1 #LyX 2.2 created this file. For more info see http://www.lyx.org/
5 \save_transient_properties true
6 \origin /systemlyxdir/doc/
9 % DO NOT ALTER THIS PREAMBLE!!!
11 % This preamble is designed to ensure that the file prints
12 % out as advertised. If you mess with this preamble,
13 % parts of this document may not print out as expected. If you
14 % have problems LaTeXing this file, please contact
15 % the documentation team
16 % email: lyx-docs@lists.lyx.org
18 % solves the following problem:
19 % If the dection number consits of too many numerals the section heading
20 % will be printed in the TOC without a space between it and the section number.
21 % As solution more space between the number and the heading is inserted:
22 \renewcommand{\l@subsection}{\@dottedtocline{2}{1.5em}{2.8em}}
23 \renewcommand{\l@subsubsection}{\@dottedtocline{3}{4.3em}{3.6em}}
25 % increase link area for cross-references and autoname them,
26 \AtBeginDocument{\renewcommand{\ref}[1]{\mbox{\autoref{#1}}}}
27 \@ifundefined{extrasenglish}{\usepackage[english]{babel}}{}
28 \@ifpackageloaded{babel}{
29 \addto\extrasenglish{%
30 \renewcommand*{\equationautorefname}[1]{}%
31 \renewcommand{\sectionautorefname}{sec.\negthinspace}%
32 \renewcommand{\subsectionautorefname}{sec.\negthinspace}%
33 \renewcommand{\subsubsectionautorefname}{sec.\negthinspace}%
37 % don't load packages twice
38 % see first footnote in sec. 9.3
39 \@ifundefined{textcolor}{\usepackage{color}}{}
41 % the pages of the TOC are numbered roman
42 % and a PDF-bookmark for the TOC is added
44 \let\myTOC\tableofcontents
45 \renewcommand{\tableofcontents}{%
47 \pdfbookmark[1]{\contentsname}{}
50 \pagenumbering{arabic}}
52 % add 0.5 mm vertical space for table rows
53 \@ifundefined{extrarowheight} {\usepackage{array}}{}
54 \setlength{\extrarowheight}{0.5mm}
56 % insert additional vertical space of 1.5 mm between footnotes,
58 \renewcommand{\footnote}[1]{\myFoot{#1\vspace{1.5mm}}}
60 % makes caption labels bold
61 \setkomafont{captionlabel}{\bfseries}
63 % enables calculation of values
66 % for multiple columns used in sec. 24.7
72 % for the Fourier transformation symbol
75 % define a color, used in sec.9.3
76 \definecolor{darkgreen}{cmyk}{0.5, 0, 1, 0.5}
78 % declare operators (see sec. 10.4 and sec. 15.2)
79 \DeclareMathOperator*{\Lozenge}{\blacklozenge}
80 \DeclareMathOperator{\sgn}{sgn}
82 % example definitions for sec. 20.1
83 \newcommand{\gr}{\Longrightarrow}
84 \newcommand{\us}[1]{\underline{#1}}
85 \newcommand{\fb}[3]{\framebox#1#2{$#3$}}
86 \newcommand{\cb}[3][white]{\fcolorbox{#2}{#1}{$#3$}}
87 \newcommand{\fracS}[3][]{\genfrac{}{}{#1}{}{#2}{#3}}
89 % example macro from sec. 19.4
90 %\def\tagform@#1{\maketag@@@{|#1|}}
93 % ------------------------------------
94 % used to check for needed LaTeX packages
97 % check for package undertilde
98 % used for the command \utilde
99 \newboolean{undertilde}
100 \IfFileExists{undertilde.sty}
101 {\usepackage{undertilde}
102 \setboolean{undertilde}{true}}
103 {\setboolean{undertilde}{false}}
105 % check for package eurosym
106 % used for the Euro symbol
108 \IfFileExists{eurosym.sty}
109 {\usepackage[gennarrow]{eurosym}
110 \setboolean{eurosym}{true}}
111 {\setboolean{eurosym}{false}}
113 % check for package braket
114 % used for physical vectors
116 \IfFileExists{braket.sty}
118 \setboolean{braket}{true}}
119 {\setboolean{braket}{false}}
121 % check for package cancel
123 \IfFileExists{cancel.sty}
125 \setboolean{cancel}{true}}
126 {\setboolean{cancel}{false}}
128 % check for package upgreek
130 \IfFileExists{upgreek.sty}
