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 2
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 To activate it, set in the document settings under
16803 \begin_inset space ~
16813 \begin_inset Index idx
16816 \begin_layout Plain Layout
16817 Packages ! mathtools
16825 \begin_inset space ~
16837 sets the space besides the operator to 0
16838 \begin_inset space \thinspace{}
16842 \begin_inset Newline newline
16846 \begin_inset CommandInset ref
16848 reference "eq:substack"
16852 , one uses the command
16855 \begin_layout Standard
16863 \begin_layout Standard
16864 and inserts the operator with its limits into the braces.
16865 Behind the brace one continues the formula:
16866 \begin_inset Formula
16868 \smashoperator{\sum_{\begin{subarray}{c}
16872 \end{subarray}}^{n}}k^{-2}
16880 \begin_layout Standard
16881 It is possible to set the space of only one side of the operator to 0
16882 \begin_inset space \thinspace{}
16886 To do this write either
16905 stands for the left and
16909 for the right side of the operator.
16910 Here is an example of the possible
16919 \begin_layout Standard
16920 \begin_inset Formula
16922 Y\smashoperator{\sum_{1\le i\le j\le n}^{n=3456}}X_{ij}=Y\smashoperator[l]{\sum_{1\le i\le j\le n}^{n=3456}}X_{ij}=Y\smashoperator[r]{\sum_{1\le i\le j\le n}^{n=3456}}X_{ij}
16930 \begin_layout Standard
16931 \begin_inset VSpace bigskip
16937 \begin_layout Standard
16938 When several consecutive operators have limits the typesetting of the limits
16939 looks often imperfect in the output, see this example:
16940 \begin_inset Formula
16942 \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}
16947 To improve the typesetting set in the document settings under
16950 \begin_inset space ~
16960 \begin_inset Index idx
16963 \begin_layout Plain Layout
16964 Packages ! mathtools
16972 \begin_inset space ~
16978 Then insert into your formula the command
16985 \begin_inset Index idx
16988 \begin_layout Plain Layout
16996 directly before the first operator.
16997 The example will then look like this:
16998 \begin_inset Formula
17000 \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}
17008 \begin_layout Standard
17009 \begin_inset VSpace bigskip
17012 How to use one limit for several operators is described in
17013 \begin_inset CommandInset ref
17015 reference "sub:Self-defined-Operators"
17022 \begin_layout Subsection
17023 Decoration for Operators
17024 \begin_inset Index idx
17027 \begin_layout Plain Layout
17028 Operators ! Decoration
17036 \begin_layout Standard
17044 \begin_inset Index idx
17047 \begin_layout Plain Layout
17062 \begin_inset Index idx
17065 \begin_layout Plain Layout
17073 characters can be placed above or below an operator, respectively.
17081 \begin_inset Index idx
17084 \begin_layout Plain Layout
17092 characters can be set before and behind a big operator.
17095 \begin_layout Standard
17097 \begin_inset space ~
17109 \begin_layout Itemize
17116 is used to set characters at the corners of the operator
17119 \begin_layout Itemize
17126 is used to set characters before and/or behind the operator (this variant
17127 represents LaTeX's original
17136 \begin_layout Itemize
17143 is used to set characters at the left corners and/or behind the operator
17146 \begin_layout Itemize
17153 is used to set characters at the right corners and/or before the operator
17156 \begin_layout Standard
17157 For example the command
17162 \begin_inset space \textvisiblespace{}
17168 \begin_inset space \textvisiblespace{}
17172 \begin_inset Formula $\to$
17176 \begin_inset Formula $\to$
17180 \begin_inset space \textvisiblespace{}
17190 \begin_inset Formula
17192 \sideset{}{'}\sum_{k=1}^{n}
17200 \begin_layout Standard
17201 \begin_inset Note Greyedout
17204 \begin_layout Plain Layout
17211 can only be used to decorate big operators, binary operators are not allowed.
17219 \begin_layout Standard
17232 can also be used to decorate symbols and characters.
17233 For example, the command
17238 \begin_inset space \textvisiblespace{}
17244 \begin_inset space \textvisiblespace{}
17250 \begin_inset Formula $\uparrow$
17258 \begin_inset Formula
17260 \overset{a}{\maltese}
17268 \begin_layout Subsection
17270 \begin_inset CommandInset label
17272 name "sub:Binary-Operators"
17277 \begin_inset Index idx
17280 \begin_layout Plain Layout
17289 \begin_layout Standard
17290 Binary operators are surrounded by space when there is a character before
17292 \begin_inset VSpace medskip
17298 \begin_layout Standard
17299 \begin_inset space \hfill{}
17303 \begin_inset Tabular
17304 <lyxtabular version="3" rows="13" columns="2">
17305 <features rotate="0" tabularvalignment="middle">
17306 <column alignment="center" valignment="top" width="0pt">
17307 <column alignment="center" valignment="top" width="0pt">
17309 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
17312 \begin_layout Plain Layout
17314 \begin_inset Note Note
17317 \begin_layout Plain Layout
17324 is only used as spacer.
17334 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
17337 \begin_layout Plain Layout
17345 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
17348 \begin_layout Plain Layout
17354 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
17357 \begin_layout Plain Layout
17358 \begin_inset Formula $+$
17368 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
17371 \begin_layout Plain Layout
17377 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
17380 \begin_layout Plain Layout
17381 \begin_inset Formula $-$
17391 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
17394 \begin_layout Plain Layout
17402 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
17405 \begin_layout Plain Layout
17406 \begin_inset Formula $\pm$
17416 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
17419 \begin_layout Plain Layout
17427 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
17430 \begin_layout Plain Layout
17431 \begin_inset Formula $\mp$
17441 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
17444 \begin_layout Plain Layout
17452 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
17455 \begin_layout Plain Layout
17456 \begin_inset Formula $\cdot$
17466 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
17469 \begin_layout Plain Layout
17477 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
17480 \begin_layout Plain Layout
17481 \begin_inset Formula $\times$
17491 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
17494 \begin_layout Plain Layout
17502 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
17505 \begin_layout Plain Layout
17506 \begin_inset Formula $\div$
17516 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
17519 \begin_layout Plain Layout
17523 \begin_layout Plain Layout
17536 \begin_layout Plain Layout
17548 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
17551 \begin_layout Plain Layout
17552 \begin_inset Formula $*$
17562 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
17565 \begin_layout Plain Layout
17573 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
17576 \begin_layout Plain Layout
17577 \begin_inset Formula $\star$
17587 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
17590 \begin_layout Plain Layout
17598 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
17601 \begin_layout Plain Layout
17602 \begin_inset Formula $\circ$
17612 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
17615 \begin_layout Plain Layout
17623 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
17626 \begin_layout Plain Layout
17627 \begin_inset Formula $\diamond$
17637 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
17640 \begin_layout Plain Layout
17648 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
17651 \begin_layout Plain Layout
17652 \begin_inset Formula $\bullet$
17666 \begin_inset space \hfill{}
17670 \begin_inset Tabular
17671 <lyxtabular version="3" rows="13" columns="2">
17672 <features rotate="0" tabularvalignment="middle">
17673 <column alignment="center" valignment="top" width="0pt">
17674 <column alignment="center" valignment="top" width="0pt">
17676 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
17679 \begin_layout Plain Layout
17685 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
17688 \begin_layout Plain Layout
17696 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
17699 \begin_layout Plain Layout
17707 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
17710 \begin_layout Plain Layout
17711 \begin_inset Formula $\nabla$
17721 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
17724 \begin_layout Plain Layout
17732 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
17735 \begin_layout Plain Layout
17736 \begin_inset Formula $\bigtriangledown$
17746 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
17749 \begin_layout Plain Layout
17757 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
17760 \begin_layout Plain Layout
17761 \begin_inset Formula $\bigtriangleup$
17771 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
17774 \begin_layout Plain Layout
17782 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
17785 \begin_layout Plain Layout
17786 \begin_inset Formula $\Box$
17796 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
17799 \begin_layout Plain Layout
17807 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
17810 \begin_layout Plain Layout
17811 \begin_inset Formula $\cap$
17821 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
17824 \begin_layout Plain Layout
17832 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
17835 \begin_layout Plain Layout
17836 \begin_inset Formula $\cup$
17846 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
17849 \begin_layout Plain Layout
17857 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
17860 \begin_layout Plain Layout
17861 \begin_inset Formula $\dagger$
17871 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
17874 \begin_layout Plain Layout
17882 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
17885 \begin_layout Plain Layout
17886 \begin_inset Formula $\ddagger$
17896 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
17899 \begin_layout Plain Layout
17907 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
17910 \begin_layout Plain Layout
17911 \begin_inset Formula $\wr$
17921 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
17924 \begin_layout Plain Layout
17932 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
17935 \begin_layout Plain Layout
17936 \begin_inset Formula $\bigcirc$
17946 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
17949 \begin_layout Plain Layout
17957 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
17960 \begin_layout Plain Layout
17961 \begin_inset Formula $\wedge$
17971 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
17974 \begin_layout Plain Layout
17982 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
17985 \begin_layout Plain Layout
17986 \begin_inset Formula $\vee$
18000 \begin_inset space \hfill{}
18004 \begin_inset Tabular
18005 <lyxtabular version="3" rows="13" columns="2">
18006 <features rotate="0" tabularvalignment="middle">
18007 <column alignment="center" valignment="top" width="0pt">
18008 <column alignment="center" valignment="top" width="0pt">
18010 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
18013 \begin_layout Plain Layout
18019 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
18022 \begin_layout Plain Layout
18030 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
18033 \begin_layout Plain Layout
18041 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
18044 \begin_layout Plain Layout
18045 \begin_inset Formula $\oplus$
18055 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
18058 \begin_layout Plain Layout
18066 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
18069 \begin_layout Plain Layout
18070 \begin_inset Formula $\ominus$
18080 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
18083 \begin_layout Plain Layout
18091 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
18094 \begin_layout Plain Layout
18095 \begin_inset Formula $\otimes$
18105 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
18108 \begin_layout Plain Layout
18116 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
18119 \begin_layout Plain Layout
18120 \begin_inset Formula $\oslash$
18130 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
18133 \begin_layout Plain Layout
18141 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
18144 \begin_layout Plain Layout
18145 \begin_inset Formula $\odot$
18155 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
18158 \begin_layout Plain Layout
18166 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
18169 \begin_layout Plain Layout
18170 \begin_inset Formula $\amalg$
18180 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
18183 \begin_layout Plain Layout
18191 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
18194 \begin_layout Plain Layout
18195 \begin_inset Formula $\uplus$
18205 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
18208 \begin_layout Plain Layout
18216 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
18219 \begin_layout Plain Layout
18220 \begin_inset Formula $\setminus$
18230 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
18233 \begin_layout Plain Layout
18241 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
18244 \begin_layout Plain Layout
18245 \begin_inset Formula $\sqcap$
18255 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
18258 \begin_layout Plain Layout
18266 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
18269 \begin_layout Plain Layout
18270 \begin_inset Formula $\sqcup$
18280 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
18283 \begin_layout Plain Layout
18291 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
18294 \begin_layout Plain Layout
18295 \begin_inset Formula $\triangleleft$
18305 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
18308 \begin_layout Plain Layout
18316 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
18319 \begin_layout Plain Layout
18320 \begin_inset Formula $\triangleright$
18334 \begin_inset space \hfill{}
18340 \begin_layout Standard
18341 All binary operators can also be inserted via the math toolbar button
18344 arg "math-insert \\pm"
18350 \begin_layout Standard
18351 To typeset the Laplace operator also
18368 \begin_inset Formula $\nabla^{2}$
18371 ) can be used instead of
18380 \begin_layout Standard
18387 Insert\SpecialChar \menuseparator
18399 \begin_layout Subsection
18400 Self-defined Operators
18401 \begin_inset CommandInset label
18403 name "sub:Self-defined-Operators"
18408 \begin_inset Index idx
18411 \begin_layout Plain Layout
18412 Operators ! self-defined
18420 \begin_layout Standard
18421 With the help of the command
18425 DeclareMathOperator
18428 \begin_inset Index idx
18431 \begin_layout Plain Layout
18436 DeclareMathOperator
18441 custom operators can be defined in the LaTeX-preamble.
18442 Its command scheme is:
18445 \begin_layout Standard
18450 DeclareMathOperator{new command}{display}
18453 \begin_layout Standard
18454 Display can be characters or symbols that define how the operator looks
18456 To define a big operator a * is set behind the command.
18457 All self-defined big operators can have limits as described in
18458 \begin_inset CommandInset ref
18460 reference "sub:Operator-Limits"
18467 \begin_layout Standard
18468 For example the LaTeX-preamble line
18471 \begin_layout Standard
18476 DeclareMathOperator*{
18483 \begin_layout Standard
18484 defines the command
18490 , that inserts a big operator consisting of the lozenge symbol from
18491 \begin_inset CommandInset ref
18493 reference "sub:Miscellaneous-Symbols"
18498 \begin_inset Formula
18500 \Lozenge_{n=1}^{\infty}
18505 The command for this formula is:
18516 \begin_inset Formula $\to$
18522 \begin_layout Standard
18523 \begin_inset VSpace bigskip
18526 When self-defined operators are not used several times in the document,
18527 they can also be defined with the commands
18534 \begin_inset Index idx
18537 \begin_layout Plain Layout
18552 \begin_inset Index idx
18555 \begin_layout Plain Layout
18563 , which have the following scheme:
18566 \begin_layout Standard
18580 \begin_layout Standard
18587 defines big operators,
18596 \begin_layout Standard
18604 \begin_inset space \thinspace{}
18608 \begin_inset space \space{}
18611 be used to use one limit for several operators:
18614 \begin_layout Standard
18615 \begin_inset Formula
18617 \mathop{\sum\negmedspace\sum}_{i,j=1}^{N}
18625 \begin_layout Standard
18626 The command for the formula above is:
18627 \begin_inset Newline newline
18643 \begin_inset space \textvisiblespace{}
18649 \begin_inset Formula $\to$
18655 \begin_inset space \textvisiblespace{}
18663 \begin_layout Section
18665 \begin_inset Index idx
18668 \begin_layout Plain Layout
18677 \begin_layout Subsection
18679 \begin_inset CommandInset label
18681 name "sub:Font-Styles"
18686 \begin_inset Index idx
18689 \begin_layout Plain Layout
18698 \begin_layout Standard
18699 Latin letters in formulas can be set in one of the following font styles:
18700 \begin_inset VSpace -2mm
18706 \begin_layout Standard
18708 \begin_inset Tabular
18709 <lyxtabular version="3" rows="7" columns="3">
18710 <features rotate="0" tabularvalignment="middle">
18711 <column alignment="center" valignment="top">
18712 <column alignment="center" valignment="top">
18713 <column alignment="center" valignment="top">
18715 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
18718 \begin_layout Plain Layout
18724 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
18727 \begin_layout Plain Layout
18733 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
18736 \begin_layout Plain Layout
18744 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
18747 \begin_layout Plain Layout
18753 \begin_inset space \textvisiblespace{}
18763 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
18766 \begin_layout Plain Layout
18767 \begin_inset Formula $\mathbb{ABC}$
18775 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
18778 \begin_layout Plain Layout
18791 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
18794 \begin_layout Plain Layout
18800 \begin_inset space \textvisiblespace{}
18810 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
18813 \begin_layout Plain Layout
18814 \begin_inset Formula $\mathbf{AbC}$
18822 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
18825 \begin_layout Plain Layout
18838 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
18841 \begin_layout Plain Layout
18847 \begin_inset space \textvisiblespace{}
18857 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
18860 \begin_layout Plain Layout
18861 \begin_inset Formula $\boldsymbol{AbC}$
18869 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
18872 \begin_layout Plain Layout
18875 arg "font-boldsymbol"
18885 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
18888 \begin_layout Plain Layout
18894 \begin_inset space \textvisiblespace{}
18904 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
18907 \begin_layout Plain Layout
18908 \begin_inset Formula $\mathcal{ABC}$
18916 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
18919 \begin_layout Plain Layout
18932 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
18935 \begin_layout Plain Layout
18941 \begin_inset space \textvisiblespace{}
18951 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
18954 \begin_layout Plain Layout
18955 \begin_inset Formula $\mathfrak{AbC}$
18963 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
18966 \begin_layout Plain Layout
18974 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
18977 \begin_layout Plain Layout
18983 \begin_inset space \textvisiblespace{}
18993 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
18996 \begin_layout Plain Layout
18997 \begin_inset Formula $\mathscr{AbC}$
19005 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
19008 \begin_layout Plain Layout
19022 \begin_layout Standard
19024 \begin_inset Tabular
19025 <lyxtabular version="3" rows="5" columns="3">
19026 <features rotate="0" tabularvalignment="middle">
19027 <column alignment="center" valignment="top">
19028 <column alignment="center" valignment="top">
19029 <column alignment="center" valignment="top">
19031 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
19034 \begin_layout Plain Layout
19040 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
19043 \begin_layout Plain Layout
19049 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
19052 \begin_layout Plain Layout
19060 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
19063 \begin_layout Plain Layout
19069 \begin_inset space \textvisiblespace{}
19079 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
19082 \begin_layout Plain Layout
19083 \begin_inset Formula $\mathit{AbC}$
19091 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
19094 \begin_layout Plain Layout
19102 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
19105 \begin_layout Plain Layout
19111 \begin_inset space \textvisiblespace{}
19121 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
19124 \begin_layout Plain Layout
19125 \begin_inset Formula $\mathrm{AbC}$
19133 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
19136 \begin_layout Plain Layout
19149 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
19152 \begin_layout Plain Layout
19158 \begin_inset space \textvisiblespace{}
19168 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
19171 \begin_layout Plain Layout
19172 \begin_inset Formula $\mathsf{AbC}$
19180 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
19183 \begin_layout Plain Layout
19196 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
19199 \begin_layout Plain Layout
19205 \begin_inset space \textvisiblespace{}
19215 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
19218 \begin_layout Plain Layout
19219 \begin_inset Formula $\mathtt{AbC}$
19227 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
19230 \begin_layout Plain Layout
19233 arg "font-typewriter"
19249 \begin_layout Standard
19250 \begin_inset Note Greyedout
19253 \begin_layout Plain Layout
19270 can only be used for big letters.
19278 \begin_layout Standard
19279 Predefined is the style
19288 \begin_layout Standard
19289 The style commands work also for letters in mathematical constructs:
19290 \begin_inset Formula
19292 \mathfrak{A=\frac{b}{C}}
19300 \begin_layout Standard
19301 Characters in mathematical text don't appear in a math font style but in
19302 the text font style
19309 That their style can't be set correctly via the text style dialog is a
19314 \begin_layout Plain Layout
19315 \begin_inset CommandInset href
19317 name "LyX-bug #4629"
19318 target "http://www.lyx.org/trac/ticket/4629"
19330 \begin_layout Standard
19331 Instead of the style commands the dialog
19333 Edit\SpecialChar \menuseparator
19334 Math\SpecialChar \menuseparator
19337 or the toolbar button
19340 arg "math-insert \\font"
19346 \begin_layout Subsection
19348 \begin_inset CommandInset label
19350 name "sub:Bold-Formulas"
19355 \begin_inset Index idx
19358 \begin_layout Plain Layout
19367 \begin_layout Standard
19368 To make a complete formula bold, the command
19374 from the previous subsection cannot be used, because it doesn't work for
19375 small Greek letters.
19376 Furthermore it prints Latin letters always upright, like in the following
19380 \begin_layout Standard
19381 \begin_inset Formula
19383 \mathbf{\int_{n}^{2}f(\theta)=\Gamma}\qquad\textrm{equation with \textbackslash mathbf}
19391 \begin_layout Standard
19392 To display the formula correctly, the command
19399 \begin_inset Formula
19401 \boldsymbol{\int_{n}^{2}f(\theta)=\Gamma\qquad\textrm{equation with \textbackslash boldsymbol}}
19406 It is also possible to set the formula in a
19408 boldmath environment
19411 This environment is created by inserting the command
19418 \begin_inset Index idx
19421 \begin_layout Plain Layout
19430 To end the environment, the command
19437 \begin_inset Index idx
19440 \begin_layout Plain Layout
19448 is inserted in TeX-mode.
19452 \begin_layout Plain Layout
19462 \begin_inset Formula
19464 \int_{n}^{2}f(\theta)=\Gamma\qquad\textrm{equation in a boldmath environment}
19473 \begin_layout Plain Layout
19485 \begin_layout Subsection
19487 \begin_inset Index idx
19490 \begin_layout Plain Layout
19499 \begin_layout Standard
19500 Formulas can be colored like normal text: Highlight a formula or a formula
19506 Here is a formula in magenta:
19507 \begin_inset Formula
19509 {\color{magenta}\int A\,\mathrm{d}x=\frac{\sqrt[5]{B}}{\ln\left(\frac{1}{3}\right)}}
19517 \begin_layout Standard
19518 You can also define your own colors as described in
19519 \begin_inset CommandInset ref
19521 reference "sub:Colored-Boxes"
19526 They can be used with the TeX code command
19533 \begin_inset Index idx
19536 \begin_layout Plain Layout
19547 \begin_layout Standard
19552 textcolor{color}{characters or formula}
19555 \begin_layout Standard
19556 The following example was colored completely dark green and partly red:
19559 \begin_layout Standard
19563 \begin_layout Plain Layout
19567 textcolor{darkgreen}{
19573 \begin_inset Formula
19575 \int A\,\mathrm{d}x=\frac{{\color{red}\sqrt[5]{B}}}{\ln\left(\frac{1}{3}\right)}
19584 \begin_layout Plain Layout
19594 \begin_layout Standard
19595 Due to a bug in LyX only complete formulas can be colored with self-defined
19600 \begin_layout Plain Layout
19601 \begin_inset CommandInset href
19603 name "LyX-bug #5269"
19604 target "http://www.lyx.org/trac/ticket/5269"
19616 \begin_layout Subsection
19618 \begin_inset CommandInset label
19620 name "sub:Font-Sizes"
19625 \begin_inset Index idx
19628 \begin_layout Plain Layout
19637 \begin_layout Standard
19638 For characters in formulas there are, analog to characters in text, the
19639 following size commands:
19642 \begin_layout Standard
19686 \begin_inset Newline newline
19708 \begin_layout Standard
19709 The size produced by the commands depends on the document font size, which
19710 corresponds to the command
19717 The other commands produce smaller or larger sizes than
19724 The font size can however not exceed a certain value.
19725 Is for example the document font size 12
19726 \begin_inset space \thinspace{}
19735 switches to the same size as
19745 \begin_layout Standard
19746 A size command is inserted in TeX-mode before the formula and sets the size
19747 for all following formula and text characters.
19748 To switch back to the initial size, the command
19754 is inserted behind the formula in TeX-mode.
19757 \begin_layout Standard
19758 Within a formula the size can be changed using the following size commands
19759 or the toolbar button
19762 arg "math-insert \\style"
19768 \begin_layout Standard
19771 \begin_inset Tabular
19772 <lyxtabular version="3" rows="5" columns="2">
19773 <features rotate="0" tabularvalignment="middle">
19774 <column alignment="center" valignment="top">
19775 <column alignment="center" valignment="top">
19777 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
19780 \begin_layout Plain Layout
19786 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
19789 \begin_layout Plain Layout
19791 \begin_inset Note Note
19794 \begin_layout Plain Layout
19801 is only used as spacer.
