295 only colors the box but not the characters in the box.
14296 To color all characters, the whole formula is highlighted and the desired
14297 color is chosen in the
14300 \begin_inset space ~
14306 The dialog can be called with the toolbar button
14309 arg "dialog-show character"
14314 Edit\SpecialChar \menuseparator
14316 \begin_inset space ~
14319 Style\SpecialChar \menuseparator
14323 The formula number then has the same color as the formula.
14324 When the formula number should get another color than the formula characters,
14325 the color must be changed within the formula.
14328 \begin_layout Standard
14332 \begin_layout Standard
14335 \begin_inset Formula
14337 \int A=B\label{eq:red}
14345 \begin_inset Formula
14347 \textcolor{red}{\int A=B}\label{eq:redgreen}
14355 \begin_layout Standard
14357 \begin_inset CommandInset ref
14363 is completely colored red.
14364 \begin_inset Newline newline
14368 \begin_inset CommandInset ref
14370 reference "eq:redgreen"
14374 was first completely colored green to set the color for the formula number.
14375 Subsequently the formula characters were colored red.
14378 \begin_layout Standard
14379 \begin_inset VSpace bigskip
14382 To color the frame different than the rest of the box, the command
14389 \begin_inset Index idx
14392 \begin_layout Plain Layout
14400 is used in the following scheme:
14403 \begin_layout Standard
14408 fcolorbox{frame color}{color}{box content}
14411 \begin_layout Standard
14418 is an extension of the command
14425 The frame width is set, like for
14448 \begin_layout Plain Layout
14460 \begin_inset Formula
14462 \fcolorbox{cyan}{magenta}{A=B}
14471 \begin_layout Plain Layout
14485 \begin_layout Standard
14486 This formula was created with the command
14487 \begin_inset Newline newline
14495 \begin_inset Formula $\to$
14501 \begin_inset Formula $\to$
14511 \begin_layout Standard
14512 \begin_inset VSpace bigskip
14515 To use other colors than the predefined ones, they have to be defined first.
14518 \begin_layout Standard
14519 One can for example define the color
14520 \begin_inset Quotes eld
14528 \begin_inset Quotes erd
14531 with the LaTeX-preamble line:
14534 \begin_layout Standard
14539 definecolor{darkgreen}{cmyk}{0.5,
14554 \begin_inset Index idx
14557 \begin_layout Plain Layout
14568 \begin_layout Standard
14573 is the color space that denotes the colors
14590 The four comma separated numbers are the portion factor for the corresponding
14591 colors of the color space.
14592 The factors can be in the range of 0
14593 \begin_inset space \thinspace{}
14597 \begin_inset space \thinspace{}
14605 also the color space
14609 can be used for definitions.
14626 , so that there are in this case three portion factors for the corresponding
14628 Furthermore there is the color space
14632 with one portion factor for the gray value.
14635 \begin_layout Standard
14636 As example a framed box with the new defined color
14640 where the characters have been colored
14645 \begin_inset Formula
14647 \colorbox{darkgreen}{\color{yellow}\boxed{\int A\,\mathrm{d}x=\frac{\sqrt[5]{B}}{\ln\left(\frac{1}{3}\right)}}}
14655 \begin_layout Standard
14656 Self-defined colors can also be used for text with the help of the command
14664 \begin_inset Index idx
14667 \begin_layout Plain Layout
14676 \begin_layout Standard
14680 \begin_layout Plain Layout
14684 textcolor{darkgreen}{
14690 \begin_inset Quotes eld
14694 \begin_inset Quotes erd
14701 \begin_layout Plain Layout
14711 \begin_layout Standard
14719 \begin_inset Index idx
14722 \begin_layout Plain Layout
14730 is used in the scheme
14734 textcolor{color}{characters to color}
14739 \begin_layout Subsection
14741 \begin_inset CommandInset label
14743 name "sub:Paragraph-Boxes"
14748 \begin_inset Index idx
14751 \begin_layout Plain Layout
14752 Boxes ! as paragraph
14760 \begin_layout Standard
14761 A box that can contain several lines and paragraphs, a so-called paragraph
14762 box (parbox), can be created with the menu
14764 Insert\SpecialChar \menuseparator
14767 or the toolbar button
14776 \begin_layout Standard
14777 The following example shows a framed parbox in a line:
14780 \begin_layout Standard
14781 \begin_inset VSpace medskip
14785 \begin_inset Box Boxed
14795 height_special "totalheight"
14798 \begin_layout Plain Layout
14799 This is a paragraph box.
14801 \begin_inset space \thinspace{}
14804 cm long and can also contain formulas:
14805 \begin_inset Formula $\int A\,\mathrm{d}s=C$
14816 \begin_layout Standard
14817 \begin_inset VSpace medskip
14823 \begin_layout Standard
14824 Such a box is created by right-clicking on the gray box inset.
14825 A dialog pops up showing the box properties.
14839 \begin_inset space \thinspace{}
14844 Vertical Box Alignment
14849 \begin_layout Standard
14850 \begin_inset VSpace medskip
14853 In LaTeX a parbox is created with the command
14860 \begin_inset Index idx
14863 \begin_layout Plain Layout
14871 which has the following scheme:
14874 \begin_layout Standard
14879 parbox[position]{width}{box content}
14882 \begin_layout Standard
14897 \begin_inset Quotes eld
14901 \begin_inset Quotes erd
14904 means that the box is aligned within the surrounding text with its last
14911 \begin_inset Quotes eld
14915 \begin_inset Quotes erd
14918 this is done with the first line.
14919 When no position is given, the box will be vertically centered, see section
14927 \begin_inset space ~
14932 manual for examples.
14935 \begin_layout Standard
14936 \begin_inset VSpace bigskip
14939 To frame formulas completely, including the formula number, the formula
14940 must be set into a parbox.
14941 To do this, the command
14955 is inserted in TeX-mode before the formula.
14963 \begin_inset Index idx
14966 \begin_layout Plain Layout
14974 is hereby the line width set for the document.
14975 Because the frame is outside the parbox, 2
14976 \begin_inset space \thinspace{}
14979 times the frame separation and the frame thickness must be subtracted from
14981 As this is not automatically done by LyX due to a bug
14985 \begin_layout Plain Layout
14986 \begin_inset CommandInset href
14988 name "LyX-bug #4483"
14989 target "http://www.lyx.org/trac/ticket/4483"
14998 , TeX-mode has to be used.
14999 To be able to multiply and subtract in arguments, the LaTeX-package
15007 \begin_layout Plain Layout
15012 is part of every LaTeX standard installation.
15018 \begin_inset Index idx
15021 \begin_layout Plain Layout
15027 must be loaded in the LaTeX-preamble with the line
15030 \begin_layout Standard
15038 \begin_layout Standard
15039 Behind the formula both boxes are closed by entering
15044 Here is an example:
15048 \begin_layout Plain Layout
15062 \begin_layout Standard
15066 \begin_layout Plain Layout
15084 \begin_inset Formula
15086 \int A\,\mathrm{d}x=\frac{\sqrt[5]{B}}{\ln\left(\frac{1}{3}\right)}
15095 \begin_layout Plain Layout
15106 \begin_layout Plain Layout
15120 \begin_layout Standard
15121 \begin_inset VSpace medskip
15124 As a parbox is used as the argument of
15130 , there is in this case no difference between
15145 \begin_layout Standard
15146 \begin_inset VSpace bigskip
15149 Paragraph boxes are very useful to comment formulas directly.
15156 is used in combination with the command
15170 \begin_inset CommandInset ref
15172 reference "sub:User-defined-Numbering"
15179 \begin_layout Standard
15180 An example of a formula commented with
15189 \begin_layout Standard
15193 \begin_layout Plain Layout
15206 This is a description.
15207 It is distinctly separated from the formula and multiline.
15211 \begin_layout Plain Layout
15223 \begin_layout Standard
15224 Such a formula must be inserted completely in TeX-mode because LyX does
15225 not yet support the command
15232 The formula is created with the following command sequence:
15235 \begin_layout Standard
15248 is inserted in TeX-mode.
15252 \begin_layout Plain Layout
15253 When the formula style
15265 can also be replaced by
15272 (formula styles see
15273 \begin_inset CommandInset ref
15275 reference "sec:Formula-Styles"
15284 Then the description follows as normal text and finally
15290 is inserted in TeX-mode.
15303 hereby create a displayed formula.
15306 \begin_layout Standard
15313 can be seen in this example that was
15314 \begin_inset Quotes eld
15318 \begin_inset Quotes erd
15321 using the mathematical textmode:
15322 \begin_inset Formula
15324 5x-7b=3b\textrm{This is a description. It is not separated from the formula ...}
15332 \begin_layout Section
15334 \begin_inset Index idx
15337 \begin_layout Plain Layout
15346 \begin_layout Subsection
15348 \begin_inset CommandInset label
15350 name "sub:Big-Operators"
15355 \begin_inset Index idx
15358 \begin_layout Plain Layout
15365 \begin_inset Index idx
15368 \begin_layout Plain Layout
15375 \begin_inset Index idx
15378 \begin_layout Plain Layout
15387 \begin_layout Standard
15388 To be able to use all integral operators listed here, the option
15390 Use esint package automatically
15392 must be set in the document settings under
15395 \begin_inset space ~
15403 \begin_layout Standard
15404 \begin_inset space \hfill{}
15408 \begin_inset Tabular
15409 <lyxtabular version="3" rows="11" columns="2">
15410 <features rotate="0" tabularvalignment="middle">
15411 <column alignment="center" valignment="top" width="0pt">
15412 <column alignment="center" valignment="top" width="0pt">
15414 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
15417 \begin_layout Plain Layout
15423 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
15426 \begin_layout Plain Layout
15434 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
15437 \begin_layout Plain Layout
15441 \begin_inset Index idx
15444 \begin_layout Plain Layout
15457 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
15460 \begin_layout Plain Layout
15461 \begin_inset Formula $\int$
15471 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
15474 \begin_layout Plain Layout
15482 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
15485 \begin_layout Plain Layout
15486 \begin_inset Formula $\oint$
15496 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
15499 \begin_layout Plain Layout
15507 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
15510 \begin_layout Plain Layout
15511 \begin_inset Formula $\ointctrclockwise$
15521 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
15524 \begin_layout Plain Layout
15532 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
15535 \begin_layout Plain Layout
15536 \begin_inset Formula $\ointclockwise$
15546 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
15549 \begin_layout Plain Layout
15557 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
15560 \begin_layout Plain Layout
15561 \begin_inset Formula $\sqint$
15571 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
15574 \begin_layout Plain Layout
15582 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
15585 \begin_layout Plain Layout
15587 \begin_inset Formula $\fint$
15597 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
15600 \begin_layout Plain Layout
15608 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
15611 \begin_layout Plain Layout
15613 \begin_inset Formula $\landupint$
15623 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
15626 \begin_layout Plain Layout
15634 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
15637 \begin_layout Plain Layout
15639 \begin_inset Formula $\landdownint$
15649 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
15652 \begin_layout Plain Layout
15660 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
15663 \begin_layout Plain Layout
15664 \begin_inset Formula $\bigcap$
15674 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
15677 \begin_layout Plain Layout
15685 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
15688 \begin_layout Plain Layout
15689 \begin_inset Formula $\bigcup$
15703 \begin_inset space \hfill{}
15707 \begin_inset Tabular
15708 <lyxtabular version="3" rows="11" columns="2">
15709 <features rotate="0" tabularvalignment="middle">
15710 <column alignment="center" valignment="top" width="0pt">
15711 <column alignment="center" valignment="top" width="0pt">
15713 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
15716 \begin_layout Plain Layout
15722 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
15725 \begin_layout Plain Layout
15733 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
15736 \begin_layout Plain Layout
15740 \begin_inset Index idx
15743 \begin_layout Plain Layout
15756 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
15759 \begin_layout Plain Layout
15760 \begin_inset Formula $\sum$
15770 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
15773 \begin_layout Plain Layout
15777 \begin_inset Index idx
15780 \begin_layout Plain Layout
15787 \begin_layout Plain Layout
15806 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
15809 \begin_layout Plain Layout
15810 \begin_inset Formula $\prod$
15820 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
15823 \begin_layout Plain Layout
15831 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
15834 \begin_layout Plain Layout
15835 \begin_inset Formula $\coprod$
15845 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
15848 \begin_layout Plain Layout
15856 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
15859 \begin_layout Plain Layout
15860 \begin_inset Formula $\bigodot$
15870 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
15873 \begin_layout Plain Layout
15881 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
15884 \begin_layout Plain Layout
15885 \begin_inset Formula $\bigotimes$
15895 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
15898 \begin_layout Plain Layout
15906 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
15909 \begin_layout Plain Layout
15910 \begin_inset Formula $\bigoplus$
15920 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
15923 \begin_layout Plain Layout
15931 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
15934 \begin_layout Plain Layout
15935 \begin_inset Formula $\bigwedge$
15945 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
15948 \begin_layout Plain Layout
15956 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
15959 \begin_layout Plain Layout
15960 \begin_inset Formula $\bigvee$
15970 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
15973 \begin_layout Plain Layout
15981 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
15984 \begin_layout Plain Layout
15985 \begin_inset Formula $\bigsqcup$
15995 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
15998 \begin_layout Plain Layout
16006 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
16009 \begin_layout Plain Layout
16010 \begin_inset Formula $\biguplus$
16024 \begin_inset space \hfill{}
16030 \begin_layout Standard
16031 All big operators can also be inserted via the math toolbar button
16034 arg "math-insert \\intop"
16040 \begin_layout Standard
16041 The operators are called big because they are bigger than the sometimes
16042 equal looking binary operators.
16043 All big operators can have limits as described in the next subsection.
16046 \begin_layout Standard
16047 For all integral operators there is a second version available, ending in
16065 These operators are different from
16072 \begin_inset space \space{}
16075 in the style the operator limits are displayed, see
16076 \begin_inset CommandInset ref
16078 reference "sub:Operator-Limits"
16086 \begin_layout Subsubsection*
16087 Advice for Integrals
16090 \begin_layout Standard
16095 in an integral is an operator, that therefore has to be set upright.
16096 This is done by highlighting the
16100 and using the keyboard shortcut
16110 \begin_layout Plain Layout
16116 \begin_inset CommandInset ref
16118 reference "sub:Font-Styles"
16128 Finally the smallest space is inserted before the
16132 , as this is usual for operators.
16136 \begin_layout Standard
16138 \begin_inset Formula $\int A(x)dx$
16142 \begin_inset Newline newline
16146 \begin_inset Phantom HPhantom
16149 \begin_layout Plain Layout
16156 \begin_inset Formula $\int A(x)\,\mathrm{d}x$
16162 \begin_layout Standard
16163 For multiple integrals there are the following commands:
16164 \begin_inset VSpace medskip
16170 \begin_layout Standard
16171 \begin_inset space \hfill{}
16175 \begin_inset Tabular
16176 <lyxtabular version="3" rows="4" columns="2">
16177 <features rotate="0" tabularvalignment="middle">
16178 <column alignment="center" valignment="top">
16179 <column alignment="center" valignment="top">
16181 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
16184 \begin_layout Plain Layout
16190 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
16193 \begin_layout Plain Layout
16195 \begin_inset Note Note
16198 \begin_layout Plain Layout
16205 is only used as spacer.
16217 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
16220 \begin_layout Plain Layout
16228 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
16231 \begin_layout Plain Layout
16232 \begin_inset Formula $\raisebox{4.5mm}{}\iint\raisebox{-2.5mm}{}$
16242 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
16245 \begin_layout Plain Layout
16253 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
16256 \begin_layout Plain Layout
16257 \begin_inset Formula $\raisebox{4.5mm}{}\oiint\raisebox{-2.5mm}{}$
16267 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
16270 \begin_layout Plain Layout
16278 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
16281 \begin_layout Plain Layout
16282 \begin_inset Formula $\raisebox{4.5mm}{}\sqiint\raisebox{-2.5mm}{}$
16296 \begin_inset space \hfill{}
16300 \begin_inset Tabular
16301 <lyxtabular version="3" rows="4" columns="2">
16302 <features rotate="0" tabularvalignment="middle">
16303 <column alignment="center" valignment="top">
16304 <column alignment="center" valignment="top">
16306 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
16309 \begin_layout Plain Layout
16315 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
16318 \begin_layout Plain Layout
16326 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
16329 \begin_layout Plain Layout
16337 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
16340 \begin_layout Plain Layout
16341 \begin_inset Formula $\raisebox{4.5mm}{}\iiint\raisebox{-2.5mm}{}$
16351 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
16354 \begin_layout Plain Layout
16362 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
16365 \begin_layout Plain Layout
16366 \begin_inset Formula $\raisebox{4.5mm}{}\iiiint\raisebox{-2.5mm}{}$
16376 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
16379 \begin_layout Plain Layout
16387 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
16390 \begin_layout Plain Layout
16391 \begin_inset Formula $\raisebox{4.5mm}{}\dotsint\raisebox{-2.5mm}{}$
16405 \begin_inset space \hfill{}
16411 \begin_layout Subsection
16413 \begin_inset CommandInset label
16415 name "sub:Operator-Limits"
16420 \begin_inset Index idx
16423 \begin_layout Plain Layout
16432 \begin_layout Standard
16433 Limits are created by super- and subscripts:
16436 \begin_layout Standard
16438 \begin_inset Tabular
16439 <lyxtabular version="3" rows="2" columns="2">
16440 <features rotate="0" tabularvalignment="middle">
16441 <column alignment="center" valignment="top" width="0pt">
16442 <column alignment="center" valignment="top" width="0pt">
16444 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
16447 \begin_layout Plain Layout
16453 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
16456 \begin_layout Plain Layout
16458 \begin_inset Note Note
16461 \begin_layout Plain Layout
16468 is only used as spacer.
16480 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
16483 \begin_layout Plain Layout
16489 \begin_inset space \textvisiblespace{}
16493 \begin_inset Formula $\to$
16497 \begin_inset Formula $\to$
16505 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
16508 \begin_layout Plain Layout
16509 \begin_inset Formula $\raisebox{5mm}{}\prod_{0}^{\infty}A(x)\raisebox{-2.5mm}{}$
16525 \begin_layout Standard
16526 Limits of inline formulas are set right beside the operator.
16527 Limits in displayed formulas are set above or below the operator, except
16528 for integral limits.
16531 \begin_layout Standard
16532 To force that the limits are set beside the operator, the cursor is set
16533 directly behind the operator and the limits type is changed with the menu
16536 Edit\SpecialChar \menuseparator
16537 Math\SpecialChar \menuseparator
16556 \begin_layout Standard
16557 The default limits type is this:
16558 \begin_inset Formula
16560 \sum_{x=0}^{\infty}\frac{1}{x^{2}}
16565 This is how it looks when the limits type was changed to
16572 \begin_inset Formula
16574 \sum\nolimits _{x=0}^{\infty}\frac{1}{x^{2}}
16579 For integrals, except those ending with
16595 etc., the limits are by default set beside the operator.
16596 But for multiple integrals the limits are often set below the operator.
16597 In the following example the limits type was therefore set to
16601 and so set below the integrals:
16602 \begin_inset Formula
16604 \iiint\limits _{V}X\,\mathrm{d}V=U\label{eq:VolInt}
16612 \begin_layout Standard
16613 \begin_inset VSpace medskip
16616 To specify conditions for limits, the commands
16623 \begin_inset Index idx
16626 \begin_layout Plain Layout
16641 \begin_inset Index idx
16644 \begin_layout Plain Layout
16653 To create for example this expression
16654 \begin_inset Formula
16656 \sum_{\begin{subarray}{c}
16660 \end{subarray}}^{n}k^{-2}\label{eq:substack}
16668 \begin_layout Standard
16669 the following has to be done:
16670 \begin_inset Newline newline
16682 \begin_inset space \textvisiblespace{}
16688 One is now in a blue box under the summation operator and insert there
16694 \begin_inset space \textvisiblespace{}
16700 The blue box is now within a purple box and now several lines can be written
16702 A new line is created by inserting a line break (
16705 arg "newline-insert newline"
16710 \begin_inset Newline newline
16715 0<k<1000 Ctrl+Return
16716 \begin_inset Newline newline
16721 is typed in, a new box appears below for the new line.
16724 \begin_layout Standard
16725 The alignment of the lines can be changed to left aligned with the
16735 Edit\SpecialChar \menuseparator
16739 To get right alignment,
16744 \begin_inset space \textvisiblespace{}
16749 is inserted at the beginning of the line.
16752 \begin_layout Standard
16765 with the difference that the lines are always centered.
16768 \begin_layout Standard
16769 \begin_inset VSpace bigskip
16773 \begin_inset CommandInset ref
16775 reference "eq:substack"
16779 there can be too much space beside an operator, because the characters
16780 following the operator are set beside the limits.
16781 To avoid this the command
16788 \begin_inset Index idx
16791 \begin_layout Plain Layout
16800 It sets the width of its content to 0
16801 \begin_inset space \thinspace{}
16805 \begin_inset Newline newline
16809 \begin_inset CommandInset ref
16811 reference "eq:substack"
16815 , one uses the command
16818 \begin_layout Standard
16828 \begin_inset space \textvisiblespace{}
16831 0<k<1000 Ctrl+Return
16834 \begin_layout Standard
16835 to create the lower limit.
16836 The summand is now directly behind the summation operator:
16837 \begin_inset Formula
16839 \sum_{\mathclap{\substack{0<k<1000\\
16851 \begin_layout Standard
16852 \begin_inset VSpace bigskip
16858 \begin_layout Standard
16859 When several consecutive operators have limits the typesetting of the limits
16860 looks often imperfect in the output, see this example:
16861 \begin_inset Formula
16863 \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}
16868 To improve the typesetting set in the document settings under
16871 \begin_inset space ~
16881 \begin_inset Index idx
16884 \begin_layout Plain Layout
16885 Packages ! mathtools
16893 \begin_inset space ~
16899 Then insert into your formula the command
16906 \begin_inset Index idx
16909 \begin_layout Plain Layout
16917 directly before the first operator.
16918 The example will then look like this:
16919 \begin_inset Formula
16921 \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}
16929 \begin_layout Standard
16930 \begin_inset VSpace bigskip
16933 How to use one limit for several operators is described in
16934 \begin_inset CommandInset ref
16936 reference "sub:Self-defined-Operators"
16943 \begin_layout Subsection
16944 Decoration for Operators
16945 \begin_inset Index idx
16948 \begin_layout Plain Layout
16949 Operators ! Decoration
16957 \begin_layout Standard
16965 \begin_inset Index idx
16968 \begin_layout Plain Layout
16983 \begin_inset Index idx
16986 \begin_layout Plain Layout
16994 characters can be placed above or below an operator, respectively.
17002 \begin_inset Index idx
17005 \begin_layout Plain Layout
17013 characters can be set before and behind a big operator.
17016 \begin_layout Standard
17018 \begin_inset space ~
17030 \begin_layout Itemize
17037 is used to set characters at the corners of the operator
17040 \begin_layout Itemize
17047 is used to set characters before and/or behind the operator (this variant
17048 represents LaTeX's original
17057 \begin_layout Itemize
17064 is used to set characters at the left corners and/or behind the operator
17067 \begin_layout Itemize
17074 is used to set characters at the right corners and/or before the operator
17077 \begin_layout Standard
17078 For example the command
17083 \begin_inset space \textvisiblespace{}
17089 \begin_inset space \textvisiblespace{}
17093 \begin_inset Formula $\to$
17097 \begin_inset Formula $\to$
17101 \begin_inset space \textvisiblespace{}
17111 \begin_inset Formula
17113 \sideset{}{'}\sum_{k=1}^{n}
17121 \begin_layout Standard
17122 \begin_inset Note Greyedout
17125 \begin_layout Plain Layout
17132 can only be used to decorate big operators, binary operators are not allowed.
17140 \begin_layout Standard
17153 can also be used to decorate symbols and characters.
17154 For example, the command
17159 \begin_inset space \textvisiblespace{}
17165 \begin_inset space \textvisiblespace{}
17171 \begin_inset Formula $\uparrow$
17179 \begin_inset Formula
17181 \overset{a}{\maltese}
17189 \begin_layout Subsection
17191 \begin_inset CommandInset label
17193 name "sub:Binary-Operators"
17198 \begin_inset Index idx
17201 \begin_layout Plain Layout
17210 \begin_layout Standard
17211 Binary operators are surrounded by space when there is a character before
17213 \begin_inset VSpace medskip
17219 \begin_layout Standard
17220 \begin_inset space \hfill{}
17224 \begin_inset Tabular
17225 <lyxtabular version="3" rows="13" columns="2">
17226 <features rotate="0" tabularvalignment="middle">
17227 <column alignment="center" valignment="top" width="0pt">
17228 <column alignment="center" valignment="top" width="0pt">
17230 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
17233 \begin_layout Plain Layout
17235 \begin_inset Note Note
17238 \begin_layout Plain Layout
17245 is only used as spacer.