131 {\usepackage{upgreek}
132 \setboolean{upgreek}{true}}
133 {\setboolean{upgreek}{false}}
135 \options bibliography=totoc,index=totoc,BCOR7.5mm,titlepage,captions=tableheading
136 \use_default_options false
137 \maintain_unincluded_children false
139 \language_package default
142 \font_roman "lmodern" "default"
143 \font_sans "lmss" "default"
144 \font_typewriter "lmtt" "default"
145 \font_math "auto" "auto"
146 \font_default_family default
147 \use_non_tex_fonts false
150 \font_sf_scale 100 100
151 \font_tt_scale 100 100
153 \default_output_format pdf2
155 \bibtex_command default
156 \index_command default
160 \pdf_title "LyX's Math Manual"
161 \pdf_author "LyX Team, Uwe Stöhr"
162 \pdf_subject "LyX-documentation about math"
163 \pdf_keywords "LyX, Mathed"
165 \pdf_bookmarksnumbered true
166 \pdf_bookmarksopen true
167 \pdf_bookmarksopenlevel 1
168 \pdf_breaklinks false
172 \pdf_pdfusetitle false
173 \pdf_quoted_options "linkcolor=black, citecolor=black, urlcolor=blue, filecolor=blue, pdfpagelayout=OneColumn, pdfnewwindow=true, pdfstartview=XYZ, plainpages=false"
176 \use_package amsmath 2
177 \use_package amssymb 2
178 \use_package cancel 0
180 \use_package mathdots 1
181 \use_package mathtools 2
182 \use_package mhchem 1
183 \use_package stackrel 0
184 \use_package stmaryrd 0
185 \use_package undertilde 0
187 \cite_engine_type default
191 \paperorientation portrait
195 \notefontcolor #0000ff
202 \paragraph_separation skip
204 \quotes_language english
207 \paperpagestyle plain
211 \tracking_changes false
212 \output_changes false
215 \html_be_strict false
222 's detailed Math manual
226 by the \SpecialChar LyX
231 \begin_layout Plain Layout
233 If you have comments or error corrections, please send them to the \SpecialChar LyX
238 \begin_inset CommandInset href
240 name "lyx-docs@lists.lyx.org"
241 target "lyx-docs@lists.lyx.org?subject=LyX's Math manual"
252 \begin_inset Note Note
255 \begin_layout Plain Layout
262 \begin_inset Newline newline
266 \begin_inset Newline newline
274 \begin_layout Standard
275 \begin_inset CommandInset toc
276 LatexCommand tableofcontents
283 \begin_layout Standard
284 \begin_inset Note Note
287 \begin_layout Plain Layout
288 To export this document to PDF, PS or DVI the \SpecialChar LaTeX
291 braket, cancel, eurosym, mathdots, mathtools, mhchem, undertilde
298 If they are not installed the document can be exported anyway but the sections
299 where the packages are required will not appear in the output.
304 ; if it is not installed, this file cannot be exported.
307 \begin_layout Plain Layout
308 The latest PDF-version of this document can be found here:
309 \begin_inset Newline newline
314 http://wiki.lyx.org/LyX/DocumentationDevelopment#Math
322 \begin_layout Standard
323 \begin_inset Newpage newpage
329 \begin_layout Section
333 \begin_layout Standard
334 This document explains \SpecialChar LyX
335 's math features and is furthermore a collection
336 of \SpecialChar LaTeX
337 -commands used for mathematical characters and constructs.
338 The explanations are designed for the usage of commands.
339 It is therefore required that you have read the section
350 \begin_layout Standard
351 Most of the characters and many constructs explained in this manual are
352 also accessible via the menu
356 \SpecialChar menuseparator
372 But everybody who has to write lots of formulas will notice that it is
373 much faster to use commands instead of the math toolbar.
374 Therefore this manual is focused on commands but also mentions the correspondin
375 g toolbar buttons when available.