19813 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
19816 \begin_layout Plain Layout
19820 \begin_inset Index idx
19823 \begin_layout Plain Layout
19836 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
19839 \begin_layout Plain Layout
19840 \begin_inset Formula $\raisebox{6.5mm}{}{\displaystyle E_{\mathrm{pot_{1}}}=\frac{K}{l+\frac{m}{n_{2}}}}\raisebox{-5.5mm}{}$
19850 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
19853 \begin_layout Plain Layout
19861 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
19864 \begin_layout Plain Layout
19865 \begin_inset Formula $\raisebox{4.5mm}{}{\textstyle E_{\mathrm{pot_{1}}}=\frac{K}{l+\frac{m}{n_{2}}}}\raisebox{-4mm}{}$
19875 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
19878 \begin_layout Plain Layout
19886 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
19889 \begin_layout Plain Layout
19890 \begin_inset Formula $\raisebox{4.5mm}{}{\scriptstyle E_{\mathrm{pot_{1}}}=\frac{K}{l+\frac{m}{n_{2}}}}\raisebox{-3.5mm}{}$
19900 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
19903 \begin_layout Plain Layout
19911 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
19914 \begin_layout Plain Layout
19915 \begin_inset Formula $\raisebox{4.5mm}{}{\scriptscriptstyle E_{\mathrm{pot_{1}}}=\frac{K}{l+\frac{m}{n_{2}}}}\raisebox{-3.5mm}{}$
19931 \begin_layout Standard
19932 After entering these commands, a blue box appears in which the formula parts
19936 \begin_layout Standard
19937 There is a further method to change the font size, that though only works
19938 for symbols or letters in mathematical text.
19939 To use it, one of the above text size commands is inserted in mathematical
19941 All following characters until the end of the mathematical text or until
19942 another size command will have the selected size.
19944 \begin_inset VSpace -2mm
19950 \begin_layout Standard
19954 \begin_layout Plain Layout
19964 \begin_inset Formula
19966 A=\frac{B}{c}\cdot\maltese
19972 \begin_inset Formula
19974 \maltese A\textrm{\Large\maltese\textit{A}}\textrm{\tiny\maltese\textit{A}}
19983 \begin_layout Plain Layout
19995 \begin_layout Standard
19996 \begin_inset VSpace medskip
19999 Before both formulas the command
20006 The command for the second formula is:
20007 \begin_inset Newline newline
20015 \begin_inset space \textvisiblespace{}
20021 \begin_inset space \textvisiblespace{}
20027 \begin_inset space \textvisiblespace{}
20033 \begin_inset space \textvisiblespace{}
20037 \begin_inset Formula $\to$
20041 \begin_inset Formula $\to$
20045 \begin_inset Newline newline
20049 \begin_inset space \hspace*{}
20060 \begin_inset space \textvisiblespace{}
20066 \begin_inset space \textvisiblespace{}
20072 \begin_inset space \textvisiblespace{}
20078 \begin_layout Standard
20079 If a symbol cannot be displayed in different sizes, it will always be displayed
20080 in the default size.
20083 \begin_layout Section
20085 \begin_inset Index idx
20088 \begin_layout Plain Layout
20097 \begin_layout Standard
20098 Greek letters can also be inserted via the toolbar button
20101 arg "math-insert \\alpha"
20105 All international typesetting norms purport that Greek letters in math
20106 have to be typeset italic/slanted.
20107 In some languages, like French or Russian, they are nevertheless sometimes
20111 \begin_layout Subsection
20113 \begin_inset Index idx
20116 \begin_layout Plain Layout
20117 Greek letters ! small
20125 \begin_layout Standard
20126 \begin_inset space \hfill{}
20130 \begin_inset Tabular
20131 <lyxtabular version="3" rows="11" columns="2">
20132 <features rotate="0" tabularvalignment="middle">
20133 <column alignment="center" valignment="top" width="0pt">
20134 <column alignment="center" valignment="top" width="0pt">
20136 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
20139 \begin_layout Plain Layout
20145 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
20148 \begin_layout Plain Layout
20156 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
20159 \begin_layout Plain Layout
20167 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
20170 \begin_layout Plain Layout
20171 \begin_inset Formula $\alpha$
20181 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
20184 \begin_layout Plain Layout
20192 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
20195 \begin_layout Plain Layout
20196 \begin_inset Formula $\beta$
20206 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
20209 \begin_layout Plain Layout
20217 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
20220 \begin_layout Plain Layout
20221 \begin_inset Formula $\gamma$
20231 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
20234 \begin_layout Plain Layout
20242 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
20245 \begin_layout Plain Layout
20246 \begin_inset Formula $\delta$
20256 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
20259 \begin_layout Plain Layout
20267 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
20270 \begin_layout Plain Layout
20271 \begin_inset Formula $\epsilon$
20281 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
20284 \begin_layout Plain Layout
20292 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
20295 \begin_layout Plain Layout
20296 \begin_inset Formula $\varepsilon$
20306 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
20309 \begin_layout Plain Layout
20317 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
20320 \begin_layout Plain Layout
20321 \begin_inset Formula $\zeta$
20331 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
20334 \begin_layout Plain Layout
20342 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
20345 \begin_layout Plain Layout
20346 \begin_inset Formula $\eta$
20356 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
20359 \begin_layout Plain Layout
20367 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
20370 \begin_layout Plain Layout
20371 \begin_inset Formula $\theta$
20381 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
20384 \begin_layout Plain Layout
20392 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
20395 \begin_layout Plain Layout
20396 \begin_inset Formula $\vartheta$
20410 \begin_inset space \hfill{}
20414 \begin_inset Tabular
20415 <lyxtabular version="3" rows="12" columns="2">
20416 <features rotate="0" tabularvalignment="middle">
20417 <column alignment="center" valignment="top" width="0pt">
20418 <column alignment="center" valignment="top" width="0pt">
20420 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
20423 \begin_layout Plain Layout
20429 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
20432 \begin_layout Plain Layout
20440 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
20443 \begin_layout Plain Layout
20451 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
20454 \begin_layout Plain Layout
20455 \begin_inset Formula $\iota$
20465 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
20468 \begin_layout Plain Layout
20476 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
20479 \begin_layout Plain Layout
20480 \begin_inset Formula $\kappa$
20490 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
20493 \begin_layout Plain Layout
20501 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
20504 \begin_layout Plain Layout
20505 \begin_inset Formula $\varkappa$
20515 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
20518 \begin_layout Plain Layout
20526 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
20529 \begin_layout Plain Layout
20530 \begin_inset Formula $\lambda$
20540 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
20543 \begin_layout Plain Layout
20551 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
20554 \begin_layout Plain Layout
20555 \begin_inset Formula $\mu$
20565 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
20568 \begin_layout Plain Layout
20576 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
20579 \begin_layout Plain Layout
20580 \begin_inset Formula $\nu$
20590 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
20593 \begin_layout Plain Layout
20601 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
20604 \begin_layout Plain Layout
20605 \begin_inset Formula $\xi$
20615 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
20618 \begin_layout Plain Layout
20624 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
20627 \begin_layout Plain Layout
20628 \begin_inset Formula $o$
20638 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
20641 \begin_layout Plain Layout
20649 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
20652 \begin_layout Plain Layout
20653 \begin_inset Formula $\pi$
20663 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
20666 \begin_layout Plain Layout
20674 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
20677 \begin_layout Plain Layout
20678 \begin_inset Formula $\varpi$
20688 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
20691 \begin_layout Plain Layout
20699 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
20702 \begin_layout Plain Layout
20703 \begin_inset Formula $\rho$
20717 \begin_inset space \hfill{}
20721 \begin_inset Tabular
20722 <lyxtabular version="3" rows="11" columns="2">
20723 <features rotate="0" tabularvalignment="middle">
20724 <column alignment="center" valignment="top" width="0pt">
20725 <column alignment="center" valignment="top" width="0pt">
20727 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
20730 \begin_layout Plain Layout
20736 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
20739 \begin_layout Plain Layout
20747 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
20750 \begin_layout Plain Layout
20758 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
20761 \begin_layout Plain Layout
20762 \begin_inset Formula $\varrho$
20772 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
20775 \begin_layout Plain Layout
20783 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
20786 \begin_layout Plain Layout
20787 \begin_inset Formula $\sigma$
20797 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
20800 \begin_layout Plain Layout
20808 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
20811 \begin_layout Plain Layout
20812 \begin_inset Formula $\varsigma$
20822 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
20825 \begin_layout Plain Layout
20833 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
20836 \begin_layout Plain Layout
20837 \begin_inset Formula $\tau$
20847 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
20850 \begin_layout Plain Layout
20858 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
20861 \begin_layout Plain Layout
20862 \begin_inset Formula $\upsilon$
20872 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
20875 \begin_layout Plain Layout
20883 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
20886 \begin_layout Plain Layout
20887 \begin_inset Formula $\phi$
20897 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
20900 \begin_layout Plain Layout
20908 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
20911 \begin_layout Plain Layout
20912 \begin_inset Formula $\varphi$
20922 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
20925 \begin_layout Plain Layout
20933 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
20936 \begin_layout Plain Layout
20937 \begin_inset Formula $\chi$
20947 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
20950 \begin_layout Plain Layout
20958 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
20961 \begin_layout Plain Layout
20962 \begin_inset Formula $\psi$
20972 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
20975 \begin_layout Plain Layout
20983 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
20986 \begin_layout Plain Layout
20987 \begin_inset Formula $\omega$
21001 \begin_inset space \hfill{}
21007 \begin_layout Standard
21008 \begin_inset VSpace medskip
21014 \begin_layout Standard
21015 How to create special upright Greek letters is explained in
21016 \begin_inset CommandInset ref
21018 reference "sub:Upright-small-Greek"
21025 \begin_layout Subsection
21027 \begin_inset Index idx
21030 \begin_layout Plain Layout
21031 Greek letters ! big
21039 \begin_layout Standard
21040 \begin_inset space \hfill{}
21044 \begin_inset Tabular
21045 <lyxtabular version="3" rows="7" columns="2">
21046 <features rotate="0" tabularvalignment="middle">
21047 <column alignment="center" valignment="top" width="0pt">
21048 <column alignment="center" valignment="top" width="0pt">
21050 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
21053 \begin_layout Plain Layout
21059 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
21062 \begin_layout Plain Layout
21070 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
21073 \begin_layout Plain Layout
21081 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
21084 \begin_layout Plain Layout
21085 \begin_inset Formula $\Gamma$
21095 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
21098 \begin_layout Plain Layout
21106 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
21109 \begin_layout Plain Layout
21110 \begin_inset Formula $\Delta$
21120 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
21123 \begin_layout Plain Layout
21131 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
21134 \begin_layout Plain Layout
21135 \begin_inset Formula $\Theta$
21145 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
21148 \begin_layout Plain Layout
21156 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
21159 \begin_layout Plain Layout
21160 \begin_inset Formula $\Lambda$
21170 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
21173 \begin_layout Plain Layout
21181 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
21184 \begin_layout Plain Layout
21185 \begin_inset Formula $\Xi$
21195 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
21198 \begin_layout Plain Layout
21206 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
21209 \begin_layout Plain Layout
21210 \begin_inset Formula $\Pi$
21224 \begin_inset space \hfill{}
21228 \begin_inset Tabular
21229 <lyxtabular version="3" rows="6" columns="2">
21230 <features rotate="0" tabularvalignment="middle">
21231 <column alignment="center" valignment="top" width="0pt">
21232 <column alignment="center" valignment="top" width="0pt">
21234 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
21237 \begin_layout Plain Layout
21243 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
21246 \begin_layout Plain Layout
21254 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
21257 \begin_layout Plain Layout
21265 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
21268 \begin_layout Plain Layout
21269 \begin_inset Formula $\Sigma$
21279 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
21282 \begin_layout Plain Layout
21290 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
21293 \begin_layout Plain Layout
21294 \begin_inset Formula $\Upsilon$
21304 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
21307 \begin_layout Plain Layout
21315 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
21318 \begin_layout Plain Layout
21319 \begin_inset Formula $\Phi$
21329 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
21332 \begin_layout Plain Layout
21340 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
21343 \begin_layout Plain Layout
21344 \begin_inset Formula $\Psi$
21354 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
21357 \begin_layout Plain Layout
21365 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
21368 \begin_layout Plain Layout
21369 \begin_inset Formula $\Omega$
21383 \begin_inset space \hfill{}
21389 \begin_layout Standard
21390 \begin_inset VSpace medskip
21393 That the big Greek letters appear upright is caused by a design bug when
21395 To get correct italic big letters, begin every command with
21400 For example the command
21407 \begin_inset Formula $\varGamma$
21411 Another way is to load the package
21419 \begin_layout Plain Layout
21424 is part of the LaTeX-package
21429 \begin_inset Index idx
21432 \begin_layout Plain Layout
21437 \begin_layout Plain Layout
21457 \begin_inset Index idx
21460 \begin_layout Plain Layout
21466 with the LaTeX-preamble line
21469 \begin_layout Standard
21474 usepackage{fixmath}
21477 \begin_layout Standard
21478 Then all big Greek letters in a document will automatically be typeset italic.
21481 \begin_layout Subsection
21483 \begin_inset Index idx
21486 \begin_layout Plain Layout
21487 Greek letters ! bold
21495 \begin_layout Standard
21496 Greek letters cannot be set with different font styles like Latin letters.
21497 They can only be made bold with the command
21504 \begin_inset Index idx
21507 \begin_layout Plain Layout
21518 \begin_layout Standard
21520 \begin_inset Tabular
21521 <lyxtabular version="3" rows="3" columns="2">
21522 <features rotate="0" tabularvalignment="middle">
21523 <column alignment="center" valignment="top">
21524 <column alignment="center" valignment="top">
21526 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
21529 \begin_layout Plain Layout
21535 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
21538 \begin_layout Plain Layout
21546 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
21549 \begin_layout Plain Layout
21561 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
21564 \begin_layout Plain Layout
21565 \begin_inset Formula $\Upsilon\boldsymbol{\Upsilon}$
21575 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
21578 \begin_layout Plain Layout
21590 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
21593 \begin_layout Plain Layout
21594 \begin_inset Formula $\theta\boldsymbol{\theta}$
21610 \begin_layout Section
21615 \begin_layout Plain Layout
21628 \begin_layout Plain Layout
21629 A list with all symbols of most of the LaTeX-packages can be found in
21630 \begin_inset CommandInset citation
21645 \begin_layout Plain Layout
21653 \begin_inset Note Note
21656 \begin_layout Plain Layout
21659 texorpdfstring is used to avoid that the footnote appears in the PDF-bookmark.
21662 \begin_layout Plain Layout
21665 texorpdfstring is in section
21666 \begin_inset CommandInset ref
21668 reference "sub:Formulas-in-Section"
21678 \begin_inset Index idx
21681 \begin_layout Plain Layout
21690 \begin_layout Standard
21691 Many of the symbols listed in this section can also be inserted via the
21695 arg "math-insert \\nabla"
21701 arg "math-insert \\digamma"
21707 \begin_layout Subsection
21708 Mathematical Symbols
21709 \begin_inset CommandInset label
21711 name "sub:Mathematical-Symbols"
21716 \begin_inset Index idx
21719 \begin_layout Plain Layout
21720 Symbols ! mathematical
21728 \begin_layout Standard
21729 \begin_inset space \hfill{}
21733 \begin_inset Tabular
21734 <lyxtabular version="3" rows="10" columns="2">
21735 <features rotate="0" tabularvalignment="middle">
21736 <column alignment="center" valignment="top" width="0pt">
21737 <column alignment="center" valignment="top" width="0pt">
21739 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
21742 \begin_layout Plain Layout
21748 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
21751 \begin_layout Plain Layout
21759 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
21762 \begin_layout Plain Layout
21770 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
21773 \begin_layout Plain Layout
21774 \begin_inset Formula $\neg$
21784 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
21787 \begin_layout Plain Layout
21795 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
21798 \begin_layout Plain Layout
21799 \begin_inset Formula $\Im$
21809 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
21812 \begin_layout Plain Layout
21820 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
21823 \begin_layout Plain Layout
21824 \begin_inset Formula $\Re$
21834 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
21837 \begin_layout Plain Layout
21845 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
21848 \begin_layout Plain Layout
21849 \begin_inset Formula $\aleph$
21859 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
21862 \begin_layout Plain Layout
21870 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
21873 \begin_layout Plain Layout
21874 \begin_inset Formula $\partial$
21884 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
21887 \begin_layout Plain Layout
21895 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
21898 \begin_layout Plain Layout
21899 \begin_inset Formula $\infty$
21909 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
21912 \begin_layout Plain Layout
21920 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
21923 \begin_layout Plain Layout
21924 \begin_inset Formula $\wp$
21934 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
21937 \begin_layout Plain Layout
21945 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
21948 \begin_layout Plain Layout
21949 \begin_inset Formula $\imath$
21959 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
21962 \begin_layout Plain Layout
21970 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
21973 \begin_layout Plain Layout
21974 \begin_inset Formula $\jmath$
21988 \begin_inset space \hfill{}
21992 \begin_inset Tabular
21993 <lyxtabular version="3" rows="10" columns="2">
21994 <features rotate="0" tabularvalignment="middle">
21995 <column alignment="center" valignment="top" width="0pt">
21996 <column alignment="center" valignment="top" width="0pt">
21998 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
22001 \begin_layout Plain Layout
22007 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
22010 \begin_layout Plain Layout
22012 \begin_inset Note Note
22015 \begin_layout Plain Layout
22022 is only used as spacer.
22034 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
22037 \begin_layout Plain Layout
22045 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
22048 \begin_layout Plain Layout
22049 \begin_inset Formula $\forall$
22059 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
22062 \begin_layout Plain Layout
22070 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
22073 \begin_layout Plain Layout
22074 \begin_inset Formula $\exists$
22084 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
22087 \begin_layout Plain Layout
22095 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
22098 \begin_layout Plain Layout
22099 \begin_inset Formula $\nexists$
22109 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
22112 \begin_layout Plain Layout
22120 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
22123 \begin_layout Plain Layout
22124 \begin_inset Formula $\emptyset$
22134 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
22137 \begin_layout Plain Layout
22145 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
22148 \begin_layout Plain Layout
22149 \begin_inset Formula $\varnothing$
22159 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
22162 \begin_layout Plain Layout
22170 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
22173 \begin_layout Plain Layout
22174 \begin_inset Formula $\dag$
22184 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
22187 \begin_layout Plain Layout
22195 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
22198 \begin_layout Plain Layout
22199 \begin_inset Formula $\ddag$
22209 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
22212 \begin_layout Plain Layout
22220 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
22223 \begin_layout Plain Layout
22227 \begin_layout Plain Layout
22237 \begin_inset Formula $\complement$
22244 \begin_layout Plain Layout
22258 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
22261 \begin_layout Plain Layout
22269 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
22272 \begin_layout Plain Layout
22273 \begin_inset Formula $\Bbbk$
22287 \begin_inset space \hfill{}
22291 \begin_inset Tabular
22292 <lyxtabular version="3" rows="10" columns="2">
22293 <features rotate="0" tabularvalignment="middle">
22294 <column alignment="center" valignment="top" width="0pt">
22295 <column alignment="center" valignment="top" width="0pt">
22297 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
22300 \begin_layout Plain Layout
22306 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
22309 \begin_layout Plain Layout
22317 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
22320 \begin_layout Plain Layout
22328 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
22331 \begin_layout Plain Layout
22332 \begin_inset Formula $\prime$
22342 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
22345 \begin_layout Plain Layout
22353 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
22356 \begin_layout Plain Layout
22357 \begin_inset Formula $\backprime$
22367 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
22370 \begin_layout Plain Layout
22378 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
22381 \begin_layout Plain Layout
22382 \begin_inset Formula $\mho$
22392 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
22395 \begin_layout Plain Layout
22403 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
22406 \begin_layout Plain Layout
22407 \begin_inset Formula $\triangle$
22417 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
22420 \begin_layout Plain Layout
22428 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
22431 \begin_layout Plain Layout
22432 \begin_inset Formula $\angle$
22442 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
22445 \begin_layout Plain Layout
22453 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
22456 \begin_layout Plain Layout
22457 \begin_inset Formula $\measuredangle$
22467 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
22470 \begin_layout Plain Layout
22478 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
22481 \begin_layout Plain Layout
22482 \begin_inset Formula $\sphericalangle$
22492 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
22495 \begin_layout Plain Layout
22503 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
22506 \begin_layout Plain Layout
22507 \begin_inset Formula $\top$
22517 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
22520 \begin_layout Plain Layout
22528 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
22531 \begin_layout Plain Layout
22532 \begin_inset Formula $\bot$
22546 \begin_inset space \hfill{}
22552 \begin_layout Subsection
22553 Miscellaneous Symbols
22554 \begin_inset CommandInset label
22556 name "sub:Miscellaneous-Symbols"
22561 \begin_inset Index idx
22564 \begin_layout Plain Layout
22565 Symbols ! miscellaneous
22573 \begin_layout Standard
22576 \begin_inset Tabular
22577 <lyxtabular version="3" rows="10" columns="2">
22578 <features rotate="0" tabularvalignment="middle">
22579 <column alignment="center" valignment="top" width="0pt">
22580 <column alignment="center" valignment="top" width="0pt">
22582 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
22585 \begin_layout Plain Layout
22591 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
22594 \begin_layout Plain Layout
22602 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
22605 \begin_layout Plain Layout
22613 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
22616 \begin_layout Plain Layout
22617 \begin_inset Formula $\flat$
22627 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
22630 \begin_layout Plain Layout
22638 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
22641 \begin_layout Plain Layout
22642 \begin_inset Formula $\natural$
22652 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
22655 \begin_layout Plain Layout
22663 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
22666 \begin_layout Plain Layout
22667 \begin_inset Formula $\sharp$
22677 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
22680 \begin_layout Plain Layout
22688 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
22691 \begin_layout Plain Layout
22692 \begin_inset Formula $\surd$
22702 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
22705 \begin_layout Plain Layout
22713 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
22716 \begin_layout Plain Layout
22717 \begin_inset Formula $\checkmark$
22727 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
22730 \begin_layout Plain Layout
22738 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
22741 \begin_layout Plain Layout
22742 \begin_inset Formula $\yen$
22752 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
22755 \begin_layout Plain Layout
22763 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
22766 \begin_layout Plain Layout
22767 \begin_inset Formula $\pounds$
22777 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
22780 \begin_layout Plain Layout
22786 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
22789 \begin_layout Plain Layout
22790 \begin_inset Formula $\$$
22800 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
22803 \begin_layout Plain Layout
22809 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
22812 \begin_layout Plain Layout
22813 \begin_inset Formula $§$
22827 \begin_inset Tabular
22828 <lyxtabular version="3" rows="10" columns="2">
22829 <features rotate="0" tabularvalignment="middle">
22830 <column alignment="center" valignment="top">
22831 <column alignment="center" valignment="top">
22833 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
22836 \begin_layout Plain Layout
22842 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
22845 \begin_layout Plain Layout
22853 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
22856 \begin_layout Plain Layout
22864 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
22867 \begin_layout Plain Layout
22868 \begin_inset Formula $\hbar$
22878 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
22881 \begin_layout Plain Layout
22889 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
22892 \begin_layout Plain Layout
22893 \begin_inset Formula $\hslash$
22903 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
22906 \begin_layout Plain Layout
22914 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
22917 \begin_layout Plain Layout
22918 \begin_inset Formula $\clubsuit$
22928 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
22931 \begin_layout Plain Layout
22939 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
22942 \begin_layout Plain Layout
22943 \begin_inset Formula $\spadesuit$
22953 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
22956 \begin_layout Plain Layout
22964 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
22967 \begin_layout Plain Layout
22968 \begin_inset Formula $\bigstar$
22978 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
22981 \begin_layout Plain Layout
22989 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
22992 \begin_layout Plain Layout
22993 \begin_inset Formula $\blacklozenge$
23003 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
23006 \begin_layout Plain Layout
23014 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
23017 \begin_layout Plain Layout
23018 \begin_inset Formula $\blacktriangle$
23028 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
23031 \begin_layout Plain Layout
23039 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
23042 \begin_layout Plain Layout
23043 \begin_inset Formula $\blacktriangledown$
23053 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
23056 \begin_layout Plain Layout
23064 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
23067 \begin_layout Plain Layout
23068 \begin_inset Formula $\bullet$
23082 \begin_inset Tabular
23083 <lyxtabular version="3" rows="10" columns="2">
23084 <features rotate="0" tabularvalignment="middle">
23085 <column alignment="center" valignment="top" width="0pt">
23086 <column alignment="center" valignment="top" width="0pt">
23088 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
23091 \begin_layout Plain Layout
23097 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
23100 \begin_layout Plain Layout
23108 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
23111 \begin_layout Plain Layout
23119 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
23122 \begin_layout Plain Layout
23123 \begin_inset Formula $\diamondsuit$
23133 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
23136 \begin_layout Plain Layout
23144 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
23147 \begin_layout Plain Layout
23148 \begin_inset Formula $\Diamond$
23158 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
23161 \begin_layout Plain Layout
23169 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
23172 \begin_layout Plain Layout
23173 \begin_inset Formula $\heartsuit$
23183 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
23186 \begin_layout Plain Layout
23194 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
23197 \begin_layout Plain Layout
23198 \begin_inset Formula $\P$
23208 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
23211 \begin_layout Plain Layout
23219 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
23222 \begin_layout Plain Layout
23223 \begin_inset Formula $\copyright$
23233 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
23236 \begin_layout Plain Layout
23244 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
23247 \begin_layout Plain Layout
23248 \begin_inset Formula $\circledR$
23258 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
23261 \begin_layout Plain Layout
23269 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
23272 \begin_layout Plain Layout
23273 \begin_inset Formula $\maltese$
23283 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
23286 \begin_layout Plain Layout
23294 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
23297 \begin_layout Plain Layout
23298 \begin_inset Formula $\diagup$
23308 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
23311 \begin_layout Plain Layout
23319 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
23322 \begin_layout Plain Layout
23323 \begin_inset Formula $\diagdown$
23339 \begin_layout Standard
23340 \begin_inset VSpace medskip
23346 \begin_layout Standard
23347 Some symbols can be displayed in different sizes, see
23348 \begin_inset CommandInset ref
23350 reference "sub:Font-Sizes"
23357 \begin_layout Subsection
23359 \begin_inset Index idx
23362 \begin_layout Plain Layout
23363 Symbols ! Euro-symbol
23369 \begin_inset Index idx
23372 \begin_layout Plain Layout
23379 \begin_layout Plain Layout
23396 \begin_layout Standard
23397 To use the Euro symbol in formulas, the LaTeX-package
23402 \begin_inset Index idx
23405 \begin_layout Plain Layout
23411 must be installed and loaded with the LaTeX-preamble line
23414 \begin_layout Standard
23419 usepackage[gennarrow]{eurosym}
23422 \begin_layout Standard
23423 The Euro symbol can now be inserted with the command
23430 \begin_inset Index idx
23433 \begin_layout Plain Layout
23444 \begin_layout Standard
23445 The Euro symbol can directly be inserted with the € key in mathematical
23446 text, without having
23461 can also be inserted in TeX-mode.
