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"
7862 As a solution for the problem, the global formula row separation
7869 \begin_inset Index idx
7872 \begin_layout Plain Layout
7880 must be changed to -6
7881 \begin_inset space \thinspace{}
7884 pt before the formula with the command
7899 is set back after the formula to the standard value of 3
7900 \begin_inset space \thinspace{}
7903 pt using the same command.
7904 More about the row separation in formulas is explained in
7905 \begin_inset CommandInset ref
7907 reference "sub:Line-Separation"
7914 \begin_layout Section
7916 \begin_inset Index idx
7919 \begin_layout Plain Layout
7928 \begin_layout Standard
7929 Arrows can be inserted via the math toolbar button
7932 arg "math-insert \\leftarrow"
7935 or the commands listed in the following subsections.
7938 \begin_layout Subsection
7940 \begin_inset Index idx
7943 \begin_layout Plain Layout
7952 \begin_layout Standard
7953 \begin_inset space \hfill{}
7957 \begin_inset Tabular
7958 <lyxtabular version="3" rows="8" columns="2">
7959 <features rotate="0" tabularvalignment="middle">
7960 <column alignment="center" valignment="top" width="0pt">
7961 <column alignment="center" valignment="top" width="0pt">
7963 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
7966 \begin_layout Plain Layout
7972 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
7975 \begin_layout Plain Layout
7983 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
7986 \begin_layout Plain Layout
7994 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
7997 \begin_layout Plain Layout
7998 \begin_inset Formula $\gets$
8008 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
8011 \begin_layout Plain Layout
8019 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
8022 \begin_layout Plain Layout
8023 \begin_inset Formula $\Leftarrow$
8033 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
8036 \begin_layout Plain Layout
8044 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
8047 \begin_layout Plain Layout
8048 \begin_inset Formula $\longleftarrow$
8058 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
8061 \begin_layout Plain Layout
8069 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
8072 \begin_layout Plain Layout
8073 \begin_inset Formula $\Longleftarrow$
8083 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
8086 \begin_layout Plain Layout
8094 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
8097 \begin_layout Plain Layout
8098 \begin_inset Formula $\leftharpoonup$
8108 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
8111 \begin_layout Plain Layout
8119 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
8122 \begin_layout Plain Layout
8123 \begin_inset Formula $\leftharpoondown$
8133 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
8136 \begin_layout Plain Layout
8144 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
8147 \begin_layout Plain Layout
8148 \begin_inset Formula $\hookleftarrow$
8162 \begin_inset space \hfill{}
8166 \begin_inset Tabular
8167 <lyxtabular version="3" rows="8" columns="2">
8168 <features rotate="0" tabularvalignment="middle">
8169 <column alignment="center" valignment="top" width="0pt">
8170 <column alignment="center" valignment="top" width="0pt">
8172 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
8175 \begin_layout Plain Layout
8181 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
8184 \begin_layout Plain Layout
8192 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
8195 \begin_layout Plain Layout
8203 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
8206 \begin_layout Plain Layout
8207 \begin_inset Formula $\to$
8217 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
8220 \begin_layout Plain Layout
8228 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
8231 \begin_layout Plain Layout
8232 \begin_inset Formula $\Rightarrow$
8242 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
8245 \begin_layout Plain Layout
8253 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
8256 \begin_layout Plain Layout
8257 \begin_inset Formula $\longrightarrow$
8267 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
8270 \begin_layout Plain Layout
8278 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
8281 \begin_layout Plain Layout
8282 \begin_inset Formula $\Longrightarrow$
8292 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
8295 \begin_layout Plain Layout
8303 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
8306 \begin_layout Plain Layout
8307 \begin_inset Formula $\rightharpoonup$
8317 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
8320 \begin_layout Plain Layout
8328 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
8331 \begin_layout Plain Layout
8332 \begin_inset Formula $\rightharpoondown$
8342 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
8345 \begin_layout Plain Layout
8353 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
8356 \begin_layout Plain Layout
8357 \begin_inset Formula $\hookrightarrow$
8371 \begin_inset space \hfill{}
8377 \begin_layout Standard
8378 \begin_inset space \hfill{}
8382 \begin_inset Tabular
8383 <lyxtabular version="3" rows="6" columns="2">
8384 <features rotate="0" tabularvalignment="middle">
8385 <column alignment="center" valignment="top" width="0pt">
8386 <column alignment="center" valignment="top" width="0pt">
8388 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
8391 \begin_layout Plain Layout
8397 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
8400 \begin_layout Plain Layout
8408 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
8411 \begin_layout Plain Layout
8419 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
8422 \begin_layout Plain Layout
8423 \begin_inset Formula $\leftrightarrow$
8433 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
8436 \begin_layout Plain Layout
8444 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
8447 \begin_layout Plain Layout
8448 \begin_inset Formula $\Leftrightarrow$
8458 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
8461 \begin_layout Plain Layout
8469 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
8472 \begin_layout Plain Layout
8473 \begin_inset Formula $\longleftrightarrow$
8483 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
8486 \begin_layout Plain Layout
8494 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
8497 \begin_layout Plain Layout
8498 \begin_inset Formula $\Longleftrightarrow$
8508 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
8511 \begin_layout Plain Layout
8519 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
8522 \begin_layout Plain Layout
8523 \begin_inset Formula $\rightleftharpoons$
8537 \begin_inset space \hspace{}
8542 \begin_inset space \hfill{}
8546 \begin_inset Tabular
8547 <lyxtabular version="3" rows="5" columns="2">
8548 <features rotate="0" tabularvalignment="middle">
8549 <column alignment="center" valignment="top" width="0pt">
8550 <column alignment="center" valignment="top" width="0pt">
8552 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
8555 \begin_layout Plain Layout
8561 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
8564 \begin_layout Plain Layout
8572 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
8575 \begin_layout Plain Layout
8583 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
8586 \begin_layout Plain Layout
8587 \begin_inset Formula $\mapsto$
8597 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
8600 \begin_layout Plain Layout
8608 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
8611 \begin_layout Plain Layout
8612 \begin_inset Formula $\longmapsto$
8622 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
8625 \begin_layout Plain Layout
8633 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
8636 \begin_layout Plain Layout
8637 \begin_inset Formula $\leadsto$
8647 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
8650 \begin_layout Plain Layout
8658 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
8661 \begin_layout Plain Layout
8662 \begin_inset Formula $\dasharrow$
8676 \begin_inset space \hfill{}
8682 \begin_layout Standard
8683 \begin_inset VSpace medskip
8686 Arrows used as accents like e.
8687 \begin_inset space \thinspace{}
8691 \begin_inset space \space{}
8694 vector arrows are listed in
8695 \begin_inset CommandInset ref
8697 reference "sec:Accents"
8704 \begin_layout Standard
8705 \begin_inset VSpace bigskip
8708 Furthermore there are the labeled arrows
8709 \begin_inset Index idx
8712 \begin_layout Plain Layout
8725 \begin_inset Index idx
8728 \begin_layout Plain Layout
8743 \begin_inset Index idx
8746 \begin_layout Plain Layout
8753 \begin_layout Plain Layout
8768 When inserting one of these commands in a formula, an arrow with two blue
8769 boxes appear where the label can be inserted.
8770 The length of the arrow adapts to the label width.
8773 \begin_layout Standard
8775 \begin_inset Tabular
8776 <lyxtabular version="3" rows="3" columns="2">
8777 <features rotate="0" tabularvalignment="middle">
8778 <column alignment="center" valignment="top" width="0pt">
8779 <column alignment="center" valignment="top" width="0pt">
8781 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
8784 \begin_layout Plain Layout
8790 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
8793 \begin_layout Plain Layout
8795 \begin_inset Note Note
8798 \begin_layout Plain Layout
8805 is only used as spacer.
8817 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
8820 \begin_layout Plain Layout
8824 \begin_inset space \textvisiblespace{}
8828 \begin_inset Formula $\downarrow$
8832 \begin_inset Formula $\to$
8840 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
8843 \begin_layout Plain Layout
8844 \begin_inset Formula $\raisebox{5.5mm}{}F(a)\xleftarrow[x>0]{x=a}F(x)\raisebox{-4mm}{}$
8854 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
8857 \begin_layout Plain Layout
8861 \begin_inset space \textvisiblespace{}
8865 \begin_inset Formula $\downarrow$
8869 \begin_inset Formula $\to$
8877 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
8880 \begin_layout Plain Layout
8881 \begin_inset Formula $\raisebox{5.5mm}{}F(x)\xrightarrow[x>0]{x=a}F(a)\raisebox{-4mm}{}$
8897 \begin_layout Standard
8898 \begin_inset VSpace medskip
8904 \begin_layout Standard
8905 If you set in the document settings under
8908 \begin_inset space ~
8918 \begin_inset Index idx
8921 \begin_layout Plain Layout
8922 Packages ! mathtools
8930 \begin_inset space ~
8935 , you have access to the following labeled arrows:
8938 \begin_layout Standard
8939 \begin_inset Newpage newpage
8945 \begin_layout Standard
8947 \begin_inset space \hspace*{\fill}
8951 \begin_inset Tabular
8952 <lyxtabular version="3" rows="7" columns="2">
8953 <features rotate="0" tabularvalignment="middle">
8954 <column alignment="center" valignment="top" width="0pt">
8955 <column alignment="center" valignment="top" width="0pt">
8957 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
8960 \begin_layout Plain Layout
8966 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
8969 \begin_layout Plain Layout
8971 \begin_inset Note Note
8974 \begin_layout Plain Layout
8981 is only used as spacer.
8993 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
8996 \begin_layout Plain Layout
9016 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
9019 \begin_layout Plain Layout
9020 \begin_inset Formula $\raisebox{6mm}{}\xleftrightarrow[x=a]{x>0}\raisebox{-4mm}{}$
9030 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
9033 \begin_layout Plain Layout
9053 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
9056 \begin_layout Plain Layout
9057 \begin_inset Formula $\raisebox{6mm}{}\xLeftarrow[x=a]{x>0}\raisebox{-4mm}{}$
9067 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
9070 \begin_layout Plain Layout
9090 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
9093 \begin_layout Plain Layout
9094 \begin_inset Formula $\raisebox{6mm}{}\xRightarrow[x=a]{x>0}\raisebox{-4mm}{}$
9104 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
9107 \begin_layout Plain Layout
9127 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
9130 \begin_layout Plain Layout
9131 \begin_inset Formula $\raisebox{6mm}{}\xLeftrightarrow[x=a]{x>0}\raisebox{-4mm}{}$
9141 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
9144 \begin_layout Plain Layout
9164 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
9167 \begin_layout Plain Layout
9168 \begin_inset Formula $\raisebox{6mm}{}\xhookleftarrow[x=a]{x>0}\raisebox{-4mm}{}$
9178 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
9181 \begin_layout Plain Layout
9201 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
9204 \begin_layout Plain Layout
9205 \begin_inset Formula $\raisebox{6mm}{}\xhookrightarrow[x=a]{x>0}\raisebox{-4mm}{}$
9219 \begin_inset space \hspace*{\fill}
9223 \begin_inset Tabular
9224 <lyxtabular version="3" rows="7" columns="2">
9225 <features rotate="0" tabularvalignment="middle">
9226 <column alignment="center" valignment="top" width="0pt">
9227 <column alignment="center" valignment="top" width="0pt">
9229 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
9232 \begin_layout Plain Layout
9238 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
9241 \begin_layout Plain Layout
9243 \begin_inset Note Note
9246 \begin_layout Plain Layout
9253 is only used as spacer.
9265 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
9268 \begin_layout Plain Layout
9288 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
9291 \begin_layout Plain Layout
9292 \begin_inset Formula $\raisebox{6mm}{}\xleftharpoondown[x=a]{x>0}\raisebox{-4mm}{}$
9302 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
9305 \begin_layout Plain Layout
9325 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
9328 \begin_layout Plain Layout
9329 \begin_inset Formula $\raisebox{6mm}{}\xleftharpoonup[x=a]{x>0}\raisebox{-4mm}{}$
9339 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
9342 \begin_layout Plain Layout
9362 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
9365 \begin_layout Plain Layout
9366 \begin_inset Formula $\raisebox{6mm}{}\xrightharpoondown[x=a]{x>0}\raisebox{-4mm}{}$
9376 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
9379 \begin_layout Plain Layout
9399 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
9402 \begin_layout Plain Layout
9403 \begin_inset Formula $\raisebox{6mm}{}\xrightharpoonup[x=a]{x>0}\raisebox{-4mm}{}$
9413 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
9416 \begin_layout Plain Layout
9436 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
9439 \begin_layout Plain Layout
9440 \begin_inset Formula $\raisebox{6mm}{}\xleftrightharpoons[x=a]{x>0}\raisebox{-4mm}{}$
9450 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
9453 \begin_layout Plain Layout
9473 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
9476 \begin_layout Plain Layout
9477 \begin_inset Formula $\raisebox{6mm}{}\xrightleftharpoons[x=a]{x>0}\raisebox{-4mm}{}$
9491 \begin_inset space \hspace*{\fill}
9497 \begin_layout Standard
9498 The command scheme is for all these arrows:
9501 \begin_layout Standard
9503 \begin_inset Tabular
9504 <lyxtabular version="3" rows="2" columns="2">
9505 <features rotate="0" tabularvalignment="middle">
9506 <column alignment="center" valignment="top" width="0pt">
9507 <column alignment="center" valignment="top" width="0pt">
9509 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
9512 \begin_layout Plain Layout
9518 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
9521 \begin_layout Plain Layout
9523 \begin_inset Note Note
9526 \begin_layout Plain Layout
9533 is only used as spacer.
9545 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
9548 \begin_layout Plain Layout
9551 xleftrightarrow[x=a]
9554 \begin_inset Formula $\to$
9562 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
9565 \begin_layout Plain Layout
9566 \begin_inset Formula $\raisebox{6mm}{}F(a)\xleftrightarrow[x=a]{x>0}F(x)\raisebox{-4mm}{}$
9582 \begin_layout Subsection
9583 Vertical and diagonal Arrows
9584 \begin_inset Index idx
9587 \begin_layout Plain Layout
9594 \begin_inset Index idx
9597 \begin_layout Plain Layout
9606 \begin_layout Standard
9607 \begin_inset space \hfill{}
9611 \begin_inset Tabular
9612 <lyxtabular version="3" rows="7" columns="2">
9613 <features rotate="0" tabularvalignment="middle">
9614 <column alignment="center" valignment="top" width="0pt">
9615 <column alignment="center" valignment="top" width="0pt">
9617 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
9620 \begin_layout Plain Layout
9626 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
9629 \begin_layout Plain Layout
9637 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
9640 \begin_layout Plain Layout
9648 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
9651 \begin_layout Plain Layout
9652 \begin_inset Formula $\uparrow$
9662 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
9665 \begin_layout Plain Layout
9673 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
9676 \begin_layout Plain Layout
9677 \begin_inset Formula $\Uparrow$
9687 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
9690 \begin_layout Plain Layout
9698 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
9701 \begin_layout Plain Layout
9702 \begin_inset Formula $\updownarrow$
9712 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
9715 \begin_layout Plain Layout
9723 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
9726 \begin_layout Plain Layout
9727 \begin_inset Formula $\Updownarrow$
9737 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
9740 \begin_layout Plain Layout
9748 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
9751 \begin_layout Plain Layout
9752 \begin_inset Formula $\Downarrow$
9762 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
9765 \begin_layout Plain Layout
9773 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
9776 \begin_layout Plain Layout
9777 \begin_inset Formula $\downarrow$
9791 \begin_inset space \hfill{}
9795 \begin_inset Tabular
9796 <lyxtabular version="3" rows="5" columns="2">
9797 <features rotate="0" tabularvalignment="middle">
9798 <column alignment="center" valignment="top" width="0pt">
9799 <column alignment="center" valignment="top" width="0pt">
9801 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
9804 \begin_layout Plain Layout
9810 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
9813 \begin_layout Plain Layout
9821 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
9824 \begin_layout Plain Layout
9832 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
9835 \begin_layout Plain Layout
9836 \begin_inset Formula $\nearrow$
9846 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
9849 \begin_layout Plain Layout
9857 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
9860 \begin_layout Plain Layout
9861 \begin_inset Formula $\searrow$
9871 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
9874 \begin_layout Plain Layout
9882 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
9885 \begin_layout Plain Layout
9886 \begin_inset Formula $\swarrow$
9896 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
9899 \begin_layout Plain Layout
9907 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
9910 \begin_layout Plain Layout
9911 \begin_inset Formula $\nwarrow$
9925 \begin_inset space \hfill{}
9931 \begin_layout Standard
9932 \begin_inset VSpace medskip
9935 Vertical arrows can be used also as delimiters together with the commands
9937 \begin_inset CommandInset ref
9939 reference "sub:Manual-Bracket-Size"
9944 \begin_inset CommandInset ref
9946 reference "sub:Automatic-Bracket-Size"
9953 \begin_layout Section
9955 \begin_inset CommandInset label
9962 \begin_inset Index idx
9965 \begin_layout Plain Layout
9974 \begin_layout Standard
9975 Accents can be inserted via the math toolbar button
9978 arg "math-insert \\hat"
9981 or the commands listed in the following subsections.
9984 \begin_layout Subsection
9985 Accents for one Character
9989 \begin_layout Plain Layout
10002 \begin_layout Plain Layout
10003 accents in text see
10004 \begin_inset CommandInset ref
10006 reference "sub:Accents-in-Text"
10019 \begin_layout Plain Layout
10027 \begin_inset Note Note
10030 \begin_layout Plain Layout
10037 is used to avoid that the footnote appears in the PDF-bookmark.
10040 \begin_layout Plain Layout
10048 \begin_inset CommandInset ref
10050 reference "sub:Formulas-in-Section"
10060 \begin_inset CommandInset label
10062 name "sub:Accents-for-one"
10067 \begin_inset Index idx
10070 \begin_layout Plain Layout
10071 Accents ! for one character
10079 \begin_layout Standard
10080 \begin_inset space \hfill{}
10084 \begin_inset Tabular
10085 <lyxtabular version="3" rows="8" columns="2">
10086 <features rotate="0" tabularvalignment="middle">
10087 <column alignment="center" valignment="top" width="0pt">
10088 <column alignment="center" valignment="top" width="0pt">
10090 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
10093 \begin_layout Plain Layout
10099 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
10102 \begin_layout Plain Layout
10104 \begin_inset Note Note
10107 \begin_layout Plain Layout
10114 is only used as spacer.
10126 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
10129 \begin_layout Plain Layout
10133 \begin_inset space \textvisiblespace{}
10141 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
10144 \begin_layout Plain Layout
10145 \begin_inset Formula $\raisebox{5mm}{}\dot{A}$
10155 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
10158 \begin_layout Plain Layout
10162 \begin_inset space \textvisiblespace{}
10170 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
10173 \begin_layout Plain Layout
10174 \begin_inset Formula $\raisebox{5mm}{}\ddot{A}$
10184 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
10187 \begin_layout Plain Layout
10191 \begin_inset space \textvisiblespace{}
10199 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
10202 \begin_layout Plain Layout
10203 \begin_inset Formula $\raisebox{5mm}{}\dddot{A}$
10213 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
10216 \begin_layout Plain Layout
10220 \begin_inset space \textvisiblespace{}
10228 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
10231 \begin_layout Plain Layout
10232 \begin_inset Formula $\raisebox{5mm}{}\ddddot{A}$
10242 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
10245 \begin_layout Plain Layout
10249 \begin_inset space \textvisiblespace{}
10253 \begin_inset Index idx
10256 \begin_layout Plain Layout
10267 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
10270 \begin_layout Plain Layout
10271 \begin_inset Formula $\raisebox{5mm}{}\vec{A}$
10281 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
10284 \begin_layout Plain Layout
10288 \begin_inset space \textvisiblespace{}
10296 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
10299 \begin_layout Plain Layout
10300 \begin_inset Formula $\raisebox{5mm}{}\bar{A}$
10310 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
10313 \begin_layout Plain Layout
10317 \begin_inset space \textvisiblespace{}
10325 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
10328 \begin_layout Plain Layout
10329 \begin_inset Formula $\raisebox{5mm}{}\mathring{A}$
10343 \begin_inset space \hfill{}
10347 \begin_inset Tabular
10348 <lyxtabular version="3" rows="7" columns="2">
10349 <features rotate="0" tabularvalignment="middle">
10350 <column alignment="center" valignment="top" width="0pt">
10351 <column alignment="center" valignment="top" width="0pt">
10353 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
10356 \begin_layout Plain Layout
10362 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
10365 \begin_layout Plain Layout
10373 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
10376 \begin_layout Plain Layout
10380 \begin_inset space \textvisiblespace{}
10388 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
10391 \begin_layout Plain Layout
10392 \begin_inset Formula $\raisebox{5mm}{}\tilde{A}$
10402 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
10405 \begin_layout Plain Layout
10409 \begin_inset space \textvisiblespace{}
10417 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
10420 \begin_layout Plain Layout
10421 \begin_inset Formula $\raisebox{5mm}{}\hat{A}$
10431 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
10434 \begin_layout Plain Layout
10438 \begin_inset space \textvisiblespace{}
10446 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
10449 \begin_layout Plain Layout
10450 \begin_inset Formula $\raisebox{5mm}{}\check{A}$
10460 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
10463 \begin_layout Plain Layout
10467 \begin_inset space \textvisiblespace{}
10475 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
10478 \begin_layout Plain Layout
10479 \begin_inset Formula $\raisebox{5mm}{}\acute{A}$
10489 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
10492 \begin_layout Plain Layout
10496 \begin_inset space \textvisiblespace{}
10504 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
10507 \begin_layout Plain Layout
10508 \begin_inset Formula $\raisebox{5mm}{}\grave{A}$
10518 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
10521 \begin_layout Plain Layout
10525 \begin_inset space \textvisiblespace{}
10533 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
10536 \begin_layout Plain Layout
10537 \begin_inset Formula $\raisebox{5mm}{}\breve{A}$
10551 \begin_inset space \hfill{}
10557 \begin_layout Standard
10558 \begin_inset VSpace bigskip
10564 \begin_layout Standard
10565 You can directly insert accents like é to formulas.
10566 LyX will transform them to the corresponding accent command.
10568 \begin_inset Index idx
10571 \begin_layout Plain Layout
10577 it is better to insert a quotation mark before the vowel.
10578 These two characters are then treated by LaTeX as
10582 character when the formula part with the umlaut is marked as German.
10590 \begin_inset Quotes eld
10594 \begin_inset Quotes erd
10597 umlauts are created as demonstrated in the following example:
10600 \begin_layout Standard
10601 \begin_inset VSpace -2mm
10607 \begin_layout Standard
10609 \begin_inset Tabular
10610 <lyxtabular version="3" rows="3" columns="2">
10611 <features rotate="0" tabularvalignment="middle">
10612 <column alignment="center" valignment="top">
10613 <column alignment="center" valignment="top">
10615 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
10618 \begin_layout Plain Layout
10624 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
10627 \begin_layout Plain Layout
10629 \begin_inset Note Note
10632 \begin_layout Plain Layout
10640 \begin_inset space \thinspace{}
10643 pt space are only used as spacer.
10655 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
10658 \begin_layout Plain Layout
10661 \begin_inset Quotes grd
10669 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
10672 \begin_layout Plain Layout
10673 \begin_inset space \hspace{}
10680 \begin_inset Formula $"i$
10690 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
10693 \begin_layout Plain Layout
10697 \begin_inset space \textvisiblespace{}
10705 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
10708 \begin_layout Plain Layout
10709 \begin_inset Formula $\raisebox{5mm}{}\ddot{i}$
10725 \begin_layout Standard
10726 Another advantage to
10732 is that umlauts can directly be converted to mathematical text because
10733 the accent commands above are
10739 in mathematical text
10742 To convert an accented character to mathematical text, only the character
10743 under the accent may be converted.
10744 This applies also for all other conversions, e.
10745 \begin_inset space \thinspace{}
10749 \begin_inset space \space{}
10755 \begin_layout Standard
10756 In mathematical text, umlauts and other accented characters can directly
10760 \begin_layout Standard
10761 \begin_inset VSpace bigskip
10767 \begin_layout Standard
10768 LyX also supports a tilde under the character if the LaTeX-package
10773 \begin_inset Index idx
10776 \begin_layout Plain Layout
10777 Packages ! undertilde
10782 is installed on your system:
10785 \begin_layout Standard
10789 \begin_layout Plain Layout
10799 \begin_inset Note Note
10802 \begin_layout Plain Layout
10803 The following table will only be displayed when the LaTeX-package
10815 \begin_layout Standard
10818 \begin_inset Tabular
10819 <lyxtabular version="3" rows="2" columns="2">
10820 <features rotate="0" tabularvalignment="middle">
10821 <column alignment="center" valignment="top" width="0pt">
10822 <column alignment="center" valignment="top" width="0pt">
10824 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
10827 \begin_layout Plain Layout
10833 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
10836 \begin_layout Plain Layout
10844 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
10847 \begin_layout Plain Layout
10851 \begin_inset space \textvisiblespace{}
10859 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
10862 \begin_layout Plain Layout
10863 \begin_inset Formula $\raisebox{5mm}{}\utilde{A}$
10879 \begin_layout Standard
10883 \begin_layout Plain Layout
10893 \begin_inset Note Note
10896 \begin_layout Plain Layout
10897 The following will be displayed when the LaTeX-package
10909 \begin_layout Standard
10910 You need to install the LaTeX-package
10914 to see the rest of this subsection in the output.
10917 \begin_layout Standard
10921 \begin_layout Plain Layout
10933 \begin_layout Standard
10934 \begin_inset Newpage newpage
10940 \begin_layout Subsection
10941 Accents for several Characters
10942 \begin_inset Index idx
10945 \begin_layout Plain Layout
10946 Accents ! for several characters
10954 \begin_layout Standard
10955 \begin_inset space \hfill{}
10959 \begin_inset Tabular
10960 <lyxtabular version="3" rows="5" columns="2">
10961 <features rotate="0" tabularvalignment="middle">
10962 <column alignment="center" valignment="top" width="0pt">
10963 <column alignment="center" valignment="top" width="0pt">
10965 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
10968 \begin_layout Plain Layout
10974 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
10977 \begin_layout Plain Layout
10979 \begin_inset Note Note
10982 \begin_layout Plain Layout
10989 is only used as spacer.
11001 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
11004 \begin_layout Plain Layout
11008 \begin_inset space \textvisiblespace{}
11016 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
11019 \begin_layout Plain Layout
11020 \begin_inset Formula $\raisebox{6mm}{}\overleftarrow{A=B}\raisebox{-2mm}{}$
11030 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
11033 \begin_layout Plain Layout
11037 \begin_inset space \textvisiblespace{}
11045 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
11048 \begin_layout Plain Layout
11049 \begin_inset Formula $\raisebox{5mm}{}\underleftarrow{A=B}\raisebox{-3mm}{}$
11059 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
11062 \begin_layout Plain Layout
11066 \begin_inset space \textvisiblespace{}
11074 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
11077 \begin_layout Plain Layout
11078 \begin_inset Formula $\raisebox{6mm}{}\overleftrightarrow{A=B}\raisebox{-2mm}{}$
11088 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
11091 \begin_layout Plain Layout
11094 underleftrightarrow
11095 \begin_inset space \textvisiblespace{}
11103 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
11106 \begin_layout Plain Layout
11107 \begin_inset Formula $\raisebox{5mm}{}\underleftrightarrow{A=B}\raisebox{-3mm}{}$
11121 \begin_inset space \hfill{}
11125 \begin_inset Tabular
11126 <lyxtabular version="3" rows="5" columns="2">
11127 <features rotate="0" tabularvalignment="middle">
11128 <column alignment="center" valignment="top" width="0pt">
11129 <column alignment="center" valignment="top" width="0pt">
11131 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
11134 \begin_layout Plain Layout
11140 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
11143 \begin_layout Plain Layout
11151 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
11154 \begin_layout Plain Layout
11158 \begin_inset space \textvisiblespace{}
11166 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
11169 \begin_layout Plain Layout
11170 \begin_inset Formula $\raisebox{6mm}{}\overrightarrow{A=B}\raisebox{-2mm}{}$
11180 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
11183 \begin_layout Plain Layout
11187 \begin_inset space \textvisiblespace{}
11195 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
11198 \begin_layout Plain Layout
11199 \begin_inset Formula $\raisebox{5mm}{}\underrightarrow{A=B}\raisebox{-3mm}{}$
11209 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
11212 \begin_layout Plain Layout
11216 \begin_inset space \textvisiblespace{}
11224 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
11227 \begin_layout Plain Layout
11228 \begin_inset Formula $\raisebox{6mm}{}\widetilde{A=B}\raisebox{-2mm}{}$
11238 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
11241 \begin_layout Plain Layout
11245 \begin_inset space \textvisiblespace{}
11253 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
11256 \begin_layout Plain Layout
11257 \begin_inset Formula $\raisebox{6mm}{}\widehat{A=B}\raisebox{-2mm}{}$
11271 \begin_inset space \hfill{}
11277 \begin_layout Standard
11278 \begin_inset VSpace medskip
11281 With these commands as many characters as you like can be accented.
11294 will only be set in the output with a length of three characters, as shown
11295 in the following example:
11296 \begin_inset Formula
11298 \widetilde{A+B=C-D}
11306 \begin_layout Standard
11314 \begin_inset Index idx
11317 \begin_layout Plain Layout
11332 \begin_inset Index idx
11335 \begin_layout Plain Layout
11343 described in the previous subsection it is also possible to accent several
11350 \begin_inset space \textvisiblespace{}
11354 \begin_inset Formula $\downarrow$
11360 \begin_inset Formula
11362 \underset{***}{A=B}
11370 \begin_layout Section
11372 \begin_inset CommandInset label
11379 \begin_inset Index idx
11382 \begin_layout Plain Layout
11391 \begin_layout Subsection
11393 \begin_inset CommandInset label
11395 name "sub:Predefined-Space"
11400 \begin_inset Index idx
11403 \begin_layout Plain Layout
11404 Space ! horizontal ! predefined
11412 \begin_layout Standard
11413 Sometimes it is necessary to insert horizontal space into a formula.
11414 This is done by inserting a protected space (shortcut
11417 arg "command-alternatives space-insert protected ; math-space"
11422 \begin_inset Quotes eld
11428 \begin_inset space \textvisiblespace{}
11434 \begin_inset Quotes erd
11437 appears and by pressing
11441 several times one can select one of eight different space sizes.
11442 The spaces can also be inserted using the math toolbar button
11445 arg "math-insert \\space"
11448 or special commands.
11449 Independent from the inserted command, one can select the size again by
11457 \begin_layout Standard
11460 \begin_inset Tabular
11461 <lyxtabular version="3" rows="6" columns="3">
11462 <features rotate="0" tabularvalignment="middle">
11463 <column alignment="center" valignment="top">
11464 <column alignment="center" valignment="top" width="15col%">
11465 <column alignment="center" valignment="top">
11467 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
11470 \begin_layout Plain Layout
11476 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
11479 \begin_layout Plain Layout
11489 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
11492 \begin_layout Plain Layout
11500 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
11503 \begin_layout Plain Layout
11511 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
11514 \begin_layout Plain Layout
11520 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
11523 \begin_layout Plain Layout
11524 \begin_inset Formula $A\, B$
11534 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
11537 \begin_layout Plain Layout
11545 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
11548 \begin_layout Plain Layout
11554 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
11557 \begin_layout Plain Layout
11558 \begin_inset Formula $A\: B$
11568 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
11571 \begin_layout Plain Layout
11579 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
11582 \begin_layout Plain Layout
11588 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
11591 \begin_layout Plain Layout
11592 \begin_inset Formula $A\; B$
11602 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
11605 \begin_layout Plain Layout
11613 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
11616 \begin_layout Plain Layout
11622 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
11625 \begin_layout Plain Layout
11626 \begin_inset Formula $A\quad B$
11636 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
11639 \begin_layout Plain Layout
11647 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
11650 \begin_layout Plain Layout
11656 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
11659 \begin_layout Plain Layout
11660 \begin_inset Formula $A\qquad B$
11674 \begin_inset space \hfill{}
11678 \begin_inset Tabular
11679 <lyxtabular version="3" rows="6" columns="3">
11680 <features rotate="0" tabularvalignment="middle">
11681 <column alignment="center" valignment="top">
11682 <column alignment="center" valignment="top" width="15col%">
11683 <column alignment="center" valignment="top">
11685 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
11688 \begin_layout Plain Layout
11694 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
11697 \begin_layout Plain Layout
11707 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
11710 \begin_layout Plain Layout
11718 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
11721 \begin_layout Plain Layout
11729 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
11732 \begin_layout Plain Layout
11738 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
11741 \begin_layout Plain Layout
11742 \begin_inset Formula $A\hfill B$
11752 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
11755 \begin_layout Plain Layout
11763 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
11766 \begin_layout Plain Layout
11772 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
11775 \begin_layout Plain Layout
11776 \begin_inset Formula $A\hspace*{1em}B$
11786 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
11789 \begin_layout Plain Layout
11797 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
11800 \begin_layout Plain Layout
11806 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
11809 \begin_layout Plain Layout
11810 \begin_inset Formula $A\hspace{1em}B$
11820 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
11823 \begin_layout Plain Layout
11827 \begin_inset space \textvisiblespace{}
11835 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
11838 \begin_layout Plain Layout
11844 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
11847 \begin_layout Plain Layout
11848 \begin_inset Formula $A\ B$
11858 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
11861 \begin_layout Plain Layout
11869 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
11872 \begin_layout Plain Layout
11878 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
11881 \begin_layout Plain Layout
11882 \begin_inset Formula $A\! B$
11898 \begin_layout Standard
11900 \begin_inset space ~
11904 \begin_inset space \thinspace{}
11908 \begin_inset space \thinspace{}
11911 7 are variable spaces which are explained in
11912 \begin_inset CommandInset ref
11914 reference "sub:Variable-Space"
11920 \begin_inset space ~
11923 9 seems to produce no space.