378 \begin_layout Standard
379 If not specially mentioned the commands are only available within formulas.
380 To be able to use all commands explained in this document, the option
384 must be checked in the document settings (menu
386 Document\SpecialChar menuseparator
387 Settings\SpecialChar menuseparator
398 \begin_layout Plain Layout
401 Use AMS math package automatically
407 \begin_layout Plain Layout
416 -math when math constructs are found that are supported by \SpecialChar LyX
425 \begin_layout Standard
426 This document doesn't list all
430 \begin_layout Plain Layout
443 \begin_layout Plain Layout
448 \begin_layout Plain Layout
457 -math commands is in the file
460 \begin_inset CommandInset href
463 target "ftp://ftp.ams.org/pub/tex/doc/amstex/amsguide.pdf"
469 , which is part of every \SpecialChar LaTeX
470 standard installation.
475 for lucidity reasons.
478 \begin_layout Section
482 \begin_layout Standard
483 To create an inline formula
484 \begin_inset Index idx
487 \begin_layout Plain Layout
493 that is embedded into a text line, use one of the shortcuts
499 or the toolbar button
506 \begin_inset Newline newline
509 To create a display style formula
510 \begin_inset Index idx
513 \begin_layout Plain Layout
514 Formula ! display style
519 which will appear bigger, has a different format, and will be in a separate
520 paragraph, use one of these shortcuts:
529 \begin_layout Standard
530 To change a display style formula to an inline formula, set the cursor into
531 the formula and use one of the shortcuts
539 Edit\SpecialChar menuseparator
540 Math\SpecialChar menuseparator
544 The same way is used to change an inline formula to a display style formula.
547 \begin_layout Standard
548 To display parts of an inline formula in the size of a display style formula,
556 \begin_inset Index idx
559 \begin_layout Plain Layout
568 Then a new blue box appears in which the desired formula part is inserted.
571 \begin_layout Standard
572 Only inline formulas are allowed inside tables.
575 \begin_layout Standard
580 can be turned on in the menu
582 View\SpecialChar menuseparator
586 When you click there on
587 \begin_inset Quotes eld
591 \begin_inset Quotes erd
594 the toolbar will be shown permanently at the bottom; this state is visualized
599 menu with a checkmark.
600 When you click in this state again on
601 \begin_inset Quotes eld
605 \begin_inset Quotes erd
616 is only shown when the cursor is within a formula; this state is visualized
617 by the renaming of the menu entry from
618 \begin_inset Quotes eld
622 \begin_inset Quotes erd
626 \begin_inset Quotes eld
634 \begin_inset Quotes erd
640 \begin_layout Standard
643 \begin_inset Index idx
646 \begin_layout Plain Layout
653 is invoked by pressing the toolbar button
661 Insert\SpecialChar menuseparator
673 \begin_layout Standard
674 To change the \SpecialChar LaTeX
676 \begin_inset Index idx
679 \begin_layout Plain Layout
688 Document\SpecialChar menuseparator
689 Settings\SpecialChar menuseparator
699 \begin_layout Standard
700 To edit matrices, case differentiations and multiline formulas subsequently,
703 Edit\SpecialChar menuseparator
708 Edit\SpecialChar menuseparator
710 \begin_inset space \thinspace{}
714 \begin_inset space \thinspace{}
724 When lines and columns are swapped via the menu, the column or line where
725 the cursor is in is exchanged with the column to the right or the line
727 Is the cursor in the last column or row, the exchange is done with the
728 column to the left or the line above.
731 \begin_layout Standard
732 To write text in formulas
736 \begin_layout Plain Layout
737 For multiline formulas the command
744 \begin_inset CommandInset ref
746 reference "subsec:Text-in-multiline"
760 \begin_inset Index idx
763 \begin_layout Plain Layout
770 \begin_inset Index idx
773 \begin_layout Plain Layout
780 This mode is invoked with the shortcut
786 or by the insertion of the command
793 \begin_inset Index idx
796 \begin_layout Plain Layout
805 The text appears black in \SpecialChar LyX
806 and can therefore be distinguished from the
807 other formula parts which appear blue.