23462 The official currency symbol can then be inserted with the command
23469 \begin_inset Index idx
23472 \begin_layout Plain Layout
23480 , that is only available in TeX-mode.
23483 \begin_layout Standard
23487 \begin_layout Plain Layout
23497 \begin_inset Note Note
23500 \begin_layout Plain Layout
23501 The following table will only be displayed when the LaTeX-package
23513 \begin_layout Standard
23514 An overview about the different Euro symbols:
23517 \begin_layout Standard
23519 \begin_inset Tabular
23520 <lyxtabular version="3" rows="4" columns="3">
23521 <features rotate="0" tabularvalignment="middle">
23522 <column alignment="center" valignment="top" width="0pt">
23523 <column alignment="center" valignment="top" width="0pt">
23524 <column alignment="center" valignment="top" width="0pt">
23526 <cell multicolumn="1" alignment="center" valignment="top" bottomline="true" usebox="none">
23529 \begin_layout Plain Layout
23535 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
23538 \begin_layout Plain Layout
23544 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
23547 \begin_layout Plain Layout
23555 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
23558 \begin_layout Plain Layout
23564 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
23567 \begin_layout Plain Layout
23575 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
23578 \begin_layout Plain Layout
23579 \begin_inset Formula $\euro$
23589 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
23592 \begin_layout Plain Layout
23598 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
23601 \begin_layout Plain Layout
23607 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
23610 \begin_layout Plain Layout
23611 \begin_inset Formula $\mbox{€}$
23621 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
23624 \begin_layout Plain Layout
23630 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
23633 \begin_layout Plain Layout
23641 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
23644 \begin_layout Plain Layout
23648 \begin_layout Plain Layout
23670 \begin_layout Standard
23674 \begin_layout Plain Layout
23684 \begin_inset Note Note
23687 \begin_layout Plain Layout
23688 The following will be displayed when the LaTeX-package
23700 \begin_layout Standard
23701 You need to install the LaTeX-package
23705 to see the rest of this subsection in the output.
23708 \begin_layout Standard
23712 \begin_layout Plain Layout
23724 \begin_layout Section
23726 \begin_inset CommandInset label
23728 name "sec:Relations"
23733 \begin_inset Index idx
23736 \begin_layout Plain Layout
23743 \begin_inset Index idx
23746 \begin_layout Plain Layout
23751 \begin_layout Plain Layout
23762 \begin_layout Plain Layout
23777 \begin_layout Standard
23778 All following relations can also be inserted via the toolbar button
23781 arg "math-insert \\leq"
23787 \begin_layout Standard
23788 \begin_inset space \hfill{}
23792 \begin_inset Tabular
23793 <lyxtabular version="3" rows="17" columns="2">
23794 <features rotate="0" tabularvalignment="middle">
23795 <column alignment="center" valignment="top" width="0pt">
23796 <column alignment="center" valignment="top" width="0pt">
23798 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
23801 \begin_layout Plain Layout
23807 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
23810 \begin_layout Plain Layout
23818 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
23821 \begin_layout Plain Layout
23827 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
23830 \begin_layout Plain Layout
23831 \begin_inset Formula $<$
23841 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
23844 \begin_layout Plain Layout
23852 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
23855 \begin_layout Plain Layout
23856 \begin_inset Formula $\le$
23866 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
23869 \begin_layout Plain Layout
23877 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
23880 \begin_layout Plain Layout
23881 \begin_inset Formula $\ll$
23891 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
23894 \begin_layout Plain Layout
23902 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
23905 \begin_layout Plain Layout
23906 \begin_inset Formula $\prec$
23916 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
23919 \begin_layout Plain Layout
23927 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
23930 \begin_layout Plain Layout
23931 \begin_inset Formula $\preceq$
23941 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
23944 \begin_layout Plain Layout
23952 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
23955 \begin_layout Plain Layout
23956 \begin_inset Formula $\subset$
23966 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
23969 \begin_layout Plain Layout
23977 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
23980 \begin_layout Plain Layout
23981 \begin_inset Formula $\subseteq$
23991 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
23994 \begin_layout Plain Layout
24002 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
24005 \begin_layout Plain Layout
24006 \begin_inset Formula $\sqsubseteq$
24016 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
24019 \begin_layout Plain Layout
24027 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
24030 \begin_layout Plain Layout
24031 \begin_inset Formula $\in$
24041 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
24044 \begin_layout Plain Layout
24052 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
24055 \begin_layout Plain Layout
24056 \begin_inset Formula $\vdash$
24066 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
24069 \begin_layout Plain Layout
24077 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
24080 \begin_layout Plain Layout
24081 \begin_inset Formula $\smile$
24091 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
24094 \begin_layout Plain Layout
24102 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
24105 \begin_layout Plain Layout
24106 \begin_inset Formula $\lhd$
24116 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
24119 \begin_layout Plain Layout
24127 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
24130 \begin_layout Plain Layout
24131 \begin_inset Formula $\unlhd$
24141 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
24144 \begin_layout Plain Layout
24152 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
24155 \begin_layout Plain Layout
24156 \begin_inset Formula $\gtrless$
24166 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
24169 \begin_layout Plain Layout
24177 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
24180 \begin_layout Plain Layout
24181 \begin_inset Formula $\mid$
24191 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
24194 \begin_layout Plain Layout
24202 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
24205 \begin_layout Plain Layout
24206 \begin_inset Formula $\nmid$
24220 \begin_inset space \hfill{}
24224 \begin_inset Tabular
24225 <lyxtabular version="3" rows="17" columns="2">
24226 <features rotate="0" tabularvalignment="middle">
24227 <column alignment="center" valignment="top" width="0pt">
24228 <column alignment="center" valignment="top" width="0pt">
24230 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
24233 \begin_layout Plain Layout
24239 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
24242 \begin_layout Plain Layout
24250 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
24253 \begin_layout Plain Layout
24259 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
24262 \begin_layout Plain Layout
24263 \begin_inset Formula $=$
24273 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
24276 \begin_layout Plain Layout
24284 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
24287 \begin_layout Plain Layout
24288 \begin_inset Formula $\not=$
24298 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
24301 \begin_layout Plain Layout
24309 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
24312 \begin_layout Plain Layout
24313 \begin_inset Formula $\equiv$
24323 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
24326 \begin_layout Plain Layout
24334 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
24337 \begin_layout Plain Layout
24338 \begin_inset Formula $\sim$
24348 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
24351 \begin_layout Plain Layout
24359 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
24362 \begin_layout Plain Layout
24363 \begin_inset Formula $\simeq$
24373 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
24376 \begin_layout Plain Layout
24384 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
24387 \begin_layout Plain Layout
24388 \begin_inset Formula $\approx$
24398 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
24401 \begin_layout Plain Layout
24409 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
24412 \begin_layout Plain Layout
24413 \begin_inset Formula $\cong$
24423 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
24426 \begin_layout Plain Layout
24434 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
24437 \begin_layout Plain Layout
24438 \begin_inset Formula $\bowtie$
24448 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
24451 \begin_layout Plain Layout
24459 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
24462 \begin_layout Plain Layout
24463 \begin_inset Formula $\notin$
24473 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
24476 \begin_layout Plain Layout
24484 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
24487 \begin_layout Plain Layout
24488 \begin_inset Formula $\perp$
24498 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
24501 \begin_layout Plain Layout
24509 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
24512 \begin_layout Plain Layout
24513 \begin_inset Formula $\propto$
24523 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
24526 \begin_layout Plain Layout
24534 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
24537 \begin_layout Plain Layout
24538 \begin_inset Formula $\asymp$
24548 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
24551 \begin_layout Plain Layout
24559 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
24562 \begin_layout Plain Layout
24563 \begin_inset Formula $\doteq$
24573 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
24576 \begin_layout Plain Layout
24584 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
24587 \begin_layout Plain Layout
24588 \begin_inset Formula $\circeq$
24598 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
24601 \begin_layout Plain Layout
24609 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
24612 \begin_layout Plain Layout
24613 \begin_inset Formula $\models$
24623 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
24626 \begin_layout Plain Layout
24634 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
24637 \begin_layout Plain Layout
24638 \begin_inset Formula $\widehat{=}$
24652 \begin_inset space \hfill{}
24656 \begin_inset Tabular
24657 <lyxtabular version="3" rows="17" columns="2">
24658 <features rotate="0" tabularvalignment="middle">
24659 <column alignment="center" valignment="top" width="0pt">
24660 <column alignment="center" valignment="top" width="0pt">
24662 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
24665 \begin_layout Plain Layout
24671 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
24674 \begin_layout Plain Layout
24682 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
24685 \begin_layout Plain Layout
24691 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
24694 \begin_layout Plain Layout
24695 \begin_inset Formula $>$
24705 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
24708 \begin_layout Plain Layout
24716 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
24719 \begin_layout Plain Layout
24720 \begin_inset Formula $\ge$
24730 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
24733 \begin_layout Plain Layout
24741 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
24744 \begin_layout Plain Layout
24745 \begin_inset Formula $\gg$
24755 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
24758 \begin_layout Plain Layout
24766 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
24769 \begin_layout Plain Layout
24770 \begin_inset Formula $\succ$
24780 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
24783 \begin_layout Plain Layout
24791 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
24794 \begin_layout Plain Layout
24795 \begin_inset Formula $\succeq$
24805 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
24808 \begin_layout Plain Layout
24816 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
24819 \begin_layout Plain Layout
24820 \begin_inset Formula $\supset$
24830 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
24833 \begin_layout Plain Layout
24841 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
24844 \begin_layout Plain Layout
24845 \begin_inset Formula $\supseteq$
24855 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
24858 \begin_layout Plain Layout
24866 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
24869 \begin_layout Plain Layout
24870 \begin_inset Formula $\sqsupseteq$
24880 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
24883 \begin_layout Plain Layout
24891 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
24894 \begin_layout Plain Layout
24895 \begin_inset Formula $\ni$
24905 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
24908 \begin_layout Plain Layout
24916 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
24919 \begin_layout Plain Layout
24920 \begin_inset Formula $\dashv$
24930 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
24933 \begin_layout Plain Layout
24941 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
24944 \begin_layout Plain Layout
24945 \begin_inset Formula $\frown$
24955 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
24958 \begin_layout Plain Layout
24966 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
24969 \begin_layout Plain Layout
24970 \begin_inset Formula $\rhd$
24980 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
24983 \begin_layout Plain Layout
24991 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
24994 \begin_layout Plain Layout
24995 \begin_inset Formula $\unrhd$
25005 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
25008 \begin_layout Plain Layout
25016 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
25019 \begin_layout Plain Layout
25020 \begin_inset Formula $\lessgtr$
25030 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
25033 \begin_layout Plain Layout
25041 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
25044 \begin_layout Plain Layout
25045 \begin_inset Formula $\parallel$
25055 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
25058 \begin_layout Plain Layout
25066 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
25069 \begin_layout Plain Layout
25070 \begin_inset Formula $\nparallel$
25084 \begin_inset space \hfill{}
25090 \begin_layout Standard
25091 \begin_inset VSpace medskip
25106 are bigger than the equal looking operators
25121 \begin_layout Standard
25122 LyX supports also many special relations.
25123 Use the toolbar button
25126 arg "math-insert \\leqq"
25129 to see a list of these relations.
25132 \begin_layout Standard
25133 Relations are, in contrary to symbols, always surrounded by space.
25136 \begin_layout Standard
25137 Relations with labels can be created with the command
25144 \begin_inset Index idx
25147 \begin_layout Plain Layout
25158 \begin_layout Standard
25160 \begin_inset Tabular
25161 <lyxtabular version="3" rows="2" columns="2">
25162 <features rotate="0" tabularvalignment="middle">
25163 <column alignment="center" valignment="top">
25164 <column alignment="center" valignment="top">
25166 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
25169 \begin_layout Plain Layout
25175 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
25178 \begin_layout Plain Layout
25180 \begin_inset Note Note
25183 \begin_layout Plain Layout
25190 is only used as spacer.
25202 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
25205 \begin_layout Plain Layout
25209 \begin_inset space \textvisiblespace{}
25217 \begin_inset space \textvisiblespace{}
25221 \begin_inset Formula $\downarrow$
25227 \begin_inset space \textvisiblespace{}
25231 \begin_inset space \textvisiblespace{}
25239 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
25242 \begin_layout Plain Layout
25243 \begin_inset Formula $\raisebox{5mm}{}A(r)\stackrel{r\to\infty}{\approx}B$
25259 \begin_layout Section
25263 \begin_layout Subsection
25264 Predefined Functions
25265 \begin_inset CommandInset label
25267 name "sub:Predefined-Functions"
25272 \begin_inset Index idx
25275 \begin_layout Plain Layout
25276 Functions ! predefined
25284 \begin_layout Standard
25285 In general, variables are set
25289 in mathematical expressions, but not function names, because
25290 \begin_inset Formula $sin$
25293 could be misunderstood as
25294 \begin_inset Formula $s\cdot i\cdot n$
25298 Therefore there are predefined functionswhich are additionally a bit separated
25300 They are inserted as commands starting with a backslash before their name.
25303 \begin_layout Standard
25305 \begin_inset Tabular
25306 <lyxtabular version="3" rows="2" columns="4">
25307 <features rotate="0" tabularvalignment="middle">
25308 <column alignment="center" valignment="top" width="0pt">
25309 <column alignment="center" valignment="top" width="0pt">
25310 <column alignment="center" valignment="top" width="0pt">
25311 <column alignment="center" valignment="top" width="0pt">
25313 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
25316 \begin_layout Plain Layout
25322 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
25325 \begin_layout Plain Layout
25331 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
25334 \begin_layout Plain Layout
25340 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
25343 \begin_layout Plain Layout
25351 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
25354 \begin_layout Plain Layout
25360 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
25363 \begin_layout Plain Layout
25364 \begin_inset Formula $Asin(x)+B$
25372 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
25375 \begin_layout Plain Layout
25383 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
25386 \begin_layout Plain Layout
25387 \begin_inset Formula $A\sin(x)+B$
25403 \begin_layout Standard
25404 The following functions are predefined:
25407 \begin_layout Standard
25408 \begin_inset VSpace -2mm
25414 \begin_layout Standard
25416 \begin_inset Tabular
25417 <lyxtabular version="3" rows="9" columns="4">
25418 <features rotate="0" tabularvalignment="middle">
25419 <column alignment="center" valignment="top" width="0pt">
25420 <column alignment="center" valignment="top" width="0pt">
25421 <column alignment="center" valignment="top" width="0pt">
25422 <column alignment="center" valignment="top" width="0pt">
25424 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
25427 \begin_layout Plain Layout
25433 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
25436 \begin_layout Plain Layout
25442 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
25445 \begin_layout Plain Layout
25451 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
25454 \begin_layout Plain Layout
25462 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
25465 \begin_layout Plain Layout
25473 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
25476 \begin_layout Plain Layout
25484 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
25487 \begin_layout Plain Layout
25495 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
25498 \begin_layout Plain Layout
25508 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
25511 \begin_layout Plain Layout
25519 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
25522 \begin_layout Plain Layout
25530 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
25533 \begin_layout Plain Layout
25541 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
25544 \begin_layout Plain Layout
25554 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
25557 \begin_layout Plain Layout
25565 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
25568 \begin_layout Plain Layout
25576 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
25579 \begin_layout Plain Layout
25587 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
25590 \begin_layout Plain Layout
25600 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
25603 \begin_layout Plain Layout
25611 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
25614 \begin_layout Plain Layout
25622 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
25625 \begin_layout Plain Layout
25633 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
25636 \begin_layout Plain Layout
25646 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
25649 \begin_layout Plain Layout
25657 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
25660 \begin_layout Plain Layout
25668 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
25671 \begin_layout Plain Layout
25679 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
25682 \begin_layout Plain Layout
25692 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
25695 \begin_layout Plain Layout
25703 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
25706 \begin_layout Plain Layout
25714 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
25717 \begin_layout Plain Layout
25725 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
25728 \begin_layout Plain Layout
25738 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
25741 \begin_layout Plain Layout
25749 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
25752 \begin_layout Plain Layout
25760 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
25763 \begin_layout Plain Layout
25771 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
25774 \begin_layout Plain Layout
25784 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
25787 \begin_layout Plain Layout
25795 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
25798 \begin_layout Plain Layout
25806 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
25809 \begin_layout Plain Layout
25817 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
25820 \begin_layout Plain Layout
25836 \begin_layout Standard
25837 They can also be inserted with the math toolbar button
25840 arg "math-insert \\functions"
25846 \begin_layout Subsection
25847 Self-defined Functions
25848 \begin_inset Index idx
25851 \begin_layout Plain Layout
25852 Functions ! self-defined
25860 \begin_layout Standard
25861 To use a function that is not predefined, like for example the sign function
25862 sgn(x), there are two possibilities:
25865 \begin_layout Itemize
25866 Define the function by inserting the following line to the LaTeX-preamble
25870 \begin_layout Plain Layout
25875 DeclareMathOperator
25878 \begin_inset CommandInset ref
25880 reference "sub:Self-defined-Operators"
25890 \begin_inset Newline newline
25894 \begin_inset VSpace -3mm
25898 \begin_inset Newline newline
25905 DeclareMathOperator{
25910 \begin_inset Index idx
25913 \begin_layout Plain Layout
25918 DeclareMathOperator
25924 \begin_inset Newline newline
25928 \begin_inset VSpace -2mm
25932 \begin_inset Newline newline
25935 Now the new defined function can be called with the command
25944 \begin_layout Itemize
25945 Write the formula as usual, mark the formula name, in our example the letters
25950 , and change it to mathematical text.
25951 Finally, a space is inserted between prefactor and function.
25954 \begin_layout Standard
25955 The result is the same with both methods as with a predefined function
25959 \begin_layout Plain Layout
25960 In LyX self-defined functions are displayed red, predefined ones black.
25968 \begin_layout Standard
25970 \begin_inset Tabular
25971 <lyxtabular version="3" rows="3" columns="2">
25972 <features rotate="0" tabularvalignment="middle">
25973 <column alignment="center" valignment="top" width="0pt">
25974 <column alignment="center" valignment="top" width="0pt">
25976 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
25979 \begin_layout Plain Layout
25985 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
25988 \begin_layout Plain Layout
25996 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
25999 \begin_layout Plain Layout
26007 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
26010 \begin_layout Plain Layout
26011 \begin_inset Formula $A\sgn(x)+B$
26021 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
26024 \begin_layout Plain Layout
26028 \begin_inset Formula $\underbrace{\textrm{sgn}}_{\textrm{Alt+M}\,\textrm{M}}$
26036 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
26039 \begin_layout Plain Layout
26040 \begin_inset Formula $A\,\textrm{sgn}(x)+B$
26056 \begin_layout Standard
26057 The first method is more suitable when the self-defined function should
26058 be used several times.
26061 \begin_layout Subsection
26063 \begin_inset Index idx
26066 \begin_layout Plain Layout
26075 \begin_layout Standard
26076 For limits, in addition to the commands
26083 \begin_inset Index idx
26086 \begin_layout Plain Layout
26106 the following functions are defined:
26109 \begin_layout Standard
26111 \begin_inset Tabular
26112 <lyxtabular version="3" rows="5" columns="2">
26113 <features rotate="0" tabularvalignment="middle">
26114 <column alignment="center" valignment="top">
26115 <column alignment="center" valignment="top">
26117 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
26120 \begin_layout Plain Layout
26126 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
26129 \begin_layout Plain Layout
26131 \begin_inset Note Note
26134 \begin_layout Plain Layout
26141 is only used as spacer.
26153 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
26156 \begin_layout Plain Layout
26164 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
26167 \begin_layout Plain Layout
26168 \begin_inset Formula $\varliminf$
26178 <cell alignment="center" valignment="top" leftline="true" usebox="none">
26181 \begin_layout Plain Layout
26189 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
26192 \begin_layout Plain Layout
26193 \begin_inset Formula $\varlimsup$
26203 <cell alignment="center" valignment="top" leftline="true" usebox="none">
26206 \begin_layout Plain Layout
26214 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
26217 \begin_layout Plain Layout
26218 \begin_inset Formula $\varprojlim$
26228 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
26231 \begin_layout Plain Layout
26239 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
26242 \begin_layout Plain Layout
26243 \begin_inset Formula $\varinjlim$
26247 \begin_inset Formula $\raisebox{-2.5mm}{}$
26263 \begin_layout Standard
26264 \begin_inset VSpace medskip
26267 The limit is created by inserting a subscript.
26268 It is set right beside the function in an inline formula:
26271 \begin_layout Standard
26273 \begin_inset Tabular
26274 <lyxtabular version="3" rows="2" columns="2">
26275 <features rotate="0" tabularvalignment="middle">
26276 <column alignment="center" valignment="top" width="0pt">
26277 <column alignment="center" valignment="top" width="0pt">
26279 <cell alignment="center" valignment="top" usebox="none">
26282 \begin_layout Plain Layout
26288 <cell alignment="center" valignment="top" usebox="none">
26291 \begin_layout Plain Layout
26292 \begin_inset space \hspace{}
26297 \begin_inset Note Note
26300 \begin_layout Plain Layout
26307 are used here as spacer.