11924 It is displayed red in LyX contrary to the other sizes, because it is a
11926 There are two more negative spaces:
11929 \begin_layout Standard
11931 \begin_inset Tabular
11932 <lyxtabular version="3" rows="3" columns="3">
11933 <features rotate="0" tabularvalignment="middle">
11934 <column alignment="center" valignment="middle" width="6.8cm">
11935 <column alignment="center" valignment="top" width="0pt">
11936 <column alignment="center" valignment="top" width="0pt">
11938 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
11941 \begin_layout Plain Layout
11947 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
11950 \begin_layout Plain Layout
11958 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
11961 \begin_layout Plain Layout
11971 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
11974 \begin_layout Plain Layout
11979 keystrokes after inserting the protected space
11984 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
11987 \begin_layout Plain Layout
11993 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
11996 \begin_layout Plain Layout
12004 <cell multicolumn="1" alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
12007 \begin_layout Plain Layout
12013 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
12016 \begin_layout Plain Layout
12017 \begin_inset Formula $A\negmedspace B$
12025 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
12028 \begin_layout Plain Layout
12029 \begin_inset Formula $A\negthickspace B$
12045 \begin_layout Standard
12046 Negative spaces can lead to characters overlapping each other.
12047 Thus they can be used to enforce ligatures, which are e.
12048 \begin_inset space \thinspace{}
12052 \begin_inset space \space{}
12055 useful for summation operators:
12058 \begin_layout Standard
12060 \begin_inset Tabular
12061 <lyxtabular version="3" rows="3" columns="2">
12062 <features rotate="0" tabularvalignment="middle">
12063 <column alignment="center" valignment="top">
12064 <column alignment="center" valignment="top">
12066 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
12069 \begin_layout Plain Layout
12075 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
12078 \begin_layout Plain Layout
12080 \begin_inset Note Note
12083 \begin_layout Plain Layout
12090 is only used as spacer.
12102 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
12105 \begin_layout Plain Layout
12111 \begin_inset space \textvisiblespace{}
12119 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
12122 \begin_layout Plain Layout
12123 \begin_inset Formula $\raisebox{4.5mm}{}\sum\sum f_{kl}\raisebox{-2.5mm}{}$
12133 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
12136 \begin_layout Plain Layout
12144 \begin_inset space \textvisiblespace{}
12152 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
12155 \begin_layout Plain Layout
12156 \begin_inset Formula $\raisebox{4.5mm}{}\sum\negmedspace\sum f_{kl}\raisebox{-2.5mm}{}$
12172 \begin_layout Standard
12174 \begin_inset VSpace medskip
12180 \begin_layout Standard
12182 Relations like for example equal signs, are always surrounded by space.
12183 To suppress this, the equal sign is placed into a TeX-brace.
12184 The following example demonstrates this:
12187 \begin_layout Standard
12189 \begin_inset Tabular
12190 <lyxtabular version="3" rows="2" columns="2">
12191 <features rotate="0" tabularvalignment="middle">
12192 <column alignment="center" valignment="top" width="0pt">
12193 <column alignment="center" valignment="top" width="0pt">
12195 <cell alignment="center" valignment="top" usebox="none">
12198 \begin_layout Plain Layout
12204 <cell alignment="center" valignment="top" usebox="none">
12207 \begin_layout Plain Layout
12208 \begin_inset Formula $A=B$
12218 <cell alignment="center" valignment="top" usebox="none">
12221 \begin_layout Plain Layout
12222 \begin_inset Note Note
12225 \begin_layout Plain Layout
12232 is only used as spacer.
12238 \begin_inset Formula $\raisebox{5mm}{}$
12241 equation without space
12246 <cell multicolumn="1" alignment="center" valignment="top" usebox="none">
12249 \begin_layout Plain Layout
12250 \begin_inset Formula $A{=}B$
12266 \begin_layout Standard
12268 The command for the last formula is:
12273 \begin_inset Formula $\to$
12279 \begin_layout Standard
12280 \begin_inset VSpace bigskip
12286 \begin_layout Standard
12287 Spaces are needed for physical units, because the space between the value
12288 and the unit is the smallest one and not a normal space.
12289 For units in text, the smallest space is inserted via the menu
12291 Insert\SpecialChar \menuseparator
12292 Formatting\SpecialChar \menuseparator
12294 \begin_inset space ~
12302 arg "space-insert thin"
12308 \begin_layout Standard
12309 An example to visualize the difference:
12312 \begin_layout Standard
12313 \begin_inset Tabular
12314 <lyxtabular version="3" rows="2" columns="2">
12315 <features rotate="0" tabularvalignment="middle">
12316 <column alignment="left" valignment="top">
12317 <column alignment="left" valignment="top">
12319 <cell alignment="center" valignment="top" usebox="none">
12322 \begin_layout Plain Layout
12324 \begin_inset Formula $\cdot$
12332 <cell alignment="center" valignment="top" usebox="none">
12335 \begin_layout Plain Layout
12336 space between value and unit
12343 <cell alignment="center" valignment="top" usebox="none">
12346 \begin_layout Plain Layout
12348 \begin_inset space \thinspace{}
12352 \begin_inset Formula $\cdot$
12360 <cell alignment="center" valignment="top" usebox="none">
12363 \begin_layout Plain Layout
12364 smallest space between value and unit
12377 \begin_layout Subsection
12382 \begin_layout Plain Layout
12395 \begin_layout Plain Layout
12396 for vertical space in formulas see
12397 \begin_inset CommandInset ref
12399 reference "sub:Line-Separation"
12412 \begin_layout Plain Layout
12420 \begin_inset Note Note
12423 \begin_layout Plain Layout
12426 texorpdfstring is used to avoid that the footnote appears in the PDF-bookmark.
12429 \begin_layout Plain Layout
12432 texorpdfstring is in section
12433 \begin_inset CommandInset ref
12435 reference "sub:Formulas-in-Section"
12445 \begin_inset CommandInset label
12447 name "sub:Variable-Space"
12452 \begin_inset Index idx
12455 \begin_layout Plain Layout
12456 Space ! horizontal ! variable
12464 \begin_layout Standard
12465 Space with a defined length can be inserted with the command
12472 \begin_inset Index idx
12475 \begin_layout Plain Layout
12485 \begin_inset Quotes eld
12491 \begin_inset space \textvisiblespace{}
12497 \begin_inset Quotes erd
12501 The length can be specified by left-clicking on the
12502 \begin_inset Quotes eld
12508 \begin_inset space \textvisiblespace{}
12514 \begin_inset Quotes erd
12518 The length may also be negative.
12519 When a space would be the first character in a line it would be omitted.
12520 To force its output use the command
12532 or left-click on the
12533 \begin_inset Quotes eld
12539 \begin_inset space \textvisiblespace{}
12545 \begin_inset Quotes erd
12548 and check the option
12553 \begin_inset Newline newline
12556 To insert as much space as is available, the command
12563 \begin_inset Index idx
12566 \begin_layout Plain Layout
12577 \begin_layout Standard
12578 \begin_inset VSpace -1mm
12584 \begin_layout Standard
12586 \begin_inset Tabular
12587 <lyxtabular version="3" rows="4" columns="2">
12588 <features rotate="0" tabularvalignment="middle">
12589 <column alignment="center" valignment="top">
12590 <column alignment="center" valignment="top">
12592 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
12595 \begin_layout Plain Layout
12603 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
12606 \begin_layout Plain Layout
12614 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
12617 \begin_layout Plain Layout
12621 \begin_inset space \textvisiblespace{}
12627 \begin_inset space \thinspace{}
12635 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
12638 \begin_layout Plain Layout
12639 \begin_inset Formula $A=B\hspace{3cm}A\not=C$
12649 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
12652 \begin_layout Plain Layout
12656 \begin_inset space \textvisiblespace{}
12662 \begin_inset space \thinspace{}
12670 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
12673 \begin_layout Plain Layout
12674 \begin_inset Formula $A\hspace{-1mm}A\not=A$
12684 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
12687 \begin_layout Plain Layout
12691 \begin_inset space \textvisiblespace{}
12699 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
12702 \begin_layout Plain Layout
12703 \begin_inset Formula $A=A\hfill B=B$
12719 \begin_layout Standard
12720 In the last example the available space is given by the longest column entry
12722 In an inline formula the space depends on the length of the line in which
12730 Thus, when the line uses the full width, no space will be created.
12737 only has an effect on displayed formulas when the formula style
12742 (Formula styles are explained in
12743 \begin_inset CommandInset ref
12745 reference "sec:Formula-Styles"
12752 \begin_layout Standard
12759 , there are the commands
12771 that fill the space with a pattern, see
12772 \begin_inset CommandInset ref
12774 reference "sub:Ellipses"
12781 \begin_layout Standard
12782 For text, variable space can be inserted via the menu
12784 Insert\SpecialChar \menuseparator
12785 Formatting\SpecialChar \menuseparator
12787 \begin_inset space ~
12795 \begin_layout Standard
12796 This is a line with
12797 \begin_inset space \hspace{}
12802 \begin_inset space \thinspace{}
12808 \begin_layout Standard
12809 This is a line with
12810 \begin_inset space \hfill{}
12816 \begin_layout Subsection
12817 Space besides inline Formulas
12818 \begin_inset Index idx
12821 \begin_layout Plain Layout
12822 Space ! besides inline formulas
12830 \begin_layout Standard
12831 The space that surrounds inline formulas can be adjusted with the length
12839 \begin_inset Index idx
12842 \begin_layout Plain Layout
12851 The value of a length is set with the command
12858 \begin_inset Index idx
12861 \begin_layout Plain Layout
12869 which has the following scheme:
12872 \begin_layout Standard
12877 setlength{length name}{value}
12880 \begin_layout Standard
12888 \begin_inset space \thinspace{}
12894 \begin_layout Standard
12904 \begin_layout Standard
12905 is inserted in TeX-mode.
12907 \begin_inset space \thinspace{}
12910 mm space will now be set around all inline formulas:
12914 \begin_layout Plain Layout
12928 \begin_layout Standard
12929 This is a line with an inline formula
12930 \begin_inset Formula $A=B$
12934 \begin_inset space \thinspace{}
12937 mm surrounding space.
12941 \begin_layout Plain Layout
12955 \begin_layout Standard
12956 To return to the predefined value,
12962 is set to the value 0
12963 \begin_inset space \thinspace{}
12969 \begin_layout Section
12971 \begin_inset Index idx
12974 \begin_layout Plain Layout
12981 \begin_inset Index idx
12984 \begin_layout Plain Layout
12989 \begin_layout Plain Layout
13000 \begin_layout Plain Layout
13015 \begin_layout Standard
13016 Boxes for text are described in chapter
13023 \begin_inset space ~
13031 \begin_layout Subsection
13033 \begin_inset CommandInset label
13035 name "sub:Boxes-with-Frame"
13040 \begin_inset Index idx
13043 \begin_layout Plain Layout
13052 \begin_layout Standard
13053 It is possible to frame a formula or part of one with the commands
13060 \begin_inset Index idx
13063 \begin_layout Plain Layout
13078 \begin_inset Index idx
13081 \begin_layout Plain Layout
13092 \begin_layout Standard
13093 When one of these commands is inserted in a formula, a blue box appears
13094 within a frame to enter formula parts.
13101 an additional formula has to be created by
13105 within this box, because the box content will otherwise be treated as mathemati
13113 is used, a new formula is automatically created inside the frame.
13116 \begin_layout Standard
13123 is not suitable to frame displayed formulas because the formula will always
13124 be set in the size of the text.
13131 is in contrary not suitable to frame inline formulas, because the formula
13132 will always be set in the size of a displayed formula.
13135 \begin_layout Standard
13149 \begin_inset Index idx
13152 \begin_layout Plain Layout
13160 where additionally the frame width and the alignment can be specified.
13167 is used in the following scheme:
13170 \begin_layout Standard
13175 framebox[frame width][position]{box content}
13178 \begin_layout Standard
13179 The position can either be
13196 right aligns the formula in the box.
13197 When no position is given, the formula will be centered.
13198 \begin_inset Newline newline
13201 If no width is given, also no position can be given.
13202 In this case the frame width is adjusted to the box content like for
13211 \begin_layout Standard
13218 is inserted, a box appears containing three blue boxes.
13219 The first two boxes are surrounded by brackets and denote the two optional
13221 The third box is for formula parts like for
13230 \begin_layout Standard
13232 \begin_inset Tabular
13233 <lyxtabular version="3" rows="5" columns="2">
13234 <features rotate="0" tabularvalignment="middle">
13235 <column alignment="center" valignment="top">
13236 <column alignment="center" valignment="top">
13238 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
13241 \begin_layout Plain Layout
13247 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
13250 \begin_layout Plain Layout
13252 \begin_inset Note Note
13255 \begin_layout Plain Layout
13262 is only used as spacer.
13274 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
13277 \begin_layout Plain Layout
13281 \begin_inset space \textvisiblespace{}
13291 \begin_inset space \textvisiblespace{}
13299 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
13302 \begin_layout Plain Layout
13303 \begin_inset Formula $\raisebox{6mm}{}\fbox{\ensuremath{\int A=B}}\raisebox{-4mm}{}$
13313 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
13316 \begin_layout Plain Layout
13320 \begin_inset space \textvisiblespace{}
13326 \begin_inset space \textvisiblespace{}
13334 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
13337 \begin_layout Plain Layout
13338 \begin_inset Formula $\raisebox{8.5mm}{}\boxed{\int A=B}\raisebox{-6.5mm}{}$
13348 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
13351 \begin_layout Plain Layout
13355 \begin_inset space \textvisiblespace{}
13363 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
13366 \begin_layout Plain Layout
13367 \begin_inset Formula $\raisebox{6mm}{}A+\fbox{B}\raisebox{-3mm}{}$
13377 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
13380 \begin_layout Plain Layout
13384 \begin_inset space \textvisiblespace{}
13388 \begin_inset Formula $\to$
13392 \begin_inset Formula $\to$
13402 \begin_inset space \textvisiblespace{}
13406 \begin_inset Formula $\downarrow$
13414 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
13417 \begin_layout Plain Layout
13418 \begin_inset Formula $\raisebox{6mm}{}$
13422 \begin_inset Formula $\framebox[20mm][]{\ensuremath{\frac{A}{B}}}$
13426 \begin_inset Formula $\raisebox{-4mm}{}$
13442 \begin_layout Standard
13443 The frame thickness can also be adjusted.
13444 To do this the following commands have to be inserted in TeX-mode before
13448 \begin_layout Standard
13458 \begin_inset Quotes eld
13462 \begin_inset Quotes erd
13476 \begin_inset Quotes eld
13480 \begin_inset Quotes erd
13486 \begin_layout Standard
13487 \begin_inset Quotes eld
13491 \begin_inset Quotes erd
13494 specifies the minimal distance between the frame and the first character
13496 An example for this is the following framed formula:
13500 \begin_layout Plain Layout
13512 \begin_inset Formula
13519 Before this formula the commands
13522 \begin_layout Standard
13544 \begin_layout Standard
13545 were inserted in TeX-mode.
13546 The given values are used for all following boxes.
13549 \begin_layout Standard
13550 To return to the standard frame size, the command
13553 \begin_layout Standard
13578 \begin_layout Plain Layout
13592 \begin_layout Standard
13593 is inserted in TeX-mode before the next formula.
13596 \begin_layout Subsection
13597 Boxes without Frame
13598 \begin_inset CommandInset label
13600 name "sub:Boxes-without-Frame"
13605 \begin_inset Index idx
13608 \begin_layout Plain Layout
13609 Boxes ! without frame
13617 \begin_layout Standard
13618 For boxes without a frame there are the following box commands:
13625 \begin_inset Index idx
13628 \begin_layout Plain Layout
13643 \begin_inset Index idx
13646 \begin_layout Plain Layout
13661 \begin_inset Index idx
13664 \begin_layout Plain Layout
13675 \begin_layout Standard
13682 a box can be super- or subscripted.
13683 But in contrary to normal super- and subscripting, the characters in the
13684 box keep their font size.
13691 is used in the following scheme:
13694 \begin_layout Standard
13699 raisebox{height}{box content}
13702 \begin_layout Standard
13703 When the box should contain a formula, an extra formula is needed like for
13714 \begin_inset Note Greyedout
13717 \begin_layout Plain Layout
13728 this extra formula is created by pressing
13732 twice instead of once because LyX doesn't yet support
13746 \begin_layout Standard
13748 \begin_inset Tabular
13749 <lyxtabular version="3" rows="4" columns="2">
13750 <features rotate="0" tabularvalignment="middle">
13751 <column alignment="center" valignment="top">
13752 <column alignment="center" valignment="top">
13754 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
13757 \begin_layout Plain Layout
13763 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
13766 \begin_layout Plain Layout
13774 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
13777 \begin_layout Plain Layout
13781 \begin_inset Formula $\to$
13787 \begin_inset Formula $\to$
13795 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
13798 \begin_layout Plain Layout
13799 \begin_inset Formula $H\raisebox{2mm}{al}lo$
13809 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
13812 \begin_layout Plain Layout
13816 \begin_inset Formula $\to$
13822 \begin_inset Formula $\to$
13830 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
13833 \begin_layout Plain Layout
13834 \begin_inset Formula $H\raisebox{-2mm}{al}lo$
13844 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
13847 \begin_layout Plain Layout
13851 \begin_inset Formula $\to$
13867 \begin_inset space \textvisiblespace{}
13875 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
13878 \begin_layout Plain Layout
13879 \begin_inset Formula $A=\raisebox{-2mm}{\mbox{\ensuremath{\sqrt{B}}}}$
13895 \begin_layout Standard
13920 , with the difference that there is no frame.
13923 \begin_layout Subsection
13925 \begin_inset CommandInset label
13927 name "sub:Colored-Boxes"
13932 \begin_inset Index idx
13935 \begin_layout Plain Layout
13944 \begin_layout Standard
13945 To be able to use all commands explained in this section, the LaTeX-package
13954 \begin_layout Plain Layout
13959 is part of every LaTeX standard installation.
13965 \begin_inset Index idx
13968 \begin_layout Plain Layout
13974 has to be loaded in the LaTeX-preamble with the line
13978 \begin_layout Plain Layout
13979 When text is colored somewhere in the document with a predefined color,
13980 LyX loads the LaTeX-package
13985 Thus it is possible that the package is loaded twice, but this does not
13992 \begin_inset Note Note
13995 \begin_layout Plain Layout
13996 To avoid that the package is loaded twice, a macro was inserted to the LaTeX-pre
14005 \begin_layout Standard
14013 \begin_layout Standard
14014 \begin_inset VSpace medskip
14017 To color boxes, the command
14024 \begin_inset Index idx
14027 \begin_layout Plain Layout
14035 is used in the following scheme:
14038 \begin_layout Standard
14043 colorbox{color}{box content}
14046 \begin_layout Standard
14047 The box content can also be a box and a
14053 can also be part of another box (see the 2nd and 3rd example).
14054 When the box should contain a formula, an extra formula has to be created,
14055 the same way as for
14065 \begin_layout Plain Layout
14066 This also applies for the command
14080 \begin_layout Standard
14081 One of the following predefined colors can be chosen:
14084 \begin_layout Standard
14118 \begin_layout Standard
14120 \begin_inset Tabular
14121 <lyxtabular version="3" rows="4" columns="2">
14122 <features rotate="0" tabularvalignment="middle">
14123 <column alignment="center" valignment="top">
14124 <column alignment="center" valignment="top">
14126 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
14129 \begin_layout Plain Layout
14135 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
14138 \begin_layout Plain Layout
14140 \begin_inset Note Note
14143 \begin_layout Plain Layout
14150 is only used as spacer.
14162 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
14165 \begin_layout Plain Layout
14169 \begin_inset Formula $\to$
14179 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
14182 \begin_layout Plain Layout
14183 \begin_inset Formula $\raisebox{6mm}{}\colorbox{yellow}{A=B}\raisebox{-3mm}{}$
14193 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
14196 \begin_layout Plain Layout
14200 \begin_inset Formula $\to$
14208 \begin_inset space \textvisiblespace{}
14216 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
14219 \begin_layout Plain Layout
14220 \begin_inset Formula $\raisebox{6mm}{}\colorbox{green}{\fbox{A=B}}\raisebox{-3mm}{}$
14230 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
14233 \begin_layout Plain Layout
14237 \begin_inset space \textvisiblespace{}
14243 \begin_inset Formula $\to$
14259 \begin_inset space \textvisiblespace{}
14267 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
14270 \begin_layout Plain Layout
14271 \begin_inset Formula $\raisebox{7mm}{}\fbox{\colorbox{green}{\mbox{\ensuremath{\int C=D}}}}\raisebox{-5mm}{}$
14287 \begin_layout Standard
14294 only colors the box but not the characters in the box.
14295 To color all characters, the whole formula is highlighted and the desired
14296 color is chosen in the
14299 \begin_inset space ~
14305 The dialog can be called with the toolbar button
14308 arg "dialog-show character"
14313 Edit\SpecialChar \menuseparator
14315 \begin_inset space ~
14318 Style\SpecialChar \menuseparator
14322 The formula number then has the same color as the formula.
14323 When the formula number should get another color than the formula characters,
14324 the color must be changed within the formula.
14327 \begin_layout Standard
14331 \begin_layout Standard
14334 \begin_inset Formula
14336 \int A=B\label{eq:red}
14344 \begin_inset Formula
14346 \textcolor{red}{\int A=B}\label{eq:redgreen}
14354 \begin_layout Standard
14356 \begin_inset CommandInset ref
14362 is completely colored red.
14363 \begin_inset Newline newline
14367 \begin_inset CommandInset ref
14369 reference "eq:redgreen"
14373 was first completely colored green to set the color for the formula number.
14374 Subsequently the formula characters were colored red.
14377 \begin_layout Standard
14378 \begin_inset VSpace bigskip
14381 To color the frame different than the rest of the box, the command
14388 \begin_inset Index idx
14391 \begin_layout Plain Layout
14399 is used in the following scheme:
14402 \begin_layout Standard
14407 fcolorbox{frame color}{color}{box content}
14410 \begin_layout Standard
14417 is an extension of the command
14424 The frame width is set, like for
14447 \begin_layout Plain Layout
14459 \begin_inset Formula
14461 \fcolorbox{cyan}{magenta}{A=B}
14470 \begin_layout Plain Layout
14484 \begin_layout Standard
14485 This formula was created with the command
14486 \begin_inset Newline newline
14494 \begin_inset Formula $\to$
14500 \begin_inset Formula $\to$
14510 \begin_layout Standard
14511 \begin_inset VSpace bigskip
14514 To use other colors than the predefined ones, they have to be defined first.
14517 \begin_layout Standard
14518 One can for example define the color
14519 \begin_inset Quotes eld
14527 \begin_inset Quotes erd
14530 with the LaTeX-preamble line:
14533 \begin_layout Standard
14538 definecolor{darkgreen}{cmyk}{0.5,
14553 \begin_inset Index idx
14556 \begin_layout Plain Layout
14567 \begin_layout Standard
14572 is the color space that denotes the colors
14589 The four comma separated numbers are the portion factor for the corresponding
14590 colors of the color space.
14591 The factors can be in the range of 0
14592 \begin_inset space \thinspace{}
14596 \begin_inset space \thinspace{}
14604 also the color space
14608 can be used for definitions.
14625 , so that there are in this case three portion factors for the corresponding
14627 Furthermore there is the color space
14631 with one portion factor for the gray value.
14634 \begin_layout Standard
14635 As example a framed box with the new defined color
14639 where the characters have been colored
14644 \begin_inset Formula
14646 \colorbox{darkgreen}{\color{yellow}\boxed{\int A\,\mathrm{d}x=\frac{\sqrt[5]{B}}{\ln\left(\frac{1}{3}\right)}}}
14654 \begin_layout Standard
14655 Self-defined colors can also be used for text with the help of the command
14663 \begin_inset Index idx
14666 \begin_layout Plain Layout
14675 \begin_layout Standard
14679 \begin_layout Plain Layout
14683 textcolor{darkgreen}{
14689 \begin_inset Quotes eld
14693 \begin_inset Quotes erd
14700 \begin_layout Plain Layout
14710 \begin_layout Standard
14718 \begin_inset Index idx
14721 \begin_layout Plain Layout
14729 is used in the scheme
14733 textcolor{color}{characters to color}
14738 \begin_layout Subsection
14740 \begin_inset CommandInset label
14742 name "sub:Paragraph-Boxes"
14747 \begin_inset Index idx
14750 \begin_layout Plain Layout
14751 Boxes ! as paragraph
14759 \begin_layout Standard
14760 A box that can contain several lines and paragraphs, a so-called paragraph
14761 box (parbox), can be created with the menu
14763 Insert\SpecialChar \menuseparator
14766 or the toolbar button
14775 \begin_layout Standard
14776 The following example shows a framed parbox in a line:
14779 \begin_layout Standard
14780 \begin_inset VSpace medskip
14784 \begin_inset Box Boxed
14794 height_special "totalheight"
14797 \begin_layout Plain Layout
14798 This is a paragraph box.
14800 \begin_inset space \thinspace{}
14803 cm long and can also contain formulas:
14804 \begin_inset Formula $\int A\,\mathrm{d}s=C$
14815 \begin_layout Standard
14816 \begin_inset VSpace medskip
14822 \begin_layout Standard
14823 Such a box is created by right-clicking on the gray box inset.
14824 A dialog pops up showing the box properties.
14838 \begin_inset space \thinspace{}
14843 Vertical Box Alignment
14848 \begin_layout Standard
14849 \begin_inset VSpace medskip
14852 In LaTeX a parbox is created with the command
14859 \begin_inset Index idx
14862 \begin_layout Plain Layout
14870 which has the following scheme:
14873 \begin_layout Standard
14878 parbox[position]{width}{box content}
14881 \begin_layout Standard
14896 \begin_inset Quotes eld
14900 \begin_inset Quotes erd
14903 means that the box is aligned within the surrounding text with its last
14910 \begin_inset Quotes eld
14914 \begin_inset Quotes erd
14917 this is done with the first line.
14918 When no position is given, the box will be vertically centered, see section
14926 \begin_inset space ~
14931 manual for examples.
14934 \begin_layout Standard
14935 \begin_inset VSpace bigskip
14938 To frame formulas completely, including the formula number, the formula
14939 must be set into a parbox.
14940 To do this, the command
14954 is inserted in TeX-mode before the formula.
14962 \begin_inset Index idx
14965 \begin_layout Plain Layout
14973 is hereby the line width set for the document.
14974 Because the frame is outside the parbox, 2
14975 \begin_inset space \thinspace{}
14978 times the frame separation and the frame thickness must be subtracted from
14980 As this is not automatically done by LyX due to a bug
14984 \begin_layout Plain Layout
14985 \begin_inset CommandInset href
14987 name "LyX-bug #4483"
14988 target "http://www.lyx.org/trac/ticket/4483"
14997 , TeX-mode has to be used.
14998 To be able to multiply and subtract in arguments, the LaTeX-package
15006 \begin_layout Plain Layout
15011 is part of every LaTeX standard installation.
15017 \begin_inset Index idx
15020 \begin_layout Plain Layout
15026 must be loaded in the LaTeX-preamble with the line
15029 \begin_layout Standard
15037 \begin_layout Standard
15038 Behind the formula both boxes are closed by entering
15043 Here is an example:
15047 \begin_layout Plain Layout
15061 \begin_layout Standard
15065 \begin_layout Plain Layout
15083 \begin_inset Formula
15085 \int A\,\mathrm{d}x=\frac{\sqrt[5]{B}}{\ln\left(\frac{1}{3}\right)}
15094 \begin_layout Plain Layout
15105 \begin_layout Plain Layout
15119 \begin_layout Standard
15120 \begin_inset VSpace medskip
15123 As a parbox is used as the argument of
15129 , there is in this case no difference between
15144 \begin_layout Standard
15145 \begin_inset VSpace bigskip
15148 Paragraph boxes are very useful to comment formulas directly.
15155 is used in combination with the command
15169 \begin_inset CommandInset ref
15171 reference "sub:User-defined-Numbering"
15178 \begin_layout Standard
15179 An example of a formula commented with
15188 \begin_layout Standard
15192 \begin_layout Plain Layout
15205 This is a description.
15206 It is distinctly separated from the formula and multiline.
15210 \begin_layout Plain Layout
15222 \begin_layout Standard
15223 Such a formula must be inserted completely in TeX-mode because LyX does
15224 not yet support the command
15231 The formula is created with the following command sequence:
15234 \begin_layout Standard
15247 is inserted in TeX-mode.
15251 \begin_layout Plain Layout
15252 When the formula style
15264 can also be replaced by
15271 (formula styles see
15272 \begin_inset CommandInset ref
15274 reference "sec:Formula-Styles"
15283 Then the description follows as normal text and finally
15289 is inserted in TeX-mode.
15302 hereby create a displayed formula.
15305 \begin_layout Standard
15312 can be seen in this example that was
15313 \begin_inset Quotes eld
15317 \begin_inset Quotes erd
15320 using the mathematical textmode:
15321 \begin_inset Formula
15323 5x-7b=3b\textrm{This is a description. It is not separated from the formula ...}
15331 \begin_layout Section
15333 \begin_inset Index idx
15336 \begin_layout Plain Layout
15345 \begin_layout Subsection
15347 \begin_inset CommandInset label
15349 name "sub:Big-Operators"
15354 \begin_inset Index idx
15357 \begin_layout Plain Layout
15364 \begin_inset Index idx
15367 \begin_layout Plain Layout
15374 \begin_inset Index idx
15377 \begin_layout Plain Layout
15386 \begin_layout Standard
15387 To be able to use all integral operators listed here, the option
15389 Use esint package automatically
15391 must be set in the document settings under
15394 \begin_inset space ~
15402 \begin_layout Standard
15403 \begin_inset space \hfill{}
15407 \begin_inset Tabular
15408 <lyxtabular version="3" rows="11" columns="2">
15409 <features rotate="0" tabularvalignment="middle">
15410 <column alignment="center" valignment="top" width="0pt">
15411 <column alignment="center" valignment="top" width="0pt">
15413 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
15416 \begin_layout Plain Layout
15422 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
15425 \begin_layout Plain Layout
15433 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
15436 \begin_layout Plain Layout
15440 \begin_inset Index idx
15443 \begin_layout Plain Layout
15456 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
15459 \begin_layout Plain Layout
15460 \begin_inset Formula $\int$
15470 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
15473 \begin_layout Plain Layout
15481 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
15484 \begin_layout Plain Layout
15485 \begin_inset Formula $\oint$
15495 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
15498 \begin_layout Plain Layout
15506 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
15509 \begin_layout Plain Layout
15510 \begin_inset Formula $\ointctrclockwise$
15520 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
15523 \begin_layout Plain Layout
15531 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
15534 \begin_layout Plain Layout
15535 \begin_inset Formula $\ointclockwise$
15545 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
15548 \begin_layout Plain Layout
15556 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
15559 \begin_layout Plain Layout
15560 \begin_inset Formula $\sqint$
15570 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
15573 \begin_layout Plain Layout
15581 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
15584 \begin_layout Plain Layout
15586 \begin_inset Formula $\fint$
15596 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
15599 \begin_layout Plain Layout
15607 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
15610 \begin_layout Plain Layout
15612 \begin_inset Formula $\landupint$
15622 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
15625 \begin_layout Plain Layout
15633 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
15636 \begin_layout Plain Layout
15638 \begin_inset Formula $\landdownint$
15648 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
15651 \begin_layout Plain Layout
15659 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
15662 \begin_layout Plain Layout
15663 \begin_inset Formula $\bigcap$
15673 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
15676 \begin_layout Plain Layout
15684 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
15687 \begin_layout Plain Layout
15688 \begin_inset Formula $\bigcup$
15702 \begin_inset space \hfill{}
15706 \begin_inset Tabular
15707 <lyxtabular version="3" rows="11" columns="2">
15708 <features rotate="0" tabularvalignment="middle">
15709 <column alignment="center" valignment="top" width="0pt">
15710 <column alignment="center" valignment="top" width="0pt">
15712 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
15715 \begin_layout Plain Layout
15721 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
15724 \begin_layout Plain Layout
15732 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
15735 \begin_layout Plain Layout
15739 \begin_inset Index idx
15742 \begin_layout Plain Layout
15755 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
15758 \begin_layout Plain Layout
15759 \begin_inset Formula $\sum$
15769 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
15772 \begin_layout Plain Layout
15776 \begin_inset Index idx
15779 \begin_layout Plain Layout
15786 \begin_layout Plain Layout
15805 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
15808 \begin_layout Plain Layout
15809 \begin_inset Formula $\prod$
15819 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
15822 \begin_layout Plain Layout
15830 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
15833 \begin_layout Plain Layout
15834 \begin_inset Formula $\coprod$
15844 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
15847 \begin_layout Plain Layout
15855 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
15858 \begin_layout Plain Layout
15859 \begin_inset Formula $\bigodot$
15869 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
15872 \begin_layout Plain Layout
15880 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
15883 \begin_layout Plain Layout
15884 \begin_inset Formula $\bigotimes$
15894 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
15897 \begin_layout Plain Layout
15905 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
15908 \begin_layout Plain Layout
15909 \begin_inset Formula $\bigoplus$
15919 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
15922 \begin_layout Plain Layout
15930 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
15933 \begin_layout Plain Layout
15934 \begin_inset Formula $\bigwedge$
15944 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
15947 \begin_layout Plain Layout
15955 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
15958 \begin_layout Plain Layout
15959 \begin_inset Formula $\bigvee$
15969 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
15972 \begin_layout Plain Layout
15980 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
15983 \begin_layout Plain Layout
15984 \begin_inset Formula $\bigsqcup$
15994 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
15997 \begin_layout Plain Layout
16005 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
16008 \begin_layout Plain Layout
16009 \begin_inset Formula $\biguplus$
16023 \begin_inset space \hfill{}
16029 \begin_layout Standard
16030 All big operators can also be inserted via the math toolbar button
16033 arg "math-insert \\intop"
16039 \begin_layout Standard
16040 The operators are called big because they are bigger than the sometimes
16041 equal looking binary operators.
