1 #LyX 2.1 created this file. For more info see http://www.lyx.org/
7 % DO NOT ALTER THIS PREAMBLE!!!
9 % This preamble is designed to ensure that the file prints
10 % out as advertised. If you mess with this preamble,
11 % parts of this document may not print out as expected. If you
12 % have problems LaTeXing this file, please contact
13 % the documentation team
14 % email: lyx-docs@lists.lyx.org
20 % set fonts for nicer pdf view
21 \IfFileExists{lmodern.sty}
22 {\usepackage{lmodern}}{}
24 \fi % end if pdflatex is used
26 % solves the following problem:
27 % If the dection number consits of too many numerals the section heading
28 % will be printed in the TOC without a space between it and the section number.
29 % As solution more space between the number and the heading is inserted:
30 \renewcommand{\l@subsection}{\@dottedtocline{2}{1.5em}{2.8em}}
31 \renewcommand{\l@subsubsection}{\@dottedtocline{3}{4.3em}{3.6em}}
33 % increase link area for cross-references and autoname them,
34 \AtBeginDocument{\renewcommand{\ref}[1]{\mbox{\autoref{#1}}}}
35 \@ifundefined{extrasenglish}{\usepackage[english]{babel}}{}
36 \addto\extrasenglish{%
37 \renewcommand*{\equationautorefname}[1]{}%
38 \renewcommand{\sectionautorefname}{sec.\negthinspace}%
39 \renewcommand{\subsectionautorefname}{sec.\negthinspace}%
40 \renewcommand{\subsubsectionautorefname}{sec.\negthinspace}%
43 % don't load packages twice
44 % see first footnote in sec. 9.3
45 \@ifundefined{textcolor}{\usepackage{color}}{}
47 % the pages of the TOC are numbered roman
48 % and a PDF-bookmark for the TOC is added
50 \let\myTOC\tableofcontents
51 \renewcommand{\tableofcontents}{%
53 \pdfbookmark[1]{\contentsname}{}
56 \pagenumbering{arabic}}
58 % insert additional vertical space of 1.5 mm between footnotes,
60 \renewcommand{\footnote}[1]{\myFoot{#1\vspace{1.5mm}}}
62 % provides caption formatting
63 \setkomafont{captionlabel}{\bfseries}
65 % enables calculation of values
68 % for multiple columns used in sec. 24.7
74 % for the Fourier transformation symbol
77 % define a color, used in sec.9.3
78 \definecolor{darkgreen}{cmyk}{0.5, 0, 1, 0.5}
80 % declare operators (see sec. 10.4 and sec. 15.2)
81 \DeclareMathOperator*{\Lozenge}{\blacklozenge}
82 \DeclareMathOperator{\sgn}{sgn}
84 % example definitions for sec. 20.1
85 \newcommand{\gr}{\Longrightarrow}
86 \newcommand{\us}[1]{\underline{#1}}
87 \newcommand{\fb}[3]{\framebox#1#2{$#3$}}
88 \newcommand{\cb}[3][white]{\fcolorbox{#2}{#1}{$#3$}}
89 \newcommand{\fracS}[3][]{\genfrac{}{}{#1}{}{#2}{#3}}
91 % example macro from sec. 19.4
92 %\def\tagform@#1{\maketag@@@{|#1|}}
95 % ------------------------------------
96 % used to check for needed LaTeX packages
99 % check for package undertilde
100 % used for the command \utilde
101 \newboolean{undertilde}
102 \IfFileExists{undertilde.sty}
103 {\usepackage{undertilde}
104 \setboolean{undertilde}{true}}
105 {\setboolean{undertilde}{false}}
107 % check for package eurosym
108 % used for the Euro symbol
110 \IfFileExists{eurosym.sty}
111 {\usepackage[gennarrow]{eurosym}
112 \setboolean{eurosym}{true}}
113 {\setboolean{eurosym}{false}}
115 % check for package braket
116 % used for physical vectors
118 \IfFileExists{braket.sty}
120 \setboolean{braket}{true}}
121 {\setboolean{braket}{false}}
123 % check for package cancel
125 \IfFileExists{cancel.sty}
127 \setboolean{cancel}{true}}
128 {\setboolean{cancel}{false}}
130 % check for package upgreek
132 \IfFileExists{upgreek.sty}
133 {\usepackage{upgreek}
134 \setboolean{upgreek}{true}}
135 {\setboolean{upgreek}{false}}
137 \options bibliography=totoc,index=totoc,BCOR7.5mm,titlepage,captions=tableheading
138 \use_default_options false
139 \maintain_unincluded_children false
141 \language_package default
146 \font_typewriter default
148 \font_default_family default
149 \use_non_tex_fonts false
155 \default_output_format default
157 \bibtex_command default
158 \index_command default
162 \pdf_title "LyX's Math Manual"
163 \pdf_author "LyX Team, Uwe Stöhr"
164 \pdf_subject "LyX-documentation about math"
165 \pdf_keywords "LyX, Mathed"
167 \pdf_bookmarksnumbered true
168 \pdf_bookmarksopen true
169 \pdf_bookmarksopenlevel 1
170 \pdf_breaklinks false
174 \pdf_pdfusetitle false
175 \pdf_quoted_options "linkcolor=black, citecolor=black, urlcolor=blue, filecolor=blue, pdfpagelayout=OneColumn, pdfnewwindow=true, pdfstartview=XYZ, plainpages=false"
178 \use_package amsmath 2
179 \use_package amssymb 2
180 \use_package cancel 0
182 \use_package mathdots 1
183 \use_package mathtools 1
184 \use_package mhchem 1
185 \use_package stackrel 0
186 \use_package stmaryrd 0
187 \use_package undertilde 0
189 \cite_engine_type default
193 \paperorientation portrait
197 \notefontcolor #0000ff
204 \paragraph_separation skip
206 \quotes_language english
209 \paperpagestyle plain
213 \tracking_changes false
214 \output_changes false
217 \html_be_strict false
223 LyX's detailed Math manual
231 \begin_layout Plain Layout
233 If you have comments or error corrections, please send them to the LyX Documenta
237 \begin_inset CommandInset href
239 name "lyx-docs@lists.lyx.org"
240 target "lyx-docs@lists.lyx.org?subject=LyX's Math manual"
251 \begin_inset Note Note
254 \begin_layout Plain Layout
261 \begin_inset Newline newline
265 \begin_inset Newline newline
273 \begin_layout Standard
274 \begin_inset CommandInset toc
275 LatexCommand tableofcontents
282 \begin_layout Standard
283 \begin_inset Note Note
286 \begin_layout Plain Layout
287 To export this document to PDF, PS or DVI the LaTeX-packages
289 braket, cancel, eurosym, mathdots, mathtools, mhchem, undertilde
296 If they are not installed the document can be exported anyway but the sections
297 where the packages are required will not appear in the output.
302 ; if it is not installed, this file cannot be exported.
305 \begin_layout Plain Layout
306 The latest PDF-version of this document can be found here:
307 \begin_inset Newline newline
312 http://wiki.lyx.org/LyX/DocumentationDevelopment#Math
320 \begin_layout Standard
321 \begin_inset Newpage newpage
327 \begin_layout Section
331 \begin_layout Standard
332 This document explains LyX's math features and is furthermore a collection
333 of LaTeX-commands used for mathematical characters and constructs.
334 The explanations are designed for the usage of commands.
335 It is therefore required that you have read the section
346 \begin_layout Standard
347 Most of the characters and many constructs explained in this manual are
348 also accessible via the menu
352 \SpecialChar \menuseparator
368 But everybody who has to write lots of formulas will notice that it is
369 much faster to use commands instead of the math toolbar.
370 Therefore this manual is focused on commands but also mentions the correspondin
371 g toolbar buttons when available.
374 \begin_layout Standard
375 If not specially mentioned the commands are only available within formulas.
376 To be able to use all commands explained in this document, the option
380 must be checked in the document settings (menu
382 Document\SpecialChar \menuseparator
383 Settings\SpecialChar \menuseparator
394 \begin_layout Plain Layout
397 Use AMS math package automatically
403 \begin_layout Plain Layout
412 -math when math constructs are found that are supported by LyX.
420 \begin_layout Standard
421 This document doesn't list all
425 \begin_layout Plain Layout
438 \begin_layout Plain Layout
443 \begin_layout Plain Layout
452 -math commands is in the file
455 \begin_inset CommandInset href
458 target "ftp://ftp.ams.org/pub/tex/doc/amstex/amsguide.pdf"
464 , which is part of every LaTeX standard installation.
469 for lucidity reasons.
472 \begin_layout Section
476 \begin_layout Standard
477 To create an inline formula
478 \begin_inset Index idx
481 \begin_layout Plain Layout
487 that is embedded into a text line, use one of the shortcuts
493 or the toolbar button
500 \begin_inset Newline newline
503 To create a display style formula
504 \begin_inset Index idx
507 \begin_layout Plain Layout
508 Formula ! display style
513 which will appear bigger, has a different format, and will be in a separate
514 paragraph, use one of these shortcuts:
523 \begin_layout Standard
524 To change a display style formula to an inline formula, set the cursor into
525 the formula and use one of the shortcuts
533 Edit\SpecialChar \menuseparator
534 Math\SpecialChar \menuseparator
538 The same way is used to change an inline formula to a display style formula.
541 \begin_layout Standard
542 To display parts of an inline formula in the size of a display style formula,
550 \begin_inset Index idx
553 \begin_layout Plain Layout
562 Then a new blue box appears in which the desired formula part is inserted.
565 \begin_layout Standard
566 Only inline formulas are allowed inside tables.
569 \begin_layout Standard
574 can be turned on in the menu
576 View\SpecialChar \menuseparator
580 When you click there on
581 \begin_inset Quotes eld
585 \begin_inset Quotes erd
588 the toolbar will be shown permanently at the bottom; this state is visualized
593 menu with a checkmark.
594 When you click in this state again on
595 \begin_inset Quotes eld
599 \begin_inset Quotes erd
610 is only shown when the cursor is within a formula; this state is visualized
611 by the renaming of the menu entry from
612 \begin_inset Quotes eld
616 \begin_inset Quotes erd
620 \begin_inset Quotes eld
628 \begin_inset Quotes erd
634 \begin_layout Standard
636 \begin_inset Index idx
639 \begin_layout Plain Layout
645 is invoked by pressing the toolbar button
653 Insert\SpecialChar \menuseparator
658 \begin_layout Plain Layout
674 \begin_inset Note Note
677 \begin_layout Plain Layout
678 In LyX there are three
679 \begin_inset Quotes eld
683 \begin_inset Quotes erd
686 that appear in the output with sub- and superscript letters: TeX, LaTeX
690 \begin_layout Plain Layout
691 To avoid that these names are recognized as proper names, a TeX-brace pair
700 \begin_layout Standard
701 To change the LaTeX-preamble
702 \begin_inset Index idx
705 \begin_layout Plain Layout
713 Document\SpecialChar \menuseparator
714 Settings\SpecialChar \menuseparator
719 \begin_layout Plain Layout
735 \begin_layout Standard
736 To edit matrices, case differentiations and multiline formulas subsequently,
739 Edit\SpecialChar \menuseparator
744 Edit\SpecialChar \menuseparator
746 \begin_inset space \thinspace{}
750 \begin_inset space \thinspace{}
760 When lines and columns are swapped via the menu, the column or line where
761 the cursor is in is exchanged with the column to the right or the line
763 Is the cursor in the last column or row, the exchange is done with the
764 column to the left or the line above.
767 \begin_layout Standard
768 To write text in formulas
772 \begin_layout Plain Layout
773 For multiline formulas the command
780 \begin_inset CommandInset ref
782 reference "sub:Text-in-multiline"
796 \begin_inset Index idx
799 \begin_layout Plain Layout
806 \begin_inset Index idx
809 \begin_layout Plain Layout
816 This mode is invoked with the shortcut
822 or by the insertion of the command
829 \begin_inset Index idx
832 \begin_layout Plain Layout
841 The text appears black in LyX and can therefore be distinguished from the
842 other formula parts which appear blue.
843 In the output mathematical text is set upright, in contrary to other formula
847 \begin_layout Subsection*
851 \begin_layout Standard
852 Most of the LaTeX-commands for math constructs have the following scheme:
855 \begin_layout Standard
871 \begin_layout Standard
872 A command always starts with a backslash
873 \begin_inset Quotes gld
883 \begin_inset Quotes grd
887 To omit optional arguments, also omit the associated brackets.
888 The braces around the required arguments are named in this document as
890 \begin_inset Index idx
893 \begin_layout Plain Layout
900 If you add in a formula a left brace to a command name, LyX automatically
902 In all other cases TeX-braces are created in formulas with the command
910 TeX-braces appear red in LyX, in contrary to normal braces which appear
912 In TeX-mode no command is needed to get TeX-braces.
913 TeX-braces don't appear in the output.
916 \begin_layout Standard
917 When commands without arguments, like commands for symbols are entered in
918 TeX-mode, a space character must
922 be behind the command to end it.
923 This space doesn't appear in the output.
924 When the space should appear in the output, the space must be followed
925 by a protected space in normal text.
928 \begin_layout Standard
929 A protected space is inserted with
932 arg "command-alternatives space-insert protected ; math-space"
938 \begin_layout Subsection*
939 \begin_inset Newpage newpage
945 \begin_layout Itemize
947 \begin_inset space \textvisiblespace{}
950 denotes a space character to be input.
953 \begin_layout Itemize
955 \begin_inset Formula $\to$
958 denotes the usage of the corresponding arrow key on the keyboard.
963 key can often be used instead of
964 \begin_inset Formula $\to$
968 \begin_inset Formula $\downarrow$
976 \begin_inset Formula $\leftarrow$
980 \begin_inset Formula $\uparrow$
986 \begin_layout Subsection*
990 \begin_layout Standard
992 \begin_inset Float table
998 \begin_layout Plain Layout
1000 \begin_inset Caption Standard
1002 \begin_layout Plain Layout
1003 \begin_inset CommandInset label
1005 name "tab:Available-units"
1017 \begin_layout Plain Layout
1019 \begin_inset Tabular
1020 <lyxtabular version="3" rows="13" columns="2">
1021 <features rotate="0" tabularvalignment="middle">
1022 <column alignment="center" valignment="top">
1023 <column alignment="center" valignment="top">
1025 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
1028 \begin_layout Plain Layout
1034 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
1037 \begin_layout Plain Layout
1045 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
1048 \begin_layout Plain Layout
1054 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
1057 \begin_layout Plain Layout
1065 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
1068 \begin_layout Plain Layout
1074 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
1077 \begin_layout Plain Layout
1085 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
1088 \begin_layout Plain Layout
1094 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
1097 \begin_layout Plain Layout
1099 \begin_inset space \thinspace{}
1103 \begin_inset space \thinspace{}
1113 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
1116 \begin_layout Plain Layout
1122 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
1125 \begin_layout Plain Layout
1127 \begin_inset space \thinspace{}
1131 \begin_inset space \thinspace{}
1141 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
1144 \begin_layout Plain Layout
1150 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
1153 \begin_layout Plain Layout
1155 \begin_inset space \thinspace{}
1159 \begin_inset space \thinspace{}
1169 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
1172 \begin_layout Plain Layout
1178 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
1181 \begin_layout Plain Layout
1183 \begin_inset space \thinspace{}
1187 \begin_inset space \thinspace{}
1197 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
1200 \begin_layout Plain Layout
1206 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
1209 \begin_layout Plain Layout
1211 \begin_inset space \thinspace{}
1215 \begin_inset space \thinspace{}
1225 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
1228 \begin_layout Plain Layout
1234 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
1237 \begin_layout Plain Layout
1239 \begin_inset space \thinspace{}
1243 \begin_inset Formula $\approx$
1247 \begin_inset space \thinspace{}
1257 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
1260 \begin_layout Plain Layout
1266 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
1269 \begin_layout Plain Layout
1271 \begin_inset space \thinspace{}
1275 \begin_inset space \thinspace{}
1285 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
1288 \begin_layout Plain Layout
1294 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
1297 \begin_layout Plain Layout
1301 \begin_inset Quotes eld
1307 \begin_inset Quotes erd
1317 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
1320 \begin_layout Plain Layout
1326 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
1329 \begin_layout Plain Layout
1331 \begin_inset Quotes eld
1339 \begin_inset Quotes erd
1349 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
1352 \begin_layout Plain Layout
1358 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
1361 \begin_layout Plain Layout
1363 \begin_inset space \thinspace{}
1367 \begin_inset Formula $\nicefrac{1}{18}$
1371 \begin_inset space \thinspace{}
1392 \begin_layout Standard
1393 \begin_inset Newpage newpage
1399 \begin_layout Section
1403 \begin_layout Subsection
1405 \begin_inset Index idx
1408 \begin_layout Plain Layout
1415 \begin_inset Index idx
1418 \begin_layout Plain Layout
1425 \begin_inset Index idx
1428 \begin_layout Plain Layout
1433 \begin_layout Plain Layout
1444 \begin_layout Plain Layout
1457 \begin_inset Index idx
1460 \begin_layout Plain Layout
1465 \begin_layout Plain Layout
1476 \begin_layout Plain Layout
1491 \begin_layout Standard
1492 Indices are created with an underscore
1493 \begin_inset Quotes eld
1497 \begin_inset Quotes erd
1500 or via the math toolbar button
1503 arg "math-subscript"
1506 , exponents with a caret
1507 \begin_inset Quotes eld
1511 \begin_inset Quotes erd
1514 or via the math toolbar button
1517 arg "math-superscript"
1523 \begin_layout Standard
1525 \begin_inset Tabular
1526 <lyxtabular version="3" rows="4" columns="2">
1527 <features rotate="0" tabularvalignment="middle">
1528 <column alignment="center" valignment="top" width="0pt">
1529 <column alignment="center" valignment="top" width="0pt">
1531 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
1534 \begin_layout Plain Layout
1540 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
1543 \begin_layout Plain Layout
1545 \begin_inset Note Note
1548 \begin_layout Plain Layout
1555 is only used as spacer.
1567 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
1570 \begin_layout Plain Layout
1576 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
1579 \begin_layout Plain Layout
1580 \begin_inset Formula $B_{V}$
1590 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
1593 \begin_layout Plain Layout
1599 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
1602 \begin_layout Plain Layout
1603 \begin_inset Formula $\raisebox{5mm}{}B^{V}$
1613 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
1616 \begin_layout Plain Layout
1618 \begin_inset space \textvisiblespace{}
1626 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
1629 \begin_layout Plain Layout
1630 \begin_inset Formula $\raisebox{5mm}{}B^{A}$
1646 \begin_layout Standard
1647 As the caret is in some languages an accent, vowels will be accentuated
1648 in this case and not set as exponents
1652 \begin_layout Plain Layout
1653 Depending on the used keyboard settings this can also happen for characters
1660 To get exponents in this case, press
1664 after the caret as in the last example.
1667 \begin_layout Subsection
1669 \begin_inset CommandInset label
1671 name "sub:Fractions"
1676 \begin_inset Index idx
1679 \begin_layout Plain Layout
1688 \begin_layout Standard
1689 Fractions are generated with the command
1696 \begin_inset Index idx
1699 \begin_layout Plain Layout
1707 or via the math toolbar button
1710 arg "math-insert \\frac"
1714 The font size is adjusted automatically, depending on whether the fraction
1715 is in an inline or display style formula.
1716 With the math toolbar button
1719 arg "math-insert \\frac-square"
1722 you can select different fraction types.
1725 \begin_layout Standard
1733 \begin_inset Index idx
1736 \begin_layout Plain Layout
1744 a fraction can be created that always has the size of a display style formula.
1752 \begin_inset Index idx
1755 \begin_layout Plain Layout
1763 the fraction appears always with the size of an inline formula.
1767 \begin_layout Standard
1768 A line with the fraction
1769 \begin_inset Formula $\frac{1}{2}$
1772 that was created with the command
1781 \begin_layout Standard
1782 A line with the fraction
1783 \begin_inset Formula $\dfrac{1}{2}$
1786 that was created with the command
1795 \begin_layout Standard
1797 \begin_inset Tabular
1798 <lyxtabular version="3" rows="4" columns="2">
1799 <features rotate="0" tabularvalignment="middle">
1800 <column alignment="center" valignment="top" width="0pt">
1801 <column alignment="center" valignment="top" width="0pt">
1803 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
1806 \begin_layout Plain Layout
1812 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
1815 \begin_layout Plain Layout
1817 \begin_inset Note Note
1820 \begin_layout Plain Layout
1827 is only used as spacer.
1839 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
1842 \begin_layout Plain Layout
1846 \begin_inset space \textvisiblespace{}
1850 \begin_inset Formula $\downarrow$
1858 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
1861 \begin_layout Plain Layout
1862 \begin_inset Formula $\raisebox{4.5mm}{}\frac{A}{B}\raisebox{-2.5mm}{}$
1872 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
1875 \begin_layout Plain Layout
1879 \begin_inset space \textvisiblespace{}
1883 \begin_inset Formula $\downarrow$
1891 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
1894 \begin_layout Plain Layout
1895 \begin_inset Formula $\raisebox{7mm}{}\dfrac{A}{B}\raisebox{-4mm}{}$
1905 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
1908 \begin_layout Plain Layout
1912 \begin_inset space \textvisiblespace{}
1918 \begin_inset space \textvisiblespace{}
1922 \begin_inset Formula $\downarrow$
1926 \begin_inset Formula $\downarrow\downarrow$
1934 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
1937 \begin_layout Plain Layout
1938 \begin_inset Formula $\raisebox{8mm}{}\dfrac{e^{\frac{1}{2}}}{3}\raisebox{-4mm}{}$
1954 \begin_layout Standard
1955 \begin_inset VSpace bigskip
1959 \begin_inset Newpage newpage
1962 For nested fractions the command
1969 \begin_inset Index idx
1972 \begin_layout Plain Layout
1982 \begin_inset VSpace -3mm
1988 \begin_layout Standard
1989 \begin_inset Formula
1991 \textrm{created with \textbf{\textbackslash frac}} & & \textrm{created with \textbf{\textbackslash cfrac}}\\
1992 \frac{A}{B+\frac{C+\frac{E}{F}}{D}} & & \cfrac{A}{B+\cfrac{C+\cfrac{E}{F}}{D}}
2000 \begin_layout Standard
2001 The command for the example above is:
2004 \begin_layout Standard
2010 \begin_inset space \textvisiblespace{}
2014 \begin_inset Formula $\downarrow$
2020 \begin_inset space \textvisiblespace{}
2026 \begin_inset space \textvisiblespace{}
2030 \begin_inset Formula $\downarrow$
2034 \begin_inset Formula $\downarrow$
2040 \begin_layout Standard
2041 \begin_inset VSpace medskip
2047 \begin_layout Standard
2054 sets the fraction always in the size of a displayed formula, also when
2055 it is part of another fraction.
2058 \begin_layout Standard
2059 It is possible to specify the alignment of the numerator.
2066 is used to left align it, the command
2079 centers the numerator.
2080 These fractions demonstrate the different alignments:
2083 \begin_layout Standard
2086 \begin_inset Formula
2088 \cfrac[l]{A}{B+C}\,,\,\cfrac{A}{B+C}\,,\,\cfrac[r]{A}{B+C}
2096 \begin_layout Standard
2097 \begin_inset Note Greyedout
2100 \begin_layout Plain Layout
2117 are no real LaTeX commands but represent the command
2121 cfrac[alignment]{numerator}{denominator}
2124 Therefore you cannot use them in TeX code.
2132 \begin_layout Standard
2133 \begin_inset VSpace medskip
2136 It is often advantageous to combine
2149 \begin_inset Formula
2151 \cfrac{A}{B+\cfrac{C+\frac{E}{F}}{D}}
2159 \begin_layout Standard
2160 For inline fractions with a sloped fraction stroke you can use the command
2168 \begin_inset Index idx
2171 \begin_layout Plain Layout
2180 \begin_inset Formula $\nicefrac{5}{31}$
2190 \begin_inset Index idx
2193 \begin_layout Plain Layout
2202 \begin_inset Formula $\unitfrac{5}{31}$
2205 There is furthermore the command
2211 that offers to write a fraction in combination with a number:
2212 \begin_inset Formula $\unitfrac[2]{1}{3}$
2218 \begin_layout Standard
2219 \begin_inset Note Greyedout
2222 \begin_layout Plain Layout
2233 is not a real LaTeX command but the command
2234 \begin_inset Newline newline
2241 unitfrac[number]{numerator}{denominator}
2244 Therefore you cannot use it in TeX code.
2252 \begin_layout Standard
2253 How to define own fractions where the fraction stroke can be changed, is
2255 \begin_inset CommandInset ref
2257 reference "sub:Self-defined-Fractions"
2264 \begin_layout Standard
2265 Multiline fractions are explained in
2266 \begin_inset CommandInset ref
2268 reference "sub:Multiline-Fractions"
2275 \begin_layout Subsection
2277 \begin_inset Index idx
2280 \begin_layout Plain Layout
2289 \begin_layout Standard
2290 Square roots are created with
2297 \begin_inset Index idx
2300 \begin_layout Plain Layout
2308 or the math toolbar button
2311 arg "math-insert \\sqrt"
2314 , all other roots with the command
2321 \begin_inset Index idx
2324 \begin_layout Plain Layout
2332 or with the math toolbar button
2335 arg "math-insert \\root"
2341 \begin_layout Standard
2343 \begin_inset Tabular
2344 <lyxtabular version="3" rows="3" columns="2">
2345 <features rotate="0" tabularvalignment="middle">
2346 <column alignment="center" valignment="top" width="0pt">
2347 <column alignment="center" valignment="top" width="0pt">
2349 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
2352 \begin_layout Plain Layout
2358 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
2361 \begin_layout Plain Layout
2363 \begin_inset Note Note
2366 \begin_layout Plain Layout
2373 is only used as spacer.
2385 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
2388 \begin_layout Plain Layout
2392 \begin_inset space \textvisiblespace{}
2400 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
2403 \begin_layout Plain Layout
2404 \begin_inset Formula $\raisebox{4.5mm}{}\sqrt{A-B}$
2414 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
2417 \begin_layout Plain Layout
2421 \begin_inset space \textvisiblespace{}
2425 \begin_inset Formula $\downarrow$
2433 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
2436 \begin_layout Plain Layout
2437 \begin_inset Formula $\raisebox{4.5mm}{}\sqrt[3]{A-B}$
2453 \begin_layout Standard
2454 A square root can also be created with
2460 when the root index field is left empty.
2463 \begin_layout Standard
2464 With certain indices the distance to the root is too small, like in this
2466 \begin_inset Formula $\sqrt[\beta]{B}$
2470 \begin_inset Newline newline
2474 \begin_inset Formula $\beta$
2478 To avoid this, the commands
2485 \begin_inset Index idx
2488 \begin_layout Plain Layout
2503 \begin_inset Index idx
2506 \begin_layout Plain Layout
2514 are used with the following scheme:
2517 \begin_layout Standard
2531 \begin_layout Standard
2532 Distance is the number of Big Points (unit bp;
2533 \begin_inset Formula $\mathrm{72\, bp=1\, inch}$
2536 ), that the index should be moved to the left or top, resp..
2537 The commands are written to the index.
2538 This way the command
2539 \begin_inset Newline newline
2549 \begin_inset Formula $\to$
2555 \begin_inset Formula $\to$
2561 \begin_inset space \textvisiblespace{}
2565 \begin_inset Formula $\to$
2569 \begin_inset Newline newline
2574 produces a correct typeset formula:
2575 \begin_inset Formula $\sqrt[\leftroot{-1}\uproot{2}\beta]{B}$
2581 \begin_layout Subsection
2582 Binomial Coefficients
2583 \begin_inset Index idx
2586 \begin_layout Plain Layout
2587 Binomial coefficients
2595 \begin_layout Standard
2596 Binomial coefficients are inserted with the command
2603 \begin_inset Index idx
2606 \begin_layout Plain Layout
2614 or with the submenu of the math toolbar button
2617 arg "math-insert \\frac-square"
2633 there are the commands
2640 \begin_inset Index idx
2643 \begin_layout Plain Layout
2658 \begin_inset Index idx
2661 \begin_layout Plain Layout
2670 For other brackets around binomial coeficients there are the commands
2677 \begin_inset Index idx
2680 \begin_layout Plain Layout
2695 \begin_inset Index idx
2698 \begin_layout Plain Layout
2709 \begin_layout Standard
2711 \begin_inset Tabular
2712 <lyxtabular version="3" rows="6" columns="2">
2713 <features rotate="0" tabularvalignment="middle">
2714 <column alignment="center" valignment="top" width="0pt">
2715 <column alignment="center" valignment="top" width="0pt">
2717 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
2720 \begin_layout Plain Layout
2726 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
2729 \begin_layout Plain Layout
2731 \begin_inset Note Note
2734 \begin_layout Plain Layout
2741 is only used as spacer.
2753 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
2756 \begin_layout Plain Layout
2760 \begin_inset space \textvisiblespace{}
2764 \begin_inset Formula $\downarrow$
2772 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
2775 \begin_layout Plain Layout
2776 \begin_inset Formula $\raisebox{5mm}{}\binom{A}{B}\raisebox{-2.5mm}{}$
2786 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
2789 \begin_layout Plain Layout
2793 \begin_inset space \textvisiblespace{}
2797 \begin_inset Formula $\downarrow$
2805 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
2808 \begin_layout Plain Layout
2809 \begin_inset Formula $\raisebox{5mm}{}\dbinom{A}{B}\raisebox{-2.5mm}{}$
2819 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
2822 \begin_layout Plain Layout
2826 \begin_inset space \textvisiblespace{}
2830 \begin_inset Formula $\downarrow$
2838 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
2841 \begin_layout Plain Layout
2842 \begin_inset Formula $\raisebox{5mm}{}\tbinom{A}{B}\raisebox{-2.5mm}{}$
2852 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
2855 \begin_layout Plain Layout
2859 \begin_inset space \textvisiblespace{}
2863 \begin_inset Formula $\downarrow$
2871 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
2874 \begin_layout Plain Layout
2875 \begin_inset Formula $\raisebox{5mm}{}{A \brack B}\raisebox{-2.5mm}{}$
2885 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
2888 \begin_layout Plain Layout
2892 \begin_inset space \textvisiblespace{}
2896 \begin_inset Formula $\downarrow$
2904 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
2907 \begin_layout Plain Layout
2908 \begin_inset Formula $\raisebox{5mm}{}{A \brace B}\raisebox{-2.5mm}{}$
2924 \begin_layout Subsection
2925 Case Differentiations
2926 \begin_inset Index idx
2929 \begin_layout Plain Layout
2930 Case differentiations
2938 \begin_layout Standard
2940 \begin_inset Tabular
2941 <lyxtabular version="3" rows="3" columns="2">
2942 <features rotate="0" tabularvalignment="middle">
2943 <column alignment="center" valignment="top" width="0pt">
2944 <column alignment="center" valignment="top" width="0pt">
2946 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
2949 \begin_layout Plain Layout
2955 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
2958 \begin_layout Plain Layout
2966 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
2969 \begin_layout Plain Layout
2973 \begin_inset space \textvisiblespace{}
2977 \begin_inset Formula $\to$
2981 \begin_inset Index idx
2984 \begin_layout Plain Layout
2997 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
3000 \begin_layout Plain Layout
3001 \begin_inset Formula $\begin{cases}
3012 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
3015 \begin_layout Plain Layout
3019 \begin_inset space \textvisiblespace{}
3025 arg "newline-insert newline"
3033 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
3036 \begin_layout Plain Layout
3037 \begin_inset Formula $\begin{cases}
3038 A & \textrm{for }x>0\\
3039 B & \textrm{for }x=0
3056 \begin_layout Standard
3063 or pressing the math toolbar button
3066 arg "math-insert \\cases"
3069 you can create new lines with the shortcut
3072 arg "newline-insert newline"
3075 or the table toolbar button
3078 arg "inset-modify tabular append-row"
3084 \begin_layout Standard
3091 is also available via the menu
3093 Insert\SpecialChar \menuseparator
3094 Math\SpecialChar \menuseparator
3100 \begin_layout Subsection
3102 \begin_inset Index idx
3105 \begin_layout Plain Layout
3114 \begin_layout Standard
3122 \begin_inset Index idx
3125 \begin_layout Plain Layout
3133 every character can be displayed canceled.
3134 The characters are quasi accentuated by a slash.
3137 \begin_layout Standard
3139 \begin_inset Tabular
3140 <lyxtabular version="3" rows="4" columns="2">
3141 <features rotate="0" tabularvalignment="middle">
3142 <column alignment="center" valignment="top" width="0pt">
3143 <column alignment="center" valignment="top" width="0pt">
3145 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
3148 \begin_layout Plain Layout
3154 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
3157 \begin_layout Plain Layout
3165 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
3168 \begin_layout Plain Layout
3176 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
3179 \begin_layout Plain Layout
3180 \begin_inset Formula $\not=$
3190 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
3193 \begin_layout Plain Layout
3203 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
3206 \begin_layout Plain Layout
3207 \begin_inset Formula $\not\le$
3217 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
3220 \begin_layout Plain Layout
3230 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
3233 \begin_layout Plain Layout
3234 \begin_inset Formula $\not\parallel$
3250 \begin_layout Standard
3251 The last example shows that not all negations look good.
3252 Therefore there are special commands for some negations (see
3253 \begin_inset CommandInset ref
3255 reference "sub:Mathematical-Symbols"
3260 \begin_inset CommandInset ref
3262 reference "sec:Relations"
3269 \begin_layout Subsection
3271 \begin_inset CommandInset label
3273 name "sub:Placeholders"
3278 \begin_inset Index idx
3281 \begin_layout Plain Layout
3288 \begin_inset Index idx
3291 \begin_layout Plain Layout
3292 Chemical characters ! Isotopes
3298 \begin_inset Index idx
3301 \begin_layout Plain Layout
3306 \begin_layout Plain Layout
3317 \begin_layout Plain Layout
3332 \begin_layout Standard
3334 \begin_inset space \thinspace{}
3338 \begin_inset space \space{}
3345 \begin_layout Plain Layout
3346 Typesetting isotopes and chemical symbols is described in
3347 \begin_inset CommandInset ref
3349 reference "sub:Chemical-Symbols-and"
3358 the following problem occurs:
3361 \begin_layout Standard
3363 \begin_inset Tabular
3364 <lyxtabular version="3" rows="2" columns="2">
3365 <features rotate="0" tabularvalignment="middle">
3366 <column alignment="center" valignment="top" width="0pt">
3367 <column alignment="center" valignment="top" width="0pt">
3369 <cell alignment="center" valignment="top" usebox="none">
3372 \begin_layout Plain Layout
3373 Indices created with sub- and superscripts:
3378 <cell alignment="center" valignment="top" usebox="none">
3381 \begin_layout Plain Layout
3382 \begin_inset Formula $_{9}^{19}\mathrm{F}\raisebox{-3mm}{}$
3392 <cell alignment="center" valignment="top" usebox="none">
3395 \begin_layout Plain Layout
3401 <cell alignment="center" valignment="top" usebox="none">
3404 \begin_layout Plain Layout
3405 \begin_inset Formula $_{\phantom{1}9}^{19}\mathrm{F}$
3419 \begin_inset Note Note
3422 \begin_layout Plain Layout
3429 is only used as spacer.
3437 \begin_layout Standard
3438 The shorter index is by default placed below or above the first character
3439 of the longer index.
3440 To avoid this there is the command
3447 \begin_inset Index idx
3450 \begin_layout Plain Layout
3458 or the math toolbar button
3459 \begin_inset space \thinspace{}
3466 \begin_layout Plain Layout
3467 can be found in the submenu of the toolbar button
3470 arg "math-insert \\space"
3479 \begin_inset Graphics
3480 filename ../images/math/phantom.png
3485 that creates one or more phantom characters.
3492 a small blue box appears that is superposed with two red arrows.
3493 The arrows indicate that the complete width and height of the box content
3494 will be created as placeholder.
3495 Phantom characters are accordingly placeholders with the size of the characters.
3498 \begin_layout Standard
3500 \begin_inset Tabular
3501 <lyxtabular version="3" rows="4" columns="2">
3502 <features rotate="0" tabularvalignment="middle">
3503 <column alignment="center" valignment="top">
3504 <column alignment="center" valignment="top">
3506 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
3509 \begin_layout Plain Layout
3515 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
3518 \begin_layout Plain Layout
3520 \begin_inset Note Note
3523 \begin_layout Plain Layout
3530 is only used as spacer.
3542 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
3545 \begin_layout Plain Layout
3547 \begin_inset space \textvisiblespace{}
3553 \begin_inset space \textvisiblespace{}
3557 \begin_inset Formula $\to$
3561 \begin_inset space \textvisiblespace{}
3569 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
3572 \begin_layout Plain Layout
3573 \begin_inset Formula $\raisebox{4.5mm}{}{}_{\phantom{1}9}^{19}\mathrm{F}\raisebox{-2.5mm}{}$
3583 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
3586 \begin_layout Plain Layout
3588 \begin_inset space \textvisiblespace{}
3594 \begin_inset space \textvisiblespace{}
3598 \begin_inset Formula $\to$
3602 \begin_inset space \textvisiblespace{}
3610 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
3613 \begin_layout Plain Layout
3614 \begin_inset Formula $\raisebox{4.5mm}{}{}_{\phantom{23}9}^{235}\mathrm{F}\raisebox{-2.5mm}{}$
3624 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
3627 \begin_layout Plain Layout
3631 \begin_inset space \textvisiblespace{}
3637 \begin_inset space \textvisiblespace{}
3641 \begin_inset Formula $\to$
3645 \begin_inset space \textvisiblespace{}
3653 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
3656 \begin_layout Plain Layout
3657 \begin_inset Formula $\raisebox{4.5mm}{}\Lambda_{MMt}^{\phantom{ii}t}\raisebox{-2.5mm}{}$
3673 \begin_layout Standard
3674 Furthermore there are the commands
3681 \begin_inset Index idx
3684 \begin_layout Plain Layout
3693 \begin_inset space ~
3697 \begin_inset Graphics
3698 filename ../images/math/vphantom.png
3710 \begin_inset Index idx
3713 \begin_layout Plain Layout
3722 \begin_inset space ~
3726 \begin_inset Graphics
3727 filename ../images/math/hphantom.png
3739 creates only space for the maximal height of the characters in the box
3740 but not for its width.
3747 creates only space for the width of the box content.
3748 Therefore the boxes of both commands have only one red arrow.
3751 \begin_layout Standard
3752 For example the command
3757 \begin_inset space \textvisiblespace{}
3764 creates space for the height of the integral sign,
3768 \begin_layout Plain Layout
3775 creates an integral sign, see
3776 \begin_inset CommandInset ref
3778 reference "sub:Big-Operators"
3787 because this is the larger character.
3788 An example application is in
3789 \begin_inset CommandInset ref
3791 reference "sub:Multiline-Brackets"
3798 \begin_layout Standard
3799 Placeholders can also be used for text when they are inserted via the menu
3802 Insert\SpecialChar \menuseparator
3803 Formatting\SpecialChar \menuseparator
3809 \begin_layout Standard
3811 \begin_inset Newline newline
3815 \begin_inset Phantom Phantom
3818 \begin_layout Plain Layout
3827 \begin_layout Subsection
3829 \begin_inset Index idx
3832 \begin_layout Plain Layout
3839 \begin_inset Index idx
3842 \begin_layout Plain Layout
3843 Formula ! underlined
3851 \begin_layout Standard
3853 \begin_inset Tabular
3854 <lyxtabular version="3" rows="4" columns="2">
3855 <features rotate="0" tabularvalignment="middle">
3856 <column alignment="center" valignment="top" width="0pt">
3857 <column alignment="center" valignment="top" width="0pt">
3859 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
3862 \begin_layout Plain Layout
3868 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
3871 \begin_layout Plain Layout
3873 \begin_inset Note Note
3876 \begin_layout Plain Layout
3883 is only used as spacer.
3895 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
3898 \begin_layout Plain Layout
3902 \begin_inset space \textvisiblespace{}
3906 \begin_inset Index idx
3909 \begin_layout Plain Layout
3922 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
3925 \begin_layout Plain Layout
3926 \begin_inset Formula $\raisebox{5mm}{}\overline{A+B}$
3936 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
3939 \begin_layout Plain Layout
3943 \begin_inset space \textvisiblespace{}
3947 \begin_inset Index idx
3950 \begin_layout Plain Layout
3963 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
3966 \begin_layout Plain Layout
3967 \begin_inset Formula $\underline{A+B}\raisebox{-2.5mm}{}$
3977 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
3980 \begin_layout Plain Layout
3984 \begin_inset space \textvisiblespace{}
3990 \begin_inset space \textvisiblespace{}
3998 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
4001 \begin_layout Plain Layout
4002 \begin_inset Formula $\raisebox{5mm}{}\overline{\underline{A+B}}\raisebox{-2.5mm}{}$
4018 \begin_layout Standard
4019 In the last example it doesn't matter if first
4034 \begin_layout Standard
4035 To double underline use
4044 \begin_layout Standard
4045 It is possible to place up to 6 lines above or below characters.
4048 \begin_layout Standard
4049 \begin_inset VSpace bigskip
4052 Custom lines can be created using the command
4059 \begin_inset Index idx
4062 \begin_layout Plain Layout
4070 which has the following scheme:
4073 \begin_layout Standard
4078 rule[vertical offset]{length}{thickness}
4081 \begin_layout Standard
4082 The optional vertical offset shifts the line upwards (or downwards, when
4083 the value is negative).
4085 \begin_inset CommandInset ref
4087 reference "tab:Available-units"
4091 can be used for the values.