26319 <cell alignment="center" valignment="top" usebox="none">
26322 \begin_layout Plain Layout
26328 \begin_inset space \textvisiblespace{}
26332 \begin_inset space \textvisiblespace{}
26340 <cell alignment="center" valignment="top" usebox="none">
26343 \begin_layout Plain Layout
26344 \begin_inset Formula $\hspace{1cm}\raisebox{5mm}{}\lim_{x\to A}x=B$
26360 \begin_layout Standard
26361 In a displayed formula the limit is set below the formula, as usual:
26362 \begin_inset Formula
26372 \begin_layout Standard
26373 \begin_inset VSpace medskip
26379 \begin_layout Standard
26380 How to adjust the typesetting of the limits see
26381 \begin_inset CommandInset ref
26383 reference "sub:Operator-Limits"
26390 \begin_layout Subsection
26392 \begin_inset Index idx
26395 \begin_layout Plain Layout
26396 Functions ! modulo-
26404 \begin_layout Standard
26405 The modulo-function is special, because it exists in four variants.
26406 The variants in a displayed formula are:
26407 \begin_inset Formula
26409 \underline{\textrm{Command}\raisebox{-0.9mm}{}} & & \underline{\textrm{Result}}\\
26410 \mathrm{a\backslash mod\textrm{␣}b} & & a\mod b\\
26411 \mathrm{a\backslash pmod\textrm{␣}b} & & a\pmod b\\
26412 \mathrm{a\backslash bmod\textrm{␣}b} & & a\bmod b\\
26413 \mathrm{a\backslash pod\textrm{␣}b} & & a\pod b
26421 \begin_layout Standard
26422 In an inline formula less space is set before the function names for all
26424 By default the modulo-functions take only the first following character
26426 To use more than one character, one has to put them into TeX-braces:
26427 \begin_inset Formula
26429 \underline{\textrm{Command}\raisebox{-0.9mm}{}} & & \underline{\textrm{Result}}\\
26430 \mathrm{a\backslash pod\textrm{␣}bcd} & & a\pod bcd\\
26431 \mathrm{a\backslash pod\backslash\{bc\to d} & & a\pod{bc}d
26439 \begin_layout Section
26441 \begin_inset Index idx
26444 \begin_layout Plain Layout
26453 \begin_layout Standard
26454 The characters ^ and _ would normally create a subscript and subscript,
26456 To get these characters you have to insert them with a leading
26461 \begin_layout Standard
26464 \begin_inset Tabular
26465 <lyxtabular version="3" rows="3" columns="2">
26466 <features rotate="0" tabularvalignment="middle">
26467 <column alignment="block" valignment="top">
26468 <column alignment="block" valignment="top">
26470 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
26473 \begin_layout Plain Layout
26479 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
26482 \begin_layout Plain Layout
26490 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
26493 \begin_layout Plain Layout
26497 \begin_inset space \textvisiblespace{}
26505 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
26508 \begin_layout Plain Layout
26509 \begin_inset Formula $\mathcircumflex$
26519 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
26522 \begin_layout Plain Layout
26530 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
26533 \begin_layout Plain Layout
26534 \begin_inset Formula $\_$
26550 \begin_layout Subsection
26551 Special Characters in Mathematical Text
26554 \begin_layout Standard
26555 The following commands can only be used in mathematical text or in TeX-mode:
26558 \begin_layout Standard
26559 \begin_inset space \hfill{}
26563 \begin_inset Tabular
26564 <lyxtabular version="3" rows="8" columns="2">
26565 <features rotate="0" tabularvalignment="middle">
26566 <column alignment="block" valignment="top">
26567 <column alignment="block" valignment="top">
26569 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
26572 \begin_layout Plain Layout
26578 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
26581 \begin_layout Plain Layout
26589 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
26592 \begin_layout Plain Layout
26600 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
26603 \begin_layout Plain Layout
26604 \begin_inset Formula $\textrm{œ}$
26614 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
26617 \begin_layout Plain Layout
26625 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
26628 \begin_layout Plain Layout
26629 \begin_inset Formula $\textrm{Œ}$
26639 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
26642 \begin_layout Plain Layout
26650 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
26653 \begin_layout Plain Layout
26654 \begin_inset Formula $\textrm{æ}$
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 $\textrm{Æ}$
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 $\textrm{\aa}$
26714 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
26717 \begin_layout Plain Layout
26721 \begin_inset Index idx
26724 \begin_layout Plain Layout
26731 \begin_layout Plain Layout
26752 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
26755 \begin_layout Plain Layout
26756 \begin_inset Formula $\textrm{Å}$
26766 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
26769 \begin_layout Plain Layout
26777 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
26780 \begin_layout Plain Layout
26781 \begin_inset Formula $\textrm{ı}$
26795 \begin_inset space \hfill{}
26799 \begin_inset Tabular
26800 <lyxtabular version="3" rows="8" columns="2">
26801 <features rotate="0" tabularvalignment="middle">
26802 <column alignment="block" valignment="top">
26803 <column alignment="center" valignment="top">
26805 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
26808 \begin_layout Plain Layout
26810 \begin_inset Note Note
26813 \begin_layout Plain Layout
26815 \begin_inset space \thinspace{}
26818 mm is used for separation, because otherwise the output will be ¡ and ¿
26829 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
26832 \begin_layout Plain Layout
26840 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
26843 \begin_layout Plain Layout
26851 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
26854 \begin_layout Plain Layout
26855 \begin_inset Formula $\textrm{ø}$
26865 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
26868 \begin_layout Plain Layout
26876 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
26879 \begin_layout Plain Layout
26880 \begin_inset Formula $\textrm{Ø}$
26890 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
26893 \begin_layout Plain Layout
26901 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
26904 \begin_layout Plain Layout
26905 \begin_inset Formula $\textrm{ł}$
26915 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
26918 \begin_layout Plain Layout
26926 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
26929 \begin_layout Plain Layout
26930 \begin_inset Formula $\textrm{Ł}$
26940 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
26943 \begin_layout Plain Layout
26945 \begin_inset space \hspace{}
26950 \begin_inset space \textvisiblespace{}
26958 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
26961 \begin_layout Plain Layout
26962 \begin_inset Formula $\textrm{!`}$
26972 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
26975 \begin_layout Plain Layout
26977 \begin_inset space \hspace{}
26982 \begin_inset space \textvisiblespace{}
26990 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
26993 \begin_layout Plain Layout
26994 \begin_inset Formula $\textrm{?`}$
27004 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
27007 \begin_layout Plain Layout
27015 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
27018 \begin_layout Plain Layout
27019 \begin_inset Formula $\textrm{ȷ}$
27033 \begin_inset space \hfill{}
27039 \begin_layout Standard
27041 \begin_inset Formula $\textrm{\textrm{Å}}$
27045 \begin_inset Formula $\textrm{\textrm{Ø}}$
27048 can also be inserted via the math toolbar button
27051 arg "math-insert \\digamma"
27057 \begin_layout Standard
27058 An exception are the commands
27061 \begin_inset space \hspace{}
27070 \begin_inset space \hspace{}
27076 , because they can be inserted in LyX directly to text.
27079 \begin_layout Subsection
27081 \begin_inset CommandInset label
27083 name "sub:Accents-in-Text"
27088 \begin_inset Index idx
27091 \begin_layout Plain Layout
27100 \begin_layout Standard
27101 With the following commands all letters can be accented.
27102 The commands must be inserted in TeX-mode.
27105 \begin_layout Standard
27106 \begin_inset space \hfill{}
27110 \begin_inset Tabular
27111 <lyxtabular version="3" rows="8" columns="2">
27112 <features rotate="0" tabularvalignment="middle">
27113 <column alignment="block" valignment="top">
27114 <column alignment="block" valignment="top">
27116 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
27119 \begin_layout Plain Layout
27125 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
27128 \begin_layout Plain Layout
27136 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
27139 \begin_layout Plain Layout
27143 \begin_inset Quotes grd
27151 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
27154 \begin_layout Plain Layout
27158 \begin_layout Plain Layout
27174 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
27177 \begin_layout Plain Layout
27185 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
27188 \begin_layout Plain Layout
27192 \begin_layout Plain Layout
27208 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
27211 \begin_layout Plain Layout
27215 \begin_inset space \textvisiblespace{}
27223 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
27226 \begin_layout Plain Layout
27230 \begin_layout Plain Layout
27246 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
27249 \begin_layout Plain Layout
27257 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
27260 \begin_layout Plain Layout
27264 \begin_layout Plain Layout
27280 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
27283 \begin_layout Plain Layout
27287 \begin_inset space \textvisiblespace{}
27295 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
27298 \begin_layout Plain Layout
27302 \begin_layout Plain Layout
27318 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
27321 \begin_layout Plain Layout
27325 \begin_inset space \textvisiblespace{}
27333 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
27336 \begin_layout Plain Layout
27340 \begin_layout Plain Layout
27356 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
27359 \begin_layout Plain Layout
27363 \begin_inset space \textvisiblespace{}
27371 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
27374 \begin_layout Plain Layout
27378 \begin_layout Plain Layout
27398 \begin_inset space \hfill{}
27402 \begin_inset Tabular
27403 <lyxtabular version="3" rows="8" columns="2">
27404 <features rotate="0" tabularvalignment="middle">
27405 <column alignment="block" valignment="top">
27406 <column alignment="center" valignment="top">
27408 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
27411 \begin_layout Plain Layout
27417 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
27420 \begin_layout Plain Layout
27428 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
27431 \begin_layout Plain Layout
27435 \begin_inset space \textvisiblespace{}
27443 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
27446 \begin_layout Plain Layout
27450 \begin_layout Plain Layout
27466 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
27469 \begin_layout Plain Layout
27477 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
27480 \begin_layout Plain Layout
27484 \begin_layout Plain Layout
27500 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
27503 \begin_layout Plain Layout
27507 \begin_inset Index idx
27510 \begin_layout Plain Layout
27521 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
27524 \begin_layout Plain Layout
27528 \begin_layout Plain Layout
27544 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
27547 \begin_layout Plain Layout
27555 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
27558 \begin_layout Plain Layout
27562 \begin_layout Plain Layout
27578 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
27581 \begin_layout Plain Layout
27585 \begin_inset space \textvisiblespace{}
27593 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
27596 \begin_layout Plain Layout
27600 \begin_layout Plain Layout
27616 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
27619 \begin_layout Plain Layout
27623 \begin_inset space \textvisiblespace{}
27631 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
27634 \begin_layout Plain Layout
27638 \begin_layout Plain Layout
27654 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
27657 \begin_layout Plain Layout
27661 \begin_inset space \textvisiblespace{}
27669 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
27672 \begin_layout Plain Layout
27676 \begin_layout Plain Layout
27696 \begin_inset space \hfill{}
27702 \begin_layout Standard
27703 \begin_inset VSpace medskip
27712 also two different characters can be accented.
27718 \begin_inset space \textvisiblespace{}
27727 \begin_layout Plain Layout
27739 \begin_layout Standard
27752 can in combination with vowels directly be inserted with the keyboard without
27754 The same applies for the tilde
27758 \begin_layout Plain Layout
27759 This only applies for keyboards where the tilde is defined as accent.
27768 in combination with
27783 \begin_layout Standard
27826 and accents that are inserted directly with the keyboard are also available
27827 in mathematical text.
27828 For the other accents there are special math commands to be used in formulas,
27830 \begin_inset CommandInset ref
27832 reference "sub:Accents-for-one"
27839 \begin_layout Standard
27840 \begin_inset VSpace bigskip
27843 Furthermore, with the command
27850 \begin_inset Index idx
27853 \begin_layout Plain Layout
27861 all numbers and letters can be set into a circle, quasi accented with a
27862 circle, similar to the copyright symbol.
27865 \begin_layout Standard
27867 \begin_inset Tabular
27868 <lyxtabular version="3" rows="3" columns="2">
27869 <features rotate="0" tabularvalignment="middle">
27870 <column alignment="center" valignment="top">
27871 <column alignment="center" valignment="top">
27873 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
27876 \begin_layout Plain Layout
27882 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
27885 \begin_layout Plain Layout
27887 \begin_inset Note Note
27890 \begin_layout Plain Layout
27897 is only used as spacer.
27909 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
27912 \begin_layout Plain Layout
27920 <cell multicolumn="1" alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
27923 \begin_layout Plain Layout
27927 \begin_layout Plain Layout
27943 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
27946 \begin_layout Plain Layout
27957 raisebox{-1.5pt}{W}}
27962 <cell multicolumn="1" alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
27965 \begin_layout Plain Layout
27966 \begin_inset Formula $\raisebox{4.5mm}{}$
27973 \begin_layout Plain Layout
27991 \begin_inset Formula $\raisebox{-2mm}{}$
28007 \begin_layout Standard
28008 One has to take care that the character fits in the circle.
28019 \begin_layout Plain Layout
28021 \begin_inset CommandInset ref
28023 reference "sub:Font-Sizes"
28032 specifies thereby the size of the circle.
28043 \begin_layout Plain Layout
28045 \begin_inset CommandInset ref
28047 reference "sub:Boxes-without-Frame"
28056 the character can be centered.
28059 \begin_layout Subsection
28061 \begin_inset Index idx
28064 \begin_layout Plain Layout
28073 \begin_layout Standard
28074 Old-style figures (also known as old-style numerals) are created with the
28082 \begin_inset Index idx
28085 \begin_layout Plain Layout
28094 The command can be used in formulas and in TeX-mode.
28095 The command scheme is:
28098 \begin_layout Standard
28103 oldstylenums{number}
28106 \begin_layout Standard
28111 oldstylenums{0123456789
28114 \begin_inset Formula $\oldstylenums{0123456789}$
28120 \begin_layout Section
28122 \begin_inset CommandInset label
28124 name "sec:Formula-Styles"
28129 \begin_inset Index idx
28132 \begin_layout Plain Layout
28141 \begin_layout Itemize
28142 There are two different alignment styles:
28146 \begin_layout Description
28147 Centered is the predefined standard
28150 \begin_layout Description
28151 Indented for this the option
28155 must be inserted in the menu
28157 Document\SpecialChar \menuseparator
28163 \begin_inset space ~
28169 \begin_layout Standard
28174 is used, the indentation can be adjusted with the length
28181 \begin_inset Index idx
28184 \begin_layout Plain Layout
28193 Should the distance be 15
28194 \begin_inset space \thinspace{}
28197 mm, the following command line is inserted in the LaTeX-preamble
28200 \begin_layout Standard
28210 \begin_layout Standard
28211 When no length is specified, the predefined value of 30
28212 \begin_inset space \thinspace{}
28219 \begin_layout Itemize
28220 And two different numbering styles:
28224 \begin_layout Description
28225 Right is the predefined standard
28228 \begin_layout Description
28229 Left for this the option
28233 must be inserted in the menu
28235 Document\SpecialChar \menuseparator
28241 \begin_inset space ~
28248 \begin_layout Standard
28257 can also be used together.
28258 In this case both options are inserted, separated by a comma.
28261 \begin_layout Standard
28262 The chosen styles are used for all displayed formulas of the document.
28263 When both, centered and indented formulas should be created in a document,
28269 The indented formulas are then set in a flalign environment, see
28270 \begin_inset CommandInset ref
28272 reference "sub:Flalign-Environment"
28279 \begin_layout Section
28281 \begin_inset CommandInset label
28283 name "sec:Multiline-Formulas"
28288 \begin_inset Index idx
28291 \begin_layout Plain Layout
28292 Formula ! multiline
28300 \begin_layout Subsection
28304 \begin_layout Standard
28305 In LyX multiline formulas are created by pressing
28308 arg "newline-insert newline"
28312 This creates either an
28314 eqnarray environment
28316 that is described in
28317 \begin_inset CommandInset ref
28319 reference "sub:Eqnarray-Environment"
28323 or, when the option
28325 Use AMS math package
28327 in the document settings is selected, an
28331 that is described in
28332 \begin_inset CommandInset ref
28334 reference "sub:Standard-align-Environment"
28339 The align environment is recommended because it provides in any case a
28340 typographically correct output.
28343 \begin_layout Standard
28344 There are other multiline formula environments that can be created via the
28347 Insert\SpecialChar \menuseparator
28351 These environments are described in the following sections.
28354 \begin_layout Standard
28355 In all multiline formula environments a new line is created by pressing
28359 arg "newline-insert newline"
28363 To add or delete lines, the math toolbar buttons
28366 arg "inset-modify tabular append-row"
28372 arg "inset-modify tabular delete-row"
28375 , respectively, or the menu
28377 Edit\SpecialChar \menuseparator
28383 \begin_layout Subsubsection
28385 \begin_inset CommandInset label
28387 name "sub:Line-Separation"
28392 \begin_inset Index idx
28395 \begin_layout Plain Layout
28396 Formula ! multiline ! Line separation
28404 \begin_layout Standard
28405 There is sometimes not enough space in multiline formulas between the lines:
28406 \begin_inset Formula
28408 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}\\
28409 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
28417 \begin_layout Standard
28418 In LaTeX additional line space is specified as optional argument of the
28420 This is not yet possible in LyX
28424 \begin_layout Plain Layout
28426 \begin_inset CommandInset href
28428 name "LyX-bug #1505"
28429 target "http://www.lyx.org/trac/ticket/1505"
28438 , therefore the whole formula must be inserted in TeX-mode.
28439 To add in our example space, the command
28447 is inserted at the end of the first line.
28452 \begin_layout Plain Layout
28459 \begin_layout Plain Layout
28461 B^{2}(B^{2}-2r_{g}^{2}+2x_{0}^{2}-2r_{k}^{2})+4x_{0}^{2}x^{2}+4x_{0}xD &
28464 textrm{-}4x^{2}B^{2}+4x_{0}xB^{2}
28471 \begin_layout Plain Layout
28475 left(B^{2}+x_{0}^{2}
28483 left(B^{2}-2r_{g}^{2}+2x_{0}^{2}-2r_{k}^{2}
28488 \begin_layout Plain Layout
28500 \begin_layout Standard
28501 \begin_inset VSpace bigskip
28504 To set the line separation for all lines in a formula, the length
28511 \begin_inset Index idx
28514 \begin_layout Plain Layout
28524 \begin_inset Formula $\mbox{line separation}=\mathrm{6\, pt+\backslash jot}$
28535 \begin_inset space \thinspace{}
28540 \begin_inset space \thinspace{}
28543 mm additional line separation as in the previous example, the command
28546 \begin_layout Standard
28556 \begin_layout Standard
28557 is inserted in TeX-mode before the formula.
28558 This requires that the LaTeX-package
28566 \begin_layout Plain Layout
28571 is part of every LaTeX standard installation.
28577 \begin_inset Index idx
28580 \begin_layout Plain Layout
28586 was loaded in LaTeX-preamble with the line
28589 \begin_layout Standard
28597 \begin_layout Standard
28602 \begin_layout Plain Layout
28614 \begin_inset Formula
28616 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}\\
28617 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
28625 \begin_layout Standard
28629 \begin_layout Plain Layout
28640 To get back to the predefined distance,
28646 is set to the value 3
28647 \begin_inset space \thinspace{}
28653 \begin_layout Subsubsection
28655 \begin_inset CommandInset label
28657 name "sub:Column-Separation"
28662 \begin_inset Index idx
28665 \begin_layout Plain Layout
28666 Formula ! multiline ! Column separation
28674 \begin_layout Standard
28675 Multiline formulas form a matrix.
28676 A formula in the eqnarray environment is for example a matrix with three
28678 By changing the column separation in this environment, the space beside
28679 the relation sign can be changed.
28682 \begin_layout Standard
28683 The column separation is specified with the length
28690 \begin_inset Index idx
28693 \begin_layout Plain Layout
28702 \begin_inset Newline newline
28705 column separation = 2
28706 \begin_inset space \thinspace{}
28716 \begin_inset Newline newline
28722 \begin_layout Standard
28732 \begin_layout Standard
28733 inserted in TeX-mode, sets for all following formulas a column separation
28735 \begin_inset space \thinspace{}
28739 To get back to the predefined distance,
28746 \begin_inset space \thinspace{}
28752 \begin_layout Standard
28754 \begin_inset space \thinspace{}
28757 cm column separation:
28761 \begin_layout Plain Layout
28773 \begin_inset Formula
28781 A formula with the predefined column separation for matrices of 10
28782 \begin_inset space \thinspace{}
28789 \begin_layout Plain Layout
28801 \begin_inset Formula
28812 \begin_layout Subsubsection
28814 \begin_inset Index idx
28817 \begin_layout Plain Layout
28826 \begin_layout Standard
28827 Long formulas can be typeset using these methods:
28830 \begin_layout Itemize
28831 When one side of the equation is much shorter than the line width, this
28832 one is chosen for the left side and the right side is typeset over two
28834 \begin_inset Formula
28836 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 \\
28837 & & -\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}
28842 The minus sign at the beginning of the second line does normally not appear
28843 as an operator because it is the first character of the line.
28844 Thus it would not be surrounded by space and could not be distinguished
28845 from the fraction bar.
28847 \begin_inset space \thinspace{}
28850 pt space was inserted behind the minus sign with the command
28860 \begin_layout Plain Layout
28868 \begin_inset CommandInset ref
28870 reference "sub:Variable-Space"
28880 \begin_inset Index idx
28883 \begin_layout Plain Layout
28894 \begin_layout Itemize
28895 When both sides of the equation are too long, the command
28902 \begin_inset Index idx
28905 \begin_layout Plain Layout
28914 It is inserted in the first column of the first line and causes all further
28915 insertions to overwrite the following columns:
28916 \begin_inset Formula
28918 \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 \\
28919 & & -\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 \\
28920 & & =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}
28925 After the insertion of
28931 , the cursor is in a purple box that is a bit shifted to the left from the
28933 In this the formula is inserted.
28934 \begin_inset Newline newline
28937 The content of the further lines is inserted to the second or another formula
28939 The greater the column number where it was inserted, the larger the indentation.
28940 \begin_inset VSpace medskip
28944 \begin_inset Newline newline
28948 \begin_inset Note Greyedout
28951 \begin_layout Plain Layout
28952 Note the following when using
28961 \begin_layout Itemize
28962 The formula doesn't use the full page width.
28964 \begin_inset space \thinspace{}
28968 \begin_inset space \space{}
28972 \begin_inset Formula $-B^{2}$
28975 is added to the first line in the above example, it would have been outside
28977 To better use the width, negative space can be inserted at the beginning
28981 \begin_layout Itemize
28982 Due to a bug in LyX the cursor cannot be set with the mouse into the first
28987 \begin_layout Plain Layout
28988 \begin_inset CommandInset href
28990 name "LyX-bug #1429"
28991 target "http://www.lyx.org/trac/ticket/1429"
29000 One can only set the cursor at the beginning of the line and move it with
29009 \begin_layout Itemize
29010 Other methods to set long formulas are offered by the environments described
29012 \begin_inset CommandInset ref
29014 reference "sub:Multline-Environment"
29019 \begin_inset CommandInset ref
29021 reference "sub:Multiline-Formula-Parts"
29028 \begin_layout Subsubsection
29029 Multiline Fractions
29030 \begin_inset CommandInset label
29032 name "sub:Multiline-Fractions"
29037 \begin_inset Index idx
29040 \begin_layout Plain Layout
29041 Fractions ! multiline
29049 \begin_layout Standard
29050 There are cases where the denominator and/or the numerator of a fraction
29051 is so long that the fraction does not fit into one line.