16042 All big operators can have limits as described in the next subsection.
16045 \begin_layout Standard
16046 For all integral operators there is a second version available, ending in
16064 These operators are different from
16071 \begin_inset space \space{}
16074 in the style the operator limits are displayed, see
16075 \begin_inset CommandInset ref
16077 reference "sub:Operator-Limits"
16085 \begin_layout Subsubsection*
16086 Advice for Integrals
16089 \begin_layout Standard
16094 in an integral is an operator, that therefore has to be set upright.
16095 This is done by highlighting the
16099 and using the keyboard shortcut
16109 \begin_layout Plain Layout
16115 \begin_inset CommandInset ref
16117 reference "sub:Font-Styles"
16127 Finally the smallest space is inserted before the
16131 , as this is usual for operators.
16135 \begin_layout Standard
16137 \begin_inset Formula $\int A(x)dx$
16141 \begin_inset Newline newline
16145 \begin_inset Phantom HPhantom
16148 \begin_layout Plain Layout
16155 \begin_inset Formula $\int A(x)\,\mathrm{d}x$
16161 \begin_layout Standard
16162 For multiple integrals there are the following commands:
16163 \begin_inset VSpace medskip
16169 \begin_layout Standard
16170 \begin_inset space \hfill{}
16174 \begin_inset Tabular
16175 <lyxtabular version="3" rows="4" columns="2">
16176 <features rotate="0" tabularvalignment="middle">
16177 <column alignment="center" valignment="top">
16178 <column alignment="center" valignment="top">
16180 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
16183 \begin_layout Plain Layout
16189 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
16192 \begin_layout Plain Layout
16194 \begin_inset Note Note
16197 \begin_layout Plain Layout
16204 is only used as spacer.
16216 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
16219 \begin_layout Plain Layout
16227 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
16230 \begin_layout Plain Layout
16231 \begin_inset Formula $\raisebox{4.5mm}{}\iint\raisebox{-2.5mm}{}$
16241 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
16244 \begin_layout Plain Layout
16252 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
16255 \begin_layout Plain Layout
16256 \begin_inset Formula $\raisebox{4.5mm}{}\oiint\raisebox{-2.5mm}{}$
16266 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
16269 \begin_layout Plain Layout
16277 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
16280 \begin_layout Plain Layout
16281 \begin_inset Formula $\raisebox{4.5mm}{}\sqiint\raisebox{-2.5mm}{}$
16295 \begin_inset space \hfill{}
16299 \begin_inset Tabular
16300 <lyxtabular version="3" rows="4" columns="2">
16301 <features rotate="0" tabularvalignment="middle">
16302 <column alignment="center" valignment="top">
16303 <column alignment="center" valignment="top">
16305 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
16308 \begin_layout Plain Layout
16314 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
16317 \begin_layout Plain Layout
16325 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
16328 \begin_layout Plain Layout
16336 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
16339 \begin_layout Plain Layout
16340 \begin_inset Formula $\raisebox{4.5mm}{}\iiint\raisebox{-2.5mm}{}$
16350 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
16353 \begin_layout Plain Layout
16361 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
16364 \begin_layout Plain Layout
16365 \begin_inset Formula $\raisebox{4.5mm}{}\iiiint\raisebox{-2.5mm}{}$
16375 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
16378 \begin_layout Plain Layout
16386 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
16389 \begin_layout Plain Layout
16390 \begin_inset Formula $\raisebox{4.5mm}{}\dotsint\raisebox{-2.5mm}{}$
16404 \begin_inset space \hfill{}
16410 \begin_layout Subsection
16412 \begin_inset CommandInset label
16414 name "sub:Operator-Limits"
16419 \begin_inset Index idx
16422 \begin_layout Plain Layout
16431 \begin_layout Standard
16432 Limits are created by super- and subscripts:
16435 \begin_layout Standard
16437 \begin_inset Tabular
16438 <lyxtabular version="3" rows="2" columns="2">
16439 <features rotate="0" tabularvalignment="middle">
16440 <column alignment="center" valignment="top" width="0pt">
16441 <column alignment="center" valignment="top" width="0pt">
16443 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
16446 \begin_layout Plain Layout
16452 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
16455 \begin_layout Plain Layout
16457 \begin_inset Note Note
16460 \begin_layout Plain Layout
16467 is only used as spacer.
16479 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
16482 \begin_layout Plain Layout
16488 \begin_inset space \textvisiblespace{}
16492 \begin_inset Formula $\to$
16496 \begin_inset Formula $\to$
16504 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
16507 \begin_layout Plain Layout
16508 \begin_inset Formula $\raisebox{5mm}{}\prod_{0}^{\infty}A(x)\raisebox{-2.5mm}{}$
16524 \begin_layout Standard
16525 Limits of inline formulas are set right beside the operator.
16526 Limits in displayed formulas are set above or below the operator, except
16527 for integral limits.
16530 \begin_layout Standard
16531 To force that the limits are set beside the operator, the cursor is set
16532 directly behind the operator and the limits type is changed with the menu
16535 Edit\SpecialChar \menuseparator
16536 Math\SpecialChar \menuseparator
16555 \begin_layout Standard
16556 The default limits type is this:
16557 \begin_inset Formula
16559 \sum_{x=0}^{\infty}\frac{1}{x^{2}}
16564 This is how it looks when the limits type was changed to
16571 \begin_inset Formula
16573 \sum\nolimits _{x=0}^{\infty}\frac{1}{x^{2}}
16578 For integrals, except those ending with
16594 etc., the limits are by default set beside the operator.
16595 But for multiple integrals the limits are often set below the operator.
16596 In the following example the limits type was therefore set to
16600 and so set below the integrals:
16601 \begin_inset Formula
16603 \iiint\limits _{V}X\,\mathrm{d}V=U\label{eq:VolInt}
16611 \begin_layout Standard
16612 \begin_inset VSpace medskip
16615 To specify conditions for limits, the commands
16622 \begin_inset Index idx
16625 \begin_layout Plain Layout
16640 \begin_inset Index idx
16643 \begin_layout Plain Layout
16652 To create for example this expression
16653 \begin_inset Formula
16655 \sum_{\begin{subarray}{c}
16659 \end{subarray}}^{n}k^{-2}\label{eq:substack}
16667 \begin_layout Standard
16668 the following has to be done:
16669 \begin_inset Newline newline
16681 \begin_inset space \textvisiblespace{}
16687 One is now in a blue box under the summation operator and insert there
16693 \begin_inset space \textvisiblespace{}
16699 The blue box is now within a purple box and now several lines can be written
16701 A new line is created by inserting a line break (
16704 arg "newline-insert newline"
16709 \begin_inset Newline newline
16714 0<k<1000 Ctrl+Return
16715 \begin_inset Newline newline
16720 is typed in, a new box appears below for the new line.
16723 \begin_layout Standard
16724 The alignment of the lines can be changed to left aligned with the
16734 Edit\SpecialChar \menuseparator
16738 To get right alignment,
16743 \begin_inset space \textvisiblespace{}
16748 is inserted at the beginning of the line.
16751 \begin_layout Standard
16764 with the difference that the lines are always centered.
16767 \begin_layout Standard
16768 \begin_inset VSpace bigskip
16772 \begin_inset CommandInset ref
16774 reference "eq:substack"
16778 there can be too much space beside an operator, because the characters
16779 following the operator are set beside the limits.
16780 To avoid this the command
16787 \begin_inset Index idx
16790 \begin_layout Plain Layout
16799 To activate it, set in the document settings under
16802 \begin_inset space ~
16812 \begin_inset Index idx
16815 \begin_layout Plain Layout
16816 Packages ! mathtools
16824 \begin_inset space ~
16836 sets the space besides the operator to 0
16837 \begin_inset space \thinspace{}
16841 \begin_inset Newline newline
16845 \begin_inset CommandInset ref
16847 reference "eq:substack"
16851 , one uses the command
16854 \begin_layout Standard
16862 \begin_layout Standard
16863 and inserts the operator with its limits into the braces.
16864 Behind the brace one continues the formula:
16865 \begin_inset Formula
16867 \smashoperator{\sum_{\begin{subarray}{c}
16871 \end{subarray}}^{n}}k^{-2}
16879 \begin_layout Standard
16880 It is possible to set the space of only one side of the operator to 0
16881 \begin_inset space \thinspace{}
16885 To do this write either
16904 stands for the left and
16908 for the right side of the operator.
16909 Here is an example of the possible
16918 \begin_layout Standard
16919 \begin_inset Formula
16921 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}
16929 \begin_layout Standard
16930 \begin_inset VSpace bigskip
16936 \begin_layout Standard
16937 When several consecutive operators have limits the typesetting of the limits
16938 looks often imperfect in the output, see this example:
16939 \begin_inset Formula
16941 \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}
16946 To improve the typesetting set in the document settings under
16949 \begin_inset space ~
16959 \begin_inset Index idx
16962 \begin_layout Plain Layout
16963 Packages ! mathtools
16971 \begin_inset space ~
16977 Then insert into your formula the command
16984 \begin_inset Index idx
16987 \begin_layout Plain Layout
16995 directly before the first operator.
16996 The example will then look like this:
16997 \begin_inset Formula
16999 \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}
17007 \begin_layout Standard
17008 \begin_inset VSpace bigskip
17011 How to use one limit for several operators is described in
17012 \begin_inset CommandInset ref
17014 reference "sub:Self-defined-Operators"
17021 \begin_layout Subsection
17022 Decoration for Operators
17023 \begin_inset Index idx
17026 \begin_layout Plain Layout
17027 Operators ! Decoration
17035 \begin_layout Standard
17043 \begin_inset Index idx
17046 \begin_layout Plain Layout
17061 \begin_inset Index idx
17064 \begin_layout Plain Layout
17072 characters can be placed above or below an operator, respectively.
17080 \begin_inset Index idx
17083 \begin_layout Plain Layout
17091 characters can be set before and behind a big operator.
17094 \begin_layout Standard
17096 \begin_inset space ~
17108 \begin_layout Itemize
17115 is used to set characters at the corners of the operator
17118 \begin_layout Itemize
17125 is used to set characters before and/or behind the operator (this variant
17126 represents LaTeX's original
17135 \begin_layout Itemize
17142 is used to set characters at the left corners and/or behind the operator
17145 \begin_layout Itemize
17152 is used to set characters at the right corners and/or before the operator
17155 \begin_layout Standard
17156 For example the command
17161 \begin_inset space \textvisiblespace{}
17167 \begin_inset space \textvisiblespace{}
17171 \begin_inset Formula $\to$
17175 \begin_inset Formula $\to$
17179 \begin_inset space \textvisiblespace{}
17189 \begin_inset Formula
17191 \sideset{}{'}\sum_{k=1}^{n}
17199 \begin_layout Standard
17200 \begin_inset Note Greyedout
17203 \begin_layout Plain Layout
17210 can only be used to decorate big operators, binary operators are not allowed.
17218 \begin_layout Standard
17231 can also be used to decorate symbols and characters.
17232 For example, the command
17237 \begin_inset space \textvisiblespace{}
17243 \begin_inset space \textvisiblespace{}
17249 \begin_inset Formula $\uparrow$
17257 \begin_inset Formula
17259 \overset{a}{\maltese}
17267 \begin_layout Subsection
17269 \begin_inset CommandInset label
17271 name "sub:Binary-Operators"
17276 \begin_inset Index idx
17279 \begin_layout Plain Layout
17288 \begin_layout Standard
17289 Binary operators are surrounded by space when there is a character before
17291 \begin_inset VSpace medskip
17297 \begin_layout Standard
17298 \begin_inset space \hfill{}
17302 \begin_inset Tabular
17303 <lyxtabular version="3" rows="13" columns="2">
17304 <features rotate="0" tabularvalignment="middle">
17305 <column alignment="center" valignment="top" width="0pt">
17306 <column alignment="center" valignment="top" width="0pt">
17308 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
17311 \begin_layout Plain Layout
17313 \begin_inset Note Note
17316 \begin_layout Plain Layout
17323 is only used as spacer.
17333 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
17336 \begin_layout Plain Layout
17344 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
17347 \begin_layout Plain Layout
17353 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
17356 \begin_layout Plain Layout
17357 \begin_inset Formula $+$
17367 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
17370 \begin_layout Plain Layout
17376 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
17379 \begin_layout Plain Layout
17380 \begin_inset Formula $-$
17390 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
17393 \begin_layout Plain Layout
17401 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
17404 \begin_layout Plain Layout
17405 \begin_inset Formula $\pm$
17415 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
17418 \begin_layout Plain Layout
17426 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
17429 \begin_layout Plain Layout
17430 \begin_inset Formula $\mp$
17440 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
17443 \begin_layout Plain Layout
17451 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
17454 \begin_layout Plain Layout
17455 \begin_inset Formula $\cdot$
17465 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
17468 \begin_layout Plain Layout
17476 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
17479 \begin_layout Plain Layout
17480 \begin_inset Formula $\times$
17490 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
17493 \begin_layout Plain Layout
17501 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
17504 \begin_layout Plain Layout
17505 \begin_inset Formula $\div$
17515 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
17518 \begin_layout Plain Layout
17522 \begin_layout Plain Layout
17535 \begin_layout Plain Layout
17547 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
17550 \begin_layout Plain Layout
17551 \begin_inset Formula $*$
17561 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
17564 \begin_layout Plain Layout
17572 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
17575 \begin_layout Plain Layout
17576 \begin_inset Formula $\star$
17586 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
17589 \begin_layout Plain Layout
17597 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
17600 \begin_layout Plain Layout
17601 \begin_inset Formula $\circ$
17611 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
17614 \begin_layout Plain Layout
17622 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
17625 \begin_layout Plain Layout
17626 \begin_inset Formula $\diamond$
17636 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
17639 \begin_layout Plain Layout
17647 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
17650 \begin_layout Plain Layout
17651 \begin_inset Formula $\bullet$
17665 \begin_inset space \hfill{}
17669 \begin_inset Tabular
17670 <lyxtabular version="3" rows="13" columns="2">
17671 <features rotate="0" tabularvalignment="middle">
17672 <column alignment="center" valignment="top" width="0pt">
17673 <column alignment="center" valignment="top" width="0pt">
17675 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
17678 \begin_layout Plain Layout
17684 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
17687 \begin_layout Plain Layout
17695 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
17698 \begin_layout Plain Layout
17706 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
17709 \begin_layout Plain Layout
17710 \begin_inset Formula $\nabla$
17720 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
17723 \begin_layout Plain Layout
17731 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
17734 \begin_layout Plain Layout
17735 \begin_inset Formula $\bigtriangledown$
17745 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
17748 \begin_layout Plain Layout
17756 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
17759 \begin_layout Plain Layout
17760 \begin_inset Formula $\bigtriangleup$
17770 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
17773 \begin_layout Plain Layout
17781 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
17784 \begin_layout Plain Layout
17785 \begin_inset Formula $\Box$
17795 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
17798 \begin_layout Plain Layout
17806 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
17809 \begin_layout Plain Layout
17810 \begin_inset Formula $\cap$
17820 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
17823 \begin_layout Plain Layout
17831 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
17834 \begin_layout Plain Layout
17835 \begin_inset Formula $\cup$
17845 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
17848 \begin_layout Plain Layout
17856 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
17859 \begin_layout Plain Layout
17860 \begin_inset Formula $\dagger$
17870 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
17873 \begin_layout Plain Layout
17881 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
17884 \begin_layout Plain Layout
17885 \begin_inset Formula $\ddagger$
17895 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
17898 \begin_layout Plain Layout
17906 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
17909 \begin_layout Plain Layout
17910 \begin_inset Formula $\wr$
17920 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
17923 \begin_layout Plain Layout
17931 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
17934 \begin_layout Plain Layout
17935 \begin_inset Formula $\bigcirc$
17945 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
17948 \begin_layout Plain Layout
17956 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
17959 \begin_layout Plain Layout
17960 \begin_inset Formula $\wedge$
17970 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
17973 \begin_layout Plain Layout
17981 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
17984 \begin_layout Plain Layout
17985 \begin_inset Formula $\vee$
17999 \begin_inset space \hfill{}
18003 \begin_inset Tabular
18004 <lyxtabular version="3" rows="13" columns="2">
18005 <features rotate="0" tabularvalignment="middle">
18006 <column alignment="center" valignment="top" width="0pt">
18007 <column alignment="center" valignment="top" width="0pt">
18009 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
18012 \begin_layout Plain Layout
18018 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
18021 \begin_layout Plain Layout
18029 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
18032 \begin_layout Plain Layout
18040 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
18043 \begin_layout Plain Layout
18044 \begin_inset Formula $\oplus$
18054 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
18057 \begin_layout Plain Layout
18065 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
18068 \begin_layout Plain Layout
18069 \begin_inset Formula $\ominus$
18079 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
18082 \begin_layout Plain Layout
18090 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
18093 \begin_layout Plain Layout
18094 \begin_inset Formula $\otimes$
18104 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
18107 \begin_layout Plain Layout
18115 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
18118 \begin_layout Plain Layout
18119 \begin_inset Formula $\oslash$
18129 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
18132 \begin_layout Plain Layout
18140 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
18143 \begin_layout Plain Layout
18144 \begin_inset Formula $\odot$
18154 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
18157 \begin_layout Plain Layout
18165 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
18168 \begin_layout Plain Layout
18169 \begin_inset Formula $\amalg$
18179 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
18182 \begin_layout Plain Layout
18190 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
18193 \begin_layout Plain Layout
18194 \begin_inset Formula $\uplus$
18204 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
18207 \begin_layout Plain Layout
18215 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
18218 \begin_layout Plain Layout
18219 \begin_inset Formula $\setminus$
18229 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
18232 \begin_layout Plain Layout
18240 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
18243 \begin_layout Plain Layout
18244 \begin_inset Formula $\sqcap$
18254 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
18257 \begin_layout Plain Layout
18265 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
18268 \begin_layout Plain Layout
18269 \begin_inset Formula $\sqcup$
18279 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
18282 \begin_layout Plain Layout
18290 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
18293 \begin_layout Plain Layout
18294 \begin_inset Formula $\triangleleft$
18304 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
18307 \begin_layout Plain Layout
18315 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
18318 \begin_layout Plain Layout
18319 \begin_inset Formula $\triangleright$
18333 \begin_inset space \hfill{}
18339 \begin_layout Standard
18340 All binary operators can also be inserted via the math toolbar button
18343 arg "math-insert \\pm"
18349 \begin_layout Standard
18350 To typeset the Laplace operator also
18367 \begin_inset Formula $\nabla^{2}$
18370 ) can be used instead of
18379 \begin_layout Standard
18386 Insert\SpecialChar \menuseparator
18398 \begin_layout Subsection
18399 Self-defined Operators
18400 \begin_inset CommandInset label
18402 name "sub:Self-defined-Operators"
18407 \begin_inset Index idx
18410 \begin_layout Plain Layout
18411 Operators ! self-defined
18419 \begin_layout Standard
18420 With the help of the command
18424 DeclareMathOperator
18427 \begin_inset Index idx
18430 \begin_layout Plain Layout
18435 DeclareMathOperator
18440 custom operators can be defined in the LaTeX-preamble.
18441 Its command scheme is:
18444 \begin_layout Standard
18449 DeclareMathOperator{new command}{display}
18452 \begin_layout Standard
18453 Display can be characters or symbols that define how the operator looks
18455 To define a big operator a * is set behind the command.
18456 All self-defined big operators can have limits as described in
18457 \begin_inset CommandInset ref
18459 reference "sub:Operator-Limits"
18466 \begin_layout Standard
18467 For example the LaTeX-preamble line
18470 \begin_layout Standard
18475 DeclareMathOperator*{
18482 \begin_layout Standard
18483 defines the command
18489 , that inserts a big operator consisting of the lozenge symbol from
18490 \begin_inset CommandInset ref
18492 reference "sub:Miscellaneous-Symbols"
18497 \begin_inset Formula
18499 \Lozenge_{n=1}^{\infty}
18504 The command for this formula is:
18515 \begin_inset Formula $\to$
18521 \begin_layout Standard
18522 \begin_inset VSpace bigskip
18525 When self-defined operators are not used several times in the document,
18526 they can also be defined with the commands
18533 \begin_inset Index idx
18536 \begin_layout Plain Layout
18551 \begin_inset Index idx
18554 \begin_layout Plain Layout
18562 , which have the following scheme:
18565 \begin_layout Standard
18579 \begin_layout Standard
18586 defines big operators,
18595 \begin_layout Standard
18603 \begin_inset space \thinspace{}
18607 \begin_inset space \space{}
18610 be used to use one limit for several operators:
18613 \begin_layout Standard
18614 \begin_inset Formula
18616 \mathop{\sum\negmedspace\sum}_{i,j=1}^{N}
18624 \begin_layout Standard
18625 The command for the formula above is:
18626 \begin_inset Newline newline
18642 \begin_inset space \textvisiblespace{}
18648 \begin_inset Formula $\to$
18654 \begin_inset space \textvisiblespace{}
18662 \begin_layout Section
18664 \begin_inset Index idx
18667 \begin_layout Plain Layout
18676 \begin_layout Subsection
18678 \begin_inset CommandInset label
18680 name "sub:Font-Styles"
18685 \begin_inset Index idx
18688 \begin_layout Plain Layout
18697 \begin_layout Standard
18698 Latin letters in formulas can be set in one of the following font styles:
18699 \begin_inset VSpace -2mm
18705 \begin_layout Standard
18707 \begin_inset Tabular
18708 <lyxtabular version="3" rows="7" columns="3">
18709 <features rotate="0" tabularvalignment="middle">
18710 <column alignment="center" valignment="top">
18711 <column alignment="center" valignment="top">
18712 <column alignment="center" valignment="top">
18714 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
18717 \begin_layout Plain Layout
18723 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
18726 \begin_layout Plain Layout
18732 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
18735 \begin_layout Plain Layout
18743 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
18746 \begin_layout Plain Layout
18752 \begin_inset space \textvisiblespace{}
18762 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
18765 \begin_layout Plain Layout
18766 \begin_inset Formula $\mathbb{ABC}$
18774 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
18777 \begin_layout Plain Layout
18790 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
18793 \begin_layout Plain Layout
18799 \begin_inset space \textvisiblespace{}
18809 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
18812 \begin_layout Plain Layout
18813 \begin_inset Formula $\mathbf{AbC}$
18821 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
18824 \begin_layout Plain Layout
18837 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
18840 \begin_layout Plain Layout
18846 \begin_inset space \textvisiblespace{}
18856 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
18859 \begin_layout Plain Layout
18860 \begin_inset Formula $\boldsymbol{AbC}$
18868 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
18871 \begin_layout Plain Layout
18874 arg "font-boldsymbol"
18884 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
18887 \begin_layout Plain Layout
18893 \begin_inset space \textvisiblespace{}
18903 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
18906 \begin_layout Plain Layout
18907 \begin_inset Formula $\mathcal{ABC}$
18915 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
18918 \begin_layout Plain Layout
18931 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
18934 \begin_layout Plain Layout
18940 \begin_inset space \textvisiblespace{}
18950 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
18953 \begin_layout Plain Layout
18954 \begin_inset Formula $\mathfrak{AbC}$
18962 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
18965 \begin_layout Plain Layout
18973 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
18976 \begin_layout Plain Layout
18982 \begin_inset space \textvisiblespace{}
18992 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
18995 \begin_layout Plain Layout
18996 \begin_inset Formula $\mathscr{AbC}$
19004 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
19007 \begin_layout Plain Layout
19021 \begin_layout Standard
19023 \begin_inset Tabular
19024 <lyxtabular version="3" rows="5" columns="3">
19025 <features rotate="0" tabularvalignment="middle">
19026 <column alignment="center" valignment="top">
19027 <column alignment="center" valignment="top">
19028 <column alignment="center" valignment="top">
19030 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
19033 \begin_layout Plain Layout
19039 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
19042 \begin_layout Plain Layout
19048 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
19051 \begin_layout Plain Layout
19059 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
19062 \begin_layout Plain Layout
19068 \begin_inset space \textvisiblespace{}
19078 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
19081 \begin_layout Plain Layout
19082 \begin_inset Formula $\mathit{AbC}$
19090 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
19093 \begin_layout Plain Layout
19101 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
19104 \begin_layout Plain Layout
19110 \begin_inset space \textvisiblespace{}
19120 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
19123 \begin_layout Plain Layout
19124 \begin_inset Formula $\mathrm{AbC}$
19132 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
19135 \begin_layout Plain Layout
19148 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
19151 \begin_layout Plain Layout
19157 \begin_inset space \textvisiblespace{}
19167 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
19170 \begin_layout Plain Layout
19171 \begin_inset Formula $\mathsf{AbC}$
19179 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
19182 \begin_layout Plain Layout
19195 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
19198 \begin_layout Plain Layout
19204 \begin_inset space \textvisiblespace{}
19214 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
19217 \begin_layout Plain Layout
19218 \begin_inset Formula $\mathtt{AbC}$
19226 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
19229 \begin_layout Plain Layout
19232 arg "font-typewriter"
19248 \begin_layout Standard
19249 \begin_inset Note Greyedout
19252 \begin_layout Plain Layout
19269 can only be used for big letters.
19277 \begin_layout Standard
19278 Predefined is the style
19287 \begin_layout Standard
19288 The style commands work also for letters in mathematical constructs:
19289 \begin_inset Formula
19291 \mathfrak{A=\frac{b}{C}}
19299 \begin_layout Standard
19300 Characters in mathematical text don't appear in a math font style but in
19301 the text font style
19308 That their style can't be set correctly via the text style dialog is a
19313 \begin_layout Plain Layout
19314 \begin_inset CommandInset href
19316 name "LyX-bug #4629"
19317 target "http://www.lyx.org/trac/ticket/4629"
19329 \begin_layout Standard
19330 Instead of the style commands the dialog
19332 Edit\SpecialChar \menuseparator
19333 Math\SpecialChar \menuseparator
19336 or the toolbar button
19339 arg "math-insert \\font"
19345 \begin_layout Subsection
19347 \begin_inset CommandInset label
19349 name "sub:Bold-Formulas"
19354 \begin_inset Index idx
19357 \begin_layout Plain Layout
19366 \begin_layout Standard
19367 To make a complete formula bold, the command
19373 from the previous subsection cannot be used, because it doesn't work for
19374 small Greek letters.
19375 Furthermore it prints Latin letters always upright, like in the following
19379 \begin_layout Standard
19380 \begin_inset Formula
19382 \mathbf{\int_{n}^{2}f(\theta)=\Gamma}\qquad\textrm{equation with \textbackslash mathbf}
19390 \begin_layout Standard
19391 To display the formula correctly, the command
19398 \begin_inset Formula
19400 \boldsymbol{\int_{n}^{2}f(\theta)=\Gamma\qquad\textrm{equation with \textbackslash boldsymbol}}
19405 It is also possible to set the formula in a
19407 boldmath environment
19410 This environment is created by inserting the command
19417 \begin_inset Index idx
19420 \begin_layout Plain Layout
19429 To end the environment, the command
19436 \begin_inset Index idx
19439 \begin_layout Plain Layout
19447 is inserted in TeX-mode.
19451 \begin_layout Plain Layout
19461 \begin_inset Formula
19463 \int_{n}^{2}f(\theta)=\Gamma\qquad\textrm{equation in a boldmath environment}
19472 \begin_layout Plain Layout
19484 \begin_layout Subsection
19486 \begin_inset Index idx
19489 \begin_layout Plain Layout
19498 \begin_layout Standard
19499 Formulas can be colored like normal text: Highlight a formula or a formula
19505 Here is a formula in magenta:
19506 \begin_inset Formula
19508 {\color{magenta}\int A\,\mathrm{d}x=\frac{\sqrt[5]{B}}{\ln\left(\frac{1}{3}\right)}}
19516 \begin_layout Standard
19517 You can also define your own colors as described in
19518 \begin_inset CommandInset ref
19520 reference "sub:Colored-Boxes"
19525 They can be used with the TeX code command
19532 \begin_inset Index idx
19535 \begin_layout Plain Layout
19546 \begin_layout Standard
19551 textcolor{color}{characters or formula}
19554 \begin_layout Standard
19555 The following example was colored completely dark green and partly red:
19558 \begin_layout Standard
19562 \begin_layout Plain Layout
19566 textcolor{darkgreen}{
19572 \begin_inset Formula
19574 \int A\,\mathrm{d}x=\frac{{\color{red}\sqrt[5]{B}}}{\ln\left(\frac{1}{3}\right)}
19583 \begin_layout Plain Layout
19593 \begin_layout Standard
19594 Due to a bug in LyX only complete formulas can be colored with self-defined
19599 \begin_layout Plain Layout
19600 \begin_inset CommandInset href
19602 name "LyX-bug #5269"
19603 target "http://www.lyx.org/trac/ticket/5269"
19615 \begin_layout Subsection
19617 \begin_inset CommandInset label
19619 name "sub:Font-Sizes"
19624 \begin_inset Index idx
19627 \begin_layout Plain Layout
19636 \begin_layout Standard
19637 For characters in formulas there are, analog to characters in text, the
19638 following size commands:
19641 \begin_layout Standard
19685 \begin_inset Newline newline
19707 \begin_layout Standard
19708 The size produced by the commands depends on the document font size, which
19709 corresponds to the command
19716 The other commands produce smaller or larger sizes than
19723 The font size can however not exceed a certain value.
19724 Is for example the document font size 12
19725 \begin_inset space \thinspace{}
19734 switches to the same size as
19744 \begin_layout Standard
19745 A size command is inserted in TeX-mode before the formula and sets the size
19746 for all following formula and text characters.
19747 To switch back to the initial size, the command
19753 is inserted behind the formula in TeX-mode.
19756 \begin_layout Standard
19757 Within a formula the size can be changed using the following size commands
19758 or the toolbar button
19761 arg "math-insert \\style"
19767 \begin_layout Standard
19770 \begin_inset Tabular
19771 <lyxtabular version="3" rows="5" columns="2">
19772 <features rotate="0" tabularvalignment="middle">
19773 <column alignment="center" valignment="top">
19774 <column alignment="center" valignment="top">
19776 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
19779 \begin_layout Plain Layout
19785 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
19788 \begin_layout Plain Layout
19790 \begin_inset Note Note
19793 \begin_layout Plain Layout
19800 is only used as spacer.
19812 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
19815 \begin_layout Plain Layout
19819 \begin_inset Index idx
19822 \begin_layout Plain Layout
19835 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
19838 \begin_layout Plain Layout
19839 \begin_inset Formula $\raisebox{6.5mm}{}{\displaystyle E_{\mathrm{pot_{1}}}=\frac{K}{l+\frac{m}{n_{2}}}}\raisebox{-5.5mm}{}$
19849 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
19852 \begin_layout Plain Layout
19860 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
19863 \begin_layout Plain Layout
19864 \begin_inset Formula $\raisebox{4.5mm}{}{\textstyle E_{\mathrm{pot_{1}}}=\frac{K}{l+\frac{m}{n_{2}}}}\raisebox{-4mm}{}$
19874 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
19877 \begin_layout Plain Layout
19885 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
19888 \begin_layout Plain Layout
19889 \begin_inset Formula $\raisebox{4.5mm}{}{\scriptstyle E_{\mathrm{pot_{1}}}=\frac{K}{l+\frac{m}{n_{2}}}}\raisebox{-3.5mm}{}$
19899 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
19902 \begin_layout Plain Layout
19910 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
19913 \begin_layout Plain Layout
19914 \begin_inset Formula $\raisebox{4.5mm}{}{\scriptscriptstyle E_{\mathrm{pot_{1}}}=\frac{K}{l+\frac{m}{n_{2}}}}\raisebox{-3.5mm}{}$
19930 \begin_layout Standard
19931 After entering these commands, a blue box appears in which the formula parts
19935 \begin_layout Standard
19936 There is a further method to change the font size, that though only works
19937 for symbols or letters in mathematical text.