17255 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
17258 \begin_layout Plain Layout
17266 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
17269 \begin_layout Plain Layout
17275 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
17278 \begin_layout Plain Layout
17279 \begin_inset Formula $+$
17289 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
17292 \begin_layout Plain Layout
17298 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
17301 \begin_layout Plain Layout
17302 \begin_inset Formula $-$
17312 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
17315 \begin_layout Plain Layout
17323 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
17326 \begin_layout Plain Layout
17327 \begin_inset Formula $\pm$
17337 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
17340 \begin_layout Plain Layout
17348 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
17351 \begin_layout Plain Layout
17352 \begin_inset Formula $\mp$
17362 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
17365 \begin_layout Plain Layout
17373 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
17376 \begin_layout Plain Layout
17377 \begin_inset Formula $\cdot$
17387 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
17390 \begin_layout Plain Layout
17398 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
17401 \begin_layout Plain Layout
17402 \begin_inset Formula $\times$
17412 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
17415 \begin_layout Plain Layout
17423 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
17426 \begin_layout Plain Layout
17427 \begin_inset Formula $\div$
17437 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
17440 \begin_layout Plain Layout
17444 \begin_layout Plain Layout
17457 \begin_layout Plain Layout
17469 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
17472 \begin_layout Plain Layout
17473 \begin_inset Formula $*$
17483 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
17486 \begin_layout Plain Layout
17494 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
17497 \begin_layout Plain Layout
17498 \begin_inset Formula $\star$
17508 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
17511 \begin_layout Plain Layout
17519 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
17522 \begin_layout Plain Layout
17523 \begin_inset Formula $\circ$
17533 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
17536 \begin_layout Plain Layout
17544 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
17547 \begin_layout Plain Layout
17548 \begin_inset Formula $\diamond$
17558 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
17561 \begin_layout Plain Layout
17569 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
17572 \begin_layout Plain Layout
17573 \begin_inset Formula $\bullet$
17587 \begin_inset space \hfill{}
17591 \begin_inset Tabular
17592 <lyxtabular version="3" rows="13" columns="2">
17593 <features rotate="0" tabularvalignment="middle">
17594 <column alignment="center" valignment="top" width="0pt">
17595 <column alignment="center" valignment="top" width="0pt">
17597 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
17600 \begin_layout Plain Layout
17606 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
17609 \begin_layout Plain Layout
17617 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
17620 \begin_layout Plain Layout
17628 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
17631 \begin_layout Plain Layout
17632 \begin_inset Formula $\nabla$
17642 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
17645 \begin_layout Plain Layout
17653 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
17656 \begin_layout Plain Layout
17657 \begin_inset Formula $\bigtriangledown$
17667 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
17670 \begin_layout Plain Layout
17678 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
17681 \begin_layout Plain Layout
17682 \begin_inset Formula $\bigtriangleup$
17692 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
17695 \begin_layout Plain Layout
17703 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
17706 \begin_layout Plain Layout
17707 \begin_inset Formula $\Box$
17717 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
17720 \begin_layout Plain Layout
17728 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
17731 \begin_layout Plain Layout
17732 \begin_inset Formula $\cap$
17742 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
17745 \begin_layout Plain Layout
17753 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
17756 \begin_layout Plain Layout
17757 \begin_inset Formula $\cup$
17767 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
17770 \begin_layout Plain Layout
17778 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
17781 \begin_layout Plain Layout
17782 \begin_inset Formula $\dagger$
17792 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
17795 \begin_layout Plain Layout
17803 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
17806 \begin_layout Plain Layout
17807 \begin_inset Formula $\ddagger$
17817 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
17820 \begin_layout Plain Layout
17828 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
17831 \begin_layout Plain Layout
17832 \begin_inset Formula $\wr$
17842 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
17845 \begin_layout Plain Layout
17853 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
17856 \begin_layout Plain Layout
17857 \begin_inset Formula $\bigcirc$
17867 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
17870 \begin_layout Plain Layout
17878 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
17881 \begin_layout Plain Layout
17882 \begin_inset Formula $\wedge$
17892 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
17895 \begin_layout Plain Layout
17903 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
17906 \begin_layout Plain Layout
17907 \begin_inset Formula $\vee$
17921 \begin_inset space \hfill{}
17925 \begin_inset Tabular
17926 <lyxtabular version="3" rows="13" columns="2">
17927 <features rotate="0" tabularvalignment="middle">
17928 <column alignment="center" valignment="top" width="0pt">
17929 <column alignment="center" valignment="top" width="0pt">
17931 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
17934 \begin_layout Plain Layout
17940 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
17943 \begin_layout Plain Layout
17951 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
17954 \begin_layout Plain Layout
17962 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
17965 \begin_layout Plain Layout
17966 \begin_inset Formula $\oplus$
17976 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
17979 \begin_layout Plain Layout
17987 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
17990 \begin_layout Plain Layout
17991 \begin_inset Formula $\ominus$
18001 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
18004 \begin_layout Plain Layout
18012 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
18015 \begin_layout Plain Layout
18016 \begin_inset Formula $\otimes$
18026 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
18029 \begin_layout Plain Layout
18037 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
18040 \begin_layout Plain Layout
18041 \begin_inset Formula $\oslash$
18051 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
18054 \begin_layout Plain Layout
18062 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
18065 \begin_layout Plain Layout
18066 \begin_inset Formula $\odot$
18076 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
18079 \begin_layout Plain Layout
18087 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
18090 \begin_layout Plain Layout
18091 \begin_inset Formula $\amalg$
18101 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
18104 \begin_layout Plain Layout
18112 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
18115 \begin_layout Plain Layout
18116 \begin_inset Formula $\uplus$
18126 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
18129 \begin_layout Plain Layout
18137 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
18140 \begin_layout Plain Layout
18141 \begin_inset Formula $\setminus$
18151 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
18154 \begin_layout Plain Layout
18162 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
18165 \begin_layout Plain Layout
18166 \begin_inset Formula $\sqcap$
18176 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
18179 \begin_layout Plain Layout
18187 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
18190 \begin_layout Plain Layout
18191 \begin_inset Formula $\sqcup$
18201 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
18204 \begin_layout Plain Layout
18212 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
18215 \begin_layout Plain Layout
18216 \begin_inset Formula $\triangleleft$
18226 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
18229 \begin_layout Plain Layout
18237 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
18240 \begin_layout Plain Layout
18241 \begin_inset Formula $\triangleright$
18255 \begin_inset space \hfill{}
18261 \begin_layout Standard
18262 All binary operators can also be inserted via the math toolbar button
18265 arg "math-insert \\pm"
18271 \begin_layout Standard
18272 To typeset the Laplace operator also
18289 \begin_inset Formula $\nabla^{2}$
18292 ) can be used instead of
18301 \begin_layout Standard
18308 Insert\SpecialChar \menuseparator
18320 \begin_layout Subsection
18321 Self-defined Operators
18322 \begin_inset CommandInset label
18324 name "sub:Self-defined-Operators"
18329 \begin_inset Index idx
18332 \begin_layout Plain Layout
18333 Operators ! self-defined
18341 \begin_layout Standard
18342 With the help of the command
18346 DeclareMathOperator
18349 \begin_inset Index idx
18352 \begin_layout Plain Layout
18357 DeclareMathOperator
18362 custom operators can be defined in the LaTeX-preamble.
18363 Its command scheme is:
18366 \begin_layout Standard
18371 DeclareMathOperator{new command}{display}
18374 \begin_layout Standard
18375 Display can be characters or symbols that define how the operator looks
18377 To define a big operator a * is set behind the command.
18378 All self-defined big operators can have limits as described in
18379 \begin_inset CommandInset ref
18381 reference "sub:Operator-Limits"
18388 \begin_layout Standard
18389 For example the LaTeX-preamble line
18392 \begin_layout Standard
18397 DeclareMathOperator*{
18404 \begin_layout Standard
18405 defines the command
18411 , that inserts a big operator consisting of the lozenge symbol from
18412 \begin_inset CommandInset ref
18414 reference "sub:Miscellaneous-Symbols"
18419 \begin_inset Formula
18421 \Lozenge_{n=1}^{\infty}
18426 The command for this formula is:
18437 \begin_inset Formula $\to$
18443 \begin_layout Standard
18444 \begin_inset VSpace bigskip
18447 When self-defined operators are not used several times in the document,
18448 they can also be defined with the commands
18455 \begin_inset Index idx
18458 \begin_layout Plain Layout
18473 \begin_inset Index idx
18476 \begin_layout Plain Layout
18484 , which have the following scheme:
18487 \begin_layout Standard
18501 \begin_layout Standard
18508 defines big operators,
18517 \begin_layout Standard
18525 \begin_inset space \thinspace{}
18529 \begin_inset space \space{}
18532 be used to use one limit for several operators:
18535 \begin_layout Standard
18536 \begin_inset Formula
18538 \mathop{\sum\negmedspace\sum}_{i,j=1}^{N}
18546 \begin_layout Standard
18547 The command for the formula above is:
18548 \begin_inset Newline newline
18564 \begin_inset space \textvisiblespace{}
18570 \begin_inset Formula $\to$
18576 \begin_inset space \textvisiblespace{}
18584 \begin_layout Section
18586 \begin_inset Index idx
18589 \begin_layout Plain Layout
18598 \begin_layout Subsection
18600 \begin_inset CommandInset label
18602 name "sub:Font-Styles"
18607 \begin_inset Index idx
18610 \begin_layout Plain Layout
18619 \begin_layout Standard
18620 Latin letters in formulas can be set in one of the following font styles:
18621 \begin_inset VSpace -2mm
18627 \begin_layout Standard
18629 \begin_inset Tabular
18630 <lyxtabular version="3" rows="7" columns="3">
18631 <features rotate="0" tabularvalignment="middle">
18632 <column alignment="center" valignment="top">
18633 <column alignment="center" valignment="top">
18634 <column alignment="center" valignment="top">
18636 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
18639 \begin_layout Plain Layout
18645 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
18648 \begin_layout Plain Layout
18654 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
18657 \begin_layout Plain Layout
18665 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
18668 \begin_layout Plain Layout
18674 \begin_inset space \textvisiblespace{}
18684 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
18687 \begin_layout Plain Layout
18688 \begin_inset Formula $\mathbb{ABC}$
18696 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
18699 \begin_layout Plain Layout
18712 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
18715 \begin_layout Plain Layout
18721 \begin_inset space \textvisiblespace{}
18731 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
18734 \begin_layout Plain Layout
18735 \begin_inset Formula $\mathbf{AbC}$
18743 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
18746 \begin_layout Plain Layout
18759 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
18762 \begin_layout Plain Layout
18768 \begin_inset space \textvisiblespace{}
18778 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
18781 \begin_layout Plain Layout
18782 \begin_inset Formula $\boldsymbol{AbC}$
18790 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
18793 \begin_layout Plain Layout
18796 arg "font-boldsymbol"
18806 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
18809 \begin_layout Plain Layout
18815 \begin_inset space \textvisiblespace{}
18825 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
18828 \begin_layout Plain Layout
18829 \begin_inset Formula $\mathcal{ABC}$
18837 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
18840 \begin_layout Plain Layout
18853 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
18856 \begin_layout Plain Layout
18862 \begin_inset space \textvisiblespace{}
18872 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
18875 \begin_layout Plain Layout
18876 \begin_inset Formula $\mathfrak{AbC}$
18884 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
18887 \begin_layout Plain Layout
18895 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
18898 \begin_layout Plain Layout
18904 \begin_inset space \textvisiblespace{}
18914 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
18917 \begin_layout Plain Layout
18918 \begin_inset Formula $\mathscr{AbC}$
18926 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
18929 \begin_layout Plain Layout
18943 \begin_layout Standard
18945 \begin_inset Tabular
18946 <lyxtabular version="3" rows="5" columns="3">
18947 <features rotate="0" tabularvalignment="middle">
18948 <column alignment="center" valignment="top">
18949 <column alignment="center" valignment="top">
18950 <column alignment="center" valignment="top">
18952 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
18955 \begin_layout Plain Layout
18961 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
18964 \begin_layout Plain Layout
18970 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
18973 \begin_layout Plain Layout
18981 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
18984 \begin_layout Plain Layout
18990 \begin_inset space \textvisiblespace{}
19000 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
19003 \begin_layout Plain Layout
19004 \begin_inset Formula $\mathit{AbC}$
19012 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
19015 \begin_layout Plain Layout
19023 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
19026 \begin_layout Plain Layout
19032 \begin_inset space \textvisiblespace{}
19042 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
19045 \begin_layout Plain Layout
19046 \begin_inset Formula $\mathrm{AbC}$
19054 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
19057 \begin_layout Plain Layout
19070 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
19073 \begin_layout Plain Layout
19079 \begin_inset space \textvisiblespace{}
19089 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
19092 \begin_layout Plain Layout
19093 \begin_inset Formula $\mathsf{AbC}$
19101 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
19104 \begin_layout Plain Layout
19117 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
19120 \begin_layout Plain Layout
19126 \begin_inset space \textvisiblespace{}
19136 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
19139 \begin_layout Plain Layout
19140 \begin_inset Formula $\mathtt{AbC}$
19148 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
19151 \begin_layout Plain Layout
19154 arg "font-typewriter"
19170 \begin_layout Standard
19171 \begin_inset Note Greyedout
19174 \begin_layout Plain Layout
19191 can only be used for big letters.
19199 \begin_layout Standard
19200 Predefined is the style
19209 \begin_layout Standard
19210 The style commands work also for letters in mathematical constructs:
19211 \begin_inset Formula
19213 \mathfrak{A=\frac{b}{C}}
19221 \begin_layout Standard
19222 Characters in mathematical text don't appear in a math font style but in
19223 the text font style
19230 That their style can't be set correctly via the text style dialog is a
19235 \begin_layout Plain Layout
19236 \begin_inset CommandInset href
19238 name "LyX-bug #4629"
19239 target "http://www.lyx.org/trac/ticket/4629"
19251 \begin_layout Standard
19252 Instead of the style commands the dialog
19254 Edit\SpecialChar \menuseparator
19255 Math\SpecialChar \menuseparator
19258 or the toolbar button
19261 arg "math-insert \\font"
19267 \begin_layout Subsection
19269 \begin_inset CommandInset label
19271 name "sub:Bold-Formulas"
19276 \begin_inset Index idx
19279 \begin_layout Plain Layout
19288 \begin_layout Standard
19289 To make a complete formula bold, the command
19295 from the previous subsection cannot be used, because it doesn't work for
19296 small Greek letters.
19297 Furthermore it prints Latin letters always upright, like in the following
19301 \begin_layout Standard
19302 \begin_inset Formula
19304 \mathbf{\int_{n}^{2}f(\theta)=\Gamma}\qquad\textrm{equation with \textbackslash mathbf}
19312 \begin_layout Standard
19313 To display the formula correctly, the command
19320 \begin_inset Formula
19322 \boldsymbol{\int_{n}^{2}f(\theta)=\Gamma\qquad\textrm{equation with \textbackslash boldsymbol}}
19327 It is also possible to set the formula in a
19329 boldmath environment
19332 This environment is created by inserting the command
19339 \begin_inset Index idx
19342 \begin_layout Plain Layout
19351 To end the environment, the command
19358 \begin_inset Index idx
19361 \begin_layout Plain Layout
19369 is inserted in TeX-mode.
19373 \begin_layout Plain Layout
19383 \begin_inset Formula
19385 \int_{n}^{2}f(\theta)=\Gamma\qquad\textrm{equation in a boldmath environment}
19394 \begin_layout Plain Layout
19406 \begin_layout Subsection
19408 \begin_inset Index idx
19411 \begin_layout Plain Layout
19420 \begin_layout Standard
19421 Formulas can be colored like normal text: Highlight a formula or a formula
19427 Here is a formula in magenta:
19428 \begin_inset Formula
19430 {\color{magenta}\int A\,\mathrm{d}x=\frac{\sqrt[5]{B}}{\ln\left(\frac{1}{3}\right)}}
19438 \begin_layout Standard
19439 You can also define your own colors as described in
19440 \begin_inset CommandInset ref
19442 reference "sub:Colored-Boxes"
19447 They can be used with the TeX code command
19454 \begin_inset Index idx
19457 \begin_layout Plain Layout
19468 \begin_layout Standard
19473 textcolor{color}{characters or formula}
19476 \begin_layout Standard
19477 The following example was colored completely dark green and partly red:
19480 \begin_layout Standard
19484 \begin_layout Plain Layout
19488 textcolor{darkgreen}{
19494 \begin_inset Formula
19496 \int A\,\mathrm{d}x=\frac{{\color{red}\sqrt[5]{B}}}{\ln\left(\frac{1}{3}\right)}
19505 \begin_layout Plain Layout
19515 \begin_layout Standard
19516 Due to a bug in LyX only complete formulas can be colored with self-defined
19521 \begin_layout Plain Layout
19522 \begin_inset CommandInset href
19524 name "LyX-bug #5269"
19525 target "http://www.lyx.org/trac/ticket/5269"
19537 \begin_layout Subsection
19539 \begin_inset CommandInset label
19541 name "sub:Font-Sizes"
19546 \begin_inset Index idx
19549 \begin_layout Plain Layout
19558 \begin_layout Standard
19559 For characters in formulas there are, analog to characters in text, the
19560 following size commands:
19563 \begin_layout Standard
19607 \begin_inset Newline newline
19629 \begin_layout Standard
19630 The size produced by the commands depends on the document font size, which
19631 corresponds to the command
19638 The other commands produce smaller or larger sizes than
19645 The font size can however not exceed a certain value.
19646 Is for example the document font size 12
19647 \begin_inset space \thinspace{}
19656 switches to the same size as
19666 \begin_layout Standard
19667 A size command is inserted in TeX-mode before the formula and sets the size
19668 for all following formula and text characters.
19669 To switch back to the initial size, the command
19675 is inserted behind the formula in TeX-mode.
19678 \begin_layout Standard
19679 Within a formula the size can be changed using the following size commands
19680 or the toolbar button
19683 arg "math-insert \\style"
19689 \begin_layout Standard
19692 \begin_inset Tabular
19693 <lyxtabular version="3" rows="5" columns="2">
19694 <features rotate="0" tabularvalignment="middle">
19695 <column alignment="center" valignment="top">
19696 <column alignment="center" valignment="top">
19698 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
19701 \begin_layout Plain Layout
19707 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
19710 \begin_layout Plain Layout
19712 \begin_inset Note Note
19715 \begin_layout Plain Layout
19722 is only used as spacer.
19734 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
19737 \begin_layout Plain Layout
19741 \begin_inset Index idx
19744 \begin_layout Plain Layout
19757 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
19760 \begin_layout Plain Layout
19761 \begin_inset Formula $\raisebox{6.5mm}{}{\displaystyle E_{\mathrm{pot_{1}}}=\frac{K}{l+\frac{m}{n_{2}}}}\raisebox{-5.5mm}{}$
19771 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
19774 \begin_layout Plain Layout
19782 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
19785 \begin_layout Plain Layout
19786 \begin_inset Formula $\raisebox{4.5mm}{}{\textstyle E_{\mathrm{pot_{1}}}=\frac{K}{l+\frac{m}{n_{2}}}}\raisebox{-4mm}{}$
19796 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
19799 \begin_layout Plain Layout
19807 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
19810 \begin_layout Plain Layout
19811 \begin_inset Formula $\raisebox{4.5mm}{}{\scriptstyle E_{\mathrm{pot_{1}}}=\frac{K}{l+\frac{m}{n_{2}}}}\raisebox{-3.5mm}{}$
19821 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
19824 \begin_layout Plain Layout
19832 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
19835 \begin_layout Plain Layout
19836 \begin_inset Formula $\raisebox{4.5mm}{}{\scriptscriptstyle E_{\mathrm{pot_{1}}}=\frac{K}{l+\frac{m}{n_{2}}}}\raisebox{-3.5mm}{}$
19852 \begin_layout Standard
19853 After entering these commands, a blue box appears in which the formula parts
19857 \begin_layout Standard
19858 There is a further method to change the font size, that though only works
19859 for symbols or letters in mathematical text.
19860 To use it, one of the above text size commands is inserted in mathematical
19862 All following characters until the end of the mathematical text or until
19863 another size command will have the selected size.
19865 \begin_inset VSpace -2mm
19871 \begin_layout Standard
19875 \begin_layout Plain Layout
19885 \begin_inset Formula
19887 A=\frac{B}{c}\cdot\maltese
19893 \begin_inset Formula
19895 \maltese A\textrm{\Large\maltese\textit{A}}\textrm{\tiny\maltese\textit{A}}
19904 \begin_layout Plain Layout
19916 \begin_layout Standard
19917 \begin_inset VSpace medskip
19920 Before both formulas the command
19927 The command for the second formula is:
19928 \begin_inset Newline newline
19936 \begin_inset space \textvisiblespace{}
19942 \begin_inset space \textvisiblespace{}
19948 \begin_inset space \textvisiblespace{}
19954 \begin_inset space \textvisiblespace{}
19958 \begin_inset Formula $\to$
19962 \begin_inset Formula $\to$
19966 \begin_inset Newline newline
19970 \begin_inset space \hspace*{}
19981 \begin_inset space \textvisiblespace{}
19987 \begin_inset space \textvisiblespace{}
19993 \begin_inset space \textvisiblespace{}
19999 \begin_layout Standard
20000 If a symbol cannot be displayed in different sizes, it will always be displayed
20001 in the default size.
20004 \begin_layout Section
20006 \begin_inset Index idx
20009 \begin_layout Plain Layout
20018 \begin_layout Standard
20019 Greek letters can also be inserted via the toolbar button
20022 arg "math-insert \\alpha"
20026 All international typesetting norms purport that Greek letters in math
20027 have to be typeset italic/slanted.
20028 In some languages, like French or Russian, they are nevertheless sometimes
20032 \begin_layout Subsection
20034 \begin_inset Index idx
20037 \begin_layout Plain Layout
20038 Greek letters ! small
20046 \begin_layout Standard
20047 \begin_inset space \hfill{}
20051 \begin_inset Tabular
20052 <lyxtabular version="3" rows="11" columns="2">
20053 <features rotate="0" tabularvalignment="middle">
20054 <column alignment="center" valignment="top" width="0pt">
20055 <column alignment="center" valignment="top" width="0pt">
20057 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
20060 \begin_layout Plain Layout
20066 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
20069 \begin_layout Plain Layout
20077 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
20080 \begin_layout Plain Layout
20088 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
20091 \begin_layout Plain Layout
20092 \begin_inset Formula $\alpha$
20102 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
20105 \begin_layout Plain Layout
20113 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
20116 \begin_layout Plain Layout
20117 \begin_inset Formula $\beta$
20127 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
20130 \begin_layout Plain Layout
20138 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
20141 \begin_layout Plain Layout
20142 \begin_inset Formula $\gamma$
20152 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
20155 \begin_layout Plain Layout
20163 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
20166 \begin_layout Plain Layout
20167 \begin_inset Formula $\delta$
20177 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
20180 \begin_layout Plain Layout
20188 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
20191 \begin_layout Plain Layout
20192 \begin_inset Formula $\epsilon$
20202 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
20205 \begin_layout Plain Layout
20213 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
20216 \begin_layout Plain Layout
20217 \begin_inset Formula $\varepsilon$
20227 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
20230 \begin_layout Plain Layout
20238 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
20241 \begin_layout Plain Layout
20242 \begin_inset Formula $\zeta$
20252 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
20255 \begin_layout Plain Layout
20263 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
20266 \begin_layout Plain Layout
20267 \begin_inset Formula $\eta$
20277 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
20280 \begin_layout Plain Layout
20288 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
20291 \begin_layout Plain Layout
20292 \begin_inset Formula $\theta$
20302 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
20305 \begin_layout Plain Layout
20313 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
20316 \begin_layout Plain Layout
20317 \begin_inset Formula $\vartheta$
20331 \begin_inset space \hfill{}
20335 \begin_inset Tabular
20336 <lyxtabular version="3" rows="12" columns="2">
20337 <features rotate="0" tabularvalignment="middle">
20338 <column alignment="center" valignment="top" width="0pt">
20339 <column alignment="center" valignment="top" width="0pt">
20341 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
20344 \begin_layout Plain Layout
20350 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
20353 \begin_layout Plain Layout
20361 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
20364 \begin_layout Plain Layout
20372 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
20375 \begin_layout Plain Layout
20376 \begin_inset Formula $\iota$
20386 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
20389 \begin_layout Plain Layout
20397 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
20400 \begin_layout Plain Layout
20401 \begin_inset Formula $\kappa$
20411 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
20414 \begin_layout Plain Layout
20422 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
20425 \begin_layout Plain Layout
20426 \begin_inset Formula $\varkappa$
20436 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
20439 \begin_layout Plain Layout
20447 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
20450 \begin_layout Plain Layout
20451 \begin_inset Formula $\lambda$
20461 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
20464 \begin_layout Plain Layout
20472 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
20475 \begin_layout Plain Layout
20476 \begin_inset Formula $\mu$
20486 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
20489 \begin_layout Plain Layout
20497 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
20500 \begin_layout Plain Layout
20501 \begin_inset Formula $\nu$
20511 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
20514 \begin_layout Plain Layout
20522 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
20525 \begin_layout Plain Layout
20526 \begin_inset Formula $\xi$
20536 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
20539 \begin_layout Plain Layout
20545 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
20548 \begin_layout Plain Layout
20549 \begin_inset Formula $o$
20559 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
20562 \begin_layout Plain Layout
20570 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
20573 \begin_layout Plain Layout
20574 \begin_inset Formula $\pi$
20584 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
20587 \begin_layout Plain Layout
20595 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
20598 \begin_layout Plain Layout
20599 \begin_inset Formula $\varpi$
20609 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
20612 \begin_layout Plain Layout
20620 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
20623 \begin_layout Plain Layout
20624 \begin_inset Formula $\rho$
20638 \begin_inset space \hfill{}
20642 \begin_inset Tabular
20643 <lyxtabular version="3" rows="11" columns="2">
20644 <features rotate="0" tabularvalignment="middle">
20645 <column alignment="center" valignment="top" width="0pt">
20646 <column alignment="center" valignment="top" width="0pt">
20648 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
20651 \begin_layout Plain Layout
20657 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
20660 \begin_layout Plain Layout
20668 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
20671 \begin_layout Plain Layout
20679 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
20682 \begin_layout Plain Layout
20683 \begin_inset Formula $\varrho$
20693 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
20696 \begin_layout Plain Layout
20704 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
20707 \begin_layout Plain Layout
20708 \begin_inset Formula $\sigma$
20718 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
20721 \begin_layout Plain Layout
20729 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
20732 \begin_layout Plain Layout
20733 \begin_inset Formula $\varsigma$
20743 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
20746 \begin_layout Plain Layout
20754 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
20757 \begin_layout Plain Layout
20758 \begin_inset Formula $\tau$
20768 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
20771 \begin_layout Plain Layout
20779 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
20782 \begin_layout Plain Layout
20783 \begin_inset Formula $\upsilon$
20793 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
20796 \begin_layout Plain Layout
20804 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
20807 \begin_layout Plain Layout
20808 \begin_inset Formula $\phi$
20818 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
20821 \begin_layout Plain Layout
20829 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
20832 \begin_layout Plain Layout
20833 \begin_inset Formula $\varphi$
20843 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
20846 \begin_layout Plain Layout
20854 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
20857 \begin_layout Plain Layout
20858 \begin_inset Formula $\chi$
20868 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
20871 \begin_layout Plain Layout
20879 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
20882 \begin_layout Plain Layout
20883 \begin_inset Formula $\psi$
20893 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
20896 \begin_layout Plain Layout
20904 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
20907 \begin_layout Plain Layout
20908 \begin_inset Formula $\omega$
20922 \begin_inset space \hfill{}
20928 \begin_layout Standard
20929 \begin_inset VSpace medskip
20935 \begin_layout Standard
20936 How to create special upright Greek letters is explained in
20937 \begin_inset CommandInset ref
20939 reference "sub:Upright-small-Greek"