808 In the output mathematical text is set upright, in contrary to other formula
812 \begin_layout Subsection*
816 \begin_layout Standard
817 Most of the \SpecialChar LaTeX
818 -commands for math constructs have the following scheme:
821 \begin_layout Standard
837 \begin_layout Standard
838 A command always starts with a backslash
839 \begin_inset Quotes gld
849 \begin_inset Quotes grd
853 To omit optional arguments, also omit the associated brackets.
854 The braces around the required arguments are named in this document as
857 \begin_inset Index idx
860 \begin_layout Plain Layout
868 If you add in a formula a left brace to a command name, \SpecialChar LyX
870 creates a \SpecialChar TeX
872 In all other cases \SpecialChar TeX
873 braces are created in formulas with the command
881 braces appear red in \SpecialChar LyX
882 , in contrary to normal braces which appear blue.
884 mode no command is needed to get \SpecialChar TeX
887 braces don't appear in the output.
890 \begin_layout Standard
891 When commands without arguments, like commands for symbols are entered in
893 mode, a space character must
897 be behind the command to end it.
898 This space doesn't appear in the output.
899 When the space should appear in the output, the space must be followed
900 by a protected space in normal text.
903 \begin_layout Standard
904 A protected space is inserted with
907 arg "command-alternatives space-insert protected ; math-space"
913 \begin_layout Subsection*
914 \begin_inset Newpage newpage
920 \begin_layout Itemize
922 \begin_inset space \textvisiblespace{}
925 denotes a space character to be input.
928 \begin_layout Itemize
930 \begin_inset Formula $\to$
933 denotes the usage of the corresponding arrow key on the keyboard.
938 key can often be used instead of
939 \begin_inset Formula $\to$
943 \begin_inset Formula $\downarrow$
951 \begin_inset Formula $\leftarrow$
955 \begin_inset Formula $\uparrow$
961 \begin_layout Subsection*
965 \begin_layout Standard
967 \begin_inset Float table
973 \begin_layout Plain Layout
975 \begin_inset Caption Standard
977 \begin_layout Plain Layout
978 \begin_inset CommandInset label
980 name "tab:Available-units"
992 \begin_layout Plain Layout
995 <lyxtabular version="3" rows="13" columns="2">
996 <features booktabs="true" tabularvalignment="middle">
997 <column alignment="center" valignment="top">
998 <column alignment="center" valignment="top" width="0pt">
1000 <cell alignment="center" valignment="top" topline="true" bottomline="true" usebox="none">
1003 \begin_layout Plain Layout
1009 <cell alignment="center" valignment="top" topline="true" bottomline="true" usebox="none">
1012 \begin_layout Plain Layout
1020 <cell alignment="center" valignment="top" leftline="true" usebox="none">
1023 \begin_layout Plain Layout
1029 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
1032 \begin_layout Plain Layout
1040 <cell alignment="center" valignment="top" leftline="true" usebox="none">
1043 \begin_layout Plain Layout
1049 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
1052 \begin_layout Plain Layout
1060 <cell alignment="center" valignment="top" leftline="true" usebox="none">
1063 \begin_layout Plain Layout
1069 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
1072 \begin_layout Plain Layout
1074 \begin_inset space \thinspace{}
1078 \begin_inset space \thinspace{}
1088 <cell alignment="center" valignment="top" leftline="true" usebox="none">
1091 \begin_layout Plain Layout
1097 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
1100 \begin_layout Plain Layout
1102 \begin_inset space \thinspace{}
1106 \begin_inset space \thinspace{}
1116 <cell alignment="center" valignment="top" leftline="true" usebox="none">
1119 \begin_layout Plain Layout
1125 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
1128 \begin_layout Plain Layout
1130 \begin_inset space \thinspace{}
1134 \begin_inset space \thinspace{}
1144 <cell alignment="center" valignment="top" leftline="true" usebox="none">
1147 \begin_layout Plain Layout
1153 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
1156 \begin_layout Plain Layout
1158 \begin_inset space \thinspace{}
1162 \begin_inset space \thinspace{}