19938 To use it, one of the above text size commands is inserted in mathematical
19940 All following characters until the end of the mathematical text or until
19941 another size command will have the selected size.
19943 \begin_inset VSpace -2mm
19949 \begin_layout Standard
19953 \begin_layout Plain Layout
19963 \begin_inset Formula
19965 A=\frac{B}{c}\cdot\maltese
19971 \begin_inset Formula
19973 \maltese A\textrm{\Large\maltese\textit{A}}\textrm{\tiny\maltese\textit{A}}
19982 \begin_layout Plain Layout
19994 \begin_layout Standard
19995 \begin_inset VSpace medskip
19998 Before both formulas the command
20005 The command for the second formula is:
20006 \begin_inset Newline newline
20014 \begin_inset space \textvisiblespace{}
20020 \begin_inset space \textvisiblespace{}
20026 \begin_inset space \textvisiblespace{}
20032 \begin_inset space \textvisiblespace{}
20036 \begin_inset Formula $\to$
20040 \begin_inset Formula $\to$
20044 \begin_inset Newline newline
20048 \begin_inset space \hspace*{}
20059 \begin_inset space \textvisiblespace{}
20065 \begin_inset space \textvisiblespace{}
20071 \begin_inset space \textvisiblespace{}
20077 \begin_layout Standard
20078 If a symbol cannot be displayed in different sizes, it will always be displayed
20079 in the default size.
20082 \begin_layout Section
20084 \begin_inset Index idx
20087 \begin_layout Plain Layout
20096 \begin_layout Standard
20097 Greek letters can also be inserted via the toolbar button
20100 arg "math-insert \\alpha"
20104 All international typesetting norms purport that Greek letters in math
20105 have to be typeset italic/slanted.
20106 In some languages, like French or Russian, they are nevertheless sometimes
20110 \begin_layout Subsection
20112 \begin_inset Index idx
20115 \begin_layout Plain Layout
20116 Greek letters ! small
20124 \begin_layout Standard
20125 \begin_inset space \hfill{}
20129 \begin_inset Tabular
20130 <lyxtabular version="3" rows="11" columns="2">
20131 <features rotate="0" tabularvalignment="middle">
20132 <column alignment="center" valignment="top" width="0pt">
20133 <column alignment="center" valignment="top" width="0pt">
20135 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
20138 \begin_layout Plain Layout
20144 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
20147 \begin_layout Plain Layout
20155 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
20158 \begin_layout Plain Layout
20166 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
20169 \begin_layout Plain Layout
20170 \begin_inset Formula $\alpha$
20180 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
20183 \begin_layout Plain Layout
20191 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
20194 \begin_layout Plain Layout
20195 \begin_inset Formula $\beta$
20205 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
20208 \begin_layout Plain Layout
20216 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
20219 \begin_layout Plain Layout
20220 \begin_inset Formula $\gamma$
20230 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
20233 \begin_layout Plain Layout
20241 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
20244 \begin_layout Plain Layout
20245 \begin_inset Formula $\delta$
20255 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
20258 \begin_layout Plain Layout
20266 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
20269 \begin_layout Plain Layout
20270 \begin_inset Formula $\epsilon$
20280 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
20283 \begin_layout Plain Layout
20291 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
20294 \begin_layout Plain Layout
20295 \begin_inset Formula $\varepsilon$
20305 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
20308 \begin_layout Plain Layout
20316 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
20319 \begin_layout Plain Layout
20320 \begin_inset Formula $\zeta$
20330 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
20333 \begin_layout Plain Layout
20341 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
20344 \begin_layout Plain Layout
20345 \begin_inset Formula $\eta$
20355 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
20358 \begin_layout Plain Layout
20366 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
20369 \begin_layout Plain Layout
20370 \begin_inset Formula $\theta$
20380 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
20383 \begin_layout Plain Layout
20391 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
20394 \begin_layout Plain Layout
20395 \begin_inset Formula $\vartheta$
20409 \begin_inset space \hfill{}
20413 \begin_inset Tabular
20414 <lyxtabular version="3" rows="12" columns="2">
20415 <features rotate="0" tabularvalignment="middle">
20416 <column alignment="center" valignment="top" width="0pt">
20417 <column alignment="center" valignment="top" width="0pt">
20419 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
20422 \begin_layout Plain Layout
20428 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
20431 \begin_layout Plain Layout
20439 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
20442 \begin_layout Plain Layout
20450 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
20453 \begin_layout Plain Layout
20454 \begin_inset Formula $\iota$
20464 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
20467 \begin_layout Plain Layout
20475 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
20478 \begin_layout Plain Layout
20479 \begin_inset Formula $\kappa$
20489 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
20492 \begin_layout Plain Layout
20500 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
20503 \begin_layout Plain Layout
20504 \begin_inset Formula $\varkappa$
20514 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
20517 \begin_layout Plain Layout
20525 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
20528 \begin_layout Plain Layout
20529 \begin_inset Formula $\lambda$
20539 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
20542 \begin_layout Plain Layout
20550 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
20553 \begin_layout Plain Layout
20554 \begin_inset Formula $\mu$
20564 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
20567 \begin_layout Plain Layout
20575 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
20578 \begin_layout Plain Layout
20579 \begin_inset Formula $\nu$
20589 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
20592 \begin_layout Plain Layout
20600 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
20603 \begin_layout Plain Layout
20604 \begin_inset Formula $\xi$
20614 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
20617 \begin_layout Plain Layout
20623 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
20626 \begin_layout Plain Layout
20627 \begin_inset Formula $o$
20637 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
20640 \begin_layout Plain Layout
20648 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
20651 \begin_layout Plain Layout
20652 \begin_inset Formula $\pi$
20662 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
20665 \begin_layout Plain Layout
20673 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
20676 \begin_layout Plain Layout
20677 \begin_inset Formula $\varpi$
20687 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
20690 \begin_layout Plain Layout
20698 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
20701 \begin_layout Plain Layout
20702 \begin_inset Formula $\rho$
20716 \begin_inset space \hfill{}
20720 \begin_inset Tabular
20721 <lyxtabular version="3" rows="11" columns="2">
20722 <features rotate="0" tabularvalignment="middle">
20723 <column alignment="center" valignment="top" width="0pt">
20724 <column alignment="center" valignment="top" width="0pt">
20726 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
20729 \begin_layout Plain Layout
20735 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
20738 \begin_layout Plain Layout
20746 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
20749 \begin_layout Plain Layout
20757 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
20760 \begin_layout Plain Layout
20761 \begin_inset Formula $\varrho$
20771 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
20774 \begin_layout Plain Layout
20782 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
20785 \begin_layout Plain Layout
20786 \begin_inset Formula $\sigma$
20796 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
20799 \begin_layout Plain Layout
20807 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
20810 \begin_layout Plain Layout
20811 \begin_inset Formula $\varsigma$
20821 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
20824 \begin_layout Plain Layout
20832 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
20835 \begin_layout Plain Layout
20836 \begin_inset Formula $\tau$
20846 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
20849 \begin_layout Plain Layout
20857 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
20860 \begin_layout Plain Layout
20861 \begin_inset Formula $\upsilon$
20871 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
20874 \begin_layout Plain Layout
20882 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
20885 \begin_layout Plain Layout
20886 \begin_inset Formula $\phi$
20896 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
20899 \begin_layout Plain Layout
20907 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
20910 \begin_layout Plain Layout
20911 \begin_inset Formula $\varphi$
20921 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
20924 \begin_layout Plain Layout
20932 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
20935 \begin_layout Plain Layout
20936 \begin_inset Formula $\chi$
20946 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
20949 \begin_layout Plain Layout
20957 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
20960 \begin_layout Plain Layout
20961 \begin_inset Formula $\psi$
20971 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
20974 \begin_layout Plain Layout
20982 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
20985 \begin_layout Plain Layout
20986 \begin_inset Formula $\omega$
21000 \begin_inset space \hfill{}
21006 \begin_layout Standard
21007 \begin_inset VSpace medskip
21013 \begin_layout Standard
21014 How to create special upright Greek letters is explained in
21015 \begin_inset CommandInset ref
21017 reference "sub:Upright-small-Greek"
21024 \begin_layout Subsection
21026 \begin_inset Index idx
21029 \begin_layout Plain Layout
21030 Greek letters ! big
21038 \begin_layout Standard
21039 \begin_inset space \hfill{}
21043 \begin_inset Tabular
21044 <lyxtabular version="3" rows="7" columns="2">
21045 <features rotate="0" tabularvalignment="middle">
21046 <column alignment="center" valignment="top" width="0pt">
21047 <column alignment="center" valignment="top" width="0pt">
21049 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
21052 \begin_layout Plain Layout
21058 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
21061 \begin_layout Plain Layout
21069 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
21072 \begin_layout Plain Layout
21080 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
21083 \begin_layout Plain Layout
21084 \begin_inset Formula $\Gamma$
21094 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
21097 \begin_layout Plain Layout
21105 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
21108 \begin_layout Plain Layout
21109 \begin_inset Formula $\Delta$
21119 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
21122 \begin_layout Plain Layout
21130 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
21133 \begin_layout Plain Layout
21134 \begin_inset Formula $\Theta$
21144 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
21147 \begin_layout Plain Layout
21155 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
21158 \begin_layout Plain Layout
21159 \begin_inset Formula $\Lambda$
21169 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
21172 \begin_layout Plain Layout
21180 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
21183 \begin_layout Plain Layout
21184 \begin_inset Formula $\Xi$
21194 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
21197 \begin_layout Plain Layout
21205 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
21208 \begin_layout Plain Layout
21209 \begin_inset Formula $\Pi$
21223 \begin_inset space \hfill{}
21227 \begin_inset Tabular
21228 <lyxtabular version="3" rows="6" columns="2">
21229 <features rotate="0" tabularvalignment="middle">
21230 <column alignment="center" valignment="top" width="0pt">
21231 <column alignment="center" valignment="top" width="0pt">
21233 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
21236 \begin_layout Plain Layout
21242 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
21245 \begin_layout Plain Layout
21253 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
21256 \begin_layout Plain Layout
21264 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
21267 \begin_layout Plain Layout
21268 \begin_inset Formula $\Sigma$
21278 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
21281 \begin_layout Plain Layout
21289 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
21292 \begin_layout Plain Layout
21293 \begin_inset Formula $\Upsilon$
21303 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
21306 \begin_layout Plain Layout
21314 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
21317 \begin_layout Plain Layout
21318 \begin_inset Formula $\Phi$
21328 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
21331 \begin_layout Plain Layout
21339 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
21342 \begin_layout Plain Layout
21343 \begin_inset Formula $\Psi$
21353 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
21356 \begin_layout Plain Layout
21364 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
21367 \begin_layout Plain Layout
21368 \begin_inset Formula $\Omega$
21382 \begin_inset space \hfill{}
21388 \begin_layout Standard
21389 \begin_inset VSpace medskip
21392 That the big Greek letters appear upright is caused by a design bug when
21394 To get correct italic big letters, begin every command with
21399 For example the command
21406 \begin_inset Formula $\varGamma$
21410 Another way is to load the package
21418 \begin_layout Plain Layout
21423 is part of the LaTeX-package
21428 \begin_inset Index idx
21431 \begin_layout Plain Layout
21436 \begin_layout Plain Layout
21456 \begin_inset Index idx
21459 \begin_layout Plain Layout
21465 with the LaTeX-preamble line
21468 \begin_layout Standard
21473 usepackage{fixmath}
21476 \begin_layout Standard
21477 Then all big Greek letters in a document will automatically be typeset italic.
21480 \begin_layout Subsection
21482 \begin_inset Index idx
21485 \begin_layout Plain Layout
21486 Greek letters ! bold
21494 \begin_layout Standard
21495 Greek letters cannot be set with different font styles like Latin letters.
21496 They can only be made bold with the command
21503 \begin_inset Index idx
21506 \begin_layout Plain Layout
21517 \begin_layout Standard
21519 \begin_inset Tabular
21520 <lyxtabular version="3" rows="3" columns="2">
21521 <features rotate="0" tabularvalignment="middle">
21522 <column alignment="center" valignment="top">
21523 <column alignment="center" valignment="top">
21525 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
21528 \begin_layout Plain Layout
21534 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
21537 \begin_layout Plain Layout
21545 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
21548 \begin_layout Plain Layout
21560 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
21563 \begin_layout Plain Layout
21564 \begin_inset Formula $\Upsilon\boldsymbol{\Upsilon}$
21574 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
21577 \begin_layout Plain Layout
21589 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
21592 \begin_layout Plain Layout
21593 \begin_inset Formula $\theta\boldsymbol{\theta}$
21609 \begin_layout Section
21614 \begin_layout Plain Layout
21627 \begin_layout Plain Layout
21628 A list with all symbols of most of the LaTeX-packages can be found in
21629 \begin_inset CommandInset citation
21644 \begin_layout Plain Layout
21652 \begin_inset Note Note
21655 \begin_layout Plain Layout
21658 texorpdfstring is used to avoid that the footnote appears in the PDF-bookmark.
21661 \begin_layout Plain Layout
21664 texorpdfstring is in section
21665 \begin_inset CommandInset ref
21667 reference "sub:Formulas-in-Section"
21677 \begin_inset Index idx
21680 \begin_layout Plain Layout
21689 \begin_layout Standard
21690 Many of the symbols listed in this section can also be inserted via the
21694 arg "math-insert \\nabla"
21700 arg "math-insert \\digamma"
21706 \begin_layout Subsection
21707 Mathematical Symbols
21708 \begin_inset CommandInset label
21710 name "sub:Mathematical-Symbols"
21715 \begin_inset Index idx
21718 \begin_layout Plain Layout
21719 Symbols ! mathematical
21727 \begin_layout Standard
21728 \begin_inset space \hfill{}
21732 \begin_inset Tabular
21733 <lyxtabular version="3" rows="10" columns="2">
21734 <features rotate="0" tabularvalignment="middle">
21735 <column alignment="center" valignment="top" width="0pt">
21736 <column alignment="center" valignment="top" width="0pt">
21738 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
21741 \begin_layout Plain Layout
21747 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
21750 \begin_layout Plain Layout
21758 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
21761 \begin_layout Plain Layout
21769 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
21772 \begin_layout Plain Layout
21773 \begin_inset Formula $\neg$
21783 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
21786 \begin_layout Plain Layout
21794 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
21797 \begin_layout Plain Layout
21798 \begin_inset Formula $\Im$
21808 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
21811 \begin_layout Plain Layout
21819 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
21822 \begin_layout Plain Layout
21823 \begin_inset Formula $\Re$
21833 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
21836 \begin_layout Plain Layout
21844 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
21847 \begin_layout Plain Layout
21848 \begin_inset Formula $\aleph$
21858 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
21861 \begin_layout Plain Layout
21869 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
21872 \begin_layout Plain Layout
21873 \begin_inset Formula $\partial$
21883 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
21886 \begin_layout Plain Layout
21894 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
21897 \begin_layout Plain Layout
21898 \begin_inset Formula $\infty$
21908 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
21911 \begin_layout Plain Layout
21919 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
21922 \begin_layout Plain Layout
21923 \begin_inset Formula $\wp$
21933 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
21936 \begin_layout Plain Layout
21944 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
21947 \begin_layout Plain Layout
21948 \begin_inset Formula $\imath$
21958 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
21961 \begin_layout Plain Layout
21969 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
21972 \begin_layout Plain Layout
21973 \begin_inset Formula $\jmath$
21987 \begin_inset space \hfill{}
21991 \begin_inset Tabular
21992 <lyxtabular version="3" rows="10" columns="2">
21993 <features rotate="0" tabularvalignment="middle">
21994 <column alignment="center" valignment="top" width="0pt">
21995 <column alignment="center" valignment="top" width="0pt">
21997 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
22000 \begin_layout Plain Layout
22006 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
22009 \begin_layout Plain Layout
22011 \begin_inset Note Note
22014 \begin_layout Plain Layout
22021 is only used as spacer.
22033 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
22036 \begin_layout Plain Layout
22044 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
22047 \begin_layout Plain Layout
22048 \begin_inset Formula $\forall$
22058 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
22061 \begin_layout Plain Layout
22069 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
22072 \begin_layout Plain Layout
22073 \begin_inset Formula $\exists$
22083 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
22086 \begin_layout Plain Layout
22094 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
22097 \begin_layout Plain Layout
22098 \begin_inset Formula $\nexists$
22108 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
22111 \begin_layout Plain Layout
22119 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
22122 \begin_layout Plain Layout
22123 \begin_inset Formula $\emptyset$
22133 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
22136 \begin_layout Plain Layout
22144 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
22147 \begin_layout Plain Layout
22148 \begin_inset Formula $\varnothing$
22158 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
22161 \begin_layout Plain Layout
22169 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
22172 \begin_layout Plain Layout
22173 \begin_inset Formula $\dag$
22183 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
22186 \begin_layout Plain Layout
22194 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
22197 \begin_layout Plain Layout
22198 \begin_inset Formula $\ddag$
22208 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
22211 \begin_layout Plain Layout
22219 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
22222 \begin_layout Plain Layout
22226 \begin_layout Plain Layout
22236 \begin_inset Formula $\complement$
22243 \begin_layout Plain Layout
22257 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
22260 \begin_layout Plain Layout
22268 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
22271 \begin_layout Plain Layout
22272 \begin_inset Formula $\Bbbk$
22286 \begin_inset space \hfill{}
22290 \begin_inset Tabular
22291 <lyxtabular version="3" rows="10" columns="2">
22292 <features rotate="0" tabularvalignment="middle">
22293 <column alignment="center" valignment="top" width="0pt">
22294 <column alignment="center" valignment="top" width="0pt">
22296 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
22299 \begin_layout Plain Layout
22305 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
22308 \begin_layout Plain Layout
22316 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
22319 \begin_layout Plain Layout
22327 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
22330 \begin_layout Plain Layout
22331 \begin_inset Formula $\prime$
22341 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
22344 \begin_layout Plain Layout
22352 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
22355 \begin_layout Plain Layout
22356 \begin_inset Formula $\backprime$
22366 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
22369 \begin_layout Plain Layout
22377 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
22380 \begin_layout Plain Layout
22381 \begin_inset Formula $\mho$
22391 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
22394 \begin_layout Plain Layout
22402 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
22405 \begin_layout Plain Layout
22406 \begin_inset Formula $\triangle$
22416 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
22419 \begin_layout Plain Layout
22427 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
22430 \begin_layout Plain Layout
22431 \begin_inset Formula $\angle$
22441 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
22444 \begin_layout Plain Layout
22452 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
22455 \begin_layout Plain Layout
22456 \begin_inset Formula $\measuredangle$
22466 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
22469 \begin_layout Plain Layout
22477 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
22480 \begin_layout Plain Layout
22481 \begin_inset Formula $\sphericalangle$
22491 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
22494 \begin_layout Plain Layout
22502 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
22505 \begin_layout Plain Layout
22506 \begin_inset Formula $\top$
22516 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
22519 \begin_layout Plain Layout
22527 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
22530 \begin_layout Plain Layout
22531 \begin_inset Formula $\bot$
22545 \begin_inset space \hfill{}
22551 \begin_layout Subsection
22552 Miscellaneous Symbols
22553 \begin_inset CommandInset label
22555 name "sub:Miscellaneous-Symbols"
22560 \begin_inset Index idx
22563 \begin_layout Plain Layout
22564 Symbols ! miscellaneous
22572 \begin_layout Standard
22575 \begin_inset Tabular
22576 <lyxtabular version="3" rows="10" columns="2">
22577 <features rotate="0" tabularvalignment="middle">
22578 <column alignment="center" valignment="top" width="0pt">
22579 <column alignment="center" valignment="top" width="0pt">
22581 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
22584 \begin_layout Plain Layout
22590 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
22593 \begin_layout Plain Layout
22601 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
22604 \begin_layout Plain Layout
22612 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
22615 \begin_layout Plain Layout
22616 \begin_inset Formula $\flat$
22626 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
22629 \begin_layout Plain Layout
22637 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
22640 \begin_layout Plain Layout
22641 \begin_inset Formula $\natural$
22651 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
22654 \begin_layout Plain Layout
22662 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
22665 \begin_layout Plain Layout
22666 \begin_inset Formula $\sharp$
22676 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
22679 \begin_layout Plain Layout
22687 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
22690 \begin_layout Plain Layout
22691 \begin_inset Formula $\surd$
22701 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
22704 \begin_layout Plain Layout
22712 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
22715 \begin_layout Plain Layout
22716 \begin_inset Formula $\checkmark$
22726 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
22729 \begin_layout Plain Layout
22737 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
22740 \begin_layout Plain Layout
22741 \begin_inset Formula $\yen$
22751 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
22754 \begin_layout Plain Layout
22762 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
22765 \begin_layout Plain Layout
22766 \begin_inset Formula $\pounds$
22776 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
22779 \begin_layout Plain Layout
22785 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
22788 \begin_layout Plain Layout
22789 \begin_inset Formula $\$$
22799 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
22802 \begin_layout Plain Layout
22808 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
22811 \begin_layout Plain Layout
22812 \begin_inset Formula $§$
22826 \begin_inset Tabular
22827 <lyxtabular version="3" rows="10" columns="2">
22828 <features rotate="0" tabularvalignment="middle">
22829 <column alignment="center" valignment="top">
22830 <column alignment="center" valignment="top">
22832 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
22835 \begin_layout Plain Layout
22841 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
22844 \begin_layout Plain Layout
22852 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
22855 \begin_layout Plain Layout
22863 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
22866 \begin_layout Plain Layout
22867 \begin_inset Formula $\hbar$
22877 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
22880 \begin_layout Plain Layout
22888 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
22891 \begin_layout Plain Layout
22892 \begin_inset Formula $\hslash$
22902 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
22905 \begin_layout Plain Layout
22913 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
22916 \begin_layout Plain Layout
22917 \begin_inset Formula $\clubsuit$
22927 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
22930 \begin_layout Plain Layout
22938 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
22941 \begin_layout Plain Layout
22942 \begin_inset Formula $\spadesuit$
22952 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
22955 \begin_layout Plain Layout
22963 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
22966 \begin_layout Plain Layout
22967 \begin_inset Formula $\bigstar$
22977 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
22980 \begin_layout Plain Layout
22988 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
22991 \begin_layout Plain Layout
22992 \begin_inset Formula $\blacklozenge$
23002 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
23005 \begin_layout Plain Layout
23013 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
23016 \begin_layout Plain Layout
23017 \begin_inset Formula $\blacktriangle$
23027 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
23030 \begin_layout Plain Layout
23038 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
23041 \begin_layout Plain Layout
23042 \begin_inset Formula $\blacktriangledown$
23052 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
23055 \begin_layout Plain Layout
23063 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
23066 \begin_layout Plain Layout
23067 \begin_inset Formula $\bullet$
23081 \begin_inset Tabular
23082 <lyxtabular version="3" rows="10" columns="2">
23083 <features rotate="0" tabularvalignment="middle">
23084 <column alignment="center" valignment="top" width="0pt">
23085 <column alignment="center" valignment="top" width="0pt">
23087 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
23090 \begin_layout Plain Layout
23096 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
23099 \begin_layout Plain Layout
23107 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
23110 \begin_layout Plain Layout
23118 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
23121 \begin_layout Plain Layout
23122 \begin_inset Formula $\diamondsuit$
23132 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
23135 \begin_layout Plain Layout
23143 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
23146 \begin_layout Plain Layout
23147 \begin_inset Formula $\Diamond$
23157 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
23160 \begin_layout Plain Layout
23168 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
23171 \begin_layout Plain Layout
23172 \begin_inset Formula $\heartsuit$
23182 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
23185 \begin_layout Plain Layout
23193 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
23196 \begin_layout Plain Layout
23197 \begin_inset Formula $\P$
23207 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
23210 \begin_layout Plain Layout
23218 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
23221 \begin_layout Plain Layout
23222 \begin_inset Formula $\copyright$
23232 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
23235 \begin_layout Plain Layout
23243 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
23246 \begin_layout Plain Layout
23247 \begin_inset Formula $\circledR$
23257 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
23260 \begin_layout Plain Layout
23268 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
23271 \begin_layout Plain Layout
23272 \begin_inset Formula $\maltese$
23282 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
23285 \begin_layout Plain Layout
23293 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
23296 \begin_layout Plain Layout
23297 \begin_inset Formula $\diagup$
23307 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
23310 \begin_layout Plain Layout
23318 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
23321 \begin_layout Plain Layout
23322 \begin_inset Formula $\diagdown$
23338 \begin_layout Standard
23339 \begin_inset VSpace medskip
23345 \begin_layout Standard
23346 Some symbols can be displayed in different sizes, see
23347 \begin_inset CommandInset ref
23349 reference "sub:Font-Sizes"
23356 \begin_layout Subsection
23358 \begin_inset Index idx
23361 \begin_layout Plain Layout
23362 Symbols ! Euro-symbol
23368 \begin_inset Index idx
23371 \begin_layout Plain Layout
23378 \begin_layout Plain Layout
23395 \begin_layout Standard
23396 To use the Euro symbol in formulas, the LaTeX-package
23401 \begin_inset Index idx
23404 \begin_layout Plain Layout
23410 must be installed and loaded with the LaTeX-preamble line
23413 \begin_layout Standard
23418 usepackage[gennarrow]{eurosym}
23421 \begin_layout Standard
23422 The Euro symbol can now be inserted with the command
23429 \begin_inset Index idx
23432 \begin_layout Plain Layout
23443 \begin_layout Standard
23444 The Euro symbol can directly be inserted with the € key in mathematical
23445 text, without having
23460 can also be inserted in TeX-mode.
23461 The official currency symbol can then be inserted with the command
23468 \begin_inset Index idx
23471 \begin_layout Plain Layout
23479 , that is only available in TeX-mode.
23482 \begin_layout Standard
23486 \begin_layout Plain Layout
23496 \begin_inset Note Note
23499 \begin_layout Plain Layout
23500 The following table will only be displayed when the LaTeX-package
23512 \begin_layout Standard
23513 An overview about the different Euro symbols:
23516 \begin_layout Standard
23518 \begin_inset Tabular
23519 <lyxtabular version="3" rows="4" columns="3">
23520 <features rotate="0" tabularvalignment="middle">
23521 <column alignment="center" valignment="top" width="0pt">
23522 <column alignment="center" valignment="top" width="0pt">
23523 <column alignment="center" valignment="top" width="0pt">
23525 <cell multicolumn="1" alignment="center" valignment="top" bottomline="true" usebox="none">
23528 \begin_layout Plain Layout
23534 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
23537 \begin_layout Plain Layout
23543 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
23546 \begin_layout Plain Layout
23554 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
23557 \begin_layout Plain Layout
23563 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
23566 \begin_layout Plain Layout
23574 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
23577 \begin_layout Plain Layout
23578 \begin_inset Formula $\euro$
23588 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
23591 \begin_layout Plain Layout
23597 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
23600 \begin_layout Plain Layout
23606 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
23609 \begin_layout Plain Layout
23610 \begin_inset Formula $\mbox{€}$
23620 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
23623 \begin_layout Plain Layout
23629 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
23632 \begin_layout Plain Layout
23640 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
23643 \begin_layout Plain Layout
23647 \begin_layout Plain Layout
23669 \begin_layout Standard
23673 \begin_layout Plain Layout
23683 \begin_inset Note Note
23686 \begin_layout Plain Layout
23687 The following will be displayed when the LaTeX-package
23699 \begin_layout Standard
23700 You need to install the LaTeX-package
23704 to see the rest of this subsection in the output.
23707 \begin_layout Standard
23711 \begin_layout Plain Layout
23723 \begin_layout Section
23725 \begin_inset CommandInset label
23727 name "sec:Relations"
23732 \begin_inset Index idx
23735 \begin_layout Plain Layout
23742 \begin_inset Index idx
23745 \begin_layout Plain Layout
23750 \begin_layout Plain Layout
23761 \begin_layout Plain Layout
23776 \begin_layout Standard
23777 All following relations can also be inserted via the toolbar button
23780 arg "math-insert \\leq"
23786 \begin_layout Standard
23787 \begin_inset space \hfill{}
23791 \begin_inset Tabular
23792 <lyxtabular version="3" rows="17" columns="2">
23793 <features rotate="0" tabularvalignment="middle">
23794 <column alignment="center" valignment="top" width="0pt">
23795 <column alignment="center" valignment="top" width="0pt">
23797 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
23800 \begin_layout Plain Layout
23806 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
23809 \begin_layout Plain Layout
23817 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
23820 \begin_layout Plain Layout
23826 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
23829 \begin_layout Plain Layout
23830 \begin_inset Formula $<$
23840 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
23843 \begin_layout Plain Layout
23851 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
23854 \begin_layout Plain Layout
23855 \begin_inset Formula $\le$
23865 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
23868 \begin_layout Plain Layout
23876 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
23879 \begin_layout Plain Layout
23880 \begin_inset Formula $\ll$
23890 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
23893 \begin_layout Plain Layout
23901 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
23904 \begin_layout Plain Layout
23905 \begin_inset Formula $\prec$
23915 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
23918 \begin_layout Plain Layout
23926 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
23929 \begin_layout Plain Layout
23930 \begin_inset Formula $\preceq$
23940 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
23943 \begin_layout Plain Layout
23951 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
23954 \begin_layout Plain Layout
23955 \begin_inset Formula $\subset$
23965 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
23968 \begin_layout Plain Layout
23976 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
23979 \begin_layout Plain Layout
23980 \begin_inset Formula $\subseteq$
23990 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
23993 \begin_layout Plain Layout
24001 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
24004 \begin_layout Plain Layout
24005 \begin_inset Formula $\sqsubseteq$
24015 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
24018 \begin_layout Plain Layout
24026 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
24029 \begin_layout Plain Layout
24030 \begin_inset Formula $\in$
24040 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
24043 \begin_layout Plain Layout
24051 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
24054 \begin_layout Plain Layout
24055 \begin_inset Formula $\vdash$
24065 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
24068 \begin_layout Plain Layout
24076 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
24079 \begin_layout Plain Layout
24080 \begin_inset Formula $\smile$
24090 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
24093 \begin_layout Plain Layout
24101 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
24104 \begin_layout Plain Layout
24105 \begin_inset Formula $\lhd$
24115 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
24118 \begin_layout Plain Layout
24126 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
24129 \begin_layout Plain Layout
24130 \begin_inset Formula $\unlhd$
24140 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
24143 \begin_layout Plain Layout
24151 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
24154 \begin_layout Plain Layout
24155 \begin_inset Formula $\gtrless$
24165 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
24168 \begin_layout Plain Layout
24176 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
24179 \begin_layout Plain Layout
24180 \begin_inset Formula $\mid$
24190 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
24193 \begin_layout Plain Layout
24201 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
24204 \begin_layout Plain Layout
24205 \begin_inset Formula $\nmid$
24219 \begin_inset space \hfill{}
24223 \begin_inset Tabular
24224 <lyxtabular version="3" rows="17" columns="2">
24225 <features rotate="0" tabularvalignment="middle">
24226 <column alignment="center" valignment="top" width="0pt">
24227 <column alignment="center" valignment="top" width="0pt">
24229 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
24232 \begin_layout Plain Layout
24238 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
24241 \begin_layout Plain Layout
24249 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
24252 \begin_layout Plain Layout
24258 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
24261 \begin_layout Plain Layout
24262 \begin_inset Formula $=$
24272 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
24275 \begin_layout Plain Layout
24283 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
24286 \begin_layout Plain Layout
24287 \begin_inset Formula $\not=$
24297 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
24300 \begin_layout Plain Layout
24308 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
24311 \begin_layout Plain Layout
24312 \begin_inset Formula $\equiv$
24322 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
24325 \begin_layout Plain Layout
24333 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
24336 \begin_layout Plain Layout
24337 \begin_inset Formula $\sim$
24347 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
24350 \begin_layout Plain Layout
24358 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
24361 \begin_layout Plain Layout
24362 \begin_inset Formula $\simeq$
24372 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
24375 \begin_layout Plain Layout
24383 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
24386 \begin_layout Plain Layout
24387 \begin_inset Formula $\approx$
24397 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
24400 \begin_layout Plain Layout
24408 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
24411 \begin_layout Plain Layout
24412 \begin_inset Formula $\cong$
24422 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
24425 \begin_layout Plain Layout
24433 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
24436 \begin_layout Plain Layout
24437 \begin_inset Formula $\bowtie$
24447 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
24450 \begin_layout Plain Layout
24458 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
24461 \begin_layout Plain Layout
24462 \begin_inset Formula $\notin$
24472 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
24475 \begin_layout Plain Layout
24483 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
24486 \begin_layout Plain Layout
24487 \begin_inset Formula $\perp$
24497 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
24500 \begin_layout Plain Layout
24508 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
24511 \begin_layout Plain Layout
24512 \begin_inset Formula $\propto$
24522 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
24525 \begin_layout Plain Layout
24533 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
24536 \begin_layout Plain Layout
24537 \begin_inset Formula $\asymp$
24547 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
24550 \begin_layout Plain Layout
24558 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
24561 \begin_layout Plain Layout
24562 \begin_inset Formula $\doteq$
24572 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
24575 \begin_layout Plain Layout
24583 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
24586 \begin_layout Plain Layout
24587 \begin_inset Formula $\circeq$
24597 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
24600 \begin_layout Plain Layout
24608 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
24611 \begin_layout Plain Layout
24612 \begin_inset Formula $\models$
24622 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
24625 \begin_layout Plain Layout
24633 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
24636 \begin_layout Plain Layout
24637 \begin_inset Formula $\widehat{=}$
24651 \begin_inset space \hfill{}
24655 \begin_inset Tabular
24656 <lyxtabular version="3" rows="17" columns="2">
24657 <features rotate="0" tabularvalignment="middle">
24658 <column alignment="center" valignment="top" width="0pt">
24659 <column alignment="center" valignment="top" width="0pt">
24661 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
24664 \begin_layout Plain Layout
24670 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
24673 \begin_layout Plain Layout
24681 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
24684 \begin_layout Plain Layout
24690 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
24693 \begin_layout Plain Layout
24694 \begin_inset Formula $>$
24704 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
24707 \begin_layout Plain Layout
24715 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
24718 \begin_layout Plain Layout
24719 \begin_inset Formula $\ge$
24729 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
24732 \begin_layout Plain Layout
24740 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
24743 \begin_layout Plain Layout
24744 \begin_inset Formula $\gg$
24754 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
24757 \begin_layout Plain Layout
24765 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
24768 \begin_layout Plain Layout
24769 \begin_inset Formula $\succ$
24779 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
24782 \begin_layout Plain Layout
24790 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
24793 \begin_layout Plain Layout
24794 \begin_inset Formula $\succeq$
24804 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
24807 \begin_layout Plain Layout
24815 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
24818 \begin_layout Plain Layout
24819 \begin_inset Formula $\supset$
24829 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
24832 \begin_layout Plain Layout
24840 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
24843 \begin_layout Plain Layout
24844 \begin_inset Formula $\supseteq$
24854 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
24857 \begin_layout Plain Layout
24865 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
24868 \begin_layout Plain Layout
24869 \begin_inset Formula $\sqsupseteq$
24879 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
24882 \begin_layout Plain Layout
24890 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
24893 \begin_layout Plain Layout
24894 \begin_inset Formula $\ni$
24904 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
24907 \begin_layout Plain Layout
24915 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
24918 \begin_layout Plain Layout
24919 \begin_inset Formula $\dashv$
24929 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
24932 \begin_layout Plain Layout
24940 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
24943 \begin_layout Plain Layout
24944 \begin_inset Formula $\frown$
24954 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
24957 \begin_layout Plain Layout
24965 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
24968 \begin_layout Plain Layout
24969 \begin_inset Formula $\rhd$
24979 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
24982 \begin_layout Plain Layout
24990 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
24993 \begin_layout Plain Layout
24994 \begin_inset Formula $\unrhd$
25004 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
25007 \begin_layout Plain Layout
25015 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
25018 \begin_layout Plain Layout
25019 \begin_inset Formula $\lessgtr$
25029 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
25032 \begin_layout Plain Layout
25040 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
25043 \begin_layout Plain Layout
25044 \begin_inset Formula $\parallel$
25054 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
25057 \begin_layout Plain Layout
25065 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
25068 \begin_layout Plain Layout
25069 \begin_inset Formula $\nparallel$
25083 \begin_inset space \hfill{}
25089 \begin_layout Standard
25090 \begin_inset VSpace medskip
25105 are bigger than the equal looking operators
25120 \begin_layout Standard
25121 LyX supports also many special relations.
25122 Use the toolbar button
25125 arg "math-insert \\leqq"
25128 to see a list of these relations.