20946 \begin_layout Subsection
20948 \begin_inset Index idx
20951 \begin_layout Plain Layout
20952 Greek letters ! big
20960 \begin_layout Standard
20961 \begin_inset space \hfill{}
20965 \begin_inset Tabular
20966 <lyxtabular version="3" rows="7" columns="2">
20967 <features rotate="0" tabularvalignment="middle">
20968 <column alignment="center" valignment="top" width="0pt">
20969 <column alignment="center" valignment="top" width="0pt">
20971 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
20974 \begin_layout Plain Layout
20980 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
20983 \begin_layout Plain Layout
20991 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
20994 \begin_layout Plain Layout
21002 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
21005 \begin_layout Plain Layout
21006 \begin_inset Formula $\Gamma$
21016 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
21019 \begin_layout Plain Layout
21027 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
21030 \begin_layout Plain Layout
21031 \begin_inset Formula $\Delta$
21041 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
21044 \begin_layout Plain Layout
21052 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
21055 \begin_layout Plain Layout
21056 \begin_inset Formula $\Theta$
21066 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
21069 \begin_layout Plain Layout
21077 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
21080 \begin_layout Plain Layout
21081 \begin_inset Formula $\Lambda$
21091 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
21094 \begin_layout Plain Layout
21102 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
21105 \begin_layout Plain Layout
21106 \begin_inset Formula $\Xi$
21116 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
21119 \begin_layout Plain Layout
21127 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
21130 \begin_layout Plain Layout
21131 \begin_inset Formula $\Pi$
21145 \begin_inset space \hfill{}
21149 \begin_inset Tabular
21150 <lyxtabular version="3" rows="6" columns="2">
21151 <features rotate="0" tabularvalignment="middle">
21152 <column alignment="center" valignment="top" width="0pt">
21153 <column alignment="center" valignment="top" width="0pt">
21155 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
21158 \begin_layout Plain Layout
21164 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
21167 \begin_layout Plain Layout
21175 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
21178 \begin_layout Plain Layout
21186 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
21189 \begin_layout Plain Layout
21190 \begin_inset Formula $\Sigma$
21200 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
21203 \begin_layout Plain Layout
21211 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
21214 \begin_layout Plain Layout
21215 \begin_inset Formula $\Upsilon$
21225 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
21228 \begin_layout Plain Layout
21236 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
21239 \begin_layout Plain Layout
21240 \begin_inset Formula $\Phi$
21250 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
21253 \begin_layout Plain Layout
21261 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
21264 \begin_layout Plain Layout
21265 \begin_inset Formula $\Psi$
21275 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
21278 \begin_layout Plain Layout
21286 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
21289 \begin_layout Plain Layout
21290 \begin_inset Formula $\Omega$
21304 \begin_inset space \hfill{}
21310 \begin_layout Standard
21311 \begin_inset VSpace medskip
21314 That the big Greek letters appear upright is caused by a design bug when
21316 To get correct italic big letters, begin every command with
21321 For example the command
21328 \begin_inset Formula $\varGamma$
21332 Another way is to load the package
21340 \begin_layout Plain Layout
21345 is part of the LaTeX-package
21350 \begin_inset Index idx
21353 \begin_layout Plain Layout
21358 \begin_layout Plain Layout
21378 \begin_inset Index idx
21381 \begin_layout Plain Layout
21387 with the LaTeX-preamble line
21390 \begin_layout Standard
21395 usepackage{fixmath}
21398 \begin_layout Standard
21399 Then all big Greek letters in a document will automatically be typeset italic.
21402 \begin_layout Subsection
21404 \begin_inset Index idx
21407 \begin_layout Plain Layout
21408 Greek letters ! bold
21416 \begin_layout Standard
21417 Greek letters cannot be set with different font styles like Latin letters.
21418 They can only be made bold with the command
21425 \begin_inset Index idx
21428 \begin_layout Plain Layout
21439 \begin_layout Standard
21441 \begin_inset Tabular
21442 <lyxtabular version="3" rows="3" columns="2">
21443 <features rotate="0" tabularvalignment="middle">
21444 <column alignment="center" valignment="top">
21445 <column alignment="center" valignment="top">
21447 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
21450 \begin_layout Plain Layout
21456 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
21459 \begin_layout Plain Layout
21467 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
21470 \begin_layout Plain Layout
21482 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
21485 \begin_layout Plain Layout
21486 \begin_inset Formula $\Upsilon\boldsymbol{\Upsilon}$
21496 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
21499 \begin_layout Plain Layout
21511 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
21514 \begin_layout Plain Layout
21515 \begin_inset Formula $\theta\boldsymbol{\theta}$
21531 \begin_layout Section
21536 \begin_layout Plain Layout
21549 \begin_layout Plain Layout
21550 A list with all symbols of most of the LaTeX-packages can be found in
21551 \begin_inset CommandInset citation
21566 \begin_layout Plain Layout
21574 \begin_inset Note Note
21577 \begin_layout Plain Layout
21580 texorpdfstring is used to avoid that the footnote appears in the PDF-bookmark.
21583 \begin_layout Plain Layout
21586 texorpdfstring is in section
21587 \begin_inset CommandInset ref
21589 reference "sub:Formulas-in-Section"
21599 \begin_inset Index idx
21602 \begin_layout Plain Layout
21611 \begin_layout Standard
21612 Many of the symbols listed in this section can also be inserted via the
21616 arg "math-insert \\nabla"
21622 arg "math-insert \\digamma"
21628 \begin_layout Subsection
21629 Mathematical Symbols
21630 \begin_inset CommandInset label
21632 name "sub:Mathematical-Symbols"
21637 \begin_inset Index idx
21640 \begin_layout Plain Layout
21641 Symbols ! mathematical
21649 \begin_layout Standard
21650 \begin_inset space \hfill{}
21654 \begin_inset Tabular
21655 <lyxtabular version="3" rows="10" columns="2">
21656 <features rotate="0" tabularvalignment="middle">
21657 <column alignment="center" valignment="top" width="0pt">
21658 <column alignment="center" valignment="top" width="0pt">
21660 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
21663 \begin_layout Plain Layout
21669 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
21672 \begin_layout Plain Layout
21680 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
21683 \begin_layout Plain Layout
21691 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
21694 \begin_layout Plain Layout
21695 \begin_inset Formula $\neg$
21705 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
21708 \begin_layout Plain Layout
21716 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
21719 \begin_layout Plain Layout
21720 \begin_inset Formula $\Im$
21730 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
21733 \begin_layout Plain Layout
21741 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
21744 \begin_layout Plain Layout
21745 \begin_inset Formula $\Re$
21755 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
21758 \begin_layout Plain Layout
21766 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
21769 \begin_layout Plain Layout
21770 \begin_inset Formula $\aleph$
21780 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
21783 \begin_layout Plain Layout
21791 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
21794 \begin_layout Plain Layout
21795 \begin_inset Formula $\partial$
21805 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
21808 \begin_layout Plain Layout
21816 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
21819 \begin_layout Plain Layout
21820 \begin_inset Formula $\infty$
21830 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
21833 \begin_layout Plain Layout
21841 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
21844 \begin_layout Plain Layout
21845 \begin_inset Formula $\wp$
21855 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
21858 \begin_layout Plain Layout
21866 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
21869 \begin_layout Plain Layout
21870 \begin_inset Formula $\imath$
21880 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
21883 \begin_layout Plain Layout
21891 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
21894 \begin_layout Plain Layout
21895 \begin_inset Formula $\jmath$
21909 \begin_inset space \hfill{}
21913 \begin_inset Tabular
21914 <lyxtabular version="3" rows="10" columns="2">
21915 <features rotate="0" tabularvalignment="middle">
21916 <column alignment="center" valignment="top" width="0pt">
21917 <column alignment="center" valignment="top" width="0pt">
21919 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
21922 \begin_layout Plain Layout
21928 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
21931 \begin_layout Plain Layout
21933 \begin_inset Note Note
21936 \begin_layout Plain Layout
21943 is only used as spacer.
21955 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
21958 \begin_layout Plain Layout
21966 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
21969 \begin_layout Plain Layout
21970 \begin_inset Formula $\forall$
21980 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
21983 \begin_layout Plain Layout
21991 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
21994 \begin_layout Plain Layout
21995 \begin_inset Formula $\exists$
22005 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
22008 \begin_layout Plain Layout
22016 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
22019 \begin_layout Plain Layout
22020 \begin_inset Formula $\nexists$
22030 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
22033 \begin_layout Plain Layout
22041 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
22044 \begin_layout Plain Layout
22045 \begin_inset Formula $\emptyset$
22055 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
22058 \begin_layout Plain Layout
22066 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
22069 \begin_layout Plain Layout
22070 \begin_inset Formula $\varnothing$
22080 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
22083 \begin_layout Plain Layout
22091 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
22094 \begin_layout Plain Layout
22095 \begin_inset Formula $\dag$
22105 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
22108 \begin_layout Plain Layout
22116 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
22119 \begin_layout Plain Layout
22120 \begin_inset Formula $\ddag$
22130 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
22133 \begin_layout Plain Layout
22141 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
22144 \begin_layout Plain Layout
22148 \begin_layout Plain Layout
22158 \begin_inset Formula $\complement$
22165 \begin_layout Plain Layout
22179 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
22182 \begin_layout Plain Layout
22190 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
22193 \begin_layout Plain Layout
22194 \begin_inset Formula $\Bbbk$
22208 \begin_inset space \hfill{}
22212 \begin_inset Tabular
22213 <lyxtabular version="3" rows="10" columns="2">
22214 <features rotate="0" tabularvalignment="middle">
22215 <column alignment="center" valignment="top" width="0pt">
22216 <column alignment="center" valignment="top" width="0pt">
22218 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
22221 \begin_layout Plain Layout
22227 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
22230 \begin_layout Plain Layout
22238 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
22241 \begin_layout Plain Layout
22249 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
22252 \begin_layout Plain Layout
22253 \begin_inset Formula $\prime$
22263 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
22266 \begin_layout Plain Layout
22274 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
22277 \begin_layout Plain Layout
22278 \begin_inset Formula $\backprime$
22288 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
22291 \begin_layout Plain Layout
22299 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
22302 \begin_layout Plain Layout
22303 \begin_inset Formula $\mho$
22313 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
22316 \begin_layout Plain Layout
22324 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
22327 \begin_layout Plain Layout
22328 \begin_inset Formula $\triangle$
22338 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
22341 \begin_layout Plain Layout
22349 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
22352 \begin_layout Plain Layout
22353 \begin_inset Formula $\angle$
22363 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
22366 \begin_layout Plain Layout
22374 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
22377 \begin_layout Plain Layout
22378 \begin_inset Formula $\measuredangle$
22388 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
22391 \begin_layout Plain Layout
22399 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
22402 \begin_layout Plain Layout
22403 \begin_inset Formula $\sphericalangle$
22413 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
22416 \begin_layout Plain Layout
22424 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
22427 \begin_layout Plain Layout
22428 \begin_inset Formula $\top$
22438 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
22441 \begin_layout Plain Layout
22449 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
22452 \begin_layout Plain Layout
22453 \begin_inset Formula $\bot$
22467 \begin_inset space \hfill{}
22473 \begin_layout Subsection
22474 Miscellaneous Symbols
22475 \begin_inset CommandInset label
22477 name "sub:Miscellaneous-Symbols"
22482 \begin_inset Index idx
22485 \begin_layout Plain Layout
22486 Symbols ! miscellaneous
22494 \begin_layout Standard
22497 \begin_inset Tabular
22498 <lyxtabular version="3" rows="10" columns="2">
22499 <features rotate="0" tabularvalignment="middle">
22500 <column alignment="center" valignment="top" width="0pt">
22501 <column alignment="center" valignment="top" width="0pt">
22503 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
22506 \begin_layout Plain Layout
22512 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
22515 \begin_layout Plain Layout
22523 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
22526 \begin_layout Plain Layout
22534 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
22537 \begin_layout Plain Layout
22538 \begin_inset Formula $\flat$
22548 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
22551 \begin_layout Plain Layout
22559 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
22562 \begin_layout Plain Layout
22563 \begin_inset Formula $\natural$
22573 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
22576 \begin_layout Plain Layout
22584 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
22587 \begin_layout Plain Layout
22588 \begin_inset Formula $\sharp$
22598 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
22601 \begin_layout Plain Layout
22609 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
22612 \begin_layout Plain Layout
22613 \begin_inset Formula $\surd$
22623 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
22626 \begin_layout Plain Layout
22634 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
22637 \begin_layout Plain Layout
22638 \begin_inset Formula $\checkmark$
22648 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
22651 \begin_layout Plain Layout
22659 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
22662 \begin_layout Plain Layout
22663 \begin_inset Formula $\yen$
22673 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
22676 \begin_layout Plain Layout
22684 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
22687 \begin_layout Plain Layout
22688 \begin_inset Formula $\pounds$
22698 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
22701 \begin_layout Plain Layout
22707 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
22710 \begin_layout Plain Layout
22711 \begin_inset Formula $\$$
22721 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
22724 \begin_layout Plain Layout
22730 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
22733 \begin_layout Plain Layout
22734 \begin_inset Formula $§$
22748 \begin_inset Tabular
22749 <lyxtabular version="3" rows="10" columns="2">
22750 <features rotate="0" tabularvalignment="middle">
22751 <column alignment="center" valignment="top">
22752 <column alignment="center" valignment="top">
22754 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
22757 \begin_layout Plain Layout
22763 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
22766 \begin_layout Plain Layout
22774 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
22777 \begin_layout Plain Layout
22785 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
22788 \begin_layout Plain Layout
22789 \begin_inset Formula $\hbar$
22799 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
22802 \begin_layout Plain Layout
22810 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
22813 \begin_layout Plain Layout
22814 \begin_inset Formula $\hslash$
22824 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
22827 \begin_layout Plain Layout
22835 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
22838 \begin_layout Plain Layout
22839 \begin_inset Formula $\clubsuit$
22849 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
22852 \begin_layout Plain Layout
22860 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
22863 \begin_layout Plain Layout
22864 \begin_inset Formula $\spadesuit$
22874 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
22877 \begin_layout Plain Layout
22885 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
22888 \begin_layout Plain Layout
22889 \begin_inset Formula $\bigstar$
22899 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
22902 \begin_layout Plain Layout
22910 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
22913 \begin_layout Plain Layout
22914 \begin_inset Formula $\blacklozenge$
22924 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
22927 \begin_layout Plain Layout
22935 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
22938 \begin_layout Plain Layout
22939 \begin_inset Formula $\blacktriangle$
22949 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
22952 \begin_layout Plain Layout
22960 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
22963 \begin_layout Plain Layout
22964 \begin_inset Formula $\blacktriangledown$
22974 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
22977 \begin_layout Plain Layout
22985 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
22988 \begin_layout Plain Layout
22989 \begin_inset Formula $\bullet$
23003 \begin_inset Tabular
23004 <lyxtabular version="3" rows="10" columns="2">
23005 <features rotate="0" tabularvalignment="middle">
23006 <column alignment="center" valignment="top" width="0pt">
23007 <column alignment="center" valignment="top" width="0pt">
23009 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
23012 \begin_layout Plain Layout
23018 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
23021 \begin_layout Plain Layout
23029 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
23032 \begin_layout Plain Layout
23040 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
23043 \begin_layout Plain Layout
23044 \begin_inset Formula $\diamondsuit$
23054 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
23057 \begin_layout Plain Layout
23065 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
23068 \begin_layout Plain Layout
23069 \begin_inset Formula $\Diamond$
23079 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
23082 \begin_layout Plain Layout
23090 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
23093 \begin_layout Plain Layout
23094 \begin_inset Formula $\heartsuit$
23104 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
23107 \begin_layout Plain Layout
23115 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
23118 \begin_layout Plain Layout
23119 \begin_inset Formula $\P$
23129 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
23132 \begin_layout Plain Layout
23140 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
23143 \begin_layout Plain Layout
23144 \begin_inset Formula $\copyright$
23154 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
23157 \begin_layout Plain Layout
23165 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
23168 \begin_layout Plain Layout
23169 \begin_inset Formula $\circledR$
23179 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
23182 \begin_layout Plain Layout
23190 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
23193 \begin_layout Plain Layout
23194 \begin_inset Formula $\maltese$
23204 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
23207 \begin_layout Plain Layout
23215 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
23218 \begin_layout Plain Layout
23219 \begin_inset Formula $\diagup$
23229 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
23232 \begin_layout Plain Layout
23240 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
23243 \begin_layout Plain Layout
23244 \begin_inset Formula $\diagdown$
23260 \begin_layout Standard
23261 \begin_inset VSpace medskip
23267 \begin_layout Standard
23268 Some symbols can be displayed in different sizes, see
23269 \begin_inset CommandInset ref
23271 reference "sub:Font-Sizes"
23278 \begin_layout Subsection
23280 \begin_inset Index idx
23283 \begin_layout Plain Layout
23284 Symbols ! Euro-symbol
23290 \begin_inset Index idx
23293 \begin_layout Plain Layout
23300 \begin_layout Plain Layout
23317 \begin_layout Standard
23318 To use the Euro symbol in formulas, the LaTeX-package
23323 \begin_inset Index idx
23326 \begin_layout Plain Layout
23332 must be installed and loaded with the LaTeX-preamble line
23335 \begin_layout Standard
23340 usepackage[gennarrow]{eurosym}
23343 \begin_layout Standard
23344 The Euro symbol can now be inserted with the command
23351 \begin_inset Index idx
23354 \begin_layout Plain Layout
23365 \begin_layout Standard
23366 The Euro symbol can directly be inserted with the € key in mathematical
23367 text, without having
23382 can also be inserted in TeX-mode.
23383 The official currency symbol can then be inserted with the command
23390 \begin_inset Index idx
23393 \begin_layout Plain Layout
23401 , that is only available in TeX-mode.
23404 \begin_layout Standard
23408 \begin_layout Plain Layout
23418 \begin_inset Note Note
23421 \begin_layout Plain Layout
23422 The following table will only be displayed when the LaTeX-package
23434 \begin_layout Standard
23435 An overview about the different Euro symbols:
23438 \begin_layout Standard
23440 \begin_inset Tabular
23441 <lyxtabular version="3" rows="4" columns="3">
23442 <features rotate="0" tabularvalignment="middle">
23443 <column alignment="center" valignment="top" width="0pt">
23444 <column alignment="center" valignment="top" width="0pt">
23445 <column alignment="center" valignment="top" width="0pt">
23447 <cell multicolumn="1" alignment="center" valignment="top" bottomline="true" usebox="none">
23450 \begin_layout Plain Layout
23456 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
23459 \begin_layout Plain Layout
23465 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
23468 \begin_layout Plain Layout
23476 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
23479 \begin_layout Plain Layout
23485 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
23488 \begin_layout Plain Layout
23496 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
23499 \begin_layout Plain Layout
23500 \begin_inset Formula $\euro$
23510 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
23513 \begin_layout Plain Layout
23519 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
23522 \begin_layout Plain Layout
23528 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
23531 \begin_layout Plain Layout
23532 \begin_inset Formula $\mbox{€}$
23542 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
23545 \begin_layout Plain Layout
23551 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
23554 \begin_layout Plain Layout
23562 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
23565 \begin_layout Plain Layout
23569 \begin_layout Plain Layout
23591 \begin_layout Standard
23595 \begin_layout Plain Layout
23605 \begin_inset Note Note
23608 \begin_layout Plain Layout
23609 The following will be displayed when the LaTeX-package
23621 \begin_layout Standard
23622 You need to install the LaTeX-package
23626 to see the rest of this subsection in the output.
23629 \begin_layout Standard
23633 \begin_layout Plain Layout
23645 \begin_layout Section
23647 \begin_inset CommandInset label
23649 name "sec:Relations"
23654 \begin_inset Index idx
23657 \begin_layout Plain Layout
23664 \begin_inset Index idx
23667 \begin_layout Plain Layout
23672 \begin_layout Plain Layout
23683 \begin_layout Plain Layout
23698 \begin_layout Standard
23699 All following relations can also be inserted via the toolbar button
23702 arg "math-insert \\leq"
23708 \begin_layout Standard
23709 \begin_inset space \hfill{}
23713 \begin_inset Tabular
23714 <lyxtabular version="3" rows="17" columns="2">
23715 <features rotate="0" tabularvalignment="middle">
23716 <column alignment="center" valignment="top" width="0pt">
23717 <column alignment="center" valignment="top" width="0pt">
23719 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
23722 \begin_layout Plain Layout
23728 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
23731 \begin_layout Plain Layout
23739 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
23742 \begin_layout Plain Layout
23748 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
23751 \begin_layout Plain Layout
23752 \begin_inset Formula $<$
23762 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
23765 \begin_layout Plain Layout
23773 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
23776 \begin_layout Plain Layout
23777 \begin_inset Formula $\le$
23787 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
23790 \begin_layout Plain Layout
23798 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
23801 \begin_layout Plain Layout
23802 \begin_inset Formula $\ll$
23812 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
23815 \begin_layout Plain Layout
23823 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
23826 \begin_layout Plain Layout
23827 \begin_inset Formula $\prec$
23837 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
23840 \begin_layout Plain Layout
23848 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
23851 \begin_layout Plain Layout
23852 \begin_inset Formula $\preceq$
23862 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
23865 \begin_layout Plain Layout
23873 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
23876 \begin_layout Plain Layout
23877 \begin_inset Formula $\subset$
23887 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
23890 \begin_layout Plain Layout
23898 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
23901 \begin_layout Plain Layout
23902 \begin_inset Formula $\subseteq$
23912 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
23915 \begin_layout Plain Layout
23923 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
23926 \begin_layout Plain Layout
23927 \begin_inset Formula $\sqsubseteq$
23937 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
23940 \begin_layout Plain Layout
23948 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
23951 \begin_layout Plain Layout
23952 \begin_inset Formula $\in$
23962 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
23965 \begin_layout Plain Layout
23973 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
23976 \begin_layout Plain Layout
23977 \begin_inset Formula $\vdash$
23987 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
23990 \begin_layout Plain Layout
23998 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
24001 \begin_layout Plain Layout
24002 \begin_inset Formula $\smile$
24012 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
24015 \begin_layout Plain Layout
24023 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
24026 \begin_layout Plain Layout
24027 \begin_inset Formula $\lhd$
24037 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
24040 \begin_layout Plain Layout
24048 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
24051 \begin_layout Plain Layout
24052 \begin_inset Formula $\unlhd$
24062 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
24065 \begin_layout Plain Layout
24073 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
24076 \begin_layout Plain Layout
24077 \begin_inset Formula $\gtrless$
24087 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
24090 \begin_layout Plain Layout
24098 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
24101 \begin_layout Plain Layout
24102 \begin_inset Formula $\mid$
24112 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
24115 \begin_layout Plain Layout
24123 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
24126 \begin_layout Plain Layout
24127 \begin_inset Formula $\nmid$
24141 \begin_inset space \hfill{}
24145 \begin_inset Tabular
24146 <lyxtabular version="3" rows="17" columns="2">
24147 <features rotate="0" tabularvalignment="middle">
24148 <column alignment="center" valignment="top" width="0pt">
24149 <column alignment="center" valignment="top" width="0pt">
24151 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
24154 \begin_layout Plain Layout
24160 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
24163 \begin_layout Plain Layout
24171 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
24174 \begin_layout Plain Layout
24180 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
24183 \begin_layout Plain Layout
24184 \begin_inset Formula $=$
24194 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
24197 \begin_layout Plain Layout
24205 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
24208 \begin_layout Plain Layout
24209 \begin_inset Formula $\not=$
24219 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
24222 \begin_layout Plain Layout
24230 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
24233 \begin_layout Plain Layout
24234 \begin_inset Formula $\equiv$
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" rightline="true" usebox="none">
24258 \begin_layout Plain Layout
24259 \begin_inset Formula $\sim$
24269 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
24272 \begin_layout Plain Layout
24280 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
24283 \begin_layout Plain Layout
24284 \begin_inset Formula $\simeq$
24294 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
24297 \begin_layout Plain Layout
24305 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
24308 \begin_layout Plain Layout
24309 \begin_inset Formula $\approx$
24319 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
24322 \begin_layout Plain Layout
24330 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
24333 \begin_layout Plain Layout
24334 \begin_inset Formula $\cong$
24344 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
24347 \begin_layout Plain Layout
24355 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
24358 \begin_layout Plain Layout
24359 \begin_inset Formula $\bowtie$
24369 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
24372 \begin_layout Plain Layout
24380 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
24383 \begin_layout Plain Layout
24384 \begin_inset Formula $\notin$
24394 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
24397 \begin_layout Plain Layout
24405 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
24408 \begin_layout Plain Layout
24409 \begin_inset Formula $\perp$
24419 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
24422 \begin_layout Plain Layout
24430 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
24433 \begin_layout Plain Layout
24434 \begin_inset Formula $\propto$
24444 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
24447 \begin_layout Plain Layout
24455 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
24458 \begin_layout Plain Layout
24459 \begin_inset Formula $\asymp$
24469 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
24472 \begin_layout Plain Layout
24480 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
24483 \begin_layout Plain Layout
24484 \begin_inset Formula $\doteq$
24494 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
24497 \begin_layout Plain Layout
24505 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
24508 \begin_layout Plain Layout
24509 \begin_inset Formula $\circeq$
24519 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
24522 \begin_layout Plain Layout
24530 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
24533 \begin_layout Plain Layout
24534 \begin_inset Formula $\models$
24544 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
24547 \begin_layout Plain Layout
24555 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
24558 \begin_layout Plain Layout
24559 \begin_inset Formula $\widehat{=}$
24573 \begin_inset space \hfill{}
24577 \begin_inset Tabular
24578 <lyxtabular version="3" rows="17" columns="2">
24579 <features rotate="0" tabularvalignment="middle">
24580 <column alignment="center" valignment="top" width="0pt">
24581 <column alignment="center" valignment="top" width="0pt">
24583 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
24586 \begin_layout Plain Layout
24592 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
24595 \begin_layout Plain Layout
24603 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
24606 \begin_layout Plain Layout
24612 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
24615 \begin_layout Plain Layout
24616 \begin_inset Formula $>$
24626 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
24629 \begin_layout Plain Layout
24637 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
24640 \begin_layout Plain Layout
24641 \begin_inset Formula $\ge$
24651 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
24654 \begin_layout Plain Layout
24662 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
24665 \begin_layout Plain Layout
24666 \begin_inset Formula $\gg$
24676 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
24679 \begin_layout Plain Layout
24687 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
24690 \begin_layout Plain Layout
24691 \begin_inset Formula $\succ$
24701 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
24704 \begin_layout Plain Layout
24712 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
24715 \begin_layout Plain Layout
24716 \begin_inset Formula $\succeq$
24726 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
24729 \begin_layout Plain Layout
24737 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
24740 \begin_layout Plain Layout
24741 \begin_inset Formula $\supset$
24751 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
24754 \begin_layout Plain Layout
24762 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
24765 \begin_layout Plain Layout
24766 \begin_inset Formula $\supseteq$
24776 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
24779 \begin_layout Plain Layout
24787 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
24790 \begin_layout Plain Layout
24791 \begin_inset Formula $\sqsupseteq$
24801 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
24804 \begin_layout Plain Layout
24812 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
24815 \begin_layout Plain Layout
24816 \begin_inset Formula $\ni$
24826 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
24829 \begin_layout Plain Layout
24837 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
24840 \begin_layout Plain Layout
24841 \begin_inset Formula $\dashv$
24851 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
24854 \begin_layout Plain Layout
24862 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
24865 \begin_layout Plain Layout
24866 \begin_inset Formula $\frown$
24876 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
24879 \begin_layout Plain Layout
24887 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
24890 \begin_layout Plain Layout
24891 \begin_inset Formula $\rhd$
24901 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
24904 \begin_layout Plain Layout
24912 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
24915 \begin_layout Plain Layout
24916 \begin_inset Formula $\unrhd$
24926 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
24929 \begin_layout Plain Layout
24937 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
24940 \begin_layout Plain Layout
24941 \begin_inset Formula $\lessgtr$
24951 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
24954 \begin_layout Plain Layout
24962 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
24965 \begin_layout Plain Layout
24966 \begin_inset Formula $\parallel$
24976 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
24979 \begin_layout Plain Layout
24987 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
24990 \begin_layout Plain Layout
24991 \begin_inset Formula $\nparallel$
25005 \begin_inset space \hfill{}
25011 \begin_layout Standard
25012 \begin_inset VSpace medskip
25027 are bigger than the equal looking operators
25042 \begin_layout Standard
25043 LyX supports also many special relations.
25044 Use the toolbar button
25047 arg "math-insert \\leqq"
25050 to see a list of these relations.