4092 Here are two example lines created with the commands
4093 \begin_inset Newline newline
4100 rule[-2ex]{3cm}{2pt}
4111 \begin_layout Standard
4113 \begin_inset Formula $\rule[-2ex]{3cm}{2pt}\rule{2cm}{1pt}$
4119 \begin_layout Standard
4126 can also be used for text when a line is inserted via the menu
4128 Insert\SpecialChar \menuseparator
4129 Formatting\SpecialChar \menuseparator
4131 \begin_inset space ~
4139 \begin_layout Standard
4141 \begin_inset CommandInset line
4152 \begin_layout Subsection
4154 \begin_inset CommandInset label
4161 \begin_inset Index idx
4164 \begin_layout Plain Layout
4173 \begin_layout Standard
4174 There are different types of ellipses available.
4178 \begin_layout Plain Layout
4179 In the math toolbar in the submenu of the button
4182 arg "math-insert \\ldots"
4190 For listings dots at the baseline are used (
4197 \begin_inset Index idx
4200 \begin_layout Plain Layout
4208 ), while for operations dots are needed that are on the same height as the
4216 \begin_inset Index idx
4219 \begin_layout Plain Layout
4228 When using the command
4235 \begin_inset Index idx
4238 \begin_layout Plain Layout
4246 , LaTeX decides on the basis of the next character what type is used.
4249 \begin_layout Standard
4251 \begin_inset Tabular
4252 <lyxtabular version="3" rows="9" columns="2">
4253 <features rotate="0" tabularvalignment="middle">
4254 <column alignment="center" valignment="top" width="0pt">
4255 <column alignment="center" valignment="top" width="0pt">
4257 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
4260 \begin_layout Plain Layout
4266 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
4269 \begin_layout Plain Layout
4277 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
4280 \begin_layout Plain Layout
4282 \begin_inset space \textvisiblespace{}
4288 \begin_inset space \textvisiblespace{}
4296 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
4299 \begin_layout Plain Layout
4300 \begin_inset Formula $A_{1},\dots,A_{n}$
4310 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
4313 \begin_layout Plain Layout
4315 \begin_inset space \textvisiblespace{}
4321 \begin_inset space \textvisiblespace{}
4329 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
4332 \begin_layout Plain Layout
4333 \begin_inset Formula $A_{1}+\dots+A_{n}$
4343 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
4346 \begin_layout Plain Layout
4348 \begin_inset space \textvisiblespace{}
4354 \begin_inset space \textvisiblespace{}
4362 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
4365 \begin_layout Plain Layout
4366 \begin_inset Formula $A_{1},\ldots,A_{n}$
4376 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
4379 \begin_layout Plain Layout
4381 \begin_inset space \textvisiblespace{}
4387 \begin_inset space \textvisiblespace{}
4395 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
4398 \begin_layout Plain Layout
4399 \begin_inset Formula $A_{1}+\cdots+A_{n}$
4409 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
4412 \begin_layout Plain Layout
4420 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
4423 \begin_layout Plain Layout
4424 \begin_inset Formula $\vdots$
4434 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
4437 \begin_layout Plain Layout
4445 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
4448 \begin_layout Plain Layout
4449 \begin_inset Formula $\ddots$
4459 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
4462 \begin_layout Plain Layout
4470 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
4473 \begin_layout Plain Layout
4474 \begin_inset Formula $\iddots$
4484 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
4487 \begin_layout Plain Layout
4489 \begin_inset space \thinspace{}
4492 matrix with the different dots
4497 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
4500 \begin_layout Plain Layout
4501 \begin_inset Formula $\begin{array}{ccc}
4502 A_{11} & \cdots & A_{1m}\\
4503 \vdots & \ddots & \vdots\\
4504 A_{n1} & \cdots & A_{nm}
4521 \begin_layout Standard
4522 The ellipses available in menu
4524 Insert\SpecialChar \menuseparator
4526 \begin_inset space ~
4540 \begin_layout Standard
4541 \begin_inset VSpace medskip
4550 , one of the options
4552 Use mathdots package (automatically)
4554 must be set in the document settings under
4557 \begin_inset space ~
4563 \begin_inset Newline newline
4568 Use mathdots package
4570 will improve the appearance of all dots in the documents if their font
4571 style or size is not the default.
4574 \begin_layout Standard
4575 \begin_inset VSpace medskip
4578 Specially for matrices there are ellipses that span over several columns.
4579 They are created with the command
4586 \begin_inset Index idx
4589 \begin_layout Plain Layout
4597 , that has the following scheme:
4600 \begin_layout Standard
4605 hdotsfor[distance]{number of columns}
4608 \begin_layout Standard
4609 The number of columns specifies how many columns should be spanned.
4610 Distance is a factor for the distance between the dots.
4613 \begin_layout Standard
4614 In the following matrix the command
4620 was inserted in the first box of the second line, to get an ellipsis with
4621 a dot distance twice as long as with the command
4628 \begin_inset Formula
4630 \left(\begin{array}{cccc}
4639 Note that the matrix fields that should be spanned must be empty, otherwise
4640 you get LaTeX-errors.
4643 \begin_layout Standard
4644 \begin_inset VSpace bigskip
4647 Furthermore you can fill with the command
4654 \begin_inset Index idx
4657 \begin_layout Plain Layout
4665 the rest of a line with dots.
4666 The effect of these commands is the same as with
4673 \begin_inset CommandInset ref
4675 reference "sub:Variable-Space"
4682 \begin_layout Standard
4683 For example the command
4688 \begin_inset space \textvisiblespace{}
4696 \begin_layout Standard
4697 \begin_inset Formula $A\dotfill B$
4703 \begin_layout Standard
4710 there is for a line the command
4717 \begin_inset Index idx
4720 \begin_layout Plain Layout
4731 \begin_layout Standard
4732 \begin_inset Formula $A\hrulefill B$
4738 \begin_layout Standard
4739 To use the commands for text, they have to be inserted in TeX-mode.
4742 \begin_layout Section
4744 \begin_inset CommandInset label
4751 \begin_inset Index idx
4754 \begin_layout Plain Layout
4763 \begin_layout Standard
4764 Matrices can be inserted via the math toolbar button
4767 arg "dialog-show mathmatrix"
4772 Insert\SpecialChar \menuseparator
4773 Math\SpecialChar \menuseparator
4777 In the matrix dialog you can specify the number of columns and rows, the
4778 alignment and the decoration.
4779 The vertical alignment is only of importance for matrices in inline formulas:
4782 \begin_layout Standard
4783 The first matrix is top
4784 \begin_inset Formula $\begin{array}[t]{cccc}
4792 \begin_inset Formula $\begin{array}{cccc}
4799 and the third bottom
4800 \begin_inset Formula $\begin{array}[b]{cccc}
4810 \begin_layout Standard
4811 The horizontal alignment specifies how the column entries should be aligned.
4812 It is set by entering a letter for every column.
4817 denotes left aligned,
4826 To create for example a 4
4831 \begin_inset space ~
4834 matrix where the first column is left aligned, the second and third are
4835 centered and the last one is right aligned, one enters for the horizontal
4841 Normally in a matrix all columns are centered, therefore the default for
4849 \begin_layout Standard
4850 Horizontal alignment:
4853 \begin_layout Standard
4859 \begin_inset Formula $\begin{array}{lll}
4871 \begin_inset Formula $\begin{array}{ccc}
4883 \begin_inset Formula $\begin{array}{rrr}
4893 \begin_layout Standard
4894 To add or delete rows and columns subsequently, the math toolbar buttons
4898 arg "inset-modify tabular append-row"
4904 arg "inset-modify tabular delete-row"
4908 \begin_inset space \thinspace{}
4913 Edit\SpecialChar \menuseparator
4917 New rows can also be created with
4920 arg "newline-insert newline"
4926 \begin_layout Standard
4927 \begin_inset VSpace bigskip
4934 adds parentheses in the selected style around the matrix.
4935 Alternatively, parentheses can can either be created with the commands
4943 \begin_inset Index idx
4946 \begin_layout Plain Layout
4961 \begin_inset Index idx
4964 \begin_layout Plain Layout
4975 \begin_inset space ~
4981 \begin_inset CommandInset ref
4983 reference "sub:Automatic-Bracket-Size"
4987 , or by using the following commands:
4988 \begin_inset VSpace medskip
4994 \begin_layout Standard
4995 \begin_inset space \hfill{}
4999 \begin_inset Tabular
5000 <lyxtabular version="3" rows="4" columns="2">
5001 <features rotate="0" tabularvalignment="middle">
5002 <column alignment="center" valignment="top">
5003 <column alignment="center" valignment="top">
5005 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
5008 \begin_layout Plain Layout
5014 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
5017 \begin_layout Plain Layout
5019 \begin_inset Note Note
5022 \begin_layout Plain Layout
5029 is only used as spacer.
5041 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
5044 \begin_layout Plain Layout
5048 \begin_inset space \textvisiblespace{}
5056 \begin_inset space \thinspace{}
5064 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
5067 \begin_layout Plain Layout
5068 \begin_inset Formula $\raisebox{7.5mm}{}\begin{bmatrix}\begin{array}{cc}
5069 0 & \textrm{-}\mathrm{i}\\
5071 \end{array}\end{bmatrix}\raisebox{-5.3mm}{}$
5081 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
5084 \begin_layout Plain Layout
5088 \begin_inset space \textvisiblespace{}
5096 \begin_inset space \thinspace{}
5104 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
5107 \begin_layout Plain Layout
5108 \begin_inset Formula $\raisebox{7.5mm}{}\begin{Bmatrix}\begin{array}{cc}
5109 0 & \textrm{-}\mathrm{i}\\
5111 \end{array}\end{Bmatrix}\raisebox{-5.3mm}{}$
5121 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
5124 \begin_layout Plain Layout
5128 \begin_inset space \textvisiblespace{}
5136 \begin_inset space \thinspace{}
5144 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
5147 \begin_layout Plain Layout
5148 \begin_inset Formula $\raisebox{7.5mm}{}\begin{pmatrix}\begin{array}{cc}
5149 0 & \textrm{-}\mathrm{i}\\
5151 \end{array}\end{pmatrix}\raisebox{-5.3mm}{}$
5165 \begin_inset space \hfill{}
5169 \begin_inset Tabular
5170 <lyxtabular version="3" rows="4" columns="2">
5171 <features rotate="0" tabularvalignment="middle">
5172 <column alignment="center" valignment="top">
5173 <column alignment="center" valignment="top">
5175 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
5178 \begin_layout Plain Layout
5184 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
5187 \begin_layout Plain Layout
5195 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
5198 \begin_layout Plain Layout
5202 \begin_inset space \textvisiblespace{}
5210 \begin_inset space \thinspace{}
5218 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
5221 \begin_layout Plain Layout
5222 \begin_inset Formula $\raisebox{7.5mm}{}\begin{vmatrix}\begin{array}{cc}
5223 0 & \textrm{-}\mathrm{i}\\
5225 \end{array}\end{vmatrix}\raisebox{-5.3mm}{}$
5235 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
5238 \begin_layout Plain Layout
5242 \begin_inset space \textvisiblespace{}
5250 \begin_inset space \thinspace{}
5258 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
5261 \begin_layout Plain Layout
5262 \begin_inset Formula $\raisebox{7.5mm}{}\begin{Vmatrix}\begin{array}{cc}
5263 0 & \textrm{-}\mathrm{i}\\
5265 \end{array}\end{Vmatrix}\raisebox{-5.3mm}{}$
5275 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
5278 \begin_layout Plain Layout
5282 \begin_inset space \textvisiblespace{}
5290 \begin_inset space \thinspace{}
5298 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
5301 \begin_layout Plain Layout
5302 \begin_inset Formula $\raisebox{7.5mm}{}\begin{matrix}\begin{array}{cc}
5303 0 & \textrm{-}\mathrm{i}\\
5305 \end{array}\end{matrix}\raisebox{-5.3mm}{}$
5319 \begin_inset space \hfill{}
5325 \begin_layout Standard
5326 \begin_inset VSpace medskip
5330 \begin_inset space \thinspace{}
5334 \begin_inset space \space{}
5343 is inserted, a blue box appears between two vertical lines where the matrix
5345 \begin_inset Newline newline
5348 Note that decorated matrices ignore the vertical alignment.
5351 \begin_layout Standard
5352 \begin_inset VSpace bigskip
5355 As all multiline formulas are matrices, the length
5362 \begin_inset Index idx
5365 \begin_layout Plain Layout
5373 that is described in
5374 \begin_inset CommandInset ref
5376 reference "sub:Column-Separation"
5380 can also be used to change the column separation of matrices.
5383 \begin_layout Standard
5384 To change the row separation, the command
5391 \begin_inset Index idx
5394 \begin_layout Plain Layout
5403 It is used as follows:
5406 \begin_layout Standard
5413 arraystretch}{stretch factor}
5414 \begin_inset Index idx
5417 \begin_layout Plain Layout
5428 \begin_layout Standard
5435 assigns the stretch factor to the predefined command
5443 \begin_inset space \thinspace{}
5447 \begin_inset space \space{}
5450 the row separation, use the factor 2.
5451 This is then used for all following matrices.
5452 To go back to the original separation, assign the factor 1 to
5461 \begin_layout Standard
5462 To set matrices into a text line, the command
5469 \begin_inset Index idx
5472 \begin_layout Plain Layout
5481 When it is inserted a blue box with two dashed lines appears.
5482 In this box the matrix is inserted.
5485 \begin_layout Standard
5487 \begin_inset Formula $\left(\begin{smallmatrix}A & B\\
5489 \end{smallmatrix}\right)$
5495 \begin_layout Section
5496 Brackets and Delimiters
5497 \begin_inset Index idx
5500 \begin_layout Plain Layout
5507 \begin_inset Index idx
5510 \begin_layout Plain Layout
5519 \begin_layout Subsection
5520 Vertical Brackets and Delimiters
5521 \begin_inset Index idx
5524 \begin_layout Plain Layout
5533 \begin_layout Standard
5534 \begin_inset space \hfill{}
5538 \begin_inset Tabular
5539 <lyxtabular version="3" rows="9" columns="2">
5540 <features rotate="0" tabularvalignment="middle">
5541 <column alignment="center" valignment="top" width="0pt">
5542 <column alignment="center" valignment="top" width="0pt">
5544 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
5547 \begin_layout Plain Layout
5553 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
5556 \begin_layout Plain Layout
5564 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
5567 \begin_layout Plain Layout
5573 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
5576 \begin_layout Plain Layout
5577 \begin_inset Formula $($
5587 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
5590 \begin_layout Plain Layout
5596 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
5599 \begin_layout Plain Layout
5600 \begin_inset Formula $\{$
5610 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
5613 \begin_layout Plain Layout
5619 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
5622 \begin_layout Plain Layout
5623 \begin_inset Formula $[$
5633 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
5636 \begin_layout Plain Layout
5644 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
5647 \begin_layout Plain Layout
5648 \begin_inset Formula $\langle$
5658 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
5661 \begin_layout Plain Layout
5669 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
5672 \begin_layout Plain Layout
5673 \begin_inset Formula $\lceil$
5683 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
5686 \begin_layout Plain Layout
5694 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
5697 \begin_layout Plain Layout
5698 \begin_inset Formula $\lfloor$
5708 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
5711 \begin_layout Plain Layout
5717 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
5720 \begin_layout Plain Layout
5721 \begin_inset Formula $/$
5731 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
5734 \begin_layout Plain Layout
5740 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
5743 \begin_layout Plain Layout
5744 \begin_inset Formula $|$
5758 \begin_inset space \hfill{}
5762 \begin_inset Tabular
5763 <lyxtabular version="3" rows="9" columns="2">
5764 <features rotate="0" tabularvalignment="middle">
5765 <column alignment="center" valignment="top" width="0pt">
5766 <column alignment="center" valignment="top" width="0pt">
5768 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
5771 \begin_layout Plain Layout
5777 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
5780 \begin_layout Plain Layout
5788 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
5791 \begin_layout Plain Layout
5797 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
5800 \begin_layout Plain Layout
5801 \begin_inset Formula $)$
5811 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
5814 \begin_layout Plain Layout
5820 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
5823 \begin_layout Plain Layout
5824 \begin_inset Formula $\}$
5834 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
5837 \begin_layout Plain Layout
5843 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
5846 \begin_layout Plain Layout
5847 \begin_inset Formula $]$
5857 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
5860 \begin_layout Plain Layout
5868 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
5871 \begin_layout Plain Layout
5872 \begin_inset Formula $\rangle$
5882 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
5885 \begin_layout Plain Layout
5893 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
5896 \begin_layout Plain Layout
5897 \begin_inset Formula $\rceil$
5907 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
5910 \begin_layout Plain Layout
5918 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
5921 \begin_layout Plain Layout
5922 \begin_inset Formula $\rfloor$
5932 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
5935 \begin_layout Plain Layout
5945 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
5948 \begin_layout Plain Layout
5949 \begin_inset Formula $\backslash$
5959 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
5962 \begin_layout Plain Layout
5970 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
5973 \begin_layout Plain Layout
5974 \begin_inset Formula $\|$
5988 \begin_inset space \hfill{}
5994 \begin_layout Standard
5997 \begin_inset Note Greyedout
6000 \begin_layout Plain Layout
6005 In TeX-mode the command
6012 \begin_inset Index idx
6015 \begin_layout Plain Layout
6023 must be used for the backslash, because the command
6031 produces a line break there.
6039 \begin_layout Standard
6040 For all characters listed above the size can be adjusted with the commands
6041 described in the following two subsections.
6042 When using these commands, the characters < and > can directly be used
6043 instead of the commands
6058 \begin_layout Subsubsection
6060 \begin_inset CommandInset label
6062 name "sub:Manual-Bracket-Size"
6067 \begin_inset Index idx
6070 \begin_layout Plain Layout
6071 Bracket size ! manual
6079 \begin_layout Standard
6080 The bracket size can be specified manually by the LaTeX-commands
6087 \begin_inset Index idx
6090 \begin_layout Plain Layout
6123 denotes the smallest and
6129 the largest bracket size.
6132 \begin_layout Standard
6133 These commands are used to emphasize levels of brackets:
6136 \begin_layout Standard
6138 \begin_inset Tabular
6139 <lyxtabular version="3" rows="2" columns="2">
6140 <features rotate="0" tabularvalignment="middle">
6141 <column alignment="center" valignment="top" width="0pt">
6142 <column alignment="center" valignment="top" width="0pt">
6144 <cell alignment="center" valignment="top" usebox="none">
6147 \begin_layout Plain Layout
6148 all brackets in the same size:
6153 <cell alignment="center" valignment="top" usebox="none">
6156 \begin_layout Plain Layout
6157 \begin_inset Formula $((A+B)(A-B))^{C}\raisebox{-4mm}{}$
6167 <cell alignment="center" valignment="top" usebox="none">
6170 \begin_layout Plain Layout
6176 <cell alignment="center" valignment="top" usebox="none">
6179 \begin_layout Plain Layout
6180 \begin_inset Formula $\Big((A+B)(A-B)\Big)^{C}$
6194 \begin_inset Note Note
6197 \begin_layout Plain Layout
6204 is only used as spacer.
6212 \begin_layout Standard
6213 For the second formula the command
6220 \begin_inset space \textvisiblespace{}
6228 \begin_layout Standard
6229 Here is an overview about all bracket sizes:
6232 \begin_layout Standard
6249 \begin_inset space \textvisiblespace{}
6257 \begin_inset space \textvisiblespace{}
6261 \begin_inset space \textvisiblespace{}
6271 \begin_layout Standard
6273 \begin_inset Formula $\Bigg(\exp\bigg<\Big[\big\{\ln(3x)\big\}^{2}\sin(x)\Big]^{A}\bigg>\Bigg)^{0,5}$
6279 \begin_layout Standard
6286 -commands there is the variant
6293 \begin_inset Index idx
6296 \begin_layout Plain Layout
6304 that adds a bit more space between the bracket and its content, and the
6318 \begin_inset Index idx
6321 \begin_layout Plain Layout
6331 , that don't add additional space.
6336 at the end of the command
6342 is for a left bracket; for a right bracket this will be replaced by an
6348 A left or right bracket can each be an opening or closing bracket.
6351 \begin_layout Standard
6352 In the following table is a comparison of the variants:
6355 \begin_layout Standard
6357 \begin_inset Tabular
6358 <lyxtabular version="3" rows="5" columns="2">
6359 <features rotate="0" tabularvalignment="middle">
6360 <column alignment="center" valignment="middle">
6361 <column alignment="center" valignment="middle">
6363 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
6366 \begin_layout Plain Layout
6372 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
6375 \begin_layout Plain Layout
6377 \begin_inset Note Note
6380 \begin_layout Plain Layout
6387 is only used as spacer.
6399 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
6402 \begin_layout Plain Layout
6412 \begin_inset space \textvisiblespace{}
6422 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
6425 \begin_layout Plain Layout
6426 \begin_inset Formula $\raisebox{5.5mm}{}\Bigm(\bigm(\ln(3x)\bigm)^{2}\Bigm)\raisebox{-3.25mm}{}$
6436 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
6439 \begin_layout Plain Layout
6449 \begin_inset space \textvisiblespace{}
6459 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
6462 \begin_layout Plain Layout
6463 \begin_inset Formula $\raisebox{5.5mm}{}\Big(\big(\ln(3x)\big)^{2}\Big)\raisebox{-3.25mm}{}$
6473 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
6476 \begin_layout Plain Layout
6486 \begin_inset space \textvisiblespace{}
6496 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
6499 \begin_layout Plain Layout
6500 \begin_inset Formula $\raisebox{5.5mm}{}\Bigl(\bigl(\ln(3x)\bigr)^{2}\Bigr)\raisebox{-3.25mm}{}$
6510 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
6513 \begin_layout Plain Layout
6525 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
6528 \begin_layout Plain Layout
6529 \begin_inset Formula $\raisebox{4.5mm}{}\bigl)\ln(3x)\bigr(\raisebox{-2mm}{}$
6545 \begin_layout Subsubsection
6546 Automatic Bracket Size
6547 \begin_inset CommandInset label
6549 name "sub:Automatic-Bracket-Size"
6554 \begin_inset Index idx
6557 \begin_layout Plain Layout
6558 Bracket size ! automatic
6566 \begin_layout Standard
6567 Brackets with variable size can be inserted with the commands
6574 \begin_inset Index idx
6577 \begin_layout Plain Layout
6592 \begin_inset Index idx
6595 \begin_layout Plain Layout
6603 or via the math toolbar button
6606 arg "dialog-show mathdelimiter"
6622 the wanted bracket must be inserted.
6623 The bracket size will then automatically be calculated for the output.
6626 \begin_layout Standard
6628 normal bracket: The command
6635 \begin_inset space \textvisiblespace{}
6639 \begin_inset Formula $\downarrow$
6643 \begin_inset space \textvisiblespace{}
6649 \begin_inset Formula
6659 \begin_layout Standard
6661 multiline bracket: The command
6670 \begin_inset space \textvisiblespace{}
6674 \begin_inset Formula $\downarrow$
6678 \begin_inset space \textvisiblespace{}
6686 \begin_inset Formula
6688 \ln\left(\frac{A}{C}\right)
6696 \begin_layout Standard
6712 \begin_inset space ~
6718 This has the advantage that you can see in LyX immediately the real bracket
6719 size and that the matching right bracket will be created too.
6720 \begin_inset Newline newline
6723 The command for the last example would then be:
6734 \begin_inset space \textvisiblespace{}
6738 \begin_inset Formula $\downarrow$
6744 \begin_layout Standard
6745 To omit a left or right bracket, a dot is inserted for the omitted bracket.
6746 For example the command
6753 \begin_inset space \textvisiblespace{}
6757 \begin_inset Formula $\downarrow$
6761 \begin_inset space \textvisiblespace{}
6771 \begin_inset Formula
6773 \left.\frac{A}{B}\right\}
6792 will be converted by LyX to brackets in the right size when the document
6793 is reloaded and an omitted bracket will appear as dashed line.
6796 \begin_layout Standard
6797 \begin_inset VSpace bigskip
6800 Because all popular LaTeX-Distributions use eTeX, an extension to LaTeX,
6808 \begin_inset Index idx
6811 \begin_layout Plain Layout
6819 is additionally available for all brackets and limits.
6820 With this command the height of the following character is adapted to the
6821 one of the surrounding brackets, what is e.
6822 \begin_inset space \thinspace{}
6826 \begin_inset space \space{}
6829 needed for physical vectors:
6830 \begin_inset Formula
6832 \left\langle \phi\:\middle|\: J=\frac{3}{2}\,,\, M_{J}\right\rangle
6837 For physical vectors there is a special LaTeX-package, described in
6838 \begin_inset CommandInset ref
6840 reference "sub:Physical-Vectors"
6847 \begin_layout Subsection
6849 \begin_inset Index idx
6852 \begin_layout Plain Layout
6853 Brackets ! horizontal
6861 \begin_layout Standard
6863 \begin_inset Tabular
6864 <lyxtabular version="3" rows="4" columns="2">
6865 <features rotate="0" tabularvalignment="middle">
6866 <column alignment="center" valignment="top" width="0pt">
6867 <column alignment="center" valignment="top" width="0pt">
6869 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
6872 \begin_layout Plain Layout
6874 \begin_inset Note Note
6877 \begin_layout Plain Layout
6884 is only used as spacer.
6894 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
6897 \begin_layout Plain Layout
6905 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
6908 \begin_layout Plain Layout
6912 \begin_layout Plain Layout
6924 \begin_inset space \textvisiblespace{}
6928 \begin_inset space \textvisiblespace{}
6935 \begin_layout Plain Layout
6943 \begin_inset Index idx
6946 \begin_layout Plain Layout
6959 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
6962 \begin_layout Plain Layout
6963 \begin_inset Formula $\overbrace{A+B}^{3}$
6973 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
6976 \begin_layout Plain Layout
6980 \begin_layout Plain Layout
6992 \begin_inset space \textvisiblespace{}
6996 \begin_inset space \textvisiblespace{}
7003 \begin_layout Plain Layout
7011 \begin_inset Index idx
7014 \begin_layout Plain Layout
7027 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
7030 \begin_layout Plain Layout
7031 \begin_inset Formula $\underbrace{A+B}_{5}$
7041 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
7044 \begin_layout Plain Layout
7048 \begin_inset space \textvisiblespace{}
7054 \begin_inset space \textvisiblespace{}
7058 \begin_inset space \textvisiblespace{}
7062 \begin_inset space \textvisiblespace{}
7066 \begin_inset space \textvisiblespace{}
7070 \begin_inset space \textvisiblespace{}
7074 \begin_inset space \textvisiblespace{}
7082 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
7085 \begin_layout Plain Layout
7086 \begin_inset Formula $\overbrace{\underbrace{A+B_{w}}_{7}}^{C}$
7102 \begin_layout Standard
7103 In the last example it doesn't matter if
7115 is inserted at first.
7118 \begin_layout Standard
7119 \begin_inset VSpace bigskip
7122 When brackets are needed that overlap each other, multiline formulas, as
7124 \begin_inset CommandInset ref
7126 reference "sec:Multiline-Formulas"
7131 \begin_inset Formula
7133 A & = & \underbrace{gggg+bbqq}_{r}+\: dddd\\
7134 & & \hphantom{gggg+\:}\underbrace{\hphantom{bbqq+dddd}}_{s}
7139 In the first row the formula is inserted together with the first brace.
7140 It is hereby important that the space command
7144 \begin_layout Plain Layout
7145 Space commands are explained in
7146 \begin_inset CommandInset ref
7148 reference "sub:Predefined-Space"
7163 is inserted before the first
7164 \begin_inset Formula $d$
7167 , because the brace that ends behind the
7168 \begin_inset Formula $q$
7171 prevents that the following
7172 \begin_inset Quotes eld
7176 \begin_inset Quotes erd
7179 is surrounded by space.
7183 \begin_layout Plain Layout
7184 because a bracket is not handled as a character, see
7185 \begin_inset CommandInset ref
7187 reference "sub:Binary-Operators"
7196 In the second row the second brace is inserted.
7197 As it should begin before the
7198 \begin_inset Formula $b$
7213 \begin_layout Plain Layout
7221 \begin_inset CommandInset ref
7223 reference "sub:Placeholders"
7232 This space is needed because the
7233 \begin_inset Quotes eld
7237 \begin_inset Quotes erd
7240 is also surrounded by space in the formula.
7241 The brace is placed under the command
7250 \begin_layout Standard
7251 It gets more complicated when brackets overlap each other, like in the following
7256 \begin_layout Plain Layout
7268 \begin_inset Formula
7270 & & \hphantom{gggg+\:}\overbrace{\hphantom{bbqq+dddd}}^{s}\\
7271 A & = & \underbrace{gggg+bbqq}_{r}+\: dddd
7280 \begin_layout Plain Layout
7291 The first formula row is the same as the second row of the previous example,
7292 with the difference that the brace is above.
7293 The second row contains the formula together with the second brace.
7294 To avoid that there is space between the upper brace in the first row and
7295 the formula, the row spacing needs to be reduced.
7296 This is not easily possible due to a bug in LyX
7300 \begin_layout Plain Layout
7301 \begin_inset CommandInset href
7303 name "LyX-bug #1505"
7304 target "http://www.lyx.org/trac/ticket/1505"
7314 As a solution for the problem, the global formula row separation
7321 \begin_inset Index idx
7324 \begin_layout Plain Layout
7332 must be changed to -6
7333 \begin_inset space \thinspace{}
7336 pt before the formula with the command
7351 is set back after the formula to the standard value of 3
7352 \begin_inset space \thinspace{}
7355 pt using the same command.
7356 More about the row separation in formulas is explained in
7357 \begin_inset CommandInset ref
7359 reference "sub:Line-Separation"
7366 \begin_layout Section
7368 \begin_inset Index idx
7371 \begin_layout Plain Layout
7380 \begin_layout Standard
7381 Arrows can be inserted via the math toolbar button
7384 arg "math-insert \\leftarrow"
7387 or the commands listed in the following subsections.
7390 \begin_layout Subsection
7392 \begin_inset Index idx
7395 \begin_layout Plain Layout
7404 \begin_layout Standard
7405 \begin_inset space \hfill{}
7409 \begin_inset Tabular
7410 <lyxtabular version="3" rows="8" columns="2">
7411 <features rotate="0" tabularvalignment="middle">
7412 <column alignment="center" valignment="top" width="0pt">
7413 <column alignment="center" valignment="top" width="0pt">
7415 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
7418 \begin_layout Plain Layout
7424 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
7427 \begin_layout Plain Layout
7435 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
7438 \begin_layout Plain Layout
7446 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
7449 \begin_layout Plain Layout
7450 \begin_inset Formula $\gets$
7460 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
7463 \begin_layout Plain Layout
7471 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
7474 \begin_layout Plain Layout
7475 \begin_inset Formula $\Leftarrow$
7485 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
7488 \begin_layout Plain Layout
7496 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
7499 \begin_layout Plain Layout
7500 \begin_inset Formula $\longleftarrow$
7510 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
7513 \begin_layout Plain Layout
7521 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
7524 \begin_layout Plain Layout
7525 \begin_inset Formula $\Longleftarrow$
7535 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
7538 \begin_layout Plain Layout
7546 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
7549 \begin_layout Plain Layout
7550 \begin_inset Formula $\leftharpoonup$
7560 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
7563 \begin_layout Plain Layout
7571 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
7574 \begin_layout Plain Layout
7575 \begin_inset Formula $\leftharpoondown$
7585 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
7588 \begin_layout Plain Layout
7596 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
7599 \begin_layout Plain Layout
7600 \begin_inset Formula $\hookleftarrow$
7614 \begin_inset space \hfill{}
7618 \begin_inset Tabular
7619 <lyxtabular version="3" rows="8" columns="2">
7620 <features rotate="0" tabularvalignment="middle">
7621 <column alignment="center" valignment="top" width="0pt">
7622 <column alignment="center" valignment="top" width="0pt">
7624 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
7627 \begin_layout Plain Layout
7633 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
7636 \begin_layout Plain Layout
7644 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
7647 \begin_layout Plain Layout
7655 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
7658 \begin_layout Plain Layout
7659 \begin_inset Formula $\to$
7669 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
7672 \begin_layout Plain Layout
7680 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
7683 \begin_layout Plain Layout
7684 \begin_inset Formula $\Rightarrow$
7694 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
7697 \begin_layout Plain Layout
7705 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
7708 \begin_layout Plain Layout
7709 \begin_inset Formula $\longrightarrow$
7719 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
7722 \begin_layout Plain Layout
7730 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
7733 \begin_layout Plain Layout
7734 \begin_inset Formula $\Longrightarrow$
7744 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
7747 \begin_layout Plain Layout
7755 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
7758 \begin_layout Plain Layout
7759 \begin_inset Formula $\rightharpoonup$
7769 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
7772 \begin_layout Plain Layout
7780 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
7783 \begin_layout Plain Layout
7784 \begin_inset Formula $\rightharpoondown$
7794 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
7797 \begin_layout Plain Layout
7805 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
7808 \begin_layout Plain Layout
7809 \begin_inset Formula $\hookrightarrow$
7823 \begin_inset space \hfill{}
7829 \begin_layout Standard
7830 \begin_inset space \hfill{}
7834 \begin_inset Tabular
7835 <lyxtabular version="3" rows="6" columns="2">
7836 <features rotate="0" tabularvalignment="middle">
7837 <column alignment="center" valignment="top" width="0pt">
7838 <column alignment="center" valignment="top" width="0pt">
7840 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
7843 \begin_layout Plain Layout
7849 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
7852 \begin_layout Plain Layout
7860 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
7863 \begin_layout Plain Layout
7871 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
7874 \begin_layout Plain Layout
7875 \begin_inset Formula $\leftrightarrow$
7885 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
7888 \begin_layout Plain Layout
7896 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
7899 \begin_layout Plain Layout
7900 \begin_inset Formula $\Leftrightarrow$
7910 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
7913 \begin_layout Plain Layout
7921 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
7924 \begin_layout Plain Layout
7925 \begin_inset Formula $\longleftrightarrow$
7935 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
7938 \begin_layout Plain Layout
7946 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
7949 \begin_layout Plain Layout
7950 \begin_inset Formula $\Longleftrightarrow$
7960 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
7963 \begin_layout Plain Layout
7971 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
7974 \begin_layout Plain Layout
7975 \begin_inset Formula $\rightleftharpoons$
7989 \begin_inset space \hspace{}
7994 \begin_inset space \hfill{}
7998 \begin_inset Tabular
7999 <lyxtabular version="3" rows="5" columns="2">
8000 <features rotate="0" tabularvalignment="middle">
8001 <column alignment="center" valignment="top" width="0pt">
8002 <column alignment="center" valignment="top" width="0pt">
8004 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
8007 \begin_layout Plain Layout
8013 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
8016 \begin_layout Plain Layout
8024 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
8027 \begin_layout Plain Layout
8035 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
8038 \begin_layout Plain Layout
8039 \begin_inset Formula $\mapsto$
8049 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
8052 \begin_layout Plain Layout
8060 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
8063 \begin_layout Plain Layout
8064 \begin_inset Formula $\longmapsto$
8074 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
8077 \begin_layout Plain Layout
8085 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
8088 \begin_layout Plain Layout
8089 \begin_inset Formula $\leadsto$
8099 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
8102 \begin_layout Plain Layout
8110 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
8113 \begin_layout Plain Layout
8114 \begin_inset Formula $\dasharrow$
8128 \begin_inset space \hfill{}
8134 \begin_layout Standard
8135 \begin_inset VSpace medskip
8138 Arrows used as accents like e.
8139 \begin_inset space \thinspace{}
8143 \begin_inset space \space{}
8146 vector arrows are listed in
8147 \begin_inset CommandInset ref
8149 reference "sec:Accents"
8156 \begin_layout Standard
8157 \begin_inset VSpace bigskip
8160 Furthermore there are the labeled arrows
8161 \begin_inset Index idx
8164 \begin_layout Plain Layout
8177 \begin_inset Index idx
8180 \begin_layout Plain Layout
8195 \begin_inset Index idx
8198 \begin_layout Plain Layout
8205 \begin_layout Plain Layout
8220 When inserting one of these commands in a formula, an arrow with two blue
8221 boxes appear where the label can be inserted.
8222 The length of the arrow adapts to the label width.
8225 \begin_layout Standard
8227 \begin_inset Tabular
8228 <lyxtabular version="3" rows="3" columns="2">
8229 <features rotate="0" tabularvalignment="middle">
8230 <column alignment="center" valignment="top" width="0pt">
8231 <column alignment="center" valignment="top" width="0pt">
8233 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
8236 \begin_layout Plain Layout
8242 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
8245 \begin_layout Plain Layout
8247 \begin_inset Note Note
8250 \begin_layout Plain Layout
8257 is only used as spacer.
8269 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
8272 \begin_layout Plain Layout
8276 \begin_inset space \textvisiblespace{}
8280 \begin_inset Formula $\downarrow$
8284 \begin_inset Formula $\to$
8292 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
8295 \begin_layout Plain Layout
8296 \begin_inset Formula $\raisebox{5.5mm}{}F(a)\xleftarrow[x>0]{x=a}F(x)\raisebox{-4mm}{}$
8306 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
8309 \begin_layout Plain Layout
8313 \begin_inset space \textvisiblespace{}
8317 \begin_inset Formula $\downarrow$
8321 \begin_inset Formula $\to$
8329 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
8332 \begin_layout Plain Layout
8333 \begin_inset Formula $\raisebox{5.5mm}{}F(x)\xrightarrow[x>0]{x=a}F(a)\raisebox{-4mm}{}$
8349 \begin_layout Standard
8350 \begin_inset VSpace medskip
8356 \begin_layout Standard
8357 If you set in the document settings under
8360 \begin_inset space ~
8370 \begin_inset Index idx
8373 \begin_layout Plain Layout
8374 Packages ! mathtools
8382 \begin_inset space ~
8387 , you have access to the following labeled arrows:
8390 \begin_layout Standard
8392 \begin_inset space \hspace*{\fill}
8396 \begin_inset Tabular
8397 <lyxtabular version="3" rows="7" columns="2">
8398 <features rotate="0" tabularvalignment="middle">
8399 <column alignment="center" valignment="top" width="0pt">
8400 <column alignment="center" valignment="top" width="0pt">
8402 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
8405 \begin_layout Plain Layout
8411 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
8414 \begin_layout Plain Layout
8416 \begin_inset Note Note
8419 \begin_layout Plain Layout
8426 is only used as spacer.
8438 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
8441 \begin_layout Plain Layout
8461 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
8464 \begin_layout Plain Layout
8465 \begin_inset Formula $\raisebox{6mm}{}\xleftrightarrow[x=a]{x>0}\raisebox{-4mm}{}$
8475 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
8478 \begin_layout Plain Layout
8498 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
8501 \begin_layout Plain Layout
8502 \begin_inset Formula $\raisebox{6mm}{}\xLeftarrow[x=a]{x>0}\raisebox{-4mm}{}$
8512 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
8515 \begin_layout Plain Layout
8535 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
8538 \begin_layout Plain Layout
8539 \begin_inset Formula $\raisebox{6mm}{}\xRightarrow[x=a]{x>0}\raisebox{-4mm}{}$
8549 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
8552 \begin_layout Plain Layout
8572 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
8575 \begin_layout Plain Layout
8576 \begin_inset Formula $\raisebox{6mm}{}\xLeftrightarrow[x=a]{x>0}\raisebox{-4mm}{}$
8586 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
8589 \begin_layout Plain Layout
8609 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
8612 \begin_layout Plain Layout
8613 \begin_inset Formula $\raisebox{6mm}{}\xhookleftarrow[x=a]{x>0}\raisebox{-4mm}{}$
8623 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
8626 \begin_layout Plain Layout
8646 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
8649 \begin_layout Plain Layout
8650 \begin_inset Formula $\raisebox{6mm}{}\xhookrightarrow[x=a]{x>0}\raisebox{-4mm}{}$
8664 \begin_inset space \hspace*{\fill}
8668 \begin_inset Tabular
8669 <lyxtabular version="3" rows="7" columns="2">
8670 <features rotate="0" tabularvalignment="middle">
8671 <column alignment="center" valignment="top" width="0pt">
8672 <column alignment="center" valignment="top" width="0pt">
8674 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
8677 \begin_layout Plain Layout
8683 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
8686 \begin_layout Plain Layout
8688 \begin_inset Note Note
8691 \begin_layout Plain Layout
8698 is only used as spacer.
8710 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
8713 \begin_layout Plain Layout
8733 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
8736 \begin_layout Plain Layout
8737 \begin_inset Formula $\raisebox{6mm}{}\xleftharpoondown[x=a]{x>0}\raisebox{-4mm}{}$
8747 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
8750 \begin_layout Plain Layout
8770 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
8773 \begin_layout Plain Layout
8774 \begin_inset Formula $\raisebox{6mm}{}\xleftharpoonup[x=a]{x>0}\raisebox{-4mm}{}$
8784 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
8787 \begin_layout Plain Layout
8807 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
8810 \begin_layout Plain Layout
8811 \begin_inset Formula $\raisebox{6mm}{}\xrightharpoondown[x=a]{x>0}\raisebox{-4mm}{}$
8821 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
8824 \begin_layout Plain Layout
8844 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
8847 \begin_layout Plain Layout
8848 \begin_inset Formula $\raisebox{6mm}{}\xrightharpoonup[x=a]{x>0}\raisebox{-4mm}{}$
8858 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
8861 \begin_layout Plain Layout
8881 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
8884 \begin_layout Plain Layout
8885 \begin_inset Formula $\raisebox{6mm}{}\xleftrightharpoons[x=a]{x>0}\raisebox{-4mm}{}$
8895 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
8898 \begin_layout Plain Layout
8918 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
8921 \begin_layout Plain Layout
8922 \begin_inset Formula $\raisebox{6mm}{}\xrightleftharpoons[x=a]{x>0}\raisebox{-4mm}{}$
8936 \begin_inset space \hspace*{\fill}
8942 \begin_layout Standard
8943 The command scheme is for all these arrows:
8946 \begin_layout Standard
8948 \begin_inset Tabular
8949 <lyxtabular version="3" rows="2" columns="2">
8950 <features rotate="0" tabularvalignment="middle">
8951 <column alignment="center" valignment="top" width="0pt">
8952 <column alignment="center" valignment="top" width="0pt">
8954 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
8957 \begin_layout Plain Layout
8963 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
8966 \begin_layout Plain Layout
8968 \begin_inset Note Note
8971 \begin_layout Plain Layout
8978 is only used as spacer.