25131 \begin_layout Standard
25132 Relations are, in contrary to symbols, always surrounded by space.
25135 \begin_layout Standard
25136 Relations with labels can be created with the command
25143 \begin_inset Index idx
25146 \begin_layout Plain Layout
25157 \begin_layout Standard
25159 \begin_inset Tabular
25160 <lyxtabular version="3" rows="2" columns="2">
25161 <features rotate="0" tabularvalignment="middle">
25162 <column alignment="center" valignment="top">
25163 <column alignment="center" valignment="top">
25165 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
25168 \begin_layout Plain Layout
25174 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
25177 \begin_layout Plain Layout
25179 \begin_inset Note Note
25182 \begin_layout Plain Layout
25189 is only used as spacer.
25201 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
25204 \begin_layout Plain Layout
25208 \begin_inset space \textvisiblespace{}
25216 \begin_inset space \textvisiblespace{}
25220 \begin_inset Formula $\downarrow$
25226 \begin_inset space \textvisiblespace{}
25230 \begin_inset space \textvisiblespace{}
25238 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
25241 \begin_layout Plain Layout
25242 \begin_inset Formula $\raisebox{5mm}{}A(r)\stackrel{r\to\infty}{\approx}B$
25258 \begin_layout Section
25262 \begin_layout Subsection
25263 Predefined Functions
25264 \begin_inset CommandInset label
25266 name "sub:Predefined-Functions"
25271 \begin_inset Index idx
25274 \begin_layout Plain Layout
25275 Functions ! predefined
25283 \begin_layout Standard
25284 In general, variables are set
25288 in mathematical expressions, but not function names, because
25289 \begin_inset Formula $sin$
25292 could be misunderstood as
25293 \begin_inset Formula $s\cdot i\cdot n$
25297 Therefore there are predefined functionswhich are additionally a bit separated
25299 They are inserted as commands starting with a backslash before their name.
25302 \begin_layout Standard
25304 \begin_inset Tabular
25305 <lyxtabular version="3" rows="2" columns="4">
25306 <features rotate="0" tabularvalignment="middle">
25307 <column alignment="center" valignment="top" width="0pt">
25308 <column alignment="center" valignment="top" width="0pt">
25309 <column alignment="center" valignment="top" width="0pt">
25310 <column alignment="center" valignment="top" width="0pt">
25312 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
25315 \begin_layout Plain Layout
25321 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
25324 \begin_layout Plain Layout
25330 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
25333 \begin_layout Plain Layout
25339 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
25342 \begin_layout Plain Layout
25350 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
25353 \begin_layout Plain Layout
25359 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
25362 \begin_layout Plain Layout
25363 \begin_inset Formula $Asin(x)+B$
25371 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
25374 \begin_layout Plain Layout
25382 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
25385 \begin_layout Plain Layout
25386 \begin_inset Formula $A\sin(x)+B$
25402 \begin_layout Standard
25403 The following functions are predefined:
25406 \begin_layout Standard
25407 \begin_inset VSpace -2mm
25413 \begin_layout Standard
25415 \begin_inset Tabular
25416 <lyxtabular version="3" rows="9" columns="4">
25417 <features rotate="0" tabularvalignment="middle">
25418 <column alignment="center" valignment="top" width="0pt">
25419 <column alignment="center" valignment="top" width="0pt">
25420 <column alignment="center" valignment="top" width="0pt">
25421 <column alignment="center" valignment="top" width="0pt">
25423 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
25426 \begin_layout Plain Layout
25432 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
25435 \begin_layout Plain Layout
25441 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
25444 \begin_layout Plain Layout
25450 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
25453 \begin_layout Plain Layout
25461 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
25464 \begin_layout Plain Layout
25472 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
25475 \begin_layout Plain Layout
25483 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
25486 \begin_layout Plain Layout
25494 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
25497 \begin_layout Plain Layout
25507 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
25510 \begin_layout Plain Layout
25518 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
25521 \begin_layout Plain Layout
25529 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
25532 \begin_layout Plain Layout
25540 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
25543 \begin_layout Plain Layout
25553 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
25556 \begin_layout Plain Layout
25564 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
25567 \begin_layout Plain Layout
25575 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
25578 \begin_layout Plain Layout
25586 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
25589 \begin_layout Plain Layout
25599 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
25602 \begin_layout Plain Layout
25610 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
25613 \begin_layout Plain Layout
25621 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
25624 \begin_layout Plain Layout
25632 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
25635 \begin_layout Plain Layout
25645 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
25648 \begin_layout Plain Layout
25656 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
25659 \begin_layout Plain Layout
25667 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
25670 \begin_layout Plain Layout
25678 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
25681 \begin_layout Plain Layout
25691 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
25694 \begin_layout Plain Layout
25702 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
25705 \begin_layout Plain Layout
25713 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
25716 \begin_layout Plain Layout
25724 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
25727 \begin_layout Plain Layout
25737 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
25740 \begin_layout Plain Layout
25748 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
25751 \begin_layout Plain Layout
25759 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
25762 \begin_layout Plain Layout
25770 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
25773 \begin_layout Plain Layout
25783 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
25786 \begin_layout Plain Layout
25794 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
25797 \begin_layout Plain Layout
25805 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
25808 \begin_layout Plain Layout
25816 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
25819 \begin_layout Plain Layout
25835 \begin_layout Standard
25836 They can also be inserted with the math toolbar button
25839 arg "math-insert \\functions"
25845 \begin_layout Subsection
25846 Self-defined Functions
25847 \begin_inset Index idx
25850 \begin_layout Plain Layout
25851 Functions ! self-defined
25859 \begin_layout Standard
25860 To use a function that is not predefined, like for example the sign function
25861 sgn(x), there are two possibilities:
25864 \begin_layout Itemize
25865 Define the function by inserting the following line to the LaTeX-preamble
25869 \begin_layout Plain Layout
25874 DeclareMathOperator
25877 \begin_inset CommandInset ref
25879 reference "sub:Self-defined-Operators"
25889 \begin_inset Newline newline
25893 \begin_inset VSpace -3mm
25897 \begin_inset Newline newline
25904 DeclareMathOperator{
25909 \begin_inset Index idx
25912 \begin_layout Plain Layout
25917 DeclareMathOperator
25923 \begin_inset Newline newline
25927 \begin_inset VSpace -2mm
25931 \begin_inset Newline newline
25934 Now the new defined function can be called with the command
25943 \begin_layout Itemize
25944 Write the formula as usual, mark the formula name, in our example the letters
25949 , and change it to mathematical text.
25950 Finally, a space is inserted between prefactor and function.
25953 \begin_layout Standard
25954 The result is the same with both methods as with a predefined function
25958 \begin_layout Plain Layout
25959 In LyX self-defined functions are displayed red, predefined ones black.
25967 \begin_layout Standard
25969 \begin_inset Tabular
25970 <lyxtabular version="3" rows="3" columns="2">
25971 <features rotate="0" tabularvalignment="middle">
25972 <column alignment="center" valignment="top" width="0pt">
25973 <column alignment="center" valignment="top" width="0pt">
25975 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
25978 \begin_layout Plain Layout
25984 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
25987 \begin_layout Plain Layout
25995 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
25998 \begin_layout Plain Layout
26006 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
26009 \begin_layout Plain Layout
26010 \begin_inset Formula $A\sgn(x)+B$
26020 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
26023 \begin_layout Plain Layout
26027 \begin_inset Formula $\underbrace{\textrm{sgn}}_{\textrm{Alt+M}\,\textrm{M}}$
26035 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
26038 \begin_layout Plain Layout
26039 \begin_inset Formula $A\,\textrm{sgn}(x)+B$
26055 \begin_layout Standard
26056 The first method is more suitable when the self-defined function should
26057 be used several times.
26060 \begin_layout Subsection
26062 \begin_inset Index idx
26065 \begin_layout Plain Layout
26074 \begin_layout Standard
26075 For limits, in addition to the commands
26082 \begin_inset Index idx
26085 \begin_layout Plain Layout
26105 the following functions are defined:
26108 \begin_layout Standard
26110 \begin_inset Tabular
26111 <lyxtabular version="3" rows="5" columns="2">
26112 <features rotate="0" tabularvalignment="middle">
26113 <column alignment="center" valignment="top">
26114 <column alignment="center" valignment="top">
26116 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
26119 \begin_layout Plain Layout
26125 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
26128 \begin_layout Plain Layout
26130 \begin_inset Note Note
26133 \begin_layout Plain Layout
26140 is only used as spacer.
26152 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
26155 \begin_layout Plain Layout
26163 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
26166 \begin_layout Plain Layout
26167 \begin_inset Formula $\varliminf$
26177 <cell alignment="center" valignment="top" leftline="true" usebox="none">
26180 \begin_layout Plain Layout
26188 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
26191 \begin_layout Plain Layout
26192 \begin_inset Formula $\varlimsup$
26202 <cell alignment="center" valignment="top" leftline="true" usebox="none">
26205 \begin_layout Plain Layout
26213 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
26216 \begin_layout Plain Layout
26217 \begin_inset Formula $\varprojlim$
26227 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
26230 \begin_layout Plain Layout
26238 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
26241 \begin_layout Plain Layout
26242 \begin_inset Formula $\varinjlim$
26246 \begin_inset Formula $\raisebox{-2.5mm}{}$
26262 \begin_layout Standard
26263 \begin_inset VSpace medskip
26266 The limit is created by inserting a subscript.
26267 It is set right beside the function in an inline formula:
26270 \begin_layout Standard
26272 \begin_inset Tabular
26273 <lyxtabular version="3" rows="2" columns="2">
26274 <features rotate="0" tabularvalignment="middle">
26275 <column alignment="center" valignment="top" width="0pt">
26276 <column alignment="center" valignment="top" width="0pt">
26278 <cell alignment="center" valignment="top" usebox="none">
26281 \begin_layout Plain Layout
26287 <cell alignment="center" valignment="top" usebox="none">
26290 \begin_layout Plain Layout
26291 \begin_inset space \hspace{}
26296 \begin_inset Note Note
26299 \begin_layout Plain Layout
26306 are used here as spacer.
26318 <cell alignment="center" valignment="top" usebox="none">
26321 \begin_layout Plain Layout
26327 \begin_inset space \textvisiblespace{}
26331 \begin_inset space \textvisiblespace{}
26339 <cell alignment="center" valignment="top" usebox="none">
26342 \begin_layout Plain Layout
26343 \begin_inset Formula $\hspace{1cm}\raisebox{5mm}{}\lim_{x\to A}x=B$
26359 \begin_layout Standard
26360 In a displayed formula the limit is set below the formula, as usual:
26361 \begin_inset Formula
26371 \begin_layout Standard
26372 \begin_inset VSpace medskip
26378 \begin_layout Standard
26379 How to adjust the typesetting of the limits see
26380 \begin_inset CommandInset ref
26382 reference "sub:Operator-Limits"
26389 \begin_layout Subsection
26391 \begin_inset Index idx
26394 \begin_layout Plain Layout
26395 Functions ! modulo-
26403 \begin_layout Standard
26404 The modulo-function is special, because it exists in four variants.
26405 The variants in a displayed formula are:
26406 \begin_inset Formula
26408 \underline{\textrm{Command}\raisebox{-0.9mm}{}} & & \underline{\textrm{Result}}\\
26409 \mathrm{a\backslash mod\textrm{␣}b} & & a\mod b\\
26410 \mathrm{a\backslash pmod\textrm{␣}b} & & a\pmod b\\
26411 \mathrm{a\backslash bmod\textrm{␣}b} & & a\bmod b\\
26412 \mathrm{a\backslash pod\textrm{␣}b} & & a\pod b
26420 \begin_layout Standard
26421 In an inline formula less space is set before the function names for all
26423 By default the modulo-functions take only the first following character
26425 To use more than one character, one has to put them into TeX-braces:
26426 \begin_inset Formula
26428 \underline{\textrm{Command}\raisebox{-0.9mm}{}} & & \underline{\textrm{Result}}\\
26429 \mathrm{a\backslash pod\textrm{␣}bcd} & & a\pod bcd\\
26430 \mathrm{a\backslash pod\backslash\{bc\to d} & & a\pod{bc}d
26438 \begin_layout Section
26440 \begin_inset Index idx
26443 \begin_layout Plain Layout
26452 \begin_layout Standard
26453 The characters ^ and _ would normally create a subscript and subscript,
26455 To get these characters you have to insert them with a leading
26460 \begin_layout Standard
26463 \begin_inset Tabular
26464 <lyxtabular version="3" rows="3" columns="2">
26465 <features rotate="0" tabularvalignment="middle">
26466 <column alignment="block" valignment="top">
26467 <column alignment="block" valignment="top">
26469 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
26472 \begin_layout Plain Layout
26478 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
26481 \begin_layout Plain Layout
26489 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
26492 \begin_layout Plain Layout
26496 \begin_inset space \textvisiblespace{}
26504 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
26507 \begin_layout Plain Layout
26508 \begin_inset Formula $\mathcircumflex$
26518 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
26521 \begin_layout Plain Layout
26529 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
26532 \begin_layout Plain Layout
26533 \begin_inset Formula $\_$
26549 \begin_layout Subsection
26550 Special Characters in Mathematical Text
26553 \begin_layout Standard
26554 The following commands can only be used in mathematical text or in TeX-mode:
26557 \begin_layout Standard
26558 \begin_inset space \hfill{}
26562 \begin_inset Tabular
26563 <lyxtabular version="3" rows="8" columns="2">
26564 <features rotate="0" tabularvalignment="middle">
26565 <column alignment="block" valignment="top">
26566 <column alignment="block" valignment="top">
26568 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
26571 \begin_layout Plain Layout
26577 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
26580 \begin_layout Plain Layout
26588 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
26591 \begin_layout Plain Layout
26599 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
26602 \begin_layout Plain Layout
26603 \begin_inset Formula $\textrm{œ}$
26613 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
26616 \begin_layout Plain Layout
26624 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
26627 \begin_layout Plain Layout
26628 \begin_inset Formula $\textrm{Œ}$
26638 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
26641 \begin_layout Plain Layout
26649 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
26652 \begin_layout Plain Layout
26653 \begin_inset Formula $\textrm{æ}$
26663 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
26666 \begin_layout Plain Layout
26674 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
26677 \begin_layout Plain Layout
26678 \begin_inset Formula $\textrm{Æ}$
26688 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
26691 \begin_layout Plain Layout
26699 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
26702 \begin_layout Plain Layout
26703 \begin_inset Formula $\textrm{\aa}$
26713 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
26716 \begin_layout Plain Layout
26720 \begin_inset Index idx
26723 \begin_layout Plain Layout
26730 \begin_layout Plain Layout
26751 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
26754 \begin_layout Plain Layout
26755 \begin_inset Formula $\textrm{Å}$
26765 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
26768 \begin_layout Plain Layout
26776 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
26779 \begin_layout Plain Layout
26780 \begin_inset Formula $\textrm{ı}$
26794 \begin_inset space \hfill{}
26798 \begin_inset Tabular
26799 <lyxtabular version="3" rows="8" columns="2">
26800 <features rotate="0" tabularvalignment="middle">
26801 <column alignment="block" valignment="top">
26802 <column alignment="center" valignment="top">
26804 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
26807 \begin_layout Plain Layout
26809 \begin_inset Note Note
26812 \begin_layout Plain Layout
26814 \begin_inset space \thinspace{}
26817 mm is used for separation, because otherwise the output will be ¡ and ¿
26828 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
26831 \begin_layout Plain Layout
26839 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
26842 \begin_layout Plain Layout
26850 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
26853 \begin_layout Plain Layout
26854 \begin_inset Formula $\textrm{ø}$
26864 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
26867 \begin_layout Plain Layout
26875 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
26878 \begin_layout Plain Layout
26879 \begin_inset Formula $\textrm{Ø}$
26889 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
26892 \begin_layout Plain Layout
26900 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
26903 \begin_layout Plain Layout
26904 \begin_inset Formula $\textrm{ł}$
26914 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
26917 \begin_layout Plain Layout
26925 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
26928 \begin_layout Plain Layout
26929 \begin_inset Formula $\textrm{Ł}$
26939 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
26942 \begin_layout Plain Layout
26944 \begin_inset space \hspace{}
26949 \begin_inset space \textvisiblespace{}
26957 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
26960 \begin_layout Plain Layout
26961 \begin_inset Formula $\textrm{!`}$
26971 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
26974 \begin_layout Plain Layout
26976 \begin_inset space \hspace{}
26981 \begin_inset space \textvisiblespace{}
26989 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
26992 \begin_layout Plain Layout
26993 \begin_inset Formula $\textrm{?`}$
27003 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
27006 \begin_layout Plain Layout
27014 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
27017 \begin_layout Plain Layout
27018 \begin_inset Formula $\textrm{ȷ}$
27032 \begin_inset space \hfill{}
27038 \begin_layout Standard
27040 \begin_inset Formula $\textrm{\textrm{Å}}$
27044 \begin_inset Formula $\textrm{\textrm{Ø}}$
27047 can also be inserted via the math toolbar button
27050 arg "math-insert \\digamma"
27056 \begin_layout Standard
27057 An exception are the commands
27060 \begin_inset space \hspace{}
27069 \begin_inset space \hspace{}
27075 , because they can be inserted in LyX directly to text.
27078 \begin_layout Subsection
27080 \begin_inset CommandInset label
27082 name "sub:Accents-in-Text"
27087 \begin_inset Index idx
27090 \begin_layout Plain Layout
27099 \begin_layout Standard
27100 With the following commands all letters can be accented.
27101 The commands must be inserted in TeX-mode.
27104 \begin_layout Standard
27105 \begin_inset space \hfill{}
27109 \begin_inset Tabular
27110 <lyxtabular version="3" rows="8" columns="2">
27111 <features rotate="0" tabularvalignment="middle">
27112 <column alignment="block" valignment="top">
27113 <column alignment="block" valignment="top">
27115 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
27118 \begin_layout Plain Layout
27124 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
27127 \begin_layout Plain Layout
27135 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
27138 \begin_layout Plain Layout
27142 \begin_inset Quotes grd
27150 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
27153 \begin_layout Plain Layout
27157 \begin_layout Plain Layout
27173 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
27176 \begin_layout Plain Layout
27184 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
27187 \begin_layout Plain Layout
27191 \begin_layout Plain Layout
27207 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
27210 \begin_layout Plain Layout
27214 \begin_inset space \textvisiblespace{}
27222 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
27225 \begin_layout Plain Layout
27229 \begin_layout Plain Layout
27245 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
27248 \begin_layout Plain Layout
27256 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
27259 \begin_layout Plain Layout
27263 \begin_layout Plain Layout
27279 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
27282 \begin_layout Plain Layout
27286 \begin_inset space \textvisiblespace{}
27294 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
27297 \begin_layout Plain Layout
27301 \begin_layout Plain Layout
27317 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
27320 \begin_layout Plain Layout
27324 \begin_inset space \textvisiblespace{}
27332 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
27335 \begin_layout Plain Layout
27339 \begin_layout Plain Layout
27355 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
27358 \begin_layout Plain Layout
27362 \begin_inset space \textvisiblespace{}
27370 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
27373 \begin_layout Plain Layout
27377 \begin_layout Plain Layout
27397 \begin_inset space \hfill{}
27401 \begin_inset Tabular
27402 <lyxtabular version="3" rows="8" columns="2">
27403 <features rotate="0" tabularvalignment="middle">
27404 <column alignment="block" valignment="top">
27405 <column alignment="center" valignment="top">
27407 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
27410 \begin_layout Plain Layout
27416 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
27419 \begin_layout Plain Layout
27427 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
27430 \begin_layout Plain Layout
27434 \begin_inset space \textvisiblespace{}
27442 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
27445 \begin_layout Plain Layout
27449 \begin_layout Plain Layout
27465 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
27468 \begin_layout Plain Layout
27476 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
27479 \begin_layout Plain Layout
27483 \begin_layout Plain Layout
27499 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
27502 \begin_layout Plain Layout
27506 \begin_inset Index idx
27509 \begin_layout Plain Layout
27520 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
27523 \begin_layout Plain Layout
27527 \begin_layout Plain Layout
27543 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
27546 \begin_layout Plain Layout
27554 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
27557 \begin_layout Plain Layout
27561 \begin_layout Plain Layout
27577 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
27580 \begin_layout Plain Layout
27584 \begin_inset space \textvisiblespace{}
27592 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
27595 \begin_layout Plain Layout
27599 \begin_layout Plain Layout
27615 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
27618 \begin_layout Plain Layout
27622 \begin_inset space \textvisiblespace{}
27630 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
27633 \begin_layout Plain Layout
27637 \begin_layout Plain Layout
27653 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
27656 \begin_layout Plain Layout
27660 \begin_inset space \textvisiblespace{}
27668 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
27671 \begin_layout Plain Layout
27675 \begin_layout Plain Layout
27695 \begin_inset space \hfill{}
27701 \begin_layout Standard
27702 \begin_inset VSpace medskip
27711 also two different characters can be accented.
27717 \begin_inset space \textvisiblespace{}
27726 \begin_layout Plain Layout
27738 \begin_layout Standard
27751 can in combination with vowels directly be inserted with the keyboard without
27753 The same applies for the tilde
27757 \begin_layout Plain Layout
27758 This only applies for keyboards where the tilde is defined as accent.
27767 in combination with
27782 \begin_layout Standard
27825 and accents that are inserted directly with the keyboard are also available
27826 in mathematical text.
27827 For the other accents there are special math commands to be used in formulas,
27829 \begin_inset CommandInset ref
27831 reference "sub:Accents-for-one"
27838 \begin_layout Standard
27839 \begin_inset VSpace bigskip
27842 Furthermore, with the command
27849 \begin_inset Index idx
27852 \begin_layout Plain Layout
27860 all numbers and letters can be set into a circle, quasi accented with a
27861 circle, similar to the copyright symbol.
27864 \begin_layout Standard
27866 \begin_inset Tabular
27867 <lyxtabular version="3" rows="3" columns="2">
27868 <features rotate="0" tabularvalignment="middle">
27869 <column alignment="center" valignment="top">
27870 <column alignment="center" valignment="top">
27872 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
27875 \begin_layout Plain Layout
27881 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
27884 \begin_layout Plain Layout
27886 \begin_inset Note Note
27889 \begin_layout Plain Layout
27896 is only used as spacer.
27908 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
27911 \begin_layout Plain Layout
27919 <cell multicolumn="1" alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
27922 \begin_layout Plain Layout
27926 \begin_layout Plain Layout
27942 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
27945 \begin_layout Plain Layout
27956 raisebox{-1.5pt}{W}}
27961 <cell multicolumn="1" alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
27964 \begin_layout Plain Layout
27965 \begin_inset Formula $\raisebox{4.5mm}{}$
27972 \begin_layout Plain Layout
27990 \begin_inset Formula $\raisebox{-2mm}{}$
28006 \begin_layout Standard
28007 One has to take care that the character fits in the circle.
28018 \begin_layout Plain Layout
28020 \begin_inset CommandInset ref
28022 reference "sub:Font-Sizes"
28031 specifies thereby the size of the circle.
28042 \begin_layout Plain Layout
28044 \begin_inset CommandInset ref
28046 reference "sub:Boxes-without-Frame"
28055 the character can be centered.
28058 \begin_layout Subsection
28060 \begin_inset Index idx
28063 \begin_layout Plain Layout
28072 \begin_layout Standard
28073 Old-style figures (also known as old-style numerals) are created with the
28081 \begin_inset Index idx
28084 \begin_layout Plain Layout
28093 The command can be used in formulas and in TeX-mode.
28094 The command scheme is:
28097 \begin_layout Standard
28102 oldstylenums{number}
28105 \begin_layout Standard
28110 oldstylenums{0123456789
28113 \begin_inset Formula $\oldstylenums{0123456789}$
28119 \begin_layout Section
28121 \begin_inset CommandInset label
28123 name "sec:Formula-Styles"
28128 \begin_inset Index idx
28131 \begin_layout Plain Layout
28140 \begin_layout Itemize
28141 There are two different alignment styles:
28145 \begin_layout Description
28146 Centered is the predefined standard
28149 \begin_layout Description
28150 Indented for this the option
28154 must be inserted in the menu
28156 Document\SpecialChar \menuseparator
28162 \begin_inset space ~
28168 \begin_layout Standard
28173 is used, the indentation can be adjusted with the length
28180 \begin_inset Index idx
28183 \begin_layout Plain Layout
28192 Should the distance be 15
28193 \begin_inset space \thinspace{}
28196 mm, the following command line is inserted in the LaTeX-preamble
28199 \begin_layout Standard
28209 \begin_layout Standard
28210 When no length is specified, the predefined value of 30
28211 \begin_inset space \thinspace{}
28218 \begin_layout Itemize
28219 And two different numbering styles:
28223 \begin_layout Description
28224 Right is the predefined standard
28227 \begin_layout Description
28228 Left for this the option
28232 must be inserted in the menu
28234 Document\SpecialChar \menuseparator
28240 \begin_inset space ~
28247 \begin_layout Standard
28256 can also be used together.
28257 In this case both options are inserted, separated by a comma.
28260 \begin_layout Standard
28261 The chosen styles are used for all displayed formulas of the document.
28262 When both, centered and indented formulas should be created in a document,
28268 The indented formulas are then set in a flalign environment, see
28269 \begin_inset CommandInset ref
28271 reference "sub:Flalign-Environment"
28278 \begin_layout Section
28280 \begin_inset CommandInset label
28282 name "sec:Multiline-Formulas"
28287 \begin_inset Index idx
28290 \begin_layout Plain Layout
28291 Formula ! multiline
28299 \begin_layout Subsection
28303 \begin_layout Standard
28304 In LyX multiline formulas are created by pressing
28307 arg "newline-insert newline"
28311 This creates either an
28313 eqnarray environment
28315 that is described in
28316 \begin_inset CommandInset ref
28318 reference "sub:Eqnarray-Environment"
28322 or, when the option
28324 Use AMS math package
28326 in the document settings is selected, an
28330 that is described in
28331 \begin_inset CommandInset ref
28333 reference "sub:Standard-align-Environment"
28338 The align environment is recommended because it provides in any case a
28339 typographically correct output.
28342 \begin_layout Standard
28343 There are other multiline formula environments that can be created via the
28346 Insert\SpecialChar \menuseparator
28350 These environments are described in the following sections.
28353 \begin_layout Standard
28354 In all multiline formula environments a new line is created by pressing
28358 arg "newline-insert newline"
28362 To add or delete lines, the math toolbar buttons
28365 arg "inset-modify tabular append-row"
28371 arg "inset-modify tabular delete-row"
28374 , respectively, or the menu
28376 Edit\SpecialChar \menuseparator
28382 \begin_layout Subsubsection
28384 \begin_inset CommandInset label
28386 name "sub:Line-Separation"
28391 \begin_inset Index idx
28394 \begin_layout Plain Layout
28395 Formula ! multiline ! Line separation
28403 \begin_layout Standard
28404 There is sometimes not enough space in multiline formulas between the lines:
28405 \begin_inset Formula
28407 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}\\
28408 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
28416 \begin_layout Standard
28417 In LaTeX additional line space is specified as optional argument of the
28419 This is not yet possible in LyX
28423 \begin_layout Plain Layout
28425 \begin_inset CommandInset href
28427 name "LyX-bug #1505"
28428 target "http://www.lyx.org/trac/ticket/1505"
28437 , therefore the whole formula must be inserted in TeX-mode.
28438 To add in our example space, the command
28446 is inserted at the end of the first line.
28451 \begin_layout Plain Layout
28458 \begin_layout Plain Layout
28460 B^{2}(B^{2}-2r_{g}^{2}+2x_{0}^{2}-2r_{k}^{2})+4x_{0}^{2}x^{2}+4x_{0}xD &
28463 textrm{-}4x^{2}B^{2}+4x_{0}xB^{2}
28470 \begin_layout Plain Layout
28474 left(B^{2}+x_{0}^{2}
28482 left(B^{2}-2r_{g}^{2}+2x_{0}^{2}-2r_{k}^{2}
28487 \begin_layout Plain Layout
28499 \begin_layout Standard
28500 \begin_inset VSpace bigskip
28503 To set the line separation for all lines in a formula, the length
28510 \begin_inset Index idx
28513 \begin_layout Plain Layout
28523 \begin_inset Formula $\mbox{line separation}=\mathrm{6\, pt+\backslash jot}$
28534 \begin_inset space \thinspace{}
28539 \begin_inset space \thinspace{}
28542 mm additional line separation as in the previous example, the command
28545 \begin_layout Standard
28555 \begin_layout Standard
28556 is inserted in TeX-mode before the formula.
28557 This requires that the LaTeX-package
28565 \begin_layout Plain Layout
28570 is part of every LaTeX standard installation.
28576 \begin_inset Index idx
28579 \begin_layout Plain Layout
28585 was loaded in LaTeX-preamble with the line
28588 \begin_layout Standard
28596 \begin_layout Standard
28601 \begin_layout Plain Layout
28613 \begin_inset Formula
28615 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}\\
28616 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
28624 \begin_layout Standard
28628 \begin_layout Plain Layout
28639 To get back to the predefined distance,
28645 is set to the value 3
28646 \begin_inset space \thinspace{}
28652 \begin_layout Subsubsection
28654 \begin_inset CommandInset label
28656 name "sub:Column-Separation"
28661 \begin_inset Index idx
28664 \begin_layout Plain Layout
28665 Formula ! multiline ! Column separation
28673 \begin_layout Standard
28674 Multiline formulas form a matrix.
28675 A formula in the eqnarray environment is for example a matrix with three
28677 By changing the column separation in this environment, the space beside
28678 the relation sign can be changed.