25053 \begin_layout Standard
25054 Relations are, in contrary to symbols, always surrounded by space.
25057 \begin_layout Standard
25058 Relations with labels can be created with the command
25065 \begin_inset Index idx
25068 \begin_layout Plain Layout
25079 \begin_layout Standard
25081 \begin_inset Tabular
25082 <lyxtabular version="3" rows="2" columns="2">
25083 <features rotate="0" tabularvalignment="middle">
25084 <column alignment="center" valignment="top">
25085 <column alignment="center" valignment="top">
25087 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
25090 \begin_layout Plain Layout
25096 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
25099 \begin_layout Plain Layout
25101 \begin_inset Note Note
25104 \begin_layout Plain Layout
25111 is only used as spacer.
25123 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
25126 \begin_layout Plain Layout
25130 \begin_inset space \textvisiblespace{}
25138 \begin_inset space \textvisiblespace{}
25142 \begin_inset Formula $\downarrow$
25148 \begin_inset space \textvisiblespace{}
25152 \begin_inset space \textvisiblespace{}
25160 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
25163 \begin_layout Plain Layout
25164 \begin_inset Formula $\raisebox{5mm}{}A(r)\stackrel{r\to\infty}{\approx}B$
25180 \begin_layout Section
25184 \begin_layout Subsection
25185 Predefined Functions
25186 \begin_inset CommandInset label
25188 name "sub:Predefined-Functions"
25193 \begin_inset Index idx
25196 \begin_layout Plain Layout
25197 Functions ! predefined
25205 \begin_layout Standard
25206 In general, variables are set
25210 in mathematical expressions, but not function names, because
25211 \begin_inset Formula $sin$
25214 could be misunderstood as
25215 \begin_inset Formula $s\cdot i\cdot n$
25219 Therefore there are predefined functionswhich are additionally a bit separated
25221 They are inserted as commands starting with a backslash before their name.
25224 \begin_layout Standard
25226 \begin_inset Tabular
25227 <lyxtabular version="3" rows="2" columns="4">
25228 <features rotate="0" tabularvalignment="middle">
25229 <column alignment="center" valignment="top" width="0pt">
25230 <column alignment="center" valignment="top" width="0pt">
25231 <column alignment="center" valignment="top" width="0pt">
25232 <column alignment="center" valignment="top" width="0pt">
25234 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
25237 \begin_layout Plain Layout
25243 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
25246 \begin_layout Plain Layout
25252 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
25255 \begin_layout Plain Layout
25261 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
25264 \begin_layout Plain Layout
25272 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
25275 \begin_layout Plain Layout
25281 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
25284 \begin_layout Plain Layout
25285 \begin_inset Formula $Asin(x)+B$
25293 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
25296 \begin_layout Plain Layout
25304 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
25307 \begin_layout Plain Layout
25308 \begin_inset Formula $A\sin(x)+B$
25324 \begin_layout Standard
25325 The following functions are predefined:
25328 \begin_layout Standard
25329 \begin_inset VSpace -2mm
25335 \begin_layout Standard
25337 \begin_inset Tabular
25338 <lyxtabular version="3" rows="9" columns="4">
25339 <features rotate="0" tabularvalignment="middle">
25340 <column alignment="center" valignment="top" width="0pt">
25341 <column alignment="center" valignment="top" width="0pt">
25342 <column alignment="center" valignment="top" width="0pt">
25343 <column alignment="center" valignment="top" width="0pt">
25345 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
25348 \begin_layout Plain Layout
25354 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
25357 \begin_layout Plain Layout
25363 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
25366 \begin_layout Plain Layout
25372 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
25375 \begin_layout Plain Layout
25383 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
25386 \begin_layout Plain Layout
25394 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
25397 \begin_layout Plain Layout
25405 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
25408 \begin_layout Plain Layout
25416 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
25419 \begin_layout Plain Layout
25429 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
25432 \begin_layout Plain Layout
25440 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
25443 \begin_layout Plain Layout
25451 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
25454 \begin_layout Plain Layout
25462 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
25465 \begin_layout Plain Layout
25475 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
25478 \begin_layout Plain Layout
25486 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
25489 \begin_layout Plain Layout
25497 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
25500 \begin_layout Plain Layout
25508 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
25511 \begin_layout Plain Layout
25521 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
25524 \begin_layout Plain Layout
25532 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
25535 \begin_layout Plain Layout
25543 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
25546 \begin_layout Plain Layout
25554 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
25557 \begin_layout Plain Layout
25567 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
25570 \begin_layout Plain Layout
25578 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
25581 \begin_layout Plain Layout
25589 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
25592 \begin_layout Plain Layout
25600 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
25603 \begin_layout Plain Layout
25613 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
25616 \begin_layout Plain Layout
25624 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
25627 \begin_layout Plain Layout
25635 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
25638 \begin_layout Plain Layout
25646 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
25649 \begin_layout Plain Layout
25659 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
25662 \begin_layout Plain Layout
25670 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
25673 \begin_layout Plain Layout
25681 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
25684 \begin_layout Plain Layout
25692 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
25695 \begin_layout Plain Layout
25705 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
25708 \begin_layout Plain Layout
25716 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
25719 \begin_layout Plain Layout
25727 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
25730 \begin_layout Plain Layout
25738 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
25741 \begin_layout Plain Layout
25757 \begin_layout Standard
25758 They can also be inserted with the math toolbar button
25761 arg "math-insert \\functions"
25767 \begin_layout Subsection
25768 Self-defined Functions
25769 \begin_inset Index idx
25772 \begin_layout Plain Layout
25773 Functions ! self-defined
25781 \begin_layout Standard
25782 To use a function that is not predefined, like for example the sign function
25783 sgn(x), there are two possibilities:
25786 \begin_layout Itemize
25787 Define the function by inserting the following line to the LaTeX-preamble
25791 \begin_layout Plain Layout
25796 DeclareMathOperator
25799 \begin_inset CommandInset ref
25801 reference "sub:Self-defined-Operators"
25811 \begin_inset Newline newline
25815 \begin_inset VSpace -3mm
25819 \begin_inset Newline newline
25826 DeclareMathOperator{
25831 \begin_inset Index idx
25834 \begin_layout Plain Layout
25839 DeclareMathOperator
25845 \begin_inset Newline newline
25849 \begin_inset VSpace -2mm
25853 \begin_inset Newline newline
25856 Now the new defined function can be called with the command
25865 \begin_layout Itemize
25866 Write the formula as usual, mark the formula name, in our example the letters
25871 , and change it to mathematical text.
25872 Finally, a space is inserted between prefactor and function.
25875 \begin_layout Standard
25876 The result is the same with both methods as with a predefined function
25880 \begin_layout Plain Layout
25881 In LyX self-defined functions are displayed red, predefined ones black.
25889 \begin_layout Standard
25891 \begin_inset Tabular
25892 <lyxtabular version="3" rows="3" columns="2">
25893 <features rotate="0" tabularvalignment="middle">
25894 <column alignment="center" valignment="top" width="0pt">
25895 <column alignment="center" valignment="top" width="0pt">
25897 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
25900 \begin_layout Plain Layout
25906 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
25909 \begin_layout Plain Layout
25917 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
25920 \begin_layout Plain Layout
25928 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
25931 \begin_layout Plain Layout
25932 \begin_inset Formula $A\sgn(x)+B$
25942 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
25945 \begin_layout Plain Layout
25949 \begin_inset Formula $\underbrace{\textrm{sgn}}_{\textrm{Alt+M}\,\textrm{M}}$
25957 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
25960 \begin_layout Plain Layout
25961 \begin_inset Formula $A\,\textrm{sgn}(x)+B$
25977 \begin_layout Standard
25978 The first method is more suitable when the self-defined function should
25979 be used several times.
25982 \begin_layout Subsection
25984 \begin_inset Index idx
25987 \begin_layout Plain Layout
25996 \begin_layout Standard
25997 For limits, in addition to the commands
26004 \begin_inset Index idx
26007 \begin_layout Plain Layout
26027 the following functions are defined:
26030 \begin_layout Standard
26032 \begin_inset Tabular
26033 <lyxtabular version="3" rows="5" columns="2">
26034 <features rotate="0" tabularvalignment="middle">
26035 <column alignment="center" valignment="top">
26036 <column alignment="center" valignment="top">
26038 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
26041 \begin_layout Plain Layout
26047 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
26050 \begin_layout Plain Layout
26052 \begin_inset Note Note
26055 \begin_layout Plain Layout
26062 is only used as spacer.
26074 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
26077 \begin_layout Plain Layout
26085 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
26088 \begin_layout Plain Layout
26089 \begin_inset Formula $\varliminf$
26099 <cell alignment="center" valignment="top" leftline="true" usebox="none">
26102 \begin_layout Plain Layout
26110 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
26113 \begin_layout Plain Layout
26114 \begin_inset Formula $\varlimsup$
26124 <cell alignment="center" valignment="top" leftline="true" usebox="none">
26127 \begin_layout Plain Layout
26135 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
26138 \begin_layout Plain Layout
26139 \begin_inset Formula $\varprojlim$
26149 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
26152 \begin_layout Plain Layout
26160 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
26163 \begin_layout Plain Layout
26164 \begin_inset Formula $\varinjlim$
26168 \begin_inset Formula $\raisebox{-2.5mm}{}$
26184 \begin_layout Standard
26185 \begin_inset VSpace medskip
26188 The limit is created by inserting a subscript.
26189 It is set right beside the function in an inline formula:
26192 \begin_layout Standard
26194 \begin_inset Tabular
26195 <lyxtabular version="3" rows="2" columns="2">
26196 <features rotate="0" tabularvalignment="middle">
26197 <column alignment="center" valignment="top" width="0pt">
26198 <column alignment="center" valignment="top" width="0pt">
26200 <cell alignment="center" valignment="top" usebox="none">
26203 \begin_layout Plain Layout
26209 <cell alignment="center" valignment="top" usebox="none">
26212 \begin_layout Plain Layout
26213 \begin_inset space \hspace{}
26218 \begin_inset Note Note
26221 \begin_layout Plain Layout
26228 are used here as spacer.
26240 <cell alignment="center" valignment="top" usebox="none">
26243 \begin_layout Plain Layout
26249 \begin_inset space \textvisiblespace{}
26253 \begin_inset space \textvisiblespace{}
26261 <cell alignment="center" valignment="top" usebox="none">
26264 \begin_layout Plain Layout
26265 \begin_inset Formula $\hspace{1cm}\raisebox{5mm}{}\lim_{x\to A}x=B$
26281 \begin_layout Standard
26282 In a displayed formula the limit is set below the formula, as usual:
26283 \begin_inset Formula
26293 \begin_layout Standard
26294 \begin_inset VSpace medskip
26300 \begin_layout Standard
26301 How to adjust the typesetting of the limits see
26302 \begin_inset CommandInset ref
26304 reference "sub:Operator-Limits"
26311 \begin_layout Subsection
26313 \begin_inset Index idx
26316 \begin_layout Plain Layout
26317 Functions ! modulo-
26325 \begin_layout Standard
26326 The modulo-function is special, because it exists in four variants.
26327 The variants in a displayed formula are:
26328 \begin_inset Formula
26330 \underline{\textrm{Command}\raisebox{-0.9mm}{}} & & \underline{\textrm{Result}}\\
26331 \mathrm{a\backslash mod\textrm{␣}b} & & a\mod b\\
26332 \mathrm{a\backslash pmod\textrm{␣}b} & & a\pmod b\\
26333 \mathrm{a\backslash bmod\textrm{␣}b} & & a\bmod b\\
26334 \mathrm{a\backslash pod\textrm{␣}b} & & a\pod b
26342 \begin_layout Standard
26343 In an inline formula less space is set before the function names for all
26345 By default the modulo-functions take only the first following character
26347 To use more than one character, one has to put them into TeX-braces:
26348 \begin_inset Formula
26350 \underline{\textrm{Command}\raisebox{-0.9mm}{}} & & \underline{\textrm{Result}}\\
26351 \mathrm{a\backslash pod\textrm{␣}bcd} & & a\pod bcd\\
26352 \mathrm{a\backslash pod\backslash\{bc\to d} & & a\pod{bc}d
26360 \begin_layout Section
26362 \begin_inset Index idx
26365 \begin_layout Plain Layout
26374 \begin_layout Subsection
26375 Special Characters in Mathematical Text
26378 \begin_layout Standard
26379 The following commands can only be used in mathematical text or in TeX-mode:
26382 \begin_layout Standard
26383 \begin_inset space \hfill{}
26387 \begin_inset Tabular
26388 <lyxtabular version="3" rows="8" columns="2">
26389 <features rotate="0" tabularvalignment="middle">
26390 <column alignment="block" valignment="top">
26391 <column alignment="block" valignment="top">
26393 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
26396 \begin_layout Plain Layout
26402 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
26405 \begin_layout Plain Layout
26413 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
26416 \begin_layout Plain Layout
26424 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
26427 \begin_layout Plain Layout
26428 \begin_inset Formula $\textrm{œ}$
26438 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
26441 \begin_layout Plain Layout
26449 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
26452 \begin_layout Plain Layout
26453 \begin_inset Formula $\textrm{Œ}$
26463 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
26466 \begin_layout Plain Layout
26474 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
26477 \begin_layout Plain Layout
26478 \begin_inset Formula $\textrm{æ}$
26488 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
26491 \begin_layout Plain Layout
26499 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
26502 \begin_layout Plain Layout
26503 \begin_inset Formula $\textrm{Æ}$
26513 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
26516 \begin_layout Plain Layout
26524 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
26527 \begin_layout Plain Layout
26528 \begin_inset Formula $\textrm{\aa}$
26538 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
26541 \begin_layout Plain Layout
26545 \begin_inset Index idx
26548 \begin_layout Plain Layout
26555 \begin_layout Plain Layout
26576 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
26579 \begin_layout Plain Layout
26580 \begin_inset Formula $\textrm{Å}$
26590 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
26593 \begin_layout Plain Layout
26601 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
26604 \begin_layout Plain Layout
26605 \begin_inset Formula $\textrm{ı}$
26619 \begin_inset space \hfill{}
26623 \begin_inset Tabular
26624 <lyxtabular version="3" rows="8" columns="2">
26625 <features rotate="0" tabularvalignment="middle">
26626 <column alignment="block" valignment="top">
26627 <column alignment="center" valignment="top">
26629 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
26632 \begin_layout Plain Layout
26634 \begin_inset Note Note
26637 \begin_layout Plain Layout
26639 \begin_inset space \thinspace{}
26642 mm is used for separation, because otherwise the output will be ¡ and ¿
26653 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
26656 \begin_layout Plain Layout
26664 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
26667 \begin_layout Plain Layout
26675 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
26678 \begin_layout Plain Layout
26679 \begin_inset Formula $\textrm{ø}$
26689 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
26692 \begin_layout Plain Layout
26700 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
26703 \begin_layout Plain Layout
26704 \begin_inset Formula $\textrm{Ø}$
26714 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
26717 \begin_layout Plain Layout
26725 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
26728 \begin_layout Plain Layout
26729 \begin_inset Formula $\textrm{ł}$
26739 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
26742 \begin_layout Plain Layout
26750 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
26753 \begin_layout Plain Layout
26754 \begin_inset Formula $\textrm{Ł}$
26764 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
26767 \begin_layout Plain Layout
26769 \begin_inset space \hspace{}
26774 \begin_inset space \textvisiblespace{}
26782 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
26785 \begin_layout Plain Layout
26786 \begin_inset Formula $\textrm{!`}$
26796 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
26799 \begin_layout Plain Layout
26801 \begin_inset space \hspace{}
26806 \begin_inset space \textvisiblespace{}
26814 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
26817 \begin_layout Plain Layout
26818 \begin_inset Formula $\textrm{?`}$
26828 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
26831 \begin_layout Plain Layout
26839 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
26842 \begin_layout Plain Layout
26843 \begin_inset Formula $\textrm{ȷ}$
26857 \begin_inset space \hfill{}
26863 \begin_layout Standard
26865 \begin_inset Formula $\textrm{\textrm{Å}}$
26869 \begin_inset Formula $\textrm{\textrm{Ø}}$
26872 can also be inserted via the math toolbar button
26875 arg "math-insert \\digamma"
26881 \begin_layout Standard
26882 An exception are the commands
26885 \begin_inset space \hspace{}
26894 \begin_inset space \hspace{}
26900 , because they can be inserted in LyX directly to text.
26903 \begin_layout Subsection
26905 \begin_inset CommandInset label
26907 name "sub:Accents-in-Text"
26912 \begin_inset Index idx
26915 \begin_layout Plain Layout
26924 \begin_layout Standard
26925 With the following commands all letters can be accented.
26926 The commands must be inserted in TeX-mode.
26929 \begin_layout Standard
26930 \begin_inset space \hfill{}
26934 \begin_inset Tabular
26935 <lyxtabular version="3" rows="8" columns="2">
26936 <features rotate="0" tabularvalignment="middle">
26937 <column alignment="block" valignment="top">
26938 <column alignment="block" valignment="top">
26940 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
26943 \begin_layout Plain Layout
26949 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
26952 \begin_layout Plain Layout
26960 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
26963 \begin_layout Plain Layout
26967 \begin_inset Quotes grd
26975 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
26978 \begin_layout Plain Layout
26982 \begin_layout Plain Layout
26998 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
27001 \begin_layout Plain Layout
27009 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
27012 \begin_layout Plain Layout
27016 \begin_layout Plain Layout
27032 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
27035 \begin_layout Plain Layout
27039 \begin_inset space \textvisiblespace{}
27047 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
27050 \begin_layout Plain Layout
27054 \begin_layout Plain Layout
27070 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
27073 \begin_layout Plain Layout
27081 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
27084 \begin_layout Plain Layout
27088 \begin_layout Plain Layout
27104 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
27107 \begin_layout Plain Layout
27111 \begin_inset space \textvisiblespace{}
27119 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
27122 \begin_layout Plain Layout
27126 \begin_layout Plain Layout
27142 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
27145 \begin_layout Plain Layout
27149 \begin_inset space \textvisiblespace{}
27157 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
27160 \begin_layout Plain Layout
27164 \begin_layout Plain Layout
27180 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
27183 \begin_layout Plain Layout
27187 \begin_inset space \textvisiblespace{}
27195 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
27198 \begin_layout Plain Layout
27202 \begin_layout Plain Layout
27222 \begin_inset space \hfill{}
27226 \begin_inset Tabular
27227 <lyxtabular version="3" rows="8" columns="2">
27228 <features rotate="0" tabularvalignment="middle">
27229 <column alignment="block" valignment="top">
27230 <column alignment="center" valignment="top">
27232 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
27235 \begin_layout Plain Layout
27241 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
27244 \begin_layout Plain Layout
27252 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
27255 \begin_layout Plain Layout
27259 \begin_inset space \textvisiblespace{}
27267 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
27270 \begin_layout Plain Layout
27274 \begin_layout Plain Layout
27290 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
27293 \begin_layout Plain Layout
27301 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
27304 \begin_layout Plain Layout
27308 \begin_layout Plain Layout
27324 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
27327 \begin_layout Plain Layout
27331 \begin_inset Index idx
27334 \begin_layout Plain Layout
27345 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
27348 \begin_layout Plain Layout
27352 \begin_layout Plain Layout
27368 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
27371 \begin_layout Plain Layout
27379 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
27382 \begin_layout Plain Layout
27386 \begin_layout Plain Layout
27402 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
27405 \begin_layout Plain Layout
27409 \begin_inset space \textvisiblespace{}
27417 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
27420 \begin_layout Plain Layout
27424 \begin_layout Plain Layout
27440 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
27443 \begin_layout Plain Layout
27447 \begin_inset space \textvisiblespace{}
27455 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
27458 \begin_layout Plain Layout
27462 \begin_layout Plain Layout
27478 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
27481 \begin_layout Plain Layout
27485 \begin_inset space \textvisiblespace{}
27493 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
27496 \begin_layout Plain Layout
27500 \begin_layout Plain Layout
27520 \begin_inset space \hfill{}
27526 \begin_layout Standard
27527 \begin_inset VSpace medskip
27536 also two different characters can be accented.
27542 \begin_inset space \textvisiblespace{}
27551 \begin_layout Plain Layout
27563 \begin_layout Standard
27576 can in combination with vowels directly be inserted with the keyboard without
27578 The same applies for the tilde
27582 \begin_layout Plain Layout
27583 This only applies for keyboards where the tilde is defined as accent.
27592 in combination with
27607 \begin_layout Standard
27650 and accents that are inserted directly with the keyboard are also available
27651 in mathematical text.
27652 For the other accents there are special math commands to be used in formulas,
27654 \begin_inset CommandInset ref
27656 reference "sub:Accents-for-one"
27663 \begin_layout Standard
27664 \begin_inset VSpace bigskip
27667 Furthermore, with the command
27674 \begin_inset Index idx
27677 \begin_layout Plain Layout
27685 all numbers and letters can be set into a circle, quasi accented with a
27686 circle, similar to the copyright symbol.
27689 \begin_layout Standard
27691 \begin_inset Tabular
27692 <lyxtabular version="3" rows="3" columns="2">
27693 <features rotate="0" tabularvalignment="middle">
27694 <column alignment="center" valignment="top">
27695 <column alignment="center" valignment="top">
27697 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
27700 \begin_layout Plain Layout
27706 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
27709 \begin_layout Plain Layout
27711 \begin_inset Note Note
27714 \begin_layout Plain Layout
27721 is only used as spacer.
27733 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
27736 \begin_layout Plain Layout
27744 <cell multicolumn="1" alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
27747 \begin_layout Plain Layout
27751 \begin_layout Plain Layout
27767 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
27770 \begin_layout Plain Layout
27781 raisebox{-1.5pt}{W}}
27786 <cell multicolumn="1" alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
27789 \begin_layout Plain Layout
27790 \begin_inset Formula $\raisebox{4.5mm}{}$
27797 \begin_layout Plain Layout
27815 \begin_inset Formula $\raisebox{-2mm}{}$
27831 \begin_layout Standard
27832 One has to take care that the character fits in the circle.
27843 \begin_layout Plain Layout
27845 \begin_inset CommandInset ref
27847 reference "sub:Font-Sizes"
27856 specifies thereby the size of the circle.
27867 \begin_layout Plain Layout
27869 \begin_inset CommandInset ref
27871 reference "sub:Boxes-without-Frame"
27880 the character can be centered.