29052 It is then necessary to add a line break within the fraction.
29053 This can be done using the command
29060 \begin_inset Index idx
29063 \begin_layout Plain Layout
29072 To activate it, set in the document settings under
29075 \begin_inset space ~
29085 \begin_inset Index idx
29088 \begin_layout Plain Layout
29089 Packages ! mathtools
29097 \begin_inset space ~
29112 \begin_layout Standard
29117 splitfrac{first line}{second line}
29120 \begin_layout Standard
29121 and is used as denominator and/or numerator:
29124 \begin_layout Standard
29125 \begin_inset Formula
29127 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}
29132 The command for the first numerator above is:
29135 \begin_layout Standard
29140 splitfrac{xy+xy+xy+xy+xy
29141 \begin_inset space \textvisiblespace{}
29149 \begin_layout Subsubsection
29151 \begin_inset CommandInset label
29153 name "sub:Multiline-Brackets"
29158 \begin_inset Index idx
29161 \begin_layout Plain Layout
29162 Brackets ! for multiline expressions
29170 \begin_layout Standard
29171 For brackets spanning multiple lines the following problem occurs:
29172 \begin_inset Formula
29174 A & = & \sin(x)\left[\prod_{R=1}^{\infty}\frac{1}{R}+\cdots\right.\\
29175 & & \left.\cdots+B-D\right]
29183 \begin_layout Standard
29184 The closing bracket is smaller than the opening bracket because brackets
29185 with variable size may not span multiple lines.
29188 \begin_layout Standard
29189 To set the bracket size for the second line correctly, the first line is
29197 \begin_inset Index idx
29200 \begin_layout Plain Layout
29208 and the second line with
29216 \begin_layout Plain Layout
29230 \begin_inset CommandInset ref
29232 reference "sub:Automatic-Bracket-Size"
29244 \begin_inset Index idx
29247 \begin_layout Plain Layout
29270 \begin_inset space \textvisiblespace{}
29280 \begin_inset space \textvisiblespace{}
29290 \begin_inset space \textvisiblespace{}
29296 \begin_inset Formula $\downarrow$
29302 \begin_inset Index idx
29305 \begin_layout Plain Layout
29313 is inserted, because the multiplication operator with its limits is the
29314 largest symbol in the first line and this should be the size for the bracket
29315 in the second line.
29318 \begin_layout Standard
29319 The result is this:
29320 \begin_inset Formula
29322 A & = & \sin(x)\left[\prod_{R=1}^{\infty}\frac{1}{R}+\cdots\right.\\
29323 & & \left.\vphantom{\prod_{R=1}^{\infty}}\cdots+B-D\right]
29331 \begin_layout Subsection
29335 \begin_layout Standard
29336 Align environments can be used for every kind of multiline formulas.
29337 They are especially useful to set several formulas side by side.
29340 \begin_layout Standard
29341 Align environments consist of columns.
29342 The odd columns are right aligned, the even ones left aligned.
29343 Every line in an Align environment can be numbered.
29346 \begin_layout Standard
29347 Align environments are created via the menu
29349 Insert\SpecialChar \menuseparator
29355 Edit\SpecialChar \menuseparator
29356 Math\SpecialChar \menuseparator
29357 Change Formula Type
29359 already existing formulas can be converted to Align environments.
29362 \begin_layout Standard
29363 To add or delete columns, the math toolbar buttons
29366 arg "inset-modify tabular append-column"
29372 arg "inset-modify tabular delete-column"
29375 , respectively, or the menu
29377 Edit\SpecialChar \menuseparator
29383 \begin_layout Subsubsection
29384 Standard align Environment
29385 \begin_inset CommandInset label
29387 name "sub:Standard-align-Environment"
29392 \begin_inset Index idx
29395 \begin_layout Plain Layout
29396 Formula ! multiline ! align environment
29404 \begin_layout Standard
29405 This Align environment is created by pressing
29408 arg "newline-insert newline"
29411 in a formula or by the menu
29413 Insert\SpecialChar \menuseparator
29414 Math\SpecialChar \menuseparator
29415 AMS align Environment
29420 \begin_layout Standard
29421 An example for two formulas set side by side, that are created with a four
29422 column align environment:
29423 \begin_inset Formula
29425 A & =\sin(B) & C & =D\\
29426 C & \ne A & B & \ne D
29431 As it can be seen, the formulas in this environment are placed so as if
29440 \begin_layout Plain Layout
29448 \begin_inset CommandInset ref
29450 reference "sub:Variable-Space"
29461 before the first and after every even column.
29462 When the formula style
29468 \begin_layout Plain Layout
29470 \begin_inset CommandInset ref
29472 reference "sec:Formula-Styles"
29483 is used, the formula is set without the
29489 before the first column.
29492 \begin_layout Subsubsection
29493 Alignat Environment
29494 \begin_inset Index idx
29497 \begin_layout Plain Layout
29498 Formula ! multiline ! alignat environment
29506 \begin_layout Standard
29507 The alignat environment has no predefined column separation.
29508 It can be inserted manually with the spaces that are described
29509 \begin_inset CommandInset ref
29511 reference "sub:Space"
29518 \begin_layout Standard
29519 The above example in the alignat environment where 1
29520 \begin_inset space \thinspace{}
29523 cm space was inserted at the beginning of the second formula:
29524 \begin_inset Formula
29525 \begin{alignat*}{2}
29526 A & =\sin(B) & \hspace{1cm}C & =D\\
29527 C & \ne A & B & \ne D
29532 Because the column separation can be set separately for every column, this
29533 environment is especially suitable to set three and more formulas side
29537 \begin_layout Subsubsection
29538 Flalign Environment
29539 \begin_inset CommandInset label
29541 name "sub:Flalign-Environment"
29546 \begin_inset Index idx
29549 \begin_layout Plain Layout
29550 Formula ! multiline ! flalign environment
29558 \begin_layout Standard
29559 In this environment the first two columns are always set as much as possible
29560 to the left and the last two ones to the right.
29562 \begin_inset Formula
29564 A & =1 & B & =2 & C & =3\\
29565 X & =\textrm{-}1 & Y & =\textrm{-}2 & Z & =4
29573 \begin_layout Standard
29574 By creating a flalign environment with an odd number of columns where an
29575 empty TeX-brace is inserted to the last column, several formulas in a document
29576 can be set to the left, although the formula style
29581 As example the indented formula
29582 \begin_inset CommandInset ref
29584 reference "eq:VolInt"
29589 \begin_inset Formula
29591 \hspace{30pt}\iiint\limits _{V}X\,\mathrm{d}V & =U & {}
29596 The first two columns contain the formula.
29597 To indent it as with the formula style
29602 \begin_inset space \thinspace{}
29605 pt space was inserted at the beginning of the first column.
29608 \begin_layout Subsection
29609 Eqnarray Environment
29610 \begin_inset CommandInset label
29612 name "sub:Eqnarray-Environment"
29617 \begin_inset Index idx
29620 \begin_layout Plain Layout
29621 Formula ! multiline ! eqnarray environment
29629 \begin_layout Standard
29630 When this environment has been created, three blue boxes appear.
29631 The content of the first box is right aligned, the content of the last
29633 The content of the middle box appears centered and a bit smaller, because
29634 it is designed to insert there only relation characters.
29635 \begin_inset Formula
29637 \frac{ABC}{D} & \frac{ABC}{D} & \frac{ABC}{D}\\
29647 \begin_layout Subsection
29649 \begin_inset Index idx
29652 \begin_layout Plain Layout
29653 Formula ! multiline ! gather environment
29661 \begin_layout Standard
29662 This environment consists of only one centered column.
29663 Every line can be numbered.
29664 \begin_inset Formula
29675 \begin_layout Subsection
29676 Multline Environment
29677 \begin_inset CommandInset label
29679 name "sub:Multline-Environment"
29684 \begin_inset Index idx
29687 \begin_layout Plain Layout
29688 Formula ! multiline ! multline environment
29696 \begin_layout Standard
29697 The multline environment consists, like the gather environment, of only
29699 But the first line is left aligned, the last one right aligned.
29700 All other lines are centered.
29701 Therefore this environment is suitable for long formulas.
29703 \begin_inset CommandInset ref
29705 reference "eq:lefteqn"
29709 in the multline environment:
29710 \begin_inset Formula
29712 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}\\
29713 -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}\\
29714 =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}}
29722 \begin_layout Standard
29723 In the output only the last (first) line of a multline environment appears
29724 numbered when the document numbering is right (left).
29728 \begin_layout Plain Layout
29729 numbering styles see
29730 \begin_inset CommandInset ref
29732 reference "sec:Formula-Styles"
29744 \begin_layout Standard
29752 \begin_inset Index idx
29755 \begin_layout Plain Layout
29770 \begin_inset Index idx
29773 \begin_layout Plain Layout
29781 a centered line can be right or left aligned, respectively.
29782 The commands are used as follows:
29785 \begin_layout Standard
29790 shoveright{line content}
29796 shoveleft{line content}
29799 \begin_layout Standard
29800 \begin_inset VSpace medskip
29810 \begin_inset Index idx
29813 \begin_layout Plain Layout
29821 specifies the distance of the first line from the left page margin.
29822 Predefined is the length 0
29823 \begin_inset space \thinspace{}
29829 \begin_layout Standard
29830 As example the above formula where the command
29833 \begin_layout Standard
29843 \begin_layout Standard
29844 was inserted in TeX-mode before:
29848 \begin_layout Plain Layout
29860 \begin_inset Formula
29862 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}\\
29863 \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}}\\
29864 =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}}
29873 \begin_layout Plain Layout
29884 The second line was left aligned using
29893 \begin_layout Subsection
29894 Multiline Formula Parts
29895 \begin_inset CommandInset label
29897 name "sub:Multiline-Formula-Parts"
29902 \begin_inset Index idx
29905 \begin_layout Plain Layout
29906 Formula ! multiline ! formula parts
29914 \begin_layout Standard
29915 To display only parts of a formula with multiple lines, one of the following
29916 environments is used:
29933 They can be inserted via the menu
29935 Insert\SpecialChar \menuseparator
29938 or by using the commands described in this section.
29941 \begin_layout Standard
29942 The first three have the same properties as the corresponding multiline
29943 formula environments, but it is possible to set further formula parts beside
29946 \begin_inset Formula
29948 \left.\begin{aligned}\Delta x\Delta p & \ge\frac{\hbar}{2}\\
29949 \Delta E\Delta t & \ge\frac{\hbar}{2}
29951 \right\} \textrm{Uncertainty relations}
29959 \begin_layout Standard
29960 To get this formula, a displayed formula is created where the command
29967 \begin_inset Index idx
29970 \begin_layout Plain Layout
29979 A purple box appears around the blue formula box where now columns and
29980 lines can be added.
29981 Outside the multiline environment other formula parts can be set, like
29985 \begin_layout Standard
29986 The aligned environment is also suitable for long formulas whose lines are
29987 horizontally aligned.
29988 Using aligned in a displayed formula has the advantage that the formula
29989 number is vertically centered behind the lines.
29991 \begin_inset CommandInset ref
29993 reference "eq:shortlong"
29997 in the aligned environment:
29998 \begin_inset Formula
30000 \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}|}\\
30001 & -\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}|}
30010 \begin_layout Standard
30011 To use the environments
30030 \begin_inset Index idx
30033 \begin_layout Plain Layout
30048 \begin_inset Index idx
30051 \begin_layout Plain Layout
30066 \begin_inset Index idx
30069 \begin_layout Plain Layout
30077 are inserted, respectively.
30078 The split environment has the same properties as the aligned environment
30079 but it can only have two columns.
30082 \begin_layout Subsection
30083 Text in multiline Formulas
30084 \begin_inset CommandInset label
30086 name "sub:Text-in-multiline"
30091 \begin_inset Index idx
30094 \begin_layout Plain Layout
30101 \begin_inset Index idx
30104 \begin_layout Plain Layout
30105 Formula ! multiline ! text
30113 \begin_layout Standard
30114 In the Align environments, and the multline and gather environment, text
30115 can be inserted that will appear in a separate line and doesn't affect
30116 the column alignment.
30117 To do this, the command
30124 \begin_inset Index idx
30127 \begin_layout Plain Layout
30135 is used in the following scheme:
30138 \begin_layout Standard
30146 \begin_layout Standard
30147 The text should not be longer than a line because it cannot be hyphenated.
30148 As LyX doesn't yet support
30154 directly, the text is written as mathematical text.
30161 must hereby be at the beginning of a line and appears in the output above
30163 An example where the text was inserted at the beginning of the second line:
30164 \begin_inset Formula
30166 I & =a\sqrt{2}\int_{0}^{2\pi}\sqrt{1+\cos(\phi)}\;\mathrm{d}\phi\\
30167 \intertext{\text{integrand is symmetric to \ensuremath{\phi=\pi}, therefore}} & =2a\sqrt{2}\int_{0}^{\pi}\sqrt{1+\cos(\phi)}\;\mathrm{d}\phi
30175 \begin_layout Standard
30182 always creates some vertical space between the text and the formula lines.
30183 To avoid this space, set in the document settings under
30186 \begin_inset space ~
30196 \begin_inset Index idx
30199 \begin_layout Plain Layout
30200 Packages ! mathtools
30208 \begin_inset space ~
30214 Then you can use the command
30221 \begin_inset Index idx
30224 \begin_layout Plain Layout
30241 \begin_layout Standard
30242 \begin_inset Formula
30244 I & =a\sqrt{2}\int_{0}^{2\pi}\sqrt{1+\cos(\phi)}\;\mathrm{d}\phi\\
30245 \shortintertext{\text{integrand is symmetric to \ensuremath{\phi=\pi}, therefore}} & =2a\sqrt{2}\int_{0}^{\pi}\sqrt{1+\cos(\phi)}\;\mathrm{d}\phi
30253 \begin_layout Section
30255 \begin_inset Index idx
30258 \begin_layout Plain Layout
30265 \begin_inset Index idx
30268 \begin_layout Plain Layout
30269 Formula ! numbering|see
30273 \begin_layout Plain Layout
30284 \begin_layout Plain Layout
30299 \begin_layout Subsection
30303 \begin_layout Standard
30304 Numbered formulas can be created with the menu
30306 Insert\SpecialChar \menuseparator
30307 Math\SpecialChar \menuseparator
30309 \begin_inset space ~
30317 \begin_inset space ~
30323 Existing formulas can be numbered with the menu
30325 Edit\SpecialChar \menuseparator
30326 Math\SpecialChar \menuseparator
30328 \begin_inset space ~
30336 arg "math-number-toggle"
30340 The formula number is displayed in LyX behind the formula as a number sign
30342 The number sign is replaced in the output by the formula number.
30345 \begin_layout Standard
30346 When numbering is turned on in multiline formulas, all lines will be numbered.
30347 But the numbering can be controlled with the menu
30349 Edit\SpecialChar \menuseparator
30350 Math\SpecialChar \menuseparator
30352 \begin_inset space ~
30356 \begin_inset space ~
30360 \begin_inset space ~
30368 arg "math-number-line-toggle"
30374 \begin_layout Standard
30375 Except for inline formulas, all formulas can be numbered with two different
30377 \begin_inset CommandInset ref
30379 reference "sec:Formula-Styles"
30386 \begin_layout Subsection
30388 \begin_inset Index idx
30391 \begin_layout Plain Layout
30392 Cross-references ! to formulas
30400 \begin_layout Standard
30401 All labeled formulas can be cross-referenced.
30402 A label is added by the menu
30404 Insert\SpecialChar \menuseparator
30407 or the toolbar button
30414 The cursor must hereby be inside a displayed formula.
30415 Alternatively you can right-click on the formula and choose
30420 A dialog pops up displaying the prefix
30425 The label is inserted there behind the prefix.
30426 The predefined prefix means
30427 \begin_inset Quotes eld
30431 \begin_inset Quotes erd
30434 and makes it easier to find labels in large documents because it marks
30435 it as formula label to divide it from e.
30436 \begin_inset space \thinspace{}
30440 \begin_inset space \space{}
30444 To change a label, the menu
30446 Insert\SpecialChar \menuseparator
30449 is used again or you right-click on a formula and then on
30456 \begin_layout Standard
30457 The name of the label is displayed in LyX within two parentheses behind
30459 A formula with a label is always numbered.
30462 \begin_layout Standard
30463 Cross-references are inserted via the menu
30465 Insert\SpecialChar \menuseparator
30468 or with the toolbar button
30471 arg "dialog-show-new-inset ref"
30475 A formula cross-reference appears in the output as formula number.
30476 When in the cross-reference dialog window the format
30480 is chosen, the cross-reference appears in the output as formula number
30482 \begin_inset Newline newline
30485 By right-clicking on a cross-reference in LyX, one jumps to the formula
30486 that is referenced.
30489 \begin_layout Standard
30490 Here are as examples cross-references to formulas of the following subsections:
30491 \begin_inset Note Note
30494 \begin_layout Plain Layout
30495 Note the different cross-reference types.
30503 \begin_layout Standard
30505 \begin_inset CommandInset ref
30512 \begin_inset CommandInset ref
30520 \begin_inset CommandInset ref
30526 ) big Latin letters are used for the numbering in contrary to (
30527 \begin_inset CommandInset ref
30536 \begin_layout Standard
30537 \begin_inset VSpace medskip
30540 When the argument of
30548 \begin_layout Plain Layout
30556 \begin_inset CommandInset ref
30558 reference "sub:User-defined-Numbering"
30569 contains a box like in
30570 \begin_inset CommandInset ref
30572 reference "sub:Paragraph-Boxes"
30576 , the formula cannot be referenced.
30579 \begin_layout Subsection
30581 \begin_inset Index idx
30584 \begin_layout Plain Layout
30585 Formula numbering ! subnumbering
30593 \begin_layout Standard
30594 With the help of the commands
30598 begin{subequations}
30606 formulas can be subnumbered.
30607 Both commands are inserted in TeX-mode.
30610 \begin_layout Standard
30612 \begin_inset Formula
30623 \begin_layout Plain Layout
30627 addtocounter{equation}{-1}
30636 \begin_layout Plain Layout
30640 begin{subequations}
30646 \begin_inset VSpace -5mm
30650 \begin_inset Formula
30658 \begin_inset Formula
30668 \begin_layout Standard
30672 \begin_layout Plain Layout
30684 \begin_layout Standard
30685 To create the example, the following is done:
30688 \begin_layout Enumerate
30689 first formula is inserted
30692 \begin_layout Enumerate
30697 addtocounter{equation}{-1}
30699 begin{subequations}
30700 \begin_inset Index idx
30703 \begin_layout Plain Layout
30712 \begin_inset Newline newline
30717 is inserted after the first formula
30720 \begin_layout Enumerate
30721 second formula is inserted
30724 \begin_layout Enumerate
30725 third formula is inserted
30728 \begin_layout Enumerate
30735 is inserted after the third formula
30738 \begin_layout Standard
30739 Every formula between the commands
30751 is subnumbered as a, b,
30752 \begin_inset Newline linebreak
30755 c, \SpecialChar \ldots{}
30756 For multiline formulas every line will be subnumbered.
30757 All subnumbered formulas are treated as
30762 But as every numbered formula increases the counter
30766 by one, the command
30772 is needed to decrease it.
30773 Otherwise the formulas
30774 \begin_inset CommandInset ref
30781 \begin_inset CommandInset ref
30788 \begin_inset CommandInset ref
30794 would be numbered as
30795 \begin_inset CommandInset ref
30802 \begin_inset CommandInset ref
30809 \begin_inset CommandInset ref
30818 \begin_layout Standard
30819 By inserting the commands in TeX-mode, a space is created between the first
30822 \begin_inset space \thinspace{}
30825 mm vertical space is inserted after the command
30829 begin{subequations}
30832 When the formula style
30838 \begin_layout Plain Layout
30840 \begin_inset CommandInset ref
30842 reference "sec:Formula-Styles"
30854 \begin_inset space \thinspace{}
30857 mm space is inserted instead.
30860 \begin_layout Standard
30861 Here is an example for a multiline formula where the numbering was turned
30862 off for the second line:
30866 \begin_layout Plain Layout
30870 begin{subequations}
30876 \begin_inset Formula
30878 A & = & (B-Z)^{2}=(B-Z)(B-Z)\label{eq:d}\\
30879 & = & B^{2}-ZB-BZ+Z^{2}\nonumber \\
30880 & = & B^{2}-2BZ+Z^{2}\label{eq:f}
30889 \begin_layout Plain Layout
30901 \begin_layout Subsection
30902 User-defined Numbering
30903 \begin_inset CommandInset label
30905 name "sub:User-defined-Numbering"
30910 \begin_inset Index idx
30913 \begin_layout Plain Layout
30914 Formula numbering ! user-defined
30922 \begin_layout Standard
30923 \begin_inset Index idx
30926 \begin_layout Plain Layout
30927 Formula numbering ! self-defined delimiters
30932 With the standard numbering parentheses are set around the formula number.
30933 To replace the parentheses for example by vertical bars, the following
30934 line is added to the LaTeX-preamble:
30937 \begin_layout Standard
30949 \begin_inset Note Note
30952 \begin_layout Plain Layout
30953 This macro is already declared in the LaTeX-preamble for testing.
30954 To activate it, remove the percent sign at the beginning.
30962 \begin_layout Standard
30963 To use other characters, the vertical bars besides the
30967 are replaced by one ore more characters.
30968 To get only the formula number the vertical bars are omitted.
30971 \begin_layout Standard
30972 \begin_inset VSpace bigskip
30975 When there should be an expression of your choice instead of the consecutive
30976 formula number in parentheses behind the formula, the command
30983 \begin_inset Index idx
30986 \begin_layout Plain Layout
30995 \begin_inset Formula
30997 A+B=C\tag{something}\label{eq:tag}
31002 In this example the command
31007 \begin_inset space \textvisiblespace{}
31012 was inserted in the formula.
31015 \begin_layout Standard
31021 \begin_inset space \textvisiblespace{}
31026 is inserted instead, the star prevents the parentheses around the expression:
31027 \begin_inset Formula
31029 A+B=C\tag*{something}
31037 \begin_layout Standard
31038 \begin_inset VSpace bigskip
31041 To restart the formula numbering with new document parts or sections, the
31042 following command is used:
31045 \begin_layout Standard
31050 @addtoreset{equation}{part}
31053 \begin_inset Index idx
31056 \begin_layout Plain Layout
31061 \begin_layout Plain Layout
31072 \begin_layout Plain Layout
31085 \begin_layout Plain Layout
31096 \begin_layout Plain Layout
31109 \begin_inset Newline newline
31113 \begin_inset Newline newline
31120 @addtoreset{equation}{section}
31123 \begin_layout Standard
31124 To be able to use these commands in TeX-mode, the
31125 \begin_inset Quotes eld
31129 \begin_inset Quotes erd
31132 character has to be made
31133 \begin_inset Quotes eld
31137 \begin_inset Quotes erd
31140 for LaTeX using the command
31154 So the command sequence in TeX-mode is:
31157 \begin_layout Standard
31163 \begin_inset Newline newline
31168 @addtoreset{equation}{section}
31169 \begin_inset Newline newline
31177 \begin_layout Standard
31178 In the LaTeX-preamble
31190 can be omitted as they are automatically internally inserted by LyX.
31193 \begin_layout Standard
31208 \begin_layout Plain Layout
31213 is part of the LaTeX-package
31218 \begin_inset Index idx
31221 \begin_layout Plain Layout
31222 Packages ! carlisle
31227 that is part of every LaTeX standard installation.