28681 \begin_layout Standard
28682 The column separation is specified with the length
28689 \begin_inset Index idx
28692 \begin_layout Plain Layout
28701 \begin_inset Newline newline
28704 column separation = 2
28705 \begin_inset space \thinspace{}
28715 \begin_inset Newline newline
28721 \begin_layout Standard
28731 \begin_layout Standard
28732 inserted in TeX-mode, sets for all following formulas a column separation
28734 \begin_inset space \thinspace{}
28738 To get back to the predefined distance,
28745 \begin_inset space \thinspace{}
28751 \begin_layout Standard
28753 \begin_inset space \thinspace{}
28756 cm column separation:
28760 \begin_layout Plain Layout
28772 \begin_inset Formula
28780 A formula with the predefined column separation for matrices of 10
28781 \begin_inset space \thinspace{}
28788 \begin_layout Plain Layout
28800 \begin_inset Formula
28811 \begin_layout Subsubsection
28813 \begin_inset Index idx
28816 \begin_layout Plain Layout
28825 \begin_layout Standard
28826 Long formulas can be typeset using these methods:
28829 \begin_layout Itemize
28830 When one side of the equation is much shorter than the line width, this
28831 one is chosen for the left side and the right side is typeset over two
28833 \begin_inset Formula
28835 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 \\
28836 & & -\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}
28841 The minus sign at the beginning of the second line does normally not appear
28842 as an operator because it is the first character of the line.
28843 Thus it would not be surrounded by space and could not be distinguished
28844 from the fraction bar.
28846 \begin_inset space \thinspace{}
28849 pt space was inserted behind the minus sign with the command
28859 \begin_layout Plain Layout
28867 \begin_inset CommandInset ref
28869 reference "sub:Variable-Space"
28879 \begin_inset Index idx
28882 \begin_layout Plain Layout
28893 \begin_layout Itemize
28894 When both sides of the equation are too long, the command
28901 \begin_inset Index idx
28904 \begin_layout Plain Layout
28913 It is inserted in the first column of the first line and causes all further
28914 insertions to overwrite the following columns:
28915 \begin_inset Formula
28917 \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 \\
28918 & & -\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 \\
28919 & & =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}
28924 After the insertion of
28930 , the cursor is in a purple box that is a bit shifted to the left from the
28932 In this the formula is inserted.
28933 \begin_inset Newline newline
28936 The content of the further lines is inserted to the second or another formula
28938 The greater the column number where it was inserted, the larger the indentation.
28939 \begin_inset VSpace medskip
28943 \begin_inset Newline newline
28947 \begin_inset Note Greyedout
28950 \begin_layout Plain Layout
28951 Note the following when using
28960 \begin_layout Itemize
28961 The formula doesn't use the full page width.
28963 \begin_inset space \thinspace{}
28967 \begin_inset space \space{}
28971 \begin_inset Formula $-B^{2}$
28974 is added to the first line in the above example, it would have been outside
28976 To better use the width, negative space can be inserted at the beginning
28980 \begin_layout Itemize
28981 Due to a bug in LyX the cursor cannot be set with the mouse into the first
28986 \begin_layout Plain Layout
28987 \begin_inset CommandInset href
28989 name "LyX-bug #1429"
28990 target "http://www.lyx.org/trac/ticket/1429"
28999 One can only set the cursor at the beginning of the line and move it with
29008 \begin_layout Itemize
29009 Other methods to set long formulas are offered by the environments described
29011 \begin_inset CommandInset ref
29013 reference "sub:Multline-Environment"
29018 \begin_inset CommandInset ref
29020 reference "sub:Multiline-Formula-Parts"
29027 \begin_layout Subsubsection
29028 Multiline Fractions
29029 \begin_inset CommandInset label
29031 name "sub:Multiline-Fractions"
29036 \begin_inset Index idx
29039 \begin_layout Plain Layout
29040 Fractions ! multiline
29048 \begin_layout Standard
29049 There are cases where the denominator and/or the numerator of a fraction
29050 is so long that the fraction does not fit into one line.
29051 It is then necessary to add a line break within the fraction.
29052 This can be done using the command
29059 \begin_inset Index idx
29062 \begin_layout Plain Layout
29071 To activate it, set in the document settings under
29074 \begin_inset space ~
29084 \begin_inset Index idx
29087 \begin_layout Plain Layout
29088 Packages ! mathtools
29096 \begin_inset space ~
29111 \begin_layout Standard
29116 splitfrac{first line}{second line}
29119 \begin_layout Standard
29120 and is used as denominator and/or numerator:
29123 \begin_layout Standard
29124 \begin_inset Formula
29126 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}
29131 The command for the first numerator above is:
29134 \begin_layout Standard
29139 splitfrac{xy+xy+xy+xy+xy
29140 \begin_inset space \textvisiblespace{}
29148 \begin_layout Subsubsection
29150 \begin_inset CommandInset label
29152 name "sub:Multiline-Brackets"
29157 \begin_inset Index idx
29160 \begin_layout Plain Layout
29161 Brackets ! for multiline expressions
29169 \begin_layout Standard
29170 For brackets spanning multiple lines the following problem occurs:
29171 \begin_inset Formula
29173 A & = & \sin(x)\left[\prod_{R=1}^{\infty}\frac{1}{R}+\cdots\right.\\
29174 & & \left.\cdots+B-D\right]
29182 \begin_layout Standard
29183 The closing bracket is smaller than the opening bracket because brackets
29184 with variable size may not span multiple lines.
29187 \begin_layout Standard
29188 To set the bracket size for the second line correctly, the first line is
29196 \begin_inset Index idx
29199 \begin_layout Plain Layout
29207 and the second line with
29215 \begin_layout Plain Layout
29229 \begin_inset CommandInset ref
29231 reference "sub:Automatic-Bracket-Size"
29243 \begin_inset Index idx
29246 \begin_layout Plain Layout
29269 \begin_inset space \textvisiblespace{}
29279 \begin_inset space \textvisiblespace{}
29289 \begin_inset space \textvisiblespace{}
29295 \begin_inset Formula $\downarrow$
29301 \begin_inset Index idx
29304 \begin_layout Plain Layout
29312 is inserted, because the multiplication operator with its limits is the
29313 largest symbol in the first line and this should be the size for the bracket
29314 in the second line.
29317 \begin_layout Standard
29318 The result is this:
29319 \begin_inset Formula
29321 A & = & \sin(x)\left[\prod_{R=1}^{\infty}\frac{1}{R}+\cdots\right.\\
29322 & & \left.\vphantom{\prod_{R=1}^{\infty}}\cdots+B-D\right]
29330 \begin_layout Subsection
29334 \begin_layout Standard
29335 Align environments can be used for every kind of multiline formulas.
29336 They are especially useful to set several formulas side by side.
29339 \begin_layout Standard
29340 Align environments consist of columns.
29341 The odd columns are right aligned, the even ones left aligned.
29342 Every line in an Align environment can be numbered.
29345 \begin_layout Standard
29346 Align environments are created via the menu
29348 Insert\SpecialChar \menuseparator
29354 Edit\SpecialChar \menuseparator
29355 Math\SpecialChar \menuseparator
29356 Change Formula Type
29358 already existing formulas can be converted to Align environments.
29361 \begin_layout Standard
29362 To add or delete columns, the math toolbar buttons
29365 arg "inset-modify tabular append-column"
29371 arg "inset-modify tabular delete-column"
29374 , respectively, or the menu
29376 Edit\SpecialChar \menuseparator
29382 \begin_layout Subsubsection
29383 Standard align Environment
29384 \begin_inset CommandInset label
29386 name "sub:Standard-align-Environment"
29391 \begin_inset Index idx
29394 \begin_layout Plain Layout
29395 Formula ! multiline ! align environment
29403 \begin_layout Standard
29404 This Align environment is created by pressing
29407 arg "newline-insert newline"
29410 in a formula or by the menu
29412 Insert\SpecialChar \menuseparator
29413 Math\SpecialChar \menuseparator
29414 AMS align Environment
29419 \begin_layout Standard
29420 An example for two formulas set side by side, that are created with a four
29421 column align environment:
29422 \begin_inset Formula
29424 A & =\sin(B) & C & =D\\
29425 C & \ne A & B & \ne D
29430 As it can be seen, the formulas in this environment are placed so as if
29439 \begin_layout Plain Layout
29447 \begin_inset CommandInset ref
29449 reference "sub:Variable-Space"
29460 before the first and after every even column.
29461 When the formula style
29467 \begin_layout Plain Layout
29469 \begin_inset CommandInset ref
29471 reference "sec:Formula-Styles"
29482 is used, the formula is set without the
29488 before the first column.
29491 \begin_layout Subsubsection
29492 Alignat Environment
29493 \begin_inset Index idx
29496 \begin_layout Plain Layout
29497 Formula ! multiline ! alignat environment
29505 \begin_layout Standard
29506 The alignat environment has no predefined column separation.
29507 It can be inserted manually with the spaces that are described
29508 \begin_inset CommandInset ref
29510 reference "sub:Space"
29517 \begin_layout Standard
29518 The above example in the alignat environment where 1
29519 \begin_inset space \thinspace{}
29522 cm space was inserted at the beginning of the second formula:
29523 \begin_inset Formula
29524 \begin{alignat*}{2}
29525 A & =\sin(B) & \hspace{1cm}C & =D\\
29526 C & \ne A & B & \ne D
29531 Because the column separation can be set separately for every column, this
29532 environment is especially suitable to set three and more formulas side
29536 \begin_layout Subsubsection
29537 Flalign Environment
29538 \begin_inset CommandInset label
29540 name "sub:Flalign-Environment"
29545 \begin_inset Index idx
29548 \begin_layout Plain Layout
29549 Formula ! multiline ! flalign environment
29557 \begin_layout Standard
29558 In this environment the first two columns are always set as much as possible
29559 to the left and the last two ones to the right.
29561 \begin_inset Formula
29563 A & =1 & B & =2 & C & =3\\
29564 X & =\textrm{-}1 & Y & =\textrm{-}2 & Z & =4
29572 \begin_layout Standard
29573 By creating a flalign environment with an odd number of columns where an
29574 empty TeX-brace is inserted to the last column, several formulas in a document
29575 can be set to the left, although the formula style
29580 As example the indented formula
29581 \begin_inset CommandInset ref
29583 reference "eq:VolInt"
29588 \begin_inset Formula
29590 \hspace{30pt}\iiint\limits _{V}X\,\mathrm{d}V & =U & {}
29595 The first two columns contain the formula.
29596 To indent it as with the formula style
29601 \begin_inset space \thinspace{}
29604 pt space was inserted at the beginning of the first column.
29607 \begin_layout Subsection
29608 Eqnarray Environment
29609 \begin_inset CommandInset label
29611 name "sub:Eqnarray-Environment"
29616 \begin_inset Index idx
29619 \begin_layout Plain Layout
29620 Formula ! multiline ! eqnarray environment
29628 \begin_layout Standard
29629 When this environment has been created, three blue boxes appear.
29630 The content of the first box is right aligned, the content of the last
29632 The content of the middle box appears centered and a bit smaller, because
29633 it is designed to insert there only relation characters.
29634 \begin_inset Formula
29636 \frac{ABC}{D} & \frac{ABC}{D} & \frac{ABC}{D}\\
29646 \begin_layout Subsection
29648 \begin_inset Index idx
29651 \begin_layout Plain Layout
29652 Formula ! multiline ! gather environment
29660 \begin_layout Standard
29661 This environment consists of only one centered column.
29662 Every line can be numbered.
29663 \begin_inset Formula
29674 \begin_layout Subsection
29675 Multline Environment
29676 \begin_inset CommandInset label
29678 name "sub:Multline-Environment"
29683 \begin_inset Index idx
29686 \begin_layout Plain Layout
29687 Formula ! multiline ! multline environment
29695 \begin_layout Standard
29696 The multline environment consists, like the gather environment, of only
29698 But the first line is left aligned, the last one right aligned.
29699 All other lines are centered.
29700 Therefore this environment is suitable for long formulas.
29702 \begin_inset CommandInset ref
29704 reference "eq:lefteqn"
29708 in the multline environment:
29709 \begin_inset Formula
29711 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}\\
29712 -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}\\
29713 =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}}
29721 \begin_layout Standard
29722 In the output only the last (first) line of a multline environment appears
29723 numbered when the document numbering is right (left).
29727 \begin_layout Plain Layout
29728 numbering styles see
29729 \begin_inset CommandInset ref
29731 reference "sec:Formula-Styles"
29743 \begin_layout Standard
29751 \begin_inset Index idx
29754 \begin_layout Plain Layout
29769 \begin_inset Index idx
29772 \begin_layout Plain Layout
29780 a centered line can be right or left aligned, respectively.
29781 The commands are used as follows:
29784 \begin_layout Standard
29789 shoveright{line content}
29795 shoveleft{line content}
29798 \begin_layout Standard
29799 \begin_inset VSpace medskip
29809 \begin_inset Index idx
29812 \begin_layout Plain Layout
29820 specifies the distance of the first line from the left page margin.
29821 Predefined is the length 0
29822 \begin_inset space \thinspace{}
29828 \begin_layout Standard
29829 As example the above formula where the command
29832 \begin_layout Standard
29842 \begin_layout Standard
29843 was inserted in TeX-mode before:
29847 \begin_layout Plain Layout
29859 \begin_inset Formula
29861 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}\\
29862 \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}}\\
29863 =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}}
29872 \begin_layout Plain Layout
29883 The second line was left aligned using
29892 \begin_layout Subsection
29893 Multiline Formula Parts
29894 \begin_inset CommandInset label
29896 name "sub:Multiline-Formula-Parts"
29901 \begin_inset Index idx
29904 \begin_layout Plain Layout
29905 Formula ! multiline ! formula parts
29913 \begin_layout Standard
29914 To display only parts of a formula with multiple lines, one of the following
29915 environments is used:
29932 They can be inserted via the menu
29934 Insert\SpecialChar \menuseparator
29937 or by using the commands described in this section.
29940 \begin_layout Standard
29941 The first three have the same properties as the corresponding multiline
29942 formula environments, but it is possible to set further formula parts beside
29945 \begin_inset Formula
29947 \left.\begin{aligned}\Delta x\Delta p & \ge\frac{\hbar}{2}\\
29948 \Delta E\Delta t & \ge\frac{\hbar}{2}
29950 \right\} \textrm{Uncertainty relations}
29958 \begin_layout Standard
29959 To get this formula, a displayed formula is created where the command
29966 \begin_inset Index idx
29969 \begin_layout Plain Layout
29978 A purple box appears around the blue formula box where now columns and
29979 lines can be added.
29980 Outside the multiline environment other formula parts can be set, like
29984 \begin_layout Standard
29985 The aligned environment is also suitable for long formulas whose lines are
29986 horizontally aligned.
29987 Using aligned in a displayed formula has the advantage that the formula
29988 number is vertically centered behind the lines.
29990 \begin_inset CommandInset ref
29992 reference "eq:shortlong"
29996 in the aligned environment:
29997 \begin_inset Formula
29999 \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}|}\\
30000 & -\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}|}
30009 \begin_layout Standard
30010 To use the environments
30029 \begin_inset Index idx
30032 \begin_layout Plain Layout
30047 \begin_inset Index idx
30050 \begin_layout Plain Layout
30065 \begin_inset Index idx
30068 \begin_layout Plain Layout
30076 are inserted, respectively.
30077 The split environment has the same properties as the aligned environment
30078 but it can only have two columns.
30081 \begin_layout Subsection
30082 Text in multiline Formulas
30083 \begin_inset CommandInset label
30085 name "sub:Text-in-multiline"
30090 \begin_inset Index idx
30093 \begin_layout Plain Layout
30100 \begin_inset Index idx
30103 \begin_layout Plain Layout
30104 Formula ! multiline ! text
30112 \begin_layout Standard
30113 In the Align environments, and the multline and gather environment, text
30114 can be inserted that will appear in a separate line and doesn't affect
30115 the column alignment.
30116 To do this, the command
30123 \begin_inset Index idx
30126 \begin_layout Plain Layout
30134 is used in the following scheme:
30137 \begin_layout Standard
30145 \begin_layout Standard
30146 The text should not be longer than a line because it cannot be hyphenated.
30147 As LyX doesn't yet support
30153 directly, the text is written as mathematical text.
30160 must hereby be at the beginning of a line and appears in the output above
30162 An example where the text was inserted at the beginning of the second line:
30163 \begin_inset Formula
30165 I & =a\sqrt{2}\int_{0}^{2\pi}\sqrt{1+\cos(\phi)}\;\mathrm{d}\phi\\
30166 \intertext{\text{integrand is symmetric to \ensuremath{\phi=\pi}, therefore}} & =2a\sqrt{2}\int_{0}^{\pi}\sqrt{1+\cos(\phi)}\;\mathrm{d}\phi
30174 \begin_layout Standard
30181 always creates some vertical space between the text and the formula lines.
30182 To avoid this space, set in the document settings under
30185 \begin_inset space ~
30195 \begin_inset Index idx
30198 \begin_layout Plain Layout
30199 Packages ! mathtools
30207 \begin_inset space ~
30213 Then you can use the command
30220 \begin_inset Index idx
30223 \begin_layout Plain Layout
30240 \begin_layout Standard
30241 \begin_inset Formula
30243 I & =a\sqrt{2}\int_{0}^{2\pi}\sqrt{1+\cos(\phi)}\;\mathrm{d}\phi\\
30244 \shortintertext{\text{integrand is symmetric to \ensuremath{\phi=\pi}, therefore}} & =2a\sqrt{2}\int_{0}^{\pi}\sqrt{1+\cos(\phi)}\;\mathrm{d}\phi
30252 \begin_layout Section
30254 \begin_inset Index idx
30257 \begin_layout Plain Layout
30264 \begin_inset Index idx
30267 \begin_layout Plain Layout
30268 Formula ! numbering|see
30272 \begin_layout Plain Layout
30283 \begin_layout Plain Layout
30298 \begin_layout Subsection
30302 \begin_layout Standard
30303 Numbered formulas can be created with the menu
30305 Insert\SpecialChar \menuseparator
30306 Math\SpecialChar \menuseparator
30308 \begin_inset space ~
30316 \begin_inset space ~
30322 Existing formulas can be numbered with the menu
30324 Edit\SpecialChar \menuseparator
30325 Math\SpecialChar \menuseparator
30327 \begin_inset space ~
30335 arg "math-number-toggle"
30339 The formula number is displayed in LyX behind the formula as a number sign
30341 The number sign is replaced in the output by the formula number.
30344 \begin_layout Standard
30345 When numbering is turned on in multiline formulas, all lines will be numbered.
30346 But the numbering can be controlled with the menu
30348 Edit\SpecialChar \menuseparator
30349 Math\SpecialChar \menuseparator
30351 \begin_inset space ~
30355 \begin_inset space ~
30359 \begin_inset space ~
30367 arg "math-number-line-toggle"
30373 \begin_layout Standard
30374 Except for inline formulas, all formulas can be numbered with two different
30376 \begin_inset CommandInset ref
30378 reference "sec:Formula-Styles"
30385 \begin_layout Subsection
30387 \begin_inset Index idx
30390 \begin_layout Plain Layout
30391 Cross-references ! to formulas
30399 \begin_layout Standard
30400 All labeled formulas can be cross-referenced.
30401 A label is added by the menu
30403 Insert\SpecialChar \menuseparator
30406 or the toolbar button
30413 The cursor must hereby be inside a displayed formula.
30414 Alternatively you can right-click on the formula and choose
30419 A dialog pops up displaying the prefix
30424 The label is inserted there behind the prefix.
30425 The predefined prefix means
30426 \begin_inset Quotes eld
30430 \begin_inset Quotes erd
30433 and makes it easier to find labels in large documents because it marks
30434 it as formula label to divide it from e.
30435 \begin_inset space \thinspace{}
30439 \begin_inset space \space{}
30443 To change a label, the menu
30445 Insert\SpecialChar \menuseparator
30448 is used again or you right-click on a formula and then on
30455 \begin_layout Standard
30456 The name of the label is displayed in LyX within two parentheses behind
30458 A formula with a label is always numbered.
30461 \begin_layout Standard
30462 Cross-references are inserted via the menu
30464 Insert\SpecialChar \menuseparator
30467 or with the toolbar button
30470 arg "dialog-show-new-inset ref"
30474 A formula cross-reference appears in the output as formula number.
30475 When in the cross-reference dialog window the format
30479 is chosen, the cross-reference appears in the output as formula number
30481 \begin_inset Newline newline
30484 By right-clicking on a cross-reference in LyX, one jumps to the formula
30485 that is referenced.
30488 \begin_layout Standard
30489 Here are as examples cross-references to formulas of the following subsections:
30490 \begin_inset Note Note
30493 \begin_layout Plain Layout
30494 Note the different cross-reference types.
30502 \begin_layout Standard
30504 \begin_inset CommandInset ref
30511 \begin_inset CommandInset ref
30519 \begin_inset CommandInset ref
30525 ) big Latin letters are used for the numbering in contrary to (
30526 \begin_inset CommandInset ref
30535 \begin_layout Standard
30536 \begin_inset VSpace medskip
30539 When the argument of
30547 \begin_layout Plain Layout
30555 \begin_inset CommandInset ref
30557 reference "sub:User-defined-Numbering"
30568 contains a box like in
30569 \begin_inset CommandInset ref
30571 reference "sub:Paragraph-Boxes"
30575 , the formula cannot be referenced.
30578 \begin_layout Subsection
30580 \begin_inset Index idx
30583 \begin_layout Plain Layout
30584 Formula numbering ! subnumbering
30592 \begin_layout Standard
30593 With the help of the commands
30597 begin{subequations}
30605 formulas can be subnumbered.
30606 Both commands are inserted in TeX-mode.
30609 \begin_layout Standard
30611 \begin_inset Formula
30622 \begin_layout Plain Layout
30626 addtocounter{equation}{-1}
30635 \begin_layout Plain Layout
30639 begin{subequations}
30645 \begin_inset VSpace -5mm
30649 \begin_inset Formula
30657 \begin_inset Formula
30667 \begin_layout Standard
30671 \begin_layout Plain Layout
30683 \begin_layout Standard
30684 To create the example, the following is done:
30687 \begin_layout Enumerate
30688 first formula is inserted
30691 \begin_layout Enumerate
30696 addtocounter{equation}{-1}
30698 begin{subequations}
30699 \begin_inset Index idx
30702 \begin_layout Plain Layout
30711 \begin_inset Newline newline
30716 is inserted after the first formula
30719 \begin_layout Enumerate
30720 second formula is inserted
30723 \begin_layout Enumerate
30724 third formula is inserted
30727 \begin_layout Enumerate
30734 is inserted after the third formula
30737 \begin_layout Standard
30738 Every formula between the commands
30750 is subnumbered as a, b,
30751 \begin_inset Newline linebreak
30754 c, \SpecialChar \ldots{}
30755 For multiline formulas every line will be subnumbered.
30756 All subnumbered formulas are treated as
30761 But as every numbered formula increases the counter
30765 by one, the command
30771 is needed to decrease it.
30772 Otherwise the formulas
30773 \begin_inset CommandInset ref
30780 \begin_inset CommandInset ref
30787 \begin_inset CommandInset ref
30793 would be numbered as
30794 \begin_inset CommandInset ref
30801 \begin_inset CommandInset ref
30808 \begin_inset CommandInset ref
30817 \begin_layout Standard
30818 By inserting the commands in TeX-mode, a space is created between the first
30821 \begin_inset space \thinspace{}
30824 mm vertical space is inserted after the command
30828 begin{subequations}
30831 When the formula style
30837 \begin_layout Plain Layout
30839 \begin_inset CommandInset ref
30841 reference "sec:Formula-Styles"
30853 \begin_inset space \thinspace{}
30856 mm space is inserted instead.
30859 \begin_layout Standard
30860 Here is an example for a multiline formula where the numbering was turned
30861 off for the second line:
30865 \begin_layout Plain Layout
30869 begin{subequations}
30875 \begin_inset Formula
30877 A & = & (B-Z)^{2}=(B-Z)(B-Z)\label{eq:d}\\
30878 & = & B^{2}-ZB-BZ+Z^{2}\nonumber \\
30879 & = & B^{2}-2BZ+Z^{2}\label{eq:f}
30888 \begin_layout Plain Layout
30900 \begin_layout Subsection
30901 User-defined Numbering
30902 \begin_inset CommandInset label
30904 name "sub:User-defined-Numbering"
30909 \begin_inset Index idx
30912 \begin_layout Plain Layout
30913 Formula numbering ! user-defined
30921 \begin_layout Standard
30922 \begin_inset Index idx
30925 \begin_layout Plain Layout
30926 Formula numbering ! self-defined delimiters
30931 With the standard numbering parentheses are set around the formula number.
30932 To replace the parentheses for example by vertical bars, the following
30933 line is added to the LaTeX-preamble:
30936 \begin_layout Standard
30948 \begin_inset Note Note
30951 \begin_layout Plain Layout
30952 This macro is already declared in the LaTeX-preamble for testing.
30953 To activate it, remove the percent sign at the beginning.
30961 \begin_layout Standard
30962 To use other characters, the vertical bars besides the
30966 are replaced by one ore more characters.
30967 To get only the formula number the vertical bars are omitted.
30970 \begin_layout Standard
30971 \begin_inset VSpace bigskip
30974 When there should be an expression of your choice instead of the consecutive
30975 formula number in parentheses behind the formula, the command
30982 \begin_inset Index idx
30985 \begin_layout Plain Layout
30994 \begin_inset Formula
30996 A+B=C\tag{something}\label{eq:tag}
31001 In this example the command
31006 \begin_inset space \textvisiblespace{}
31011 was inserted in the formula.
31014 \begin_layout Standard
31020 \begin_inset space \textvisiblespace{}
31025 is inserted instead, the star prevents the parentheses around the expression:
31026 \begin_inset Formula
31028 A+B=C\tag*{something}
31036 \begin_layout Standard
31037 \begin_inset VSpace bigskip
31040 To restart the formula numbering with new document parts or sections, the
31041 following command is used:
31044 \begin_layout Standard
31049 @addtoreset{equation}{part}
31052 \begin_inset Index idx
31055 \begin_layout Plain Layout
31060 \begin_layout Plain Layout
31071 \begin_layout Plain Layout
31084 \begin_layout Plain Layout
31095 \begin_layout Plain Layout
31108 \begin_inset Newline newline
31112 \begin_inset Newline newline
31119 @addtoreset{equation}{section}
31122 \begin_layout Standard
31123 To be able to use these commands in TeX-mode, the
31124 \begin_inset Quotes eld
31128 \begin_inset Quotes erd
31131 character has to be made
31132 \begin_inset Quotes eld
31136 \begin_inset Quotes erd
31139 for LaTeX using the command
31153 So the command sequence in TeX-mode is:
31156 \begin_layout Standard
31162 \begin_inset Newline newline
31167 @addtoreset{equation}{section}
31168 \begin_inset Newline newline
31176 \begin_layout Standard
31177 In the LaTeX-preamble
31189 can be omitted as they are automatically internally inserted by LyX.
31192 \begin_layout Standard
31207 \begin_layout Plain Layout
31212 is part of the LaTeX-package
31217 \begin_inset Index idx
31220 \begin_layout Plain Layout
31221 Packages ! carlisle
31226 that is part of every LaTeX standard installation.
31232 \begin_inset Index idx
31235 \begin_layout Plain Layout
31236 Packages ! remreset
31241 has to be loaded in the LaTeX-preamble with the line
31244 \begin_layout Standard
31249 usepackage{remreset}
31252 \begin_layout Standard
31260 \begin_inset Index idx
31263 \begin_layout Plain Layout
31268 \begin_layout Plain Layout
31279 \begin_layout Plain Layout
31292 \begin_layout Plain Layout
31303 \begin_layout Plain Layout
31315 can be used with the same scheme as
31324 \begin_layout Standard
31325 \begin_inset VSpace bigskip
31328 Sometimes formulas should be numbered in the following form:
31331 \begin_layout Standard
31334 (section number.formula number)
31337 \begin_layout Standard
31338 The formula number should start with every section with
31339 \begin_inset Quotes eld
31343 \begin_inset Quotes erd
31349 \begin_layout Standard
31350 For this case there is the command
31357 \begin_inset Index idx
31360 \begin_layout Plain Layout
31368 , which is used with the following scheme:
31371 \begin_layout Standard
31376 numberwithin{counter}{sectioning}
31379 \begin_layout Standard
31380 Counter denotes what kind of numbering is affected, sectioning denotes what
31381 number is before the dot.
31384 \begin_layout Standard
31385 Thus in our case the following LaTeX-preamble or TeX code line is used:
31388 \begin_layout Standard
31393 numberwithin{equation}{section}
31396 \begin_layout Standard
31397 This is the result:
31401 \begin_layout Plain Layout
31405 numberwithin{equation}{section}
31411 \begin_inset Formula
31421 \begin_layout Standard
31423 \begin_inset space \thinspace{}
31427 \begin_inset space \space{}
31430 tables so that the number of the part is the sectioning,
31431 \begin_inset Newline newline
31438 numberwithin{table}{part}
31443 \begin_layout Standard
31444 To go back to the standard numbering or to prevent this kind of numbering
31445 when it is defined by the document class, the following command is inserted
31446 as TeX code or to the LaTeX-preamble:
31449 \begin_layout Standard
31459 \begin_inset Index idx
31462 \begin_layout Plain Layout
31476 \begin_layout Plain Layout
31492 \begin_inset Newline newline
31500 \begin_inset Newline newline
31512 \begin_layout Standard
31519 uses internally the command
31525 , described above, that also needs to be reverted.
31529 \begin_layout Plain Layout
31536 \begin_layout Plain Layout
31540 @removefromreset{equation}{section}
31543 \begin_layout Plain Layout
31555 \begin_layout Subsection
31556 Numbering with Roman Numbers and Letters
31557 \begin_inset Index idx
31560 \begin_layout Plain Layout
31561 Formula numbering ! with letters
31567 \begin_inset Index idx
31570 \begin_layout Plain Layout
31571 Formula numbering ! with Roman numbers
31579 \begin_layout Standard
31580 Formulas can also be numbered with Roman numbers and Latin letters.
31581 To number for example with small Roman numbers, the command
31584 \begin_layout Standard
31596 \begin_layout Standard
31597 is inserted before the formula in TeX-mode.
31605 \begin_inset Index idx
31608 \begin_layout Plain Layout
31616 redefines the predefined command
31632 \begin_layout Plain Layout
31639 has the same scheme like the command
31645 that is described in
31646 \begin_inset CommandInset ref
31648 reference "sub:The-Command-newcommand"
31661 is the formula counter.
31668 is used as prefix for a counter, the value of the counter is output as
31670 When a formula is numbered, LaTeX sets internally the command
31676 behind the formula.
31682 \begin_inset Index idx
31685 \begin_layout Plain Layout
31695 outputs the counter as small Roman number.
31698 \begin_layout Standard
31699 All formulas behind the command
31709 are now numbered Roman.
31710 To switch to numbering with big Roman numbers, the command is inserted
31724 \begin_inset Index idx
31727 \begin_layout Plain Layout
31739 \begin_inset Quotes eld
31743 \begin_inset Quotes erd
31746 with small Latin letters there is the command
31753 \begin_inset Index idx
31756 \begin_layout Plain Layout
31764 , for big ones there is the command
31771 \begin_inset Index idx
31774 \begin_layout Plain Layout
31787 \begin_layout Standard
31788 \begin_inset Note Greyedout
31791 \begin_layout Plain Layout
31798 \begin_inset space ~
31801 formulas can be numbered with Latin letters in one document.
31809 \begin_layout Standard
31810 \begin_inset Newpage newpage
31816 \begin_layout Standard
31820 \begin_layout Plain Layout
31836 \begin_layout Standard
31837 \begin_inset Formula
31839 A=\textrm{small roman}
31848 \begin_layout Plain Layout
31862 \begin_inset Formula
31864 B=\textrm{big Roman}\label{eq:Rom}
31873 \begin_layout Plain Layout
31887 \begin_inset Formula
31889 C=\textrm{small Latin}
31898 \begin_layout Plain Layout
31912 \begin_inset Formula
31914 D=\textrm{big Latin}\label{eq:Lat}
31922 \begin_layout Standard
31923 To switch back to the default numbering, insert the command:
31926 \begin_layout Standard
31936 \begin_inset Index idx
31939 \begin_layout Plain Layout
31950 \begin_layout Standard
31954 \begin_layout Plain Layout
31968 \begin_inset Formula
31978 \begin_layout Standard
31979 \begin_inset VSpace medskip
31982 As you see, formulas are numbered serially independent from the numbering
31984 When then numbering should start with
31985 \begin_inset Quotes eld
31989 \begin_inset Quotes erd
31992 when the style is changed, new equation counters have to be defined.