27883 \begin_layout Subsection
27885 \begin_inset Index idx
27888 \begin_layout Plain Layout
27897 \begin_layout Standard
27898 Old-style figures (also known as old-style numerals) are created with the
27906 \begin_inset Index idx
27909 \begin_layout Plain Layout
27918 The command can be used in formulas and in TeX-mode.
27919 The command scheme is:
27922 \begin_layout Standard
27927 oldstylenums{number}
27930 \begin_layout Standard
27935 oldstylenums{0123456789
27938 \begin_inset Formula $\oldstylenums{0123456789}$
27944 \begin_layout Section
27946 \begin_inset CommandInset label
27948 name "sec:Formula-Styles"
27953 \begin_inset Index idx
27956 \begin_layout Plain Layout
27965 \begin_layout Itemize
27966 There are two different alignment styles:
27970 \begin_layout Description
27971 Centered is the predefined standard
27974 \begin_layout Description
27975 Indented for this the option
27979 must be inserted in the menu
27981 Document\SpecialChar \menuseparator
27987 \begin_inset space ~
27993 \begin_layout Standard
27998 is used, the indentation can be adjusted with the length
28005 \begin_inset Index idx
28008 \begin_layout Plain Layout
28017 Should the distance be 15
28018 \begin_inset space \thinspace{}
28021 mm, the following command line is inserted in the LaTeX-preamble
28024 \begin_layout Standard
28034 \begin_layout Standard
28035 When no length is specified, the predefined value of 30
28036 \begin_inset space \thinspace{}
28043 \begin_layout Itemize
28044 And two different numbering styles:
28048 \begin_layout Description
28049 Right is the predefined standard
28052 \begin_layout Description
28053 Left for this the option
28057 must be inserted in the menu
28059 Document\SpecialChar \menuseparator
28065 \begin_inset space ~
28072 \begin_layout Standard
28081 can also be used together.
28082 In this case both options are inserted, separated by a comma.
28085 \begin_layout Standard
28086 The chosen styles are used for all displayed formulas of the document.
28087 When both, centered and indented formulas should be created in a document,
28093 The indented formulas are then set in a flalign environment, see
28094 \begin_inset CommandInset ref
28096 reference "sub:Flalign-Environment"
28103 \begin_layout Section
28105 \begin_inset CommandInset label
28107 name "sec:Multiline-Formulas"
28112 \begin_inset Index idx
28115 \begin_layout Plain Layout
28116 Formula ! multiline
28124 \begin_layout Subsection
28128 \begin_layout Standard
28129 In LyX multiline formulas are created by pressing
28132 arg "newline-insert newline"
28136 This creates either an
28138 eqnarray environment
28140 that is described in
28141 \begin_inset CommandInset ref
28143 reference "sub:Eqnarray-Environment"
28147 or, when the option
28149 Use AMS math package
28151 in the document settings is selected, an
28155 that is described in
28156 \begin_inset CommandInset ref
28158 reference "sub:Standard-align-Environment"
28163 The align environment is recommended because it provides in any case a
28164 typographically correct output.
28167 \begin_layout Standard
28168 There are other multiline formula environments that can be created via the
28171 Insert\SpecialChar \menuseparator
28175 These environments are described in the following sections.
28178 \begin_layout Standard
28179 In all multiline formula environments a new line is created by pressing
28183 arg "newline-insert newline"
28187 To add or delete lines, the math toolbar buttons
28190 arg "inset-modify tabular append-row"
28196 arg "inset-modify tabular delete-row"
28199 , respectively, or the menu
28201 Edit\SpecialChar \menuseparator
28207 \begin_layout Subsubsection
28209 \begin_inset CommandInset label
28211 name "sub:Line-Separation"
28216 \begin_inset Index idx
28219 \begin_layout Plain Layout
28220 Formula ! multiline ! Line separation
28228 \begin_layout Standard
28229 There is sometimes not enough space in multiline formulas between the lines:
28230 \begin_inset Formula
28232 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}\\
28233 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
28241 \begin_layout Standard
28242 In LaTeX additional line space is specified as optional argument of the
28244 This is not yet possible in LyX
28248 \begin_layout Plain Layout
28250 \begin_inset CommandInset href
28252 name "LyX-bug #1505"
28253 target "http://www.lyx.org/trac/ticket/1505"
28262 , therefore the whole formula must be inserted in TeX-mode.
28263 To add in our example space, the command
28271 is inserted at the end of the first line.
28276 \begin_layout Plain Layout
28283 \begin_layout Plain Layout
28285 B^{2}(B^{2}-2r_{g}^{2}+2x_{0}^{2}-2r_{k}^{2})+4x_{0}^{2}x^{2}+4x_{0}xD &
28288 textrm{-}4x^{2}B^{2}+4x_{0}xB^{2}
28295 \begin_layout Plain Layout
28299 left(B^{2}+x_{0}^{2}
28307 left(B^{2}-2r_{g}^{2}+2x_{0}^{2}-2r_{k}^{2}
28312 \begin_layout Plain Layout
28324 \begin_layout Standard
28325 \begin_inset VSpace bigskip
28328 To set the line separation for all lines in a formula, the length
28335 \begin_inset Index idx
28338 \begin_layout Plain Layout
28348 \begin_inset Formula $\mbox{line separation}=\mathrm{6\, pt+\backslash jot}$
28359 \begin_inset space \thinspace{}
28364 \begin_inset space \thinspace{}
28367 mm additional line separation as in the previous example, the command
28370 \begin_layout Standard
28380 \begin_layout Standard
28381 is inserted in TeX-mode before the formula.
28382 This requires that the LaTeX-package
28390 \begin_layout Plain Layout
28395 is part of every LaTeX standard installation.
28401 \begin_inset Index idx
28404 \begin_layout Plain Layout
28410 was loaded in LaTeX-preamble with the line
28413 \begin_layout Standard
28421 \begin_layout Standard
28426 \begin_layout Plain Layout
28438 \begin_inset Formula
28440 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}\\
28441 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
28449 \begin_layout Standard
28453 \begin_layout Plain Layout
28464 To get back to the predefined distance,
28470 is set to the value 3
28471 \begin_inset space \thinspace{}
28477 \begin_layout Subsubsection
28479 \begin_inset CommandInset label
28481 name "sub:Column-Separation"
28486 \begin_inset Index idx
28489 \begin_layout Plain Layout
28490 Formula ! multiline ! Column separation
28498 \begin_layout Standard
28499 Multiline formulas form a matrix.
28500 A formula in the eqnarray environment is for example a matrix with three
28502 By changing the column separation in this environment, the space beside
28503 the relation sign can be changed.
28506 \begin_layout Standard
28507 The column separation is specified with the length
28514 \begin_inset Index idx
28517 \begin_layout Plain Layout
28526 \begin_inset Newline newline
28529 column separation = 2
28530 \begin_inset space \thinspace{}
28540 \begin_inset Newline newline
28546 \begin_layout Standard
28556 \begin_layout Standard
28557 inserted in TeX-mode, sets for all following formulas a column separation
28559 \begin_inset space \thinspace{}
28563 To get back to the predefined distance,
28570 \begin_inset space \thinspace{}
28576 \begin_layout Standard
28578 \begin_inset space \thinspace{}
28581 cm column separation:
28585 \begin_layout Plain Layout
28597 \begin_inset Formula
28605 A formula with the predefined column separation for matrices of 10
28606 \begin_inset space \thinspace{}
28613 \begin_layout Plain Layout
28625 \begin_inset Formula
28636 \begin_layout Subsubsection
28638 \begin_inset Index idx
28641 \begin_layout Plain Layout
28650 \begin_layout Standard
28651 Long formulas can be typeset using these methods:
28654 \begin_layout Itemize
28655 When one side of the equation is much shorter than the line width, this
28656 one is chosen for the left side and the right side is typeset over two
28658 \begin_inset Formula
28660 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 \\
28661 & & -\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}
28666 The minus sign at the beginning of the second line does normally not appear
28667 as an operator because it is the first character of the line.
28668 Thus it would not be surrounded by space and could not be distinguished
28669 from the fraction bar.
28671 \begin_inset space \thinspace{}
28674 pt space was inserted behind the minus sign with the command
28684 \begin_layout Plain Layout
28692 \begin_inset CommandInset ref
28694 reference "sub:Variable-Space"
28704 \begin_inset Index idx
28707 \begin_layout Plain Layout
28718 \begin_layout Itemize
28719 When both sides of the equation are too long, the command
28726 \begin_inset Index idx
28729 \begin_layout Plain Layout
28738 It is inserted in the first column of the first line and causes all further
28739 insertions to overwrite the following columns:
28740 \begin_inset Formula
28742 \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 \\
28743 & & -\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 \\
28744 & & =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}
28749 After the insertion of
28755 , the cursor is in a purple box that is a bit shifted to the left from the
28757 In this the formula is inserted.
28758 \begin_inset Newline newline
28761 The content of the further lines is inserted to the second or another formula
28763 The greater the column number where it was inserted, the larger the indentation.
28764 \begin_inset VSpace medskip
28768 \begin_inset Newline newline
28772 \begin_inset Note Greyedout
28775 \begin_layout Plain Layout
28776 Note the following when using
28785 \begin_layout Itemize
28786 The formula doesn't use the full page width.
28788 \begin_inset space \thinspace{}
28792 \begin_inset space \space{}
28796 \begin_inset Formula $-B^{2}$
28799 is added to the first line in the above example, it would have been outside
28801 To better use the width, negative space can be inserted at the beginning
28805 \begin_layout Itemize
28806 Due to a bug in LyX the cursor cannot be set with the mouse into the first
28811 \begin_layout Plain Layout
28812 \begin_inset CommandInset href
28814 name "LyX-bug #1429"
28815 target "http://www.lyx.org/trac/ticket/1429"
28824 One can only set the cursor at the beginning of the line and move it with
28833 \begin_layout Itemize
28834 Other methods to set long formulas are offered by the environments described
28836 \begin_inset CommandInset ref
28838 reference "sub:Multline-Environment"
28843 \begin_inset CommandInset ref
28845 reference "sub:Multiline-Formula-Parts"
28852 \begin_layout Subsubsection
28853 Multiline Fractions
28854 \begin_inset CommandInset label
28856 name "sub:Multiline-Fractions"
28861 \begin_inset Index idx
28864 \begin_layout Plain Layout
28865 Fractions ! multiline
28873 \begin_layout Standard
28874 There are cases where the denominator and/or the numerator of a fraction
28875 is so long that the fraction does not fit into one line.
28876 It is then necessary to add a line break within the fraction.
28877 This can be done using the command
28884 \begin_inset Index idx
28887 \begin_layout Plain Layout
28896 To activate it, set in the document settings under
28899 \begin_inset space ~
28909 \begin_inset Index idx
28912 \begin_layout Plain Layout
28913 Packages ! mathtools
28921 \begin_inset space ~
28936 \begin_layout Standard
28941 splitfrac{first line}{second line}
28944 \begin_layout Standard
28945 and is used as denominator and/or numerator:
28948 \begin_layout Standard
28949 \begin_inset Formula
28951 a=\frac{\splitfrac{xy+xy+xy+xy+xy}{+wy+wy+wy+wy}}{z}\ne\frac{\splitdfrac{xy+\frac{xy}{z}+xy+xy+xy}{+xy+xy+xy+xy}}{z}
28956 The command for the first numerator above is:
28959 \begin_layout Standard
28964 splitfrac{xy+xy+xy+xy+xy
28965 \begin_inset space \textvisiblespace{}
28973 \begin_layout Subsubsection
28975 \begin_inset CommandInset label
28977 name "sub:Multiline-Brackets"
28982 \begin_inset Index idx
28985 \begin_layout Plain Layout
28986 Brackets ! for multiline expressions
28994 \begin_layout Standard
28995 For brackets spanning multiple lines the following problem occurs:
28996 \begin_inset Formula
28998 A & = & \sin(x)\left[\prod_{R=1}^{\infty}\frac{1}{R}+\cdots\right.\\
28999 & & \left.\cdots+B-D\right]
29007 \begin_layout Standard
29008 The closing bracket is smaller than the opening bracket because brackets
29009 with variable size may not span multiple lines.
29012 \begin_layout Standard
29013 To set the bracket size for the second line correctly, the first line is
29021 \begin_inset Index idx
29024 \begin_layout Plain Layout
29032 and the second line with
29040 \begin_layout Plain Layout
29054 \begin_inset CommandInset ref
29056 reference "sub:Automatic-Bracket-Size"
29068 \begin_inset Index idx
29071 \begin_layout Plain Layout
29094 \begin_inset space \textvisiblespace{}
29104 \begin_inset space \textvisiblespace{}
29114 \begin_inset space \textvisiblespace{}
29120 \begin_inset Formula $\downarrow$
29126 \begin_inset Index idx
29129 \begin_layout Plain Layout
29137 is inserted, because the multiplication operator with its limits is the
29138 largest symbol in the first line and this should be the size for the bracket
29139 in the second line.
29142 \begin_layout Standard
29143 The result is this:
29144 \begin_inset Formula
29146 A & = & \sin(x)\left[\prod_{R=1}^{\infty}\frac{1}{R}+\cdots\right.\\
29147 & & \left.\vphantom{\prod_{R=1}^{\infty}}\cdots+B-D\right]
29155 \begin_layout Subsection
29159 \begin_layout Standard
29160 Align environments can be used for every kind of multiline formulas.
29161 They are especially useful to set several formulas side by side.
29164 \begin_layout Standard
29165 Align environments consist of columns.
29166 The odd columns are right aligned, the even ones left aligned.
29167 Every line in an Align environment can be numbered.
29170 \begin_layout Standard
29171 Align environments are created via the menu
29173 Insert\SpecialChar \menuseparator
29179 Edit\SpecialChar \menuseparator
29180 Math\SpecialChar \menuseparator
29181 Change Formula Type
29183 already existing formulas can be converted to Align environments.
29186 \begin_layout Standard
29187 To add or delete columns, the math toolbar buttons
29190 arg "inset-modify tabular append-column"
29196 arg "inset-modify tabular delete-column"
29199 , respectively, or the menu
29201 Edit\SpecialChar \menuseparator
29207 \begin_layout Subsubsection
29208 Standard align Environment
29209 \begin_inset CommandInset label
29211 name "sub:Standard-align-Environment"
29216 \begin_inset Index idx
29219 \begin_layout Plain Layout
29220 Formula ! multiline ! align environment
29228 \begin_layout Standard
29229 This Align environment is created by pressing
29232 arg "newline-insert newline"
29235 in a formula or by the menu
29237 Insert\SpecialChar \menuseparator
29238 Math\SpecialChar \menuseparator
29239 AMS align Environment
29244 \begin_layout Standard
29245 An example for two formulas set side by side, that are created with a four
29246 column align environment:
29247 \begin_inset Formula
29249 A & =\sin(B) & C & =D\\
29250 C & \ne A & B & \ne D
29255 As it can be seen, the formulas in this environment are placed so as if
29264 \begin_layout Plain Layout
29272 \begin_inset CommandInset ref
29274 reference "sub:Variable-Space"
29285 before the first and after every even column.
29286 When the formula style
29292 \begin_layout Plain Layout
29294 \begin_inset CommandInset ref
29296 reference "sec:Formula-Styles"
29307 is used, the formula is set without the
29313 before the first column.
29316 \begin_layout Subsubsection
29317 Alignat Environment
29318 \begin_inset Index idx
29321 \begin_layout Plain Layout
29322 Formula ! multiline ! alignat environment
29330 \begin_layout Standard
29331 The alignat environment has no predefined column separation.
29332 It can be inserted manually with the spaces that are described
29333 \begin_inset CommandInset ref
29335 reference "sub:Space"
29342 \begin_layout Standard
29343 The above example in the alignat environment where 1
29344 \begin_inset space \thinspace{}
29347 cm space was inserted at the beginning of the second formula:
29348 \begin_inset Formula
29349 \begin{alignat*}{2}
29350 A & =\sin(B) & \hspace{1cm}C & =D\\
29351 C & \ne A & B & \ne D
29356 Because the column separation can be set separately for every column, this
29357 environment is especially suitable to set three and more formulas side
29361 \begin_layout Subsubsection
29362 Flalign Environment
29363 \begin_inset CommandInset label
29365 name "sub:Flalign-Environment"
29370 \begin_inset Index idx
29373 \begin_layout Plain Layout
29374 Formula ! multiline ! flalign environment
29382 \begin_layout Standard
29383 In this environment the first two columns are always set as much as possible
29384 to the left and the last two ones to the right.
29386 \begin_inset Formula
29388 A & =1 & B & =2 & C & =3\\
29389 X & =\textrm{-}1 & Y & =\textrm{-}2 & Z & =4
29397 \begin_layout Standard
29398 By creating a flalign environment with an odd number of columns where an
29399 empty TeX-brace is inserted to the last column, several formulas in a document
29400 can be set to the left, although the formula style
29405 As example the indented formula
29406 \begin_inset CommandInset ref
29408 reference "eq:VolInt"
29413 \begin_inset Formula
29415 \hspace{30pt}\iiint\limits _{V}X\,\mathrm{d}V & =U & {}
29420 The first two columns contain the formula.
29421 To indent it as with the formula style
29426 \begin_inset space \thinspace{}
29429 pt space was inserted at the beginning of the first column.
29432 \begin_layout Subsection
29433 Eqnarray Environment
29434 \begin_inset CommandInset label
29436 name "sub:Eqnarray-Environment"
29441 \begin_inset Index idx
29444 \begin_layout Plain Layout
29445 Formula ! multiline ! eqnarray environment
29453 \begin_layout Standard
29454 When this environment has been created, three blue boxes appear.
29455 The content of the first box is right aligned, the content of the last
29457 The content of the middle box appears centered and a bit smaller, because
29458 it is designed to insert there only relation characters.
29459 \begin_inset Formula
29461 \frac{ABC}{D} & \frac{ABC}{D} & \frac{ABC}{D}\\
29471 \begin_layout Subsection
29473 \begin_inset Index idx
29476 \begin_layout Plain Layout
29477 Formula ! multiline ! gather environment
29485 \begin_layout Standard
29486 This environment consists of only one centered column.
29487 Every line can be numbered.
29488 \begin_inset Formula
29499 \begin_layout Subsection
29500 Multline Environment
29501 \begin_inset CommandInset label
29503 name "sub:Multline-Environment"
29508 \begin_inset Index idx
29511 \begin_layout Plain Layout
29512 Formula ! multiline ! multline environment
29520 \begin_layout Standard
29521 The multline environment consists, like the gather environment, of only
29523 But the first line is left aligned, the last one right aligned.
29524 All other lines are centered.
29525 Therefore this environment is suitable for long formulas.
29527 \begin_inset CommandInset ref
29529 reference "eq:lefteqn"
29533 in the multline environment:
29534 \begin_inset Formula
29536 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}\\
29537 -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}\\
29538 =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}}
29546 \begin_layout Standard
29547 In the output only the last (first) line of a multline environment appears
29548 numbered when the document numbering is right (left).
29552 \begin_layout Plain Layout
29553 numbering styles see
29554 \begin_inset CommandInset ref
29556 reference "sec:Formula-Styles"
29568 \begin_layout Standard
29576 \begin_inset Index idx
29579 \begin_layout Plain Layout
29594 \begin_inset Index idx
29597 \begin_layout Plain Layout
29605 a centered line can be right or left aligned, respectively.
29606 The commands are used as follows:
29609 \begin_layout Standard
29614 shoveright{line content}
29620 shoveleft{line content}
29623 \begin_layout Standard
29624 \begin_inset VSpace medskip
29634 \begin_inset Index idx
29637 \begin_layout Plain Layout
29645 specifies the distance of the first line from the left page margin.
29646 Predefined is the length 0
29647 \begin_inset space \thinspace{}
29653 \begin_layout Standard
29654 As example the above formula where the command
29657 \begin_layout Standard
29667 \begin_layout Standard
29668 was inserted in TeX-mode before:
29672 \begin_layout Plain Layout
29684 \begin_inset Formula
29686 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}\\
29687 \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}}\\
29688 =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}}
29697 \begin_layout Plain Layout
29708 The second line was left aligned using
29717 \begin_layout Subsection
29718 Multiline Formula Parts
29719 \begin_inset CommandInset label
29721 name "sub:Multiline-Formula-Parts"
29726 \begin_inset Index idx
29729 \begin_layout Plain Layout
29730 Formula ! multiline ! formula parts
29738 \begin_layout Standard
29739 To display only parts of a formula with multiple lines, one of the following
29740 environments is used:
29757 They can be inserted via the menu
29759 Insert\SpecialChar \menuseparator
29762 or by using the commands described in this section.
29765 \begin_layout Standard
29766 The first three have the same properties as the corresponding multiline
29767 formula environments, but it is possible to set further formula parts beside
29770 \begin_inset Formula
29772 \left.\begin{aligned}\Delta x\Delta p & \ge\frac{\hbar}{2}\\
29773 \Delta E\Delta t & \ge\frac{\hbar}{2}
29775 \right\} \textrm{Uncertainty relations}
29783 \begin_layout Standard
29784 To get this formula, a displayed formula is created where the command
29791 \begin_inset Index idx
29794 \begin_layout Plain Layout
29803 A purple box appears around the blue formula box where now columns and
29804 lines can be added.
29805 Outside the multiline environment other formula parts can be set, like
29809 \begin_layout Standard
29810 The aligned environment is also suitable for long formulas whose lines are
29811 horizontally aligned.
29812 Using aligned in a displayed formula has the advantage that the formula
29813 number is vertically centered behind the lines.
29815 \begin_inset CommandInset ref
29817 reference "eq:shortlong"
29821 in the aligned environment:
29822 \begin_inset Formula
29824 \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}|}\\
29825 & -\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}|}
29834 \begin_layout Standard
29835 To use the environments
29854 \begin_inset Index idx
29857 \begin_layout Plain Layout
29872 \begin_inset Index idx
29875 \begin_layout Plain Layout
29890 \begin_inset Index idx
29893 \begin_layout Plain Layout
29901 are inserted, respectively.
29902 The split environment has the same properties as the aligned environment
29903 but it can only have two columns.
29906 \begin_layout Subsection
29907 Text in multiline Formulas
29908 \begin_inset CommandInset label
29910 name "sub:Text-in-multiline"
29915 \begin_inset Index idx
29918 \begin_layout Plain Layout
29925 \begin_inset Index idx
29928 \begin_layout Plain Layout
29929 Formula ! multiline ! text
29937 \begin_layout Standard
29938 In the Align environments, and the multline and gather environment, text
29939 can be inserted that will appear in a separate line and doesn't affect
29940 the column alignment.
29941 To do this, the command
29948 \begin_inset Index idx
29951 \begin_layout Plain Layout
29959 is used in the following scheme:
29962 \begin_layout Standard
29970 \begin_layout Standard
29971 The text should not be longer than a line because it cannot be hyphenated.
29972 As LyX doesn't yet support
29978 directly, the text is written as mathematical text.
29985 must hereby be at the beginning of a line and appears in the output above
29987 An example where the text was inserted at the beginning of the second line:
29988 \begin_inset Formula
29990 I & =a\sqrt{2}\int_{0}^{2\pi}\sqrt{1+\cos(\phi)}\;\mathrm{d}\phi\\
29991 \intertext{\text{integrand is symmetric to \ensuremath{\phi=\pi}, therefore}} & =2a\sqrt{2}\int_{0}^{\pi}\sqrt{1+\cos(\phi)}\;\mathrm{d}\phi
29999 \begin_layout Standard
30006 always creates some vertical space between the text and the formula lines.
30007 To avoid this space, set in the document settings under
30010 \begin_inset space ~
30020 \begin_inset Index idx
30023 \begin_layout Plain Layout
30024 Packages ! mathtools
30032 \begin_inset space ~
30038 Then you can use the command
30045 \begin_inset Index idx
30048 \begin_layout Plain Layout
30065 \begin_layout Standard
30066 \begin_inset Formula
30068 I & =a\sqrt{2}\int_{0}^{2\pi}\sqrt{1+\cos(\phi)}\;\mathrm{d}\phi\\
30069 \shortintertext{\text{integrand is symmetric to \ensuremath{\phi=\pi}, therefore}} & =2a\sqrt{2}\int_{0}^{\pi}\sqrt{1+\cos(\phi)}\;\mathrm{d}\phi
30077 \begin_layout Section
30079 \begin_inset Index idx
30082 \begin_layout Plain Layout
30089 \begin_inset Index idx
30092 \begin_layout Plain Layout
30093 Formula ! numbering|see
30097 \begin_layout Plain Layout
30108 \begin_layout Plain Layout
30123 \begin_layout Subsection
30127 \begin_layout Standard
30128 Numbered formulas can be created with the menu
30130 Insert\SpecialChar \menuseparator
30131 Math\SpecialChar \menuseparator
30133 \begin_inset space ~
30141 \begin_inset space ~
30147 Existing formulas can be numbered with the menu
30149 Edit\SpecialChar \menuseparator
30150 Math\SpecialChar \menuseparator
30152 \begin_inset space ~
30160 arg "math-number-toggle"
30164 The formula number is displayed in LyX behind the formula as a number sign
30166 The number sign is replaced in the output by the formula number.
30169 \begin_layout Standard
30170 When numbering is turned on in multiline formulas, all lines will be numbered.
30171 But the numbering can be controlled with the menu
30173 Edit\SpecialChar \menuseparator
30174 Math\SpecialChar \menuseparator
30176 \begin_inset space ~
30180 \begin_inset space ~
30184 \begin_inset space ~
30192 arg "math-number-line-toggle"
30198 \begin_layout Standard
30199 Except for inline formulas, all formulas can be numbered with two different
30201 \begin_inset CommandInset ref
30203 reference "sec:Formula-Styles"
30210 \begin_layout Subsection
30212 \begin_inset Index idx
30215 \begin_layout Plain Layout
30216 Cross-references ! to formulas
30224 \begin_layout Standard
30225 All labeled formulas can be cross-referenced.
30226 A label is added by the menu
30228 Insert\SpecialChar \menuseparator
30231 or the toolbar button
30238 The cursor must hereby be inside a displayed formula.
30239 Alternatively you can right-click on the formula and choose
30244 A dialog pops up displaying the prefix
30249 The label is inserted there behind the prefix.
30250 The predefined prefix means
30251 \begin_inset Quotes eld
30255 \begin_inset Quotes erd
30258 and makes it easier to find labels in large documents because it marks
30259 it as formula label to divide it from e.
30260 \begin_inset space \thinspace{}
30264 \begin_inset space \space{}
30268 To change a label, the menu
30270 Insert\SpecialChar \menuseparator
30273 is used again or you right-click on a formula and then on
30280 \begin_layout Standard
30281 The name of the label is displayed in LyX within two parentheses behind
30283 A formula with a label is always numbered.
30286 \begin_layout Standard
30287 Cross-references are inserted via the menu
30289 Insert\SpecialChar \menuseparator
30292 or with the toolbar button
30295 arg "dialog-show-new-inset ref"
30299 A formula cross-reference appears in the output as formula number.
30300 When in the cross-reference dialog window the format
30304 is chosen, the cross-reference appears in the output as formula number
30306 \begin_inset Newline newline
30309 By right-clicking on a cross-reference in LyX, one jumps to the formula
30310 that is referenced.