1172 <cell alignment="center" valignment="top" leftline="true" usebox="none">
1175 \begin_layout Plain Layout
1181 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
1184 \begin_layout Plain Layout
1186 \begin_inset space \thinspace{}
1190 \begin_inset space \thinspace{}
1200 <cell alignment="center" valignment="top" leftline="true" usebox="none">
1203 \begin_layout Plain Layout
1209 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
1212 \begin_layout Plain Layout
1214 \begin_inset space \thinspace{}
1218 \begin_inset Formula $\approx$
1222 \begin_inset space \thinspace{}
1232 <cell alignment="center" valignment="top" leftline="true" usebox="none">
1235 \begin_layout Plain Layout
1241 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
1244 \begin_layout Plain Layout
1246 \begin_inset space \thinspace{}
1250 \begin_inset space \thinspace{}
1260 <cell alignment="center" valignment="top" leftline="true" usebox="none">
1263 \begin_layout Plain Layout
1269 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
1272 \begin_layout Plain Layout
1276 \begin_inset Quotes eld
1282 \begin_inset Quotes erd
1292 <cell alignment="center" valignment="top" leftline="true" usebox="none">
1295 \begin_layout Plain Layout
1301 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
1304 \begin_layout Plain Layout
1306 \begin_inset Quotes eld
1314 \begin_inset Quotes erd
1324 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
1327 \begin_layout Plain Layout
1333 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
1336 \begin_layout Plain Layout
1338 \begin_inset space \thinspace{}
1342 \begin_inset Formula $\nicefrac{1}{18}$
1346 \begin_inset space \thinspace{}
1367 \begin_layout Standard
1368 \begin_inset Newpage newpage
1374 \begin_layout Section
1378 \begin_layout Subsection
1380 \begin_inset Index idx
1383 \begin_layout Plain Layout
1390 \begin_inset Index idx
1393 \begin_layout Plain Layout
1400 \begin_inset Index idx
1403 \begin_layout Plain Layout
1408 \begin_layout Plain Layout
1419 \begin_layout Plain Layout
1432 \begin_inset Index idx
1435 \begin_layout Plain Layout
1440 \begin_layout Plain Layout
1451 \begin_layout Plain Layout
1466 \begin_layout Standard
1467 Indices are created with an underscore
1468 \begin_inset Quotes eld
1472 \begin_inset Quotes erd
1475 or via the math toolbar button
1478 arg "math-subscript"
1481 , exponents with a caret
1482 \begin_inset Quotes eld
1486 \begin_inset Quotes erd
1489 or via the math toolbar button
1492 arg "math-superscript"
1498 \begin_layout Standard
1500 \begin_inset Tabular
1501 <lyxtabular version="3" rows="4" columns="2">
1502 <features booktabs="true" tabularvalignment="middle">
1503 <column alignment="center" valignment="top" width="0pt">
1504 <column alignment="center" valignment="top" width="0pt">
1506 <cell alignment="center" valignment="top" topline="true" bottomline="true" usebox="none">
1509 \begin_layout Plain Layout
1515 <cell alignment="center" valignment="top" topline="true" bottomline="true" usebox="none">
1518 \begin_layout Plain Layout
1526 <cell alignment="center" valignment="top" usebox="none">
1529 \begin_layout Plain Layout
1535 <cell alignment="center" valignment="top" usebox="none">
1538 \begin_layout Plain Layout
1539 \begin_inset Formula $B_{V}$
1548 <row topspace="1.5mm">
1549 <cell alignment="center" valignment="top" usebox="none">
1552 \begin_layout Plain Layout
1558 <cell alignment="center" valignment="top" usebox="none">
1561 \begin_layout Plain Layout
1562 \begin_inset Formula $B^{V}$
1571 <row topspace="1.5mm">
1572 <cell alignment="center" valignment="top" topline="true" bottomline="true" usebox="none">
1575 \begin_layout Plain Layout
1577 \begin_inset space \textvisiblespace{}
1585 <cell alignment="center" valignment="top" topline="true" bottomline="true" usebox="none">
1588 \begin_layout Plain Layout
1589 \begin_inset Formula $B^{A}$
1605 \begin_layout Standard
1606 As the caret is in some languages an accent, vowels will be accentuated
1607 in this case and not set as exponents
1611 \begin_layout Plain Layout
1612 Depending on the used keyboard settings this can also happen for characters
1619 To get exponents in this case, press
1623 after the caret as in the last example.