31993 A description about this can be found in the file
31994 \begin_inset CommandInset href
31996 name "Formula-numbering.lyx"
31997 target "run:Formula-numbering.lyx"
32004 \begin_layout Section
32005 Chemical Symbols and Equations
32006 \begin_inset CommandInset label
32008 name "sub:Chemical-Symbols-and"
32013 \begin_inset Index idx
32016 \begin_layout Plain Layout
32017 Chemical characters ! Symbols
32023 \begin_inset Index idx
32026 \begin_layout Plain Layout
32033 \begin_inset Index idx
32036 \begin_layout Plain Layout
32045 \begin_layout Standard
32046 An example text from chemistry:
32049 \begin_layout Quote
32051 \begin_inset Formula $\mathrm{SO_{4}^{2-}}$
32054 -ion reacts with two
32055 \begin_inset Formula $\mathrm{Na^{+}}$
32058 -ions to sodium sulfate
32059 \begin_inset Formula $\left(\mathrm{Na_{2}SO_{4}}\right)$
32063 The chemical equation for this is:
32064 \begin_inset Formula
32066 \mathrm{2\, Na^{+}+SO_{4}^{2-}\longrightarrow Na_{2}SO_{4}}\label{eq:chem-reaction}
32074 \begin_layout Standard
32075 This chemical equation can directly be created as formula.
32076 To avoid that the symbols appear italic, everything is highlighted and
32077 changed by the shortcut
32083 to the upright font style.
32087 \begin_layout Plain Layout
32093 \begin_inset CommandInset ref
32095 reference "sub:Font-Styles"
32107 \begin_layout Standard
32108 A more convenient way to typeset chemical formulas is to use the command
32116 \begin_inset Index idx
32119 \begin_layout Plain Layout
32127 that is available when the LaTeX-package
32132 \begin_inset Index idx
32135 \begin_layout Plain Layout
32148 to a formula a new blue box appears where chemical formulas can be inserted
32149 in an intuitive way.
32152 \begin_layout Standard
32154 \begin_inset Tabular
32155 <lyxtabular version="3" rows="9" columns="2">
32156 <features rotate="0" tabularvalignment="middle">
32157 <column alignment="center" valignment="top">
32158 <column alignment="center" valignment="top">
32160 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
32163 \begin_layout Plain Layout
32169 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
32172 \begin_layout Plain Layout
32174 \begin_inset Note Note
32177 \begin_layout Plain Layout
32184 is only used as spacer.
32196 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
32199 \begin_layout Plain Layout
32203 \begin_inset space \textvisiblespace{}
32211 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
32214 \begin_layout Plain Layout
32215 \begin_inset Formula $\raisebox{4.5mm}{}\ce{H2CO3}\raisebox{-2mm}{}$
32225 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
32228 \begin_layout Plain Layout
32232 \begin_inset space \textvisiblespace{}
32240 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
32243 \begin_layout Plain Layout
32244 \begin_inset Formula $\raisebox{5mm}{}\ce{SO4^{2-}}\raisebox{-2mm}{}$
32254 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
32257 \begin_layout Plain Layout
32261 \begin_inset space \textvisiblespace{}
32269 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
32272 \begin_layout Plain Layout
32273 \begin_inset Formula $\raisebox{4.5mm}{}\ce{(NH4)2S}\raisebox{-2mm}{}$
32283 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
32286 \begin_layout Plain Layout
32290 \begin_inset space \textvisiblespace{}
32298 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
32301 \begin_layout Plain Layout
32302 \begin_inset Formula $\raisebox{4.5mm}{}\ce{KCr(SO4)2.12H2O}\raisebox{-2mm}{}$
32312 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
32315 \begin_layout Plain Layout
32319 \begin_inset space \textvisiblespace{}
32325 \begin_inset space \textvisiblespace{}
32331 \begin_inset space \textvisiblespace{}
32339 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
32342 \begin_layout Plain Layout
32343 \begin_inset Formula $\raisebox{4.5mm}{}\ce{A-B\dbond C\tbond D}\raisebox{-2mm}{}$
32353 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
32356 \begin_layout Plain Layout
32360 \begin_inset space \textvisiblespace{}
32364 \begin_inset Formula $\downarrow$
32368 \begin_inset Formula $\to$
32376 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
32379 \begin_layout Plain Layout
32380 \begin_inset Formula $\raisebox{5mm}{}\ce{_{90}^{227}Th+}\raisebox{-2mm}{}$
32390 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
32393 \begin_layout Plain Layout
32397 \begin_inset space \textvisiblespace{}
32401 \begin_inset space \textvisiblespace{}
32405 \begin_inset space \textvisiblespace{}
32409 \begin_inset space \textvisiblespace{}
32413 \begin_inset space \textvisiblespace{}
32421 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
32424 \begin_layout Plain Layout
32425 \begin_inset Formula $\raisebox{4.5mm}{}\ce{CO2 + C <=> 2CO}\raisebox{-2mm}{}$
32435 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
32438 \begin_layout Plain Layout
32442 \begin_inset space \textvisiblespace{}
32446 \begin_inset space \textvisiblespace{}
32450 \begin_inset space \textvisiblespace{}
32454 \begin_inset space \textvisiblespace{}
32462 \begin_inset space \textvisiblespace{}
32470 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
32473 \begin_layout Plain Layout
32474 \begin_inset Formula $\raisebox{5mm}{}\ce{CO2 + C ->[\alpha][\beta] 2CO}\raisebox{-4mm}{}$
32490 \begin_layout Standard
32491 \begin_inset Note Greyedout
32494 \begin_layout Plain Layout
32500 Inserting a formula to a
32506 box will lead to LaTeX errors due to a LyX bug.
32512 \begin_layout Plain Layout
32513 \begin_inset CommandInset href
32515 name "LyX-bug #8566"
32516 target "http://www.lyx.org/trac/ticket/8566"
32527 In this case TeX code has to be used like for
32541 \begin_layout Plain Layout
32562 \begin_layout Standard
32563 \begin_inset Note Greyedout
32566 \begin_layout Plain Layout
32572 It is not possible in LyX to use the character ^ to get an up-arrow as
32578 One instead uses a negative thin space followed by the command
32585 \begin_inset Formula $\ce{Fe + 2H+ -> Fe^{2+} + H2\negthinspace\uparrow}$
32596 \begin_layout Standard
32603 the command for equation
32604 \begin_inset space ~
32608 \begin_inset CommandInset ref
32610 reference "eq:chem-reaction"
32615 \begin_inset Newline newline
32623 \begin_inset space \textvisiblespace{}
32627 \begin_inset space \textvisiblespace{}
32631 \begin_inset space \textvisiblespace{}
32635 \begin_inset space \textvisiblespace{}
32639 \begin_inset space \textvisiblespace{}
32643 \begin_inset space \textvisiblespace{}
32649 \begin_layout Standard
32650 To create multiline chemical equations first a multiline formula is created
32652 \begin_inset CommandInset ref
32654 reference "sec:Multiline-Formulas"
32659 Afterwards the command
32665 is used in every small blue box of the formula.
32667 \begin_inset CommandInset ref
32669 reference "eq:TEOS-reaction-1"
32674 \begin_inset CommandInset ref
32676 reference "eq:TEOS-reaction-2"
32680 are an example of a multi-stage chemical reaction where every equation
32681 has its own number.
32682 \begin_inset Formula
32684 \ce{TEOS + 4O} & \ce{->} & \ce{Si(OH)4 + 4C2H4O}\label{eq:TEOS-reaction-1}\\
32685 \ce{Si(OH)4} & \ce{->} & \ce{SiO2 + 2H2O}\label{eq:TEOS-reaction-2}
32693 \begin_layout Standard
32704 package provides the command
32711 \begin_inset Index idx
32714 \begin_layout Plain Layout
32722 that has to be used for special cases.
32723 For more information about
32729 and more examples have a look at the documentation of
32734 \begin_inset CommandInset citation
32743 \begin_layout Section
32747 \begin_layout Standard
32748 LyX supports two types of commutative diagrams:
32756 that are explained in the following.
32759 \begin_layout Subsection
32761 \begin_inset Index idx
32764 \begin_layout Plain Layout
32773 \begin_layout Standard
32774 Diagrams of this type visualize relations by vertical and horizontal lines
32776 \begin_inset Formula
32778 \begin{CD}A@>>>B@>>>C\\
32789 \begin_layout Standard
32790 To get them, the command
32795 \begin_inset Index idx
32798 \begin_layout Plain Layout
32808 is inserted to a formula.
32809 A blue box appears with two dashed lines where further commands can be
32814 arg "newline-insert newline"
32817 a new line is created.
32818 Horizontal relations are inserted in odd, vertical in even formula lines.
32821 \begin_layout Standard
32822 To create the relations there are the following commands:
32825 \begin_layout Itemize
32830 creates a left arrow,
32841 \begin_layout Itemize
32846 creates an up arrow,
32854 a vertical equal sign
32857 \begin_layout Itemize
32863 is a placeholder for non-existent relations
32866 \begin_layout Standard
32867 All arrows can be labeled as follows:
32870 \begin_layout Itemize
32871 If text inserted between the first and second < or >, resp., it is placed
32873 When it is inserted between the second and third one, it appears under
32877 \begin_layout Itemize
32878 When text for vertical arrows is inserted between the first and second A
32879 or V, resp., it is placed left beside the arrow.
32880 When it is inserted between the second and third one, it appears right
32882 If the text contains an A or V, these letters must be set into a TeX-brace.
32885 \begin_layout Standard
32886 As example a diagram with all possible relations:
32889 \begin_layout Standard
32890 \begin_inset Formula
32892 \begin{CD}A@>j>>B@>>k>C@=F\\
32903 \begin_layout Standard
32904 The command for this is:
32905 \begin_inset Newline newline
32913 \begin_inset space \textvisiblespace{}
32916 A@>j>>B@>>k>C@=F Ctrl+Return
32917 \begin_inset Newline newline
32921 \begin_inset Phantom HPhantom
32924 \begin_layout Plain Layout
32930 \begin_inset space \textvisiblespace{}
32943 \begin_inset Formula $\to$
32949 \begin_inset Newline newline
32953 \begin_inset Phantom HPhantom
32956 \begin_layout Plain Layout
32962 \begin_inset space \textvisiblespace{}
32973 \begin_layout Subsection
32975 \begin_inset Index idx
32978 \begin_layout Plain Layout
32979 Diagrams ! xymatrix
32987 \begin_layout Standard
32988 To be able to use xymatrices, the LaTeX-package
32993 A xymatrix is created by inserting the command
33000 Then you are able to add new matrix columns and rows like for normal matrices,
33002 \begin_inset CommandInset ref
33004 reference "sec:Matrices"
33011 \begin_layout Standard
33012 In contrary to amscd diagrams, xymatrices supports diagonal and curved arrows,
33014 All possibilities to create commutative diagrams and decorations are explained
33019 that you find in the menu
33021 Help\SpecialChar \menuseparator
33023 \begin_inset space ~
33031 \begin_layout Subsection
33037 \begin_inset Index idx
33040 \begin_layout Plain Layout
33049 \begin_layout Standard
33054 -diagrams, the LaTeX-package
33063 -diagram is created by inserting the command
33070 Then you are able to add new matrix columns and rows like for normal matrices,
33072 \begin_inset CommandInset ref
33074 reference "sec:Matrices"
33081 \begin_layout Standard
33082 Examples how to create
33086 diagrams in LyX is given in the
33088 Feynman-diagram manual
33090 that you find in the menu
33092 Help\SpecialChar \menuseparator
33094 \begin_inset space ~
33102 \begin_layout Section
33103 User-defined Commands
33104 \begin_inset Index idx
33107 \begin_layout Plain Layout
33108 User-defined commands
33116 \begin_layout Standard
33117 \begin_inset Note Greyedout
33120 \begin_layout Plain Layout
33125 The names of user-defined commands and macros may only consist of Latin
33134 \begin_layout Subsection
33138 \begin_inset CommandInset label
33140 name "sub:The-Command-newcommand"
33145 \begin_inset Index idx
33148 \begin_layout Plain Layout
33149 User-defined commands !
33157 \begin_inset Index idx
33160 \begin_layout Plain Layout
33171 \begin_layout Standard
33172 Many LaTeX-commands are too long to be used frequently.
33173 But it is possible to define with the command
33179 new shorter commands.
33182 \begin_layout Standard
33183 The command scheme of
33192 \begin_layout Standard
33197 newcommand{new command name}[number of arguments][optional
33202 \begin_inset Newline newline
33206 \begin_inset Phantom HPhantom
33209 \begin_layout Plain Layout
33219 {command definition}
33222 \begin_layout Standard
33223 \begin_inset Note Greyedout
33226 \begin_layout Plain Layout
33231 Assure that the name of the new command is not already used in your document
33232 or by LaTeX-packages that you use.
33233 When you for example define the command
33245 , you get an error message because
33251 is already defined as command for
33252 \begin_inset Quotes eld
33256 \begin_inset Formula $\le$
33260 \begin_inset Quotes erd
33271 \begin_layout Standard
33272 The number of arguments is an integer in the range 0
33273 \begin_inset space \thinspace{}
33277 \begin_inset space \thinspace{}
33280 9 and specifies how many arguments the new command should have.
33281 With the optional value a value for an optional argument can be predefined.
33282 When this is done, the
33290 rgument of the new command is automatically an optional one.
33293 \begin_layout Standard
33294 Here are some examples:
33297 \begin_layout Itemize
33298 To define the command
33310 , the LaTeX-preamble line is:
33311 \begin_inset VSpace medskip
33315 \begin_inset Newline newline
33329 \begin_layout Itemize
33330 To define the command
33342 , the argument (that should be underlined) must be taken into account.
33343 For this the preamble line is:
33344 \begin_inset VSpace medskip
33348 \begin_inset Newline newline
33362 \begin_inset VSpace medskip
33366 \begin_inset Newline newline
33373 acts as argument placeholder, the
33377 behind it denotes that it is the placeholder for the first argument.
33380 \begin_layout Itemize
33388 \begin_inset space \thinspace{}
33392 \begin_inset space \space{}
33402 \begin_inset VSpace medskip
33406 \begin_inset Newline newline
33417 framebox#1#2{$#3$}}
33420 \begin_inset VSpace medskip
33424 \begin_inset Newline newline
33427 The two Dollar signs creates the extra formula needed for
33434 \begin_inset CommandInset ref
33436 reference "sub:Boxes-with-Frame"
33443 \begin_layout Itemize
33444 To create a new command for
33450 where the color for the box need not be specified, the argument for the
33451 color is defined optional:
33452 \begin_inset VSpace medskip
33456 \begin_inset Newline newline
33467 fcolorbox{#2}{#1}{$#3$}}
33470 \begin_inset VSpace medskip
33474 \begin_inset Newline newline
33477 When the color is not specified when using
33483 , the predefined color
33490 \begin_layout Standard
33491 A test of the new defined commands:
33494 \begin_layout Standard
33496 \begin_inset Tabular
33497 <lyxtabular version="3" rows="6" columns="2">
33498 <features rotate="0" tabularvalignment="middle">
33499 <column alignment="center" valignment="top">
33500 <column alignment="center" valignment="top">
33502 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
33505 \begin_layout Plain Layout
33511 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
33514 \begin_layout Plain Layout
33516 \begin_inset Note Note
33519 \begin_layout Plain Layout
33526 is only used as spacer.
33538 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
33541 \begin_layout Plain Layout
33545 \begin_inset space \textvisiblespace{}
33553 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
33556 \begin_layout Plain Layout
33557 \begin_inset Formula $A\gr B$
33567 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
33570 \begin_layout Plain Layout
33578 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
33581 \begin_layout Plain Layout
33582 \begin_inset Formula $\raisebox{4.5mm}{}\us{ABcd}\raisebox{-2mm}{}$
33592 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
33595 \begin_layout Plain Layout
33599 \begin_inset Formula $\to$
33605 \begin_inset Formula $\to$
33613 \begin_inset space \textvisiblespace{}
33621 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
33624 \begin_layout Plain Layout
33625 \begin_inset Formula $\raisebox{6mm}{}\fb{[2cm]}{}{\int A=B}\raisebox{-4mm}{}$
33635 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
33638 \begin_layout Plain Layout
33642 \begin_inset Formula $\to$
33650 \begin_inset space \textvisiblespace{}
33658 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
33661 \begin_layout Plain Layout
33662 \begin_inset Formula $\raisebox{6mm}{}\cb{red}{\int A=B}\raisebox{-4mm}{}$
33672 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
33675 \begin_layout Plain Layout
33681 \begin_inset Formula $\to$
33689 \begin_inset space \textvisiblespace{}
33697 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
33700 \begin_layout Plain Layout
33701 \begin_inset Formula $\raisebox{6mm}{}\cb[green]{red}{\int A=B}\raisebox{-4mm}{}$
33717 \begin_layout Subsection
33719 \begin_inset Index idx
33722 \begin_layout Plain Layout
33723 User-defined commands! Math macros
33729 \begin_inset Index idx
33732 \begin_layout Plain Layout
33741 \begin_layout Standard
33742 User-defined commands are especially convenient for complex expressions.
33743 When you are for example dealing with a document that has quadratic equations,
33744 the same solution type occurs several times.
33745 The general form of a quadratic equation is
33746 \begin_inset Formula
33748 0=\lambda^{2}+p\lambda+q
33753 The general form of the solution is
33754 \begin_inset Formula
33756 \lambda_{1,2}=-\frac{p}{2}\pm\sqrt{\frac{p²}{4}-q}
33764 \begin_layout Standard
33765 To define a command for the solution formula where only the three parameters
33767 \begin_inset Formula $\lambda$
33771 \begin_inset Formula $p$
33775 \begin_inset Formula $q$
33778 need to be specified and the index of
33779 \begin_inset Formula $\lambda$
33782 can be given optionally, the LaTeX-preamble line is
33783 \begin_inset Newline newline
33799 \begin_inset Newline newline
33803 \begin_inset Phantom HPhantom
33806 \begin_layout Plain Layout
33820 frac{#3^{2}}{4}-#4}}
33823 \begin_layout Standard
33824 To create with this the solution formula, the command
33825 \begin_inset Newline newline
33835 \begin_inset Formula $\to$
33841 \begin_inset Formula $\to$
33848 is inserted to a formula
33853 \begin_layout Standard
33854 The definition of the new command is unintuitive because one has to know
33855 the schemes of all used LaTeX commands, e.
33856 \begin_inset space \thinspace{}
33860 \begin_inset space \space{}
33863 that a fraction is inserted in LaTeX as
33867 frac{numerator}{denominator}
33870 Furthermore one can easily forget a brace in the definition and cannot
33871 see in LyX what the new command is doing.
33872 To avoid these problems LyX offers the possibility to use math macros instead
33882 \begin_layout Standard
33883 A math macro is created by using the menu
33885 Insert\SpecialChar \menuseparator
33886 Math\SpecialChar \menuseparator
33889 or the toolbar button
33892 arg "math-macro newmacroname_newcommand"
33896 The math macro toolbar appears together with the following box where the
33898 \begin_inset Newline newline
33902 \begin_inset space \hspace*{\fill}
33906 \begin_inset Graphics
33907 filename clipart/macrobox.png
33912 \begin_inset space \hspace*{\fill}
33916 \begin_inset Newline newline
33920 \begin_inset FormulaMacro
33921 \newcommand{\qG}[4][1,\,2]{#2_{#1}=-\frac{#3}{2}\pm\sqrt{\frac{#3^{2}}{4}-#4}}
33926 newmacroname is the default name of the macro that should be changed to
33927 something sensible.
33928 The wanted formula is inserted in the first blue box.
33929 An argument placeholder is inserted with the command
33936 \begin_inset space \thinspace{}
33940 \begin_inset space \space{}
33949 or by using the macro toolbar button
33952 arg "math-macro-add-param"
33956 Argument placeholders are displayed red.
33958 \begin_inset space ~
33961 arguments are possible.
33962 Optional arguments are created with the toolbar button
33965 arg "math-macro-add-optional-param"
33969 The first non-optional argument can be transformed to an optional one with
33973 arg "math-macro-make-optional"
33977 In the second blue box the appearance of the macro in LyX can be defined.
33978 Normally you want to see it as it is defined, so the box is kept empty.
33979 But when you have created a macro that needs lot of space on the screen,
33980 you can insert in the box for example
33981 \begin_inset Newline newline
34011 \begin_inset Newline newline
34016 For the macro only the arguments with the macro name in front of them will
34017 then be displayed in LyX, leading to a better overview.
34018 The formula appears in the output as defined in the first box.
34019 \begin_inset Newline newline
34022 The appearance of macros in formulas can furthermore be changed for single
34023 macros by setting the cursor in the macro and using the menu
34025 View\SpecialChar \menuseparator
34027 \begin_inset space ~
34031 \begin_inset space ~
34039 \begin_layout Standard
34040 To use a macro, the macro name is inserted as command to a formula, in our
34048 Our macro looks in LyX like this:
34049 \begin_inset Newline newline
34053 \begin_inset space \hspace*{\fill}
34057 \begin_inset Graphics
34058 filename clipart/macrouse.png
34063 \begin_inset space \hspace*{\fill}
34067 \begin_inset Newline newline
34070 Here is our macro example with the arguments
34071 \begin_inset Formula $x$
34075 \begin_inset Formula $\ln(x)$
34079 \begin_inset Formula $B$
34085 \begin_layout Standard
34086 \begin_inset Formula
34096 \begin_layout Standard
34097 LyX offers in the menu
34099 Tools\SpecialChar \menuseparator
34100 Preferences\SpecialChar \menuseparator
34101 Editing\SpecialChar \menuseparator
34104 different styles to edit macros.
34105 To find the style that suits you the most, choose a style and set the cursor
34106 in a macro formula to see the difference.
34109 \begin_layout Standard
34110 A math macro is transformed internally to a
34116 command when exporting the document.
34123 command is not placed in the LaTeX-preamble, therefore macros can only
34124 be used in formulas that are in the document below the macro definition
34128 \begin_layout Standard
34129 Math macros can also be directly created from a
34136 When writing for example the command
34139 \begin_inset Newline newline
34148 xleftarrow[#2]{#1}}
34149 \begin_inset Newline newline
34154 in LyX as normal text, highlighting it completely and using then the shortcut
34159 , the command will be transformed to a math macro.
34160 Using this method you need to be careful that the
34166 command is typed correctly, otherwise you get a faulty macro leading to
34170 \begin_layout Standard
34171 Math macros currently have the problem that further formulas in macro definition
34172 s are handled wrongly.
34173 Therefore the example
34180 \begin_inset CommandInset ref
34182 reference "sub:The-Command-newcommand"
34186 cannot be created as macro.
34189 \begin_layout Standard
34190 When the cursor is in a macro definition box, you will see the macro toolbar
34194 \begin_layout Standard
34195 \begin_inset VSpace defskip
34201 \begin_layout Standard
34202 \begin_inset Graphics
34203 filename clipart/MacroToolbar.png
34208 \begin_inset Index idx
34211 \begin_layout Plain Layout
34220 \begin_layout Standard
34221 \begin_inset VSpace defskip
34227 \begin_layout Standard
34228 The macro toolbar contains from left to right the following buttons:
34231 \begin_layout Standard
34232 \begin_inset VSpace defskip
34238 \begin_layout Standard
34239 \begin_inset Tabular
34240 <lyxtabular version="3" rows="9" columns="2">
34241 <features rotate="0" islongtable="true" longtabularalignment="center">
34242 <column alignment="left" valignment="top">
34243 <column alignment="left" valignment="top" width="85col%">
34244 <row interlinespace="2.5mm">
34245 <cell alignment="center" valignment="top" usebox="none">
34248 \begin_layout Plain Layout
34251 arg "math-macro-remove-param"
34259 <cell alignment="center" valignment="top" usebox="none">
34262 \begin_layout Plain Layout
34265 Edit\SpecialChar \menuseparator
34266 Math\SpecialChar \menuseparator
34268 \begin_inset space ~
34271 Definition\SpecialChar \menuseparator
34272 Remove Last Argument
34278 <row interlinespace="2.5mm">
34279 <cell alignment="center" valignment="top" usebox="none">
34282 \begin_layout Plain Layout
34285 arg "math-macro-add-param"
34293 <cell alignment="center" valignment="top" usebox="none">
34296 \begin_layout Plain Layout
34299 Edit\SpecialChar \menuseparator
34300 Math\SpecialChar \menuseparator
34302 \begin_inset space ~
34305 Definition\SpecialChar \menuseparator
34312 <row interlinespace="2.5mm">
34313 <cell alignment="center" valignment="top" usebox="none">
34316 \begin_layout Plain Layout
34319 arg "math-macro-make-optional"
34327 <cell alignment="center" valignment="top" usebox="none">
34330 \begin_layout Plain Layout
34333 Edit\SpecialChar \menuseparator
34334 Math\SpecialChar \menuseparator
34336 \begin_inset space ~
34339 Definition\SpecialChar \menuseparator
34340 Transform First Non-Optional to
34341 \begin_inset Newline newline
34345 \begin_inset Phantom HPhantom
34348 \begin_layout Plain Layout
34351 Edit\SpecialChar \menuseparator
34352 Math\SpecialChar \menuseparator
34354 \begin_inset space ~
34357 Definition\SpecialChar \menuseparator
34369 <row interlinespace="2.5mm">
34370 <cell alignment="center" valignment="top" usebox="none">
34373 \begin_layout Plain Layout
34376 arg "math-macro-make-nonoptional"
34384 <cell alignment="center" valignment="top" usebox="none">
34387 \begin_layout Plain Layout
34390 Edit\SpecialChar \menuseparator
34391 Math\SpecialChar \menuseparator
34393 \begin_inset space ~
34396 Definition\SpecialChar \menuseparator
34397 Transform Last Optional to
34398 \begin_inset Newline newline
34402 \begin_inset Phantom HPhantom
34405 \begin_layout Plain Layout
34408 Edit\SpecialChar \menuseparator
34409 Math\SpecialChar \menuseparator
34411 \begin_inset space ~
34414 Definition\SpecialChar \menuseparator
34420 Non-Optional Argument
34426 <row interlinespace="2.5mm">
34427 <cell alignment="center" valignment="top" usebox="none">
34430 \begin_layout Plain Layout
34433 arg "math-macro-remove-optional-param"
34441 <cell alignment="center" valignment="top" usebox="none">
34444 \begin_layout Plain Layout
34447 Edit\SpecialChar \menuseparator
34448 Math\SpecialChar \menuseparator
34450 \begin_inset space ~
34453 Definition\SpecialChar \menuseparator
34454 Remove Optional Argument
34460 <row interlinespace="2.5mm">
34461 <cell alignment="center" valignment="top" usebox="none">
34464 \begin_layout Plain Layout
34467 arg "math-macro-add-optional-param"
34475 <cell alignment="center" valignment="top" usebox="none">
34478 \begin_layout Plain Layout
34481 Edit\SpecialChar \menuseparator
34482 Math\SpecialChar \menuseparator
34484 \begin_inset space ~
34487 Definition\SpecialChar \menuseparator
34488 Insert Optional Argument
34494 <row interlinespace="2.5mm">
34495 <cell alignment="center" valignment="top" usebox="none">
34498 \begin_layout Plain Layout
34501 arg "math-macro-remove-greedy-param"
34509 <cell alignment="center" valignment="top" usebox="none">
34512 \begin_layout Plain Layout
34515 Edit\SpecialChar \menuseparator
34516 Math\SpecialChar \menuseparator
34518 \begin_inset space ~
34521 Definition\SpecialChar \menuseparator
34522 Remove Last Argument
34523 \begin_inset Newline newline
34527 \begin_inset Phantom HPhantom
34530 \begin_layout Plain Layout
34533 Edit\SpecialChar \menuseparator
34534 Math\SpecialChar \menuseparator
34536 \begin_inset space ~
34539 Definition\SpecialChar \menuseparator
34545 Spitting Out To The Right
34551 <row interlinespace="2.5mm">
34552 <cell alignment="center" valignment="top" usebox="none">
34555 \begin_layout Plain Layout
34558 arg "math-macro-append-greedy-param"
34566 <cell alignment="center" valignment="top" usebox="none">
34569 \begin_layout Plain Layout
34572 Edit\SpecialChar \menuseparator
34573 Math\SpecialChar \menuseparator
34575 \begin_inset space ~
34578 Definition\SpecialChar \menuseparator
34580 \begin_inset Newline newline
34584 \begin_inset Phantom HPhantom
34587 \begin_layout Plain Layout
34590 Edit\SpecialChar \menuseparator
34591 Math\SpecialChar \menuseparator
34593 \begin_inset space ~
34596 Definition\SpecialChar \menuseparator
34602 Eating From The Right
34608 <row interlinespace="2.5mm">
34609 <cell alignment="center" valignment="top" usebox="none">
34612 \begin_layout Plain Layout
34615 arg "math-macro-add-greedy-optional-param"
34623 <cell alignment="center" valignment="top" usebox="none">
34626 \begin_layout Plain Layout
34629 Edit\SpecialChar \menuseparator
34630 Math\SpecialChar \menuseparator
34632 \begin_inset space ~
34635 Definition\SpecialChar \menuseparator
34636 Append Optional Argument
34637 \begin_inset Newline newline
34641 \begin_inset Phantom HPhantom
34644 \begin_layout Plain Layout
34647 Edit\SpecialChar \menuseparator
34648 Math\SpecialChar \menuseparator
34650 \begin_inset space ~
34653 Definition\SpecialChar \menuseparator
34659 Eating From The Right
34672 \begin_layout Section
34673 Computer Algebra Systems
34676 \begin_layout Standard
34677 LyX offers the exchange between mathematical expressions written in LyX's
34678 math editor and external applications or user defined scripts.
34679 Currently supported applications are
34696 Note that the set of supported mathematical constructs is limited only
34697 to very simple cases.
34700 \begin_layout Subsection
34704 \begin_layout Standard
34705 Write some expression in a formula, go to the
34707 Edit\SpecialChar \menuseparator
34708 Math\SpecialChar \menuseparator
34709 Use Computer Algebra System
34711 menu and choose the application you have installed on the computer.
34712 After that the result of computation should show on the right side of the
34713 expression together with the
34714 \begin_inset Quotes eld
34718 \begin_inset Quotes erd
34724 \begin_layout Standard
34725 Here are few simple examples (with results from
34729 ) to show what kind of computations can be performed:
34732 \begin_layout Itemize
34733 \begin_inset Formula $\frac{37}{3}*2-\sum_{i=1}^{3}i^{i}=-\frac{22}{3}$
34739 \begin_layout Itemize
34740 \begin_inset Formula $\frac{37.0}{3}=12.33333333333333$
34746 \begin_layout Itemize
34747 \begin_inset Formula $\int_{1}^{2}\sin(x)dx=\cos1-\cos2$
34753 \begin_layout Itemize
34754 \begin_inset Formula $\det\left[\begin{array}{ccc}
34758 \end{array}\right]=-56$
34764 \begin_layout Itemize
34765 \begin_inset Formula $\lim_{x\rightarrow0}\left(\frac{\sin(x)}{x}\right)=1$
34771 \begin_layout Subsection
34775 \begin_layout Standard
34776 Currently there is no keyboard shortcut for calling the algebra applications.
34777 One can easily bind a shortcut to the
34781 LyX function (see the
34789 \begin_inset space \thinspace{}
34793 \begin_inset space \space{}
34800 key inside the math editor.
34805 one would use this shortcut definition command:
34808 \begin_layout Standard
34811 command-alternatives break-paragraph;math-extern maxima
34814 \begin_layout Section
34816 \begin_inset Index idx
34819 \begin_layout Plain Layout
34828 \begin_layout Subsection
34830 \begin_inset Index idx
34833 \begin_layout Plain Layout
34842 \begin_layout Standard
34843 Negative numbers often look ugly in formulas because the minus sign before
34844 the number is set with the same length as the minus operator sign.
34845 When writing the negative number in normal text, the minus sign appears
34849 \begin_layout Standard
34850 Thus, the problem disappears when converting the minus sign to mathematical
34854 \begin_layout Standard
34855 An example to visualize the problem:
34858 \begin_layout Standard
34860 \begin_inset Tabular
34861 <lyxtabular version="3" rows="3" columns="2">
34862 <features rotate="0" tabularvalignment="middle">
34863 <column alignment="right" valignment="top">
34864 <column alignment="left" valignment="top">
34866 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
34869 \begin_layout Plain Layout
34875 <cell alignment="center" valignment="top" topline="true" rightline="true" usebox="none">
34878 \begin_layout Plain Layout
34886 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
34889 \begin_layout Plain Layout
34895 <cell alignment="center" valignment="top" topline="true" bottomline="true" rightline="true" usebox="none">
34898 \begin_layout Plain Layout
34899 \begin_inset Formula $x=-2$
34909 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
34912 \begin_layout Plain Layout
34918 <cell alignment="center" valignment="top" topline="true" bottomline="true" rightline="true" usebox="none">
34921 \begin_layout Plain Layout
34922 \begin_inset Formula $x=\textrm{-}2$
34938 \begin_layout Subsection
34939 Comma as decimal Separator
34940 \begin_inset Index idx
34943 \begin_layout Plain Layout
34952 \begin_layout Standard
34953 In LaTeX a comma inside a formula is used, according to the English convention,
34954 as number group separator.