31233 \begin_inset Index idx
31236 \begin_layout Plain Layout
31237 Packages ! remreset
31242 has to be loaded in the LaTeX-preamble with the line
31245 \begin_layout Standard
31250 usepackage{remreset}
31253 \begin_layout Standard
31261 \begin_inset Index idx
31264 \begin_layout Plain Layout
31269 \begin_layout Plain Layout
31280 \begin_layout Plain Layout
31293 \begin_layout Plain Layout
31304 \begin_layout Plain Layout
31316 can be used with the same scheme as
31325 \begin_layout Standard
31326 \begin_inset VSpace bigskip
31329 Sometimes formulas should be numbered in the following form:
31332 \begin_layout Standard
31335 (section number.formula number)
31338 \begin_layout Standard
31339 The formula number should start with every section with
31340 \begin_inset Quotes eld
31344 \begin_inset Quotes erd
31350 \begin_layout Standard
31351 For this case there is the command
31358 \begin_inset Index idx
31361 \begin_layout Plain Layout
31369 , which is used with the following scheme:
31372 \begin_layout Standard
31377 numberwithin{counter}{sectioning}
31380 \begin_layout Standard
31381 Counter denotes what kind of numbering is affected, sectioning denotes what
31382 number is before the dot.
31385 \begin_layout Standard
31386 Thus in our case the following LaTeX-preamble or TeX code line is used:
31389 \begin_layout Standard
31394 numberwithin{equation}{section}
31397 \begin_layout Standard
31398 This is the result:
31402 \begin_layout Plain Layout
31406 numberwithin{equation}{section}
31412 \begin_inset Formula
31422 \begin_layout Standard
31424 \begin_inset space \thinspace{}
31428 \begin_inset space \space{}
31431 tables so that the number of the part is the sectioning,
31432 \begin_inset Newline newline
31439 numberwithin{table}{part}
31444 \begin_layout Standard
31445 To go back to the standard numbering or to prevent this kind of numbering
31446 when it is defined by the document class, the following command is inserted
31447 as TeX code or to the LaTeX-preamble:
31450 \begin_layout Standard
31460 \begin_inset Index idx
31463 \begin_layout Plain Layout
31477 \begin_layout Plain Layout
31493 \begin_inset Newline newline
31501 \begin_inset Newline newline
31513 \begin_layout Standard
31520 uses internally the command
31526 , described above, that also needs to be reverted.
31530 \begin_layout Plain Layout
31537 \begin_layout Plain Layout
31541 @removefromreset{equation}{section}
31544 \begin_layout Plain Layout
31556 \begin_layout Subsection
31557 Numbering with Roman Numbers and Letters
31558 \begin_inset Index idx
31561 \begin_layout Plain Layout
31562 Formula numbering ! with letters
31568 \begin_inset Index idx
31571 \begin_layout Plain Layout
31572 Formula numbering ! with Roman numbers
31580 \begin_layout Standard
31581 Formulas can also be numbered with Roman numbers and Latin letters.
31582 To number for example with small Roman numbers, the command
31585 \begin_layout Standard
31597 \begin_layout Standard
31598 is inserted before the formula in TeX-mode.
31606 \begin_inset Index idx
31609 \begin_layout Plain Layout
31617 redefines the predefined command
31633 \begin_layout Plain Layout
31640 has the same scheme like the command
31646 that is described in
31647 \begin_inset CommandInset ref
31649 reference "sub:The-Command-newcommand"
31662 is the formula counter.
31669 is used as prefix for a counter, the value of the counter is output as
31671 When a formula is numbered, LaTeX sets internally the command
31677 behind the formula.
31683 \begin_inset Index idx
31686 \begin_layout Plain Layout
31696 outputs the counter as small Roman number.
31699 \begin_layout Standard
31700 All formulas behind the command
31710 are now numbered Roman.
31711 To switch to numbering with big Roman numbers, the command is inserted
31725 \begin_inset Index idx
31728 \begin_layout Plain Layout
31740 \begin_inset Quotes eld
31744 \begin_inset Quotes erd
31747 with small Latin letters there is the command
31754 \begin_inset Index idx
31757 \begin_layout Plain Layout
31765 , for big ones there is the command
31772 \begin_inset Index idx
31775 \begin_layout Plain Layout
31788 \begin_layout Standard
31789 \begin_inset Note Greyedout
31792 \begin_layout Plain Layout
31799 \begin_inset space ~
31802 formulas can be numbered with Latin letters in one document.
31810 \begin_layout Standard
31811 \begin_inset Newpage newpage
31817 \begin_layout Standard
31821 \begin_layout Plain Layout
31837 \begin_layout Standard
31838 \begin_inset Formula
31840 A=\textrm{small roman}
31849 \begin_layout Plain Layout
31863 \begin_inset Formula
31865 B=\textrm{big Roman}\label{eq:Rom}
31874 \begin_layout Plain Layout
31888 \begin_inset Formula
31890 C=\textrm{small Latin}
31899 \begin_layout Plain Layout
31913 \begin_inset Formula
31915 D=\textrm{big Latin}\label{eq:Lat}
31923 \begin_layout Standard
31924 To switch back to the default numbering, insert the command:
31927 \begin_layout Standard
31937 \begin_inset Index idx
31940 \begin_layout Plain Layout
31951 \begin_layout Standard
31955 \begin_layout Plain Layout
31969 \begin_inset Formula
31979 \begin_layout Standard
31980 \begin_inset VSpace medskip
31983 As you see, formulas are numbered serially independent from the numbering
31985 When then numbering should start with
31986 \begin_inset Quotes eld
31990 \begin_inset Quotes erd
31993 when the style is changed, new equation counters have to be defined.
31994 A description about this can be found in the file
31995 \begin_inset CommandInset href
31997 name "Formula-numbering.lyx"
31998 target "run:Formula-numbering.lyx"
32005 \begin_layout Section
32006 Chemical Symbols and Equations
32007 \begin_inset CommandInset label
32009 name "sub:Chemical-Symbols-and"
32014 \begin_inset Index idx
32017 \begin_layout Plain Layout
32018 Chemical characters ! Symbols
32024 \begin_inset Index idx
32027 \begin_layout Plain Layout
32034 \begin_inset Index idx
32037 \begin_layout Plain Layout
32046 \begin_layout Standard
32047 An example text from chemistry:
32050 \begin_layout Quote
32052 \begin_inset Formula $\mathrm{SO_{4}^{2-}}$
32055 -ion reacts with two
32056 \begin_inset Formula $\mathrm{Na^{+}}$
32059 -ions to sodium sulfate
32060 \begin_inset Formula $\left(\mathrm{Na_{2}SO_{4}}\right)$
32064 The chemical equation for this is:
32065 \begin_inset Formula
32067 \mathrm{2\, Na^{+}+SO_{4}^{2-}\longrightarrow Na_{2}SO_{4}}\label{eq:chem-reaction}
32075 \begin_layout Standard
32076 This chemical equation can directly be created as formula.
32077 To avoid that the symbols appear italic, everything is highlighted and
32078 changed by the shortcut
32084 to the upright font style.
32088 \begin_layout Plain Layout
32094 \begin_inset CommandInset ref
32096 reference "sub:Font-Styles"
32108 \begin_layout Standard
32109 A more convenient way to typeset chemical formulas is to use the command
32117 \begin_inset Index idx
32120 \begin_layout Plain Layout
32128 that is available when the LaTeX-package
32133 \begin_inset Index idx
32136 \begin_layout Plain Layout
32149 to a formula a new blue box appears where chemical formulas can be inserted
32150 in an intuitive way.
32153 \begin_layout Standard
32155 \begin_inset Tabular
32156 <lyxtabular version="3" rows="9" columns="2">
32157 <features rotate="0" tabularvalignment="middle">
32158 <column alignment="center" valignment="top">
32159 <column alignment="center" valignment="top">
32161 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
32164 \begin_layout Plain Layout
32170 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
32173 \begin_layout Plain Layout
32175 \begin_inset Note Note
32178 \begin_layout Plain Layout
32185 is only used as spacer.
32197 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
32200 \begin_layout Plain Layout
32204 \begin_inset space \textvisiblespace{}
32212 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
32215 \begin_layout Plain Layout
32216 \begin_inset Formula $\raisebox{4.5mm}{}\ce{H2CO3}\raisebox{-2mm}{}$
32226 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
32229 \begin_layout Plain Layout
32233 \begin_inset space \textvisiblespace{}
32241 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
32244 \begin_layout Plain Layout
32245 \begin_inset Formula $\raisebox{5mm}{}\ce{SO4^{2-}}\raisebox{-2mm}{}$
32255 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
32258 \begin_layout Plain Layout
32262 \begin_inset space \textvisiblespace{}
32270 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
32273 \begin_layout Plain Layout
32274 \begin_inset Formula $\raisebox{4.5mm}{}\ce{(NH4)2S}\raisebox{-2mm}{}$
32284 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
32287 \begin_layout Plain Layout
32291 \begin_inset space \textvisiblespace{}
32299 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
32302 \begin_layout Plain Layout
32303 \begin_inset Formula $\raisebox{4.5mm}{}\ce{KCr(SO4)2.12H2O}\raisebox{-2mm}{}$
32313 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
32316 \begin_layout Plain Layout
32320 \begin_inset space \textvisiblespace{}
32326 \begin_inset space \textvisiblespace{}
32332 \begin_inset space \textvisiblespace{}
32340 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
32343 \begin_layout Plain Layout
32344 \begin_inset Formula $\raisebox{4.5mm}{}\ce{A-B\dbond C\tbond D}\raisebox{-2mm}{}$
32354 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
32357 \begin_layout Plain Layout
32361 \begin_inset space \textvisiblespace{}
32365 \begin_inset Formula $\downarrow$
32369 \begin_inset Formula $\to$
32377 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
32380 \begin_layout Plain Layout
32381 \begin_inset Formula $\raisebox{5mm}{}\ce{_{90}^{227}Th+}\raisebox{-2mm}{}$
32391 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
32394 \begin_layout Plain Layout
32398 \begin_inset space \textvisiblespace{}
32402 \begin_inset space \textvisiblespace{}
32406 \begin_inset space \textvisiblespace{}
32410 \begin_inset space \textvisiblespace{}
32414 \begin_inset space \textvisiblespace{}
32422 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
32425 \begin_layout Plain Layout
32426 \begin_inset Formula $\raisebox{4.5mm}{}\ce{CO2 + C <=> 2CO}\raisebox{-2mm}{}$
32436 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
32439 \begin_layout Plain Layout
32443 \begin_inset space \textvisiblespace{}
32447 \begin_inset space \textvisiblespace{}
32451 \begin_inset space \textvisiblespace{}
32455 \begin_inset space \textvisiblespace{}
32463 \begin_inset space \textvisiblespace{}
32471 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
32474 \begin_layout Plain Layout
32475 \begin_inset Formula $\raisebox{5mm}{}\ce{CO2 + C ->[\alpha][\beta] 2CO}\raisebox{-4mm}{}$
32491 \begin_layout Standard
32492 \begin_inset Note Greyedout
32495 \begin_layout Plain Layout
32501 Inserting a formula to a
32507 box will lead to LaTeX errors due to a LyX bug.
32513 \begin_layout Plain Layout
32514 \begin_inset CommandInset href
32516 name "LyX-bug #8566"
32517 target "http://www.lyx.org/trac/ticket/8566"
32528 In this case TeX code has to be used like for
32542 \begin_layout Plain Layout
32563 \begin_layout Standard
32564 \begin_inset Note Greyedout
32567 \begin_layout Plain Layout
32573 It is not possible in LyX to use the character ^ to get an up-arrow as
32579 One instead uses a negative thin space followed by the command
32586 \begin_inset Formula $\ce{Fe + 2H+ -> Fe^{2+} + H2\negthinspace\uparrow}$
32597 \begin_layout Standard
32604 the command for equation
32605 \begin_inset space ~
32609 \begin_inset CommandInset ref
32611 reference "eq:chem-reaction"
32616 \begin_inset Newline newline
32624 \begin_inset space \textvisiblespace{}
32628 \begin_inset space \textvisiblespace{}
32632 \begin_inset space \textvisiblespace{}
32636 \begin_inset space \textvisiblespace{}
32640 \begin_inset space \textvisiblespace{}
32644 \begin_inset space \textvisiblespace{}
32650 \begin_layout Standard
32651 To create multiline chemical equations first a multiline formula is created
32653 \begin_inset CommandInset ref
32655 reference "sec:Multiline-Formulas"
32660 Afterwards the command
32666 is used in every small blue box of the formula.
32668 \begin_inset CommandInset ref
32670 reference "eq:TEOS-reaction-1"
32675 \begin_inset CommandInset ref
32677 reference "eq:TEOS-reaction-2"
32681 are an example of a multi-stage chemical reaction where every equation
32682 has its own number.
32683 \begin_inset Formula
32685 \ce{TEOS + 4O} & \ce{->} & \ce{Si(OH)4 + 4C2H4O}\label{eq:TEOS-reaction-1}\\
32686 \ce{Si(OH)4} & \ce{->} & \ce{SiO2 + 2H2O}\label{eq:TEOS-reaction-2}
32694 \begin_layout Standard
32705 package provides the command
32712 \begin_inset Index idx
32715 \begin_layout Plain Layout
32723 that has to be used for special cases.
32724 For more information about
32730 and more examples have a look at the documentation of
32735 \begin_inset CommandInset citation
32744 \begin_layout Section
32748 \begin_layout Standard
32749 LyX supports two types of commutative diagrams:
32757 that are explained in the following.
32760 \begin_layout Subsection
32762 \begin_inset Index idx
32765 \begin_layout Plain Layout
32774 \begin_layout Standard
32775 Diagrams of this type visualize relations by vertical and horizontal lines
32777 \begin_inset Formula
32779 \begin{CD}A@>>>B@>>>C\\
32790 \begin_layout Standard
32791 To get them, the command
32796 \begin_inset Index idx
32799 \begin_layout Plain Layout
32809 is inserted to a formula.
32810 A blue box appears with two dashed lines where further commands can be
32815 arg "newline-insert newline"
32818 a new line is created.
32819 Horizontal relations are inserted in odd, vertical in even formula lines.
32822 \begin_layout Standard
32823 To create the relations there are the following commands:
32826 \begin_layout Itemize
32831 creates a left arrow,
32842 \begin_layout Itemize
32847 creates an up arrow,
32855 a vertical equal sign
32858 \begin_layout Itemize
32864 is a placeholder for non-existent relations
32867 \begin_layout Standard
32868 All arrows can be labeled as follows:
32871 \begin_layout Itemize
32872 If text inserted between the first and second < or >, resp., it is placed
32874 When it is inserted between the second and third one, it appears under
32878 \begin_layout Itemize
32879 When text for vertical arrows is inserted between the first and second A
32880 or V, resp., it is placed left beside the arrow.
32881 When it is inserted between the second and third one, it appears right
32883 If the text contains an A or V, these letters must be set into a TeX-brace.
32886 \begin_layout Standard
32887 As example a diagram with all possible relations:
32890 \begin_layout Standard
32891 \begin_inset Formula
32893 \begin{CD}A@>j>>B@>>k>C@=F\\
32904 \begin_layout Standard
32905 The command for this is:
32906 \begin_inset Newline newline
32914 \begin_inset space \textvisiblespace{}
32917 A@>j>>B@>>k>C@=F Ctrl+Return
32918 \begin_inset Newline newline
32922 \begin_inset Phantom HPhantom
32925 \begin_layout Plain Layout
32931 \begin_inset space \textvisiblespace{}
32944 \begin_inset Formula $\to$
32950 \begin_inset Newline newline
32954 \begin_inset Phantom HPhantom
32957 \begin_layout Plain Layout
32963 \begin_inset space \textvisiblespace{}
32974 \begin_layout Subsection
32976 \begin_inset Index idx
32979 \begin_layout Plain Layout
32980 Diagrams ! xymatrix
32988 \begin_layout Standard
32989 To be able to use xymatrices, the LaTeX-package
32994 A xymatrix is created by inserting the command
33001 Then you are able to add new matrix columns and rows like for normal matrices,
33003 \begin_inset CommandInset ref
33005 reference "sec:Matrices"
33012 \begin_layout Standard
33013 In contrary to amscd diagrams, xymatrices supports diagonal and curved arrows,
33015 All possibilities to create commutative diagrams and decorations are explained
33020 that you find in the menu
33022 Help\SpecialChar \menuseparator
33024 \begin_inset space ~
33032 \begin_layout Subsection
33038 \begin_inset Index idx
33041 \begin_layout Plain Layout
33050 \begin_layout Standard
33055 -diagrams, the LaTeX-package
33064 -diagram is created by inserting the command
33071 Then you are able to add new matrix columns and rows like for normal matrices,
33073 \begin_inset CommandInset ref
33075 reference "sec:Matrices"
33082 \begin_layout Standard
33083 Examples how to create
33087 diagrams in LyX is given in the
33089 Feynman-diagram manual
33091 that you find in the menu
33093 Help\SpecialChar \menuseparator
33095 \begin_inset space ~
33103 \begin_layout Section
33104 User-defined Commands
33105 \begin_inset Index idx
33108 \begin_layout Plain Layout
33109 User-defined commands
33117 \begin_layout Standard
33118 \begin_inset Note Greyedout
33121 \begin_layout Plain Layout
33126 The names of user-defined commands and macros may only consist of Latin
33135 \begin_layout Subsection
33139 \begin_inset CommandInset label
33141 name "sub:The-Command-newcommand"
33146 \begin_inset Index idx
33149 \begin_layout Plain Layout
33150 User-defined commands !
33158 \begin_inset Index idx
33161 \begin_layout Plain Layout
33172 \begin_layout Standard
33173 Many LaTeX-commands are too long to be used frequently.
33174 But it is possible to define with the command
33180 new shorter commands.
33183 \begin_layout Standard
33184 The command scheme of
33193 \begin_layout Standard
33198 newcommand{new command name}[number of arguments][optional
33203 \begin_inset Newline newline
33207 \begin_inset Phantom HPhantom
33210 \begin_layout Plain Layout
33220 {command definition}
33223 \begin_layout Standard
33224 \begin_inset Note Greyedout
33227 \begin_layout Plain Layout
33232 Assure that the name of the new command is not already used in your document
33233 or by LaTeX-packages that you use.
33234 When you for example define the command
33246 , you get an error message because
33252 is already defined as command for
33253 \begin_inset Quotes eld
33257 \begin_inset Formula $\le$
33261 \begin_inset Quotes erd
33272 \begin_layout Standard
33273 The number of arguments is an integer in the range 0
33274 \begin_inset space \thinspace{}
33278 \begin_inset space \thinspace{}
33281 9 and specifies how many arguments the new command should have.
33282 With the optional value a value for an optional argument can be predefined.
33283 When this is done, the
33291 rgument of the new command is automatically an optional one.
33294 \begin_layout Standard
33295 Here are some examples:
33298 \begin_layout Itemize
33299 To define the command
33311 , the LaTeX-preamble line is:
33312 \begin_inset VSpace medskip
33316 \begin_inset Newline newline
33330 \begin_layout Itemize
33331 To define the command
33343 , the argument (that should be underlined) must be taken into account.
33344 For this the preamble line is:
33345 \begin_inset VSpace medskip
33349 \begin_inset Newline newline
33363 \begin_inset VSpace medskip
33367 \begin_inset Newline newline
33374 acts as argument placeholder, the
33378 behind it denotes that it is the placeholder for the first argument.
33381 \begin_layout Itemize
33389 \begin_inset space \thinspace{}
33393 \begin_inset space \space{}
33403 \begin_inset VSpace medskip
33407 \begin_inset Newline newline
33418 framebox#1#2{$#3$}}
33421 \begin_inset VSpace medskip
33425 \begin_inset Newline newline
33428 The two Dollar signs creates the extra formula needed for
33435 \begin_inset CommandInset ref
33437 reference "sub:Boxes-with-Frame"
33444 \begin_layout Itemize
33445 To create a new command for
33451 where the color for the box need not be specified, the argument for the
33452 color is defined optional:
33453 \begin_inset VSpace medskip
33457 \begin_inset Newline newline
33468 fcolorbox{#2}{#1}{$#3$}}
33471 \begin_inset VSpace medskip
33475 \begin_inset Newline newline
33478 When the color is not specified when using
33484 , the predefined color
33491 \begin_layout Standard
33492 A test of the new defined commands:
33495 \begin_layout Standard
33497 \begin_inset Tabular
33498 <lyxtabular version="3" rows="6" columns="2">
33499 <features rotate="0" tabularvalignment="middle">
33500 <column alignment="center" valignment="top">
33501 <column alignment="center" valignment="top">
33503 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
33506 \begin_layout Plain Layout
33512 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
33515 \begin_layout Plain Layout
33517 \begin_inset Note Note
33520 \begin_layout Plain Layout
33527 is only used as spacer.
33539 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
33542 \begin_layout Plain Layout
33546 \begin_inset space \textvisiblespace{}
33554 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
33557 \begin_layout Plain Layout
33558 \begin_inset Formula $A\gr B$
33568 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
33571 \begin_layout Plain Layout
33579 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
33582 \begin_layout Plain Layout
33583 \begin_inset Formula $\raisebox{4.5mm}{}\us{ABcd}\raisebox{-2mm}{}$
33593 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
33596 \begin_layout Plain Layout
33600 \begin_inset Formula $\to$
33606 \begin_inset Formula $\to$
33614 \begin_inset space \textvisiblespace{}
33622 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
33625 \begin_layout Plain Layout
33626 \begin_inset Formula $\raisebox{6mm}{}\fb{[2cm]}{}{\int A=B}\raisebox{-4mm}{}$
33636 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
33639 \begin_layout Plain Layout
33643 \begin_inset Formula $\to$
33651 \begin_inset space \textvisiblespace{}
33659 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
33662 \begin_layout Plain Layout
33663 \begin_inset Formula $\raisebox{6mm}{}\cb{red}{\int A=B}\raisebox{-4mm}{}$
33673 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
33676 \begin_layout Plain Layout
33682 \begin_inset Formula $\to$
33690 \begin_inset space \textvisiblespace{}
33698 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
33701 \begin_layout Plain Layout
33702 \begin_inset Formula $\raisebox{6mm}{}\cb[green]{red}{\int A=B}\raisebox{-4mm}{}$
33718 \begin_layout Subsection
33720 \begin_inset Index idx
33723 \begin_layout Plain Layout
33724 User-defined commands! Math macros
33730 \begin_inset Index idx
33733 \begin_layout Plain Layout
33742 \begin_layout Standard
33743 User-defined commands are especially convenient for complex expressions.
33744 When you are for example dealing with a document that has quadratic equations,
33745 the same solution type occurs several times.
33746 The general form of a quadratic equation is
33747 \begin_inset Formula
33749 0=\lambda^{2}+p\lambda+q
33754 The general form of the solution is
33755 \begin_inset Formula
33757 \lambda_{1,2}=-\frac{p}{2}\pm\sqrt{\frac{p²}{4}-q}
33765 \begin_layout Standard
33766 To define a command for the solution formula where only the three parameters
33768 \begin_inset Formula $\lambda$
33772 \begin_inset Formula $p$
33776 \begin_inset Formula $q$
33779 need to be specified and the index of
33780 \begin_inset Formula $\lambda$
33783 can be given optionally, the LaTeX-preamble line is
33784 \begin_inset Newline newline
33800 \begin_inset Newline newline
33804 \begin_inset Phantom HPhantom
33807 \begin_layout Plain Layout
33821 frac{#3^{2}}{4}-#4}}
33824 \begin_layout Standard
33825 To create with this the solution formula, the command
33826 \begin_inset Newline newline
33836 \begin_inset Formula $\to$
33842 \begin_inset Formula $\to$
33849 is inserted to a formula
33854 \begin_layout Standard
33855 The definition of the new command is unintuitive because one has to know
33856 the schemes of all used LaTeX commands, e.