30313 \begin_layout Standard
30314 Here are as examples cross-references to formulas of the following subsections:
30315 \begin_inset Note Note
30318 \begin_layout Plain Layout
30319 Note the different cross-reference types.
30327 \begin_layout Standard
30329 \begin_inset CommandInset ref
30336 \begin_inset CommandInset ref
30344 \begin_inset CommandInset ref
30350 ) big Latin letters are used for the numbering in contrary to (
30351 \begin_inset CommandInset ref
30360 \begin_layout Standard
30361 \begin_inset VSpace medskip
30364 When the argument of
30372 \begin_layout Plain Layout
30380 \begin_inset CommandInset ref
30382 reference "sub:User-defined-Numbering"
30393 contains a box like in
30394 \begin_inset CommandInset ref
30396 reference "sub:Paragraph-Boxes"
30400 , the formula cannot be referenced.
30403 \begin_layout Subsection
30405 \begin_inset Index idx
30408 \begin_layout Plain Layout
30409 Formula numbering ! subnumbering
30417 \begin_layout Standard
30418 With the help of the commands
30422 begin{subequations}
30430 formulas can be subnumbered.
30431 Both commands are inserted in TeX-mode.
30434 \begin_layout Standard
30436 \begin_inset Formula
30447 \begin_layout Plain Layout
30451 addtocounter{equation}{-1}
30460 \begin_layout Plain Layout
30464 begin{subequations}
30470 \begin_inset VSpace -5mm
30474 \begin_inset Formula
30482 \begin_inset Formula
30492 \begin_layout Standard
30496 \begin_layout Plain Layout
30508 \begin_layout Standard
30509 To create the example, the following is done:
30512 \begin_layout Enumerate
30513 first formula is inserted
30516 \begin_layout Enumerate
30521 addtocounter{equation}{-1}
30523 begin{subequations}
30524 \begin_inset Index idx
30527 \begin_layout Plain Layout
30536 \begin_inset Newline newline
30541 is inserted after the first formula
30544 \begin_layout Enumerate
30545 second formula is inserted
30548 \begin_layout Enumerate
30549 third formula is inserted
30552 \begin_layout Enumerate
30559 is inserted after the third formula
30562 \begin_layout Standard
30563 Every formula between the commands
30575 is subnumbered as a, b,
30576 \begin_inset Newline linebreak
30579 c, \SpecialChar \ldots{}
30580 For multiline formulas every line will be subnumbered.
30581 All subnumbered formulas are treated as
30586 But as every numbered formula increases the counter
30590 by one, the command
30596 is needed to decrease it.
30597 Otherwise the formulas
30598 \begin_inset CommandInset ref
30605 \begin_inset CommandInset ref
30612 \begin_inset CommandInset ref
30618 would be numbered as
30619 \begin_inset CommandInset ref
30626 \begin_inset CommandInset ref
30633 \begin_inset CommandInset ref
30642 \begin_layout Standard
30643 By inserting the commands in TeX-mode, a space is created between the first
30646 \begin_inset space \thinspace{}
30649 mm vertical space is inserted after the command
30653 begin{subequations}
30656 When the formula style
30662 \begin_layout Plain Layout
30664 \begin_inset CommandInset ref
30666 reference "sec:Formula-Styles"
30678 \begin_inset space \thinspace{}
30681 mm space is inserted instead.
30684 \begin_layout Standard
30685 Here is an example for a multiline formula where the numbering was turned
30686 off for the second line:
30690 \begin_layout Plain Layout
30694 begin{subequations}
30700 \begin_inset Formula
30702 A & = & (B-Z)^{2}=(B-Z)(B-Z)\label{eq:d}\\
30703 & = & B^{2}-ZB-BZ+Z^{2}\nonumber \\
30704 & = & B^{2}-2BZ+Z^{2}\label{eq:f}
30713 \begin_layout Plain Layout
30725 \begin_layout Subsection
30726 User-defined Numbering
30727 \begin_inset CommandInset label
30729 name "sub:User-defined-Numbering"
30734 \begin_inset Index idx
30737 \begin_layout Plain Layout
30738 Formula numbering ! user-defined
30746 \begin_layout Standard
30747 \begin_inset Index idx
30750 \begin_layout Plain Layout
30751 Formula numbering ! self-defined delimiters
30756 With the standard numbering parentheses are set around the formula number.
30757 To replace the parentheses for example by vertical bars, the following
30758 line is added to the LaTeX-preamble:
30761 \begin_layout Standard
30773 \begin_inset Note Note
30776 \begin_layout Plain Layout
30777 This macro is already declared in the LaTeX-preamble for testing.
30778 To activate it, remove the percent sign at the beginning.
30786 \begin_layout Standard
30787 To use other characters, the vertical bars besides the
30791 are replaced by one ore more characters.
30792 To get only the formula number the vertical bars are omitted.
30795 \begin_layout Standard
30796 \begin_inset VSpace bigskip
30799 When there should be an expression of your choice instead of the consecutive
30800 formula number in parentheses behind the formula, the command
30807 \begin_inset Index idx
30810 \begin_layout Plain Layout
30819 \begin_inset Formula
30821 A+B=C\tag{something}\label{eq:tag}
30826 In this example the command
30831 \begin_inset space \textvisiblespace{}
30836 was inserted in the formula.
30839 \begin_layout Standard
30845 \begin_inset space \textvisiblespace{}
30850 is inserted instead, the star prevents the parentheses around the expression:
30851 \begin_inset Formula
30853 A+B=C\tag*{something}
30861 \begin_layout Standard
30862 \begin_inset VSpace bigskip
30865 To restart the formula numbering with new document parts or sections, the
30866 following command is used:
30869 \begin_layout Standard
30874 @addtoreset{equation}{part}
30877 \begin_inset Index idx
30880 \begin_layout Plain Layout
30885 \begin_layout Plain Layout
30896 \begin_layout Plain Layout
30909 \begin_layout Plain Layout
30920 \begin_layout Plain Layout
30933 \begin_inset Newline newline
30937 \begin_inset Newline newline
30944 @addtoreset{equation}{section}
30947 \begin_layout Standard
30948 To be able to use these commands in TeX-mode, the
30949 \begin_inset Quotes eld
30953 \begin_inset Quotes erd
30956 character has to be made
30957 \begin_inset Quotes eld
30961 \begin_inset Quotes erd
30964 for LaTeX using the command
30978 So the command sequence in TeX-mode is:
30981 \begin_layout Standard
30987 \begin_inset Newline newline
30992 @addtoreset{equation}{section}
30993 \begin_inset Newline newline
31001 \begin_layout Standard
31002 In the LaTeX-preamble
31014 can be omitted as they are automatically internally inserted by LyX.
31017 \begin_layout Standard
31032 \begin_layout Plain Layout
31037 is part of the LaTeX-package
31042 \begin_inset Index idx
31045 \begin_layout Plain Layout
31046 Packages ! carlisle
31051 that is part of every LaTeX standard installation.
31057 \begin_inset Index idx
31060 \begin_layout Plain Layout
31061 Packages ! remreset
31066 has to be loaded in the LaTeX-preamble with the line
31069 \begin_layout Standard
31074 usepackage{remreset}
31077 \begin_layout Standard
31085 \begin_inset Index idx
31088 \begin_layout Plain Layout
31093 \begin_layout Plain Layout
31104 \begin_layout Plain Layout
31117 \begin_layout Plain Layout
31128 \begin_layout Plain Layout
31140 can be used with the same scheme as
31149 \begin_layout Standard
31150 \begin_inset VSpace bigskip
31153 Sometimes formulas should be numbered in the following form:
31156 \begin_layout Standard
31159 (section number.formula number)
31162 \begin_layout Standard
31163 The formula number should start with every section with
31164 \begin_inset Quotes eld
31168 \begin_inset Quotes erd
31174 \begin_layout Standard
31175 For this case there is the command
31182 \begin_inset Index idx
31185 \begin_layout Plain Layout
31193 , which is used with the following scheme:
31196 \begin_layout Standard
31201 numberwithin{counter}{sectioning}
31204 \begin_layout Standard
31205 Counter denotes what kind of numbering is affected, sectioning denotes what
31206 number is before the dot.
31209 \begin_layout Standard
31210 Thus in our case the following LaTeX-preamble or TeX code line is used:
31213 \begin_layout Standard
31218 numberwithin{equation}{section}
31221 \begin_layout Standard
31222 This is the result:
31226 \begin_layout Plain Layout
31230 numberwithin{equation}{section}
31236 \begin_inset Formula
31246 \begin_layout Standard
31248 \begin_inset space \thinspace{}
31252 \begin_inset space \space{}
31255 tables so that the number of the part is the sectioning,
31256 \begin_inset Newline newline
31263 numberwithin{table}{part}
31268 \begin_layout Standard
31269 To go back to the standard numbering or to prevent this kind of numbering
31270 when it is defined by the document class, the following command is inserted
31271 as TeX code or to the LaTeX-preamble:
31274 \begin_layout Standard
31284 \begin_inset Index idx
31287 \begin_layout Plain Layout
31301 \begin_layout Plain Layout
31317 \begin_inset Newline newline
31325 \begin_inset Newline newline
31337 \begin_layout Standard
31344 uses internally the command
31350 , described above, that also needs to be reverted.
31354 \begin_layout Plain Layout
31361 \begin_layout Plain Layout
31365 @removefromreset{equation}{section}
31368 \begin_layout Plain Layout
31380 \begin_layout Subsection
31381 Numbering with Roman Numbers and Letters
31382 \begin_inset Index idx
31385 \begin_layout Plain Layout
31386 Formula numbering ! with letters
31392 \begin_inset Index idx
31395 \begin_layout Plain Layout
31396 Formula numbering ! with Roman numbers
31404 \begin_layout Standard
31405 Formulas can also be numbered with Roman numbers and Latin letters.
31406 To number for example with small Roman numbers, the command
31409 \begin_layout Standard
31421 \begin_layout Standard
31422 is inserted before the formula in TeX-mode.
31430 \begin_inset Index idx
31433 \begin_layout Plain Layout
31441 redefines the predefined command
31457 \begin_layout Plain Layout
31464 has the same scheme like the command
31470 that is described in
31471 \begin_inset CommandInset ref
31473 reference "sub:The-Command-newcommand"
31486 is the formula counter.
31493 is used as prefix for a counter, the value of the counter is output as
31495 When a formula is numbered, LaTeX sets internally the command
31501 behind the formula.
31507 \begin_inset Index idx
31510 \begin_layout Plain Layout
31520 outputs the counter as small Roman number.
31523 \begin_layout Standard
31524 All formulas behind the command
31534 are now numbered Roman.
31535 To switch to numbering with big Roman numbers, the command is inserted
31549 \begin_inset Index idx
31552 \begin_layout Plain Layout
31564 \begin_inset Quotes eld
31568 \begin_inset Quotes erd
31571 with small Latin letters there is the command
31578 \begin_inset Index idx
31581 \begin_layout Plain Layout
31589 , for big ones there is the command
31596 \begin_inset Index idx
31599 \begin_layout Plain Layout
31612 \begin_layout Standard
31613 \begin_inset Note Greyedout
31616 \begin_layout Plain Layout
31623 \begin_inset space ~
31626 formulas can be numbered with Latin letters in one document.
31634 \begin_layout Standard
31638 \begin_layout Plain Layout
31654 \begin_layout Standard
31655 \begin_inset Formula
31657 A=\textrm{small roman}
31666 \begin_layout Plain Layout
31680 \begin_inset Formula
31682 B=\textrm{big Roman}\label{eq:Rom}
31691 \begin_layout Plain Layout
31705 \begin_inset Formula
31707 C=\textrm{small Latin}
31716 \begin_layout Plain Layout
31730 \begin_inset Formula
31732 D=\textrm{big Latin}\label{eq:Lat}
31740 \begin_layout Standard
31741 To switch back to the default numbering, insert the command:
31744 \begin_layout Standard
31754 \begin_inset Index idx
31757 \begin_layout Plain Layout
31768 \begin_layout Standard
31772 \begin_layout Plain Layout
31786 \begin_inset Formula
31796 \begin_layout Standard
31797 \begin_inset VSpace medskip
31800 As you see, formulas are numbered serially independent from the numbering
31802 When then numbering should start with
31803 \begin_inset Quotes eld
31807 \begin_inset Quotes erd
31810 when the style is changed, new equation counters have to be defined.
31811 A description about this can be found in the file
31812 \begin_inset CommandInset href
31814 name "Formula-numbering.lyx"
31815 target "run:Formula-numbering.lyx"
31822 \begin_layout Standard
31823 \begin_inset Newpage newpage
31829 \begin_layout Section
31830 Chemical Symbols and Equations
31831 \begin_inset CommandInset label
31833 name "sub:Chemical-Symbols-and"
31838 \begin_inset Index idx
31841 \begin_layout Plain Layout
31842 Chemical characters ! Symbols
31848 \begin_inset Index idx
31851 \begin_layout Plain Layout
31858 \begin_inset Index idx
31861 \begin_layout Plain Layout
31870 \begin_layout Standard
31871 An example text from chemistry:
31874 \begin_layout Quote
31876 \begin_inset Formula $\mathrm{SO_{4}^{2-}}$
31879 -ion reacts with two
31880 \begin_inset Formula $\mathrm{Na^{+}}$
31883 -ions to sodium sulfate
31884 \begin_inset Formula $\left(\mathrm{Na_{2}SO_{4}}\right)$
31888 The chemical equation for this is:
31889 \begin_inset Formula
31891 \mathrm{2\, Na^{+}+SO_{4}^{2-}\longrightarrow Na_{2}SO_{4}}\label{eq:chem-reaction}
31899 \begin_layout Standard
31900 This chemical equation can directly be created as formula.
31901 To avoid that the symbols appear italic, everything is highlighted and
31902 changed by the shortcut
31908 to the upright font style.
31912 \begin_layout Plain Layout
31918 \begin_inset CommandInset ref
31920 reference "sub:Font-Styles"
31932 \begin_layout Standard
31933 A more convenient way to typeset chemical formulas is to use the command
31941 \begin_inset Index idx
31944 \begin_layout Plain Layout
31952 that is available when the LaTeX-package
31957 \begin_inset Index idx
31960 \begin_layout Plain Layout
31973 to a formula a new blue box appears where chemical formulas can be inserted
31974 in an intuitive way.
31977 \begin_layout Standard
31979 \begin_inset Tabular
31980 <lyxtabular version="3" rows="9" columns="2">
31981 <features rotate="0" tabularvalignment="middle">
31982 <column alignment="center" valignment="top">
31983 <column alignment="center" valignment="top">
31985 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
31988 \begin_layout Plain Layout
31994 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
31997 \begin_layout Plain Layout
31999 \begin_inset Note Note
32002 \begin_layout Plain Layout
32009 is only used as spacer.
32021 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
32024 \begin_layout Plain Layout
32028 \begin_inset space \textvisiblespace{}
32036 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
32039 \begin_layout Plain Layout
32040 \begin_inset Formula $\raisebox{4.5mm}{}\ce{H2CO3}\raisebox{-2mm}{}$
32050 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
32053 \begin_layout Plain Layout
32057 \begin_inset space \textvisiblespace{}
32065 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
32068 \begin_layout Plain Layout
32069 \begin_inset Formula $\raisebox{5mm}{}\ce{SO4^{2-}}\raisebox{-2mm}{}$
32079 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
32082 \begin_layout Plain Layout
32086 \begin_inset space \textvisiblespace{}
32094 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
32097 \begin_layout Plain Layout
32098 \begin_inset Formula $\raisebox{4.5mm}{}\ce{(NH4)2S}\raisebox{-2mm}{}$
32108 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
32111 \begin_layout Plain Layout
32115 \begin_inset space \textvisiblespace{}
32123 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
32126 \begin_layout Plain Layout
32127 \begin_inset Formula $\raisebox{4.5mm}{}\ce{KCr(SO4)2.12H2O}\raisebox{-2mm}{}$
32137 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
32140 \begin_layout Plain Layout
32144 \begin_inset space \textvisiblespace{}
32150 \begin_inset space \textvisiblespace{}
32156 \begin_inset space \textvisiblespace{}
32164 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
32167 \begin_layout Plain Layout
32168 \begin_inset Formula $\raisebox{4.5mm}{}\ce{A-B\dbond C\tbond D}\raisebox{-2mm}{}$
32178 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
32181 \begin_layout Plain Layout
32185 \begin_inset space \textvisiblespace{}
32189 \begin_inset Formula $\downarrow$
32193 \begin_inset Formula $\to$
32201 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
32204 \begin_layout Plain Layout
32205 \begin_inset Formula $\raisebox{5mm}{}\ce{_{90}^{227}Th+}\raisebox{-2mm}{}$
32215 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
32218 \begin_layout Plain Layout
32222 \begin_inset space \textvisiblespace{}
32226 \begin_inset space \textvisiblespace{}
32230 \begin_inset space \textvisiblespace{}
32234 \begin_inset space \textvisiblespace{}
32238 \begin_inset space \textvisiblespace{}
32246 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
32249 \begin_layout Plain Layout
32250 \begin_inset Formula $\raisebox{4.5mm}{}\ce{CO2 + C <=> 2CO}\raisebox{-2mm}{}$
32260 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
32263 \begin_layout Plain Layout
32267 \begin_inset space \textvisiblespace{}
32271 \begin_inset space \textvisiblespace{}
32275 \begin_inset space \textvisiblespace{}
32279 \begin_inset space \textvisiblespace{}
32287 \begin_inset space \textvisiblespace{}
32295 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
32298 \begin_layout Plain Layout
32299 \begin_inset Formula $\raisebox{5mm}{}\ce{CO2 + C ->[\alpha][\beta] 2CO}\raisebox{-4mm}{}$
32315 \begin_layout Standard
32316 \begin_inset Note Greyedout
32319 \begin_layout Plain Layout
32325 Inserting a formula to a
32331 box will lead to LaTeX errors due to a LyX bug.
32337 \begin_layout Plain Layout
32338 \begin_inset CommandInset href
32340 name "LyX-bug #8566"
32341 target "http://www.lyx.org/trac/ticket/8566"
32352 In this case TeX code has to be used like for
32366 \begin_layout Plain Layout
32387 \begin_layout Standard
32388 \begin_inset Note Greyedout
32391 \begin_layout Plain Layout
32397 It is not possible in LyX to use the character ^ to get an up-arrow as
32403 One instead uses a negative thin space followed by the command
32410 \begin_inset Formula $\ce{Fe + 2H+ -> Fe^{2+} + H2\negthinspace\uparrow}$
32421 \begin_layout Standard
32428 the command for equation
32429 \begin_inset space ~
32433 \begin_inset CommandInset ref
32435 reference "eq:chem-reaction"
32440 \begin_inset Newline newline
32448 \begin_inset space \textvisiblespace{}
32452 \begin_inset space \textvisiblespace{}
32456 \begin_inset space \textvisiblespace{}
32460 \begin_inset space \textvisiblespace{}
32464 \begin_inset space \textvisiblespace{}
32468 \begin_inset space \textvisiblespace{}
32474 \begin_layout Standard
32475 To create multiline chemical equations first a multiline formula is created
32477 \begin_inset CommandInset ref
32479 reference "sec:Multiline-Formulas"
32484 Afterwards the command
32490 is used in every small blue box of the formula.
32492 \begin_inset CommandInset ref
32494 reference "eq:TEOS-reaction-1"
32499 \begin_inset CommandInset ref
32501 reference "eq:TEOS-reaction-2"
32505 are an example of a multi-stage chemical reaction where every equation
32506 has its own number.
32507 \begin_inset Formula
32509 \ce{TEOS + 4O} & \ce{->} & \ce{Si(OH)4 + 4C2H4O}\label{eq:TEOS-reaction-1}\\
32510 \ce{Si(OH)4} & \ce{->} & \ce{SiO2 + 2H2O}\label{eq:TEOS-reaction-2}
32518 \begin_layout Standard
32529 package provides the command
32536 \begin_inset Index idx
32539 \begin_layout Plain Layout
32547 that has to be used for special cases.
32548 For more information about
32554 and more examples have a look at the documentation of
32559 \begin_inset CommandInset citation
32568 \begin_layout Section
32572 \begin_layout Standard
32573 LyX supports two types of commutative diagrams:
32581 that are explained in the following.
32584 \begin_layout Subsection
32586 \begin_inset Index idx
32589 \begin_layout Plain Layout
32598 \begin_layout Standard
32599 Diagrams of this type visualize relations by vertical and horizontal lines
32601 \begin_inset Formula
32603 \begin{CD}A@>>>B@>>>C\\
32614 \begin_layout Standard
32615 To get them, the command
32620 \begin_inset Index idx
32623 \begin_layout Plain Layout
32633 is inserted to a formula.
32634 A blue box appears with two dashed lines where further commands can be
32639 arg "newline-insert newline"
32642 a new line is created.
32643 Horizontal relations are inserted in odd, vertical in even formula lines.
32646 \begin_layout Standard
32647 To create the relations there are the following commands:
32650 \begin_layout Itemize
32655 creates a left arrow,
32666 \begin_layout Itemize
32671 creates an up arrow,
32679 a vertical equal sign
32682 \begin_layout Itemize
32688 is a placeholder for non-existent relations
32691 \begin_layout Standard
32692 All arrows can be labeled as follows:
32695 \begin_layout Itemize
32696 If text inserted between the first and second < or >, resp., it is placed
32698 When it is inserted between the second and third one, it appears under
32702 \begin_layout Itemize
32703 When text for vertical arrows is inserted between the first and second A
32704 or V, resp., it is placed left beside the arrow.
32705 When it is inserted between the second and third one, it appears right
32707 If the text contains an A or V, these letters must be set into a TeX-brace.
32710 \begin_layout Standard
32711 As example a diagram with all possible relations:
32714 \begin_layout Standard
32715 \begin_inset Formula
32717 \begin{CD}A@>j>>B@>>k>C@=F\\
32728 \begin_layout Standard
32729 The command for this is:
32730 \begin_inset Newline newline
32738 \begin_inset space \textvisiblespace{}
32741 A@>j>>B@>>k>C@=F Ctrl+Return
32742 \begin_inset Newline newline
32746 \begin_inset Phantom HPhantom
32749 \begin_layout Plain Layout
32755 \begin_inset space \textvisiblespace{}
32768 \begin_inset Formula $\to$
32774 \begin_inset Newline newline
32778 \begin_inset Phantom HPhantom
32781 \begin_layout Plain Layout
32787 \begin_inset space \textvisiblespace{}
32798 \begin_layout Subsection
32800 \begin_inset Index idx
32803 \begin_layout Plain Layout
32804 Diagrams ! xymatrix
32812 \begin_layout Standard
32813 To be able to use xymatrices, the LaTeX-package
32818 A xymatrix is created by inserting the command
32825 Then you are able to add new matrix columns and rows like for normal matrices,
32827 \begin_inset CommandInset ref
32829 reference "sec:Matrices"
32836 \begin_layout Standard
32837 In contrary to amscd diagrams, xymatrices supports diagonal and curved arrows,
32839 All possibilities to create commutative diagrams and decorations are explained
32844 that you find in the menu
32846 Help\SpecialChar \menuseparator
32848 \begin_inset space ~
32856 \begin_layout Subsection
32862 \begin_inset Index idx
32865 \begin_layout Plain Layout
32874 \begin_layout Standard
32879 -diagrams, the LaTeX-package
32888 -diagram is created by inserting the command
32895 Then you are able to add new matrix columns and rows like for normal matrices,
32897 \begin_inset CommandInset ref
32899 reference "sec:Matrices"
32906 \begin_layout Standard
32907 Examples how to create
32911 diagrams in LyX is given in the
32913 Feynman-diagram manual
32915 that you find in the menu
32917 Help\SpecialChar \menuseparator
32919 \begin_inset space ~
32927 \begin_layout Standard
32928 \begin_inset Newpage newpage
32934 \begin_layout Section
32935 User-defined Commands
32936 \begin_inset Index idx
32939 \begin_layout Plain Layout
32940 User-defined commands
32948 \begin_layout Standard
32949 \begin_inset Note Greyedout
32952 \begin_layout Plain Layout
32957 The names of user-defined commands and macros may only consist of Latin
32966 \begin_layout Subsection
32970 \begin_inset CommandInset label
32972 name "sub:The-Command-newcommand"
32977 \begin_inset Index idx
32980 \begin_layout Plain Layout
32981 User-defined commands !
32989 \begin_inset Index idx
32992 \begin_layout Plain Layout
33003 \begin_layout Standard
33004 Many LaTeX-commands are too long to be used frequently.
33005 But it is possible to define with the command
33011 new shorter commands.
33014 \begin_layout Standard
33015 The command scheme of
33024 \begin_layout Standard
33029 newcommand{new command name}[number of arguments][optional
33034 \begin_inset Newline newline
33038 \begin_inset Phantom HPhantom
33041 \begin_layout Plain Layout
33051 {command definition}
33054 \begin_layout Standard
33055 \begin_inset Note Greyedout
33058 \begin_layout Plain Layout
33063 Assure that the name of the new command is not already used in your document
33064 or by LaTeX-packages that you use.
33065 When you for example define the command
33077 , you get an error message because
33083 is already defined as command for
33084 \begin_inset Quotes eld
33088 \begin_inset Formula $\le$
33092 \begin_inset Quotes erd
33103 \begin_layout Standard
33104 The number of arguments is an integer in the range 0
33105 \begin_inset space \thinspace{}
33109 \begin_inset space \thinspace{}
33112 9 and specifies how many arguments the new command should have.
33113 With the optional value a value for an optional argument can be predefined.
33114 When this is done, the
33122 rgument of the new command is automatically an optional one.
33125 \begin_layout Standard
33126 Here are some examples:
33129 \begin_layout Itemize
33130 To define the command
33142 , the LaTeX-preamble line is:
33143 \begin_inset VSpace medskip
33147 \begin_inset Newline newline
33161 \begin_layout Itemize
33162 To define the command
33174 , the argument (that should be underlined) must be taken into account.