8990 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
8993 \begin_layout Plain Layout
8996 xleftrightarrow[x=a]
8999 \begin_inset Formula $\to$
9007 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
9010 \begin_layout Plain Layout
9011 \begin_inset Formula $\raisebox{6mm}{}F(a)\xleftrightarrow[x=a]{x>0}F(x)\raisebox{-4mm}{}$
9027 \begin_layout Subsection
9028 Vertical and diagonal Arrows
9029 \begin_inset Index idx
9032 \begin_layout Plain Layout
9039 \begin_inset Index idx
9042 \begin_layout Plain Layout
9051 \begin_layout Standard
9052 \begin_inset space \hfill{}
9056 \begin_inset Tabular
9057 <lyxtabular version="3" rows="7" columns="2">
9058 <features rotate="0" tabularvalignment="middle">
9059 <column alignment="center" valignment="top" width="0pt">
9060 <column alignment="center" valignment="top" width="0pt">
9062 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
9065 \begin_layout Plain Layout
9071 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
9074 \begin_layout Plain Layout
9082 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
9085 \begin_layout Plain Layout
9093 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
9096 \begin_layout Plain Layout
9097 \begin_inset Formula $\uparrow$
9107 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
9110 \begin_layout Plain Layout
9118 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
9121 \begin_layout Plain Layout
9122 \begin_inset Formula $\Uparrow$
9132 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
9135 \begin_layout Plain Layout
9143 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
9146 \begin_layout Plain Layout
9147 \begin_inset Formula $\updownarrow$
9157 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
9160 \begin_layout Plain Layout
9168 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
9171 \begin_layout Plain Layout
9172 \begin_inset Formula $\Updownarrow$
9182 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
9185 \begin_layout Plain Layout
9193 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
9196 \begin_layout Plain Layout
9197 \begin_inset Formula $\Downarrow$
9207 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
9210 \begin_layout Plain Layout
9218 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
9221 \begin_layout Plain Layout
9222 \begin_inset Formula $\downarrow$
9236 \begin_inset space \hfill{}
9240 \begin_inset Tabular
9241 <lyxtabular version="3" rows="5" columns="2">
9242 <features rotate="0" tabularvalignment="middle">
9243 <column alignment="center" valignment="top" width="0pt">
9244 <column alignment="center" valignment="top" width="0pt">
9246 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
9249 \begin_layout Plain Layout
9255 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
9258 \begin_layout Plain Layout
9266 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
9269 \begin_layout Plain Layout
9277 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
9280 \begin_layout Plain Layout
9281 \begin_inset Formula $\nearrow$
9291 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
9294 \begin_layout Plain Layout
9302 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
9305 \begin_layout Plain Layout
9306 \begin_inset Formula $\searrow$
9316 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
9319 \begin_layout Plain Layout
9327 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
9330 \begin_layout Plain Layout
9331 \begin_inset Formula $\swarrow$
9341 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
9344 \begin_layout Plain Layout
9352 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
9355 \begin_layout Plain Layout
9356 \begin_inset Formula $\nwarrow$
9370 \begin_inset space \hfill{}
9376 \begin_layout Standard
9377 \begin_inset VSpace medskip
9380 Vertical arrows can be used also as delimiters together with the commands
9382 \begin_inset CommandInset ref
9384 reference "sub:Manual-Bracket-Size"
9389 \begin_inset CommandInset ref
9391 reference "sub:Automatic-Bracket-Size"
9398 \begin_layout Section
9400 \begin_inset CommandInset label
9407 \begin_inset Index idx
9410 \begin_layout Plain Layout
9419 \begin_layout Standard
9420 Accents can be inserted via the math toolbar button
9423 arg "math-insert \\hat"
9426 or the commands listed in the following subsections.
9429 \begin_layout Subsection
9430 Accents for one Character
9434 \begin_layout Plain Layout
9447 \begin_layout Plain Layout
9449 \begin_inset CommandInset ref
9451 reference "sub:Accents-in-Text"
9464 \begin_layout Plain Layout
9472 \begin_inset Note Note
9475 \begin_layout Plain Layout
9482 is used to avoid that the footnote appears in the PDF-bookmark.
9485 \begin_layout Plain Layout
9493 \begin_inset CommandInset ref
9495 reference "sub:Formulas-in-Section"
9505 \begin_inset CommandInset label
9507 name "sub:Accents-for-one"
9512 \begin_inset Index idx
9515 \begin_layout Plain Layout
9516 Accents ! for one character
9524 \begin_layout Standard
9525 \begin_inset space \hfill{}
9529 \begin_inset Tabular
9530 <lyxtabular version="3" rows="8" columns="2">
9531 <features rotate="0" tabularvalignment="middle">
9532 <column alignment="center" valignment="top" width="0pt">
9533 <column alignment="center" valignment="top" width="0pt">
9535 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
9538 \begin_layout Plain Layout
9544 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
9547 \begin_layout Plain Layout
9549 \begin_inset Note Note
9552 \begin_layout Plain Layout
9559 is only used as spacer.
9571 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
9574 \begin_layout Plain Layout
9578 \begin_inset space \textvisiblespace{}
9586 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
9589 \begin_layout Plain Layout
9590 \begin_inset Formula $\raisebox{5mm}{}\dot{A}$
9600 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
9603 \begin_layout Plain Layout
9607 \begin_inset space \textvisiblespace{}
9615 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
9618 \begin_layout Plain Layout
9619 \begin_inset Formula $\raisebox{5mm}{}\ddot{A}$
9629 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
9632 \begin_layout Plain Layout
9636 \begin_inset space \textvisiblespace{}
9644 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
9647 \begin_layout Plain Layout
9648 \begin_inset Formula $\raisebox{5mm}{}\dddot{A}$
9658 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
9661 \begin_layout Plain Layout
9665 \begin_inset space \textvisiblespace{}
9673 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
9676 \begin_layout Plain Layout
9677 \begin_inset Formula $\raisebox{5mm}{}\ddddot{A}$
9687 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
9690 \begin_layout Plain Layout
9694 \begin_inset space \textvisiblespace{}
9698 \begin_inset Index idx
9701 \begin_layout Plain Layout
9712 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
9715 \begin_layout Plain Layout
9716 \begin_inset Formula $\raisebox{5mm}{}\vec{A}$
9726 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
9729 \begin_layout Plain Layout
9733 \begin_inset space \textvisiblespace{}
9741 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
9744 \begin_layout Plain Layout
9745 \begin_inset Formula $\raisebox{5mm}{}\bar{A}$
9755 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
9758 \begin_layout Plain Layout
9762 \begin_inset space \textvisiblespace{}
9770 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
9773 \begin_layout Plain Layout
9774 \begin_inset Formula $\raisebox{5mm}{}\mathring{A}$
9788 \begin_inset space \hfill{}
9792 \begin_inset Tabular
9793 <lyxtabular version="3" rows="7" columns="2">
9794 <features rotate="0" tabularvalignment="middle">
9795 <column alignment="center" valignment="top" width="0pt">
9796 <column alignment="center" valignment="top" width="0pt">
9798 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
9801 \begin_layout Plain Layout
9807 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
9810 \begin_layout Plain Layout
9818 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
9821 \begin_layout Plain Layout
9825 \begin_inset space \textvisiblespace{}
9833 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
9836 \begin_layout Plain Layout
9837 \begin_inset Formula $\raisebox{5mm}{}\tilde{A}$
9847 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
9850 \begin_layout Plain Layout
9854 \begin_inset space \textvisiblespace{}
9862 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
9865 \begin_layout Plain Layout
9866 \begin_inset Formula $\raisebox{5mm}{}\hat{A}$
9876 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
9879 \begin_layout Plain Layout
9883 \begin_inset space \textvisiblespace{}
9891 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
9894 \begin_layout Plain Layout
9895 \begin_inset Formula $\raisebox{5mm}{}\check{A}$
9905 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
9908 \begin_layout Plain Layout
9912 \begin_inset space \textvisiblespace{}
9920 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
9923 \begin_layout Plain Layout
9924 \begin_inset Formula $\raisebox{5mm}{}\acute{A}$
9934 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
9937 \begin_layout Plain Layout
9941 \begin_inset space \textvisiblespace{}
9949 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
9952 \begin_layout Plain Layout
9953 \begin_inset Formula $\raisebox{5mm}{}\grave{A}$
9963 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
9966 \begin_layout Plain Layout
9970 \begin_inset space \textvisiblespace{}
9978 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
9981 \begin_layout Plain Layout
9982 \begin_inset Formula $\raisebox{5mm}{}\breve{A}$
9996 \begin_inset space \hfill{}
10002 \begin_layout Standard
10003 \begin_inset VSpace bigskip
10009 \begin_layout Standard
10010 You can directly insert accents like é to formulas.
10011 LyX will transform them to the corresponding accent command.
10013 \begin_inset Index idx
10016 \begin_layout Plain Layout
10022 it is better to insert a quotation mark before the vowel.
10023 These two characters are then treated by LaTeX as
10027 character when the formula part with the umlaut is marked as German.
10035 \begin_inset Quotes eld
10039 \begin_inset Quotes erd
10042 umlauts are created as demonstrated in the following example:
10045 \begin_layout Standard
10046 \begin_inset VSpace -2mm
10052 \begin_layout Standard
10054 \begin_inset Tabular
10055 <lyxtabular version="3" rows="3" columns="2">
10056 <features rotate="0" tabularvalignment="middle">
10057 <column alignment="center" valignment="top">
10058 <column alignment="center" valignment="top">
10060 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
10063 \begin_layout Plain Layout
10069 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
10072 \begin_layout Plain Layout
10074 \begin_inset Note Note
10077 \begin_layout Plain Layout
10085 \begin_inset space \thinspace{}
10088 pt space are only used as spacer.
10100 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
10103 \begin_layout Plain Layout
10106 \begin_inset Quotes grd
10114 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
10117 \begin_layout Plain Layout
10118 \begin_inset space \hspace{}
10125 \begin_inset Formula $"i$
10135 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
10138 \begin_layout Plain Layout
10142 \begin_inset space \textvisiblespace{}
10150 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
10153 \begin_layout Plain Layout
10154 \begin_inset Formula $\raisebox{5mm}{}\ddot{i}$
10170 \begin_layout Standard
10171 Another advantage to
10177 is that umlauts can directly be converted to mathematical text because
10178 the accent commands above are
10184 in mathematical text
10187 To convert an accented character to mathematical text, only the character
10188 under the accent may be converted.
10189 This applies also for all other conversions, e.
10190 \begin_inset space \thinspace{}
10194 \begin_inset space \space{}
10200 \begin_layout Standard
10201 In mathematical text, umlauts and other accented characters can directly
10205 \begin_layout Standard
10206 \begin_inset VSpace bigskip
10212 \begin_layout Standard
10213 LyX also supports a tilde under the character if the LaTeX-package
10218 \begin_inset Index idx
10221 \begin_layout Plain Layout
10222 Packages ! undertilde
10227 is installed on your system:
10230 \begin_layout Standard
10234 \begin_layout Plain Layout
10244 \begin_inset Note Note
10247 \begin_layout Plain Layout
10248 The following table will only be displayed when the LaTeX-package
10260 \begin_layout Standard
10263 \begin_inset Tabular
10264 <lyxtabular version="3" rows="2" columns="2">
10265 <features rotate="0" tabularvalignment="middle">
10266 <column alignment="center" valignment="top" width="0pt">
10267 <column alignment="center" valignment="top" width="0pt">
10269 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
10272 \begin_layout Plain Layout
10278 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
10281 \begin_layout Plain Layout
10289 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
10292 \begin_layout Plain Layout
10296 \begin_inset space \textvisiblespace{}
10304 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
10307 \begin_layout Plain Layout
10308 \begin_inset Formula $\raisebox{5mm}{}\utilde{A}$
10324 \begin_layout Standard
10328 \begin_layout Plain Layout
10338 \begin_inset Note Note
10341 \begin_layout Plain Layout
10342 The following will be displayed when the LaTeX-package
10354 \begin_layout Standard
10355 You need to install the LaTeX-package
10359 to see the rest of this subsection in the output.
10362 \begin_layout Standard
10366 \begin_layout Plain Layout
10378 \begin_layout Subsection
10379 Accents for several Characters
10380 \begin_inset Index idx
10383 \begin_layout Plain Layout
10384 Accents ! for several characters
10392 \begin_layout Standard
10393 \begin_inset space \hfill{}
10397 \begin_inset Tabular
10398 <lyxtabular version="3" rows="5" columns="2">
10399 <features rotate="0" tabularvalignment="middle">
10400 <column alignment="center" valignment="top" width="0pt">
10401 <column alignment="center" valignment="top" width="0pt">
10403 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
10406 \begin_layout Plain Layout
10412 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
10415 \begin_layout Plain Layout
10417 \begin_inset Note Note
10420 \begin_layout Plain Layout
10427 is only used as spacer.
10439 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
10442 \begin_layout Plain Layout
10446 \begin_inset space \textvisiblespace{}
10454 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
10457 \begin_layout Plain Layout
10458 \begin_inset Formula $\raisebox{6mm}{}\overleftarrow{A=B}\raisebox{-2mm}{}$
10468 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
10471 \begin_layout Plain Layout
10475 \begin_inset space \textvisiblespace{}
10483 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
10486 \begin_layout Plain Layout
10487 \begin_inset Formula $\raisebox{5mm}{}\underleftarrow{A=B}\raisebox{-3mm}{}$
10497 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
10500 \begin_layout Plain Layout
10504 \begin_inset space \textvisiblespace{}
10512 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
10515 \begin_layout Plain Layout
10516 \begin_inset Formula $\raisebox{6mm}{}\overleftrightarrow{A=B}\raisebox{-2mm}{}$
10526 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
10529 \begin_layout Plain Layout
10532 underleftrightarrow
10533 \begin_inset space \textvisiblespace{}
10541 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
10544 \begin_layout Plain Layout
10545 \begin_inset Formula $\raisebox{5mm}{}\underleftrightarrow{A=B}\raisebox{-3mm}{}$
10559 \begin_inset space \hfill{}
10563 \begin_inset Tabular
10564 <lyxtabular version="3" rows="5" columns="2">
10565 <features rotate="0" tabularvalignment="middle">
10566 <column alignment="center" valignment="top" width="0pt">
10567 <column alignment="center" valignment="top" width="0pt">
10569 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
10572 \begin_layout Plain Layout
10578 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
10581 \begin_layout Plain Layout
10589 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
10592 \begin_layout Plain Layout
10596 \begin_inset space \textvisiblespace{}
10604 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
10607 \begin_layout Plain Layout
10608 \begin_inset Formula $\raisebox{6mm}{}\overrightarrow{A=B}\raisebox{-2mm}{}$
10618 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
10621 \begin_layout Plain Layout
10625 \begin_inset space \textvisiblespace{}
10633 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
10636 \begin_layout Plain Layout
10637 \begin_inset Formula $\raisebox{5mm}{}\underrightarrow{A=B}\raisebox{-3mm}{}$
10647 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
10650 \begin_layout Plain Layout
10654 \begin_inset space \textvisiblespace{}
10662 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
10665 \begin_layout Plain Layout
10666 \begin_inset Formula $\raisebox{6mm}{}\widetilde{A=B}\raisebox{-2mm}{}$
10676 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
10679 \begin_layout Plain Layout
10683 \begin_inset space \textvisiblespace{}
10691 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
10694 \begin_layout Plain Layout
10695 \begin_inset Formula $\raisebox{6mm}{}\widehat{A=B}\raisebox{-2mm}{}$
10709 \begin_inset space \hfill{}
10715 \begin_layout Standard
10716 \begin_inset VSpace medskip
10719 With these commands as many characters as you like can be accented.
10732 will only be set in the output with a length of three characters, as shown
10733 in the following example:
10734 \begin_inset Formula
10736 \widetilde{A+B=C-D}
10744 \begin_layout Standard
10752 \begin_inset Index idx
10755 \begin_layout Plain Layout
10770 \begin_inset Index idx
10773 \begin_layout Plain Layout
10781 described in the previous subsection it is also possible to accent several
10788 \begin_inset space \textvisiblespace{}
10792 \begin_inset Formula $\downarrow$
10798 \begin_inset Formula
10800 \underset{***}{A=B}
10808 \begin_layout Section
10810 \begin_inset CommandInset label
10817 \begin_inset Index idx
10820 \begin_layout Plain Layout
10829 \begin_layout Subsection
10831 \begin_inset CommandInset label
10833 name "sub:Predefined-Space"
10838 \begin_inset Index idx
10841 \begin_layout Plain Layout
10842 Space ! horizontal ! predefined
10850 \begin_layout Standard
10851 Sometimes it is necessary to insert horizontal space into a formula.
10852 This is done by inserting a protected space (shortcut
10855 arg "command-alternatives space-insert protected ; math-space"
10860 \begin_inset Quotes eld
10866 \begin_inset space \textvisiblespace{}
10872 \begin_inset Quotes erd
10875 appears and by pressing
10879 several times one can select one of eight different space sizes.
10880 The spaces can also be inserted using the math toolbar button
10883 arg "math-insert \\space"
10886 or special commands.
10887 Independent from the inserted command, one can select the size again by
10895 \begin_layout Standard
10898 \begin_inset Tabular
10899 <lyxtabular version="3" rows="6" columns="3">
10900 <features rotate="0" tabularvalignment="middle">
10901 <column alignment="center" valignment="top">
10902 <column alignment="center" valignment="top" width="15col%">
10903 <column alignment="center" valignment="top">
10905 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
10908 \begin_layout Plain Layout
10914 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
10917 \begin_layout Plain Layout
10927 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
10930 \begin_layout Plain Layout
10938 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
10941 \begin_layout Plain Layout
10949 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
10952 \begin_layout Plain Layout
10958 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
10961 \begin_layout Plain Layout
10962 \begin_inset Formula $A\, B$
10972 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
10975 \begin_layout Plain Layout
10983 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
10986 \begin_layout Plain Layout
10992 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
10995 \begin_layout Plain Layout
10996 \begin_inset Formula $A\: B$
11006 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
11009 \begin_layout Plain Layout
11017 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
11020 \begin_layout Plain Layout
11026 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
11029 \begin_layout Plain Layout
11030 \begin_inset Formula $A\; B$
11040 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
11043 \begin_layout Plain Layout
11051 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
11054 \begin_layout Plain Layout
11060 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
11063 \begin_layout Plain Layout
11064 \begin_inset Formula $A\quad B$
11074 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
11077 \begin_layout Plain Layout
11085 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
11088 \begin_layout Plain Layout
11094 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
11097 \begin_layout Plain Layout
11098 \begin_inset Formula $A\qquad B$
11112 \begin_inset space \hfill{}
11116 \begin_inset Tabular
11117 <lyxtabular version="3" rows="6" columns="3">
11118 <features rotate="0" tabularvalignment="middle">
11119 <column alignment="center" valignment="top">
11120 <column alignment="center" valignment="top" width="15col%">
11121 <column alignment="center" valignment="top">
11123 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
11126 \begin_layout Plain Layout
11132 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
11135 \begin_layout Plain Layout
11145 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
11148 \begin_layout Plain Layout
11156 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
11159 \begin_layout Plain Layout
11167 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
11170 \begin_layout Plain Layout
11176 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
11179 \begin_layout Plain Layout
11180 \begin_inset Formula $A\hfill B$
11190 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
11193 \begin_layout Plain Layout
11201 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
11204 \begin_layout Plain Layout
11210 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
11213 \begin_layout Plain Layout
11214 \begin_inset Formula $A\hspace*{1em}B$
11224 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
11227 \begin_layout Plain Layout
11235 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
11238 \begin_layout Plain Layout
11244 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
11247 \begin_layout Plain Layout
11248 \begin_inset Formula $A\hspace{1em}B$
11258 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
11261 \begin_layout Plain Layout
11265 \begin_inset space \textvisiblespace{}
11273 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
11276 \begin_layout Plain Layout
11282 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
11285 \begin_layout Plain Layout
11286 \begin_inset Formula $A\ B$
11296 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
11299 \begin_layout Plain Layout
11307 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
11310 \begin_layout Plain Layout
11316 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
11319 \begin_layout Plain Layout
11320 \begin_inset Formula $A\! B$
11336 \begin_layout Standard
11338 \begin_inset space ~
11342 \begin_inset space \thinspace{}
11346 \begin_inset space \thinspace{}
11349 7 are variable spaces which are explained in
11350 \begin_inset CommandInset ref
11352 reference "sub:Variable-Space"
11358 \begin_inset space ~
11361 9 seems to produce no space.
11362 It is displayed red in LyX contrary to the other sizes, because it is a
11364 There are two more negative spaces:
11367 \begin_layout Standard
11369 \begin_inset Tabular
11370 <lyxtabular version="3" rows="3" columns="3">
11371 <features rotate="0" tabularvalignment="middle">
11372 <column alignment="center" valignment="middle" width="6.8cm">
11373 <column alignment="center" valignment="top" width="0pt">
11374 <column alignment="center" valignment="top" width="0pt">
11376 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
11379 \begin_layout Plain Layout
11385 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
11388 \begin_layout Plain Layout
11396 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
11399 \begin_layout Plain Layout
11409 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
11412 \begin_layout Plain Layout
11417 keystrokes after inserting the protected space
11422 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
11425 \begin_layout Plain Layout
11431 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
11434 \begin_layout Plain Layout
11442 <cell multicolumn="1" alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
11445 \begin_layout Plain Layout
11451 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
11454 \begin_layout Plain Layout
11455 \begin_inset Formula $A\negmedspace B$
11463 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
11466 \begin_layout Plain Layout
11467 \begin_inset Formula $A\negthickspace B$
11483 \begin_layout Standard
11484 Negative spaces can lead to characters overlapping each other.
11485 Thus they can be used to enforce ligatures, which are e.
11486 \begin_inset space \thinspace{}
11490 \begin_inset space \space{}
11493 useful for summation operators:
11496 \begin_layout Standard
11498 \begin_inset Tabular
11499 <lyxtabular version="3" rows="3" columns="2">
11500 <features rotate="0" tabularvalignment="middle">
11501 <column alignment="center" valignment="top">
11502 <column alignment="center" valignment="top">
11504 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
11507 \begin_layout Plain Layout
11513 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
11516 \begin_layout Plain Layout
11518 \begin_inset Note Note
11521 \begin_layout Plain Layout
11528 is only used as spacer.
11540 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
11543 \begin_layout Plain Layout
11549 \begin_inset space \textvisiblespace{}
11557 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
11560 \begin_layout Plain Layout
11561 \begin_inset Formula $\raisebox{4.5mm}{}\sum\sum f_{kl}\raisebox{-2.5mm}{}$
11571 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
11574 \begin_layout Plain Layout
11582 \begin_inset space \textvisiblespace{}
11590 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
11593 \begin_layout Plain Layout
11594 \begin_inset Formula $\raisebox{4.5mm}{}\sum\negmedspace\sum f_{kl}\raisebox{-2.5mm}{}$
11610 \begin_layout Standard
11612 \begin_inset VSpace medskip
11618 \begin_layout Standard
11620 Relations like for example equal signs, are always surrounded by space.
11621 To suppress this, the equal sign is placed into a TeX-brace.
11622 The following example demonstrates this:
11625 \begin_layout Standard
11627 \begin_inset Tabular
11628 <lyxtabular version="3" rows="2" columns="2">
11629 <features rotate="0" tabularvalignment="middle">
11630 <column alignment="center" valignment="top" width="0pt">
11631 <column alignment="center" valignment="top" width="0pt">
11633 <cell alignment="center" valignment="top" usebox="none">
11636 \begin_layout Plain Layout
11642 <cell alignment="center" valignment="top" usebox="none">
11645 \begin_layout Plain Layout
11646 \begin_inset Formula $A=B$
11656 <cell alignment="center" valignment="top" usebox="none">
11659 \begin_layout Plain Layout
11660 \begin_inset Note Note
11663 \begin_layout Plain Layout
11670 is only used as spacer.
11676 \begin_inset Formula $\raisebox{5mm}{}$
11679 equation without space
11684 <cell multicolumn="1" alignment="center" valignment="top" usebox="none">
11687 \begin_layout Plain Layout
11688 \begin_inset Formula $A{=}B$
11704 \begin_layout Standard
11706 The command for the last formula is:
11711 \begin_inset Formula $\to$
11717 \begin_layout Standard
11718 \begin_inset VSpace bigskip
11724 \begin_layout Standard
11725 Spaces are needed for physical units, because the space between the value
11726 and the unit is the smallest one and not a normal space.
11727 For units in text, the smallest space is inserted via the menu
11729 Insert\SpecialChar \menuseparator
11730 Formatting\SpecialChar \menuseparator
11732 \begin_inset space ~
11740 arg "space-insert thin"
11746 \begin_layout Standard
11747 An example to visualize the difference:
11750 \begin_layout Standard
11751 \begin_inset Tabular
11752 <lyxtabular version="3" rows="2" columns="2">
11753 <features rotate="0" tabularvalignment="middle">
11754 <column alignment="left" valignment="top">
11755 <column alignment="left" valignment="top">
11757 <cell alignment="center" valignment="top" usebox="none">
11760 \begin_layout Plain Layout
11762 \begin_inset Formula $\cdot$
11770 <cell alignment="center" valignment="top" usebox="none">
11773 \begin_layout Plain Layout
11774 space between value and unit
11781 <cell alignment="center" valignment="top" usebox="none">
11784 \begin_layout Plain Layout
11786 \begin_inset space \thinspace{}
11790 \begin_inset Formula $\cdot$
11798 <cell alignment="center" valignment="top" usebox="none">
11801 \begin_layout Plain Layout
11802 smallest space between value and unit
11815 \begin_layout Subsection
11820 \begin_layout Plain Layout
11833 \begin_layout Plain Layout
11834 for vertical space in formulas see
11835 \begin_inset CommandInset ref
11837 reference "sub:Line-Separation"
11850 \begin_layout Plain Layout
11858 \begin_inset Note Note
11861 \begin_layout Plain Layout
11864 texorpdfstring is used to avoid that the footnote appears in the PDF-bookmark.
11867 \begin_layout Plain Layout
11870 texorpdfstring is in section
11871 \begin_inset CommandInset ref
11873 reference "sub:Formulas-in-Section"
11883 \begin_inset CommandInset label
11885 name "sub:Variable-Space"
11890 \begin_inset Index idx
11893 \begin_layout Plain Layout
11894 Space ! horizontal ! variable
11902 \begin_layout Standard
11903 Space with a defined length can be inserted with the command
11910 \begin_inset Index idx
11913 \begin_layout Plain Layout
11923 \begin_inset Quotes eld
11929 \begin_inset space \textvisiblespace{}
11935 \begin_inset Quotes erd
11939 The length can be specified by left-clicking on the
11940 \begin_inset Quotes eld
11946 \begin_inset space \textvisiblespace{}
11952 \begin_inset Quotes erd
11956 The length may also be negative.
11957 When a space would be the first character in a line it would be omitted.
11958 To force its output use the command
11970 or left-click on the
11971 \begin_inset Quotes eld
11977 \begin_inset space \textvisiblespace{}
11983 \begin_inset Quotes erd
11986 and check the option
11991 \begin_inset Newline newline
11994 To insert as much space as is available, the command
12001 \begin_inset Index idx
12004 \begin_layout Plain Layout
12015 \begin_layout Standard
12016 \begin_inset VSpace -1mm
12022 \begin_layout Standard
12024 \begin_inset Tabular
12025 <lyxtabular version="3" rows="4" columns="2">
12026 <features rotate="0" tabularvalignment="middle">
12027 <column alignment="center" valignment="top">
12028 <column alignment="center" valignment="top">
12030 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
12033 \begin_layout Plain Layout
12041 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
12044 \begin_layout Plain Layout
12052 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
12055 \begin_layout Plain Layout
12059 \begin_inset space \textvisiblespace{}
12065 \begin_inset space \thinspace{}
12073 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
12076 \begin_layout Plain Layout
12077 \begin_inset Formula $A=B\hspace{3cm}A\not=C$
12087 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
12090 \begin_layout Plain Layout
12094 \begin_inset space \textvisiblespace{}
12100 \begin_inset space \thinspace{}
12108 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
12111 \begin_layout Plain Layout
12112 \begin_inset Formula $A\hspace{-1mm}A\not=A$
12122 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
12125 \begin_layout Plain Layout
12129 \begin_inset space \textvisiblespace{}
12137 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
12140 \begin_layout Plain Layout
12141 \begin_inset Formula $A=A\hfill B=B$
12157 \begin_layout Standard
12158 In the last example the available space is given by the longest column entry
12160 In an inline formula the space depends on the length of the line in which
12168 Thus, when the line uses the full width, no space will be created.
12175 only has an effect on displayed formulas when the formula style
12180 (Formula styles are explained in
12181 \begin_inset CommandInset ref
12183 reference "sec:Formula-Styles"
12190 \begin_layout Standard
12197 , there are the commands
12209 that fill the space with a pattern, see
12210 \begin_inset CommandInset ref
12212 reference "sub:Ellipses"
12219 \begin_layout Standard
12220 For text, variable space can be inserted via the menu
12222 Insert\SpecialChar \menuseparator
12223 Formatting\SpecialChar \menuseparator
12225 \begin_inset space ~
12233 \begin_layout Standard
12234 This is a line with
12235 \begin_inset space \hspace{}
12240 \begin_inset space \thinspace{}
12246 \begin_layout Standard
12247 This is a line with
12248 \begin_inset space \hfill{}
12254 \begin_layout Subsection
12255 Space besides inline Formulas
12256 \begin_inset Index idx
12259 \begin_layout Plain Layout
12260 Space ! besides inline formulas
12268 \begin_layout Standard
12269 The space that surrounds inline formulas can be adjusted with the length
12277 \begin_inset Index idx
12280 \begin_layout Plain Layout
12289 The value of a length is set with the command
12296 \begin_inset Index idx
12299 \begin_layout Plain Layout
12307 which has the following scheme:
12310 \begin_layout Standard
12315 setlength{length name}{value}
12318 \begin_layout Standard
12326 \begin_inset space \thinspace{}
12332 \begin_layout Standard
12342 \begin_layout Standard
12343 is inserted in TeX-mode.
12345 \begin_inset space \thinspace{}
12348 mm space will now be set around all inline formulas:
12352 \begin_layout Plain Layout
12366 \begin_layout Standard
12367 This is a line with an inline formula
12368 \begin_inset Formula $A=B$
12372 \begin_inset space \thinspace{}
12375 mm surrounding space.
12379 \begin_layout Plain Layout
12393 \begin_layout Standard
12394 To return to the predefined value,
12400 is set to the value 0
12401 \begin_inset space \thinspace{}
12407 \begin_layout Section
12409 \begin_inset Index idx
12412 \begin_layout Plain Layout
12419 \begin_inset Index idx
12422 \begin_layout Plain Layout
12427 \begin_layout Plain Layout
12438 \begin_layout Plain Layout
12453 \begin_layout Standard
12454 Boxes for text are described in chapter
12461 \begin_inset space ~
12469 \begin_layout Subsection
12471 \begin_inset CommandInset label
12473 name "sub:Boxes-with-Frame"
12478 \begin_inset Index idx
12481 \begin_layout Plain Layout
12490 \begin_layout Standard
12491 It is possible to frame a formula or part of one with the commands
12498 \begin_inset Index idx
12501 \begin_layout Plain Layout
12516 \begin_inset Index idx
12519 \begin_layout Plain Layout
12530 \begin_layout Standard
12531 When one of these commands is inserted in a formula, a blue box appears
12532 within a frame to enter formula parts.
12539 an additional formula has to be created by
12543 within this box, because the box content will otherwise be treated as mathemati
12551 is used, a new formula is automatically created inside the frame.
12554 \begin_layout Standard
12561 is not suitable to frame displayed formulas because the formula will always
12562 be set in the size of the text.
12569 is in contrary not suitable to frame inline formulas, because the formula
12570 will always be set in the size of a displayed formula.
12573 \begin_layout Standard
12587 \begin_inset Index idx
12590 \begin_layout Plain Layout
12598 where additionally the frame width and the alignment can be specified.
12605 is used in the following scheme:
12608 \begin_layout Standard
12613 framebox[frame width][position]{box content}
12616 \begin_layout Standard
12617 The position can either be
12634 right aligns the formula in the box.
12635 When no position is given, the formula will be centered.
12636 \begin_inset Newline newline
12639 If no width is given, also no position can be given.
12640 In this case the frame width is adjusted to the box content like for
12649 \begin_layout Standard
12656 is inserted, a box appears containing three blue boxes.
12657 The first two boxes are surrounded by brackets and denote the two optional
12659 The third box is for formula parts like for
12668 \begin_layout Standard
12670 \begin_inset Tabular
12671 <lyxtabular version="3" rows="5" columns="2">
12672 <features rotate="0" tabularvalignment="middle">
12673 <column alignment="center" valignment="top">
12674 <column alignment="center" valignment="top">
12676 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
12679 \begin_layout Plain Layout
12685 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
12688 \begin_layout Plain Layout
12690 \begin_inset Note Note
12693 \begin_layout Plain Layout
12700 is only used as spacer.
12712 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
12715 \begin_layout Plain Layout
12719 \begin_inset space \textvisiblespace{}
12729 \begin_inset space \textvisiblespace{}
12737 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
12740 \begin_layout Plain Layout
12741 \begin_inset Formula $\raisebox{6mm}{}\fbox{\ensuremath{\int A=B}}\raisebox{-4mm}{}$
12751 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
12754 \begin_layout Plain Layout
12758 \begin_inset space \textvisiblespace{}
12764 \begin_inset space \textvisiblespace{}
12772 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
12775 \begin_layout Plain Layout
12776 \begin_inset Formula $\raisebox{8.5mm}{}\boxed{\int A=B}\raisebox{-6.5mm}{}$
12786 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
12789 \begin_layout Plain Layout
12793 \begin_inset space \textvisiblespace{}
12801 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
12804 \begin_layout Plain Layout
12805 \begin_inset Formula $\raisebox{6mm}{}A+\fbox{B}\raisebox{-3mm}{}$
12815 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
12818 \begin_layout Plain Layout
12822 \begin_inset space \textvisiblespace{}
12826 \begin_inset Formula $\to$
12830 \begin_inset Formula $\to$
12840 \begin_inset space \textvisiblespace{}
12844 \begin_inset Formula $\downarrow$
12852 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
12855 \begin_layout Plain Layout
12856 \begin_inset Formula $\raisebox{6mm}{}$
12860 \begin_inset Formula $\framebox[20mm][]{\ensuremath{\frac{A}{B}}}$
12864 \begin_inset Formula $\raisebox{-4mm}{}$
12880 \begin_layout Standard
12881 The frame thickness can also be adjusted.
12882 To do this the following commands have to be inserted in TeX-mode before
12886 \begin_layout Standard
12896 \begin_inset Quotes eld
12900 \begin_inset Quotes erd
12914 \begin_inset Quotes eld
12918 \begin_inset Quotes erd
12924 \begin_layout Standard
12925 \begin_inset Quotes eld
12929 \begin_inset Quotes erd
12932 specifies the minimal distance between the frame and the first character
12934 An example for this is the following framed formula:
12938 \begin_layout Plain Layout
12950 \begin_inset Formula
12957 Before this formula the commands
12960 \begin_layout Standard
12982 \begin_layout Standard
12983 were inserted in TeX-mode.
12984 The given values are used for all following boxes.
12987 \begin_layout Standard
12988 To return to the standard frame size, the command
12991 \begin_layout Standard
13016 \begin_layout Plain Layout
13030 \begin_layout Standard
13031 is inserted in TeX-mode before the next formula.
13034 \begin_layout Subsection
13035 Boxes without Frame
13036 \begin_inset CommandInset label
13038 name "sub:Boxes-without-Frame"
13043 \begin_inset Index idx
13046 \begin_layout Plain Layout
13047 Boxes ! without frame
13055 \begin_layout Standard
13056 For boxes without a frame there are the following box commands:
13063 \begin_inset Index idx
13066 \begin_layout Plain Layout
13081 \begin_inset Index idx
13084 \begin_layout Plain Layout
13099 \begin_inset Index idx
13102 \begin_layout Plain Layout
13113 \begin_layout Standard
13120 a box can be super- or subscripted.
13121 But in contrary to normal super- and subscripting, the characters in the
13122 box keep their font size.
13129 is used in the following scheme:
13132 \begin_layout Standard
13137 raisebox{height}{box content}
13140 \begin_layout Standard
13141 When the box should contain a formula, an extra formula is needed like for
13152 \begin_inset Note Greyedout
13155 \begin_layout Plain Layout
13166 this extra formula is created by pressing
13170 twice instead of once because LyX doesn't yet support
13184 \begin_layout Standard
13186 \begin_inset Tabular
13187 <lyxtabular version="3" rows="4" columns="2">
13188 <features rotate="0" tabularvalignment="middle">
13189 <column alignment="center" valignment="top">
13190 <column alignment="center" valignment="top">
13192 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
13195 \begin_layout Plain Layout
13201 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
13204 \begin_layout Plain Layout
13212 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
13215 \begin_layout Plain Layout
13219 \begin_inset Formula $\to$
13225 \begin_inset Formula $\to$
13233 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
13236 \begin_layout Plain Layout
13237 \begin_inset Formula $H\raisebox{2mm}{al}lo$
13247 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
13250 \begin_layout Plain Layout
13254 \begin_inset Formula $\to$
13260 \begin_inset Formula $\to$
13268 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
13271 \begin_layout Plain Layout
13272 \begin_inset Formula $H\raisebox{-2mm}{al}lo$
13282 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
13285 \begin_layout Plain Layout
13289 \begin_inset Formula $\to$
13305 \begin_inset space \textvisiblespace{}
13313 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
13316 \begin_layout Plain Layout
13317 \begin_inset Formula $A=\raisebox{-2mm}{\mbox{\ensuremath{\sqrt{B}}}}$
13333 \begin_layout Standard
13358 , with the difference that there is no frame.
13361 \begin_layout Subsection
13363 \begin_inset CommandInset label
13365 name "sub:Colored-Boxes"
13370 \begin_inset Index idx
13373 \begin_layout Plain Layout
13382 \begin_layout Standard
13383 To be able to use all commands explained in this section, the LaTeX-package
13392 \begin_layout Plain Layout
13397 is part of every LaTeX standard installation.
13403 \begin_inset Index idx
13406 \begin_layout Plain Layout
13412 has to be loaded in the LaTeX-preamble with the line
13416 \begin_layout Plain Layout
13417 When text is colored somewhere in the document with a predefined color,
13418 LyX loads the LaTeX-package
13423 Thus it is possible that the package is loaded twice, but this does not
13430 \begin_inset Note Note
13433 \begin_layout Plain Layout
13434 To avoid that the package is loaded twice, a macro was inserted to the LaTeX-pre
13443 \begin_layout Standard
13451 \begin_layout Standard
13452 \begin_inset VSpace medskip
13455 To color boxes, the command
13462 \begin_inset Index idx
13465 \begin_layout Plain Layout
13473 is used in the following scheme:
13476 \begin_layout Standard
13481 colorbox{color}{box content}
13484 \begin_layout Standard
13485 The box content can also be a box and a
13491 can also be part of another box (see the 2nd and 3rd example).
13492 When the box should contain a formula, an extra formula has to be created,
13493 the same way as for
13503 \begin_layout Plain Layout
13504 This also applies for the command
13518 \begin_layout Standard
13519 One of the following predefined colors can be chosen:
13522 \begin_layout Standard
13556 \begin_layout Standard
13558 \begin_inset Tabular
13559 <lyxtabular version="3" rows="4" columns="2">
13560 <features rotate="0" tabularvalignment="middle">
13561 <column alignment="center" valignment="top">
13562 <column alignment="center" valignment="top">
13564 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
13567 \begin_layout Plain Layout
13573 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
13576 \begin_layout Plain Layout
13578 \begin_inset Note Note
13581 \begin_layout Plain Layout
13588 is only used as spacer.
13600 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
13603 \begin_layout Plain Layout
13607 \begin_inset Formula $\to$
13617 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
13620 \begin_layout Plain Layout
13621 \begin_inset Formula $\raisebox{6mm}{}\colorbox{yellow}{A=B}\raisebox{-3mm}{}$
13631 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
13634 \begin_layout Plain Layout
13638 \begin_inset Formula $\to$
13646 \begin_inset space \textvisiblespace{}
13654 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
13657 \begin_layout Plain Layout
13658 \begin_inset Formula $\raisebox{6mm}{}\colorbox{green}{\fbox{A=B}}\raisebox{-3mm}{}$
13668 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
13671 \begin_layout Plain Layout
13675 \begin_inset space \textvisiblespace{}
13681 \begin_inset Formula $\to$
13697 \begin_inset space \textvisiblespace{}
13705 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
13708 \begin_layout Plain Layout
13709 \begin_inset Formula $\raisebox{7mm}{}\fbox{\colorbox{green}{\mbox{\ensuremath{\int C=D}}}}\raisebox{-5mm}{}$
13725 \begin_layout Standard
13732 only colors the box but not the characters in the box.