33857 \begin_inset space \thinspace{}
33861 \begin_inset space \space{}
33864 that a fraction is inserted in LaTeX as
33868 frac{numerator}{denominator}
33871 Furthermore one can easily forget a brace in the definition and cannot
33872 see in LyX what the new command is doing.
33873 To avoid these problems LyX offers the possibility to use math macros instead
33883 \begin_layout Standard
33884 A math macro is created by using the menu
33886 Insert\SpecialChar \menuseparator
33887 Math\SpecialChar \menuseparator
33890 or the toolbar button
33893 arg "math-macro newmacroname_newcommand"
33897 The math macro toolbar appears together with the following box where the
33899 \begin_inset Newline newline
33903 \begin_inset space \hspace*{\fill}
33907 \begin_inset Graphics
33908 filename clipart/macrobox.png
33913 \begin_inset space \hspace*{\fill}
33917 \begin_inset Newline newline
33921 \begin_inset FormulaMacro
33922 \newcommand{\qG}[4][1,\,2]{#2_{#1}=-\frac{#3}{2}\pm\sqrt{\frac{#3^{2}}{4}-#4}}
33927 newmacroname is the default name of the macro that should be changed to
33928 something sensible.
33929 The wanted formula is inserted in the first blue box.
33930 An argument placeholder is inserted with the command
33937 \begin_inset space \thinspace{}
33941 \begin_inset space \space{}
33950 or by using the macro toolbar button
33953 arg "math-macro-add-param"
33957 Argument placeholders are displayed red.
33959 \begin_inset space ~
33962 arguments are possible.
33963 Optional arguments are created with the toolbar button
33966 arg "math-macro-add-optional-param"
33970 The first non-optional argument can be transformed to an optional one with
33974 arg "math-macro-make-optional"
33978 In the second blue box the appearance of the macro in LyX can be defined.
33979 Normally you want to see it as it is defined, so the box is kept empty.
33980 But when you have created a macro that needs lot of space on the screen,
33981 you can insert in the box for example
33982 \begin_inset Newline newline
34012 \begin_inset Newline newline
34017 For the macro only the arguments with the macro name in front of them will
34018 then be displayed in LyX, leading to a better overview.
34019 The formula appears in the output as defined in the first box.
34020 \begin_inset Newline newline
34023 The appearance of macros in formulas can furthermore be changed for single
34024 macros by setting the cursor in the macro and using the menu
34026 View\SpecialChar \menuseparator
34028 \begin_inset space ~
34032 \begin_inset space ~
34040 \begin_layout Standard
34041 To use a macro, the macro name is inserted as command to a formula, in our
34049 Our macro looks in LyX like this:
34050 \begin_inset Newline newline
34054 \begin_inset space \hspace*{\fill}
34058 \begin_inset Graphics
34059 filename clipart/macrouse.png
34064 \begin_inset space \hspace*{\fill}
34068 \begin_inset Newline newline
34071 Here is our macro example with the arguments
34072 \begin_inset Formula $x$
34076 \begin_inset Formula $\ln(x)$
34080 \begin_inset Formula $B$
34086 \begin_layout Standard
34087 \begin_inset Formula
34097 \begin_layout Standard
34098 LyX offers in the menu
34100 Tools\SpecialChar \menuseparator
34101 Preferences\SpecialChar \menuseparator
34102 Editing\SpecialChar \menuseparator
34105 different styles to edit macros.
34106 To find the style that suits you the most, choose a style and set the cursor
34107 in a macro formula to see the difference.
34110 \begin_layout Standard
34111 A math macro is transformed internally to a
34117 command when exporting the document.
34124 command is not placed in the LaTeX-preamble, therefore macros can only
34125 be used in formulas that are in the document below the macro definition
34129 \begin_layout Standard
34130 Math macros can also be directly created from a
34137 When writing for example the command
34140 \begin_inset Newline newline
34149 xleftarrow[#2]{#1}}
34150 \begin_inset Newline newline
34155 in LyX as normal text, highlighting it completely and using then the shortcut
34160 , the command will be transformed to a math macro.
34161 Using this method you need to be careful that the
34167 command is typed correctly, otherwise you get a faulty macro leading to
34171 \begin_layout Standard
34172 Math macros currently have the problem that further formulas in macro definition
34173 s are handled wrongly.
34174 Therefore the example
34181 \begin_inset CommandInset ref
34183 reference "sub:The-Command-newcommand"
34187 cannot be created as macro.
34190 \begin_layout Standard
34191 When the cursor is in a macro definition box, you will see the macro toolbar
34195 \begin_layout Standard
34196 \begin_inset VSpace defskip
34202 \begin_layout Standard
34203 \begin_inset Graphics
34204 filename clipart/MacroToolbar.png
34209 \begin_inset Index idx
34212 \begin_layout Plain Layout
34221 \begin_layout Standard
34222 \begin_inset VSpace defskip
34228 \begin_layout Standard
34229 The macro toolbar contains from left to right the following buttons:
34232 \begin_layout Standard
34233 \begin_inset VSpace defskip
34239 \begin_layout Standard
34240 \begin_inset Tabular
34241 <lyxtabular version="3" rows="9" columns="2">
34242 <features rotate="0" islongtable="true" longtabularalignment="center">
34243 <column alignment="left" valignment="top">
34244 <column alignment="left" valignment="top" width="85col%">
34245 <row interlinespace="2.5mm">
34246 <cell alignment="center" valignment="top" usebox="none">
34249 \begin_layout Plain Layout
34252 arg "math-macro-remove-param"
34260 <cell alignment="center" valignment="top" usebox="none">
34263 \begin_layout Plain Layout
34266 Edit\SpecialChar \menuseparator
34267 Math\SpecialChar \menuseparator
34269 \begin_inset space ~
34272 Definition\SpecialChar \menuseparator
34273 Remove Last Argument
34279 <row interlinespace="2.5mm">
34280 <cell alignment="center" valignment="top" usebox="none">
34283 \begin_layout Plain Layout
34286 arg "math-macro-add-param"
34294 <cell alignment="center" valignment="top" usebox="none">
34297 \begin_layout Plain Layout
34300 Edit\SpecialChar \menuseparator
34301 Math\SpecialChar \menuseparator
34303 \begin_inset space ~
34306 Definition\SpecialChar \menuseparator
34313 <row interlinespace="2.5mm">
34314 <cell alignment="center" valignment="top" usebox="none">
34317 \begin_layout Plain Layout
34320 arg "math-macro-make-optional"
34328 <cell alignment="center" valignment="top" usebox="none">
34331 \begin_layout Plain Layout
34334 Edit\SpecialChar \menuseparator
34335 Math\SpecialChar \menuseparator
34337 \begin_inset space ~
34340 Definition\SpecialChar \menuseparator
34341 Transform First Non-Optional to
34342 \begin_inset Newline newline
34346 \begin_inset Phantom HPhantom
34349 \begin_layout Plain Layout
34352 Edit\SpecialChar \menuseparator
34353 Math\SpecialChar \menuseparator
34355 \begin_inset space ~
34358 Definition\SpecialChar \menuseparator
34370 <row interlinespace="2.5mm">
34371 <cell alignment="center" valignment="top" usebox="none">
34374 \begin_layout Plain Layout
34377 arg "math-macro-make-nonoptional"
34385 <cell alignment="center" valignment="top" usebox="none">
34388 \begin_layout Plain Layout
34391 Edit\SpecialChar \menuseparator
34392 Math\SpecialChar \menuseparator
34394 \begin_inset space ~
34397 Definition\SpecialChar \menuseparator
34398 Transform Last Optional to
34399 \begin_inset Newline newline
34403 \begin_inset Phantom HPhantom
34406 \begin_layout Plain Layout
34409 Edit\SpecialChar \menuseparator
34410 Math\SpecialChar \menuseparator
34412 \begin_inset space ~
34415 Definition\SpecialChar \menuseparator
34421 Non-Optional Argument
34427 <row interlinespace="2.5mm">
34428 <cell alignment="center" valignment="top" usebox="none">
34431 \begin_layout Plain Layout
34434 arg "math-macro-remove-optional-param"
34442 <cell alignment="center" valignment="top" usebox="none">
34445 \begin_layout Plain Layout
34448 Edit\SpecialChar \menuseparator
34449 Math\SpecialChar \menuseparator
34451 \begin_inset space ~
34454 Definition\SpecialChar \menuseparator
34455 Remove Optional Argument
34461 <row interlinespace="2.5mm">
34462 <cell alignment="center" valignment="top" usebox="none">
34465 \begin_layout Plain Layout
34468 arg "math-macro-add-optional-param"
34476 <cell alignment="center" valignment="top" usebox="none">
34479 \begin_layout Plain Layout
34482 Edit\SpecialChar \menuseparator
34483 Math\SpecialChar \menuseparator
34485 \begin_inset space ~
34488 Definition\SpecialChar \menuseparator
34489 Insert Optional Argument
34495 <row interlinespace="2.5mm">
34496 <cell alignment="center" valignment="top" usebox="none">
34499 \begin_layout Plain Layout
34502 arg "math-macro-remove-greedy-param"
34510 <cell alignment="center" valignment="top" usebox="none">
34513 \begin_layout Plain Layout
34516 Edit\SpecialChar \menuseparator
34517 Math\SpecialChar \menuseparator
34519 \begin_inset space ~
34522 Definition\SpecialChar \menuseparator
34523 Remove Last Argument
34524 \begin_inset Newline newline
34528 \begin_inset Phantom HPhantom
34531 \begin_layout Plain Layout
34534 Edit\SpecialChar \menuseparator
34535 Math\SpecialChar \menuseparator
34537 \begin_inset space ~
34540 Definition\SpecialChar \menuseparator
34546 Spitting Out To The Right
34552 <row interlinespace="2.5mm">
34553 <cell alignment="center" valignment="top" usebox="none">
34556 \begin_layout Plain Layout
34559 arg "math-macro-append-greedy-param"
34567 <cell alignment="center" valignment="top" usebox="none">
34570 \begin_layout Plain Layout
34573 Edit\SpecialChar \menuseparator
34574 Math\SpecialChar \menuseparator
34576 \begin_inset space ~
34579 Definition\SpecialChar \menuseparator
34581 \begin_inset Newline newline
34585 \begin_inset Phantom HPhantom
34588 \begin_layout Plain Layout
34591 Edit\SpecialChar \menuseparator
34592 Math\SpecialChar \menuseparator
34594 \begin_inset space ~
34597 Definition\SpecialChar \menuseparator
34603 Eating From The Right
34609 <row interlinespace="2.5mm">
34610 <cell alignment="center" valignment="top" usebox="none">
34613 \begin_layout Plain Layout
34616 arg "math-macro-add-greedy-optional-param"
34624 <cell alignment="center" valignment="top" usebox="none">
34627 \begin_layout Plain Layout
34630 Edit\SpecialChar \menuseparator
34631 Math\SpecialChar \menuseparator
34633 \begin_inset space ~
34636 Definition\SpecialChar \menuseparator
34637 Append Optional Argument
34638 \begin_inset Newline newline
34642 \begin_inset Phantom HPhantom
34645 \begin_layout Plain Layout
34648 Edit\SpecialChar \menuseparator
34649 Math\SpecialChar \menuseparator
34651 \begin_inset space ~
34654 Definition\SpecialChar \menuseparator
34660 Eating From The Right
34673 \begin_layout Section
34674 Computer Algebra Systems
34677 \begin_layout Standard
34678 LyX offers the exchange between mathematical expressions written in LyX's
34679 math editor and external applications or user defined scripts.
34680 Currently supported applications are
34697 Note that the set of supported mathematical constructs is limited only
34698 to very simple cases.
34701 \begin_layout Subsection
34705 \begin_layout Standard
34706 Write some expression in a formula, go to the
34708 Edit\SpecialChar \menuseparator
34709 Math\SpecialChar \menuseparator
34710 Use Computer Algebra System
34712 menu and choose the application you have installed on the computer.
34713 After that the result of computation should show on the right side of the
34714 expression together with the
34715 \begin_inset Quotes eld
34719 \begin_inset Quotes erd
34725 \begin_layout Standard
34726 Here are few simple examples (with results from
34730 ) to show what kind of computations can be performed:
34733 \begin_layout Itemize
34734 \begin_inset Formula $\frac{37}{3}*2-\sum_{i=1}^{3}i^{i}=-\frac{22}{3}$
34740 \begin_layout Itemize
34741 \begin_inset Formula $\frac{37.0}{3}=12.33333333333333$
34747 \begin_layout Itemize
34748 \begin_inset Formula $\int_{1}^{2}\sin(x)dx=\cos1-\cos2$
34754 \begin_layout Itemize
34755 \begin_inset Formula $\det\left[\begin{array}{ccc}
34759 \end{array}\right]=-56$
34765 \begin_layout Itemize
34766 \begin_inset Formula $\lim_{x\rightarrow0}\left(\frac{\sin(x)}{x}\right)=1$
34772 \begin_layout Subsection
34776 \begin_layout Standard
34777 Currently there is no keyboard shortcut for calling the algebra applications.
34778 One can easily bind a shortcut to the
34782 LyX function (see the
34790 \begin_inset space \thinspace{}
34794 \begin_inset space \space{}
34801 key inside the math editor.
34806 one would use this shortcut definition command:
34809 \begin_layout Standard
34812 command-alternatives break-paragraph;math-extern maxima
34815 \begin_layout Section
34817 \begin_inset Index idx
34820 \begin_layout Plain Layout
34829 \begin_layout Subsection
34831 \begin_inset Index idx
34834 \begin_layout Plain Layout
34843 \begin_layout Standard
34844 Negative numbers often look ugly in formulas because the minus sign before
34845 the number is set with the same length as the minus operator sign.
34846 When writing the negative number in normal text, the minus sign appears
34850 \begin_layout Standard
34851 Thus, the problem disappears when converting the minus sign to mathematical
34855 \begin_layout Standard
34856 An example to visualize the problem:
34859 \begin_layout Standard
34861 \begin_inset Tabular
34862 <lyxtabular version="3" rows="3" columns="2">
34863 <features rotate="0" tabularvalignment="middle">
34864 <column alignment="right" valignment="top">
34865 <column alignment="left" valignment="top">
34867 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
34870 \begin_layout Plain Layout
34876 <cell alignment="center" valignment="top" topline="true" rightline="true" usebox="none">
34879 \begin_layout Plain Layout
34887 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
34890 \begin_layout Plain Layout
34896 <cell alignment="center" valignment="top" topline="true" bottomline="true" rightline="true" usebox="none">
34899 \begin_layout Plain Layout
34900 \begin_inset Formula $x=-2$
34910 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
34913 \begin_layout Plain Layout
34919 <cell alignment="center" valignment="top" topline="true" bottomline="true" rightline="true" usebox="none">
34922 \begin_layout Plain Layout
34923 \begin_inset Formula $x=\textrm{-}2$
34939 \begin_layout Subsection
34940 Comma as decimal Separator
34941 \begin_inset Index idx
34944 \begin_layout Plain Layout
34953 \begin_layout Standard
34954 In LaTeX a comma inside a formula is used, according to the English convention,
34955 as number group separator.
34956 So there will be space added behind all commas in formulas.
34959 \begin_layout Standard
34960 To avoid this, the comma is highlighted and changed to mathematical text
34970 \begin_layout Standard
34971 To use all formula commas in the document as decimal separator, the file
34980 \begin_layout Plain Layout
34985 is part of the LaTeX-package
34990 \begin_inset Index idx
34993 \begin_layout Plain Layout
34998 \begin_layout Plain Layout
35018 \begin_inset Index idx
35021 \begin_layout Plain Layout
35027 is loaded with the LaTeX-preamble line
35030 \begin_layout Standard
35038 \begin_layout Subsection
35040 \begin_inset CommandInset label
35042 name "sub:Physical-Vectors"
35047 \begin_inset Index idx
35050 \begin_layout Plain Layout
35059 \begin_layout Standard
35060 Predefined vectors are offered by the LaTeX-package
35065 \begin_inset Index idx
35068 \begin_layout Plain Layout
35074 that is loaded with the LaTeX-preamble line
35077 \begin_layout Standard
35085 \begin_layout Standard
35089 \begin_layout Plain Layout
35099 \begin_inset Note Note
35102 \begin_layout Plain Layout
35103 The following table will only be displayed when the LaTeX-package
35115 \begin_layout Standard
35116 The following commands are defined:
35119 \begin_layout Standard
35121 \begin_inset Tabular
35122 <lyxtabular version="3" rows="4" columns="2">
35123 <features rotate="0" tabularvalignment="middle">
35124 <column alignment="center" valignment="top">
35125 <column alignment="center" valignment="top">
35127 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
35130 \begin_layout Plain Layout
35136 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
35139 \begin_layout Plain Layout
35147 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
35150 \begin_layout Plain Layout
35160 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
35163 \begin_layout Plain Layout
35164 \begin_inset Formula $\Bra{\psi}$
35174 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
35177 \begin_layout Plain Layout
35187 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
35190 \begin_layout Plain Layout
35191 \begin_inset Formula $\Ket{\psi}$
35201 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
35204 \begin_layout Plain Layout
35216 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
35219 \begin_layout Plain Layout
35220 \begin_inset Formula $\Braket{\psi|\phi}$
35236 \begin_layout Standard
35243 assures that all vertical bars are set in the size of the surrounding brackets:
35244 \begin_inset Formula
35246 \Braket{\phi|J=\frac{3}{2}\,,\, M_{J}}
35255 \begin_layout Plain Layout
35265 \begin_inset Note Note
35268 \begin_layout Plain Layout
35269 The following will be displayed when the LaTeX-package
35281 \begin_layout Standard
35282 You need to install the LaTeX-package
35286 to see the rest of this subsection in the output.
35289 \begin_layout Standard
35293 \begin_layout Plain Layout
35305 \begin_layout Standard
35312 can also be achieved using the command
35318 , that is described in
35319 \begin_inset CommandInset ref
35321 reference "sub:Automatic-Bracket-Size"
35328 \begin_layout Subsection
35329 Self-defined Fractions
35330 \begin_inset CommandInset label
35332 name "sub:Self-defined-Fractions"
35337 \begin_inset Index idx
35340 \begin_layout Plain Layout
35341 Fractions ! self-defined
35349 \begin_layout Standard
35350 To define custom commands for fractions, the command
35357 \begin_inset Index idx
35360 \begin_layout Plain Layout
35367 \begin_layout Plain Layout
35381 is used in the following scheme:
35384 \begin_layout Standard
35397 bracket}{fraction bar thickness}{style}
35398 \begin_inset Newline newline
35402 \begin_inset Phantom HPhantom
35405 \begin_layout Plain Layout
35415 {numerator}{denominator}
35418 \begin_layout Standard
35419 The style is a number in the range of 0
35420 \begin_inset space \thinspace{}
35424 \begin_inset space \thinspace{}
35430 \begin_layout Standard
35432 \begin_inset Tabular
35433 <lyxtabular version="3" rows="5" columns="2">
35434 <features rotate="0" tabularvalignment="middle">
35435 <column alignment="center" valignment="top">
35436 <column alignment="center" valignment="top">
35438 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
35441 \begin_layout Plain Layout
35447 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
35450 \begin_layout Plain Layout
35458 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
35461 \begin_layout Plain Layout
35467 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
35470 \begin_layout Plain Layout
35471 display style formula
35478 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
35481 \begin_layout Plain Layout
35487 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
35490 \begin_layout Plain Layout
35498 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
35501 \begin_layout Plain Layout
35507 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
35510 \begin_layout Plain Layout
35518 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
35521 \begin_layout Plain Layout
35527 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
35530 \begin_layout Plain Layout
35544 \begin_layout Standard
35545 When no style is given, the size is adjusted to the surrounding environment
35546 like for the command
35555 \begin_layout Standard
35556 When no fraction bar thickness is given, the predefined value of 0.4
35557 \begin_inset space \thinspace{}
35563 \begin_layout Standard
35564 \begin_inset VSpace medskip
35567 For example, the commands
35580 \begin_inset CommandInset ref
35582 reference "sub:Fractions"
35586 are defined with the commands
35589 \begin_layout Standard
35598 genfrac{}{}{}{0}{#1}{#2}}
35601 \begin_layout Standard
35605 \begin_layout Standard
35614 genfrac{(}{)}{0pt}{1}{#1}{#2}}
35617 \begin_layout Standard
35618 \begin_inset VSpace medskip
35621 To define a fraction where the fraction bar thickness can be given as optional
35622 argument, the following line is inserted to the LaTeX-preamble:
35625 \begin_layout Standard
35634 genfrac{}{}{#1}{}{#2}{#3}}
35637 \begin_layout Standard
35639 \begin_inset Formula
35641 \text{Command} & & \mathrm{\backslash fracS[1mm]\backslash\{A\to\backslash\{B} & & \mathrm{\backslash fracS[5mm]\backslash\{A\to\backslash\{B}\\
35642 \text{Result} & & \fracS[1mm]{A}{B} & & \fracS[5mm]{A}{B}
35647 As one can see, the distance of the numerator and the denominator to the
35648 fraction bar is round about three times the bar thickness.
35651 \begin_layout Subsection
35653 \begin_inset Index idx
35656 \begin_layout Plain Layout
35665 \begin_layout Standard
35666 There are four ways to cancel formulas or parts of formulas:
35669 \begin_layout Standard
35673 \begin_layout Plain Layout
35683 \begin_inset Note Note
35686 \begin_layout Plain Layout
35687 The following table will only be displayed when the LaTeX-package
35699 \begin_layout Standard
35701 \begin_inset Tabular
35702 <lyxtabular version="3" rows="5" columns="2">
35703 <features rotate="0" tabularvalignment="middle">
35704 <column alignment="center" valignment="top">
35705 <column alignment="center" valignment="top">
35707 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
35710 \begin_layout Plain Layout
35716 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
35719 \begin_layout Plain Layout
35721 \begin_inset Note Note
35724 \begin_layout Plain Layout
35731 are used here as spacer.
35743 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
35746 \begin_layout Plain Layout
35750 \begin_inset space \textvisiblespace{}
35756 \begin_inset space \textvisiblespace{}
35764 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
35767 \begin_layout Plain Layout
35768 \begin_inset Formula $\raisebox{4.5mm}{}\cancel{\int A=B}\raisebox{-2.5mm}{}$
35778 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
35781 \begin_layout Plain Layout
35785 \begin_inset space \textvisiblespace{}
35791 \begin_inset space \textvisiblespace{}
35799 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
35802 \begin_layout Plain Layout
35803 \begin_inset Formula $\raisebox{4.5mm}{}\bcancel{\int A=B}\raisebox{-2.5mm}{}$
35813 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
35816 \begin_layout Plain Layout
35820 \begin_inset space \textvisiblespace{}
35826 \begin_inset space \textvisiblespace{}
35834 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
35837 \begin_layout Plain Layout
35838 \begin_inset Formula $\raisebox{4.5mm}{}\xcancel{\int A=B}\raisebox{-2.5mm}{}$
35848 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
35851 \begin_layout Plain Layout
35855 \begin_inset space \textvisiblespace{}
35861 \begin_inset space \textvisiblespace{}
35865 \begin_inset Formula $\to$
35873 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
35876 \begin_layout Plain Layout
35877 \begin_inset Formula $\raisebox{7mm}{}\cancelto{1}{\int A=B}\raisebox{-2.5mm}{}\hspace{3mm}$
35893 \begin_layout Standard
35900 is especially suitable to visualize the reduction of fractions within formulas:
35901 \begin_inset Formula
35903 \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}}}
35911 \begin_layout Standard
35912 To change the size of
35919 \begin_inset Quotes eld
35923 \begin_inset Quotes erd
35926 value one can add the LaTeX-preamble line
35929 \begin_layout Standard
35934 PassOptionsToPackage{option}{cancel}
35937 \begin_layout Standard
35946 which leads to the same size as for the canceled value, or
35950 which makes is it a bit smaller than normal.