33175 For this the preamble line is:
33176 \begin_inset VSpace medskip
33180 \begin_inset Newline newline
33194 \begin_inset VSpace medskip
33198 \begin_inset Newline newline
33205 acts as argument placeholder, the
33209 behind it denotes that it is the placeholder for the first argument.
33212 \begin_layout Itemize
33220 \begin_inset space \thinspace{}
33224 \begin_inset space \space{}
33234 \begin_inset VSpace medskip
33238 \begin_inset Newline newline
33249 framebox#1#2{$#3$}}
33252 \begin_inset VSpace medskip
33256 \begin_inset Newline newline
33259 The two Dollar signs creates the extra formula needed for
33266 \begin_inset CommandInset ref
33268 reference "sub:Boxes-with-Frame"
33275 \begin_layout Itemize
33276 To create a new command for
33282 where the color for the box need not be specified, the argument for the
33283 color is defined optional:
33284 \begin_inset VSpace medskip
33288 \begin_inset Newline newline
33299 fcolorbox{#2}{#1}{$#3$}}
33302 \begin_inset VSpace medskip
33306 \begin_inset Newline newline
33309 When the color is not specified when using
33315 , the predefined color
33322 \begin_layout Standard
33323 A test of the new defined commands:
33326 \begin_layout Standard
33328 \begin_inset Tabular
33329 <lyxtabular version="3" rows="6" columns="2">
33330 <features rotate="0" tabularvalignment="middle">
33331 <column alignment="center" valignment="top">
33332 <column alignment="center" valignment="top">
33334 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
33337 \begin_layout Plain Layout
33343 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
33346 \begin_layout Plain Layout
33348 \begin_inset Note Note
33351 \begin_layout Plain Layout
33358 is only used as spacer.
33370 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
33373 \begin_layout Plain Layout
33377 \begin_inset space \textvisiblespace{}
33385 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
33388 \begin_layout Plain Layout
33389 \begin_inset Formula $A\gr B$
33399 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
33402 \begin_layout Plain Layout
33410 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
33413 \begin_layout Plain Layout
33414 \begin_inset Formula $\raisebox{4.5mm}{}\us{ABcd}\raisebox{-2mm}{}$
33424 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
33427 \begin_layout Plain Layout
33431 \begin_inset Formula $\to$
33437 \begin_inset Formula $\to$
33445 \begin_inset space \textvisiblespace{}
33453 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
33456 \begin_layout Plain Layout
33457 \begin_inset Formula $\raisebox{6mm}{}\fb{[2cm]}{}{\int A=B}\raisebox{-4mm}{}$
33467 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
33470 \begin_layout Plain Layout
33474 \begin_inset Formula $\to$
33482 \begin_inset space \textvisiblespace{}
33490 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
33493 \begin_layout Plain Layout
33494 \begin_inset Formula $\raisebox{6mm}{}\cb{red}{\int A=B}\raisebox{-4mm}{}$
33504 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
33507 \begin_layout Plain Layout
33513 \begin_inset Formula $\to$
33521 \begin_inset space \textvisiblespace{}
33529 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
33532 \begin_layout Plain Layout
33533 \begin_inset Formula $\raisebox{6mm}{}\cb[green]{red}{\int A=B}\raisebox{-4mm}{}$
33549 \begin_layout Subsection
33551 \begin_inset Index idx
33554 \begin_layout Plain Layout
33555 User-defined commands! Math macros
33561 \begin_inset Index idx
33564 \begin_layout Plain Layout
33573 \begin_layout Standard
33574 User-defined commands are especially convenient for complex expressions.
33575 When you are for example dealing with a document that has quadratic equations,
33576 the same solution type occurs several times.
33577 The general form of a quadratic equation is
33578 \begin_inset Formula
33580 0=\lambda^{2}+p\lambda+q
33585 The general form of the solution is
33586 \begin_inset Formula
33588 \lambda_{1,2}=-\frac{p}{2}\pm\sqrt{\frac{p²}{4}-q}
33596 \begin_layout Standard
33597 To define a command for the solution formula where only the three parameters
33599 \begin_inset Formula $\lambda$
33603 \begin_inset Formula $p$
33607 \begin_inset Formula $q$
33610 need to be specified and the index of
33611 \begin_inset Formula $\lambda$
33614 can be given optionally, the LaTeX-preamble line is
33615 \begin_inset Newline newline
33631 \begin_inset Newline newline
33635 \begin_inset Phantom HPhantom
33638 \begin_layout Plain Layout
33652 frac{#3^{2}}{4}-#4}}
33655 \begin_layout Standard
33656 To create with this the solution formula, the command
33657 \begin_inset Newline newline
33667 \begin_inset Formula $\to$
33673 \begin_inset Formula $\to$
33680 is inserted to a formula
33685 \begin_layout Standard
33686 The definition of the new command is unintuitive because one has to know
33687 the schemes of all used LaTeX commands, e.
33688 \begin_inset space \thinspace{}
33692 \begin_inset space \space{}
33695 that a fraction is inserted in LaTeX as
33699 frac{numerator}{denominator}
33702 Furthermore one can easily forget a brace in the definition and cannot
33703 see in LyX what the new command is doing.
33704 To avoid these problems LyX offers the possibility to use math macros instead
33714 \begin_layout Standard
33715 A math macro is created by using the menu
33717 Insert\SpecialChar \menuseparator
33718 Math\SpecialChar \menuseparator
33721 or the toolbar button
33724 arg "math-macro newmacroname_newcommand"
33728 The math macro toolbar appears together with the following box where the
33730 \begin_inset Newline newline
33734 \begin_inset space \hspace*{\fill}
33738 \begin_inset Graphics
33739 filename clipart/macrobox.png
33744 \begin_inset space \hspace*{\fill}
33748 \begin_inset Newline newline
33752 \begin_inset FormulaMacro
33753 \newcommand{\qG}[4][1,\,2]{#2_{#1}=-\frac{#3}{2}\pm\sqrt{\frac{#3^{2}}{4}-#4}}
33758 newmacroname is the default name of the macro that should be changed to
33759 something sensible.
33760 The wanted formula is inserted in the first blue box.
33761 An argument placeholder is inserted with the command
33768 \begin_inset space \thinspace{}
33772 \begin_inset space \space{}
33781 or by using the macro toolbar button
33784 arg "math-macro-add-param"
33788 Argument placeholders are displayed red.
33790 \begin_inset space ~
33793 arguments are possible.
33794 Optional arguments are created with the toolbar button
33797 arg "math-macro-add-optional-param"
33801 The first non-optional argument can be transformed to an optional one with
33805 arg "math-macro-make-optional"
33809 In the second blue box the appearance of the macro in LyX can be defined.
33810 Normally you want to see it as it is defined, so the box is kept empty.
33811 But when you have created a macro that needs lot of space on the screen,
33812 you can insert in the box for example
33813 \begin_inset Newline newline
33843 \begin_inset Newline newline
33848 For the macro only the arguments with the macro name in front of them will
33849 then be displayed in LyX, leading to a better overview.
33850 The formula appears in the output as defined in the first box.
33851 \begin_inset Newline newline
33854 The appearance of macros in formulas can furthermore be changed for single
33855 macros by setting the cursor in the macro and using the menu
33857 View\SpecialChar \menuseparator
33859 \begin_inset space ~
33863 \begin_inset space ~
33871 \begin_layout Standard
33872 To use a macro, the macro name is inserted as command to a formula, in our
33880 Our macro looks in LyX like this:
33881 \begin_inset Newline newline
33885 \begin_inset space \hspace*{\fill}
33889 \begin_inset Graphics
33890 filename clipart/macrouse.png
33895 \begin_inset space \hspace*{\fill}
33899 \begin_inset Newline newline
33902 Here is our macro example with the arguments
33903 \begin_inset Formula $x$
33907 \begin_inset Formula $\ln(x)$
33911 \begin_inset Formula $B$
33917 \begin_layout Standard
33918 \begin_inset Formula
33928 \begin_layout Standard
33929 LyX offers in the menu
33931 Tools\SpecialChar \menuseparator
33932 Preferences\SpecialChar \menuseparator
33933 Editing\SpecialChar \menuseparator
33936 different styles to edit macros.
33937 To find the style that suits you the most, choose a style and set the cursor
33938 in a macro formula to see the difference.
33941 \begin_layout Standard
33942 A math macro is transformed internally to a
33948 command when exporting the document.
33955 command is not placed in the LaTeX-preamble, therefore macros can only
33956 be used in formulas that are in the document below the macro definition
33960 \begin_layout Standard
33961 Math macros can also be directly created from a
33968 When writing for example the command
33971 \begin_inset Newline newline
33980 xleftarrow[#2]{#1}}
33981 \begin_inset Newline newline
33986 in LyX as normal text, highlighting it completely and using then the shortcut
33991 , the command will be transformed to a math macro.
33992 Using this method you need to be careful that the
33998 command is typed correctly, otherwise you get a faulty macro leading to
34002 \begin_layout Standard
34003 Math macros currently have the problem that further formulas in macro definition
34004 s are handled wrongly.
34005 Therefore the example
34012 \begin_inset CommandInset ref
34014 reference "sub:The-Command-newcommand"
34018 cannot be created as macro.
34021 \begin_layout Standard
34022 When the cursor is in a macro definition box, you will see the macro toolbar
34026 \begin_layout Standard
34027 \begin_inset VSpace defskip
34033 \begin_layout Standard
34034 \begin_inset Graphics
34035 filename clipart/MacroToolbar.png
34040 \begin_inset Index idx
34043 \begin_layout Plain Layout
34052 \begin_layout Standard
34053 \begin_inset VSpace defskip
34059 \begin_layout Standard
34060 The macro toolbar contains from left to right the following buttons:
34063 \begin_layout Standard
34064 \begin_inset VSpace defskip
34070 \begin_layout Standard
34071 \begin_inset Tabular
34072 <lyxtabular version="3" rows="9" columns="2">
34073 <features rotate="0" islongtable="true" longtabularalignment="center">
34074 <column alignment="left" valignment="top">
34075 <column alignment="left" valignment="top" width="85col%">
34076 <row interlinespace="2.5mm">
34077 <cell alignment="center" valignment="top" usebox="none">
34080 \begin_layout Plain Layout
34083 arg "math-macro-remove-param"
34091 <cell alignment="center" valignment="top" usebox="none">
34094 \begin_layout Plain Layout
34097 Edit\SpecialChar \menuseparator
34098 Math\SpecialChar \menuseparator
34100 \begin_inset space ~
34103 Definition\SpecialChar \menuseparator
34104 Remove Last Argument
34110 <row interlinespace="2.5mm">
34111 <cell alignment="center" valignment="top" usebox="none">
34114 \begin_layout Plain Layout
34117 arg "math-macro-add-param"
34125 <cell alignment="center" valignment="top" usebox="none">
34128 \begin_layout Plain Layout
34131 Edit\SpecialChar \menuseparator
34132 Math\SpecialChar \menuseparator
34134 \begin_inset space ~
34137 Definition\SpecialChar \menuseparator
34144 <row interlinespace="2.5mm">
34145 <cell alignment="center" valignment="top" usebox="none">
34148 \begin_layout Plain Layout
34151 arg "math-macro-make-optional"
34159 <cell alignment="center" valignment="top" usebox="none">
34162 \begin_layout Plain Layout
34165 Edit\SpecialChar \menuseparator
34166 Math\SpecialChar \menuseparator
34168 \begin_inset space ~
34171 Definition\SpecialChar \menuseparator
34172 Transform First Non-Optional to
34173 \begin_inset Newline newline
34177 \begin_inset Phantom HPhantom
34180 \begin_layout Plain Layout
34183 Edit\SpecialChar \menuseparator
34184 Math\SpecialChar \menuseparator
34186 \begin_inset space ~
34189 Definition\SpecialChar \menuseparator
34201 <row interlinespace="2.5mm">
34202 <cell alignment="center" valignment="top" usebox="none">
34205 \begin_layout Plain Layout
34208 arg "math-macro-make-nonoptional"
34216 <cell alignment="center" valignment="top" usebox="none">
34219 \begin_layout Plain Layout
34222 Edit\SpecialChar \menuseparator
34223 Math\SpecialChar \menuseparator
34225 \begin_inset space ~
34228 Definition\SpecialChar \menuseparator
34229 Transform Last Optional to
34230 \begin_inset Newline newline
34234 \begin_inset Phantom HPhantom
34237 \begin_layout Plain Layout
34240 Edit\SpecialChar \menuseparator
34241 Math\SpecialChar \menuseparator
34243 \begin_inset space ~
34246 Definition\SpecialChar \menuseparator
34252 Non-Optional Argument
34258 <row interlinespace="2.5mm">
34259 <cell alignment="center" valignment="top" usebox="none">
34262 \begin_layout Plain Layout
34265 arg "math-macro-remove-optional-param"
34273 <cell alignment="center" valignment="top" usebox="none">
34276 \begin_layout Plain Layout
34279 Edit\SpecialChar \menuseparator
34280 Math\SpecialChar \menuseparator
34282 \begin_inset space ~
34285 Definition\SpecialChar \menuseparator
34286 Remove Optional Argument
34292 <row interlinespace="2.5mm">
34293 <cell alignment="center" valignment="top" usebox="none">
34296 \begin_layout Plain Layout
34299 arg "math-macro-add-optional-param"
34307 <cell alignment="center" valignment="top" usebox="none">
34310 \begin_layout Plain Layout
34313 Edit\SpecialChar \menuseparator
34314 Math\SpecialChar \menuseparator
34316 \begin_inset space ~
34319 Definition\SpecialChar \menuseparator
34320 Insert Optional Argument
34326 <row interlinespace="2.5mm">
34327 <cell alignment="center" valignment="top" usebox="none">
34330 \begin_layout Plain Layout
34333 arg "math-macro-remove-greedy-param"
34341 <cell alignment="center" valignment="top" usebox="none">
34344 \begin_layout Plain Layout
34347 Edit\SpecialChar \menuseparator
34348 Math\SpecialChar \menuseparator
34350 \begin_inset space ~
34353 Definition\SpecialChar \menuseparator
34354 Remove Last Argument
34355 \begin_inset Newline newline
34359 \begin_inset Phantom HPhantom
34362 \begin_layout Plain Layout
34365 Edit\SpecialChar \menuseparator
34366 Math\SpecialChar \menuseparator
34368 \begin_inset space ~
34371 Definition\SpecialChar \menuseparator
34377 Spitting Out To The Right
34383 <row interlinespace="2.5mm">
34384 <cell alignment="center" valignment="top" usebox="none">
34387 \begin_layout Plain Layout
34390 arg "math-macro-append-greedy-param"
34398 <cell alignment="center" valignment="top" usebox="none">
34401 \begin_layout Plain Layout
34404 Edit\SpecialChar \menuseparator
34405 Math\SpecialChar \menuseparator
34407 \begin_inset space ~
34410 Definition\SpecialChar \menuseparator
34412 \begin_inset Newline newline
34416 \begin_inset Phantom HPhantom
34419 \begin_layout Plain Layout
34422 Edit\SpecialChar \menuseparator
34423 Math\SpecialChar \menuseparator
34425 \begin_inset space ~
34428 Definition\SpecialChar \menuseparator
34434 Eating From The Right
34440 <row interlinespace="2.5mm">
34441 <cell alignment="center" valignment="top" usebox="none">
34444 \begin_layout Plain Layout
34447 arg "math-macro-add-greedy-optional-param"
34455 <cell alignment="center" valignment="top" usebox="none">
34458 \begin_layout Plain Layout
34461 Edit\SpecialChar \menuseparator
34462 Math\SpecialChar \menuseparator
34464 \begin_inset space ~
34467 Definition\SpecialChar \menuseparator
34468 Append Optional Argument
34469 \begin_inset Newline newline
34473 \begin_inset Phantom HPhantom
34476 \begin_layout Plain Layout
34479 Edit\SpecialChar \menuseparator
34480 Math\SpecialChar \menuseparator
34482 \begin_inset space ~
34485 Definition\SpecialChar \menuseparator
34491 Eating From The Right
34504 \begin_layout Section
34505 Computer Algebra Systems
34508 \begin_layout Standard
34509 LyX offers the exchange between mathematical expressions written in LyX's
34510 math editor and external applications or user defined scripts.
34511 Currently supported applications are
34528 Note that the set of supported mathematical constructs is limited only
34529 to very simple cases.
34532 \begin_layout Subsection
34536 \begin_layout Standard
34537 Write some expression in a formula, go to the
34539 Edit\SpecialChar \menuseparator
34540 Math\SpecialChar \menuseparator
34541 Use Computer Algebra System
34543 menu and choose the application you have installed on the computer.
34544 After that the result of computation should show on the right side of the
34545 expression together with the
34546 \begin_inset Quotes eld
34550 \begin_inset Quotes erd
34556 \begin_layout Standard
34557 Here are few simple examples (with results from
34561 ) to show what kind of computations can be performed:
34564 \begin_layout Itemize
34565 \begin_inset Formula $\frac{37}{3}*2-\sum_{i=1}^{3}i^{i}=-\frac{22}{3}$
34571 \begin_layout Itemize
34572 \begin_inset Formula $\frac{37.0}{3}=12.33333333333333$
34578 \begin_layout Itemize
34579 \begin_inset Formula $\int_{1}^{2}\sin(x)dx=\cos1-\cos2$
34585 \begin_layout Itemize
34586 \begin_inset Formula $\det\left[\begin{array}{ccc}
34590 \end{array}\right]=-56$
34596 \begin_layout Itemize
34597 \begin_inset Formula $\lim_{x\rightarrow0}\left(\frac{\sin(x)}{x}\right)=1$
34603 \begin_layout Subsection
34607 \begin_layout Standard
34608 Currently there is no keyboard shortcut for calling the algebra applications.
34609 One can easily bind a shortcut to the
34613 LyX function (see the
34621 \begin_inset space \thinspace{}
34625 \begin_inset space \space{}
34632 key inside the math editor.
34637 one would use this shortcut definition command:
34640 \begin_layout Standard
34643 command-alternatives break-paragraph;math-extern maxima
34646 \begin_layout Section
34648 \begin_inset Index idx
34651 \begin_layout Plain Layout
34660 \begin_layout Subsection
34662 \begin_inset Index idx
34665 \begin_layout Plain Layout
34674 \begin_layout Standard
34675 Negative numbers often look ugly in formulas because the minus sign before
34676 the number is set with the same length as the minus operator sign.
34677 When writing the negative number in normal text, the minus sign appears
34681 \begin_layout Standard
34682 Thus, the problem disappears when converting the minus sign to mathematical
34686 \begin_layout Standard
34687 An example to visualize the problem:
34690 \begin_layout Standard
34692 \begin_inset Tabular
34693 <lyxtabular version="3" rows="3" columns="2">
34694 <features rotate="0" tabularvalignment="middle">
34695 <column alignment="right" valignment="top">
34696 <column alignment="left" valignment="top">
34698 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
34701 \begin_layout Plain Layout
34707 <cell alignment="center" valignment="top" topline="true" rightline="true" usebox="none">
34710 \begin_layout Plain Layout
34718 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
34721 \begin_layout Plain Layout
34727 <cell alignment="center" valignment="top" topline="true" bottomline="true" rightline="true" usebox="none">
34730 \begin_layout Plain Layout
34731 \begin_inset Formula $x=-2$
34741 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
34744 \begin_layout Plain Layout
34750 <cell alignment="center" valignment="top" topline="true" bottomline="true" rightline="true" usebox="none">
34753 \begin_layout Plain Layout
34754 \begin_inset Formula $x=\textrm{-}2$
34770 \begin_layout Subsection
34771 Comma as decimal Separator
34772 \begin_inset Index idx
34775 \begin_layout Plain Layout
34784 \begin_layout Standard
34785 In LaTeX a comma inside a formula is used, according to the English convention,
34786 as number group separator.
34787 So there will be space added behind all commas in formulas.
34790 \begin_layout Standard
34791 To avoid this, the comma is highlighted and changed to mathematical text
34801 \begin_layout Standard
34802 To use all formula commas in the document as decimal separator, the file
34811 \begin_layout Plain Layout
34816 is part of the LaTeX-package
34821 \begin_inset Index idx
34824 \begin_layout Plain Layout
34829 \begin_layout Plain Layout
34849 \begin_inset Index idx
34852 \begin_layout Plain Layout
34858 is loaded with the LaTeX-preamble line
34861 \begin_layout Standard
34869 \begin_layout Subsection
34871 \begin_inset CommandInset label
34873 name "sub:Physical-Vectors"
34878 \begin_inset Index idx
34881 \begin_layout Plain Layout
34890 \begin_layout Standard
34891 Predefined vectors are offered by the LaTeX-package
34896 \begin_inset Index idx
34899 \begin_layout Plain Layout
34905 that is loaded with the LaTeX-preamble line
34908 \begin_layout Standard
34916 \begin_layout Standard
34920 \begin_layout Plain Layout
34930 \begin_inset Note Note
34933 \begin_layout Plain Layout
34934 The following table will only be displayed when the LaTeX-package
34946 \begin_layout Standard
34947 The following commands are defined:
34950 \begin_layout Standard
34952 \begin_inset Tabular
34953 <lyxtabular version="3" rows="4" columns="2">
34954 <features rotate="0" tabularvalignment="middle">
34955 <column alignment="center" valignment="top">
34956 <column alignment="center" valignment="top">
34958 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
34961 \begin_layout Plain Layout
34967 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
34970 \begin_layout Plain Layout
34978 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
34981 \begin_layout Plain Layout
34991 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
34994 \begin_layout Plain Layout
34995 \begin_inset Formula $\Bra{\psi}$
35005 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
35008 \begin_layout Plain Layout
35018 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
35021 \begin_layout Plain Layout
35022 \begin_inset Formula $\Ket{\psi}$
35032 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
35035 \begin_layout Plain Layout
35047 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
35050 \begin_layout Plain Layout
35051 \begin_inset Formula $\Braket{\psi|\phi}$
35067 \begin_layout Standard
35074 assures that all vertical bars are set in the size of the surrounding brackets:
35075 \begin_inset Formula
35077 \Braket{\phi|J=\frac{3}{2}\,,\, M_{J}}
35086 \begin_layout Plain Layout
35096 \begin_inset Note Note
35099 \begin_layout Plain Layout
35100 The following will be displayed when the LaTeX-package
35112 \begin_layout Standard
35113 You need to install the LaTeX-package
35117 to see the rest of this subsection in the output.
35120 \begin_layout Standard
35124 \begin_layout Plain Layout
35136 \begin_layout Standard
35143 can also be achieved using the command
35149 , that is described in
35150 \begin_inset CommandInset ref
35152 reference "sub:Automatic-Bracket-Size"
35159 \begin_layout Subsection
35160 Self-defined Fractions
35161 \begin_inset CommandInset label
35163 name "sub:Self-defined-Fractions"
35168 \begin_inset Index idx
35171 \begin_layout Plain Layout
35172 Fractions ! self-defined
35180 \begin_layout Standard
35181 To define custom commands for fractions, the command
35188 \begin_inset Index idx
35191 \begin_layout Plain Layout
35198 \begin_layout Plain Layout
35212 is used in the following scheme:
35215 \begin_layout Standard
35228 bracket}{fraction bar thickness}{style}
35229 \begin_inset Newline newline
35233 \begin_inset Phantom HPhantom
35236 \begin_layout Plain Layout
35246 {numerator}{denominator}
35249 \begin_layout Standard
35250 The style is a number in the range of 0
35251 \begin_inset space \thinspace{}
35255 \begin_inset space \thinspace{}
35261 \begin_layout Standard
35263 \begin_inset Tabular
35264 <lyxtabular version="3" rows="5" columns="2">
35265 <features rotate="0" tabularvalignment="middle">
35266 <column alignment="center" valignment="top">
35267 <column alignment="center" valignment="top">
35269 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
35272 \begin_layout Plain Layout
35278 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
35281 \begin_layout Plain Layout
35289 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
35292 \begin_layout Plain Layout
35298 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
35301 \begin_layout Plain Layout
35302 display style formula
35309 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
35312 \begin_layout Plain Layout
35318 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
35321 \begin_layout Plain Layout
35329 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
35332 \begin_layout Plain Layout
35338 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
35341 \begin_layout Plain Layout
35349 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
35352 \begin_layout Plain Layout
35358 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
35361 \begin_layout Plain Layout
35375 \begin_layout Standard
35376 When no style is given, the size is adjusted to the surrounding environment
35377 like for the command
35386 \begin_layout Standard
35387 When no fraction bar thickness is given, the predefined value of 0.4
35388 \begin_inset space \thinspace{}
35394 \begin_layout Standard
35395 \begin_inset VSpace medskip
35398 For example, the commands
35411 \begin_inset CommandInset ref
35413 reference "sub:Fractions"
35417 are defined with the commands
35420 \begin_layout Standard
35429 genfrac{}{}{}{0}{#1}{#2}}
35432 \begin_layout Standard
35436 \begin_layout Standard
35445 genfrac{(}{)}{0pt}{1}{#1}{#2}}
35448 \begin_layout Standard
35449 \begin_inset VSpace medskip
35452 To define a fraction where the fraction bar thickness can be given as optional
35453 argument, the following line is inserted to the LaTeX-preamble:
35456 \begin_layout Standard
35465 genfrac{}{}{#1}{}{#2}{#3}}
35468 \begin_layout Standard
35470 \begin_inset Formula
35472 \text{Command} & & \mathrm{\backslash fracS[1mm]\backslash\{A\to\backslash\{B} & & \mathrm{\backslash fracS[5mm]\backslash\{A\to\backslash\{B}\\
35473 \text{Result} & & \fracS[1mm]{A}{B} & & \fracS[5mm]{A}{B}
35478 As one can see, the distance of the numerator and the denominator to the
35479 fraction bar is round about three times the bar thickness.