13733 To color all characters, the whole formula is highlighted and the desired
13734 color is chosen in the
13737 \begin_inset space ~
13743 The dialog can be called with the toolbar button
13746 arg "dialog-show character"
13751 Edit\SpecialChar \menuseparator
13753 \begin_inset space ~
13756 Style\SpecialChar \menuseparator
13760 The formula number then has the same color as the formula.
13761 When the formula number should get another color than the formula characters,
13762 the color must be changed within the formula.
13765 \begin_layout Standard
13769 \begin_layout Standard
13772 \begin_inset Formula
13774 \int A=B\label{eq:red}
13782 \begin_inset Formula
13784 \textcolor{red}{\int A=B}\label{eq:redgreen}
13792 \begin_layout Standard
13794 \begin_inset CommandInset ref
13800 is completely colored red.
13801 \begin_inset Newline newline
13805 \begin_inset CommandInset ref
13807 reference "eq:redgreen"
13811 was first completely colored green to set the color for the formula number.
13812 Subsequently the formula characters were colored red.
13815 \begin_layout Standard
13816 \begin_inset VSpace bigskip
13819 To color the frame different than the rest of the box, the command
13826 \begin_inset Index idx
13829 \begin_layout Plain Layout
13837 is used in the following scheme:
13840 \begin_layout Standard
13845 fcolorbox{frame color}{color}{box content}
13848 \begin_layout Standard
13855 is an extension of the command
13862 The frame width is set, like for
13885 \begin_layout Plain Layout
13897 \begin_inset Formula
13899 \fcolorbox{cyan}{magenta}{A=B}
13908 \begin_layout Plain Layout
13922 \begin_layout Standard
13923 This formula was created with the command
13924 \begin_inset Newline newline
13932 \begin_inset Formula $\to$
13938 \begin_inset Formula $\to$
13948 \begin_layout Standard
13949 \begin_inset VSpace bigskip
13952 To use other colors than the predefined ones, they have to be defined first.
13955 \begin_layout Standard
13956 One can for example define the color
13957 \begin_inset Quotes eld
13965 \begin_inset Quotes erd
13968 with the LaTeX-preamble line:
13971 \begin_layout Standard
13976 definecolor{darkgreen}{cmyk}{0.5,
13991 \begin_inset Index idx
13994 \begin_layout Plain Layout
14005 \begin_layout Standard
14010 is the color space that denotes the colors
14027 The four comma separated numbers are the portion factor for the corresponding
14028 colors of the color space.
14029 The factors can be in the range of 0
14030 \begin_inset space \thinspace{}
14034 \begin_inset space \thinspace{}
14042 also the color space
14046 can be used for definitions.
14063 , so that there are in this case three portion factors for the corresponding
14065 Furthermore there is the color space
14069 with one portion factor for the gray value.
14072 \begin_layout Standard
14073 As example a framed box with the new defined color
14077 where the characters have been colored
14082 \begin_inset Formula
14084 \colorbox{darkgreen}{\color{yellow}\boxed{\int A\,\mathrm{d}x=\frac{\sqrt[5]{B}}{\ln\left(\frac{1}{3}\right)}}}
14092 \begin_layout Standard
14093 Self-defined colors can also be used for text with the help of the command
14101 \begin_inset Index idx
14104 \begin_layout Plain Layout
14113 \begin_layout Standard
14117 \begin_layout Plain Layout
14121 textcolor{darkgreen}{
14127 \begin_inset Quotes eld
14131 \begin_inset Quotes erd
14138 \begin_layout Plain Layout
14148 \begin_layout Standard
14156 \begin_inset Index idx
14159 \begin_layout Plain Layout
14167 is used in the scheme
14171 textcolor{color}{characters to color}
14176 \begin_layout Subsection
14178 \begin_inset CommandInset label
14180 name "sub:Paragraph-Boxes"
14185 \begin_inset Index idx
14188 \begin_layout Plain Layout
14189 Boxes ! as paragraph
14197 \begin_layout Standard
14198 A box that can contain several lines and paragraphs, a so-called paragraph
14199 box (parbox), can be created with the menu
14201 Insert\SpecialChar \menuseparator
14204 or the toolbar button
14213 \begin_layout Standard
14214 The following example shows a framed parbox in a line:
14217 \begin_layout Standard
14218 \begin_inset VSpace medskip
14222 \begin_inset Box Boxed
14232 height_special "totalheight"
14235 \begin_layout Plain Layout
14236 This is a paragraph box.
14238 \begin_inset space \thinspace{}
14241 cm long and can also contain formulas:
14242 \begin_inset Formula $\int A\,\mathrm{d}s=C$
14253 \begin_layout Standard
14254 \begin_inset VSpace medskip
14260 \begin_layout Standard
14261 Such a box is created by right-clicking on the gray box inset.
14262 A dialog pops up showing the box properties.
14276 \begin_inset space \thinspace{}
14281 Vertical Box Alignment
14286 \begin_layout Standard
14287 \begin_inset VSpace medskip
14290 In LaTeX a parbox is created with the command
14297 \begin_inset Index idx
14300 \begin_layout Plain Layout
14308 which has the following scheme:
14311 \begin_layout Standard
14316 parbox[position]{width}{box content}
14319 \begin_layout Standard
14334 \begin_inset Quotes eld
14338 \begin_inset Quotes erd
14341 means that the box is aligned within the surrounding text with its last
14348 \begin_inset Quotes eld
14352 \begin_inset Quotes erd
14355 this is done with the first line.
14356 When no position is given, the box will be vertically centered, see section
14364 \begin_inset space ~
14369 manual for examples.
14372 \begin_layout Standard
14373 \begin_inset VSpace bigskip
14376 To frame formulas completely, including the formula number, the formula
14377 must be set into a parbox.
14378 To do this, the command
14392 is inserted in TeX-mode before the formula.
14400 \begin_inset Index idx
14403 \begin_layout Plain Layout
14411 is hereby the line width set for the document.
14412 Because the frame is outside the parbox, 2
14413 \begin_inset space \thinspace{}
14416 times the frame separation and the frame thickness must be subtracted from
14418 As this is not automatically done by LyX due to a bug
14422 \begin_layout Plain Layout
14423 \begin_inset CommandInset href
14425 name "LyX-bug #4483"
14426 target "http://www.lyx.org/trac/ticket/4483"
14435 , TeX-mode has to be used.
14436 To be able to multiply and subtract in arguments, the LaTeX-package
14444 \begin_layout Plain Layout
14449 is part of every LaTeX standard installation.
14455 \begin_inset Index idx
14458 \begin_layout Plain Layout
14464 must be loaded in the LaTeX-preamble with the line
14467 \begin_layout Standard
14475 \begin_layout Standard
14476 Behind the formula both boxes are closed by entering
14481 Here is an example:
14485 \begin_layout Plain Layout
14499 \begin_layout Standard
14503 \begin_layout Plain Layout
14521 \begin_inset Formula
14523 \int A\,\mathrm{d}x=\frac{\sqrt[5]{B}}{\ln\left(\frac{1}{3}\right)}
14532 \begin_layout Plain Layout
14543 \begin_layout Plain Layout
14557 \begin_layout Standard
14558 \begin_inset VSpace medskip
14561 As a parbox is used as the argument of
14567 , there is in this case no difference between
14582 \begin_layout Standard
14583 \begin_inset VSpace bigskip
14586 Paragraph boxes are very useful to comment formulas directly.
14593 is used in combination with the command
14607 \begin_inset CommandInset ref
14609 reference "sub:User-defined-Numbering"
14616 \begin_layout Standard
14617 An example of a formula commented with
14626 \begin_layout Standard
14630 \begin_layout Plain Layout
14643 This is a description.
14644 It is distinctly separated from the formula and multiline.
14648 \begin_layout Plain Layout
14660 \begin_layout Standard
14661 Such a formula must be inserted completely in TeX-mode because LyX does
14662 not yet support the command
14669 The formula is created with the following command sequence:
14672 \begin_layout Standard
14685 is inserted in TeX-mode.
14689 \begin_layout Plain Layout
14690 When the formula style
14702 can also be replaced by
14709 (formula styles see
14710 \begin_inset CommandInset ref
14712 reference "sec:Formula-Styles"
14721 Then the description follows as normal text and finally
14727 is inserted in TeX-mode.
14740 hereby create a displayed formula.
14743 \begin_layout Standard
14750 can be seen in this example that was
14751 \begin_inset Quotes eld
14755 \begin_inset Quotes erd
14758 using the mathematical textmode:
14759 \begin_inset Formula
14761 5x-7b=3b\textrm{This is a description. It is not separated from the formula ...}
14769 \begin_layout Section
14771 \begin_inset Index idx
14774 \begin_layout Plain Layout
14783 \begin_layout Subsection
14785 \begin_inset CommandInset label
14787 name "sub:Big-Operators"
14792 \begin_inset Index idx
14795 \begin_layout Plain Layout
14802 \begin_inset Index idx
14805 \begin_layout Plain Layout
14812 \begin_inset Index idx
14815 \begin_layout Plain Layout
14824 \begin_layout Standard
14825 To be able to use all integral operators listed here, the option
14827 Use esint package automatically
14829 must be set in the document settings under
14832 \begin_inset space ~
14840 \begin_layout Standard
14841 \begin_inset space \hfill{}
14845 \begin_inset Tabular
14846 <lyxtabular version="3" rows="11" columns="2">
14847 <features rotate="0" tabularvalignment="middle">
14848 <column alignment="center" valignment="top" width="0pt">
14849 <column alignment="center" valignment="top" width="0pt">
14851 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
14854 \begin_layout Plain Layout
14860 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
14863 \begin_layout Plain Layout
14871 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
14874 \begin_layout Plain Layout
14878 \begin_inset Index idx
14881 \begin_layout Plain Layout
14894 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
14897 \begin_layout Plain Layout
14898 \begin_inset Formula $\int$
14908 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
14911 \begin_layout Plain Layout
14919 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
14922 \begin_layout Plain Layout
14923 \begin_inset Formula $\oint$
14933 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
14936 \begin_layout Plain Layout
14944 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
14947 \begin_layout Plain Layout
14948 \begin_inset Formula $\ointctrclockwise$
14958 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
14961 \begin_layout Plain Layout
14969 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
14972 \begin_layout Plain Layout
14973 \begin_inset Formula $\ointclockwise$
14983 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
14986 \begin_layout Plain Layout
14994 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
14997 \begin_layout Plain Layout
14998 \begin_inset Formula $\sqint$
15008 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
15011 \begin_layout Plain Layout
15019 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
15022 \begin_layout Plain Layout
15024 \begin_inset Formula $\fint$
15034 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
15037 \begin_layout Plain Layout
15045 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
15048 \begin_layout Plain Layout
15050 \begin_inset Formula $\landupint$
15060 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
15063 \begin_layout Plain Layout
15071 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
15074 \begin_layout Plain Layout
15076 \begin_inset Formula $\landdownint$
15086 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
15089 \begin_layout Plain Layout
15097 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
15100 \begin_layout Plain Layout
15101 \begin_inset Formula $\bigcap$
15111 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
15114 \begin_layout Plain Layout
15122 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
15125 \begin_layout Plain Layout
15126 \begin_inset Formula $\bigcup$
15140 \begin_inset space \hfill{}
15144 \begin_inset Tabular
15145 <lyxtabular version="3" rows="11" columns="2">
15146 <features rotate="0" tabularvalignment="middle">
15147 <column alignment="center" valignment="top" width="0pt">
15148 <column alignment="center" valignment="top" width="0pt">
15150 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
15153 \begin_layout Plain Layout
15159 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
15162 \begin_layout Plain Layout
15170 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
15173 \begin_layout Plain Layout
15177 \begin_inset Index idx
15180 \begin_layout Plain Layout
15193 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
15196 \begin_layout Plain Layout
15197 \begin_inset Formula $\sum$
15207 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
15210 \begin_layout Plain Layout
15214 \begin_inset Index idx
15217 \begin_layout Plain Layout
15224 \begin_layout Plain Layout
15243 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
15246 \begin_layout Plain Layout
15247 \begin_inset Formula $\prod$
15257 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
15260 \begin_layout Plain Layout
15268 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
15271 \begin_layout Plain Layout
15272 \begin_inset Formula $\coprod$
15282 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
15285 \begin_layout Plain Layout
15293 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
15296 \begin_layout Plain Layout
15297 \begin_inset Formula $\bigodot$
15307 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
15310 \begin_layout Plain Layout
15318 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
15321 \begin_layout Plain Layout
15322 \begin_inset Formula $\bigotimes$
15332 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
15335 \begin_layout Plain Layout
15343 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
15346 \begin_layout Plain Layout
15347 \begin_inset Formula $\bigoplus$
15357 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
15360 \begin_layout Plain Layout
15368 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
15371 \begin_layout Plain Layout
15372 \begin_inset Formula $\bigwedge$
15382 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
15385 \begin_layout Plain Layout
15393 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
15396 \begin_layout Plain Layout
15397 \begin_inset Formula $\bigvee$
15407 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
15410 \begin_layout Plain Layout
15418 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
15421 \begin_layout Plain Layout
15422 \begin_inset Formula $\bigsqcup$
15432 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
15435 \begin_layout Plain Layout
15443 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
15446 \begin_layout Plain Layout
15447 \begin_inset Formula $\biguplus$
15461 \begin_inset space \hfill{}
15467 \begin_layout Standard
15468 All big operators can also be inserted via the math toolbar button
15471 arg "math-insert \\intop"
15477 \begin_layout Standard
15478 The operators are called big because they are bigger than the sometimes
15479 equal looking binary operators.
15480 All big operators can have limits as described in the next subsection.
15483 \begin_layout Standard
15484 For all integral operators there is a second version available, ending in
15502 These operators are different from
15509 \begin_inset space \space{}
15512 in the style the operator limits are displayed, see
15513 \begin_inset CommandInset ref
15515 reference "sub:Operator-Limits"
15523 \begin_layout Subsubsection*
15524 Advice for Integrals
15527 \begin_layout Standard
15532 in an integral is an operator, that therefore has to be set upright.
15533 This is done by highlighting the
15537 and using the keyboard shortcut
15547 \begin_layout Plain Layout
15553 \begin_inset CommandInset ref
15555 reference "sub:Font-Styles"
15565 Finally the smallest space is inserted before the
15569 , as this is usual for operators.
15573 \begin_layout Standard
15575 \begin_inset Formula $\int A(x)dx$
15579 \begin_inset Newline newline
15583 \begin_inset Phantom HPhantom
15586 \begin_layout Plain Layout
15593 \begin_inset Formula $\int A(x)\,\mathrm{d}x$
15599 \begin_layout Standard
15600 For multiple integrals there are the following commands:
15601 \begin_inset VSpace medskip
15607 \begin_layout Standard
15608 \begin_inset space \hfill{}
15612 \begin_inset Tabular
15613 <lyxtabular version="3" rows="4" columns="2">
15614 <features rotate="0" tabularvalignment="middle">
15615 <column alignment="center" valignment="top">
15616 <column alignment="center" valignment="top">
15618 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
15621 \begin_layout Plain Layout
15627 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
15630 \begin_layout Plain Layout
15632 \begin_inset Note Note
15635 \begin_layout Plain Layout
15642 is only used as spacer.
15654 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
15657 \begin_layout Plain Layout
15665 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
15668 \begin_layout Plain Layout
15669 \begin_inset Formula $\raisebox{4.5mm}{}\iint\raisebox{-2.5mm}{}$
15679 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
15682 \begin_layout Plain Layout
15690 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
15693 \begin_layout Plain Layout
15694 \begin_inset Formula $\raisebox{4.5mm}{}\oiint\raisebox{-2.5mm}{}$
15704 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
15707 \begin_layout Plain Layout
15715 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
15718 \begin_layout Plain Layout
15719 \begin_inset Formula $\raisebox{4.5mm}{}\sqiint\raisebox{-2.5mm}{}$
15733 \begin_inset space \hfill{}
15737 \begin_inset Tabular
15738 <lyxtabular version="3" rows="4" columns="2">
15739 <features rotate="0" tabularvalignment="middle">
15740 <column alignment="center" valignment="top">
15741 <column alignment="center" valignment="top">
15743 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
15746 \begin_layout Plain Layout
15752 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
15755 \begin_layout Plain Layout
15763 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
15766 \begin_layout Plain Layout
15774 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
15777 \begin_layout Plain Layout
15778 \begin_inset Formula $\raisebox{4.5mm}{}\iiint\raisebox{-2.5mm}{}$
15788 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
15791 \begin_layout Plain Layout
15799 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
15802 \begin_layout Plain Layout
15803 \begin_inset Formula $\raisebox{4.5mm}{}\iiiint\raisebox{-2.5mm}{}$
15813 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
15816 \begin_layout Plain Layout
15824 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
15827 \begin_layout Plain Layout
15828 \begin_inset Formula $\raisebox{4.5mm}{}\dotsint\raisebox{-2.5mm}{}$
15842 \begin_inset space \hfill{}
15848 \begin_layout Standard
15849 \begin_inset Newpage newpage
15855 \begin_layout Subsection
15857 \begin_inset CommandInset label
15859 name "sub:Operator-Limits"
15864 \begin_inset Index idx
15867 \begin_layout Plain Layout
15876 \begin_layout Standard
15877 Limits are created by super- and subscripts:
15880 \begin_layout Standard
15882 \begin_inset Tabular
15883 <lyxtabular version="3" rows="2" columns="2">
15884 <features rotate="0" tabularvalignment="middle">
15885 <column alignment="center" valignment="top" width="0pt">
15886 <column alignment="center" valignment="top" width="0pt">
15888 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
15891 \begin_layout Plain Layout
15897 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
15900 \begin_layout Plain Layout
15902 \begin_inset Note Note
15905 \begin_layout Plain Layout
15912 is only used as spacer.
15924 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
15927 \begin_layout Plain Layout
15933 \begin_inset space \textvisiblespace{}
15937 \begin_inset Formula $\to$
15941 \begin_inset Formula $\to$
15949 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
15952 \begin_layout Plain Layout
15953 \begin_inset Formula $\raisebox{5mm}{}\prod_{0}^{\infty}A(x)\raisebox{-2.5mm}{}$
15969 \begin_layout Standard
15970 Limits of inline formulas are set right beside the operator.
15971 Limits in displayed formulas are set above or below the operator, except
15972 for integral limits.
15975 \begin_layout Standard
15976 To force that the limits are set beside the operator, the cursor is set
15977 directly behind the operator and the limits type is changed with the menu
15980 Edit\SpecialChar \menuseparator
15981 Math\SpecialChar \menuseparator
16000 \begin_layout Standard
16001 The default limits type is this:
16002 \begin_inset Formula
16004 \sum_{x=0}^{\infty}\frac{1}{x^{2}}
16009 This is how it looks when the limits type was changed to
16016 \begin_inset Formula
16018 \sum\nolimits _{x=0}^{\infty}\frac{1}{x^{2}}
16023 For integrals, except those ending with
16039 etc., the limits are by default set beside the operator.
16040 But for multiple integrals the limits are often set below the operator.
16041 In the following example the limits type was therefore set to
16045 and so set below the integrals:
16046 \begin_inset Formula
16048 \iiint\limits _{V}X\,\mathrm{d}V=U\label{eq:VolInt}
16056 \begin_layout Standard
16057 \begin_inset VSpace medskip
16060 To specify conditions for limits, the commands
16067 \begin_inset Index idx
16070 \begin_layout Plain Layout
16085 \begin_inset Index idx
16088 \begin_layout Plain Layout
16097 To create for example this expression
16098 \begin_inset Formula
16100 \sum_{\begin{subarray}{c}
16104 \end{subarray}}^{n}k^{-2}\label{eq:substack}
16112 \begin_layout Standard
16113 the following has to be done:
16114 \begin_inset Newline newline
16126 \begin_inset space \textvisiblespace{}
16132 One is now in a blue box under the summation operator and insert there
16138 \begin_inset space \textvisiblespace{}
16144 The blue box is now within a purple box and now several lines can be written
16146 A new line is created by inserting a line break (
16149 arg "newline-insert newline"
16154 \begin_inset Newline newline
16159 0<k<1000 Ctrl+Return
16160 \begin_inset Newline newline
16165 is typed in, a new box appears below for the new line.
16168 \begin_layout Standard
16169 The alignment of the lines can be changed to left aligned with the
16179 Edit\SpecialChar \menuseparator
16183 To get right alignment,
16188 \begin_inset space \textvisiblespace{}
16193 is inserted at the beginning of the line.
16196 \begin_layout Standard
16209 with the difference that the lines are always centered.
16212 \begin_layout Standard
16213 \begin_inset VSpace bigskip
16217 \begin_inset CommandInset ref
16219 reference "eq:substack"
16223 there can be too much space beside an operator, because the characters
16224 following the operator are set beside the limits.
16225 To avoid this the command
16232 \begin_inset Index idx
16235 \begin_layout Plain Layout
16244 It sets the width of its content to 0
16245 \begin_inset space \thinspace{}
16249 \begin_inset Newline newline
16253 \begin_inset CommandInset ref
16255 reference "eq:substack"
16259 , one uses the command
16262 \begin_layout Standard
16272 \begin_inset space \textvisiblespace{}
16275 0<k<1000 Ctrl+Return
16278 \begin_layout Standard
16279 to create the lower limit.
16280 The summand is now directly behind the summation operator:
16281 \begin_inset Formula
16283 \sum_{\mathclap{\substack{0<k<1000\\
16295 \begin_layout Standard
16296 \begin_inset VSpace bigskip
16302 \begin_layout Standard
16303 When several consecutive operators have limits the typesetting of the limits
16304 looks often imperfect in the output, see this example:
16305 \begin_inset Formula
16307 \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}
16312 To improve the typesetting set in the document settings under
16315 \begin_inset space ~
16325 \begin_inset Index idx
16328 \begin_layout Plain Layout
16329 Packages ! mathtools
16337 \begin_inset space ~
16343 Then insert into your formula the command
16350 \begin_inset Index idx
16353 \begin_layout Plain Layout
16361 directly before the first operator.
16362 The example will then look like this:
16363 \begin_inset Formula
16365 \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}
16373 \begin_layout Standard
16374 \begin_inset VSpace bigskip
16377 How to use one limit for several operators is described in
16378 \begin_inset CommandInset ref
16380 reference "sub:Self-defined-Operators"
16387 \begin_layout Subsection
16388 Decoration for Operators
16389 \begin_inset Index idx
16392 \begin_layout Plain Layout
16393 Operators ! Decoration
16401 \begin_layout Standard
16409 \begin_inset Index idx
16412 \begin_layout Plain Layout
16427 \begin_inset Index idx
16430 \begin_layout Plain Layout
16438 characters can be placed above or below an operator, respectively.
16446 \begin_inset Index idx
16449 \begin_layout Plain Layout
16457 characters can be set before and behind a big operator.
16460 \begin_layout Standard
16462 \begin_inset space ~
16474 \begin_layout Itemize
16481 is used to set characters at the corners of the operator
16484 \begin_layout Itemize
16491 is used to set characters before and/or behind the operator (this variant
16492 represents LaTeX's original
16501 \begin_layout Itemize
16508 is used to set characters at the left corners and/or behind the operator
16511 \begin_layout Itemize
16518 is used to set characters at the right corners and/or before the operator
16521 \begin_layout Standard
16522 For example the command
16527 \begin_inset space \textvisiblespace{}
16533 \begin_inset space \textvisiblespace{}
16537 \begin_inset Formula $\to$
16541 \begin_inset Formula $\to$
16545 \begin_inset space \textvisiblespace{}
16555 \begin_inset Formula
16557 \sideset{}{'}\sum_{k=1}^{n}
16565 \begin_layout Standard
16566 \begin_inset Note Greyedout
16569 \begin_layout Plain Layout
16576 can only be used to decorate big operators, binary operators are not allowed.
16584 \begin_layout Standard
16597 can also be used to decorate symbols and characters.
16598 For example, the command
16603 \begin_inset space \textvisiblespace{}
16609 \begin_inset space \textvisiblespace{}
16615 \begin_inset Formula $\uparrow$
16623 \begin_inset Formula
16625 \overset{a}{\maltese}
16633 \begin_layout Subsection
16635 \begin_inset CommandInset label
16637 name "sub:Binary-Operators"
16642 \begin_inset Index idx
16645 \begin_layout Plain Layout
16654 \begin_layout Standard
16655 Binary operators are surrounded by space when there is a character before
16657 \begin_inset VSpace medskip
16663 \begin_layout Standard
16664 \begin_inset space \hfill{}
16668 \begin_inset Tabular
16669 <lyxtabular version="3" rows="13" columns="2">
16670 <features rotate="0" tabularvalignment="middle">
16671 <column alignment="center" valignment="top" width="0pt">
16672 <column alignment="center" valignment="top" width="0pt">
16674 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
16677 \begin_layout Plain Layout
16679 \begin_inset Note Note
16682 \begin_layout Plain Layout
16689 is only used as spacer.
16699 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
16702 \begin_layout Plain Layout
16710 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
16713 \begin_layout Plain Layout
16719 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
16722 \begin_layout Plain Layout
16723 \begin_inset Formula $+$
16733 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
16736 \begin_layout Plain Layout
16742 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
16745 \begin_layout Plain Layout
16746 \begin_inset Formula $-$
16756 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
16759 \begin_layout Plain Layout
16767 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
16770 \begin_layout Plain Layout
16771 \begin_inset Formula $\pm$
16781 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
16784 \begin_layout Plain Layout
16792 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
16795 \begin_layout Plain Layout
16796 \begin_inset Formula $\mp$
16806 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
16809 \begin_layout Plain Layout
16817 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
16820 \begin_layout Plain Layout
16821 \begin_inset Formula $\cdot$
16831 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
16834 \begin_layout Plain Layout
16842 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
16845 \begin_layout Plain Layout
16846 \begin_inset Formula $\times$
16856 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
16859 \begin_layout Plain Layout
16867 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
16870 \begin_layout Plain Layout
16871 \begin_inset Formula $\div$
16881 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
16884 \begin_layout Plain Layout
16888 \begin_layout Plain Layout
16901 \begin_layout Plain Layout
16913 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
16916 \begin_layout Plain Layout
16917 \begin_inset Formula $*$
16927 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
16930 \begin_layout Plain Layout
16938 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
16941 \begin_layout Plain Layout
16942 \begin_inset Formula $\star$
16952 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
16955 \begin_layout Plain Layout
16963 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
16966 \begin_layout Plain Layout
16967 \begin_inset Formula $\circ$
16977 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
16980 \begin_layout Plain Layout
16988 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
16991 \begin_layout Plain Layout
16992 \begin_inset Formula $\diamond$
17002 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
17005 \begin_layout Plain Layout
17013 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
17016 \begin_layout Plain Layout
17017 \begin_inset Formula $\bullet$
17031 \begin_inset space \hfill{}
17035 \begin_inset Tabular
17036 <lyxtabular version="3" rows="13" columns="2">
17037 <features rotate="0" tabularvalignment="middle">
17038 <column alignment="center" valignment="top" width="0pt">
17039 <column alignment="center" valignment="top" width="0pt">
17041 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
17044 \begin_layout Plain Layout
17050 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
17053 \begin_layout Plain Layout
17061 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
17064 \begin_layout Plain Layout
17072 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
17075 \begin_layout Plain Layout
17076 \begin_inset Formula $\nabla$
17086 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
17089 \begin_layout Plain Layout
17097 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
17100 \begin_layout Plain Layout
17101 \begin_inset Formula $\bigtriangledown$
17111 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
17114 \begin_layout Plain Layout
17122 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
17125 \begin_layout Plain Layout
17126 \begin_inset Formula $\bigtriangleup$
17136 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
17139 \begin_layout Plain Layout
17147 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
17150 \begin_layout Plain Layout
17151 \begin_inset Formula $\Box$
17161 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
17164 \begin_layout Plain Layout
17172 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
17175 \begin_layout Plain Layout
17176 \begin_inset Formula $\cap$
17186 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
17189 \begin_layout Plain Layout
17197 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
17200 \begin_layout Plain Layout
17201 \begin_inset Formula $\cup$
17211 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
17214 \begin_layout Plain Layout
17222 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
17225 \begin_layout Plain Layout
17226 \begin_inset Formula $\dagger$
17236 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
17239 \begin_layout Plain Layout
17247 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
17250 \begin_layout Plain Layout
17251 \begin_inset Formula $\ddagger$
17261 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
17264 \begin_layout Plain Layout
17272 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
17275 \begin_layout Plain Layout
17276 \begin_inset Formula $\wr$
17286 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
17289 \begin_layout Plain Layout
17297 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
17300 \begin_layout Plain Layout
17301 \begin_inset Formula $\bigcirc$
17311 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
17314 \begin_layout Plain Layout
17322 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
17325 \begin_layout Plain Layout
17326 \begin_inset Formula $\wedge$
17336 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
17339 \begin_layout Plain Layout
17347 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
17350 \begin_layout Plain Layout
17351 \begin_inset Formula $\vee$
17365 \begin_inset space \hfill{}
17369 \begin_inset Tabular
17370 <lyxtabular version="3" rows="13" columns="2">
17371 <features rotate="0" tabularvalignment="middle">
17372 <column alignment="center" valignment="top" width="0pt">
17373 <column alignment="center" valignment="top" width="0pt">
17375 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
17378 \begin_layout Plain Layout
17384 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
17387 \begin_layout Plain Layout
17395 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
17398 \begin_layout Plain Layout
17406 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
17409 \begin_layout Plain Layout
17410 \begin_inset Formula $\oplus$
17420 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
17423 \begin_layout Plain Layout
17431 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
17434 \begin_layout Plain Layout
17435 \begin_inset Formula $\ominus$
17445 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
17448 \begin_layout Plain Layout
17456 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
17459 \begin_layout Plain Layout
17460 \begin_inset Formula $\otimes$
17470 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
17473 \begin_layout Plain Layout
17481 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
17484 \begin_layout Plain Layout
17485 \begin_inset Formula $\oslash$
17495 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
17498 \begin_layout Plain Layout
17506 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
17509 \begin_layout Plain Layout
17510 \begin_inset Formula $\odot$
17520 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
17523 \begin_layout Plain Layout
17531 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
17534 \begin_layout Plain Layout
17535 \begin_inset Formula $\amalg$
17545 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
17548 \begin_layout Plain Layout
17556 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
17559 \begin_layout Plain Layout
17560 \begin_inset Formula $\uplus$
17570 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
17573 \begin_layout Plain Layout
17581 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
17584 \begin_layout Plain Layout
17585 \begin_inset Formula $\setminus$
17595 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
17598 \begin_layout Plain Layout
17606 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
17609 \begin_layout Plain Layout
17610 \begin_inset Formula $\sqcap$
17620 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
17623 \begin_layout Plain Layout
17631 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
17634 \begin_layout Plain Layout
17635 \begin_inset Formula $\sqcup$
17645 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
17648 \begin_layout Plain Layout
17656 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
17659 \begin_layout Plain Layout
17660 \begin_inset Formula $\triangleleft$
17670 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
17673 \begin_layout Plain Layout
17681 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
17684 \begin_layout Plain Layout
17685 \begin_inset Formula $\triangleright$
17699 \begin_inset space \hfill{}
17705 \begin_layout Standard
17706 All binary operators can also be inserted via the math toolbar button
17709 arg "math-insert \\pm"
17715 \begin_layout Standard
17716 To typeset the Laplace operator also
17733 \begin_inset Formula $\nabla^{2}$
17736 ) can be used instead of
17745 \begin_layout Standard
17752 Insert\SpecialChar \menuseparator
17764 \begin_layout Subsection
17765 Self-defined Operators
17766 \begin_inset CommandInset label
17768 name "sub:Self-defined-Operators"
17773 \begin_inset Index idx
17776 \begin_layout Plain Layout
17777 Operators ! self-defined
17785 \begin_layout Standard
17786 With the help of the command
17790 DeclareMathOperator
17793 \begin_inset Index idx
17796 \begin_layout Plain Layout
17801 DeclareMathOperator
17806 custom operators can be defined in the LaTeX-preamble.
17807 Its command scheme is:
17810 \begin_layout Standard
17815 DeclareMathOperator{new command}{display}
17818 \begin_layout Standard
17819 Display can be characters or symbols that define how the operator looks
17821 To define a big operator a * is set behind the command.
17822 All self-defined big operators can have limits as described in
17823 \begin_inset CommandInset ref
17825 reference "sub:Operator-Limits"
17832 \begin_layout Standard
17833 For example the LaTeX-preamble line
17836 \begin_layout Standard
17841 DeclareMathOperator*{
17848 \begin_layout Standard
17849 defines the command
17855 , that inserts a big operator consisting of the lozenge symbol from
17856 \begin_inset CommandInset ref
17858 reference "sub:Miscellaneous-Symbols"
17863 \begin_inset Formula
17865 \Lozenge_{n=1}^{\infty}
17870 The command for this formula is:
17881 \begin_inset Formula $\to$
17887 \begin_layout Standard
17888 \begin_inset VSpace bigskip
17891 When self-defined operators are not used several times in the document,
17892 they can also be defined with the commands
17899 \begin_inset Index idx
17902 \begin_layout Plain Layout
17917 \begin_inset Index idx
17920 \begin_layout Plain Layout
17928 , which have the following scheme:
17931 \begin_layout Standard
17945 \begin_layout Standard
17952 defines big operators,
17961 \begin_layout Standard
17969 \begin_inset space \thinspace{}
17973 \begin_inset space \space{}
17976 be used to use one limit for several operators:
17979 \begin_layout Standard
17980 \begin_inset Formula
17982 \mathop{\sum\negmedspace\sum}_{i,j=1}^{N}
17990 \begin_layout Standard
17991 The command for the formula above is:
17992 \begin_inset Newline newline
18008 \begin_inset space \textvisiblespace{}
18014 \begin_inset Formula $\to$
18020 \begin_inset space \textvisiblespace{}
18028 \begin_layout Section
18030 \begin_inset Index idx
18033 \begin_layout Plain Layout
18042 \begin_layout Subsection
18044 \begin_inset CommandInset label
18046 name "sub:Font-Styles"
18051 \begin_inset Index idx
18054 \begin_layout Plain Layout
18063 \begin_layout Standard
18064 Latin letters in formulas can be set in one of the following font styles:
18065 \begin_inset VSpace -2mm
18071 \begin_layout Standard
18073 \begin_inset Tabular
18074 <lyxtabular version="3" rows="7" columns="3">
18075 <features rotate="0" tabularvalignment="middle">
18076 <column alignment="center" valignment="top">
18077 <column alignment="center" valignment="top">
18078 <column alignment="center" valignment="top">
18080 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
18083 \begin_layout Plain Layout
18089 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
18092 \begin_layout Plain Layout
18098 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
18101 \begin_layout Plain Layout
18109 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
18112 \begin_layout Plain Layout
18118 \begin_inset space \textvisiblespace{}
18128 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
18131 \begin_layout Plain Layout
18132 \begin_inset Formula $\mathbb{ABC}$
18140 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
18143 \begin_layout Plain Layout
18156 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
18159 \begin_layout Plain Layout
18165 \begin_inset space \textvisiblespace{}
18175 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
18178 \begin_layout Plain Layout
18179 \begin_inset Formula $\mathbf{AbC}$
18187 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
18190 \begin_layout Plain Layout
18203 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
18206 \begin_layout Plain Layout
18212 \begin_inset space \textvisiblespace{}
18222 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
18225 \begin_layout Plain Layout
18226 \begin_inset Formula $\boldsymbol{AbC}$
18234 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
18237 \begin_layout Plain Layout
18240 arg "font-boldsymbol"
18250 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
18253 \begin_layout Plain Layout
18259 \begin_inset space \textvisiblespace{}
18269 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
18272 \begin_layout Plain Layout
18273 \begin_inset Formula $\mathcal{ABC}$
18281 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
18284 \begin_layout Plain Layout
18297 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
18300 \begin_layout Plain Layout
18306 \begin_inset space \textvisiblespace{}
18316 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
18319 \begin_layout Plain Layout
18320 \begin_inset Formula $\mathfrak{AbC}$
18328 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
18331 \begin_layout Plain Layout
18339 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
18342 \begin_layout Plain Layout
18348 \begin_inset space \textvisiblespace{}
18358 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
18361 \begin_layout Plain Layout
18362 \begin_inset Formula $\mathscr{AbC}$
18370 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
18373 \begin_layout Plain Layout
18387 \begin_layout Standard
18389 \begin_inset Tabular
18390 <lyxtabular version="3" rows="5" columns="3">
18391 <features rotate="0" tabularvalignment="middle">
18392 <column alignment="center" valignment="top">
18393 <column alignment="center" valignment="top">
18394 <column alignment="center" valignment="top">
18396 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
18399 \begin_layout Plain Layout
18405 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
18408 \begin_layout Plain Layout
18414 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
18417 \begin_layout Plain Layout
18425 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
18428 \begin_layout Plain Layout
18434 \begin_inset space \textvisiblespace{}
18444 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
18447 \begin_layout Plain Layout
18448 \begin_inset Formula $\mathit{AbC}$
18456 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
18459 \begin_layout Plain Layout
18467 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
18470 \begin_layout Plain Layout
18476 \begin_inset space \textvisiblespace{}
18486 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
18489 \begin_layout Plain Layout
18490 \begin_inset Formula $\mathrm{AbC}$
18498 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
18501 \begin_layout Plain Layout
18514 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
18517 \begin_layout Plain Layout
18523 \begin_inset space \textvisiblespace{}
18533 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
18536 \begin_layout Plain Layout
18537 \begin_inset Formula $\mathsf{AbC}$
18545 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
18548 \begin_layout Plain Layout
18561 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
18564 \begin_layout Plain Layout
18570 \begin_inset space \textvisiblespace{}
18580 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
18583 \begin_layout Plain Layout
18584 \begin_inset Formula $\mathtt{AbC}$
18592 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
18595 \begin_layout Plain Layout
18598 arg "font-typewriter"
18614 \begin_layout Standard
18615 \begin_inset Note Greyedout
18618 \begin_layout Plain Layout
18635 can only be used for big letters.
18643 \begin_layout Standard
18644 Predefined is the style
18653 \begin_layout Standard
18654 The style commands work also for letters in mathematical constructs:
18655 \begin_inset Formula
18657 \mathfrak{A=\frac{b}{C}}
18665 \begin_layout Standard
18666 Characters in mathematical text don't appear in a math font style but in
18667 the text font style
18674 That their style can't be set correctly via the text style dialog is a
18679 \begin_layout Plain Layout
18680 \begin_inset CommandInset href
18682 name "LyX-bug #4629"
18683 target "http://www.lyx.org/trac/ticket/4629"
18695 \begin_layout Standard
18696 Instead of the style commands the dialog
18698 Edit\SpecialChar \menuseparator
18699 Math\SpecialChar \menuseparator
18702 or the toolbar button
18705 arg "math-insert \\font"
18711 \begin_layout Subsection
18713 \begin_inset CommandInset label
18715 name "sub:Bold-Formulas"
18720 \begin_inset Index idx
18723 \begin_layout Plain Layout
18732 \begin_layout Standard
18733 To make a complete formula bold, the command
18739 from the previous subsection cannot be used, because it doesn't work for
18740 small Greek letters.
18741 Furthermore it prints Latin letters always upright, like in the following
18745 \begin_layout Standard
18746 \begin_inset Formula
18748 \mathbf{\int_{n}^{2}f(\theta)=\Gamma}\qquad\textrm{equation with \textbackslash mathbf}
18756 \begin_layout Standard
18757 To display the formula correctly, the command
18764 \begin_inset Formula
18766 \boldsymbol{\int_{n}^{2}f(\theta)=\Gamma\qquad\textrm{equation with \textbackslash boldsymbol}}
18771 It is also possible to set the formula in a
18773 boldmath environment
18776 This environment is created by inserting the command
18783 \begin_inset Index idx
18786 \begin_layout Plain Layout
18795 To end the environment, the command
18802 \begin_inset Index idx
18805 \begin_layout Plain Layout
18813 is inserted in TeX-mode.
18817 \begin_layout Plain Layout
18827 \begin_inset Formula
18829 \int_{n}^{2}f(\theta)=\Gamma\qquad\textrm{equation in a boldmath environment}
18838 \begin_layout Plain Layout
18850 \begin_layout Subsection
18852 \begin_inset Index idx
18855 \begin_layout Plain Layout
18864 \begin_layout Standard
18865 Formulas can be colored like normal text: Highlight a formula or a formula
18871 Here is a formula in magenta:
18872 \begin_inset Formula
18874 {\color{magenta}\int A\,\mathrm{d}x=\frac{\sqrt[5]{B}}{\ln\left(\frac{1}{3}\right)}}
18882 \begin_layout Standard
18883 You can also define your own colors as described in
18884 \begin_inset CommandInset ref
18886 reference "sub:Colored-Boxes"
18891 They can be used with the TeX code command
18898 \begin_inset Index idx
18901 \begin_layout Plain Layout
18912 \begin_layout Standard
18917 textcolor{color}{characters or formula}
18920 \begin_layout Standard
18921 The following example was colored completely dark green and partly red:
18924 \begin_layout Standard
18928 \begin_layout Plain Layout
18932 textcolor{darkgreen}{
18938 \begin_inset Formula
18940 \int A\,\mathrm{d}x=\frac{{\color{red}\sqrt[5]{B}}}{\ln\left(\frac{1}{3}\right)}
18949 \begin_layout Plain Layout
18959 \begin_layout Standard
18960 Due to a bug in LyX only complete formulas can be colored with self-defined
18965 \begin_layout Plain Layout
18966 \begin_inset CommandInset href
18968 name "LyX-bug #5269"
18969 target "http://www.lyx.org/trac/ticket/5269"
18981 \begin_layout Subsection
18983 \begin_inset CommandInset label
18985 name "sub:Font-Sizes"
18990 \begin_inset Index idx
18993 \begin_layout Plain Layout
19002 \begin_layout Standard
19003 For characters in formulas there are, analog to characters in text, the
19004 following size commands:
19007 \begin_layout Standard
19051 \begin_inset Newline newline
19073 \begin_layout Standard
19074 The size produced by the commands depends on the document font size, which
19075 corresponds to the command
19082 The other commands produce smaller or larger sizes than
19089 The font size can however not exceed a certain value.
19090 Is for example the document font size 12
19091 \begin_inset space \thinspace{}
19100 switches to the same size as
19110 \begin_layout Standard
19111 A size command is inserted in TeX-mode before the formula and sets the size
19112 for all following formula and text characters.