35953 \begin_layout Standard
35954 To color the cancellation bar one adds this command as TeX code:
35957 \begin_layout Standard
35969 \begin_layout Standard
35974 can be replaced by a color of your choice.
35977 \begin_layout Standard
35981 \begin_layout Plain Layout
35997 \begin_layout Standard
35998 \begin_inset Formula
36000 \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}}}
36008 \begin_layout Standard
36012 \begin_layout Plain Layout
36026 \begin_inset Note Note
36029 \begin_layout Plain Layout
36038 \begin_layout Standard
36039 For further customizations, see the documentation of the package
36044 \begin_inset CommandInset citation
36051 \begin_inset Index idx
36054 \begin_layout Plain Layout
36063 \begin_layout Standard
36067 \begin_layout Plain Layout
36077 \begin_inset Note Note
36080 \begin_layout Plain Layout
36081 The following will be displayed when the LaTeX-package
36093 \begin_layout Standard
36094 You need to install the LaTeX-package
36098 to see the rest of this subsection in the output.
36101 \begin_layout Standard
36105 \begin_layout Plain Layout
36117 \begin_layout Subsection
36118 Formulas in Section Headings
36119 \begin_inset CommandInset label
36121 name "sub:Formulas-in-Section"
36126 \begin_inset Index idx
36129 \begin_layout Plain Layout
36130 Formula ! in section headings
36138 \begin_layout Standard
36139 When formulas are used in section headings, the following has to be taken
36143 \begin_layout Standard
36144 \begin_inset Note Greyedout
36147 \begin_layout Plain Layout
36153 \begin_inset Index idx
36156 \begin_layout Plain Layout
36157 Packages ! hyperref
36162 support is enabled in the document settings dialog under
36165 \begin_inset space ~
36170 , PDF-bookmarks are created for every section heading in the table of contents.
36171 If a section heading contains formulas, they are incorrectly displayed
36172 in the bookmark text, because formulas in bookmarks infringe the PDF convention
36181 \begin_layout Standard
36182 Both problems can be solved by inserting at the end of the section heading
36183 a short title with the menu
36185 Insert\SpecialChar \menuseparator
36187 \begin_inset space ~
36193 Short titles are used as alternative for multiline section headings to
36194 keep the table of contents clearly arranged.
36195 Only the short title appears in the table of contents and therefore also
36196 in the PDF-bookmark.
36199 \begin_layout Standard
36200 When formulas should be used in the table of contents but
36204 is used, one can use the following command in TeX-mode:
36207 \begin_layout Standard
36212 texorpdfstring{part}{alternative}
36213 \begin_inset Index idx
36216 \begin_layout Plain Layout
36227 \begin_layout Standard
36228 Part is the part of the heading that shouldn't appear in the PDF-bookmark.
36229 This can be characters, formulas, footnotes, but also cross-references.
36230 The alternative is used instead of the part for the bookmark.
36233 \begin_layout Standard
36234 Here are two example headings:
36235 \begin_inset VSpace -3mm
36242 \begin_layout Plain Layout
36254 \begin_layout Subsubsection
36255 Heading without formula in table of contents
36256 \begin_inset Formula $\sqrt{-1}=\mathrm{i}$
36260 \begin_inset Argument 1
36263 \begin_layout Plain Layout
36264 Heading without formula in table of contents
36272 \begin_layout Subsubsection
36273 Heading with formula in table of contents
36277 \begin_layout Plain Layout
36287 \begin_inset Formula $\sqrt{-1}=\mathrm{i}$
36294 \begin_layout Plain Layout
36304 \begin_layout Standard
36308 \begin_layout Plain Layout
36317 In the first heading a short title was used, in the second one
36326 \begin_layout Standard
36327 To get the same formatting as for the other headings, the complete heading
36336 \begin_layout Plain Layout
36338 \begin_inset CommandInset ref
36340 reference "sub:Bold-Formulas"
36352 \begin_layout Subsection
36353 Formulas in multi-column Text
36354 \begin_inset Index idx
36357 \begin_layout Plain Layout
36358 Formula ! in multi-column text
36366 \begin_layout Standard
36367 Formulas in multi-column text are often too wide to fit into a column and
36368 thus need to be set over the whole page width.
36369 This is done by using the LaTeX-package
36377 \begin_layout Plain Layout
36382 is part of every LaTeX standard installation.
36388 \begin_inset Index idx
36391 \begin_layout Plain Layout
36392 Packages ! multicol
36397 , that is loaded with the LaTeX-preamble line
36400 \begin_layout Standard
36405 usepackage{multicol}
36408 \begin_layout Standard
36409 \begin_inset Note Greyedout
36412 \begin_layout Plain Layout
36413 Note that in this case the setting
36416 \begin_inset space ~
36423 Document\SpecialChar \menuseparator
36429 \begin_inset space ~
36449 \begin_layout Standard
36450 Before the multi-column text the command
36453 \begin_layout Standard
36458 begin{multicols}{column number}
36461 \begin_layout Standard
36462 is written in TeX-mode.
36463 The column number is a number in the range of 2
36464 \begin_inset space \thinspace{}
36468 \begin_inset space \thinspace{}
36472 Before the formula the multi-column text is ended by inserting the command
36475 \begin_layout Standard
36483 \begin_layout Standard
36487 \begin_layout Standard
36488 Due to the command some space is automatically added before the formula.
36490 \begin_inset space \thinspace{}
36493 mm vertical space is inserted before the formula.
36494 When the formula style
36500 \begin_layout Plain Layout
36502 \begin_inset CommandInset ref
36504 reference "sec:Formula-Styles"
36516 \begin_inset space \thinspace{}
36519 mm space is inserted instead.
36522 \begin_layout Standard
36523 As example a multi-column text with a displayed formula:
36526 \begin_layout Standard
36532 \begin_layout Plain Layout
36536 begin{multicols}{2}
36541 Das Spektrum wird fouriertransformiert.
36542 Die Fouriertransformation wird verwendet, um die überlagerten Signale (Netzwerk
36543 , Lösungsmittel) zu trennen.
36544 Nachdem wir die Phasenverschiebung bestimmen konnten, interessiert uns
36545 nun das Aussehen des Ausgangssignals.
36546 Im Experiment haben wir es mit sehr vielen Teilchen zu tun, so dass man
36547 über alle Phasen integrieren muss.
36549 \begin_inset Formula $S$
36552 unser normiertes Ausgangssignal und
36553 \begin_inset Formula $P$
36556 die Phasenverteilungsfunktion, so ergibt sich die Beziehung
36560 \begin_layout Plain Layout
36570 \begin_inset VSpace -6mm
36574 \begin_inset Formula
36576 S(t)=S_{0}(t)\int_{-\infty}^{\infty}P(\phi,t)\mathrm{e}^{\mathrm{i}\phi}\,\mathrm{d}\phi
36585 \begin_layout Plain Layout
36589 begin{multicols}{2}
36595 \begin_inset Formula $S_{0}$
36598 das Signal ohne Gradient ist und die Normierungsbedingung
36599 \begin_inset Formula $\int_{-\infty}^{\infty}P(\phi,t)\,\mathrm{d}\phi=1$
36603 Nun dürfen wir aber nicht den Relaxationsprozess außer Acht lassen.
36605 \begin_inset Formula $\nicefrac{\pi}{2}$
36609 \begin_inset space \thinspace{}
36612 -rf-Puls beginnt sich die Magnetisierung zu entfokussieren, wodurch sich
36613 das Signal zusätzlich abschwächt.
36614 Diese Abschwächung verläuft exponentiell in Abhängigkeit der so genannten
36616 \begin_inset Formula $T_{2}$
36622 \begin_layout Standard
36628 \begin_layout Plain Layout
36640 \begin_layout Subsection
36641 Formulas with Description of Variables
36642 \begin_inset Index idx
36645 \begin_layout Plain Layout
36646 Formula ! with description of variables
36654 \begin_layout Standard
36655 To describe variables within a formula, like in formula
36656 \begin_inset CommandInset ref
36658 reference "eq:within"
36667 \begin_inset Formula $n$
36671 \begin_inset space ~
36674 matrix is used with left aligned columns for the
36675 \begin_inset Formula $n$
36682 \begin_layout Plain Layout
36684 \begin_inset CommandInset ref
36686 reference "sec:Matrices"
36695 To set the description in a smaller size, before the matrix e.
36696 \begin_inset space \thinspace{}
36700 \begin_inset space \space{}
36713 \begin_layout Plain Layout
36715 \begin_inset CommandInset ref
36717 reference "sub:Font-Sizes"
36729 \begin_layout Standard
36730 When the formula style
36736 \begin_layout Plain Layout
36738 \begin_inset CommandInset ref
36740 reference "sec:Formula-Styles"
36761 \begin_layout Plain Layout
36768 only works in formulas with the style
36773 \begin_inset CommandInset ref
36775 reference "sub:Variable-Space"
36784 is inserted before and after the matrix to have the same separation of
36785 the matrix from the equation and the side margin.
36788 \begin_layout Standard
36789 When the formula style
36793 is used, the method described in
36794 \begin_inset CommandInset ref
36796 reference "sub:Flalign-Environment"
36800 is used to indent formulas.
36802 \begin_inset CommandInset ref
36804 reference "eq:within"
36808 consists of five columns where in the first two columns contain the equation,
36809 the third the matrix and the last one an empty TeX-brace.
36810 \begin_inset Formula
36812 \hspace{30pt}F_{A} & =\rho·V·g & \footnotesize\begin{array}{ll}
36813 \rho & \textrm{density}\\
36814 V & \textrm{volume}\\
36815 g & \textrm{gravitational acceleration}
36816 \end{array} & & {}\label{eq:within}
36824 \begin_layout Subsection
36825 Upright small Greek Letters
36826 \begin_inset CommandInset label
36828 name "sub:Upright-small-Greek"
36833 \begin_inset Index idx
36836 \begin_layout Plain Layout
36837 Greek letters ! upright
36845 \begin_layout Standard
36846 Most of the math fonts only provide italic small Greek letters.
36847 But for symbols of elementary particles like pions and neutrinos, upright
36848 Greek letters are needed.
36857 \begin_layout Plain Layout
36862 is part of the LaTeX-package
36867 \begin_inset Index idx
36870 \begin_layout Plain Layout
36875 \begin_layout Plain Layout
36895 \begin_inset Index idx
36898 \begin_layout Plain Layout
36904 that is loaded with the LaTeX-preamble line
36907 \begin_layout Standard
36912 usepackage{upgreek}
36915 \begin_layout Standard
36921 \begin_layout Plain Layout
36931 \begin_inset Note Note
36934 \begin_layout Plain Layout
36935 The following table will only be displayed when the LaTeX-package
36944 They are created when the command for a small Greek letter is started with
36950 For example the command
36957 \begin_inset Formula $\uptau$
36963 \begin_layout Standard
36964 With these commands reactions of elementary particles can be typeset:
36965 \begin_inset Formula
36967 \uppi^{+}\to\upmu^{+}+\upnu_{\upmu}
36975 \begin_layout Standard
36976 The upright letters are more bold and wider than the italic ones.
36977 They should therefore not be used for units like
36978 \begin_inset Quotes eld
36982 \begin_inset Quotes erd
36988 \begin_layout Standard
36992 \begin_layout Plain Layout
37002 \begin_inset Note Note
37005 \begin_layout Plain Layout
37006 The following will be displayed when the LaTeX-package
37018 \begin_layout Standard
37019 You need to install the LaTeX-package
37023 to see the rest of this subsection in the output.
37026 \begin_layout Standard
37030 \begin_layout Plain Layout
37042 \begin_layout Subsection
37043 Text Characters in Formulas
37044 \begin_inset Index idx
37047 \begin_layout Plain Layout
37056 \begin_layout Standard
37057 In some cases you might want to insert text characters directly into formulas.
37058 When for example the centered dot · is often used in formulas like
37059 \begin_inset Formula $\nu=5·10^{5}\,\mathrm{Hz}$
37062 , one would have to insert the command
37072 \begin_layout Plain Layout
37074 \begin_inset CommandInset ref
37076 reference "sub:Binary-Operators"
37085 all the time, because this character is defined in all encodings as text
37087 But the encoding can be changed by this LaTeX-preamble line:
37090 \begin_layout Standard
37095 Declare Inputtext{183}{
37105 f\SpecialChar \textcompwordmark{}
37109 \begin_layout Standard
37110 The character encoding (menu
37112 Document\SpecialChar \menuseparator
37113 Settings\SpecialChar \menuseparator
37116 ) specifies what character appears when a keyboard key is pressed.
37117 When the key for the character '·' is pressed, internally the command
37124 But this command is not available in a formula so that you would get LaTeX-erro
37126 With the changed encoding the right command is chosen automatically, depending
37127 on if the character was inserted into a formula or not.
37130 \begin_layout Standard
37131 The encoding of several characters is saved in definition files.
37132 For example the encoding
37136 is defined in the file
37140 which is in the installation folder of LaTeX.
37141 Encodings should only be changed via the LaTeX-preamble and not in the
37143 Otherwise documents could not be edited by other LyX users working on other
37147 \begin_layout Standard
37148 \begin_inset VSpace medskip
37151 Besides the centered dot, in this document the degree sign ° is defined
37152 with the following LaTeX-preamble line so that it can be directly inserted
37156 \begin_layout Standard
37161 DeclareInputtext{176}{
37171 f\SpecialChar \textcompwordmark{}
37175 \begin_layout Standard
37176 \begin_inset Newpage newpage
37182 \begin_layout Section
37185 \begin_inset Index idx
37188 \begin_layout Plain Layout
37197 \begin_layout Standard
37198 This section is a summary of the most important typographic rules, listed
37203 \begin_layout Plain Layout
37204 This collection was partly taken from the German semi-official dictionary
37206 \begin_inset Quotes eld
37210 \begin_inset Quotes erd
37214 \begin_inset CommandInset citation
37220 that lists some of the ISO rules.
37221 More rules are listed in
37222 \begin_inset CommandInset citation
37236 \begin_layout Itemize
37245 \begin_layout Plain Layout
37246 done with font styles, see
37247 \begin_inset CommandInset ref
37249 reference "sub:Font-Styles"
37258 , no matter if they appear in italic text: 30
37259 \begin_inset space \thinspace{}
37263 \begin_inset Newline newline
37266 Between the value and the unit is the smallest space, see
37267 \begin_inset CommandInset ref
37269 reference "sub:Predefined-Space"
37274 \begin_inset Newline newline
37277 This convention is automatically fulfilled when the command
37284 When it is entered to a formula, two boxes appear.
37285 In the first one the value is inserted, in the second one the unit, and
37287 \begin_inset Formula $\unit[30]{km/h}$
37291 \begin_inset space \thinspace{}
37301 is not a real LaTeX command but the command
37307 , therefore you cannot use it in TeX code.
37310 \begin_layout Itemize
37311 Percent and perthousand signs are set like physical units:
37312 \begin_inset Newline newline
37316 \begin_inset space \thinspace{}
37322 \begin_layout Itemize
37323 The degree sign follows directly on the value: 15°, but not when it is used
37325 \begin_inset space \thinspace{}
37331 \begin_layout Itemize
37332 In numbers with more than four digits the smallest space is inserted before
37333 every third digit to group them:
37343 \begin_inset space \thinspace{}
37347 \begin_inset space \thinspace{}
37353 \begin_layout Itemize
37354 For dimensions like 120×90×40
37355 \begin_inset space \thinspace{}
37358 cm the multiplication sign
37359 \begin_inset Quotes eld
37363 \begin_inset Quotes erd
37367 It is available either via the command
37375 Insert\SpecialChar \menuseparator
37376 Special Character\SpecialChar \menuseparator
37382 \begin_layout Itemize
37383 Functions with names consisting of several letters are set upright to avoid
37385 \begin_inset CommandInset ref
37387 reference "sub:Predefined-Functions"
37394 \begin_layout Itemize
37395 Indices consisting of several letters, are set upright:
37396 \begin_inset Formula $E_{\mathrm{kin}}$
37400 \begin_inset Newline newline
37403 Components of matrices are set italic:
37404 \begin_inset Formula $\hat{H}_{kl}$
37410 \begin_layout Itemize
37411 The differentiation/integration operator 'd', the Euler's number 'e' and
37412 the imaginary unit 'i' should be set upright, to avoid mixing them up with
37416 \begin_layout Itemize
37417 The character that denotes a
37421 transformation is inserted either by the command
37426 \begin_inset space \textvisiblespace{}
37433 Insert\SpecialChar \menuseparator
37434 Special Character\SpecialChar \menuseparator
37435 Symbols\SpecialChar \menuseparator
37437 \begin_inset space ~
37443 \begin_inset Formula $\mathscr{F}$
37449 \begin_layout Standard
37450 \begin_inset Newpage newpage
37456 \begin_layout Section
37458 \begin_inset Index idx
37461 \begin_layout Plain Layout
37470 \begin_layout Standard
37471 Some characters and symbols can be created with several commands.
37472 Here is a list of the synonym commands:
37475 \begin_layout Standard
37476 \begin_inset VSpace bigskip
37480 \begin_inset space \hfill{}
37484 \begin_inset Tabular
37485 <lyxtabular version="3" rows="12" columns="2">
37486 <features rotate="0" tabularvalignment="middle">
37487 <column alignment="center" valignment="top" width="0pt">
37488 <column alignment="center" valignment="top" width="0pt">
37490 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
37493 \begin_layout Plain Layout
37499 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
37502 \begin_layout Plain Layout
37504 \begin_inset Note Note
37507 \begin_layout Plain Layout
37514 is only used as spacer.
37526 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
37529 \begin_layout Plain Layout
37537 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
37540 \begin_layout Plain Layout
37544 \begin_layout Plain Layout
37557 \begin_layout Plain Layout
37571 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
37574 \begin_layout Plain Layout
37582 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
37585 \begin_layout Plain Layout
37595 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
37598 \begin_layout Plain Layout
37606 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
37609 \begin_layout Plain Layout
37619 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
37622 \begin_layout Plain Layout
37630 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
37633 \begin_layout Plain Layout
37641 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
37644 \begin_layout Plain Layout
37652 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
37655 \begin_layout Plain Layout
37663 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
37666 \begin_layout Plain Layout
37674 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
37677 \begin_layout Plain Layout
37687 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
37690 \begin_layout Plain Layout
37698 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
37701 \begin_layout Plain Layout
37711 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
37714 \begin_layout Plain Layout
37722 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
37725 \begin_layout Plain Layout
37735 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
37738 \begin_layout Plain Layout
37746 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
37749 \begin_layout Plain Layout
37759 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
37762 \begin_layout Plain Layout
37770 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
37773 \begin_layout Plain Layout
37781 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
37784 \begin_layout Plain Layout
37792 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
37795 \begin_layout Plain Layout
37807 \begin_inset space \hfill{}
37811 \begin_inset Tabular
37812 <lyxtabular version="3" rows="12" columns="2">
37813 <features rotate="0" tabularvalignment="middle">
37814 <column alignment="center" valignment="top" width="0pt">
37815 <column alignment="center" valignment="top" width="0pt">
37817 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
37820 \begin_layout Plain Layout
37826 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
37829 \begin_layout Plain Layout
37837 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
37840 \begin_layout Plain Layout
37848 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
37851 \begin_layout Plain Layout
37863 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
37866 \begin_layout Plain Layout
37874 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
37877 \begin_layout Plain Layout
37887 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
37890 \begin_layout Plain Layout
37898 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
37901 \begin_layout Plain Layout
37911 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
37914 \begin_layout Plain Layout
37922 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
37925 \begin_layout Plain Layout
37933 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
37936 \begin_layout Plain Layout
37944 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
37947 \begin_layout Plain Layout
37955 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
37958 \begin_layout Plain Layout
37966 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
37969 \begin_layout Plain Layout
37979 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
37982 \begin_layout Plain Layout
37990 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
37993 \begin_layout Plain Layout
38003 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
38006 \begin_layout Plain Layout
38014 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
38017 \begin_layout Plain Layout
38027 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
38030 \begin_layout Plain Layout
38038 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
38041 \begin_layout Plain Layout
38051 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
38054 \begin_layout Plain Layout
38062 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
38065 \begin_layout Plain Layout
38075 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
38078 \begin_layout Plain Layout
38086 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
38089 \begin_layout Plain Layout
38103 \begin_inset space \hfill{}
38109 \begin_layout Standard
38110 \begin_inset Newpage newpage
38116 \begin_layout Bibliography
38117 \begin_inset CommandInset bibitem
38118 LatexCommand bibitem
38130 The LaTeX Companion
38133 Addison Wesley, 2004
38136 \begin_layout Bibliography
38137 \begin_inset CommandInset bibitem
38138 LatexCommand bibitem
38144 \begin_inset CommandInset href
38147 target "ftp://ftp.dante.de/tex-archive/info/math/voss/mathmode/Mathmode.pdf"
38151 of LaTeX's math abilities
38154 \begin_layout Bibliography
38155 \begin_inset CommandInset bibitem
38156 LatexCommand bibitem
38162 \begin_inset CommandInset href
38165 target "http://mirrors.ctan.org/macros/latex/required/amslatex/math/amsldoc.pdf"
38173 \begin_layout Plain Layout
38185 \begin_layout Bibliography
38186 \begin_inset CommandInset bibitem
38187 LatexCommand bibitem
38193 \begin_inset CommandInset href
38196 target "ftp://ftp.dante.de/tex-archive/info/symbols/comprehensive/symbols-a4.pdf"
38200 of all symbols available with LaTeX-packages
38203 \begin_layout Bibliography
38204 \begin_inset CommandInset bibitem
38205 LatexCommand bibitem
38211 \begin_inset CommandInset href
38213 name "Documentation"
38214 target "http://mirrors.ctan.org/macros/latex/contrib/cancel/cancel.pdf"
38218 of the LaTeX-package
38223 \begin_inset Index idx
38226 \begin_layout Plain Layout
38235 \begin_layout Bibliography
38236 \begin_inset CommandInset bibitem
38237 LatexCommand bibitem
38243 \begin_inset CommandInset href
38245 name "Documentation"
38246 target "http://www.tug.org/applications/hyperref/ftp/doc/manual.pdf"
38250 of the LaTeX-package
38255 \begin_inset Index idx
38258 \begin_layout Plain Layout
38259 Packages ! hyperref
38267 \begin_layout Bibliography
38268 \begin_inset CommandInset bibitem
38269 LatexCommand bibitem
38275 \begin_inset CommandInset href
38277 name "Documentation"
38278 target "http://www.ctan.org/tex-archive/macros/latex/contrib/mhchem/mhchem.pdf"
38282 of the LaTeX-package
38287 \begin_inset Index idx
38290 \begin_layout Plain Layout
38299 \begin_layout Bibliography
38300 \begin_inset CommandInset bibitem
38301 LatexCommand bibitem
38312 Auflage, Duden 2001
38315 \begin_layout Bibliography
38316 \begin_inset CommandInset bibitem
38317 LatexCommand bibitem
38323 \begin_inset CommandInset href
38326 target "http://physics.nist.gov/Document/checklist.pdf"
38330 for reviewing manuscripts
38333 \begin_layout Standard
38334 \begin_inset CommandInset index_print
38335 LatexCommand printindex