35482 \begin_layout Subsection
35484 \begin_inset Index idx
35487 \begin_layout Plain Layout
35496 \begin_layout Standard
35497 There are four ways to cancel formulas or parts of formulas:
35500 \begin_layout Standard
35504 \begin_layout Plain Layout
35514 \begin_inset Note Note
35517 \begin_layout Plain Layout
35518 The following table will only be displayed when the LaTeX-package
35530 \begin_layout Standard
35532 \begin_inset Tabular
35533 <lyxtabular version="3" rows="5" columns="2">
35534 <features rotate="0" tabularvalignment="middle">
35535 <column alignment="center" valignment="top">
35536 <column alignment="center" valignment="top">
35538 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
35541 \begin_layout Plain Layout
35547 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
35550 \begin_layout Plain Layout
35552 \begin_inset Note Note
35555 \begin_layout Plain Layout
35562 are used here as spacer.
35574 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
35577 \begin_layout Plain Layout
35581 \begin_inset space \textvisiblespace{}
35587 \begin_inset space \textvisiblespace{}
35595 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
35598 \begin_layout Plain Layout
35599 \begin_inset Formula $\raisebox{4.5mm}{}\cancel{\int A=B}\raisebox{-2.5mm}{}$
35609 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
35612 \begin_layout Plain Layout
35616 \begin_inset space \textvisiblespace{}
35622 \begin_inset space \textvisiblespace{}
35630 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
35633 \begin_layout Plain Layout
35634 \begin_inset Formula $\raisebox{4.5mm}{}\bcancel{\int A=B}\raisebox{-2.5mm}{}$
35644 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
35647 \begin_layout Plain Layout
35651 \begin_inset space \textvisiblespace{}
35657 \begin_inset space \textvisiblespace{}
35665 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
35668 \begin_layout Plain Layout
35669 \begin_inset Formula $\raisebox{4.5mm}{}\xcancel{\int A=B}\raisebox{-2.5mm}{}$
35679 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
35682 \begin_layout Plain Layout
35686 \begin_inset space \textvisiblespace{}
35692 \begin_inset space \textvisiblespace{}
35696 \begin_inset Formula $\to$
35704 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
35707 \begin_layout Plain Layout
35708 \begin_inset Formula $\raisebox{7mm}{}\cancelto{1}{\int A=B}\raisebox{-2.5mm}{}\hspace{3mm}$
35724 \begin_layout Standard
35731 is especially suitable to visualize the reduction of fractions within formulas:
35732 \begin_inset Formula
35734 \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}}}
35742 \begin_layout Standard
35743 To change the size of
35750 \begin_inset Quotes eld
35754 \begin_inset Quotes erd
35757 value one can add the LaTeX-preamble line
35760 \begin_layout Standard
35765 PassOptionsToPackage{option}{cancel}
35768 \begin_layout Standard
35777 which leads to the same size as for the canceled value, or
35781 which makes is it a bit smaller than normal.
35784 \begin_layout Standard
35785 To color the cancellation bar one adds this command as TeX code:
35788 \begin_layout Standard
35800 \begin_layout Standard
35805 can be replaced by a color of your choice.
35808 \begin_layout Standard
35812 \begin_layout Plain Layout
35828 \begin_layout Standard
35829 \begin_inset Formula
35831 \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}}}
35839 \begin_layout Standard
35843 \begin_layout Plain Layout
35857 \begin_inset Note Note
35860 \begin_layout Plain Layout
35869 \begin_layout Standard
35870 For further customizations, see the documentation of the package
35875 \begin_inset CommandInset citation
35882 \begin_inset Index idx
35885 \begin_layout Plain Layout
35894 \begin_layout Standard
35898 \begin_layout Plain Layout
35908 \begin_inset Note Note
35911 \begin_layout Plain Layout
35912 The following will be displayed when the LaTeX-package
35924 \begin_layout Standard
35925 You need to install the LaTeX-package
35929 to see the rest of this subsection in the output.
35932 \begin_layout Standard
35936 \begin_layout Plain Layout
35948 \begin_layout Standard
35949 \begin_inset Newpage newpage
35955 \begin_layout Subsection
35956 Formulas in Section Headings
35957 \begin_inset CommandInset label
35959 name "sub:Formulas-in-Section"
35964 \begin_inset Index idx
35967 \begin_layout Plain Layout
35968 Formula ! in section headings
35976 \begin_layout Standard
35977 When formulas are used in section headings, the following has to be taken
35981 \begin_layout Standard
35982 \begin_inset Note Greyedout
35985 \begin_layout Plain Layout
35991 \begin_inset Index idx
35994 \begin_layout Plain Layout
35995 Packages ! hyperref
36000 support is enabled in the document settings dialog under
36003 \begin_inset space ~
36008 , PDF-bookmarks are created for every section heading in the table of contents.
36009 If a section heading contains formulas, they are incorrectly displayed
36010 in the bookmark text, because formulas in bookmarks infringe the PDF convention
36019 \begin_layout Standard
36020 Both problems can be solved by inserting at the end of the section heading
36021 a short title with the menu
36023 Insert\SpecialChar \menuseparator
36025 \begin_inset space ~
36031 Short titles are used as alternative for multiline section headings to
36032 keep the table of contents clearly arranged.
36033 Only the short title appears in the table of contents and therefore also
36034 in the PDF-bookmark.
36037 \begin_layout Standard
36038 When formulas should be used in the table of contents but
36042 is used, one can use the following command in TeX-mode:
36045 \begin_layout Standard
36050 texorpdfstring{part}{alternative}
36051 \begin_inset Index idx
36054 \begin_layout Plain Layout
36065 \begin_layout Standard
36066 Part is the part of the heading that shouldn't appear in the PDF-bookmark.
36067 This can be characters, formulas, footnotes, but also cross-references.
36068 The alternative is used instead of the part for the bookmark.
36071 \begin_layout Standard
36072 Here are two example headings:
36073 \begin_inset VSpace -3mm
36080 \begin_layout Plain Layout
36092 \begin_layout Subsubsection
36093 Heading without formula in table of contents
36094 \begin_inset Formula $\sqrt{-1}=\mathrm{i}$
36098 \begin_inset Argument 1
36101 \begin_layout Plain Layout
36102 Heading without formula in table of contents
36110 \begin_layout Subsubsection
36111 Heading with formula in table of contents
36115 \begin_layout Plain Layout
36125 \begin_inset Formula $\sqrt{-1}=\mathrm{i}$
36132 \begin_layout Plain Layout
36142 \begin_layout Standard
36146 \begin_layout Plain Layout
36155 In the first heading a short title was used, in the second one
36164 \begin_layout Standard
36165 To get the same formatting as for the other headings, the complete heading
36174 \begin_layout Plain Layout
36176 \begin_inset CommandInset ref
36178 reference "sub:Bold-Formulas"
36190 \begin_layout Subsection
36191 Formulas in multi-column Text
36192 \begin_inset Index idx
36195 \begin_layout Plain Layout
36196 Formula ! in multi-column text
36204 \begin_layout Standard
36205 Formulas in multi-column text are often too wide to fit into a column and
36206 thus need to be set over the whole page width.
36207 This is done by using the LaTeX-package
36215 \begin_layout Plain Layout
36220 is part of every LaTeX standard installation.
36226 \begin_inset Index idx
36229 \begin_layout Plain Layout
36230 Packages ! multicol
36235 , that is loaded with the LaTeX-preamble line
36238 \begin_layout Standard
36243 usepackage{multicol}
36246 \begin_layout Standard
36247 \begin_inset Note Greyedout
36250 \begin_layout Plain Layout
36251 Note that in this case the setting
36254 \begin_inset space ~
36261 Document\SpecialChar \menuseparator
36267 \begin_inset space ~
36287 \begin_layout Standard
36288 Before the multi-column text the command
36291 \begin_layout Standard
36296 begin{multicols}{column number}
36299 \begin_layout Standard
36300 is written in TeX-mode.
36301 The column number is a number in the range of 2
36302 \begin_inset space \thinspace{}
36306 \begin_inset space \thinspace{}
36310 Before the formula the multi-column text is ended by inserting the command
36313 \begin_layout Standard
36321 \begin_layout Standard
36325 \begin_layout Standard
36326 Due to the command some space is automatically added before the formula.
36328 \begin_inset space \thinspace{}
36331 mm vertical space is inserted before the formula.
36332 When the formula style
36338 \begin_layout Plain Layout
36340 \begin_inset CommandInset ref
36342 reference "sec:Formula-Styles"
36354 \begin_inset space \thinspace{}
36357 mm space is inserted instead.
36360 \begin_layout Standard
36361 As example a multi-column text with a displayed formula:
36364 \begin_layout Standard
36370 \begin_layout Plain Layout
36374 begin{multicols}{2}
36379 Das Spektrum wird fouriertransformiert.
36380 Die Fouriertransformation wird verwendet, um die überlagerten Signale (Netzwerk
36381 , Lösungsmittel) zu trennen.
36382 Nachdem wir die Phasenverschiebung bestimmen konnten, interessiert uns
36383 nun das Aussehen des Ausgangssignals.
36384 Im Experiment haben wir es mit sehr vielen Teilchen zu tun, so dass man
36385 über alle Phasen integrieren muss.
36387 \begin_inset Formula $S$
36390 unser normiertes Ausgangssignal und
36391 \begin_inset Formula $P$
36394 die Phasenverteilungsfunktion, so ergibt sich die Beziehung
36398 \begin_layout Plain Layout
36408 \begin_inset VSpace -6mm
36412 \begin_inset Formula
36414 S(t)=S_{0}(t)\int_{-\infty}^{\infty}P(\phi,t)\mathrm{e}^{\mathrm{i}\phi}\,\mathrm{d}\phi
36423 \begin_layout Plain Layout
36427 begin{multicols}{2}
36433 \begin_inset Formula $S_{0}$
36436 das Signal ohne Gradient ist und die Normierungsbedingung
36437 \begin_inset Formula $\int_{-\infty}^{\infty}P(\phi,t)\,\mathrm{d}\phi=1$
36441 Nun dürfen wir aber nicht den Relaxationsprozess außer Acht lassen.
36443 \begin_inset Formula $\nicefrac{\pi}{2}$
36447 \begin_inset space \thinspace{}
36450 -rf-Puls beginnt sich die Magnetisierung zu entfokussieren, wodurch sich
36451 das Signal zusätzlich abschwächt.
36452 Diese Abschwächung verläuft exponentiell in Abhängigkeit der so genannten
36454 \begin_inset Formula $T_{2}$
36460 \begin_layout Standard
36466 \begin_layout Plain Layout
36478 \begin_layout Subsection
36479 Formulas with Description of Variables
36480 \begin_inset Index idx
36483 \begin_layout Plain Layout
36484 Formula ! with description of variables
36492 \begin_layout Standard
36493 To describe variables within a formula, like in formula
36494 \begin_inset CommandInset ref
36496 reference "eq:within"
36505 \begin_inset Formula $n$
36509 \begin_inset space ~
36512 matrix is used with left aligned columns for the
36513 \begin_inset Formula $n$
36520 \begin_layout Plain Layout
36522 \begin_inset CommandInset ref
36524 reference "sec:Matrices"
36533 To set the description in a smaller size, before the matrix e.
36534 \begin_inset space \thinspace{}
36538 \begin_inset space \space{}
36551 \begin_layout Plain Layout
36553 \begin_inset CommandInset ref
36555 reference "sub:Font-Sizes"
36567 \begin_layout Standard
36568 When the formula style
36574 \begin_layout Plain Layout
36576 \begin_inset CommandInset ref
36578 reference "sec:Formula-Styles"
36599 \begin_layout Plain Layout
36606 only works in formulas with the style
36611 \begin_inset CommandInset ref
36613 reference "sub:Variable-Space"
36622 is inserted before and after the matrix to have the same separation of
36623 the matrix from the equation and the side margin.
36626 \begin_layout Standard
36627 When the formula style
36631 is used, the method described in
36632 \begin_inset CommandInset ref
36634 reference "sub:Flalign-Environment"
36638 is used to indent formulas.
36640 \begin_inset CommandInset ref
36642 reference "eq:within"
36646 consists of five columns where in the first two columns contain the equation,
36647 the third the matrix and the last one an empty TeX-brace.
36648 \begin_inset Formula
36650 \hspace{30pt}F_{A} & =\rho·V·g & \footnotesize\begin{array}{ll}
36651 \rho & \textrm{density}\\
36652 V & \textrm{volume}\\
36653 g & \textrm{gravitational acceleration}
36654 \end{array} & & {}\label{eq:within}
36662 \begin_layout Subsection
36663 Upright small Greek Letters
36664 \begin_inset CommandInset label
36666 name "sub:Upright-small-Greek"
36671 \begin_inset Index idx
36674 \begin_layout Plain Layout
36675 Greek letters ! upright
36683 \begin_layout Standard
36684 Most of the math fonts only provide italic small Greek letters.
36685 But for symbols of elementary particles like pions and neutrinos, upright
36686 Greek letters are needed.
36695 \begin_layout Plain Layout
36700 is part of the LaTeX-package
36705 \begin_inset Index idx
36708 \begin_layout Plain Layout
36713 \begin_layout Plain Layout
36733 \begin_inset Index idx
36736 \begin_layout Plain Layout
36742 that is loaded with the LaTeX-preamble line
36745 \begin_layout Standard
36750 usepackage{upgreek}
36753 \begin_layout Standard
36759 \begin_layout Plain Layout
36769 \begin_inset Note Note
36772 \begin_layout Plain Layout
36773 The following table will only be displayed when the LaTeX-package
36782 They are created when the command for a small Greek letter is started with
36788 For example the command
36795 \begin_inset Formula $\uptau$
36801 \begin_layout Standard
36802 With these commands reactions of elementary particles can be typeset:
36803 \begin_inset Formula
36805 \uppi^{+}\to\upmu^{+}+\upnu_{\upmu}
36813 \begin_layout Standard
36814 The upright letters are more bold and wider than the italic ones.
36815 They should therefore not be used for units like
36816 \begin_inset Quotes eld
36820 \begin_inset Quotes erd
36826 \begin_layout Standard
36830 \begin_layout Plain Layout
36840 \begin_inset Note Note
36843 \begin_layout Plain Layout
36844 The following will be displayed when the LaTeX-package
36856 \begin_layout Standard
36857 You need to install the LaTeX-package
36861 to see the rest of this subsection in the output.
36864 \begin_layout Standard
36868 \begin_layout Plain Layout
36880 \begin_layout Subsection
36881 Text Characters in Formulas
36882 \begin_inset CommandInset label
36884 name "sub:Text-Characters-in"
36889 \begin_inset Index idx
36892 \begin_layout Plain Layout
36901 \begin_layout Standard
36902 In some cases you might want to insert text characters directly into formulas.
36903 When for example the centered dot · is often used in formulas like
36904 \begin_inset Formula $\nu=5·10^{5}\,\mathrm{Hz}$
36907 , one would have to insert the command
36917 \begin_layout Plain Layout
36919 \begin_inset CommandInset ref
36921 reference "sub:Binary-Operators"
36930 all the time, because this character is defined in all encodings as text
36932 But the encoding can be changed by this LaTeX-preamble line:
36935 \begin_layout Standard
36940 Declare Inputtext{183}{
36950 f\SpecialChar \textcompwordmark{}
36954 \begin_layout Standard
36955 The character encoding (menu
36957 Document\SpecialChar \menuseparator
36958 Settings\SpecialChar \menuseparator
36961 ) specifies what character appears when a keyboard key is pressed.
36962 When the key for the character '·' is pressed, internally the command
36969 But this command is not available in a formula so that you would get LaTeX-erro
36971 With the changed encoding the right command is chosen automatically, depending
36972 on if the character was inserted into a formula or not.
36975 \begin_layout Standard
36976 The encoding of several characters is saved in definition files.
36977 For example the encoding
36981 is defined in the file
36985 which is in the installation folder of LaTeX.
36986 Encodings should only be changed via the LaTeX-preamble and not in the
36988 Otherwise documents could not be edited by other LyX users working on other
36992 \begin_layout Standard
36993 \begin_inset VSpace medskip
36996 Besides the centered dot, in this document the degree sign ° is defined
36997 with the following LaTeX-preamble line so that it can be directly inserted
37001 \begin_layout Standard
37006 DeclareInputtext{176}{
37016 f\SpecialChar \textcompwordmark{}
37020 \begin_layout Standard
37021 \begin_inset Newpage newpage
37027 \begin_layout Section
37030 \begin_inset Index idx
37033 \begin_layout Plain Layout
37042 \begin_layout Standard
37043 This section is a summary of the most important typographic rules, listed
37048 \begin_layout Plain Layout
37049 This collection was partly taken from the German semi-official dictionary
37051 \begin_inset Quotes eld
37055 \begin_inset Quotes erd
37059 \begin_inset CommandInset citation
37065 that lists some of the ISO rules.
37066 More rules are listed in
37067 \begin_inset CommandInset citation
37081 \begin_layout Itemize
37090 \begin_layout Plain Layout
37091 done with font styles, see
37092 \begin_inset CommandInset ref
37094 reference "sub:Font-Styles"
37103 , no matter if they appear in italic text: 30
37104 \begin_inset space \thinspace{}
37108 \begin_inset Newline newline
37111 Between the value and the unit is the smallest space, see
37112 \begin_inset CommandInset ref
37114 reference "sub:Predefined-Space"
37119 \begin_inset Newline newline
37122 This convention is automatically fulfilled when the command
37129 When it is entered to a formula, two boxes appear.
37130 In the first one the value is inserted, in the second one the unit, and
37132 \begin_inset Formula $\unit[30]{km/h}$
37136 \begin_inset space \thinspace{}
37146 is not a real LaTeX command but the command
37152 , therefore you cannot use it in TeX code.
37155 \begin_layout Itemize
37156 Percent and perthousand signs are set like physical units:
37157 \begin_inset Newline newline
37161 \begin_inset space \thinspace{}
37167 \begin_layout Itemize
37168 The degree sign follows directly on the value: 15°, but not when it is used
37170 \begin_inset space \thinspace{}
37176 \begin_layout Itemize
37177 In numbers with more than four digits the smallest space is inserted before
37178 every third digit to group them:
37188 \begin_inset space \thinspace{}
37192 \begin_inset space \thinspace{}
37198 \begin_layout Itemize
37199 For dimensions like 120×90×40
37200 \begin_inset space \thinspace{}
37203 cm the multiplication sign
37204 \begin_inset Quotes eld
37208 \begin_inset Quotes erd
37212 It is available either via the command
37220 Insert\SpecialChar \menuseparator
37221 Special Character\SpecialChar \menuseparator
37227 \begin_layout Itemize
37228 Functions with names consisting of several letters are set upright to avoid
37230 \begin_inset CommandInset ref
37232 reference "sub:Predefined-Functions"
37239 \begin_layout Itemize
37240 Indices consisting of several letters, are set upright:
37241 \begin_inset Formula $E_{\mathrm{kin}}$
37245 \begin_inset Newline newline
37248 Components of matrices are set italic:
37249 \begin_inset Formula $\hat{H}_{kl}$
37255 \begin_layout Itemize
37256 The differentiation/integration operator 'd', the Euler's number 'e' and
37257 the imaginary unit 'i' should be set upright, to avoid mixing them up with
37261 \begin_layout Itemize
37262 The character that denotes a
37266 transformation is inserted either by the command
37271 \begin_inset space \textvisiblespace{}
37278 Insert\SpecialChar \menuseparator
37279 Special Character\SpecialChar \menuseparator
37280 Symbols\SpecialChar \menuseparator
37282 \begin_inset space ~
37288 \begin_inset Formula $\mathscr{F}$
37294 \begin_layout Standard
37295 \begin_inset Newpage newpage
37301 \begin_layout Section
37303 \begin_inset Index idx
37306 \begin_layout Plain Layout
37315 \begin_layout Standard
37316 Some characters and symbols can be created with several commands.
37317 Here is a list of the synonym commands:
37320 \begin_layout Standard
37321 \begin_inset VSpace bigskip
37325 \begin_inset space \hfill{}
37329 \begin_inset Tabular
37330 <lyxtabular version="3" rows="12" columns="2">
37331 <features rotate="0" tabularvalignment="middle">
37332 <column alignment="center" valignment="top" width="0pt">
37333 <column alignment="center" valignment="top" width="0pt">
37335 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
37338 \begin_layout Plain Layout
37344 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
37347 \begin_layout Plain Layout
37349 \begin_inset Note Note
37352 \begin_layout Plain Layout
37359 is only used as spacer.
37371 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
37374 \begin_layout Plain Layout
37382 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
37385 \begin_layout Plain Layout
37389 \begin_layout Plain Layout
37402 \begin_layout Plain Layout
37416 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
37419 \begin_layout Plain Layout
37427 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
37430 \begin_layout Plain Layout
37440 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
37443 \begin_layout Plain Layout
37451 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
37454 \begin_layout Plain Layout
37464 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
37467 \begin_layout Plain Layout
37475 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
37478 \begin_layout Plain Layout
37486 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
37489 \begin_layout Plain Layout
37497 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
37500 \begin_layout Plain Layout
37508 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
37511 \begin_layout Plain Layout
37519 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
37522 \begin_layout Plain Layout
37532 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
37535 \begin_layout Plain Layout
37543 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
37546 \begin_layout Plain Layout
37556 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
37559 \begin_layout Plain Layout
37567 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
37570 \begin_layout Plain Layout
37580 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
37583 \begin_layout Plain Layout
37591 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
37594 \begin_layout Plain Layout
37604 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
37607 \begin_layout Plain Layout
37615 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
37618 \begin_layout Plain Layout
37626 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
37629 \begin_layout Plain Layout
37637 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
37640 \begin_layout Plain Layout
37652 \begin_inset space \hfill{}
37656 \begin_inset Tabular
37657 <lyxtabular version="3" rows="12" columns="2">
37658 <features rotate="0" tabularvalignment="middle">
37659 <column alignment="center" valignment="top" width="0pt">
37660 <column alignment="center" valignment="top" width="0pt">
37662 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
37665 \begin_layout Plain Layout
37671 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
37674 \begin_layout Plain Layout
37682 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
37685 \begin_layout Plain Layout
37693 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
37696 \begin_layout Plain Layout
37708 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
37711 \begin_layout Plain Layout
37719 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
37722 \begin_layout Plain Layout
37732 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
37735 \begin_layout Plain Layout
37743 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
37746 \begin_layout Plain Layout
37756 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
37759 \begin_layout Plain Layout
37767 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
37770 \begin_layout Plain Layout
37778 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
37781 \begin_layout Plain Layout
37789 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
37792 \begin_layout Plain Layout
37800 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
37803 \begin_layout Plain Layout
37811 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
37814 \begin_layout Plain Layout
37824 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
37827 \begin_layout Plain Layout
37835 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
37838 \begin_layout Plain Layout
37848 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
37851 \begin_layout Plain Layout
37859 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
37862 \begin_layout Plain Layout
37872 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
37875 \begin_layout Plain Layout
37883 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
37886 \begin_layout Plain Layout
37896 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
37899 \begin_layout Plain Layout
37907 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
37910 \begin_layout Plain Layout
37920 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
37923 \begin_layout Plain Layout
37931 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
37934 \begin_layout Plain Layout
37948 \begin_inset space \hfill{}
37954 \begin_layout Standard
37955 \begin_inset Newpage newpage
37961 \begin_layout Bibliography
37962 \begin_inset CommandInset bibitem
37963 LatexCommand bibitem
37975 The LaTeX Companion
37978 Addison Wesley, 2004
37981 \begin_layout Bibliography
37982 \begin_inset CommandInset bibitem
37983 LatexCommand bibitem
37989 \begin_inset CommandInset href
37992 target "ftp://ftp.dante.de/tex-archive/info/math/voss/mathmode/Mathmode.pdf"
37996 of LaTeX's math abilities
37999 \begin_layout Bibliography
38000 \begin_inset CommandInset bibitem
38001 LatexCommand bibitem
38007 \begin_inset CommandInset href
38010 target "http://mirrors.ctan.org/macros/latex/required/amslatex/math/amsldoc.pdf"
38018 \begin_layout Plain Layout
38030 \begin_layout Bibliography
38031 \begin_inset CommandInset bibitem
38032 LatexCommand bibitem
38038 \begin_inset CommandInset href
38041 target "ftp://ftp.dante.de/tex-archive/info/symbols/comprehensive/symbols-a4.pdf"
38045 of all symbols available with LaTeX-packages
38048 \begin_layout Bibliography
38049 \begin_inset CommandInset bibitem
38050 LatexCommand bibitem
38056 \begin_inset CommandInset href
38058 name "Documentation"
38059 target "http://mirrors.ctan.org/macros/latex/contrib/cancel/cancel.pdf"
38063 of the LaTeX-package
38068 \begin_inset Index idx
38071 \begin_layout Plain Layout
38080 \begin_layout Bibliography
38081 \begin_inset CommandInset bibitem
38082 LatexCommand bibitem
38088 \begin_inset CommandInset href
38090 name "Documentation"
38091 target "http://www.tug.org/applications/hyperref/ftp/doc/manual.pdf"
38095 of the LaTeX-package
38100 \begin_inset Index idx
38103 \begin_layout Plain Layout
38104 Packages ! hyperref
38112 \begin_layout Bibliography
38113 \begin_inset CommandInset bibitem
38114 LatexCommand bibitem
38120 \begin_inset CommandInset href
38122 name "Documentation"
38123 target "http://www.ctan.org/tex-archive/macros/latex/contrib/mhchem/mhchem.pdf"
38127 of the LaTeX-package
38132 \begin_inset Index idx
38135 \begin_layout Plain Layout
38144 \begin_layout Bibliography
38145 \begin_inset CommandInset bibitem
38146 LatexCommand bibitem
38152 \begin_inset CommandInset href
38155 target "http://www.tug.org/TUGboat/Articles/tb22-4/tb72perlS.pdf"
38166 \begin_inset CommandInset ref
38168 reference "sub:Operator-Limits"
38173 \begin_inset Index idx
38176 \begin_layout Plain Layout
38187 \begin_layout Bibliography
38188 \begin_inset CommandInset bibitem
38189 LatexCommand bibitem
38200 Auflage, Duden 2001
38203 \begin_layout Bibliography
38204 \begin_inset CommandInset bibitem
38205 LatexCommand bibitem
38211 \begin_inset CommandInset href
38214 target "http://physics.nist.gov/Document/checklist.pdf"
38218 for reviewing manuscripts
38221 \begin_layout Standard
38222 \begin_inset CommandInset index_print
38223 LatexCommand printindex