19113 To switch back to the initial size, the command
19119 is inserted behind the formula in TeX-mode.
19122 \begin_layout Standard
19123 Within a formula the size can be changed using the following size commands
19124 or the toolbar button
19127 arg "math-insert \\style"
19133 \begin_layout Standard
19136 \begin_inset Tabular
19137 <lyxtabular version="3" rows="5" columns="2">
19138 <features rotate="0" tabularvalignment="middle">
19139 <column alignment="center" valignment="top">
19140 <column alignment="center" valignment="top">
19142 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
19145 \begin_layout Plain Layout
19151 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
19154 \begin_layout Plain Layout
19156 \begin_inset Note Note
19159 \begin_layout Plain Layout
19166 is only used as spacer.
19178 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
19181 \begin_layout Plain Layout
19185 \begin_inset Index idx
19188 \begin_layout Plain Layout
19201 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
19204 \begin_layout Plain Layout
19205 \begin_inset Formula $\raisebox{6.5mm}{}{\displaystyle E_{\mathrm{pot_{1}}}=\frac{K}{l+\frac{m}{n_{2}}}}\raisebox{-5.5mm}{}$
19215 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
19218 \begin_layout Plain Layout
19226 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
19229 \begin_layout Plain Layout
19230 \begin_inset Formula $\raisebox{4.5mm}{}{\textstyle E_{\mathrm{pot_{1}}}=\frac{K}{l+\frac{m}{n_{2}}}}\raisebox{-4mm}{}$
19240 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
19243 \begin_layout Plain Layout
19251 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
19254 \begin_layout Plain Layout
19255 \begin_inset Formula $\raisebox{4.5mm}{}{\scriptstyle E_{\mathrm{pot_{1}}}=\frac{K}{l+\frac{m}{n_{2}}}}\raisebox{-3.5mm}{}$
19265 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
19268 \begin_layout Plain Layout
19276 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
19279 \begin_layout Plain Layout
19280 \begin_inset Formula $\raisebox{4.5mm}{}{\scriptscriptstyle E_{\mathrm{pot_{1}}}=\frac{K}{l+\frac{m}{n_{2}}}}\raisebox{-3.5mm}{}$
19296 \begin_layout Standard
19297 After entering these commands, a blue box appears in which the formula parts
19301 \begin_layout Standard
19302 There is a further method to change the font size, that though only works
19303 for symbols or letters in mathematical text.
19304 To use it, one of the above text size commands is inserted in mathematical
19306 All following characters until the end of the mathematical text or until
19307 another size command will have the selected size.
19309 \begin_inset VSpace -2mm
19315 \begin_layout Standard
19319 \begin_layout Plain Layout
19329 \begin_inset Formula
19331 A=\frac{B}{c}\cdot\maltese
19337 \begin_inset Formula
19339 \maltese A\textrm{\Large\maltese\textit{A}}\textrm{\tiny\maltese\textit{A}}
19348 \begin_layout Plain Layout
19360 \begin_layout Standard
19361 \begin_inset VSpace medskip
19364 Before both formulas the command
19371 The command for the second formula is:
19372 \begin_inset Newline newline
19380 \begin_inset space \textvisiblespace{}
19386 \begin_inset space \textvisiblespace{}
19392 \begin_inset space \textvisiblespace{}
19398 \begin_inset space \textvisiblespace{}
19402 \begin_inset Formula $\to$
19406 \begin_inset Formula $\to$
19410 \begin_inset Newline newline
19414 \begin_inset space \hspace*{}
19425 \begin_inset space \textvisiblespace{}
19431 \begin_inset space \textvisiblespace{}
19437 \begin_inset space \textvisiblespace{}
19443 \begin_layout Standard
19444 If a symbol cannot be displayed in different sizes, it will always be displayed
19445 in the default size.
19448 \begin_layout Section
19450 \begin_inset Index idx
19453 \begin_layout Plain Layout
19462 \begin_layout Standard
19463 Greek letters can also be inserted via the toolbar button
19466 arg "math-insert \\alpha"
19470 All international typesetting norms purport that Greek letters in math
19471 have to be typeset italic/slanted.
19472 In some languages, like French or Russian, they are nevertheless sometimes
19476 \begin_layout Subsection
19478 \begin_inset Index idx
19481 \begin_layout Plain Layout
19482 Greek letters ! small
19490 \begin_layout Standard
19491 \begin_inset space \hfill{}
19495 \begin_inset Tabular
19496 <lyxtabular version="3" rows="11" columns="2">
19497 <features rotate="0" tabularvalignment="middle">
19498 <column alignment="center" valignment="top" width="0pt">
19499 <column alignment="center" valignment="top" width="0pt">
19501 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
19504 \begin_layout Plain Layout
19510 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
19513 \begin_layout Plain Layout
19521 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
19524 \begin_layout Plain Layout
19532 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
19535 \begin_layout Plain Layout
19536 \begin_inset Formula $\alpha$
19546 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
19549 \begin_layout Plain Layout
19557 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
19560 \begin_layout Plain Layout
19561 \begin_inset Formula $\beta$
19571 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
19574 \begin_layout Plain Layout
19582 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
19585 \begin_layout Plain Layout
19586 \begin_inset Formula $\gamma$
19596 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
19599 \begin_layout Plain Layout
19607 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
19610 \begin_layout Plain Layout
19611 \begin_inset Formula $\delta$
19621 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
19624 \begin_layout Plain Layout
19632 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
19635 \begin_layout Plain Layout
19636 \begin_inset Formula $\epsilon$
19646 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
19649 \begin_layout Plain Layout
19657 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
19660 \begin_layout Plain Layout
19661 \begin_inset Formula $\varepsilon$
19671 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
19674 \begin_layout Plain Layout
19682 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
19685 \begin_layout Plain Layout
19686 \begin_inset Formula $\zeta$
19696 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
19699 \begin_layout Plain Layout
19707 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
19710 \begin_layout Plain Layout
19711 \begin_inset Formula $\eta$
19721 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
19724 \begin_layout Plain Layout
19732 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
19735 \begin_layout Plain Layout
19736 \begin_inset Formula $\theta$
19746 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
19749 \begin_layout Plain Layout
19757 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
19760 \begin_layout Plain Layout
19761 \begin_inset Formula $\vartheta$
19775 \begin_inset space \hfill{}
19779 \begin_inset Tabular
19780 <lyxtabular version="3" rows="12" columns="2">
19781 <features rotate="0" tabularvalignment="middle">
19782 <column alignment="center" valignment="top" width="0pt">
19783 <column alignment="center" valignment="top" width="0pt">
19785 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
19788 \begin_layout Plain Layout
19794 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
19797 \begin_layout Plain Layout
19805 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
19808 \begin_layout Plain Layout
19816 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
19819 \begin_layout Plain Layout
19820 \begin_inset Formula $\iota$
19830 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
19833 \begin_layout Plain Layout
19841 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
19844 \begin_layout Plain Layout
19845 \begin_inset Formula $\kappa$
19855 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
19858 \begin_layout Plain Layout
19866 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
19869 \begin_layout Plain Layout
19870 \begin_inset Formula $\varkappa$
19880 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
19883 \begin_layout Plain Layout
19891 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
19894 \begin_layout Plain Layout
19895 \begin_inset Formula $\lambda$
19905 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
19908 \begin_layout Plain Layout
19916 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
19919 \begin_layout Plain Layout
19920 \begin_inset Formula $\mu$
19930 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
19933 \begin_layout Plain Layout
19941 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
19944 \begin_layout Plain Layout
19945 \begin_inset Formula $\nu$
19955 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
19958 \begin_layout Plain Layout
19966 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
19969 \begin_layout Plain Layout
19970 \begin_inset Formula $\xi$
19980 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
19983 \begin_layout Plain Layout
19989 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
19992 \begin_layout Plain Layout
19993 \begin_inset Formula $o$
20003 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
20006 \begin_layout Plain Layout
20014 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
20017 \begin_layout Plain Layout
20018 \begin_inset Formula $\pi$
20028 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
20031 \begin_layout Plain Layout
20039 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
20042 \begin_layout Plain Layout
20043 \begin_inset Formula $\varpi$
20053 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
20056 \begin_layout Plain Layout
20064 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
20067 \begin_layout Plain Layout
20068 \begin_inset Formula $\rho$
20082 \begin_inset space \hfill{}
20086 \begin_inset Tabular
20087 <lyxtabular version="3" rows="11" columns="2">
20088 <features rotate="0" tabularvalignment="middle">
20089 <column alignment="center" valignment="top" width="0pt">
20090 <column alignment="center" valignment="top" width="0pt">
20092 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
20095 \begin_layout Plain Layout
20101 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
20104 \begin_layout Plain Layout
20112 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
20115 \begin_layout Plain Layout
20123 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
20126 \begin_layout Plain Layout
20127 \begin_inset Formula $\varrho$
20137 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
20140 \begin_layout Plain Layout
20148 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
20151 \begin_layout Plain Layout
20152 \begin_inset Formula $\sigma$
20162 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
20165 \begin_layout Plain Layout
20173 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
20176 \begin_layout Plain Layout
20177 \begin_inset Formula $\varsigma$
20187 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
20190 \begin_layout Plain Layout
20198 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
20201 \begin_layout Plain Layout
20202 \begin_inset Formula $\tau$
20212 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
20215 \begin_layout Plain Layout
20223 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
20226 \begin_layout Plain Layout
20227 \begin_inset Formula $\upsilon$
20237 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
20240 \begin_layout Plain Layout
20248 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
20251 \begin_layout Plain Layout
20252 \begin_inset Formula $\phi$
20262 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
20265 \begin_layout Plain Layout
20273 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
20276 \begin_layout Plain Layout
20277 \begin_inset Formula $\varphi$
20287 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
20290 \begin_layout Plain Layout
20298 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
20301 \begin_layout Plain Layout
20302 \begin_inset Formula $\chi$
20312 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
20315 \begin_layout Plain Layout
20323 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
20326 \begin_layout Plain Layout
20327 \begin_inset Formula $\psi$
20337 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
20340 \begin_layout Plain Layout
20348 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
20351 \begin_layout Plain Layout
20352 \begin_inset Formula $\omega$
20366 \begin_inset space \hfill{}
20372 \begin_layout Standard
20373 \begin_inset VSpace medskip
20379 \begin_layout Standard
20380 How to create special upright Greek letters is explained in
20381 \begin_inset CommandInset ref
20383 reference "sub:Upright-small-Greek"
20390 \begin_layout Subsection
20392 \begin_inset Index idx
20395 \begin_layout Plain Layout
20396 Greek letters ! big
20404 \begin_layout Standard
20405 \begin_inset space \hfill{}
20409 \begin_inset Tabular
20410 <lyxtabular version="3" rows="7" columns="2">
20411 <features rotate="0" tabularvalignment="middle">
20412 <column alignment="center" valignment="top" width="0pt">
20413 <column alignment="center" valignment="top" width="0pt">
20415 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
20418 \begin_layout Plain Layout
20424 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
20427 \begin_layout Plain Layout
20435 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
20438 \begin_layout Plain Layout
20446 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
20449 \begin_layout Plain Layout
20450 \begin_inset Formula $\Gamma$
20460 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
20463 \begin_layout Plain Layout
20471 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
20474 \begin_layout Plain Layout
20475 \begin_inset Formula $\Delta$
20485 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
20488 \begin_layout Plain Layout
20496 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
20499 \begin_layout Plain Layout
20500 \begin_inset Formula $\Theta$
20510 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
20513 \begin_layout Plain Layout
20521 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
20524 \begin_layout Plain Layout
20525 \begin_inset Formula $\Lambda$
20535 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
20538 \begin_layout Plain Layout
20546 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
20549 \begin_layout Plain Layout
20550 \begin_inset Formula $\Xi$
20560 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
20563 \begin_layout Plain Layout
20571 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
20574 \begin_layout Plain Layout
20575 \begin_inset Formula $\Pi$
20589 \begin_inset space \hfill{}
20593 \begin_inset Tabular
20594 <lyxtabular version="3" rows="6" columns="2">
20595 <features rotate="0" tabularvalignment="middle">
20596 <column alignment="center" valignment="top" width="0pt">
20597 <column alignment="center" valignment="top" width="0pt">
20599 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
20602 \begin_layout Plain Layout
20608 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
20611 \begin_layout Plain Layout
20619 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
20622 \begin_layout Plain Layout
20630 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
20633 \begin_layout Plain Layout
20634 \begin_inset Formula $\Sigma$
20644 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
20647 \begin_layout Plain Layout
20655 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
20658 \begin_layout Plain Layout
20659 \begin_inset Formula $\Upsilon$
20669 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
20672 \begin_layout Plain Layout
20680 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
20683 \begin_layout Plain Layout
20684 \begin_inset Formula $\Phi$
20694 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
20697 \begin_layout Plain Layout
20705 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
20708 \begin_layout Plain Layout
20709 \begin_inset Formula $\Psi$
20719 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
20722 \begin_layout Plain Layout
20730 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
20733 \begin_layout Plain Layout
20734 \begin_inset Formula $\Omega$
20748 \begin_inset space \hfill{}
20754 \begin_layout Standard
20755 \begin_inset VSpace medskip
20758 That the big Greek letters appear upright is caused by a design bug when
20760 To get correct italic big letters, begin every command with
20765 For example the command
20772 \begin_inset Formula $\varGamma$
20776 Another way is to load the package
20784 \begin_layout Plain Layout
20789 is part of the LaTeX-package
20794 \begin_inset Index idx
20797 \begin_layout Plain Layout
20802 \begin_layout Plain Layout
20822 \begin_inset Index idx
20825 \begin_layout Plain Layout
20831 with the LaTeX-preamble line
20834 \begin_layout Standard
20839 usepackage{fixmath}
20842 \begin_layout Standard
20843 Then all big Greek letters in a document will automatically be typeset italic.
20846 \begin_layout Subsection
20848 \begin_inset Index idx
20851 \begin_layout Plain Layout
20852 Greek letters ! bold
20860 \begin_layout Standard
20861 Greek letters cannot be set with different font styles like Latin letters.
20862 They can only be made bold with the command
20869 \begin_inset Index idx
20872 \begin_layout Plain Layout
20883 \begin_layout Standard
20885 \begin_inset Tabular
20886 <lyxtabular version="3" rows="3" columns="2">
20887 <features rotate="0" tabularvalignment="middle">
20888 <column alignment="center" valignment="top">
20889 <column alignment="center" valignment="top">
20891 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
20894 \begin_layout Plain Layout
20900 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
20903 \begin_layout Plain Layout
20911 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
20914 \begin_layout Plain Layout
20926 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
20929 \begin_layout Plain Layout
20930 \begin_inset Formula $\Upsilon\boldsymbol{\Upsilon}$
20940 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
20943 \begin_layout Plain Layout
20955 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
20958 \begin_layout Plain Layout
20959 \begin_inset Formula $\theta\boldsymbol{\theta}$
20975 \begin_layout Section
20980 \begin_layout Plain Layout
20993 \begin_layout Plain Layout
20994 A list with all symbols of most of the LaTeX-packages can be found in
20995 \begin_inset CommandInset citation
21010 \begin_layout Plain Layout
21018 \begin_inset Note Note
21021 \begin_layout Plain Layout
21024 texorpdfstring is used to avoid that the footnote appears in the PDF-bookmark.
21027 \begin_layout Plain Layout
21030 texorpdfstring is in section
21031 \begin_inset CommandInset ref
21033 reference "sub:Formulas-in-Section"
21043 \begin_inset Index idx
21046 \begin_layout Plain Layout
21055 \begin_layout Standard
21056 Many of the symbols listed in this section can also be inserted via the
21060 arg "math-insert \\nabla"
21066 arg "math-insert \\digamma"
21072 \begin_layout Subsection
21073 Mathematical Symbols
21074 \begin_inset CommandInset label
21076 name "sub:Mathematical-Symbols"
21081 \begin_inset Index idx
21084 \begin_layout Plain Layout
21085 Symbols ! mathematical
21093 \begin_layout Standard
21094 \begin_inset space \hfill{}
21098 \begin_inset Tabular
21099 <lyxtabular version="3" rows="10" columns="2">
21100 <features rotate="0" tabularvalignment="middle">
21101 <column alignment="center" valignment="top" width="0pt">
21102 <column alignment="center" valignment="top" width="0pt">
21104 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
21107 \begin_layout Plain Layout
21113 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
21116 \begin_layout Plain Layout
21124 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
21127 \begin_layout Plain Layout
21135 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
21138 \begin_layout Plain Layout
21139 \begin_inset Formula $\neg$
21149 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
21152 \begin_layout Plain Layout
21160 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
21163 \begin_layout Plain Layout
21164 \begin_inset Formula $\Im$
21174 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
21177 \begin_layout Plain Layout
21185 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
21188 \begin_layout Plain Layout
21189 \begin_inset Formula $\Re$
21199 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
21202 \begin_layout Plain Layout
21210 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
21213 \begin_layout Plain Layout
21214 \begin_inset Formula $\aleph$
21224 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
21227 \begin_layout Plain Layout
21235 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
21238 \begin_layout Plain Layout
21239 \begin_inset Formula $\partial$
21249 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
21252 \begin_layout Plain Layout
21260 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
21263 \begin_layout Plain Layout
21264 \begin_inset Formula $\infty$
21274 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
21277 \begin_layout Plain Layout
21285 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
21288 \begin_layout Plain Layout
21289 \begin_inset Formula $\wp$
21299 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
21302 \begin_layout Plain Layout
21310 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
21313 \begin_layout Plain Layout
21314 \begin_inset Formula $\imath$
21324 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
21327 \begin_layout Plain Layout
21335 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
21338 \begin_layout Plain Layout
21339 \begin_inset Formula $\jmath$
21353 \begin_inset space \hfill{}
21357 \begin_inset Tabular
21358 <lyxtabular version="3" rows="10" columns="2">
21359 <features rotate="0" tabularvalignment="middle">
21360 <column alignment="center" valignment="top" width="0pt">
21361 <column alignment="center" valignment="top" width="0pt">
21363 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
21366 \begin_layout Plain Layout
21372 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
21375 \begin_layout Plain Layout
21377 \begin_inset Note Note
21380 \begin_layout Plain Layout
21387 is only used as spacer.
21399 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
21402 \begin_layout Plain Layout
21410 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
21413 \begin_layout Plain Layout
21414 \begin_inset Formula $\forall$
21424 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
21427 \begin_layout Plain Layout
21435 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
21438 \begin_layout Plain Layout
21439 \begin_inset Formula $\exists$
21449 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
21452 \begin_layout Plain Layout
21460 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
21463 \begin_layout Plain Layout
21464 \begin_inset Formula $\nexists$
21474 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
21477 \begin_layout Plain Layout
21485 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
21488 \begin_layout Plain Layout
21489 \begin_inset Formula $\emptyset$
21499 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
21502 \begin_layout Plain Layout
21510 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
21513 \begin_layout Plain Layout
21514 \begin_inset Formula $\varnothing$
21524 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
21527 \begin_layout Plain Layout
21535 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
21538 \begin_layout Plain Layout
21539 \begin_inset Formula $\dag$
21549 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
21552 \begin_layout Plain Layout
21560 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
21563 \begin_layout Plain Layout
21564 \begin_inset Formula $\ddag$
21574 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
21577 \begin_layout Plain Layout
21585 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
21588 \begin_layout Plain Layout
21592 \begin_layout Plain Layout
21602 \begin_inset Formula $\complement$
21609 \begin_layout Plain Layout
21623 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
21626 \begin_layout Plain Layout
21634 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
21637 \begin_layout Plain Layout
21638 \begin_inset Formula $\Bbbk$
21652 \begin_inset space \hfill{}
21656 \begin_inset Tabular
21657 <lyxtabular version="3" rows="10" columns="2">
21658 <features rotate="0" tabularvalignment="middle">
21659 <column alignment="center" valignment="top" width="0pt">
21660 <column alignment="center" valignment="top" width="0pt">
21662 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
21665 \begin_layout Plain Layout
21671 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
21674 \begin_layout Plain Layout
21682 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
21685 \begin_layout Plain Layout
21693 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
21696 \begin_layout Plain Layout
21697 \begin_inset Formula $\prime$
21707 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
21710 \begin_layout Plain Layout
21718 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
21721 \begin_layout Plain Layout
21722 \begin_inset Formula $\backprime$
21732 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
21735 \begin_layout Plain Layout
21743 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
21746 \begin_layout Plain Layout
21747 \begin_inset Formula $\mho$
21757 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
21760 \begin_layout Plain Layout
21768 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
21771 \begin_layout Plain Layout
21772 \begin_inset Formula $\triangle$
21782 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
21785 \begin_layout Plain Layout
21793 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
21796 \begin_layout Plain Layout
21797 \begin_inset Formula $\angle$
21807 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
21810 \begin_layout Plain Layout
21818 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
21821 \begin_layout Plain Layout
21822 \begin_inset Formula $\measuredangle$
21832 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
21835 \begin_layout Plain Layout
21843 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
21846 \begin_layout Plain Layout
21847 \begin_inset Formula $\sphericalangle$
21857 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
21860 \begin_layout Plain Layout
21868 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
21871 \begin_layout Plain Layout
21872 \begin_inset Formula $\top$
21882 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
21885 \begin_layout Plain Layout
21893 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
21896 \begin_layout Plain Layout
21897 \begin_inset Formula $\bot$
21911 \begin_inset space \hfill{}
21917 \begin_layout Subsection
21918 Miscellaneous Symbols
21919 \begin_inset CommandInset label
21921 name "sub:Miscellaneous-Symbols"
21926 \begin_inset Index idx
21929 \begin_layout Plain Layout
21930 Symbols ! miscellaneous
21938 \begin_layout Standard
21941 \begin_inset Tabular
21942 <lyxtabular version="3" rows="10" columns="2">
21943 <features rotate="0" tabularvalignment="middle">
21944 <column alignment="center" valignment="top" width="0pt">
21945 <column alignment="center" valignment="top" width="0pt">
21947 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
21950 \begin_layout Plain Layout
21956 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
21959 \begin_layout Plain Layout
21967 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
21970 \begin_layout Plain Layout
21978 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
21981 \begin_layout Plain Layout
21982 \begin_inset Formula $\flat$
21992 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
21995 \begin_layout Plain Layout
22003 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
22006 \begin_layout Plain Layout
22007 \begin_inset Formula $\natural$
22017 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
22020 \begin_layout Plain Layout
22028 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
22031 \begin_layout Plain Layout
22032 \begin_inset Formula $\sharp$
22042 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
22045 \begin_layout Plain Layout
22053 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
22056 \begin_layout Plain Layout
22057 \begin_inset Formula $\surd$
22067 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
22070 \begin_layout Plain Layout
22078 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
22081 \begin_layout Plain Layout
22082 \begin_inset Formula $\checkmark$
22092 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
22095 \begin_layout Plain Layout
22103 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
22106 \begin_layout Plain Layout
22107 \begin_inset Formula $\yen$
22117 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
22120 \begin_layout Plain Layout
22128 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
22131 \begin_layout Plain Layout
22132 \begin_inset Formula $\pounds$
22142 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
22145 \begin_layout Plain Layout
22151 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
22154 \begin_layout Plain Layout
22155 \begin_inset Formula $\$$
22165 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
22168 \begin_layout Plain Layout
22174 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
22177 \begin_layout Plain Layout
22178 \begin_inset Formula $§$
22192 \begin_inset Tabular
22193 <lyxtabular version="3" rows="10" columns="2">
22194 <features rotate="0" tabularvalignment="middle">
22195 <column alignment="center" valignment="top">
22196 <column alignment="center" valignment="top">
22198 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
22201 \begin_layout Plain Layout
22207 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
22210 \begin_layout Plain Layout
22218 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
22221 \begin_layout Plain Layout
22229 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
22232 \begin_layout Plain Layout
22233 \begin_inset Formula $\hbar$
22243 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
22246 \begin_layout Plain Layout
22254 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
22257 \begin_layout Plain Layout
22258 \begin_inset Formula $\hslash$
22268 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
22271 \begin_layout Plain Layout
22279 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
22282 \begin_layout Plain Layout
22283 \begin_inset Formula $\clubsuit$
22293 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
22296 \begin_layout Plain Layout
22304 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
22307 \begin_layout Plain Layout
22308 \begin_inset Formula $\spadesuit$
22318 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
22321 \begin_layout Plain Layout
22329 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
22332 \begin_layout Plain Layout
22333 \begin_inset Formula $\bigstar$
22343 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
22346 \begin_layout Plain Layout
22354 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
22357 \begin_layout Plain Layout
22358 \begin_inset Formula $\blacklozenge$
22368 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
22371 \begin_layout Plain Layout
22379 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
22382 \begin_layout Plain Layout
22383 \begin_inset Formula $\blacktriangle$
22393 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
22396 \begin_layout Plain Layout
22404 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
22407 \begin_layout Plain Layout
22408 \begin_inset Formula $\blacktriangledown$
22418 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
22421 \begin_layout Plain Layout
22429 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
22432 \begin_layout Plain Layout
22433 \begin_inset Formula $\bullet$
22447 \begin_inset Tabular
22448 <lyxtabular version="3" rows="10" columns="2">
22449 <features rotate="0" tabularvalignment="middle">
22450 <column alignment="center" valignment="top" width="0pt">
22451 <column alignment="center" valignment="top" width="0pt">
22453 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
22456 \begin_layout Plain Layout
22462 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
22465 \begin_layout Plain Layout
22473 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
22476 \begin_layout Plain Layout
22484 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
22487 \begin_layout Plain Layout
22488 \begin_inset Formula $\diamondsuit$
22498 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
22501 \begin_layout Plain Layout
22509 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
22512 \begin_layout Plain Layout
22513 \begin_inset Formula $\Diamond$
22523 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
22526 \begin_layout Plain Layout
22534 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
22537 \begin_layout Plain Layout
22538 \begin_inset Formula $\heartsuit$
22548 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
22551 \begin_layout Plain Layout
22559 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
22562 \begin_layout Plain Layout
22563 \begin_inset Formula $\P$
22573 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
22576 \begin_layout Plain Layout
22584 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
22587 \begin_layout Plain Layout
22588 \begin_inset Formula $\copyright$
22598 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
22601 \begin_layout Plain Layout
22609 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
22612 \begin_layout Plain Layout
22613 \begin_inset Formula $\circledR$
22623 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
22626 \begin_layout Plain Layout
22634 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
22637 \begin_layout Plain Layout
22638 \begin_inset Formula $\maltese$
22648 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
22651 \begin_layout Plain Layout
22659 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
22662 \begin_layout Plain Layout
22663 \begin_inset Formula $\diagup$
22673 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
22676 \begin_layout Plain Layout
22684 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
22687 \begin_layout Plain Layout
22688 \begin_inset Formula $\diagdown$
22704 \begin_layout Standard
22705 \begin_inset VSpace medskip
22711 \begin_layout Standard
22712 Some symbols can be displayed in different sizes, see
22713 \begin_inset CommandInset ref
22715 reference "sub:Font-Sizes"
22722 \begin_layout Subsection
22724 \begin_inset Index idx
22727 \begin_layout Plain Layout
22728 Symbols ! Euro-symbol
22734 \begin_inset Index idx
22737 \begin_layout Plain Layout
22744 \begin_layout Plain Layout
22761 \begin_layout Standard
22762 To use the Euro symbol in formulas, the LaTeX-package
22767 \begin_inset Index idx
22770 \begin_layout Plain Layout
22776 must be installed and loaded with the LaTeX-preamble line
22779 \begin_layout Standard
22784 usepackage[gennarrow]{eurosym}
22787 \begin_layout Standard
22788 The Euro symbol can now be inserted with the command
22795 \begin_inset Index idx
22798 \begin_layout Plain Layout
22809 \begin_layout Standard
22810 The Euro symbol can directly be inserted with the € key in mathematical
22811 text, without having
22826 can also be inserted in TeX-mode.
22827 The official currency symbol can then be inserted with the command
22834 \begin_inset Index idx
22837 \begin_layout Plain Layout
22845 , that is only available in TeX-mode.
22848 \begin_layout Standard
22852 \begin_layout Plain Layout
22862 \begin_inset Note Note
22865 \begin_layout Plain Layout
22866 The following table will only be displayed when the LaTeX-package
22878 \begin_layout Standard
22879 An overview about the different Euro symbols:
22882 \begin_layout Standard
22884 \begin_inset Tabular
22885 <lyxtabular version="3" rows="4" columns="3">
22886 <features rotate="0" tabularvalignment="middle">
22887 <column alignment="center" valignment="top" width="0pt">
22888 <column alignment="center" valignment="top" width="0pt">
22889 <column alignment="center" valignment="top" width="0pt">
22891 <cell multicolumn="1" alignment="center" valignment="top" bottomline="true" usebox="none">
22894 \begin_layout Plain Layout
22900 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
22903 \begin_layout Plain Layout
22909 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
22912 \begin_layout Plain Layout
22920 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
22923 \begin_layout Plain Layout
22929 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
22932 \begin_layout Plain Layout
22940 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
22943 \begin_layout Plain Layout
22944 \begin_inset Formula $\euro$
22954 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
22957 \begin_layout Plain Layout
22963 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
22966 \begin_layout Plain Layout
22972 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
22975 \begin_layout Plain Layout
22976 \begin_inset Formula $\mbox{€}$
22986 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
22989 \begin_layout Plain Layout
22995 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
22998 \begin_layout Plain Layout
23006 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
23009 \begin_layout Plain Layout
23013 \begin_layout Plain Layout
23035 \begin_layout Standard
23039 \begin_layout Plain Layout
23049 \begin_inset Note Note
23052 \begin_layout Plain Layout
23053 The following will be displayed when the LaTeX-package
23065 \begin_layout Standard
23066 You need to install the LaTeX-package
23070 to see the rest of this subsection in the output.
23073 \begin_layout Standard
23077 \begin_layout Plain Layout
23089 \begin_layout Section
23091 \begin_inset CommandInset label
23093 name "sec:Relations"
23098 \begin_inset Index idx
23101 \begin_layout Plain Layout
23108 \begin_inset Index idx
23111 \begin_layout Plain Layout
23116 \begin_layout Plain Layout
23127 \begin_layout Plain Layout
23142 \begin_layout Standard
23143 All following relations can also be inserted via the toolbar button
23146 arg "math-insert \\leq"
23152 \begin_layout Standard
23153 \begin_inset space \hfill{}
23157 \begin_inset Tabular
23158 <lyxtabular version="3" rows="17" columns="2">
23159 <features rotate="0" tabularvalignment="middle">
23160 <column alignment="center" valignment="top" width="0pt">
23161 <column alignment="center" valignment="top" width="0pt">
23163 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
23166 \begin_layout Plain Layout
23172 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
23175 \begin_layout Plain Layout
23183 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
23186 \begin_layout Plain Layout
23192 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
23195 \begin_layout Plain Layout
23196 \begin_inset Formula $<$
23206 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
23209 \begin_layout Plain Layout
23217 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
23220 \begin_layout Plain Layout
23221 \begin_inset Formula $\le$
23231 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
23234 \begin_layout Plain Layout
23242 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
23245 \begin_layout Plain Layout
23246 \begin_inset Formula $\ll$
23256 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
23259 \begin_layout Plain Layout
23267 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
23270 \begin_layout Plain Layout
23271 \begin_inset Formula $\prec$
23281 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
23284 \begin_layout Plain Layout
23292 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
23295 \begin_layout Plain Layout
23296 \begin_inset Formula $\preceq$
23306 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
23309 \begin_layout Plain Layout
23317 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
23320 \begin_layout Plain Layout
23321 \begin_inset Formula $\subset$
23331 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
23334 \begin_layout Plain Layout
23342 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
23345 \begin_layout Plain Layout
23346 \begin_inset Formula $\subseteq$
23356 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
23359 \begin_layout Plain Layout
23367 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
23370 \begin_layout Plain Layout
23371 \begin_inset Formula $\sqsubseteq$
23381 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
23384 \begin_layout Plain Layout
23392 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
23395 \begin_layout Plain Layout
23396 \begin_inset Formula $\in$
23406 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
23409 \begin_layout Plain Layout
23417 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
23420 \begin_layout Plain Layout
23421 \begin_inset Formula $\vdash$
23431 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
23434 \begin_layout Plain Layout
23442 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
23445 \begin_layout Plain Layout
23446 \begin_inset Formula $\smile$
23456 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
23459 \begin_layout Plain Layout
23467 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
23470 \begin_layout Plain Layout
23471 \begin_inset Formula $\lhd$
23481 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
23484 \begin_layout Plain Layout
23492 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
23495 \begin_layout Plain Layout
23496 \begin_inset Formula $\unlhd$
23506 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
23509 \begin_layout Plain Layout
23517 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
23520 \begin_layout Plain Layout
23521 \begin_inset Formula $\gtrless$
23531 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
23534 \begin_layout Plain Layout
23542 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
23545 \begin_layout Plain Layout
23546 \begin_inset Formula $\mid$
23556 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
23559 \begin_layout Plain Layout
23567 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
23570 \begin_layout Plain Layout
23571 \begin_inset Formula $\nmid$
23585 \begin_inset space \hfill{}
23589 \begin_inset Tabular
23590 <lyxtabular version="3" rows="17" columns="2">
23591 <features rotate="0" tabularvalignment="middle">
23592 <column alignment="center" valignment="top" width="0pt">
23593 <column alignment="center" valignment="top" width="0pt">
23595 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
23598 \begin_layout Plain Layout
23604 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
23607 \begin_layout Plain Layout
23615 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
23618 \begin_layout Plain Layout
23624 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
23627 \begin_layout Plain Layout
23628 \begin_inset Formula $=$
23638 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
23641 \begin_layout Plain Layout
23649 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
23652 \begin_layout Plain Layout
23653 \begin_inset Formula $\not=$
23663 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
23666 \begin_layout Plain Layout
23674 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
23677 \begin_layout Plain Layout
23678 \begin_inset Formula $\equiv$
23688 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
23691 \begin_layout Plain Layout
23699 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
23702 \begin_layout Plain Layout
23703 \begin_inset Formula $\sim$
23713 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
23716 \begin_layout Plain Layout
23724 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
23727 \begin_layout Plain Layout
23728 \begin_inset Formula $\simeq$
23738 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
23741 \begin_layout Plain Layout
23749 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
23752 \begin_layout Plain Layout
23753 \begin_inset Formula $\approx$
23763 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
23766 \begin_layout Plain Layout
23774 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
23777 \begin_layout Plain Layout
23778 \begin_inset Formula $\cong$
23788 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
23791 \begin_layout Plain Layout
23799 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
23802 \begin_layout Plain Layout
23803 \begin_inset Formula $\bowtie$
23813 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
23816 \begin_layout Plain Layout
23824 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
23827 \begin_layout Plain Layout
23828 \begin_inset Formula $\notin$
23838 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
23841 \begin_layout Plain Layout
23849 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
23852 \begin_layout Plain Layout
23853 \begin_inset Formula $\perp$
23863 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
23866 \begin_layout Plain Layout
23874 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
23877 \begin_layout Plain Layout
23878 \begin_inset Formula $\propto$
23888 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
23891 \begin_layout Plain Layout
23899 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
23902 \begin_layout Plain Layout
23903 \begin_inset Formula $\asymp$
23913 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
23916 \begin_layout Plain Layout
23924 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
23927 \begin_layout Plain Layout
23928 \begin_inset Formula $\doteq$
23938 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
23941 \begin_layout Plain Layout
23949 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
23952 \begin_layout Plain Layout
23953 \begin_inset Formula $\circeq$
23963 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
23966 \begin_layout Plain Layout
23974 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
23977 \begin_layout Plain Layout
23978 \begin_inset Formula $\models$
23988 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
23991 \begin_layout Plain Layout
23999 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
24002 \begin_layout Plain Layout
24003 \begin_inset Formula $\widehat{=}$
24017 \begin_inset space \hfill{}
24021 \begin_inset Tabular
24022 <lyxtabular version="3" rows="17" columns="2">
24023 <features rotate="0" tabularvalignment="middle">
24024 <column alignment="center" valignment="top" width="0pt">
24025 <column alignment="center" valignment="top" width="0pt">
24027 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
24030 \begin_layout Plain Layout
24036 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
24039 \begin_layout Plain Layout
24047 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
24050 \begin_layout Plain Layout
24056 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
24059 \begin_layout Plain Layout
24060 \begin_inset Formula $>$
24070 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
24073 \begin_layout Plain Layout
24081 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
24084 \begin_layout Plain Layout
24085 \begin_inset Formula $\ge$
24095 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
24098 \begin_layout Plain Layout
24106 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
24109 \begin_layout Plain Layout
24110 \begin_inset Formula $\gg$
24120 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
24123 \begin_layout Plain Layout
24131 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
24134 \begin_layout Plain Layout
24135 \begin_inset Formula $\succ$
24145 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
24148 \begin_layout Plain Layout
24156 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
24159 \begin_layout Plain Layout
24160 \begin_inset Formula $\succeq$
24170 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
24173 \begin_layout Plain Layout
24181 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
24184 \begin_layout Plain Layout
24185 \begin_inset Formula $\supset$
24195 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
24198 \begin_layout Plain Layout
24206 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
24209 \begin_layout Plain Layout
24210 \begin_inset Formula $\supseteq$
24220 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
24223 \begin_layout Plain Layout
24231 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
24234 \begin_layout Plain Layout
24235 \begin_inset Formula $\sqsupseteq$
24245 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
24248 \begin_layout Plain Layout
24256 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
24259 \begin_layout Plain Layout
24260 \begin_inset Formula $\ni$
24270 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
24273 \begin_layout Plain Layout
24281 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
24284 \begin_layout Plain Layout
24285 \begin_inset Formula $\dashv$
24295 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
24298 \begin_layout Plain Layout
24306 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
24309 \begin_layout Plain Layout
24310 \begin_inset Formula $\frown$
24320 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
24323 \begin_layout Plain Layout
24331 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
24334 \begin_layout Plain Layout
24335 \begin_inset Formula $\rhd$
24345 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
24348 \begin_layout Plain Layout
24356 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
24359 \begin_layout Plain Layout
24360 \begin_inset Formula $\unrhd$
24370 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
24373 \begin_layout Plain Layout
24381 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
24384 \begin_layout Plain Layout
24385 \begin_inset Formula $\lessgtr$
24395 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
24398 \begin_layout Plain Layout
24406 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
24409 \begin_layout Plain Layout
24410 \begin_inset Formula $\parallel$
24420 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
24423 \begin_layout Plain Layout
24431 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
24434 \begin_layout Plain Layout
24435 \begin_inset Formula $\nparallel$
24449 \begin_inset space \hfill{}
24455 \begin_layout Standard
24456 \begin_inset VSpace medskip
24471 are bigger than the equal looking operators
24486 \begin_layout Standard
24487 LyX supports also many special relations.
24488 Use the toolbar button
24491 arg "math-insert \\leqq"
24494 to see a list of these relations.
24497 \begin_layout Standard
24498 Relations are, in contrary to symbols, always surrounded by space.
24501 \begin_layout Standard
24502 Relations with labels can be created with the command
24509 \begin_inset Index idx
24512 \begin_layout Plain Layout
24523 \begin_layout Standard
24525 \begin_inset Tabular
24526 <lyxtabular version="3" rows="2" columns="2">
24527 <features rotate="0" tabularvalignment="middle">
24528 <column alignment="center" valignment="top">
24529 <column alignment="center" valignment="top">
24531 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
24534 \begin_layout Plain Layout
24540 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
24543 \begin_layout Plain Layout
24545 \begin_inset Note Note
24548 \begin_layout Plain Layout
24555 is only used as spacer.