34955 So there will be space added behind all commas in formulas.
34958 \begin_layout Standard
34959 To avoid this, the comma is highlighted and changed to mathematical text
34969 \begin_layout Standard
34970 To use all formula commas in the document as decimal separator, the file
34979 \begin_layout Plain Layout
34984 is part of the LaTeX-package
34989 \begin_inset Index idx
34992 \begin_layout Plain Layout
34997 \begin_layout Plain Layout
35017 \begin_inset Index idx
35020 \begin_layout Plain Layout
35026 is loaded with the LaTeX-preamble line
35029 \begin_layout Standard
35037 \begin_layout Subsection
35039 \begin_inset CommandInset label
35041 name "sub:Physical-Vectors"
35046 \begin_inset Index idx
35049 \begin_layout Plain Layout
35058 \begin_layout Standard
35059 Predefined vectors are offered by the LaTeX-package
35064 \begin_inset Index idx
35067 \begin_layout Plain Layout
35073 that is loaded with the LaTeX-preamble line
35076 \begin_layout Standard
35084 \begin_layout Standard
35088 \begin_layout Plain Layout
35098 \begin_inset Note Note
35101 \begin_layout Plain Layout
35102 The following table will only be displayed when the LaTeX-package
35114 \begin_layout Standard
35115 The following commands are defined:
35118 \begin_layout Standard
35120 \begin_inset Tabular
35121 <lyxtabular version="3" rows="4" columns="2">
35122 <features rotate="0" tabularvalignment="middle">
35123 <column alignment="center" valignment="top">
35124 <column alignment="center" valignment="top">
35126 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
35129 \begin_layout Plain Layout
35135 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
35138 \begin_layout Plain Layout
35146 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
35149 \begin_layout Plain Layout
35159 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
35162 \begin_layout Plain Layout
35163 \begin_inset Formula $\Bra{\psi}$
35173 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
35176 \begin_layout Plain Layout
35186 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
35189 \begin_layout Plain Layout
35190 \begin_inset Formula $\Ket{\psi}$
35200 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
35203 \begin_layout Plain Layout
35215 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
35218 \begin_layout Plain Layout
35219 \begin_inset Formula $\Braket{\psi|\phi}$
35235 \begin_layout Standard
35242 assures that all vertical bars are set in the size of the surrounding brackets:
35243 \begin_inset Formula
35245 \Braket{\phi|J=\frac{3}{2}\,,\, M_{J}}
35254 \begin_layout Plain Layout
35264 \begin_inset Note Note
35267 \begin_layout Plain Layout
35268 The following will be displayed when the LaTeX-package
35280 \begin_layout Standard
35281 You need to install the LaTeX-package
35285 to see the rest of this subsection in the output.
35288 \begin_layout Standard
35292 \begin_layout Plain Layout
35304 \begin_layout Standard
35311 can also be achieved using the command
35317 , that is described in
35318 \begin_inset CommandInset ref
35320 reference "sub:Automatic-Bracket-Size"
35327 \begin_layout Subsection
35328 Self-defined Fractions
35329 \begin_inset CommandInset label
35331 name "sub:Self-defined-Fractions"
35336 \begin_inset Index idx
35339 \begin_layout Plain Layout
35340 Fractions ! self-defined
35348 \begin_layout Standard
35349 To define custom commands for fractions, the command
35356 \begin_inset Index idx
35359 \begin_layout Plain Layout
35366 \begin_layout Plain Layout
35380 is used in the following scheme:
35383 \begin_layout Standard
35396 bracket}{fraction bar thickness}{style}
35397 \begin_inset Newline newline
35401 \begin_inset Phantom HPhantom
35404 \begin_layout Plain Layout
35414 {numerator}{denominator}
35417 \begin_layout Standard
35418 The style is a number in the range of 0
35419 \begin_inset space \thinspace{}
35423 \begin_inset space \thinspace{}
35429 \begin_layout Standard
35431 \begin_inset Tabular
35432 <lyxtabular version="3" rows="5" columns="2">
35433 <features rotate="0" tabularvalignment="middle">
35434 <column alignment="center" valignment="top">
35435 <column alignment="center" valignment="top">
35437 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
35440 \begin_layout Plain Layout
35446 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
35449 \begin_layout Plain Layout
35457 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
35460 \begin_layout Plain Layout
35466 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
35469 \begin_layout Plain Layout
35470 display style formula
35477 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
35480 \begin_layout Plain Layout
35486 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
35489 \begin_layout Plain Layout
35497 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
35500 \begin_layout Plain Layout
35506 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
35509 \begin_layout Plain Layout
35517 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
35520 \begin_layout Plain Layout
35526 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
35529 \begin_layout Plain Layout
35543 \begin_layout Standard
35544 When no style is given, the size is adjusted to the surrounding environment
35545 like for the command
35554 \begin_layout Standard
35555 When no fraction bar thickness is given, the predefined value of 0.4
35556 \begin_inset space \thinspace{}
35562 \begin_layout Standard
35563 \begin_inset VSpace medskip
35566 For example, the commands
35579 \begin_inset CommandInset ref
35581 reference "sub:Fractions"
35585 are defined with the commands
35588 \begin_layout Standard
35597 genfrac{}{}{}{0}{#1}{#2}}
35600 \begin_layout Standard
35604 \begin_layout Standard
35613 genfrac{(}{)}{0pt}{1}{#1}{#2}}
35616 \begin_layout Standard
35617 \begin_inset VSpace medskip
35620 To define a fraction where the fraction bar thickness can be given as optional
35621 argument, the following line is inserted to the LaTeX-preamble:
35624 \begin_layout Standard
35633 genfrac{}{}{#1}{}{#2}{#3}}
35636 \begin_layout Standard
35638 \begin_inset Formula
35640 \text{Command} & & \mathrm{\backslash fracS[1mm]\backslash\{A\to\backslash\{B} & & \mathrm{\backslash fracS[5mm]\backslash\{A\to\backslash\{B}\\
35641 \text{Result} & & \fracS[1mm]{A}{B} & & \fracS[5mm]{A}{B}
35646 As one can see, the distance of the numerator and the denominator to the
35647 fraction bar is round about three times the bar thickness.
35650 \begin_layout Subsection
35652 \begin_inset Index idx
35655 \begin_layout Plain Layout
35664 \begin_layout Standard
35665 There are four ways to cancel formulas or parts of formulas:
35668 \begin_layout Standard
35672 \begin_layout Plain Layout
35682 \begin_inset Note Note
35685 \begin_layout Plain Layout
35686 The following table will only be displayed when the LaTeX-package
35698 \begin_layout Standard
35700 \begin_inset Tabular
35701 <lyxtabular version="3" rows="5" columns="2">
35702 <features rotate="0" tabularvalignment="middle">
35703 <column alignment="center" valignment="top">
35704 <column alignment="center" valignment="top">
35706 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
35709 \begin_layout Plain Layout
35715 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
35718 \begin_layout Plain Layout
35720 \begin_inset Note Note
35723 \begin_layout Plain Layout
35730 are used here as spacer.
35742 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
35745 \begin_layout Plain Layout
35749 \begin_inset space \textvisiblespace{}
35755 \begin_inset space \textvisiblespace{}
35763 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
35766 \begin_layout Plain Layout
35767 \begin_inset Formula $\raisebox{4.5mm}{}\cancel{\int A=B}\raisebox{-2.5mm}{}$
35777 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
35780 \begin_layout Plain Layout
35784 \begin_inset space \textvisiblespace{}
35790 \begin_inset space \textvisiblespace{}
35798 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
35801 \begin_layout Plain Layout
35802 \begin_inset Formula $\raisebox{4.5mm}{}\bcancel{\int A=B}\raisebox{-2.5mm}{}$
35812 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
35815 \begin_layout Plain Layout
35819 \begin_inset space \textvisiblespace{}
35825 \begin_inset space \textvisiblespace{}
35833 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
35836 \begin_layout Plain Layout
35837 \begin_inset Formula $\raisebox{4.5mm}{}\xcancel{\int A=B}\raisebox{-2.5mm}{}$
35847 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
35850 \begin_layout Plain Layout
35854 \begin_inset space \textvisiblespace{}
35860 \begin_inset space \textvisiblespace{}
35864 \begin_inset Formula $\to$
35872 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
35875 \begin_layout Plain Layout
35876 \begin_inset Formula $\raisebox{7mm}{}\cancelto{1}{\int A=B}\raisebox{-2.5mm}{}\hspace{3mm}$
35892 \begin_layout Standard
35899 is especially suitable to visualize the reduction of fractions within formulas:
35900 \begin_inset Formula
35902 \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}}}
35910 \begin_layout Standard
35911 To change the size of
35918 \begin_inset Quotes eld
35922 \begin_inset Quotes erd
35925 value one can add the LaTeX-preamble line
35928 \begin_layout Standard
35933 PassOptionsToPackage{option}{cancel}
35936 \begin_layout Standard
35945 which leads to the same size as for the canceled value, or
35949 which makes is it a bit smaller than normal.
35952 \begin_layout Standard
35953 To color the cancellation bar one adds this command as TeX code:
35956 \begin_layout Standard
35968 \begin_layout Standard
35973 can be replaced by a color of your choice.
35976 \begin_layout Standard
35980 \begin_layout Plain Layout
35996 \begin_layout Standard
35997 \begin_inset Formula
35999 \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}}}
36007 \begin_layout Standard
36011 \begin_layout Plain Layout
36025 \begin_inset Note Note
36028 \begin_layout Plain Layout
36037 \begin_layout Standard
36038 For further customizations, see the documentation of the package
36043 \begin_inset CommandInset citation
36050 \begin_inset Index idx
36053 \begin_layout Plain Layout
36062 \begin_layout Standard
36066 \begin_layout Plain Layout
36076 \begin_inset Note Note
36079 \begin_layout Plain Layout
36080 The following will be displayed when the LaTeX-package
36092 \begin_layout Standard
36093 You need to install the LaTeX-package
36097 to see the rest of this subsection in the output.
36100 \begin_layout Standard
36104 \begin_layout Plain Layout
36116 \begin_layout Subsection
36117 Formulas in Section Headings
36118 \begin_inset CommandInset label
36120 name "sub:Formulas-in-Section"
36125 \begin_inset Index idx
36128 \begin_layout Plain Layout
36129 Formula ! in section headings
36137 \begin_layout Standard
36138 When formulas are used in section headings, the following has to be taken
36142 \begin_layout Standard
36143 \begin_inset Note Greyedout
36146 \begin_layout Plain Layout
36152 \begin_inset Index idx
36155 \begin_layout Plain Layout
36156 Packages ! hyperref
36161 support is enabled in the document settings dialog under
36164 \begin_inset space ~
36169 , PDF-bookmarks are created for every section heading in the table of contents.
36170 If a section heading contains formulas, they are incorrectly displayed
36171 in the bookmark text, because formulas in bookmarks infringe the PDF convention
36180 \begin_layout Standard
36181 Both problems can be solved by inserting at the end of the section heading
36182 a short title with the menu
36184 Insert\SpecialChar \menuseparator
36186 \begin_inset space ~
36192 Short titles are used as alternative for multiline section headings to
36193 keep the table of contents clearly arranged.
36194 Only the short title appears in the table of contents and therefore also
36195 in the PDF-bookmark.
36198 \begin_layout Standard
36199 When formulas should be used in the table of contents but
36203 is used, one can use the following command in TeX-mode:
36206 \begin_layout Standard
36211 texorpdfstring{part}{alternative}
36212 \begin_inset Index idx
36215 \begin_layout Plain Layout
36226 \begin_layout Standard
36227 Part is the part of the heading that shouldn't appear in the PDF-bookmark.
36228 This can be characters, formulas, footnotes, but also cross-references.
36229 The alternative is used instead of the part for the bookmark.
36232 \begin_layout Standard
36233 Here are two example headings:
36234 \begin_inset VSpace -3mm
36241 \begin_layout Plain Layout
36253 \begin_layout Subsubsection
36254 Heading without formula in table of contents
36255 \begin_inset Formula $\sqrt{-1}=\mathrm{i}$
36259 \begin_inset Argument 1
36262 \begin_layout Plain Layout
36263 Heading without formula in table of contents
36271 \begin_layout Subsubsection
36272 Heading with formula in table of contents
36276 \begin_layout Plain Layout
36286 \begin_inset Formula $\sqrt{-1}=\mathrm{i}$
36293 \begin_layout Plain Layout
36303 \begin_layout Standard
36307 \begin_layout Plain Layout
36316 In the first heading a short title was used, in the second one
36325 \begin_layout Standard
36326 To get the same formatting as for the other headings, the complete heading
36335 \begin_layout Plain Layout
36337 \begin_inset CommandInset ref
36339 reference "sub:Bold-Formulas"
36351 \begin_layout Subsection
36352 Formulas in multi-column Text
36353 \begin_inset Index idx
36356 \begin_layout Plain Layout
36357 Formula ! in multi-column text
36365 \begin_layout Standard
36366 Formulas in multi-column text are often too wide to fit into a column and
36367 thus need to be set over the whole page width.
36368 This is done by using the LaTeX-package
36376 \begin_layout Plain Layout
36381 is part of every LaTeX standard installation.
36387 \begin_inset Index idx
36390 \begin_layout Plain Layout
36391 Packages ! multicol
36396 , that is loaded with the LaTeX-preamble line
36399 \begin_layout Standard
36404 usepackage{multicol}
36407 \begin_layout Standard
36408 \begin_inset Note Greyedout
36411 \begin_layout Plain Layout
36412 Note that in this case the setting
36415 \begin_inset space ~
36422 Document\SpecialChar \menuseparator
36428 \begin_inset space ~
36448 \begin_layout Standard
36449 Before the multi-column text the command
36452 \begin_layout Standard
36457 begin{multicols}{column number}
36460 \begin_layout Standard
36461 is written in TeX-mode.
36462 The column number is a number in the range of 2
36463 \begin_inset space \thinspace{}
36467 \begin_inset space \thinspace{}
36471 Before the formula the multi-column text is ended by inserting the command
36474 \begin_layout Standard
36482 \begin_layout Standard
36486 \begin_layout Standard
36487 Due to the command some space is automatically added before the formula.
36489 \begin_inset space \thinspace{}
36492 mm vertical space is inserted before the formula.
36493 When the formula style
36499 \begin_layout Plain Layout
36501 \begin_inset CommandInset ref
36503 reference "sec:Formula-Styles"
36515 \begin_inset space \thinspace{}
36518 mm space is inserted instead.
36521 \begin_layout Standard
36522 As example a multi-column text with a displayed formula:
36525 \begin_layout Standard
36531 \begin_layout Plain Layout
36535 begin{multicols}{2}
36540 Das Spektrum wird fouriertransformiert.
36541 Die Fouriertransformation wird verwendet, um die überlagerten Signale (Netzwerk
36542 , Lösungsmittel) zu trennen.
36543 Nachdem wir die Phasenverschiebung bestimmen konnten, interessiert uns
36544 nun das Aussehen des Ausgangssignals.
36545 Im Experiment haben wir es mit sehr vielen Teilchen zu tun, so dass man
36546 über alle Phasen integrieren muss.
36548 \begin_inset Formula $S$
36551 unser normiertes Ausgangssignal und
36552 \begin_inset Formula $P$
36555 die Phasenverteilungsfunktion, so ergibt sich die Beziehung
36559 \begin_layout Plain Layout
36569 \begin_inset VSpace -6mm
36573 \begin_inset Formula
36575 S(t)=S_{0}(t)\int_{-\infty}^{\infty}P(\phi,t)\mathrm{e}^{\mathrm{i}\phi}\,\mathrm{d}\phi
36584 \begin_layout Plain Layout
36588 begin{multicols}{2}
36594 \begin_inset Formula $S_{0}$
36597 das Signal ohne Gradient ist und die Normierungsbedingung
36598 \begin_inset Formula $\int_{-\infty}^{\infty}P(\phi,t)\,\mathrm{d}\phi=1$
36602 Nun dürfen wir aber nicht den Relaxationsprozess außer Acht lassen.
36604 \begin_inset Formula $\nicefrac{\pi}{2}$
36608 \begin_inset space \thinspace{}
36611 -rf-Puls beginnt sich die Magnetisierung zu entfokussieren, wodurch sich
36612 das Signal zusätzlich abschwächt.
36613 Diese Abschwächung verläuft exponentiell in Abhängigkeit der so genannten
36615 \begin_inset Formula $T_{2}$
36621 \begin_layout Standard
36627 \begin_layout Plain Layout
36639 \begin_layout Subsection
36640 Formulas with Description of Variables
36641 \begin_inset Index idx
36644 \begin_layout Plain Layout
36645 Formula ! with description of variables
36653 \begin_layout Standard
36654 To describe variables within a formula, like in formula
36655 \begin_inset CommandInset ref
36657 reference "eq:within"
36666 \begin_inset Formula $n$
36670 \begin_inset space ~
36673 matrix is used with left aligned columns for the
36674 \begin_inset Formula $n$
36681 \begin_layout Plain Layout
36683 \begin_inset CommandInset ref
36685 reference "sec:Matrices"
36694 To set the description in a smaller size, before the matrix e.
36695 \begin_inset space \thinspace{}
36699 \begin_inset space \space{}
36712 \begin_layout Plain Layout
36714 \begin_inset CommandInset ref
36716 reference "sub:Font-Sizes"
36728 \begin_layout Standard
36729 When the formula style
36735 \begin_layout Plain Layout
36737 \begin_inset CommandInset ref
36739 reference "sec:Formula-Styles"
36760 \begin_layout Plain Layout
36767 only works in formulas with the style
36772 \begin_inset CommandInset ref
36774 reference "sub:Variable-Space"
36783 is inserted before and after the matrix to have the same separation of
36784 the matrix from the equation and the side margin.
36787 \begin_layout Standard
36788 When the formula style
36792 is used, the method described in
36793 \begin_inset CommandInset ref
36795 reference "sub:Flalign-Environment"
36799 is used to indent formulas.
36801 \begin_inset CommandInset ref
36803 reference "eq:within"
36807 consists of five columns where in the first two columns contain the equation,
36808 the third the matrix and the last one an empty TeX-brace.
36809 \begin_inset Formula
36811 \hspace{30pt}F_{A} & =\rho·V·g & \footnotesize\begin{array}{ll}
36812 \rho & \textrm{density}\\
36813 V & \textrm{volume}\\
36814 g & \textrm{gravitational acceleration}
36815 \end{array} & & {}\label{eq:within}
36823 \begin_layout Subsection
36824 Upright small Greek Letters
36825 \begin_inset CommandInset label
36827 name "sub:Upright-small-Greek"
36832 \begin_inset Index idx
36835 \begin_layout Plain Layout
36836 Greek letters ! upright
36844 \begin_layout Standard
36845 Most of the math fonts only provide italic small Greek letters.
36846 But for symbols of elementary particles like pions and neutrinos, upright
36847 Greek letters are needed.
36856 \begin_layout Plain Layout
36861 is part of the LaTeX-package
36866 \begin_inset Index idx
36869 \begin_layout Plain Layout
36874 \begin_layout Plain Layout
36894 \begin_inset Index idx
36897 \begin_layout Plain Layout
36903 that is loaded with the LaTeX-preamble line
36906 \begin_layout Standard
36911 usepackage{upgreek}
36914 \begin_layout Standard
36920 \begin_layout Plain Layout
36930 \begin_inset Note Note
36933 \begin_layout Plain Layout
36934 The following table will only be displayed when the LaTeX-package
36943 They are created when the command for a small Greek letter is started with
36949 For example the command
36956 \begin_inset Formula $\uptau$
36962 \begin_layout Standard
36963 With these commands reactions of elementary particles can be typeset:
36964 \begin_inset Formula
36966 \uppi^{+}\to\upmu^{+}+\upnu_{\upmu}
36974 \begin_layout Standard
36975 The upright letters are more bold and wider than the italic ones.
36976 They should therefore not be used for units like
36977 \begin_inset Quotes eld
36981 \begin_inset Quotes erd
36987 \begin_layout Standard
36991 \begin_layout Plain Layout
37001 \begin_inset Note Note
37004 \begin_layout Plain Layout
37005 The following will be displayed when the LaTeX-package
37017 \begin_layout Standard
37018 You need to install the LaTeX-package
37022 to see the rest of this subsection in the output.
37025 \begin_layout Standard
37029 \begin_layout Plain Layout
37041 \begin_layout Subsection
37042 Text Characters in Formulas
37043 \begin_inset Index idx
37046 \begin_layout Plain Layout
37055 \begin_layout Standard
37056 In some cases you might want to insert text characters directly into formulas.
37057 When for example the centered dot · is often used in formulas like
37058 \begin_inset Formula $\nu=5·10^{5}\,\mathrm{Hz}$
37061 , one would have to insert the command
37071 \begin_layout Plain Layout
37073 \begin_inset CommandInset ref
37075 reference "sub:Binary-Operators"
37084 all the time, because this character is defined in all encodings as text
37086 But the encoding can be changed by this LaTeX-preamble line:
37089 \begin_layout Standard
37094 Declare Inputtext{183}{
37104 f\SpecialChar \textcompwordmark{}
37108 \begin_layout Standard
37109 The character encoding (menu
37111 Document\SpecialChar \menuseparator
37112 Settings\SpecialChar \menuseparator
37115 ) specifies what character appears when a keyboard key is pressed.
37116 When the key for the character '·' is pressed, internally the command
37123 But this command is not available in a formula so that you would get LaTeX-erro
37125 With the changed encoding the right command is chosen automatically, depending
37126 on if the character was inserted into a formula or not.
37129 \begin_layout Standard
37130 The encoding of several characters is saved in definition files.
37131 For example the encoding
37135 is defined in the file
37139 which is in the installation folder of LaTeX.
37140 Encodings should only be changed via the LaTeX-preamble and not in the
37142 Otherwise documents could not be edited by other LyX users working on other
37146 \begin_layout Standard
37147 \begin_inset VSpace medskip
37150 Besides the centered dot, in this document the degree sign ° is defined
37151 with the following LaTeX-preamble line so that it can be directly inserted
37155 \begin_layout Standard
37160 DeclareInputtext{176}{
37170 f\SpecialChar \textcompwordmark{}
37174 \begin_layout Subsection
37175 LaTeX-comments in formulas
37176 \begin_inset Index idx
37179 \begin_layout Plain Layout
37188 \begin_layout Standard
37189 In text you can insert a comment that will only be visible in the LaTeX
37190 source code of your file with the menu
37192 Insert\SpecialChar \menuseparator
37193 Note\SpecialChar \menuseparator
37197 This is not possible in a formula but you can insert LaTeX-comments with
37201 \begin_layout Standard
37209 \begin_layout Standard
37210 This creates a box in which you can write your comment.
37211 Due to a bug in LyX
37215 \begin_layout Plain Layout
37216 \begin_inset CommandInset href
37218 name "LyX-bug #9002"
37219 target "http://www.lyx.org/trac/ticket/9002"
37228 you cannot write normal text into the comment, even when you use mathematical
37229 text, you will see its LaTeX-commands in the LaTeX-output.
37230 \begin_inset Newline newline
37233 This a formula with a LaTeX-comment:
37234 \begin_inset Formula
37236 A=B%\text{This is the comment}
37244 \begin_layout Standard
37245 \begin_inset Newpage newpage
37251 \begin_layout Section
37254 \begin_inset Index idx
37257 \begin_layout Plain Layout
37266 \begin_layout Standard
37267 This section is a summary of the most important typographic rules, listed
37272 \begin_layout Plain Layout
37273 This collection was partly taken from the German semi-official dictionary
37275 \begin_inset Quotes eld
37279 \begin_inset Quotes erd
37283 \begin_inset CommandInset citation
37289 that lists some of the ISO rules.
37290 More rules are listed in
37291 \begin_inset CommandInset citation
37305 \begin_layout Itemize
37314 \begin_layout Plain Layout
37315 done with font styles, see
37316 \begin_inset CommandInset ref
37318 reference "sub:Font-Styles"
37327 , no matter if they appear in italic text: 30
37328 \begin_inset space \thinspace{}
37332 \begin_inset Newline newline
37335 Between the value and the unit is the smallest space, see
37336 \begin_inset CommandInset ref
37338 reference "sub:Predefined-Space"
37343 \begin_inset Newline newline
37346 This convention is automatically fulfilled when the command
37353 When it is entered to a formula, two boxes appear.
37354 In the first one the value is inserted, in the second one the unit, and
37356 \begin_inset Formula $\unit[30]{km/h}$
37360 \begin_inset space \thinspace{}
37370 is not a real LaTeX command but the command
37376 , therefore you cannot use it in TeX code.
37379 \begin_layout Itemize
37380 Percent and perthousand signs are set like physical units:
37381 \begin_inset Newline newline
37385 \begin_inset space \thinspace{}
37391 \begin_layout Itemize
37392 The degree sign follows directly on the value: 15°, but not when it is used
37394 \begin_inset space \thinspace{}
37400 \begin_layout Itemize
37401 In numbers with more than four digits the smallest space is inserted before
37402 every third digit to group them:
37412 \begin_inset space \thinspace{}
37416 \begin_inset space \thinspace{}
37422 \begin_layout Itemize
37423 For dimensions like 120×90×40
37424 \begin_inset space \thinspace{}
37427 cm the multiplication sign
37428 \begin_inset Quotes eld
37432 \begin_inset Quotes erd
37436 It is available either via the command
37444 Insert\SpecialChar \menuseparator
37445 Special Character\SpecialChar \menuseparator
37451 \begin_layout Itemize
37452 Functions with names consisting of several letters are set upright to avoid
37454 \begin_inset CommandInset ref
37456 reference "sub:Predefined-Functions"
37463 \begin_layout Itemize
37464 Indices consisting of several letters, are set upright:
37465 \begin_inset Formula $E_{\mathrm{kin}}$
37469 \begin_inset Newline newline
37472 Components of matrices are set italic:
37473 \begin_inset Formula $\hat{H}_{kl}$
37479 \begin_layout Itemize
37480 The differentiation/integration operator 'd', the Euler's number 'e' and
37481 the imaginary unit 'i' should be set upright, to avoid mixing them up with
37485 \begin_layout Itemize
37486 The character that denotes a
37490 transformation is inserted either by the command
37495 \begin_inset space \textvisiblespace{}
37502 Insert\SpecialChar \menuseparator
37503 Special Character\SpecialChar \menuseparator
37504 Symbols\SpecialChar \menuseparator
37506 \begin_inset space ~
37512 \begin_inset Formula $\mathscr{F}$
37518 \begin_layout Standard
37519 \begin_inset Newpage newpage
37525 \begin_layout Section
37527 \begin_inset Index idx
37530 \begin_layout Plain Layout
37539 \begin_layout Standard
37540 Some characters and symbols can be created with several commands.
37541 Here is a list of the synonym commands:
37544 \begin_layout Standard
37545 \begin_inset VSpace bigskip
37549 \begin_inset space \hfill{}
37553 \begin_inset Tabular
37554 <lyxtabular version="3" rows="12" columns="2">
37555 <features rotate="0" tabularvalignment="middle">
37556 <column alignment="center" valignment="top" width="0pt">
37557 <column alignment="center" valignment="top" width="0pt">
37559 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
37562 \begin_layout Plain Layout
37568 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
37571 \begin_layout Plain Layout
37573 \begin_inset Note Note
37576 \begin_layout Plain Layout
37583 is only used as spacer.
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
37613 \begin_layout Plain Layout
37626 \begin_layout Plain Layout
37640 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
37643 \begin_layout Plain Layout
37651 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
37654 \begin_layout Plain Layout
37664 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
37667 \begin_layout Plain Layout
37675 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
37678 \begin_layout Plain Layout
37688 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
37691 \begin_layout Plain Layout
37699 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
37702 \begin_layout Plain Layout
37710 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
37713 \begin_layout Plain Layout
37721 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
37724 \begin_layout Plain Layout
37732 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
37735 \begin_layout Plain Layout
37743 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
37746 \begin_layout Plain Layout
37756 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
37759 \begin_layout Plain Layout
37767 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
37770 \begin_layout Plain Layout
37780 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
37783 \begin_layout Plain Layout
37791 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
37794 \begin_layout Plain Layout
37804 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
37807 \begin_layout Plain Layout
37815 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
37818 \begin_layout Plain Layout
37828 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
37831 \begin_layout Plain Layout
37839 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
37842 \begin_layout Plain Layout
37850 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
37853 \begin_layout Plain Layout
37861 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
37864 \begin_layout Plain Layout
37876 \begin_inset space \hfill{}
37880 \begin_inset Tabular
37881 <lyxtabular version="3" rows="12" columns="2">
37882 <features rotate="0" tabularvalignment="middle">
37883 <column alignment="center" valignment="top" width="0pt">
37884 <column alignment="center" valignment="top" width="0pt">
37886 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
37889 \begin_layout Plain Layout
37895 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
37898 \begin_layout Plain Layout
37906 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
37909 \begin_layout Plain Layout
37917 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
37920 \begin_layout Plain Layout
37932 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
37935 \begin_layout Plain Layout
37943 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
37946 \begin_layout Plain Layout
37956 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
37959 \begin_layout Plain Layout
37967 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
37970 \begin_layout Plain Layout
37980 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
37983 \begin_layout Plain Layout
37991 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
37994 \begin_layout Plain Layout
38002 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
38005 \begin_layout Plain Layout
38013 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
38016 \begin_layout Plain Layout
38024 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
38027 \begin_layout Plain Layout
38035 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
38038 \begin_layout Plain Layout
38048 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
38051 \begin_layout Plain Layout
38059 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
38062 \begin_layout Plain Layout
38072 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
38075 \begin_layout Plain Layout
38083 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
38086 \begin_layout Plain Layout
38096 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
38099 \begin_layout Plain Layout
38107 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
38110 \begin_layout Plain Layout
38120 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
38123 \begin_layout Plain Layout
38131 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
38134 \begin_layout Plain Layout
38144 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
38147 \begin_layout Plain Layout
38155 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
38158 \begin_layout Plain Layout
38172 \begin_inset space \hfill{}
38178 \begin_layout Standard
38179 \begin_inset Newpage newpage
38185 \begin_layout Bibliography
38186 \begin_inset CommandInset bibitem
38187 LatexCommand bibitem
38199 The LaTeX Companion
38202 Addison Wesley, 2004
38205 \begin_layout Bibliography
38206 \begin_inset CommandInset bibitem
38207 LatexCommand bibitem
38213 \begin_inset CommandInset href
38216 target "ftp://ftp.dante.de/tex-archive/info/math/voss/mathmode/Mathmode.pdf"
38220 of LaTeX's math abilities
38223 \begin_layout Bibliography
38224 \begin_inset CommandInset bibitem
38225 LatexCommand bibitem
38231 \begin_inset CommandInset href
38234 target "http://mirrors.ctan.org/macros/latex/required/amslatex/math/amsldoc.pdf"
38242 \begin_layout Plain Layout
38254 \begin_layout Bibliography
38255 \begin_inset CommandInset bibitem
38256 LatexCommand bibitem
38262 \begin_inset CommandInset href
38265 target "ftp://ftp.dante.de/tex-archive/info/symbols/comprehensive/symbols-a4.pdf"
38269 of all symbols available with LaTeX-packages
38272 \begin_layout Bibliography
38273 \begin_inset CommandInset bibitem
38274 LatexCommand bibitem
38280 \begin_inset CommandInset href
38282 name "Documentation"
38283 target "http://mirrors.ctan.org/macros/latex/contrib/cancel/cancel.pdf"
38287 of the LaTeX-package
38292 \begin_inset Index idx
38295 \begin_layout Plain Layout
38304 \begin_layout Bibliography
38305 \begin_inset CommandInset bibitem
38306 LatexCommand bibitem
38312 \begin_inset CommandInset href
38314 name "Documentation"
38315 target "http://www.tug.org/applications/hyperref/ftp/doc/manual.pdf"
38319 of the LaTeX-package
38324 \begin_inset Index idx
38327 \begin_layout Plain Layout
38328 Packages ! hyperref
38336 \begin_layout Bibliography
38337 \begin_inset CommandInset bibitem
38338 LatexCommand bibitem
38344 \begin_inset CommandInset href
38346 name "Documentation"
38347 target "http://www.ctan.org/tex-archive/macros/latex/contrib/mhchem/mhchem.pdf"
38351 of the LaTeX-package
38356 \begin_inset Index idx
38359 \begin_layout Plain Layout
38368 \begin_layout Bibliography
38369 \begin_inset CommandInset bibitem
38370 LatexCommand bibitem
38381 Auflage, Duden 2001
38384 \begin_layout Bibliography
38385 \begin_inset CommandInset bibitem
38386 LatexCommand bibitem
38392 \begin_inset CommandInset href
38395 target "http://physics.nist.gov/Document/checklist.pdf"
38399 for reviewing manuscripts
38402 \begin_layout Standard
38403 \begin_inset CommandInset index_print
38404 LatexCommand printindex