24567 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
24570 \begin_layout Plain Layout
24574 \begin_inset space \textvisiblespace{}
24582 \begin_inset space \textvisiblespace{}
24586 \begin_inset Formula $\downarrow$
24592 \begin_inset space \textvisiblespace{}
24596 \begin_inset space \textvisiblespace{}
24604 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
24607 \begin_layout Plain Layout
24608 \begin_inset Formula $\raisebox{5mm}{}A(r)\stackrel{r\to\infty}{\approx}B$
24624 \begin_layout Section
24628 \begin_layout Subsection
24629 Predefined Functions
24630 \begin_inset CommandInset label
24632 name "sub:Predefined-Functions"
24637 \begin_inset Index idx
24640 \begin_layout Plain Layout
24641 Functions ! predefined
24649 \begin_layout Standard
24650 In general, variables are set
24654 in mathematical expressions, but not function names, because
24655 \begin_inset Formula $sin$
24658 could be misunderstood as
24659 \begin_inset Formula $s\cdot i\cdot n$
24663 Therefore there are predefined functionswhich are additionally a bit separated
24665 They are inserted as commands starting with a backslash before their name.
24668 \begin_layout Standard
24670 \begin_inset Tabular
24671 <lyxtabular version="3" rows="2" columns="4">
24672 <features rotate="0" tabularvalignment="middle">
24673 <column alignment="center" valignment="top" width="0pt">
24674 <column alignment="center" valignment="top" width="0pt">
24675 <column alignment="center" valignment="top" width="0pt">
24676 <column alignment="center" valignment="top" width="0pt">
24678 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
24681 \begin_layout Plain Layout
24687 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
24690 \begin_layout Plain Layout
24696 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
24699 \begin_layout Plain Layout
24705 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
24708 \begin_layout Plain Layout
24716 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
24719 \begin_layout Plain Layout
24725 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
24728 \begin_layout Plain Layout
24729 \begin_inset Formula $Asin(x)+B$
24737 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
24740 \begin_layout Plain Layout
24748 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
24751 \begin_layout Plain Layout
24752 \begin_inset Formula $A\sin(x)+B$
24768 \begin_layout Standard
24769 The following functions are predefined:
24772 \begin_layout Standard
24773 \begin_inset VSpace -2mm
24779 \begin_layout Standard
24781 \begin_inset Tabular
24782 <lyxtabular version="3" rows="9" columns="4">
24783 <features rotate="0" tabularvalignment="middle">
24784 <column alignment="center" valignment="top" width="0pt">
24785 <column alignment="center" valignment="top" width="0pt">
24786 <column alignment="center" valignment="top" width="0pt">
24787 <column alignment="center" valignment="top" width="0pt">
24789 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
24792 \begin_layout Plain Layout
24798 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
24801 \begin_layout Plain Layout
24807 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
24810 \begin_layout Plain Layout
24816 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
24819 \begin_layout Plain Layout
24827 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
24830 \begin_layout Plain Layout
24838 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
24841 \begin_layout Plain Layout
24849 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
24852 \begin_layout Plain Layout
24860 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
24863 \begin_layout Plain Layout
24873 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
24876 \begin_layout Plain Layout
24884 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
24887 \begin_layout Plain Layout
24895 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
24898 \begin_layout Plain Layout
24906 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
24909 \begin_layout Plain Layout
24919 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
24922 \begin_layout Plain Layout
24930 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
24933 \begin_layout Plain Layout
24941 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
24944 \begin_layout Plain Layout
24952 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
24955 \begin_layout Plain Layout
24965 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
24968 \begin_layout Plain Layout
24976 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
24979 \begin_layout Plain Layout
24987 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
24990 \begin_layout Plain Layout
24998 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
25001 \begin_layout Plain Layout
25011 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
25014 \begin_layout Plain Layout
25022 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
25025 \begin_layout Plain Layout
25033 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
25036 \begin_layout Plain Layout
25044 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
25047 \begin_layout Plain Layout
25057 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
25060 \begin_layout Plain Layout
25068 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
25071 \begin_layout Plain Layout
25079 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
25082 \begin_layout Plain Layout
25090 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
25093 \begin_layout Plain Layout
25103 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
25106 \begin_layout Plain Layout
25114 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
25117 \begin_layout Plain Layout
25125 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
25128 \begin_layout Plain Layout
25136 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
25139 \begin_layout Plain Layout
25149 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
25152 \begin_layout Plain Layout
25160 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
25163 \begin_layout Plain Layout
25171 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
25174 \begin_layout Plain Layout
25182 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
25185 \begin_layout Plain Layout
25201 \begin_layout Standard
25202 They can also be inserted with the math toolbar button
25205 arg "math-insert \\functions"
25211 \begin_layout Subsection
25212 Self-defined Functions
25213 \begin_inset Index idx
25216 \begin_layout Plain Layout
25217 Functions ! self-defined
25225 \begin_layout Standard
25226 To use a function that is not predefined, like for example the sign function
25227 sgn(x), there are two possibilities:
25230 \begin_layout Itemize
25231 Define the function by inserting the following line to the LaTeX-preamble
25235 \begin_layout Plain Layout
25240 DeclareMathOperator
25243 \begin_inset CommandInset ref
25245 reference "sub:Self-defined-Operators"
25255 \begin_inset Newline newline
25259 \begin_inset VSpace -3mm
25263 \begin_inset Newline newline
25270 DeclareMathOperator{
25275 \begin_inset Index idx
25278 \begin_layout Plain Layout
25283 DeclareMathOperator
25289 \begin_inset Newline newline
25293 \begin_inset VSpace -2mm
25297 \begin_inset Newline newline
25300 Now the new defined function can be called with the command
25309 \begin_layout Itemize
25310 Write the formula as usual, mark the formula name, in our example the letters
25315 , and change it to mathematical text.
25316 Finally, a space is inserted between prefactor and function.
25319 \begin_layout Standard
25320 The result is the same with both methods as with a predefined function
25324 \begin_layout Plain Layout
25325 In LyX self-defined functions are displayed red, predefined ones black.
25333 \begin_layout Standard
25335 \begin_inset Tabular
25336 <lyxtabular version="3" rows="3" columns="2">
25337 <features rotate="0" tabularvalignment="middle">
25338 <column alignment="center" valignment="top" width="0pt">
25339 <column alignment="center" valignment="top" width="0pt">
25341 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
25344 \begin_layout Plain Layout
25350 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
25353 \begin_layout Plain Layout
25361 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
25364 \begin_layout Plain Layout
25372 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
25375 \begin_layout Plain Layout
25376 \begin_inset Formula $A\sgn(x)+B$
25386 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
25389 \begin_layout Plain Layout
25393 \begin_inset Formula $\underbrace{\textrm{sgn}}_{\textrm{Alt+M}\,\textrm{M}}$
25401 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
25404 \begin_layout Plain Layout
25405 \begin_inset Formula $A\,\textrm{sgn}(x)+B$
25421 \begin_layout Standard
25422 The first method is more suitable when the self-defined function should
25423 be used several times.
25426 \begin_layout Subsection
25428 \begin_inset Index idx
25431 \begin_layout Plain Layout
25440 \begin_layout Standard
25441 For limits, in addition to the commands
25448 \begin_inset Index idx
25451 \begin_layout Plain Layout
25471 the following functions are defined:
25474 \begin_layout Standard
25476 \begin_inset Tabular
25477 <lyxtabular version="3" rows="5" columns="2">
25478 <features rotate="0" tabularvalignment="middle">
25479 <column alignment="center" valignment="top">
25480 <column alignment="center" valignment="top">
25482 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
25485 \begin_layout Plain Layout
25491 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
25494 \begin_layout Plain Layout
25496 \begin_inset Note Note
25499 \begin_layout Plain Layout
25506 is only used as spacer.
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" rightline="true" usebox="none">
25532 \begin_layout Plain Layout
25533 \begin_inset Formula $\varliminf$
25543 <cell alignment="center" valignment="top" leftline="true" usebox="none">
25546 \begin_layout Plain Layout
25554 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
25557 \begin_layout Plain Layout
25558 \begin_inset Formula $\varlimsup$
25568 <cell alignment="center" valignment="top" leftline="true" usebox="none">
25571 \begin_layout Plain Layout
25579 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
25582 \begin_layout Plain Layout
25583 \begin_inset Formula $\varprojlim$
25593 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
25596 \begin_layout Plain Layout
25604 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
25607 \begin_layout Plain Layout
25608 \begin_inset Formula $\varinjlim$
25612 \begin_inset Formula $\raisebox{-2.5mm}{}$
25628 \begin_layout Standard
25629 \begin_inset VSpace medskip
25632 The limit is created by inserting a subscript.
25633 It is set right beside the function in an inline formula:
25636 \begin_layout Standard
25638 \begin_inset Tabular
25639 <lyxtabular version="3" rows="2" columns="2">
25640 <features rotate="0" tabularvalignment="middle">
25641 <column alignment="center" valignment="top" width="0pt">
25642 <column alignment="center" valignment="top" width="0pt">
25644 <cell alignment="center" valignment="top" usebox="none">
25647 \begin_layout Plain Layout
25653 <cell alignment="center" valignment="top" usebox="none">
25656 \begin_layout Plain Layout
25657 \begin_inset space \hspace{}
25662 \begin_inset Note Note
25665 \begin_layout Plain Layout
25672 are used here as spacer.
25684 <cell alignment="center" valignment="top" usebox="none">
25687 \begin_layout Plain Layout
25693 \begin_inset space \textvisiblespace{}
25697 \begin_inset space \textvisiblespace{}
25705 <cell alignment="center" valignment="top" usebox="none">
25708 \begin_layout Plain Layout
25709 \begin_inset Formula $\hspace{1cm}\raisebox{5mm}{}\lim_{x\to A}x=B$
25725 \begin_layout Standard
25726 In a displayed formula the limit is set below the formula, as usual:
25727 \begin_inset Formula
25737 \begin_layout Standard
25738 \begin_inset VSpace medskip
25744 \begin_layout Standard
25745 How to adjust the typesetting of the limits see
25746 \begin_inset CommandInset ref
25748 reference "sub:Operator-Limits"
25755 \begin_layout Subsection
25757 \begin_inset Index idx
25760 \begin_layout Plain Layout
25761 Functions ! modulo-
25769 \begin_layout Standard
25770 The modulo-function is special, because it exists in four variants.
25771 The variants in a displayed formula are:
25772 \begin_inset Formula
25774 \underline{\textrm{Command}\raisebox{-0.9mm}{}} & & \underline{\textrm{Result}}\\
25775 \mathrm{a\backslash mod\textrm{␣}b} & & a\mod b\\
25776 \mathrm{a\backslash pmod\textrm{␣}b} & & a\pmod b\\
25777 \mathrm{a\backslash bmod\textrm{␣}b} & & a\bmod b\\
25778 \mathrm{a\backslash pod\textrm{␣}b} & & a\pod b
25786 \begin_layout Standard
25787 In an inline formula less space is set before the function names for all
25789 By default the modulo-functions take only the first following character
25791 To use more than one character, one has to put them into TeX-braces:
25792 \begin_inset Formula
25794 \underline{\textrm{Command}\raisebox{-0.9mm}{}} & & \underline{\textrm{Result}}\\
25795 \mathrm{a\backslash pod\textrm{␣}bcd} & & a\pod bcd\\
25796 \mathrm{a\backslash pod\backslash\{bc\to d} & & a\pod{bc}d
25804 \begin_layout Section
25806 \begin_inset Index idx
25809 \begin_layout Plain Layout
25818 \begin_layout Subsection
25819 Special Characters in Mathematical Text
25822 \begin_layout Standard
25823 The following commands can only be used in mathematical text or in TeX-mode:
25826 \begin_layout Standard
25827 \begin_inset space \hfill{}
25831 \begin_inset Tabular
25832 <lyxtabular version="3" rows="8" columns="2">
25833 <features rotate="0" tabularvalignment="middle">
25834 <column alignment="block" valignment="top">
25835 <column alignment="block" valignment="top">
25837 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
25840 \begin_layout Plain Layout
25846 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
25849 \begin_layout Plain Layout
25857 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
25860 \begin_layout Plain Layout
25868 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
25871 \begin_layout Plain Layout
25872 \begin_inset Formula $\textrm{œ}$
25882 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
25885 \begin_layout Plain Layout
25893 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
25896 \begin_layout Plain Layout
25897 \begin_inset Formula $\textrm{Œ}$
25907 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
25910 \begin_layout Plain Layout
25918 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
25921 \begin_layout Plain Layout
25922 \begin_inset Formula $\textrm{æ}$
25932 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
25935 \begin_layout Plain Layout
25943 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
25946 \begin_layout Plain Layout
25947 \begin_inset Formula $\textrm{Æ}$
25957 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
25960 \begin_layout Plain Layout
25968 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
25971 \begin_layout Plain Layout
25972 \begin_inset Formula $\textrm{\aa}$
25982 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
25985 \begin_layout Plain Layout
25989 \begin_inset Index idx
25992 \begin_layout Plain Layout
25999 \begin_layout Plain Layout
26020 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
26023 \begin_layout Plain Layout
26024 \begin_inset Formula $\textrm{Å}$
26034 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
26037 \begin_layout Plain Layout
26045 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
26048 \begin_layout Plain Layout
26049 \begin_inset Formula $\textrm{ı}$
26063 \begin_inset space \hfill{}
26067 \begin_inset Tabular
26068 <lyxtabular version="3" rows="8" columns="2">
26069 <features rotate="0" tabularvalignment="middle">
26070 <column alignment="block" valignment="top">
26071 <column alignment="center" valignment="top">
26073 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
26076 \begin_layout Plain Layout
26078 \begin_inset Note Note
26081 \begin_layout Plain Layout
26083 \begin_inset space \thinspace{}
26086 mm is used for separation, because otherwise the output will be ¡ and ¿
26097 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
26100 \begin_layout Plain Layout
26108 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
26111 \begin_layout Plain Layout
26119 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
26122 \begin_layout Plain Layout
26123 \begin_inset Formula $\textrm{ø}$
26133 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
26136 \begin_layout Plain Layout
26144 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
26147 \begin_layout Plain Layout
26148 \begin_inset Formula $\textrm{Ø}$
26158 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
26161 \begin_layout Plain Layout
26169 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
26172 \begin_layout Plain Layout
26173 \begin_inset Formula $\textrm{ł}$
26183 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
26186 \begin_layout Plain Layout
26194 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
26197 \begin_layout Plain Layout
26198 \begin_inset Formula $\textrm{Ł}$
26208 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
26211 \begin_layout Plain Layout
26213 \begin_inset space \hspace{}
26218 \begin_inset space \textvisiblespace{}
26226 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
26229 \begin_layout Plain Layout
26230 \begin_inset Formula $\textrm{!`}$
26240 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
26243 \begin_layout Plain Layout
26245 \begin_inset space \hspace{}
26250 \begin_inset space \textvisiblespace{}
26258 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
26261 \begin_layout Plain Layout
26262 \begin_inset Formula $\textrm{?`}$
26272 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
26275 \begin_layout Plain Layout
26283 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
26286 \begin_layout Plain Layout
26287 \begin_inset Formula $\textrm{ȷ}$
26301 \begin_inset space \hfill{}
26307 \begin_layout Standard
26309 \begin_inset Formula $\textrm{\textrm{Å}}$
26313 \begin_inset Formula $\textrm{\textrm{Ø}}$
26316 can also be inserted via the math toolbar button
26319 arg "math-insert \\digamma"
26325 \begin_layout Standard
26326 An exception are the commands
26329 \begin_inset space \hspace{}
26338 \begin_inset space \hspace{}
26344 , because they can be inserted in LyX directly to text.
26347 \begin_layout Subsection
26349 \begin_inset CommandInset label
26351 name "sub:Accents-in-Text"
26356 \begin_inset Index idx
26359 \begin_layout Plain Layout
26368 \begin_layout Standard
26369 With the following commands all letters can be accented.
26370 The commands must be inserted in TeX-mode.
26373 \begin_layout Standard
26374 \begin_inset space \hfill{}
26378 \begin_inset Tabular
26379 <lyxtabular version="3" rows="8" columns="2">
26380 <features rotate="0" tabularvalignment="middle">
26381 <column alignment="block" valignment="top">
26382 <column alignment="block" valignment="top">
26384 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
26387 \begin_layout Plain Layout
26393 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
26396 \begin_layout Plain Layout
26404 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
26407 \begin_layout Plain Layout
26411 \begin_inset Quotes grd
26419 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
26422 \begin_layout Plain Layout
26426 \begin_layout Plain Layout
26442 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
26445 \begin_layout Plain Layout
26453 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
26456 \begin_layout Plain Layout
26460 \begin_layout Plain Layout
26476 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
26479 \begin_layout Plain Layout
26483 \begin_inset space \textvisiblespace{}
26491 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
26494 \begin_layout Plain Layout
26498 \begin_layout Plain Layout
26514 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
26517 \begin_layout Plain Layout
26525 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
26528 \begin_layout Plain Layout
26532 \begin_layout Plain Layout
26548 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
26551 \begin_layout Plain Layout
26555 \begin_inset space \textvisiblespace{}
26563 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
26566 \begin_layout Plain Layout
26570 \begin_layout Plain Layout
26586 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
26589 \begin_layout Plain Layout
26593 \begin_inset space \textvisiblespace{}
26601 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
26604 \begin_layout Plain Layout
26608 \begin_layout Plain Layout
26624 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
26627 \begin_layout Plain Layout
26631 \begin_inset space \textvisiblespace{}
26639 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
26642 \begin_layout Plain Layout
26646 \begin_layout Plain Layout
26666 \begin_inset space \hfill{}
26670 \begin_inset Tabular
26671 <lyxtabular version="3" rows="8" columns="2">
26672 <features rotate="0" tabularvalignment="middle">
26673 <column alignment="block" valignment="top">
26674 <column alignment="center" valignment="top">
26676 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
26679 \begin_layout Plain Layout
26685 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
26688 \begin_layout Plain Layout
26696 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
26699 \begin_layout Plain Layout
26703 \begin_inset space \textvisiblespace{}
26711 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
26714 \begin_layout Plain Layout
26718 \begin_layout Plain Layout
26734 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
26737 \begin_layout Plain Layout
26745 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
26748 \begin_layout Plain Layout
26752 \begin_layout Plain Layout
26768 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
26771 \begin_layout Plain Layout
26775 \begin_inset Index idx
26778 \begin_layout Plain Layout
26789 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
26792 \begin_layout Plain Layout
26796 \begin_layout Plain Layout
26812 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
26815 \begin_layout Plain Layout
26823 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
26826 \begin_layout Plain Layout
26830 \begin_layout Plain Layout
26846 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
26849 \begin_layout Plain Layout
26853 \begin_inset space \textvisiblespace{}
26861 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
26864 \begin_layout Plain Layout
26868 \begin_layout Plain Layout
26884 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
26887 \begin_layout Plain Layout
26891 \begin_inset space \textvisiblespace{}
26899 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
26902 \begin_layout Plain Layout
26906 \begin_layout Plain Layout
26922 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
26925 \begin_layout Plain Layout
26929 \begin_inset space \textvisiblespace{}
26937 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
26940 \begin_layout Plain Layout
26944 \begin_layout Plain Layout
26964 \begin_inset space \hfill{}
26970 \begin_layout Standard
26971 \begin_inset VSpace medskip
26980 also two different characters can be accented.
26986 \begin_inset space \textvisiblespace{}
26995 \begin_layout Plain Layout
27007 \begin_layout Standard
27020 can in combination with vowels directly be inserted with the keyboard without
27022 The same applies for the tilde
27026 \begin_layout Plain Layout
27027 This only applies for keyboards where the tilde is defined as accent.
27036 in combination with
27051 \begin_layout Standard
27094 and accents that are inserted directly with the keyboard are also available
27095 in mathematical text.
27096 For the other accents there are special math commands to be used in formulas,
27098 \begin_inset CommandInset ref
27100 reference "sub:Accents-for-one"
27107 \begin_layout Standard
27108 \begin_inset VSpace bigskip
27111 Furthermore, with the command
27118 \begin_inset Index idx
27121 \begin_layout Plain Layout
27129 all numbers and letters can be set into a circle, quasi accented with a
27130 circle, similar to the copyright symbol.
27133 \begin_layout Standard
27135 \begin_inset Tabular
27136 <lyxtabular version="3" rows="3" columns="2">
27137 <features rotate="0" tabularvalignment="middle">
27138 <column alignment="center" valignment="top">
27139 <column alignment="center" valignment="top">
27141 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
27144 \begin_layout Plain Layout
27150 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
27153 \begin_layout Plain Layout
27155 \begin_inset Note Note
27158 \begin_layout Plain Layout
27165 is only used as spacer.
27177 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
27180 \begin_layout Plain Layout
27188 <cell multicolumn="1" alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
27191 \begin_layout Plain Layout
27195 \begin_layout Plain Layout
27211 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
27214 \begin_layout Plain Layout
27225 raisebox{-1.5pt}{W}}
27230 <cell multicolumn="1" alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
27233 \begin_layout Plain Layout
27234 \begin_inset Formula $\raisebox{4.5mm}{}$
27241 \begin_layout Plain Layout
27259 \begin_inset Formula $\raisebox{-2mm}{}$
27275 \begin_layout Standard
27276 One has to take care that the character fits in the circle.
27287 \begin_layout Plain Layout
27289 \begin_inset CommandInset ref
27291 reference "sub:Font-Sizes"
27300 specifies thereby the size of the circle.
27311 \begin_layout Plain Layout
27313 \begin_inset CommandInset ref
27315 reference "sub:Boxes-without-Frame"
27324 the character can be centered.
27327 \begin_layout Subsection
27329 \begin_inset Index idx
27332 \begin_layout Plain Layout
27341 \begin_layout Standard
27342 Old-style figures (also known as old-style numerals) are created with the
27350 \begin_inset Index idx
27353 \begin_layout Plain Layout
27362 The command can be used in formulas and in TeX-mode.
27363 The command scheme is:
27366 \begin_layout Standard
27371 oldstylenums{number}
27374 \begin_layout Standard
27379 oldstylenums{0123456789
27382 \begin_inset Formula $\oldstylenums{0123456789}$
27388 \begin_layout Section
27390 \begin_inset CommandInset label
27392 name "sec:Formula-Styles"
27397 \begin_inset Index idx
27400 \begin_layout Plain Layout
27409 \begin_layout Itemize
27410 There are two different alignment styles:
27414 \begin_layout Description
27415 Centered is the predefined standard
27418 \begin_layout Description
27419 Indented for this the option
27423 must be inserted in the menu
27425 Document\SpecialChar \menuseparator
27431 \begin_inset space ~
27437 \begin_layout Standard
27442 is used, the indentation can be adjusted with the length
27449 \begin_inset Index idx
27452 \begin_layout Plain Layout
27461 Should the distance be 15
27462 \begin_inset space \thinspace{}
27465 mm, the following command line is inserted in the LaTeX-preamble
27468 \begin_layout Standard
27478 \begin_layout Standard
27479 When no length is specified, the predefined value of 30
27480 \begin_inset space \thinspace{}
27487 \begin_layout Itemize
27488 And two different numbering styles:
27492 \begin_layout Description
27493 Right is the predefined standard
27496 \begin_layout Description
27497 Left for this the option
27501 must be inserted in the menu
27503 Document\SpecialChar \menuseparator
27509 \begin_inset space ~
27516 \begin_layout Standard
27525 can also be used together.
27526 In this case both options are inserted, separated by a comma.
27529 \begin_layout Standard
27530 The chosen styles are used for all displayed formulas of the document.
27531 When both, centered and indented formulas should be created in a document,
27537 The indented formulas are then set in a flalign environment, see
27538 \begin_inset CommandInset ref
27540 reference "sub:Flalign-Environment"
27547 \begin_layout Section
27549 \begin_inset CommandInset label
27551 name "sec:Multiline-Formulas"
27556 \begin_inset Index idx
27559 \begin_layout Plain Layout
27560 Formula ! multiline
27568 \begin_layout Subsection
27572 \begin_layout Standard
27573 In LyX multiline formulas are created by pressing
27576 arg "newline-insert newline"
27580 This creates either an
27582 eqnarray environment
27584 that is described in
27585 \begin_inset CommandInset ref
27587 reference "sub:Eqnarray-Environment"
27591 or, when the option
27593 Use AMS math package
27595 in the document settings is selected, an
27599 that is described in
27600 \begin_inset CommandInset ref
27602 reference "sub:Standard-align-Environment"
27607 The align environment is recommended because it provides in any case a
27608 typographically correct output.
27611 \begin_layout Standard
27612 There are other multiline formula environments that can be created via the
27615 Insert\SpecialChar \menuseparator
27619 These environments are described in the following sections.
27622 \begin_layout Standard
27623 In all multiline formula environments a new line is created by pressing
27627 arg "newline-insert newline"
27631 To add or delete lines, the math toolbar buttons
27634 arg "inset-modify tabular append-row"
27640 arg "inset-modify tabular delete-row"
27643 , respectively, or the menu
27645 Edit\SpecialChar \menuseparator
27651 \begin_layout Subsubsection
27653 \begin_inset CommandInset label
27655 name "sub:Line-Separation"
27660 \begin_inset Index idx
27663 \begin_layout Plain Layout
27664 Formula ! multiline ! Line separation
27672 \begin_layout Standard
27673 There is sometimes not enough space in multiline formulas between the lines:
27674 \begin_inset Formula
27676 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}\\
27677 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
27685 \begin_layout Standard
27686 In LaTeX additional line space is specified as optional argument of the
27688 This is not yet possible in LyX
27692 \begin_layout Plain Layout
27694 \begin_inset CommandInset href
27696 name "LyX-bug #1505"
27697 target "http://www.lyx.org/trac/ticket/1505"
27706 , therefore the whole formula must be inserted in TeX-mode.
27707 To add in our example space, the command
27715 is inserted at the end of the first line.
27720 \begin_layout Plain Layout
27727 \begin_layout Plain Layout
27729 B^{2}(B^{2}-2r_{g}^{2}+2x_{0}^{2}-2r_{k}^{2})+4x_{0}^{2}x^{2}+4x_{0}xD &
27732 textrm{-}4x^{2}B^{2}+4x_{0}xB^{2}
27739 \begin_layout Plain Layout
27743 left(B^{2}+x_{0}^{2}
27751 left(B^{2}-2r_{g}^{2}+2x_{0}^{2}-2r_{k}^{2}
27756 \begin_layout Plain Layout
27768 \begin_layout Standard
27769 \begin_inset VSpace bigskip
27772 To set the line separation for all lines in a formula, the length
27779 \begin_inset Index idx
27782 \begin_layout Plain Layout
27792 \begin_inset Formula $\mbox{line separation}=\mathrm{6\, pt+\backslash jot}$
27803 \begin_inset space \thinspace{}
27808 \begin_inset space \thinspace{}
27811 mm additional line separation as in the previous example, the command
27814 \begin_layout Standard
27824 \begin_layout Standard
27825 is inserted in TeX-mode before the formula.
27826 This requires that the LaTeX-package
27834 \begin_layout Plain Layout
27839 is part of every LaTeX standard installation.
27845 \begin_inset Index idx
27848 \begin_layout Plain Layout
27854 was loaded in LaTeX-preamble with the line
27857 \begin_layout Standard
27865 \begin_layout Standard
27870 \begin_layout Plain Layout
27882 \begin_inset Formula
27884 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}\\
27885 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
27893 \begin_layout Standard
27897 \begin_layout Plain Layout
27908 To get back to the predefined distance,
27914 is set to the value 3
27915 \begin_inset space \thinspace{}
27921 \begin_layout Subsubsection
27923 \begin_inset CommandInset label
27925 name "sub:Column-Separation"
27930 \begin_inset Index idx
27933 \begin_layout Plain Layout
27934 Formula ! multiline ! Column separation
27942 \begin_layout Standard
27943 Multiline formulas form a matrix.
27944 A formula in the eqnarray environment is for example a matrix with three
27946 By changing the column separation in this environment, the space beside
27947 the relation sign can be changed.
27950 \begin_layout Standard
27951 The column separation is specified with the length
27958 \begin_inset Index idx
27961 \begin_layout Plain Layout
27970 \begin_inset Newline newline
27973 column separation = 2
27974 \begin_inset space \thinspace{}
27984 \begin_inset Newline newline
27990 \begin_layout Standard
28000 \begin_layout Standard
28001 inserted in TeX-mode, sets for all following formulas a column separation
28003 \begin_inset space \thinspace{}
28007 To get back to the predefined distance,
28014 \begin_inset space \thinspace{}
28020 \begin_layout Standard
28022 \begin_inset space \thinspace{}
28025 cm column separation:
28029 \begin_layout Plain Layout
28041 \begin_inset Formula
28049 A formula with the predefined column separation for matrices of 10
28050 \begin_inset space \thinspace{}
28057 \begin_layout Plain Layout
28069 \begin_inset Formula
28080 \begin_layout Subsubsection
28082 \begin_inset Index idx
28085 \begin_layout Plain Layout
28094 \begin_layout Standard
28095 Long formulas can be typeset using these methods:
28098 \begin_layout Itemize
28099 When one side of the equation is much shorter than the line width, this
28100 one is chosen for the left side and the right side is typeset over two
28102 \begin_inset Formula
28104 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 \\
28105 & & -\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}
28110 The minus sign at the beginning of the second line does normally not appear
28111 as an operator because it is the first character of the line.
28112 Thus it would not be surrounded by space and could not be distinguished
28113 from the fraction bar.
28115 \begin_inset space \thinspace{}
28118 pt space was inserted behind the minus sign with the command
28128 \begin_layout Plain Layout
28136 \begin_inset CommandInset ref
28138 reference "sub:Variable-Space"
28148 \begin_inset Index idx
28151 \begin_layout Plain Layout
28162 \begin_layout Itemize
28163 When both sides of the equation are too long, the command
28170 \begin_inset Index idx
28173 \begin_layout Plain Layout
28182 It is inserted in the first column of the first line and causes all further
28183 insertions to overwrite the following columns:
28184 \begin_inset Formula
28186 \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 \\
28187 & & -\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 \\
28188 & & =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}
28193 After the insertion of
28199 , the cursor is in a purple box that is a bit shifted to the left from the
28201 In this the formula is inserted.
28202 \begin_inset Newline newline
28205 The content of the further lines is inserted to the second or another formula
28207 The greater the column number where it was inserted, the larger the indentation.
28208 \begin_inset VSpace medskip
28212 \begin_inset Newline newline
28216 \begin_inset Note Greyedout
28219 \begin_layout Plain Layout
28220 Note the following when using
28229 \begin_layout Itemize
28230 The formula doesn't use the full page width.
28232 \begin_inset space \thinspace{}
28236 \begin_inset space \space{}
28240 \begin_inset Formula $-B^{2}$
28243 is added to the first line in the above example, it would have been outside
28245 To better use the width, negative space can be inserted at the beginning
28249 \begin_layout Itemize
28250 Due to a bug in LyX the cursor cannot be set with the mouse into the first
28255 \begin_layout Plain Layout
28256 \begin_inset CommandInset href
28258 name "LyX-bug #1429"
28259 target "http://www.lyx.org/trac/ticket/1429"
28268 One can only set the cursor at the beginning of the line and move it with
28277 \begin_layout Itemize
28278 Other methods to set long formulas are offered by the environments described
28280 \begin_inset CommandInset ref
28282 reference "sub:Multline-Environment"
28287 \begin_inset CommandInset ref
28289 reference "sub:Multiline-Formula-Parts"
28296 \begin_layout Subsubsection
28297 Multiline Fractions
28298 \begin_inset CommandInset label
28300 name "sub:Multiline-Fractions"
28305 \begin_inset Index idx
28308 \begin_layout Plain Layout
28309 Fractions ! multiline
28317 \begin_layout Standard
28318 There are cases where the denominator and/or the numerator of a fraction
28319 is so long that the fraction does not fit into one line.
28320 It is then necessary to add a line break within the fraction.
28321 This can be done using the command
28328 \begin_inset Index idx
28331 \begin_layout Plain Layout
28340 To activate it, set in the document settings under
28343 \begin_inset space ~
28353 \begin_inset Index idx
28356 \begin_layout Plain Layout
28357 Packages ! mathtools
28365 \begin_inset space ~
28380 \begin_layout Standard
28385 splitfrac{first line}{second line}
28388 \begin_layout Standard
28389 and is used as denominator and/or numerator:
28392 \begin_layout Standard
28393 \begin_inset Formula
28395 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}
28400 The command for the first numerator above is:
28403 \begin_layout Standard
28408 splitfrac{xy+xy+xy+xy+xy
28409 \begin_inset space \textvisiblespace{}
28417 \begin_layout Subsubsection
28419 \begin_inset CommandInset label
28421 name "sub:Multiline-Brackets"
28426 \begin_inset Index idx
28429 \begin_layout Plain Layout
28430 Brackets ! for multiline expressions
28438 \begin_layout Standard
28439 For brackets spanning multiple lines the following problem occurs:
28440 \begin_inset Formula
28442 A & = & \sin(x)\left[\prod_{R=1}^{\infty}\frac{1}{R}+\cdots\right.\\
28443 & & \left.\cdots+B-D\right]
28451 \begin_layout Standard
28452 The closing bracket is smaller than the opening bracket because brackets
28453 with variable size may not span multiple lines.
28456 \begin_layout Standard
28457 To set the bracket size for the second line correctly, the first line is
28465 \begin_inset Index idx
28468 \begin_layout Plain Layout
28476 and the second line with
28484 \begin_layout Plain Layout
28498 \begin_inset CommandInset ref
28500 reference "sub:Automatic-Bracket-Size"
28512 \begin_inset Index idx
28515 \begin_layout Plain Layout
28538 \begin_inset space \textvisiblespace{}
28548 \begin_inset space \textvisiblespace{}
28558 \begin_inset space \textvisiblespace{}
28564 \begin_inset Formula $\downarrow$
28570 \begin_inset Index idx
28573 \begin_layout Plain Layout
28581 is inserted, because the multiplication operator with its limits is the
28582 largest symbol in the first line and this should be the size for the bracket
28583 in the second line.
28586 \begin_layout Standard
28587 The result is this:
28588 \begin_inset Formula
28590 A & = & \sin(x)\left[\prod_{R=1}^{\infty}\frac{1}{R}+\cdots\right.\\
28591 & & \left.\vphantom{\prod_{R=1}^{\infty}}\cdots+B-D\right]
28599 \begin_layout Subsection
28603 \begin_layout Standard
28604 Align environments can be used for every kind of multiline formulas.
28605 They are especially useful to set several formulas side by side.
28608 \begin_layout Standard
28609 Align environments consist of columns.
28610 The odd columns are right aligned, the even ones left aligned.
28611 Every line in an Align environment can be numbered.
28614 \begin_layout Standard
28615 Align environments are created via the menu
28617 Insert\SpecialChar \menuseparator
28623 Edit\SpecialChar \menuseparator
28624 Math\SpecialChar \menuseparator
28625 Change Formula Type
28627 already existing formulas can be converted to Align environments.
28630 \begin_layout Standard
28631 To add or delete columns, the math toolbar buttons
28634 arg "inset-modify tabular append-column"
28640 arg "inset-modify tabular delete-column"
28643 , respectively, or the menu
28645 Edit\SpecialChar \menuseparator
28651 \begin_layout Subsubsection
28652 Standard align Environment
28653 \begin_inset CommandInset label
28655 name "sub:Standard-align-Environment"
28660 \begin_inset Index idx
28663 \begin_layout Plain Layout
28664 Formula ! multiline ! align environment
28672 \begin_layout Standard
28673 This Align environment is created by pressing
28676 arg "newline-insert newline"
28679 in a formula or by the menu
28681 Insert\SpecialChar \menuseparator
28682 Math\SpecialChar \menuseparator
28683 AMS align Environment
28688 \begin_layout Standard
28689 An example for two formulas set side by side, that are created with a four
28690 column align environment:
28691 \begin_inset Formula
28693 A & =\sin(B) & C & =D\\
28694 C & \ne A & B & \ne D
28699 As it can be seen, the formulas in this environment are placed so as if
28708 \begin_layout Plain Layout
28716 \begin_inset CommandInset ref
28718 reference "sub:Variable-Space"
28729 before the first and after every even column.
28730 When the formula style
28736 \begin_layout Plain Layout
28738 \begin_inset CommandInset ref
28740 reference "sec:Formula-Styles"
28751 is used, the formula is set without the
28757 before the first column.
28760 \begin_layout Subsubsection
28761 Alignat Environment
28762 \begin_inset Index idx
28765 \begin_layout Plain Layout
28766 Formula ! multiline ! alignat environment
28774 \begin_layout Standard
28775 The alignat environment has no predefined column separation.
28776 It can be inserted manually with the spaces that are described
28777 \begin_inset CommandInset ref
28779 reference "sub:Space"
28786 \begin_layout Standard
28787 The above example in the alignat environment where 1
28788 \begin_inset space \thinspace{}
28791 cm space was inserted at the beginning of the second formula:
28792 \begin_inset Formula
28793 \begin{alignat*}{2}
28794 A & =\sin(B) & \hspace{1cm}C & =D\\
28795 C & \ne A & B & \ne D
28800 Because the column separation can be set separately for every column, this
28801 environment is especially suitable to set three and more formulas side
28805 \begin_layout Subsubsection
28806 Flalign Environment
28807 \begin_inset CommandInset label
28809 name "sub:Flalign-Environment"
28814 \begin_inset Index idx
28817 \begin_layout Plain Layout
28818 Formula ! multiline ! flalign environment
28826 \begin_layout Standard
28827 In this environment the first two columns are always set as much as possible
28828 to the left and the last two ones to the right.
28830 \begin_inset Formula
28832 A & =1 & B & =2 & C & =3\\
28833 X & =\textrm{-}1 & Y & =\textrm{-}2 & Z & =4
28841 \begin_layout Standard
28842 By creating a flalign environment with an odd number of columns where an
28843 empty TeX-brace is inserted to the last column, several formulas in a document
28844 can be set to the left, although the formula style
28849 As example the indented formula
28850 \begin_inset CommandInset ref
28852 reference "eq:VolInt"
28857 \begin_inset Formula
28859 \hspace{30pt}\iiint\limits _{V}X\,\mathrm{d}V & =U & {}
28864 The first two columns contain the formula.
28865 To indent it as with the formula style
28870 \begin_inset space \thinspace{}
28873 pt space was inserted at the beginning of the first column.
28876 \begin_layout Subsection
28877 Eqnarray Environment
28878 \begin_inset CommandInset label
28880 name "sub:Eqnarray-Environment"
28885 \begin_inset Index idx
28888 \begin_layout Plain Layout
28889 Formula ! multiline ! eqnarray environment
28897 \begin_layout Standard
28898 When this environment has been created, three blue boxes appear.
28899 The content of the first box is right aligned, the content of the last
28901 The content of the middle box appears centered and a bit smaller, because
28902 it is designed to insert there only relation characters.
28903 \begin_inset Formula
28905 \frac{ABC}{D} & \frac{ABC}{D} & \frac{ABC}{D}\\
28915 \begin_layout Subsection
28917 \begin_inset Index idx
28920 \begin_layout Plain Layout
28921 Formula ! multiline ! gather environment
28929 \begin_layout Standard
28930 This environment consists of only one centered column.
28931 Every line can be numbered.
28932 \begin_inset Formula
28943 \begin_layout Subsection
28944 Multline Environment
28945 \begin_inset CommandInset label
28947 name "sub:Multline-Environment"
28952 \begin_inset Index idx
28955 \begin_layout Plain Layout
28956 Formula ! multiline ! multline environment
28964 \begin_layout Standard
28965 The multline environment consists, like the gather environment, of only
28967 But the first line is left aligned, the last one right aligned.
28968 All other lines are centered.
28969 Therefore this environment is suitable for long formulas.
28971 \begin_inset CommandInset ref
28973 reference "eq:lefteqn"
28977 in the multline environment:
28978 \begin_inset Formula
28980 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}\\
28981 -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}\\
28982 =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}}
28990 \begin_layout Standard
28991 In the output only the last (first) line of a multline environment appears
28992 numbered when the document numbering is right (left).
28996 \begin_layout Plain Layout
28997 numbering styles see
28998 \begin_inset CommandInset ref
29000 reference "sec:Formula-Styles"
29012 \begin_layout Standard
29020 \begin_inset Index idx
29023 \begin_layout Plain Layout
29038 \begin_inset Index idx
29041 \begin_layout Plain Layout
29049 a centered line can be right or left aligned, respectively.
29050 The commands are used as follows:
29053 \begin_layout Standard
29058 shoveright{line content}
29064 shoveleft{line content}
29067 \begin_layout Standard
29068 \begin_inset VSpace medskip
29078 \begin_inset Index idx
29081 \begin_layout Plain Layout
29089 specifies the distance of the first line from the left page margin.
29090 Predefined is the length 0
29091 \begin_inset space \thinspace{}
29097 \begin_layout Standard
29098 As example the above formula where the command
29101 \begin_layout Standard
29111 \begin_layout Standard
29112 was inserted in TeX-mode before:
29116 \begin_layout Plain Layout
29128 \begin_inset Formula
29130 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}\\
29131 \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}}\\
29132 =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}}
29141 \begin_layout Plain Layout
29152 The second line was left aligned using
29161 \begin_layout Subsection
29162 Multiline Formula Parts
29163 \begin_inset CommandInset label
29165 name "sub:Multiline-Formula-Parts"
29170 \begin_inset Index idx
29173 \begin_layout Plain Layout
29174 Formula ! multiline ! formula parts
29182 \begin_layout Standard
29183 To display only parts of a formula with multiple lines, one of the following
29184 environments is used:
29201 They can be inserted via the menu
29203 Insert\SpecialChar \menuseparator
29206 or by using the commands described in this section.
29209 \begin_layout Standard
29210 The first three have the same properties as the corresponding multiline
29211 formula environments, but it is possible to set further formula parts beside
29214 \begin_inset Formula
29216 \left.\begin{aligned}\Delta x\Delta p & \ge\frac{\hbar}{2}\\
29217 \Delta E\Delta t & \ge\frac{\hbar}{2}
29219 \right\} \textrm{Uncertainty relations}
29227 \begin_layout Standard
29228 To get this formula, a displayed formula is created where the command
29235 \begin_inset Index idx
29238 \begin_layout Plain Layout
29247 A purple box appears around the blue formula box where now columns and
29248 lines can be added.
29249 Outside the multiline environment other formula parts can be set, like
29253 \begin_layout Standard
29254 The aligned environment is also suitable for long formulas whose lines are
29255 horizontally aligned.
29256 Using aligned in a displayed formula has the advantage that the formula
29257 number is vertically centered behind the lines.
29259 \begin_inset CommandInset ref
29261 reference "eq:shortlong"
29265 in the aligned environment:
29266 \begin_inset Formula
29268 \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}|}\\
29269 & -\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}|}
29278 \begin_layout Standard
29279 To use the environments
29298 \begin_inset Index idx
29301 \begin_layout Plain Layout
29316 \begin_inset Index idx
29319 \begin_layout Plain Layout
29334 \begin_inset Index idx
29337 \begin_layout Plain Layout
29345 are inserted, respectively.
29346 The split environment has the same properties as the aligned environment
29347 but it can only have two columns.
29350 \begin_layout Subsection
29351 Text in multiline Formulas
29352 \begin_inset CommandInset label
29354 name "sub:Text-in-multiline"
29359 \begin_inset Index idx
29362 \begin_layout Plain Layout
29369 \begin_inset Index idx
29372 \begin_layout Plain Layout
29373 Formula ! multiline ! text
29381 \begin_layout Standard
29382 In the Align environments, and the multline and gather environment, text
29383 can be inserted that will appear in a separate line and doesn't affect
29384 the column alignment.
29385 To do this, the command
29392 \begin_inset Index idx
29395 \begin_layout Plain Layout
29403 is used in the following scheme:
29406 \begin_layout Standard
29414 \begin_layout Standard
29415 The text should not be longer than a line because it cannot be hyphenated.
29416 As LyX doesn't yet support
29422 directly, the text is written as mathematical text.
29429 must hereby be at the beginning of a line and appears in the output above
29431 An example where the text was inserted at the beginning of the second line:
29432 \begin_inset Formula
29434 I & =a\sqrt{2}\int_{0}^{2\pi}\sqrt{1+\cos(\phi)}\;\mathrm{d}\phi\\
29435 \intertext{\text{integrand is symmetric to \ensuremath{\phi=\pi}, therefore}} & =2a\sqrt{2}\int_{0}^{\pi}\sqrt{1+\cos(\phi)}\;\mathrm{d}\phi
29443 \begin_layout Standard
29450 always creates some vertical space between the text and the formula lines.
29451 To avoid this space, set in the document settings under
29454 \begin_inset space ~
29464 \begin_inset Index idx
29467 \begin_layout Plain Layout
29468 Packages ! mathtools
29476 \begin_inset space ~
29482 Then you can use the command
29489 \begin_inset Index idx
29492 \begin_layout Plain Layout
29507 \begin_inset Newpage newpage
29513 \begin_layout Standard
29514 \begin_inset Formula
29516 I & =a\sqrt{2}\int_{0}^{2\pi}\sqrt{1+\cos(\phi)}\;\mathrm{d}\phi\\
29517 \shortintertext{\text{integrand is symmetric to \ensuremath{\phi=\pi}, therefore}} & =2a\sqrt{2}\int_{0}^{\pi}\sqrt{1+\cos(\phi)}\;\mathrm{d}\phi
29525 \begin_layout Section
29527 \begin_inset Index idx
29530 \begin_layout Plain Layout
29537 \begin_inset Index idx
29540 \begin_layout Plain Layout
29541 Formula ! numbering|see
29545 \begin_layout Plain Layout
29556 \begin_layout Plain Layout
29571 \begin_layout Subsection
29575 \begin_layout Standard
29576 Numbered formulas can be created with the menu
29578 Insert\SpecialChar \menuseparator
29579 Math\SpecialChar \menuseparator
29581 \begin_inset space ~
29589 \begin_inset space ~
29595 Existing formulas can be numbered with the menu
29597 Edit\SpecialChar \menuseparator
29598 Math\SpecialChar \menuseparator
29600 \begin_inset space ~
29608 arg "math-number-toggle"
29612 The formula number is displayed in LyX behind the formula as a number sign
29614 The number sign is replaced in the output by the formula number.
29617 \begin_layout Standard
29618 When numbering is turned on in multiline formulas, all lines will be numbered.
29619 But the numbering can be controlled with the menu
29621 Edit\SpecialChar \menuseparator
29622 Math\SpecialChar \menuseparator
29624 \begin_inset space ~
29628 \begin_inset space ~
29632 \begin_inset space ~
29640 arg "math-number-line-toggle"
29646 \begin_layout Standard
29647 Except for inline formulas, all formulas can be numbered with two different
29649 \begin_inset CommandInset ref
29651 reference "sec:Formula-Styles"
29658 \begin_layout Subsection
29660 \begin_inset Index idx
29663 \begin_layout Plain Layout
29664 Cross-references ! to formulas
29672 \begin_layout Standard
29673 All labeled formulas can be cross-referenced.
29674 A label is added by the menu
29676 Insert\SpecialChar \menuseparator
29679 or the toolbar button
29686 The cursor must hereby be inside a displayed formula.
29687 Alternatively you can right-click on the formula and choose
29692 A dialog pops up displaying the prefix
29697 The label is inserted there behind the prefix.
29698 The predefined prefix means
29699 \begin_inset Quotes eld
29703 \begin_inset Quotes erd
29706 and makes it easier to find labels in large documents because it marks
29707 it as formula label to divide it from e.
29708 \begin_inset space \thinspace{}
29712 \begin_inset space \space{}
29716 To change a label, the menu
29718 Insert\SpecialChar \menuseparator
29721 is used again or you right-click on a formula and then on
29728 \begin_layout Standard
29729 The name of the label is displayed in LyX within two parentheses behind
29731 A formula with a label is always numbered.
29734 \begin_layout Standard
29735 Cross-references are inserted via the menu
29737 Insert\SpecialChar \menuseparator
29740 or with the toolbar button
29743 arg "dialog-show-new-inset ref"
29747 A formula cross-reference appears in the output as formula number.
29748 When in the cross-reference dialog window the format
29752 is chosen, the cross-reference appears in the output as formula number
29754 \begin_inset Newline newline
29757 By right-clicking on a cross-reference in LyX, one jumps to the formula
29758 that is referenced.
29761 \begin_layout Standard
29762 Here are as examples cross-references to formulas of the following subsections:
29763 \begin_inset Note Note
29766 \begin_layout Plain Layout
29767 Note the different cross-reference types.
29775 \begin_layout Standard
29777 \begin_inset CommandInset ref
29784 \begin_inset CommandInset ref
29792 \begin_inset CommandInset ref
29798 ) big Latin letters are used for the numbering in contrary to (
29799 \begin_inset CommandInset ref
29808 \begin_layout Standard
29809 \begin_inset VSpace medskip
29812 When the argument of
29820 \begin_layout Plain Layout
29828 \begin_inset CommandInset ref
29830 reference "sub:User-defined-Numbering"
29841 contains a box like in
29842 \begin_inset CommandInset ref
29844 reference "sub:Paragraph-Boxes"
29848 , the formula cannot be referenced.
29851 \begin_layout Subsection
29853 \begin_inset Index idx
29856 \begin_layout Plain Layout
29857 Formula numbering ! subnumbering
29865 \begin_layout Standard
29866 With the help of the commands
29870 begin{subequations}
29878 formulas can be subnumbered.
29879 Both commands are inserted in TeX-mode.
29882 \begin_layout Standard
29884 \begin_inset Formula
29895 \begin_layout Plain Layout
29899 addtocounter{equation}{-1}
29908 \begin_layout Plain Layout
29912 begin{subequations}
29918 \begin_inset VSpace -5mm
29922 \begin_inset Formula
29930 \begin_inset Formula
29940 \begin_layout Standard
29944 \begin_layout Plain Layout
29956 \begin_layout Standard
29957 To create the example, the following is done:
29960 \begin_layout Enumerate
29961 first formula is inserted
29964 \begin_layout Enumerate
29969 addtocounter{equation}{-1}
29971 begin{subequations}
29972 \begin_inset Index idx
29975 \begin_layout Plain Layout
29984 \begin_inset Newline newline
29989 is inserted after the first formula
29992 \begin_layout Enumerate
29993 second formula is inserted
29996 \begin_layout Enumerate
29997 third formula is inserted
30000 \begin_layout Enumerate
30007 is inserted after the third formula
30010 \begin_layout Standard
30011 Every formula between the commands
30023 is subnumbered as a, b,
30024 \begin_inset Newline linebreak
30027 c, \SpecialChar \ldots{}
30028 For multiline formulas every line will be subnumbered.
30029 All subnumbered formulas are treated as
30034 But as every numbered formula increases the counter
30038 by one, the command
30044 is needed to decrease it.
30045 Otherwise the formulas
30046 \begin_inset CommandInset ref
30053 \begin_inset CommandInset ref
30060 \begin_inset CommandInset ref
30066 would be numbered as
30067 \begin_inset CommandInset ref
30074 \begin_inset CommandInset ref
30081 \begin_inset CommandInset ref
30090 \begin_layout Standard
30091 By inserting the commands in TeX-mode, a space is created between the first
30094 \begin_inset space \thinspace{}
30097 mm vertical space is inserted after the command
30101 begin{subequations}
30104 When the formula style
30110 \begin_layout Plain Layout
30112 \begin_inset CommandInset ref
30114 reference "sec:Formula-Styles"
30126 \begin_inset space \thinspace{}
30129 mm space is inserted instead.
30132 \begin_layout Standard
30133 Here is an example for a multiline formula where the numbering was turned
30134 off for the second line:
30138 \begin_layout Plain Layout
30142 begin{subequations}
30148 \begin_inset Formula
30150 A & = & (B-Z)^{2}=(B-Z)(B-Z)\label{eq:d}\\
30151 & = & B^{2}-ZB-BZ+Z^{2}\nonumber \\
30152 & = & B^{2}-2BZ+Z^{2}\label{eq:f}
30161 \begin_layout Plain Layout
30173 \begin_layout Subsection
30174 User-defined Numbering
30175 \begin_inset CommandInset label
30177 name "sub:User-defined-Numbering"
30182 \begin_inset Index idx
30185 \begin_layout Plain Layout
30186 Formula numbering ! user-defined
30194 \begin_layout Standard
30195 \begin_inset Index idx
30198 \begin_layout Plain Layout
30199 Formula numbering ! self-defined delimiters
30204 With the standard numbering parentheses are set around the formula number.
30205 To replace the parentheses for example by vertical bars, the following
30206 line is added to the LaTeX-preamble:
30209 \begin_layout Standard
30221 \begin_inset Note Note
30224 \begin_layout Plain Layout
30225 This macro is already declared in the LaTeX-preamble for testing.
30226 To activate it, remove the percent sign at the beginning.
30234 \begin_layout Standard
30235 To use other characters, the vertical bars besides the
30239 are replaced by one ore more characters.
30240 To get only the formula number the vertical bars are omitted.
30243 \begin_layout Standard
30244 \begin_inset VSpace bigskip
30247 When there should be an expression of your choice instead of the consecutive
30248 formula number in parentheses behind the formula, the command
30255 \begin_inset Index idx
30258 \begin_layout Plain Layout
30267 \begin_inset Formula
30269 A+B=C\tag{something}\label{eq:tag}
30274 In this example the command
30279 \begin_inset space \textvisiblespace{}
30284 was inserted in the formula.
30287 \begin_layout Standard
30293 \begin_inset space \textvisiblespace{}
30298 is inserted instead, the star prevents the parentheses around the expression:
30299 \begin_inset Formula
30301 A+B=C\tag*{something}
30309 \begin_layout Standard
30310 \begin_inset VSpace bigskip
30313 To restart the formula numbering with new document parts or sections, the
30314 following command is used:
30317 \begin_layout Standard
30322 @addtoreset{equation}{part}
30325 \begin_inset Index idx
30328 \begin_layout Plain Layout
30333 \begin_layout Plain Layout
30344 \begin_layout Plain Layout
30357 \begin_layout Plain Layout
30368 \begin_layout Plain Layout
30381 \begin_inset Newline newline
30385 \begin_inset Newline newline
30392 @addtoreset{equation}{section}
30395 \begin_layout Standard
30396 To be able to use these commands in TeX-mode, the
30397 \begin_inset Quotes eld
30401 \begin_inset Quotes erd
30404 character has to be made
30405 \begin_inset Quotes eld
30409 \begin_inset Quotes erd
30412 for LaTeX using the command
30426 So the command sequence in TeX-mode is:
30429 \begin_layout Standard
30435 \begin_inset Newline newline
30440 @addtoreset{equation}{section}
30441 \begin_inset Newline newline
30449 \begin_layout Standard
30450 In the LaTeX-preamble
30462 can be omitted as they are automatically internally inserted by LyX.
30465 \begin_layout Standard
30480 \begin_layout Plain Layout
30485 is part of the LaTeX-package
30490 \begin_inset Index idx
30493 \begin_layout Plain Layout
30494 Packages ! carlisle
30499 that is part of every LaTeX standard installation.
30505 \begin_inset Index idx
30508 \begin_layout Plain Layout
30509 Packages ! remreset
30514 has to be loaded in the LaTeX-preamble with the line
30517 \begin_layout Standard
30522 usepackage{remreset}
30525 \begin_layout Standard
30533 \begin_inset Index idx
30536 \begin_layout Plain Layout
30541 \begin_layout Plain Layout
30552 \begin_layout Plain Layout
30565 \begin_layout Plain Layout
30576 \begin_layout Plain Layout
30588 can be used with the same scheme as
30597 \begin_layout Standard
30598 \begin_inset VSpace bigskip
30601 Sometimes formulas should be numbered in the following form:
30604 \begin_layout Standard
30607 (section number.formula number)
30610 \begin_layout Standard
30611 The formula number should start with every section with
30612 \begin_inset Quotes eld
30616 \begin_inset Quotes erd
30622 \begin_layout Standard
30623 For this case there is the command
30630 \begin_inset Index idx
30633 \begin_layout Plain Layout
30641 , which is used with the following scheme:
30644 \begin_layout Standard
30649 numberwithin{counter}{sectioning}
30652 \begin_layout Standard
30653 Counter denotes what kind of numbering is affected, sectioning denotes what
30654 number is before the dot.
30657 \begin_layout Standard
30658 Thus in our case the following LaTeX-preamble or TeX code line is used:
30661 \begin_layout Standard
30666 numberwithin{equation}{section}
30669 \begin_layout Standard
30670 This is the result:
30674 \begin_layout Plain Layout
30678 numberwithin{equation}{section}
30684 \begin_inset Formula
30694 \begin_layout Standard
30696 \begin_inset space \thinspace{}
30700 \begin_inset space \space{}
30703 tables so that the number of the part is the sectioning,
30704 \begin_inset Newline newline
30711 numberwithin{table}{part}
30716 \begin_layout Standard
30717 To go back to the standard numbering or to prevent this kind of numbering
30718 when it is defined by the document class, the following command is inserted
30719 as TeX code or to the LaTeX-preamble:
30722 \begin_layout Standard
30732 \begin_inset Index idx
30735 \begin_layout Plain Layout
30749 \begin_layout Plain Layout
30765 \begin_inset Newline newline
30773 \begin_inset Newline newline
30785 \begin_layout Standard
30792 uses internally the command
30798 , described above, that also needs to be reverted.
30802 \begin_layout Plain Layout
30809 \begin_layout Plain Layout
30813 @removefromreset{equation}{section}
30816 \begin_layout Plain Layout
30828 \begin_layout Subsection
30829 Numbering with Roman Numbers and Letters
30830 \begin_inset Index idx
30833 \begin_layout Plain Layout
30834 Formula numbering ! with letters
30840 \begin_inset Index idx
30843 \begin_layout Plain Layout
30844 Formula numbering ! with Roman numbers
30852 \begin_layout Standard
30853 Formulas can also be numbered with Roman numbers and Latin letters.
30854 To number for example with small Roman numbers, the command
30857 \begin_layout Standard
30869 \begin_layout Standard
30870 is inserted before the formula in TeX-mode.
30878 \begin_inset Index idx
30881 \begin_layout Plain Layout
30889 redefines the predefined command
30905 \begin_layout Plain Layout
30912 has the same scheme like the command
30918 that is described in
30919 \begin_inset CommandInset ref
30921 reference "sub:The-Command-newcommand"
30934 is the formula counter.
30941 is used as prefix for a counter, the value of the counter is output as
30943 When a formula is numbered, LaTeX sets internally the command
30949 behind the formula.
30955 \begin_inset Index idx
30958 \begin_layout Plain Layout
30968 outputs the counter as small Roman number.
30971 \begin_layout Standard
30972 All formulas behind the command
30982 are now numbered Roman.
30983 To switch to numbering with big Roman numbers, the command is inserted
30997 \begin_inset Index idx
31000 \begin_layout Plain Layout
31012 \begin_inset Quotes eld
31016 \begin_inset Quotes erd
31019 with small Latin letters there is the command
31026 \begin_inset Index idx
31029 \begin_layout Plain Layout
31037 , for big ones there is the command
31044 \begin_inset Index idx
31047 \begin_layout Plain Layout
31060 \begin_layout Standard
31061 \begin_inset Note Greyedout
31064 \begin_layout Plain Layout
31071 \begin_inset space ~
31074 formulas can be numbered with Latin letters in one document.
31082 \begin_layout Standard
31086 \begin_layout Plain Layout
31102 \begin_layout Standard
31103 \begin_inset Formula
31105 A=\textrm{small roman}
31114 \begin_layout Plain Layout
31128 \begin_inset Formula
31130 B=\textrm{big Roman}\label{eq:Rom}
31139 \begin_layout Plain Layout
31153 \begin_inset Formula
31155 C=\textrm{small Latin}
31164 \begin_layout Plain Layout
31178 \begin_inset Formula
31180 D=\textrm{big Latin}\label{eq:Lat}
31188 \begin_layout Standard
31189 To switch back to the default numbering, insert the command:
31192 \begin_layout Standard
31202 \begin_inset Index idx
31205 \begin_layout Plain Layout
31216 \begin_layout Standard
31220 \begin_layout Plain Layout
31234 \begin_inset Formula
31244 \begin_layout Standard
31245 \begin_inset VSpace medskip
31248 As you see, formulas are numbered serially independent from the numbering
31250 When then numbering should start with
31251 \begin_inset Quotes eld
31255 \begin_inset Quotes erd
31258 when the style is changed, new equation counters have to be defined.
31259 A description about this can be found in the file
31260 \begin_inset CommandInset href
31262 name "Formula-numbering.lyx"
31263 target "run:Formula-numbering.lyx"
31270 \begin_layout Standard
31271 \begin_inset Newpage newpage
31277 \begin_layout Section
31278 Chemical Symbols and Equations
31279 \begin_inset CommandInset label
31281 name "sub:Chemical-Symbols-and"
31286 \begin_inset Index idx
31289 \begin_layout Plain Layout
31290 Chemical characters ! Symbols
31296 \begin_inset Index idx
31299 \begin_layout Plain Layout
31306 \begin_inset Index idx
31309 \begin_layout Plain Layout
31318 \begin_layout Standard
31319 An example text from chemistry:
31322 \begin_layout Quote
31324 \begin_inset Formula $\mathrm{SO_{4}^{2-}}$
31327 -ion reacts with two
31328 \begin_inset Formula $\mathrm{Na^{+}}$
31331 -ions to sodium sulfate
31332 \begin_inset Formula $\left(\mathrm{Na_{2}SO_{4}}\right)$
31336 The chemical equation for this is:
31337 \begin_inset Formula
31339 \mathrm{2\, Na^{+}+SO_{4}^{2-}\longrightarrow Na_{2}SO_{4}}\label{eq:chem-reaction}
31347 \begin_layout Standard
31348 This chemical equation can directly be created as formula.
31349 To avoid that the symbols appear italic, everything is highlighted and
31350 changed by the shortcut
31356 to the upright font style.
31360 \begin_layout Plain Layout
31366 \begin_inset CommandInset ref
31368 reference "sub:Font-Styles"
31380 \begin_layout Standard
31381 A more convenient way to typeset chemical formulas is to use the command
31389 \begin_inset Index idx
31392 \begin_layout Plain Layout
31400 that is available when the LaTeX-package
31405 \begin_inset Index idx
31408 \begin_layout Plain Layout
31421 to a formula a new blue box appears where chemical formulas can be inserted
31422 in an intuitive way.
31425 \begin_layout Standard
31427 \begin_inset Tabular
31428 <lyxtabular version="3" rows="9" columns="2">
31429 <features rotate="0" tabularvalignment="middle">
31430 <column alignment="center" valignment="top">
31431 <column alignment="center" valignment="top">
31433 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
31436 \begin_layout Plain Layout
31442 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
31445 \begin_layout Plain Layout
31447 \begin_inset Note Note
31450 \begin_layout Plain Layout
31457 is only used as spacer.
31469 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
31472 \begin_layout Plain Layout
31476 \begin_inset space \textvisiblespace{}
31484 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
31487 \begin_layout Plain Layout
31488 \begin_inset Formula $\raisebox{4.5mm}{}\ce{H2CO3}\raisebox{-2mm}{}$
31498 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
31501 \begin_layout Plain Layout
31505 \begin_inset space \textvisiblespace{}
31513 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
31516 \begin_layout Plain Layout
31517 \begin_inset Formula $\raisebox{5mm}{}\ce{SO4^{2-}}\raisebox{-2mm}{}$
31527 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
31530 \begin_layout Plain Layout
31534 \begin_inset space \textvisiblespace{}
31542 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
31545 \begin_layout Plain Layout
31546 \begin_inset Formula $\raisebox{4.5mm}{}\ce{(NH4)2S}\raisebox{-2mm}{}$
31556 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
31559 \begin_layout Plain Layout
31563 \begin_inset space \textvisiblespace{}
31571 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
31574 \begin_layout Plain Layout
31575 \begin_inset Formula $\raisebox{4.5mm}{}\ce{KCr(SO4)2.12H2O}\raisebox{-2mm}{}$
31585 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
31588 \begin_layout Plain Layout
31592 \begin_inset space \textvisiblespace{}
31598 \begin_inset space \textvisiblespace{}
31604 \begin_inset space \textvisiblespace{}
31612 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
31615 \begin_layout Plain Layout
31616 \begin_inset Formula $\raisebox{4.5mm}{}\ce{A-B\dbond C\tbond D}\raisebox{-2mm}{}$
31626 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
31629 \begin_layout Plain Layout
31633 \begin_inset space \textvisiblespace{}
31637 \begin_inset Formula $\downarrow$
31641 \begin_inset Formula $\to$
31649 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
31652 \begin_layout Plain Layout
31653 \begin_inset Formula $\raisebox{5mm}{}\ce{_{90}^{227}Th+}\raisebox{-2mm}{}$
31663 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
31666 \begin_layout Plain Layout
31670 \begin_inset space \textvisiblespace{}
31674 \begin_inset space \textvisiblespace{}
31678 \begin_inset space \textvisiblespace{}
31682 \begin_inset space \textvisiblespace{}
31686 \begin_inset space \textvisiblespace{}
31694 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
31697 \begin_layout Plain Layout
31698 \begin_inset Formula $\raisebox{4.5mm}{}\ce{CO2 + C <=> 2CO}\raisebox{-2mm}{}$
31708 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
31711 \begin_layout Plain Layout
31715 \begin_inset space \textvisiblespace{}
31719 \begin_inset space \textvisiblespace{}
31723 \begin_inset space \textvisiblespace{}
31727 \begin_inset space \textvisiblespace{}
31735 \begin_inset space \textvisiblespace{}
31743 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
31746 \begin_layout Plain Layout
31747 \begin_inset Formula $\raisebox{5mm}{}\ce{CO2 + C ->[\alpha][\beta] 2CO}\raisebox{-4mm}{}$
31763 \begin_layout Standard
31764 \begin_inset Note Greyedout
31767 \begin_layout Plain Layout
31773 Inserting a formula to a
31779 box will lead to LaTeX errors due to a LyX bug.
31785 \begin_layout Plain Layout
31786 \begin_inset CommandInset href
31788 name "LyX-bug #8566"
31789 target "http://www.lyx.org/trac/ticket/8566"
31800 In this case TeX code has to be used like for
31814 \begin_layout Plain Layout
31835 \begin_layout Standard
31836 \begin_inset Note Greyedout
31839 \begin_layout Plain Layout
31845 It is not possible in LyX to use the character ^ to get an up-arrow as
31851 One instead uses a negative thin space followed by the command
31858 \begin_inset Formula $\ce{Fe + 2H+ -> Fe^{2+} + H2\negthinspace\uparrow}$
31869 \begin_layout Standard
31876 the command for equation
31877 \begin_inset space ~
31881 \begin_inset CommandInset ref
31883 reference "eq:chem-reaction"
31888 \begin_inset Newline newline
31896 \begin_inset space \textvisiblespace{}
31900 \begin_inset space \textvisiblespace{}
31904 \begin_inset space \textvisiblespace{}
31908 \begin_inset space \textvisiblespace{}
31912 \begin_inset space \textvisiblespace{}
31916 \begin_inset space \textvisiblespace{}
31922 \begin_layout Standard
31923 To create multiline chemical equations first a multiline formula is created
31925 \begin_inset CommandInset ref
31927 reference "sec:Multiline-Formulas"
31932 Afterwards the command
31938 is used in every small blue box of the formula.
31940 \begin_inset CommandInset ref
31942 reference "eq:TEOS-reaction-1"
31947 \begin_inset CommandInset ref
31949 reference "eq:TEOS-reaction-2"
31953 are an example of a multi-stage chemical reaction where every equation
31954 has its own number.
31955 \begin_inset Formula
31957 \ce{TEOS + 4O} & \ce{->} & \ce{Si(OH)4 + 4C2H4O}\label{eq:TEOS-reaction-1}\\
31958 \ce{Si(OH)4} & \ce{->} & \ce{SiO2 + 2H2O}\label{eq:TEOS-reaction-2}
31966 \begin_layout Standard
31977 package provides the command
31984 \begin_inset Index idx
31987 \begin_layout Plain Layout
31995 that has to be used for special cases.
31996 For more information about
32002 and more examples have a look at the documentation of
32007 \begin_inset CommandInset citation
32016 \begin_layout Section
32020 \begin_layout Standard
32021 LyX supports two types of commutative diagrams:
32029 that are explained in the following.
32032 \begin_layout Subsection
32034 \begin_inset Index idx
32037 \begin_layout Plain Layout
32046 \begin_layout Standard
32047 Diagrams of this type visualize relations by vertical and horizontal lines
32049 \begin_inset Formula
32051 \begin{CD}A@>>>B@>>>C\\
32062 \begin_layout Standard
32063 To get them, the command
32068 \begin_inset Index idx
32071 \begin_layout Plain Layout
32081 is inserted to a formula.
32082 A blue box appears with two dashed lines where further commands can be
32087 arg "newline-insert newline"
32090 a new line is created.
32091 Horizontal relations are inserted in odd, vertical in even formula lines.
32094 \begin_layout Standard
32095 To create the relations there are the following commands:
32098 \begin_layout Itemize
32103 creates a left arrow,
32114 \begin_layout Itemize
32119 creates an up arrow,
32127 a vertical equal sign
32130 \begin_layout Itemize
32136 is a placeholder for non-existent relations
32139 \begin_layout Standard
32140 All arrows can be labeled as follows:
32143 \begin_layout Itemize
32144 If text inserted between the first and second < or >, resp., it is placed
32146 When it is inserted between the second and third one, it appears under
32150 \begin_layout Itemize
32151 When text for vertical arrows is inserted between the first and second A
32152 or V, resp., it is placed left beside the arrow.
32153 When it is inserted between the second and third one, it appears right
32155 If the text contains an A or V, these letters must be set into a TeX-brace.
32158 \begin_layout Standard
32159 As example a diagram with all possible relations:
32162 \begin_layout Standard
32163 \begin_inset Formula
32165 \begin{CD}A@>j>>B@>>k>C@=F\\
32176 \begin_layout Standard
32177 The command for this is:
32178 \begin_inset Newline newline
32186 \begin_inset space \textvisiblespace{}
32189 A@>j>>B@>>k>C@=F Ctrl+Return
32190 \begin_inset Newline newline
32194 \begin_inset Phantom HPhantom
32197 \begin_layout Plain Layout
32203 \begin_inset space \textvisiblespace{}
32216 \begin_inset Formula $\to$
32222 \begin_inset Newline newline
32226 \begin_inset Phantom HPhantom
32229 \begin_layout Plain Layout
32235 \begin_inset space \textvisiblespace{}
32246 \begin_layout Subsection
32248 \begin_inset Index idx
32251 \begin_layout Plain Layout
32252 Diagrams ! xymatrix
32260 \begin_layout Standard
32261 To be able to use xymatrices, the LaTeX-package
32266 A xymatrix is created by inserting the command
32273 Then you are able to add new matrix columns and rows like for normal matrices,
32275 \begin_inset CommandInset ref
32277 reference "sec:Matrices"
32284 \begin_layout Standard
32285 In contrary to amscd diagrams, xymatrices supports diagonal and curved arrows,
32287 All possibilities to create commutative diagrams and decorations are explained
32292 that you find in the menu
32294 Help\SpecialChar \menuseparator
32296 \begin_inset space ~
32304 \begin_layout Subsection
32310 \begin_inset Index idx
32313 \begin_layout Plain Layout
32322 \begin_layout Standard
32327 -diagrams, the LaTeX-package
32336 -diagram is created by inserting the command
32343 Then you are able to add new matrix columns and rows like for normal matrices,
32345 \begin_inset CommandInset ref
32347 reference "sec:Matrices"
32354 \begin_layout Standard
32355 Examples how to create
32359 diagrams in LyX is given in the
32361 Feynman-diagram manual
32363 that you find in the menu
32365 Help\SpecialChar \menuseparator
32367 \begin_inset space ~
32375 \begin_layout Standard
32376 \begin_inset Newpage newpage
32382 \begin_layout Section
32383 User-defined Commands
32384 \begin_inset Index idx
32387 \begin_layout Plain Layout
32388 User-defined commands
32396 \begin_layout Standard
32397 \begin_inset Note Greyedout
32400 \begin_layout Plain Layout
32405 The names of user-defined commands and macros may only consist of Latin
32414 \begin_layout Subsection
32418 \begin_inset CommandInset label
32420 name "sub:The-Command-newcommand"
32425 \begin_inset Index idx
32428 \begin_layout Plain Layout
32429 User-defined commands !
32437 \begin_inset Index idx
32440 \begin_layout Plain Layout
32451 \begin_layout Standard
32452 Many LaTeX-commands are too long to be used frequently.
32453 But it is possible to define with the command
32459 new shorter commands.
32462 \begin_layout Standard
32463 The command scheme of
32472 \begin_layout Standard
32477 newcommand{new command name}[number of arguments][optional
32482 \begin_inset Newline newline
32486 \begin_inset Phantom HPhantom
32489 \begin_layout Plain Layout
32499 {command definition}
32502 \begin_layout Standard
32503 \begin_inset Note Greyedout
32506 \begin_layout Plain Layout
32511 Assure that the name of the new command is not already used in your document
32512 or by LaTeX-packages that you use.
32513 When you for example define the command
32525 , you get an error message because
32531 is already defined as command for
32532 \begin_inset Quotes eld
32536 \begin_inset Formula $\le$
32540 \begin_inset Quotes erd
32551 \begin_layout Standard
32552 The number of arguments is an integer in the range 0
32553 \begin_inset space \thinspace{}
32557 \begin_inset space \thinspace{}
32560 9 and specifies how many arguments the new command should have.
32561 With the optional value a value for an optional argument can be predefined.
32562 When this is done, the
32570 rgument of the new command is automatically an optional one.
32573 \begin_layout Standard
32574 Here are some examples:
32577 \begin_layout Itemize
32578 To define the command
32590 , the LaTeX-preamble line is:
32591 \begin_inset VSpace medskip
32595 \begin_inset Newline newline
32609 \begin_layout Itemize
32610 To define the command
32622 , the argument (that should be underlined) must be taken into account.
32623 For this the preamble line is:
32624 \begin_inset VSpace medskip
32628 \begin_inset Newline newline
32642 \begin_inset VSpace medskip
32646 \begin_inset Newline newline
32653 acts as argument placeholder, the
32657 behind it denotes that it is the placeholder for the first argument.
32660 \begin_layout Itemize
32668 \begin_inset space \thinspace{}
32672 \begin_inset space \space{}
32682 \begin_inset VSpace medskip
32686 \begin_inset Newline newline
32697 framebox#1#2{$#3$}}
32700 \begin_inset VSpace medskip
32704 \begin_inset Newline newline
32707 The two Dollar signs creates the extra formula needed for
32714 \begin_inset CommandInset ref
32716 reference "sub:Boxes-with-Frame"
32723 \begin_layout Itemize
32724 To create a new command for
32730 where the color for the box need not be specified, the argument for the
32731 color is defined optional:
32732 \begin_inset VSpace medskip
32736 \begin_inset Newline newline
32747 fcolorbox{#2}{#1}{$#3$}}
32750 \begin_inset VSpace medskip
32754 \begin_inset Newline newline
32757 When the color is not specified when using
32763 , the predefined color
32770 \begin_layout Standard
32771 A test of the new defined commands:
32774 \begin_layout Standard
32776 \begin_inset Tabular
32777 <lyxtabular version="3" rows="6" columns="2">
32778 <features rotate="0" tabularvalignment="middle">
32779 <column alignment="center" valignment="top">
32780 <column alignment="center" valignment="top">
32782 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
32785 \begin_layout Plain Layout
32791 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
32794 \begin_layout Plain Layout
32796 \begin_inset Note Note
32799 \begin_layout Plain Layout
32806 is only used as spacer.
32818 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
32821 \begin_layout Plain Layout
32825 \begin_inset space \textvisiblespace{}
32833 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
32836 \begin_layout Plain Layout
32837 \begin_inset Formula $A\gr B$
32847 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
32850 \begin_layout Plain Layout
32858 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
32861 \begin_layout Plain Layout
32862 \begin_inset Formula $\raisebox{4.5mm}{}\us{ABcd}\raisebox{-2mm}{}$
32872 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
32875 \begin_layout Plain Layout
32879 \begin_inset Formula $\to$
32885 \begin_inset Formula $\to$
32893 \begin_inset space \textvisiblespace{}
32901 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
32904 \begin_layout Plain Layout
32905 \begin_inset Formula $\raisebox{6mm}{}\fb{[2cm]}{}{\int A=B}\raisebox{-4mm}{}$
32915 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
32918 \begin_layout Plain Layout
32922 \begin_inset Formula $\to$
32930 \begin_inset space \textvisiblespace{}
32938 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
32941 \begin_layout Plain Layout
32942 \begin_inset Formula $\raisebox{6mm}{}\cb{red}{\int A=B}\raisebox{-4mm}{}$
32952 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
32955 \begin_layout Plain Layout
32961 \begin_inset Formula $\to$
32969 \begin_inset space \textvisiblespace{}
32977 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
32980 \begin_layout Plain Layout
32981 \begin_inset Formula $\raisebox{6mm}{}\cb[green]{red}{\int A=B}\raisebox{-4mm}{}$
32997 \begin_layout Subsection
32999 \begin_inset Index idx
33002 \begin_layout Plain Layout
33003 User-defined commands! Math macros
33009 \begin_inset Index idx
33012 \begin_layout Plain Layout
33021 \begin_layout Standard
33022 User-defined commands are especially convenient for complex expressions.
33023 When you are for example dealing with a document that has quadratic equations,
33024 the same solution type occurs several times.
33025 The general form of a quadratic equation is
33026 \begin_inset Formula
33028 0=\lambda^{2}+p\lambda+q
33033 The general form of the solution is
33034 \begin_inset Formula
33036 \lambda_{1,2}=-\frac{p}{2}\pm\sqrt{\frac{p²}{4}-q}
33044 \begin_layout Standard
33045 To define a command for the solution formula where only the three parameters
33047 \begin_inset Formula $\lambda$
33051 \begin_inset Formula $p$
33055 \begin_inset Formula $q$
33058 need to be specified and the index of
33059 \begin_inset Formula $\lambda$
33062 can be given optionally, the LaTeX-preamble line is
33063 \begin_inset Newline newline
33079 \begin_inset Newline newline
33083 \begin_inset Phantom HPhantom
33086 \begin_layout Plain Layout
33100 frac{#3^{2}}{4}-#4}}
33103 \begin_layout Standard
33104 To create with this the solution formula, the command
33105 \begin_inset Newline newline
33115 \begin_inset Formula $\to$
33121 \begin_inset Formula $\to$
33128 is inserted to a formula
33133 \begin_layout Standard
33134 The definition of the new command is unintuitive because one has to know
33135 the schemes of all used LaTeX commands, e.
33136 \begin_inset space \thinspace{}
33140 \begin_inset space \space{}
33143 that a fraction is inserted in LaTeX as
33147 frac{numerator}{denominator}
33150 Furthermore one can easily forget a brace in the definition and cannot
33151 see in LyX what the new command is doing.
33152 To avoid these problems LyX offers the possibility to use math macros instead
33162 \begin_layout Standard
33163 A math macro is created by using the menu
33165 Insert\SpecialChar \menuseparator
33166 Math\SpecialChar \menuseparator
33169 or the toolbar button
33172 arg "math-macro newmacroname_newcommand"
33176 The math macro toolbar appears together with the following box where the
33178 \begin_inset Newline newline
33182 \begin_inset space \hspace*{\fill}
33186 \begin_inset Graphics
33187 filename clipart/macrobox.png
33192 \begin_inset space \hspace*{\fill}
33196 \begin_inset Newline newline
33200 \begin_inset FormulaMacro
33201 \newcommand{\qG}[4][1,\,2]{#2_{#1}=-\frac{#3}{2}\pm\sqrt{\frac{#3^{2}}{4}-#4}}
33206 newmacroname is the default name of the macro that should be changed to
33207 something sensible.
33208 The wanted formula is inserted in the first blue box.
33209 An argument placeholder is inserted with the command
33216 \begin_inset space \thinspace{}
33220 \begin_inset space \space{}
33229 or by using the macro toolbar button
33232 arg "math-macro-add-param"
33236 Argument placeholders are displayed red.
33238 \begin_inset space ~
33241 arguments are possible.
33242 Optional arguments are created with the toolbar button
33245 arg "math-macro-add-optional-param"
33249 The first non-optional argument can be transformed to an optional one with
33253 arg "math-macro-make-optional"
33257 In the second blue box the appearance of the macro in LyX can be defined.
33258 Normally you want to see it as it is defined, so the box is kept empty.
33259 But when you have created a macro that needs lot of space on the screen,
33260 you can insert in the box for example
33261 \begin_inset Newline newline
33291 \begin_inset Newline newline
33296 For the macro only the arguments with the macro name in front of them will
33297 then be displayed in LyX, leading to a better overview.
33298 The formula appears in the output as defined in the first box.
33299 \begin_inset Newline newline
33302 The appearance of macros in formulas can furthermore be changed for single
33303 macros by setting the cursor in the macro and using the menu
33305 View\SpecialChar \menuseparator
33307 \begin_inset space ~
33311 \begin_inset space ~
33319 \begin_layout Standard
33320 To use a macro, the macro name is inserted as command to a formula, in our
33328 Our macro looks in LyX like this:
33329 \begin_inset Newline newline
33333 \begin_inset space \hspace*{\fill}
33337 \begin_inset Graphics
33338 filename clipart/macrouse.png
33343 \begin_inset space \hspace*{\fill}
33347 \begin_inset Newline newline
33350 Here is our macro example with the arguments
33351 \begin_inset Formula $x$
33355 \begin_inset Formula $\ln(x)$
33359 \begin_inset Formula $B$
33365 \begin_layout Standard
33366 \begin_inset Formula
33376 \begin_layout Standard
33377 LyX offers in the menu
33379 Tools\SpecialChar \menuseparator
33380 Preferences\SpecialChar \menuseparator
33381 Editing\SpecialChar \menuseparator
33384 different styles to edit macros.
33385 To find the style that suits you the most, choose a style and set the cursor
33386 in a macro formula to see the difference.
33389 \begin_layout Standard
33390 A math macro is transformed internally to a
33396 command when exporting the document.
33403 command is not placed in the LaTeX-preamble, therefore macros can only
33404 be used in formulas that are in the document below the macro definition
33408 \begin_layout Standard
33409 Math macros can also be directly created from a
33416 When writing for example the command
33419 \begin_inset Newline newline
33428 xleftarrow[#2]{#1}}
33429 \begin_inset Newline newline
33434 in LyX as normal text, highlighting it completely and using then the shortcut
33439 , the command will be transformed to a math macro.
33440 Using this method you need to be careful that the
33446 command is typed correctly, otherwise you get a faulty macro leading to
33450 \begin_layout Standard
33451 Math macros currently have the problem that further formulas in macro definition
33452 s are handled wrongly.
33453 Therefore the example
33460 \begin_inset CommandInset ref
33462 reference "sub:The-Command-newcommand"
33466 cannot be created as macro.
33469 \begin_layout Standard
33470 When the cursor is in a macro definition box, you will see the macro toolbar
33474 \begin_layout Standard
33475 \begin_inset VSpace defskip
33481 \begin_layout Standard
33482 \begin_inset Graphics
33483 filename clipart/MacroToolbar.png
33488 \begin_inset Index idx
33491 \begin_layout Plain Layout
33500 \begin_layout Standard
33501 \begin_inset VSpace defskip
33507 \begin_layout Standard
33508 The macro toolbar contains from left to right the following buttons:
33511 \begin_layout Standard
33512 \begin_inset VSpace defskip
33518 \begin_layout Standard
33519 \begin_inset Tabular
33520 <lyxtabular version="3" rows="9" columns="2">
33521 <features rotate="0" islongtable="true" longtabularalignment="center">
33522 <column alignment="left" valignment="top">
33523 <column alignment="left" valignment="top" width="85col%">
33524 <row interlinespace="2.5mm">
33525 <cell alignment="center" valignment="top" usebox="none">
33528 \begin_layout Plain Layout
33531 arg "math-macro-remove-param"
33539 <cell alignment="center" valignment="top" usebox="none">
33542 \begin_layout Plain Layout
33545 Edit\SpecialChar \menuseparator
33546 Math\SpecialChar \menuseparator
33548 \begin_inset space ~
33551 Definition\SpecialChar \menuseparator
33552 Remove Last Argument
33558 <row interlinespace="2.5mm">
33559 <cell alignment="center" valignment="top" usebox="none">
33562 \begin_layout Plain Layout
33565 arg "math-macro-add-param"
33573 <cell alignment="center" valignment="top" usebox="none">
33576 \begin_layout Plain Layout
33579 Edit\SpecialChar \menuseparator
33580 Math\SpecialChar \menuseparator
33582 \begin_inset space ~
33585 Definition\SpecialChar \menuseparator
33592 <row interlinespace="2.5mm">
33593 <cell alignment="center" valignment="top" usebox="none">
33596 \begin_layout Plain Layout
33599 arg "math-macro-make-optional"
33607 <cell alignment="center" valignment="top" usebox="none">
33610 \begin_layout Plain Layout
33613 Edit\SpecialChar \menuseparator
33614 Math\SpecialChar \menuseparator
33616 \begin_inset space ~
33619 Definition\SpecialChar \menuseparator
33620 Transform First Non-Optional to
33621 \begin_inset Newline newline
33625 \begin_inset Phantom HPhantom
33628 \begin_layout Plain Layout
33631 Edit\SpecialChar \menuseparator
33632 Math\SpecialChar \menuseparator
33634 \begin_inset space ~
33637 Definition\SpecialChar \menuseparator
33649 <row interlinespace="2.5mm">
33650 <cell alignment="center" valignment="top" usebox="none">
33653 \begin_layout Plain Layout
33656 arg "math-macro-make-nonoptional"
33664 <cell alignment="center" valignment="top" usebox="none">
33667 \begin_layout Plain Layout
33670 Edit\SpecialChar \menuseparator
33671 Math\SpecialChar \menuseparator
33673 \begin_inset space ~
33676 Definition\SpecialChar \menuseparator
33677 Transform Last Optional to
33678 \begin_inset Newline newline
33682 \begin_inset Phantom HPhantom
33685 \begin_layout Plain Layout
33688 Edit\SpecialChar \menuseparator
33689 Math\SpecialChar \menuseparator
33691 \begin_inset space ~
33694 Definition\SpecialChar \menuseparator
33700 Non-Optional Argument
33706 <row interlinespace="2.5mm">
33707 <cell alignment="center" valignment="top" usebox="none">
33710 \begin_layout Plain Layout
33713 arg "math-macro-remove-optional-param"
33721 <cell alignment="center" valignment="top" usebox="none">
33724 \begin_layout Plain Layout
33727 Edit\SpecialChar \menuseparator
33728 Math\SpecialChar \menuseparator
33730 \begin_inset space ~
33733 Definition\SpecialChar \menuseparator
33734 Remove Optional Argument
33740 <row interlinespace="2.5mm">
33741 <cell alignment="center" valignment="top" usebox="none">
33744 \begin_layout Plain Layout
33747 arg "math-macro-add-optional-param"
33755 <cell alignment="center" valignment="top" usebox="none">
33758 \begin_layout Plain Layout
33761 Edit\SpecialChar \menuseparator
33762 Math\SpecialChar \menuseparator
33764 \begin_inset space ~
33767 Definition\SpecialChar \menuseparator
33768 Insert Optional Argument
33774 <row interlinespace="2.5mm">
33775 <cell alignment="center" valignment="top" usebox="none">
33778 \begin_layout Plain Layout
33781 arg "math-macro-remove-greedy-param"
33789 <cell alignment="center" valignment="top" usebox="none">
33792 \begin_layout Plain Layout
33795 Edit\SpecialChar \menuseparator
33796 Math\SpecialChar \menuseparator
33798 \begin_inset space ~
33801 Definition\SpecialChar \menuseparator
33802 Remove Last Argument
33803 \begin_inset Newline newline
33807 \begin_inset Phantom HPhantom
33810 \begin_layout Plain Layout
33813 Edit\SpecialChar \menuseparator
33814 Math\SpecialChar \menuseparator
33816 \begin_inset space ~
33819 Definition\SpecialChar \menuseparator
33825 Spitting Out To The Right
33831 <row interlinespace="2.5mm">
33832 <cell alignment="center" valignment="top" usebox="none">
33835 \begin_layout Plain Layout
33838 arg "math-macro-append-greedy-param"
33846 <cell alignment="center" valignment="top" usebox="none">
33849 \begin_layout Plain Layout
33852 Edit\SpecialChar \menuseparator
33853 Math\SpecialChar \menuseparator
33855 \begin_inset space ~
33858 Definition\SpecialChar \menuseparator
33860 \begin_inset Newline newline
33864 \begin_inset Phantom HPhantom
33867 \begin_layout Plain Layout
33870 Edit\SpecialChar \menuseparator
33871 Math\SpecialChar \menuseparator
33873 \begin_inset space ~
33876 Definition\SpecialChar \menuseparator
33882 Eating From The Right
33888 <row interlinespace="2.5mm">
33889 <cell alignment="center" valignment="top" usebox="none">
33892 \begin_layout Plain Layout
33895 arg "math-macro-add-greedy-optional-param"
33903 <cell alignment="center" valignment="top" usebox="none">
33906 \begin_layout Plain Layout
33909 Edit\SpecialChar \menuseparator
33910 Math\SpecialChar \menuseparator
33912 \begin_inset space ~
33915 Definition\SpecialChar \menuseparator
33916 Append Optional Argument
33917 \begin_inset Newline newline
33921 \begin_inset Phantom HPhantom
33924 \begin_layout Plain Layout
33927 Edit\SpecialChar \menuseparator
33928 Math\SpecialChar \menuseparator
33930 \begin_inset space ~
33933 Definition\SpecialChar \menuseparator
33939 Eating From The Right
33952 \begin_layout Section
33953 Computer Algebra Systems
33956 \begin_layout Standard
33957 LyX offers the exchange between mathematical expressions written in LyX's
33958 math editor and external applications or user defined scripts.
33959 Currently supported applications are
33976 Note that the set of supported mathematical constructs is limited only
33977 to very simple cases.
33980 \begin_layout Subsection
33984 \begin_layout Standard
33985 Write some expression in a formula, go to the
33987 Edit\SpecialChar \menuseparator
33988 Math\SpecialChar \menuseparator
33989 Use Computer Algebra System
33991 menu and choose the application you have installed on the computer.
33992 After that the result of computation should show on the right side of the
33993 expression together with the
33994 \begin_inset Quotes eld
33998 \begin_inset Quotes erd
34004 \begin_layout Standard
34005 Here are few simple examples (with results from
34009 ) to show what kind of computations can be performed:
34012 \begin_layout Itemize
34013 \begin_inset Formula $\frac{37}{3}*2-\sum_{i=1}^{3}i^{i}=-\frac{22}{3}$
34019 \begin_layout Itemize
34020 \begin_inset Formula $\frac{37.0}{3}=12.33333333333333$
34026 \begin_layout Itemize
34027 \begin_inset Formula $\int_{1}^{2}\sin(x)dx=\cos1-\cos2$
34033 \begin_layout Itemize
34034 \begin_inset Formula $\det\left[\begin{array}{ccc}
34038 \end{array}\right]=-56$
34044 \begin_layout Itemize
34045 \begin_inset Formula $\lim_{x\rightarrow0}\left(\frac{\sin(x)}{x}\right)=1$
34051 \begin_layout Subsection
34055 \begin_layout Standard
34056 Currently there is no keyboard shortcut for calling the algebra applications.
34057 One can easily bind a shortcut to the
34061 LyX function (see the
34069 \begin_inset space \thinspace{}
34073 \begin_inset space \space{}
34080 key inside the math editor.
34085 one would use this shortcut definition command:
34088 \begin_layout Standard
34091 command-alternatives break-paragraph;math-extern maxima
34094 \begin_layout Section
34096 \begin_inset Index idx
34099 \begin_layout Plain Layout
34108 \begin_layout Subsection
34110 \begin_inset Index idx
34113 \begin_layout Plain Layout
34122 \begin_layout Standard
34123 Negative numbers often look ugly in formulas because the minus sign before
34124 the number is set with the same length as the minus operator sign.
34125 When writing the negative number in normal text, the minus sign appears
34129 \begin_layout Standard
34130 Thus, the problem disappears when converting the minus sign to mathematical
34134 \begin_layout Standard
34135 An example to visualize the problem:
34138 \begin_layout Standard
34140 \begin_inset Tabular
34141 <lyxtabular version="3" rows="3" columns="2">
34142 <features rotate="0" tabularvalignment="middle">
34143 <column alignment="right" valignment="top">
34144 <column alignment="left" valignment="top">
34146 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
34149 \begin_layout Plain Layout
34155 <cell alignment="center" valignment="top" topline="true" rightline="true" usebox="none">
34158 \begin_layout Plain Layout
34166 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
34169 \begin_layout Plain Layout
34175 <cell alignment="center" valignment="top" topline="true" bottomline="true" rightline="true" usebox="none">
34178 \begin_layout Plain Layout
34179 \begin_inset Formula $x=-2$
34189 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
34192 \begin_layout Plain Layout
34198 <cell alignment="center" valignment="top" topline="true" bottomline="true" rightline="true" usebox="none">
34201 \begin_layout Plain Layout
34202 \begin_inset Formula $x=\textrm{-}2$
34218 \begin_layout Subsection
34219 Comma as decimal Separator
34220 \begin_inset Index idx
34223 \begin_layout Plain Layout
34232 \begin_layout Standard
34233 In LaTeX a comma inside a formula is used, according to the English convention,
34234 as number group separator.
34235 So there will be space added behind all commas in formulas.
34238 \begin_layout Standard
34239 To avoid this, the comma is highlighted and changed to mathematical text
34249 \begin_layout Standard
34250 To use all formula commas in the document as decimal separator, the file
34259 \begin_layout Plain Layout
34264 is part of the LaTeX-package
34269 \begin_inset Index idx
34272 \begin_layout Plain Layout
34277 \begin_layout Plain Layout
34297 \begin_inset Index idx
34300 \begin_layout Plain Layout
34306 is loaded with the LaTeX-preamble line
34309 \begin_layout Standard
34317 \begin_layout Subsection
34319 \begin_inset CommandInset label
34321 name "sub:Physical-Vectors"
34326 \begin_inset Index idx
34329 \begin_layout Plain Layout
34338 \begin_layout Standard
34339 Predefined vectors are offered by the LaTeX-package
34344 \begin_inset Index idx
34347 \begin_layout Plain Layout
34353 that is loaded with the LaTeX-preamble line
34356 \begin_layout Standard
34364 \begin_layout Standard
34368 \begin_layout Plain Layout
34378 \begin_inset Note Note
34381 \begin_layout Plain Layout
34382 The following table will only be displayed when the LaTeX-package
34394 \begin_layout Standard
34395 The following commands are defined:
34398 \begin_layout Standard
34400 \begin_inset Tabular
34401 <lyxtabular version="3" rows="4" columns="2">
34402 <features rotate="0" tabularvalignment="middle">
34403 <column alignment="center" valignment="top">
34404 <column alignment="center" valignment="top">
34406 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
34409 \begin_layout Plain Layout
34415 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
34418 \begin_layout Plain Layout
34426 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
34429 \begin_layout Plain Layout
34439 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
34442 \begin_layout Plain Layout
34443 \begin_inset Formula $\Bra{\psi}$
34453 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
34456 \begin_layout Plain Layout
34466 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
34469 \begin_layout Plain Layout
34470 \begin_inset Formula $\Ket{\psi}$
34480 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
34483 \begin_layout Plain Layout
34495 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
34498 \begin_layout Plain Layout
34499 \begin_inset Formula $\Braket{\psi|\phi}$
34515 \begin_layout Standard
34522 assures that all vertical bars are set in the size of the surrounding brackets:
34523 \begin_inset Formula
34525 \Braket{\phi|J=\frac{3}{2}\,,\, M_{J}}
34534 \begin_layout Plain Layout
34544 \begin_inset Note Note
34547 \begin_layout Plain Layout
34548 The following will be displayed when the LaTeX-package
34560 \begin_layout Standard
34561 You need to install the LaTeX-package
34565 to see the rest of this subsection in the output.
34568 \begin_layout Standard
34572 \begin_layout Plain Layout
34584 \begin_layout Standard
34591 can also be achieved using the command
34597 , that is described in
34598 \begin_inset CommandInset ref
34600 reference "sub:Automatic-Bracket-Size"
34607 \begin_layout Subsection
34608 Self-defined Fractions
34609 \begin_inset CommandInset label
34611 name "sub:Self-defined-Fractions"
34616 \begin_inset Index idx
34619 \begin_layout Plain Layout
34620 Fractions ! self-defined
34628 \begin_layout Standard
34629 To define custom commands for fractions, the command
34636 \begin_inset Index idx
34639 \begin_layout Plain Layout
34646 \begin_layout Plain Layout
34660 is used in the following scheme:
34663 \begin_layout Standard
34676 bracket}{fraction bar thickness}{style}
34677 \begin_inset Newline newline
34681 \begin_inset Phantom HPhantom
34684 \begin_layout Plain Layout
34694 {numerator}{denominator}
34697 \begin_layout Standard
34698 The style is a number in the range of 0
34699 \begin_inset space \thinspace{}
34703 \begin_inset space \thinspace{}
34709 \begin_layout Standard
34711 \begin_inset Tabular
34712 <lyxtabular version="3" rows="5" columns="2">
34713 <features rotate="0" tabularvalignment="middle">
34714 <column alignment="center" valignment="top">
34715 <column alignment="center" valignment="top">
34717 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
34720 \begin_layout Plain Layout
34726 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
34729 \begin_layout Plain Layout
34737 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
34740 \begin_layout Plain Layout
34746 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
34749 \begin_layout Plain Layout
34750 display style formula
34757 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
34760 \begin_layout Plain Layout
34766 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
34769 \begin_layout Plain Layout
34777 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
34780 \begin_layout Plain Layout
34786 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
34789 \begin_layout Plain Layout
34797 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
34800 \begin_layout Plain Layout
34806 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
34809 \begin_layout Plain Layout
34823 \begin_layout Standard
34824 When no style is given, the size is adjusted to the surrounding environment
34825 like for the command
34834 \begin_layout Standard
34835 When no fraction bar thickness is given, the predefined value of 0.4
34836 \begin_inset space \thinspace{}
34842 \begin_layout Standard
34843 \begin_inset VSpace medskip
34846 For example, the commands
34859 \begin_inset CommandInset ref
34861 reference "sub:Fractions"
34865 are defined with the commands
34868 \begin_layout Standard
34877 genfrac{}{}{}{0}{#1}{#2}}
34880 \begin_layout Standard
34884 \begin_layout Standard
34893 genfrac{(}{)}{0pt}{1}{#1}{#2}}
34896 \begin_layout Standard
34897 \begin_inset VSpace medskip
34900 To define a fraction where the fraction bar thickness can be given as optional
34901 argument, the following line is inserted to the LaTeX-preamble:
34904 \begin_layout Standard
34913 genfrac{}{}{#1}{}{#2}{#3}}
34916 \begin_layout Standard
34918 \begin_inset Formula
34920 \text{Command} & & \mathrm{\backslash fracS[1mm]\backslash\{A\to\backslash\{B} & & \mathrm{\backslash fracS[5mm]\backslash\{A\to\backslash\{B}\\
34921 \text{Result} & & \fracS[1mm]{A}{B} & & \fracS[5mm]{A}{B}
34926 As one can see, the distance of the numerator and the denominator to the
34927 fraction bar is round about three times the bar thickness.
34930 \begin_layout Subsection
34932 \begin_inset Index idx
34935 \begin_layout Plain Layout
34944 \begin_layout Standard
34945 There are four ways to cancel formulas or parts of formulas:
34948 \begin_layout Standard
34952 \begin_layout Plain Layout
34962 \begin_inset Note Note
34965 \begin_layout Plain Layout
34966 The following table will only be displayed when the LaTeX-package
34978 \begin_layout Standard
34980 \begin_inset Tabular
34981 <lyxtabular version="3" rows="5" columns="2">
34982 <features rotate="0" tabularvalignment="middle">
34983 <column alignment="center" valignment="top">
34984 <column alignment="center" valignment="top">
34986 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
34989 \begin_layout Plain Layout
34995 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
34998 \begin_layout Plain Layout
35000 \begin_inset Note Note
35003 \begin_layout Plain Layout
35010 are used here as spacer.
35022 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
35025 \begin_layout Plain Layout
35029 \begin_inset space \textvisiblespace{}
35035 \begin_inset space \textvisiblespace{}
35043 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
35046 \begin_layout Plain Layout
35047 \begin_inset Formula $\raisebox{4.5mm}{}\cancel{\int A=B}\raisebox{-2.5mm}{}$
35057 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
35060 \begin_layout Plain Layout
35064 \begin_inset space \textvisiblespace{}
35070 \begin_inset space \textvisiblespace{}
35078 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
35081 \begin_layout Plain Layout
35082 \begin_inset Formula $\raisebox{4.5mm}{}\bcancel{\int A=B}\raisebox{-2.5mm}{}$
35092 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
35095 \begin_layout Plain Layout
35099 \begin_inset space \textvisiblespace{}
35105 \begin_inset space \textvisiblespace{}
35113 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
35116 \begin_layout Plain Layout
35117 \begin_inset Formula $\raisebox{4.5mm}{}\xcancel{\int A=B}\raisebox{-2.5mm}{}$
35127 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
35130 \begin_layout Plain Layout
35134 \begin_inset space \textvisiblespace{}
35140 \begin_inset space \textvisiblespace{}
35144 \begin_inset Formula $\to$
35152 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
35155 \begin_layout Plain Layout
35156 \begin_inset Formula $\raisebox{7mm}{}\cancelto{1}{\int A=B}\raisebox{-2.5mm}{}\hspace{3mm}$
35172 \begin_layout Standard
35179 is especially suitable to visualize the reduction of fractions within formulas:
35180 \begin_inset Formula
35182 \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}}}
35190 \begin_layout Standard
35191 To change the size of
35198 \begin_inset Quotes eld
35202 \begin_inset Quotes erd
35205 value one can add the LaTeX-preamble line
35208 \begin_layout Standard
35213 PassOptionsToPackage{option}{cancel}
35216 \begin_layout Standard
35225 which leads to the same size as for the canceled value, or
35229 which makes is it a bit smaller than normal.
35232 \begin_layout Standard
35233 To color the cancellation bar one adds this command as TeX code:
35236 \begin_layout Standard
35248 \begin_layout Standard
35253 can be replaced by a color of your choice.
35256 \begin_layout Standard
35260 \begin_layout Plain Layout
35276 \begin_layout Standard
35277 \begin_inset Formula
35279 \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}}}
35287 \begin_layout Standard
35291 \begin_layout Plain Layout
35305 \begin_inset Note Note
35308 \begin_layout Plain Layout
35317 \begin_layout Standard
35318 For further customizations, see the documentation of the package
35323 \begin_inset CommandInset citation
35330 \begin_inset Index idx
35333 \begin_layout Plain Layout
35342 \begin_layout Standard
35346 \begin_layout Plain Layout
35356 \begin_inset Note Note
35359 \begin_layout Plain Layout
35360 The following will be displayed when the LaTeX-package
35372 \begin_layout Standard
35373 You need to install the LaTeX-package
35377 to see the rest of this subsection in the output.
35380 \begin_layout Standard
35384 \begin_layout Plain Layout
35396 \begin_layout Standard
35397 \begin_inset Newpage newpage
35403 \begin_layout Subsection
35404 Formulas in Section Headings
35405 \begin_inset CommandInset label
35407 name "sub:Formulas-in-Section"
35412 \begin_inset Index idx
35415 \begin_layout Plain Layout
35416 Formula ! in section headings
35424 \begin_layout Standard
35425 When formulas are used in section headings, the following has to be taken
35429 \begin_layout Standard
35430 \begin_inset Note Greyedout
35433 \begin_layout Plain Layout
35439 \begin_inset Index idx
35442 \begin_layout Plain Layout
35443 Packages ! hyperref
35448 support is enabled in the document settings dialog under
35451 \begin_inset space ~
35456 , PDF-bookmarks are created for every section heading in the table of contents.
35457 If a section heading contains formulas, they are incorrectly displayed
35458 in the bookmark text, because formulas in bookmarks infringe the PDF convention
35467 \begin_layout Standard
35468 Both problems can be solved by inserting at the end of the section heading
35469 a short title with the menu
35471 Insert\SpecialChar \menuseparator
35473 \begin_inset space ~
35479 Short titles are used as alternative for multiline section headings to
35480 keep the table of contents clearly arranged.
35481 Only the short title appears in the table of contents and therefore also
35482 in the PDF-bookmark.
35485 \begin_layout Standard
35486 When formulas should be used in the table of contents but
35490 is used, one can use the following command in TeX-mode:
35493 \begin_layout Standard
35498 texorpdfstring{part}{alternative}
35499 \begin_inset Index idx
35502 \begin_layout Plain Layout
35513 \begin_layout Standard
35514 Part is the part of the heading that shouldn't appear in the PDF-bookmark.
35515 This can be characters, formulas, footnotes, but also cross-references.
35516 The alternative is used instead of the part for the bookmark.
35519 \begin_layout Standard
35520 Here are two example headings:
35521 \begin_inset VSpace -3mm
35528 \begin_layout Plain Layout
35540 \begin_layout Subsubsection
35541 Heading without formula in table of contents
35542 \begin_inset Formula $\sqrt{-1}=\mathrm{i}$
35546 \begin_inset Argument 1
35549 \begin_layout Plain Layout
35550 Heading without formula in table of contents
35558 \begin_layout Subsubsection
35559 Heading with formula in table of contents
35563 \begin_layout Plain Layout
35573 \begin_inset Formula $\sqrt{-1}=\mathrm{i}$
35580 \begin_layout Plain Layout
35590 \begin_layout Standard
35594 \begin_layout Plain Layout
35603 In the first heading a short title was used, in the second one
35612 \begin_layout Standard
35613 To get the same formatting as for the other headings, the complete heading
35622 \begin_layout Plain Layout
35624 \begin_inset CommandInset ref
35626 reference "sub:Bold-Formulas"
35638 \begin_layout Subsection
35639 Formulas in multi-column Text
35640 \begin_inset Index idx
35643 \begin_layout Plain Layout
35644 Formula ! in multi-column text
35652 \begin_layout Standard
35653 Formulas in multi-column text are often too wide to fit into a column and
35654 thus need to be set over the whole page width.
35655 This is done by using the LaTeX-package
35663 \begin_layout Plain Layout
35668 is part of every LaTeX standard installation.
35674 \begin_inset Index idx
35677 \begin_layout Plain Layout
35678 Packages ! multicol
35683 , that is loaded with the LaTeX-preamble line
35686 \begin_layout Standard
35691 usepackage{multicol}
35694 \begin_layout Standard
35695 \begin_inset Note Greyedout
35698 \begin_layout Plain Layout
35699 Note that in this case the setting
35702 \begin_inset space ~
35709 Document\SpecialChar \menuseparator
35715 \begin_inset space ~
35735 \begin_layout Standard
35736 Before the multi-column text the command
35739 \begin_layout Standard
35744 begin{multicols}{column number}
35747 \begin_layout Standard
35748 is written in TeX-mode.
35749 The column number is a number in the range of 2
35750 \begin_inset space \thinspace{}
35754 \begin_inset space \thinspace{}
35758 Before the formula the multi-column text is ended by inserting the command
35761 \begin_layout Standard
35769 \begin_layout Standard
35773 \begin_layout Standard
35774 Due to the command some space is automatically added before the formula.
35776 \begin_inset space \thinspace{}
35779 mm vertical space is inserted before the formula.
35780 When the formula style
35786 \begin_layout Plain Layout
35788 \begin_inset CommandInset ref
35790 reference "sec:Formula-Styles"
35802 \begin_inset space \thinspace{}
35805 mm space is inserted instead.
35808 \begin_layout Standard
35809 As example a multi-column text with a displayed formula:
35812 \begin_layout Standard
35818 \begin_layout Plain Layout
35822 begin{multicols}{2}
35827 Das Spektrum wird fouriertransformiert.
35828 Die Fouriertransformation wird verwendet, um die überlagerten Signale (Netzwerk
35829 , Lösungsmittel) zu trennen.
35830 Nachdem wir die Phasenverschiebung bestimmen konnten, interessiert uns
35831 nun das Aussehen des Ausgangssignals.
35832 Im Experiment haben wir es mit sehr vielen Teilchen zu tun, so dass man
35833 über alle Phasen integrieren muss.
35835 \begin_inset Formula $S$
35838 unser normiertes Ausgangssignal und
35839 \begin_inset Formula $P$
35842 die Phasenverteilungsfunktion, so ergibt sich die Beziehung
35846 \begin_layout Plain Layout
35856 \begin_inset VSpace -6mm
35860 \begin_inset Formula
35862 S(t)=S_{0}(t)\int_{-\infty}^{\infty}P(\phi,t)\mathrm{e}^{\mathrm{i}\phi}\,\mathrm{d}\phi
35871 \begin_layout Plain Layout
35875 begin{multicols}{2}
35881 \begin_inset Formula $S_{0}$
35884 das Signal ohne Gradient ist und die Normierungsbedingung
35885 \begin_inset Formula $\int_{-\infty}^{\infty}P(\phi,t)\,\mathrm{d}\phi=1$
35889 Nun dürfen wir aber nicht den Relaxationsprozess außer Acht lassen.
35891 \begin_inset Formula $\nicefrac{\pi}{2}$
35895 \begin_inset space \thinspace{}
35898 -rf-Puls beginnt sich die Magnetisierung zu entfokussieren, wodurch sich
35899 das Signal zusätzlich abschwächt.
35900 Diese Abschwächung verläuft exponentiell in Abhängigkeit der so genannten
35902 \begin_inset Formula $T_{2}$
35908 \begin_layout Standard
35914 \begin_layout Plain Layout
35926 \begin_layout Subsection
35927 Formulas with Description of Variables
35928 \begin_inset Index idx
35931 \begin_layout Plain Layout
35932 Formula ! with description of variables
35940 \begin_layout Standard
35941 To describe variables within a formula, like in formula
35942 \begin_inset CommandInset ref
35944 reference "eq:within"
35953 \begin_inset Formula $n$
35957 \begin_inset space ~
35960 matrix is used with left aligned columns for the
35961 \begin_inset Formula $n$
35968 \begin_layout Plain Layout
35970 \begin_inset CommandInset ref
35972 reference "sec:Matrices"
35981 To set the description in a smaller size, before the matrix e.
35982 \begin_inset space \thinspace{}
35986 \begin_inset space \space{}
35999 \begin_layout Plain Layout
36001 \begin_inset CommandInset ref
36003 reference "sub:Font-Sizes"
36015 \begin_layout Standard
36016 When the formula style
36022 \begin_layout Plain Layout
36024 \begin_inset CommandInset ref
36026 reference "sec:Formula-Styles"
36047 \begin_layout Plain Layout
36054 only works in formulas with the style
36059 \begin_inset CommandInset ref
36061 reference "sub:Variable-Space"
36070 is inserted before and after the matrix to have the same separation of
36071 the matrix from the equation and the side margin.
36074 \begin_layout Standard
36075 When the formula style
36079 is used, the method described in
36080 \begin_inset CommandInset ref
36082 reference "sub:Flalign-Environment"
36086 is used to indent formulas.
36088 \begin_inset CommandInset ref
36090 reference "eq:within"
36094 consists of five columns where in the first two columns contain the equation,
36095 the third the matrix and the last one an empty TeX-brace.
36096 \begin_inset Formula
36098 \hspace{30pt}F_{A} & =\rho·V·g & \footnotesize\begin{array}{ll}
36099 \rho & \textrm{density}\\
36100 V & \textrm{volume}\\
36101 g & \textrm{gravitational acceleration}
36102 \end{array} & & {}\label{eq:within}
36110 \begin_layout Subsection
36111 Upright small Greek Letters
36112 \begin_inset CommandInset label
36114 name "sub:Upright-small-Greek"
36119 \begin_inset Index idx
36122 \begin_layout Plain Layout
36123 Greek letters ! upright
36131 \begin_layout Standard
36132 Most of the math fonts only provide italic small Greek letters.
36133 But for symbols of elementary particles like pions and neutrinos, upright
36134 Greek letters are needed.
36143 \begin_layout Plain Layout
36148 is part of the LaTeX-package
36153 \begin_inset Index idx
36156 \begin_layout Plain Layout
36161 \begin_layout Plain Layout
36181 \begin_inset Index idx
36184 \begin_layout Plain Layout
36190 that is loaded with the LaTeX-preamble line
36193 \begin_layout Standard
36198 usepackage{upgreek}
36201 \begin_layout Standard
36207 \begin_layout Plain Layout
36217 \begin_inset Note Note
36220 \begin_layout Plain Layout
36221 The following table will only be displayed when the LaTeX-package
36230 They are created when the command for a small Greek letter is started with
36236 For example the command
36243 \begin_inset Formula $\uptau$
36249 \begin_layout Standard
36250 With these commands reactions of elementary particles can be typeset:
36251 \begin_inset Formula
36253 \uppi^{+}\to\upmu^{+}+\upnu_{\upmu}
36261 \begin_layout Standard
36262 The upright letters are more bold and wider than the italic ones.
36263 They should therefore not be used for units like
36264 \begin_inset Quotes eld
36268 \begin_inset Quotes erd
36274 \begin_layout Standard
36278 \begin_layout Plain Layout
36288 \begin_inset Note Note
36291 \begin_layout Plain Layout
36292 The following will be displayed when the LaTeX-package
36304 \begin_layout Standard
36305 You need to install the LaTeX-package
36309 to see the rest of this subsection in the output.
36312 \begin_layout Standard
36316 \begin_layout Plain Layout
36328 \begin_layout Subsection
36329 Text Characters in Formulas
36330 \begin_inset CommandInset label
36332 name "sub:Text-Characters-in"
36337 \begin_inset Index idx
36340 \begin_layout Plain Layout
36349 \begin_layout Standard
36350 In some cases you might want to insert text characters directly into formulas.
36351 When for example the centered dot · is often used in formulas like
36352 \begin_inset Formula $\nu=5·10^{5}\,\mathrm{Hz}$
36355 , one would have to insert the command
36365 \begin_layout Plain Layout
36367 \begin_inset CommandInset ref
36369 reference "sub:Binary-Operators"
36378 all the time, because this character is defined in all encodings as text
36380 But the encoding can be changed by this LaTeX-preamble line:
36383 \begin_layout Standard
36388 Declare Inputtext{183}{
36398 f\SpecialChar \textcompwordmark{}
36402 \begin_layout Standard
36403 The character encoding (menu
36405 Document\SpecialChar \menuseparator
36406 Settings\SpecialChar \menuseparator
36409 ) specifies what character appears when a keyboard key is pressed.
36410 When the key for the character '·' is pressed, internally the command
36417 But this command is not available in a formula so that you would get LaTeX-erro
36419 With the changed encoding the right command is chosen automatically, depending
36420 on if the character was inserted into a formula or not.
36423 \begin_layout Standard
36424 The encoding of several characters is saved in definition files.
36425 For example the encoding
36429 is defined in the file
36433 which is in the installation folder of LaTeX.
36434 Encodings should only be changed via the LaTeX-preamble and not in the
36436 Otherwise documents could not be edited by other LyX users working on other
36440 \begin_layout Standard
36441 \begin_inset VSpace medskip
36444 Besides the centered dot, in this document the degree sign ° is defined
36445 with the following LaTeX-preamble line so that it can be directly inserted
36449 \begin_layout Standard
36454 DeclareInputtext{176}{
36464 f\SpecialChar \textcompwordmark{}
36468 \begin_layout Standard
36469 \begin_inset Newpage newpage
36475 \begin_layout Section
36478 \begin_inset Index idx
36481 \begin_layout Plain Layout
36490 \begin_layout Standard
36491 This section is a summary of the most important typographic rules, listed
36496 \begin_layout Plain Layout
36497 This collection was partly taken from the German semi-official dictionary
36499 \begin_inset Quotes eld
36503 \begin_inset Quotes erd
36507 \begin_inset CommandInset citation
36513 that lists some of the ISO rules.
36514 More rules are listed in
36515 \begin_inset CommandInset citation
36529 \begin_layout Itemize
36538 \begin_layout Plain Layout
36539 done with font styles, see
36540 \begin_inset CommandInset ref
36542 reference "sub:Font-Styles"
36551 , no matter if they appear in italic text: 30
36552 \begin_inset space \thinspace{}
36556 \begin_inset Newline newline
36559 Between the value and the unit is the smallest space, see
36560 \begin_inset CommandInset ref
36562 reference "sub:Predefined-Space"
36567 \begin_inset Newline newline
36570 This convention is automatically fulfilled when the command
36577 When it is entered to a formula, two boxes appear.
36578 In the first one the value is inserted, in the second one the unit, and
36580 \begin_inset Formula $\unit[30]{km/h}$
36584 \begin_inset space \thinspace{}
36594 is not a real LaTeX command but the command
36600 , therefore you cannot use it in TeX code.
36603 \begin_layout Itemize
36604 Percent and perthousand signs are set like physical units:
36605 \begin_inset Newline newline
36609 \begin_inset space \thinspace{}
36615 \begin_layout Itemize
36616 The degree sign follows directly on the value: 15°, but not when it is used
36618 \begin_inset space \thinspace{}
36624 \begin_layout Itemize
36625 In numbers with more than four digits the smallest space is inserted before
36626 every third digit to group them:
36636 \begin_inset space \thinspace{}
36640 \begin_inset space \thinspace{}
36646 \begin_layout Itemize
36647 For dimensions like 120×90×40
36648 \begin_inset space \thinspace{}
36651 cm the multiplication sign
36652 \begin_inset Quotes eld
36656 \begin_inset Quotes erd
36660 It is available either via the command
36668 Insert\SpecialChar \menuseparator
36669 Special Character\SpecialChar \menuseparator
36675 \begin_layout Itemize
36676 Functions with names consisting of several letters are set upright to avoid
36678 \begin_inset CommandInset ref
36680 reference "sub:Predefined-Functions"
36687 \begin_layout Itemize
36688 Indices consisting of several letters, are set upright:
36689 \begin_inset Formula $E_{\mathrm{kin}}$
36693 \begin_inset Newline newline
36696 Components of matrices are set italic:
36697 \begin_inset Formula $\hat{H}_{kl}$
36703 \begin_layout Itemize
36704 The differentiation/integration operator 'd', the Euler's number 'e' and
36705 the imaginary unit 'i' should be set upright, to avoid mixing them up with
36709 \begin_layout Itemize
36710 The character that denotes a
36714 transformation is inserted either by the command
36719 \begin_inset space \textvisiblespace{}
36726 Insert\SpecialChar \menuseparator
36727 Special Character\SpecialChar \menuseparator
36728 Symbols\SpecialChar \menuseparator
36730 \begin_inset space ~
36736 \begin_inset Formula $\mathscr{F}$
36742 \begin_layout Standard
36743 \begin_inset Newpage newpage
36749 \begin_layout Section
36751 \begin_inset Index idx
36754 \begin_layout Plain Layout
36763 \begin_layout Standard
36764 Some characters and symbols can be created with several commands.
36765 Here is a list of the synonym commands:
36768 \begin_layout Standard
36769 \begin_inset VSpace bigskip
36773 \begin_inset space \hfill{}
36777 \begin_inset Tabular
36778 <lyxtabular version="3" rows="12" columns="2">
36779 <features rotate="0" tabularvalignment="middle">
36780 <column alignment="center" valignment="top" width="0pt">
36781 <column alignment="center" valignment="top" width="0pt">
36783 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
36786 \begin_layout Plain Layout
36792 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
36795 \begin_layout Plain Layout
36797 \begin_inset Note Note
36800 \begin_layout Plain Layout
36807 is only used as spacer.
36819 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
36822 \begin_layout Plain Layout
36830 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
36833 \begin_layout Plain Layout
36837 \begin_layout Plain Layout
36850 \begin_layout Plain Layout
36864 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
36867 \begin_layout Plain Layout
36875 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
36878 \begin_layout Plain Layout
36888 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
36891 \begin_layout Plain Layout
36899 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
36902 \begin_layout Plain Layout
36912 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
36915 \begin_layout Plain Layout
36923 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
36926 \begin_layout Plain Layout
36934 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
36937 \begin_layout Plain Layout
36945 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
36948 \begin_layout Plain Layout
36956 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
36959 \begin_layout Plain Layout
36967 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
36970 \begin_layout Plain Layout
36980 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
36983 \begin_layout Plain Layout
36991 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
36994 \begin_layout Plain Layout
37004 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
37007 \begin_layout Plain Layout
37015 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
37018 \begin_layout Plain Layout
37028 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
37031 \begin_layout Plain Layout
37039 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
37042 \begin_layout Plain Layout
37052 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
37055 \begin_layout Plain Layout
37063 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
37066 \begin_layout Plain Layout
37074 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
37077 \begin_layout Plain Layout
37085 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
37088 \begin_layout Plain Layout
37100 \begin_inset space \hfill{}
37104 \begin_inset Tabular
37105 <lyxtabular version="3" rows="12" columns="2">
37106 <features rotate="0" tabularvalignment="middle">
37107 <column alignment="center" valignment="top" width="0pt">
37108 <column alignment="center" valignment="top" width="0pt">
37110 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
37113 \begin_layout Plain Layout
37119 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
37122 \begin_layout Plain Layout
37130 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
37133 \begin_layout Plain Layout
37141 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
37144 \begin_layout Plain Layout
37156 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
37159 \begin_layout Plain Layout
37167 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
37170 \begin_layout Plain Layout
37180 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
37183 \begin_layout Plain Layout
37191 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
37194 \begin_layout Plain Layout
37204 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
37207 \begin_layout Plain Layout
37215 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
37218 \begin_layout Plain Layout
37226 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
37229 \begin_layout Plain Layout
37237 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
37240 \begin_layout Plain Layout
37248 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
37251 \begin_layout Plain Layout
37259 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
37262 \begin_layout Plain Layout
37272 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
37275 \begin_layout Plain Layout
37283 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
37286 \begin_layout Plain Layout
37296 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
37299 \begin_layout Plain Layout
37307 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
37310 \begin_layout Plain Layout
37320 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
37323 \begin_layout Plain Layout
37331 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
37334 \begin_layout Plain Layout
37344 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
37347 \begin_layout Plain Layout
37355 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
37358 \begin_layout Plain Layout
37368 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
37371 \begin_layout Plain Layout
37379 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
37382 \begin_layout Plain Layout
37396 \begin_inset space \hfill{}
37402 \begin_layout Standard
37403 \begin_inset Newpage newpage
37409 \begin_layout Bibliography
37410 \begin_inset CommandInset bibitem
37411 LatexCommand bibitem
37423 The LaTeX Companion
37426 Addison Wesley, 2004
37429 \begin_layout Bibliography
37430 \begin_inset CommandInset bibitem
37431 LatexCommand bibitem
37437 \begin_inset CommandInset href
37440 target "ftp://ftp.dante.de/tex-archive/info/math/voss/mathmode/Mathmode.pdf"
37444 of LaTeX's math abilities
37447 \begin_layout Bibliography
37448 \begin_inset CommandInset bibitem
37449 LatexCommand bibitem
37455 \begin_inset CommandInset href
37458 target "http://mirrors.ctan.org/macros/latex/required/amslatex/math/amsldoc.pdf"
37466 \begin_layout Plain Layout
37478 \begin_layout Bibliography
37479 \begin_inset CommandInset bibitem
37480 LatexCommand bibitem
37486 \begin_inset CommandInset href
37489 target "ftp://ftp.dante.de/tex-archive/info/symbols/comprehensive/symbols-a4.pdf"
37493 of all symbols available with LaTeX-packages
37496 \begin_layout Bibliography
37497 \begin_inset CommandInset bibitem
37498 LatexCommand bibitem
37504 \begin_inset CommandInset href
37506 name "Documentation"
37507 target "http://mirrors.ctan.org/macros/latex/contrib/cancel/cancel.pdf"
37511 of the LaTeX-package
37516 \begin_inset Index idx
37519 \begin_layout Plain Layout
37528 \begin_layout Bibliography
37529 \begin_inset CommandInset bibitem
37530 LatexCommand bibitem
37536 \begin_inset CommandInset href
37538 name "Documentation"
37539 target "http://www.tug.org/applications/hyperref/ftp/doc/manual.pdf"
37543 of the LaTeX-package
37548 \begin_inset Index idx
37551 \begin_layout Plain Layout
37552 Packages ! hyperref
37560 \begin_layout Bibliography
37561 \begin_inset CommandInset bibitem
37562 LatexCommand bibitem
37568 \begin_inset CommandInset href
37570 name "Documentation"
37571 target "http://www.ctan.org/tex-archive/macros/latex/contrib/mhchem/mhchem.pdf"
37575 of the LaTeX-package
37580 \begin_inset Index idx
37583 \begin_layout Plain Layout
37592 \begin_layout Bibliography
37593 \begin_inset CommandInset bibitem
37594 LatexCommand bibitem
37600 \begin_inset CommandInset href
37603 target "http://www.tug.org/TUGboat/Articles/tb22-4/tb72perlS.pdf"
37614 \begin_inset CommandInset ref
37616 reference "sub:Operator-Limits"
37621 \begin_inset Index idx
37624 \begin_layout Plain Layout
37635 \begin_layout Bibliography
37636 \begin_inset CommandInset bibitem
37637 LatexCommand bibitem
37648 Auflage, Duden 2001
37651 \begin_layout Bibliography
37652 \begin_inset CommandInset bibitem
37653 LatexCommand bibitem
37659 \begin_inset CommandInset href
37662 target "http://physics.nist.gov/Document/checklist.pdf"
37666 for reviewing manuscripts
37669 \begin_layout Standard
37670 \begin_inset CommandInset index_print
37671 LatexCommand printindex