1626 \begin_layout Subsection
1628 \begin_inset CommandInset label
1630 name "subsec:Fractions"
1635 \begin_inset Index idx
1638 \begin_layout Plain Layout
1647 \begin_layout Standard
1648 Fractions are generated with the command
1655 \begin_inset Index idx
1658 \begin_layout Plain Layout
1666 or via the math toolbar button
1669 arg "math-insert \\frac"
1673 The font size is adjusted automatically, depending on whether the fraction
1674 is in an inline or display style formula.
1675 With the math toolbar button
1678 arg "math-insert \\frac-square"
1681 you can select different fraction types.
1684 \begin_layout Standard
1692 \begin_inset Index idx
1695 \begin_layout Plain Layout
1703 a fraction can be created that always has the size of a display style formula.
1711 \begin_inset Index idx
1714 \begin_layout Plain Layout
1722 the fraction appears always with the size of an inline formula.
1726 \begin_layout Standard
1727 A line with the fraction
1728 \begin_inset Formula $\frac{1}{2}$
1731 that was created with the command
1740 \begin_layout Standard
1741 A line with the fraction
1742 \begin_inset Formula $\dfrac{1}{2}$
1745 that was created with the command
1754 \begin_layout Standard
1756 \begin_inset Tabular
1757 <lyxtabular version="3" rows="4" columns="2">
1758 <features booktabs="true" tabularvalignment="middle">
1759 <column alignment="center" valignment="top" width="0pt">
1760 <column alignment="center" valignment="top" width="0pt">
1762 <cell alignment="center" valignment="top" topline="true" bottomline="true" usebox="none">
1765 \begin_layout Plain Layout
1771 <cell alignment="center" valignment="top" topline="true" bottomline="true" usebox="none">
1774 \begin_layout Plain Layout
1781 <row topspace="1.5mm">
1782 <cell alignment="center" valignment="top" usebox="none">
1785 \begin_layout Plain Layout
1789 \begin_inset space \textvisiblespace{}
1793 \begin_inset Formula $\downarrow$
1801 <cell alignment="center" valignment="top" usebox="none">
1804 \begin_layout Plain Layout
1805 \begin_inset Formula $\frac{A}{B}$
1814 <row topspace="2mm">
1815 <cell alignment="center" valignment="top" usebox="none">
1818 \begin_layout Plain Layout
1822 \begin_inset space \textvisiblespace{}
1826 \begin_inset Formula $\downarrow$
1834 <cell alignment="center" valignment="top" usebox="none">
1837 \begin_layout Plain Layout
1838 \begin_inset Formula $\dfrac{A}{B}$
1847 <row topspace="2mm" bottomspace="1mm">
1848 <cell alignment="center" valignment="top" bottomline="true" usebox="none">
1851 \begin_layout Plain Layout
1855 \begin_inset space \textvisiblespace{}
1861 \begin_inset space \textvisiblespace{}
1865 \begin_inset Formula $\downarrow$
1869 \begin_inset Formula $\downarrow\downarrow$
1877 <cell alignment="center" valignment="top" bottomline="true" usebox="none">
1880 \begin_layout Plain Layout
1881 \begin_inset Formula $\dfrac{e^{\frac{1}{2}}}{3}$
1897 \begin_layout Standard
1898 \begin_inset VSpace bigskip
1902 \begin_inset Newpage newpage
1905 For nested fractions the command
1912 \begin_inset Index idx
1915 \begin_layout Plain Layout
1925 \begin_inset VSpace -3mm
1931 \begin_layout Standard
1932 \begin_inset Formula
1934 \textrm{created with \textbf{\textbackslash frac}} & & \textrm{created with \textbf{\textbackslash cfrac}}\\
1935 \frac{A}{B+\frac{C+\frac{E}{F}}{D}} & & \cfrac{A}{B+\cfrac{C+\cfrac{E}{F}}{D}}
1943 \begin_layout Standard
1944 The command for the example above is:
1947 \begin_layout Standard
1953 \begin_inset space \textvisiblespace{}
1957 \begin_inset Formula $\downarrow$
1963 \begin_inset space \textvisiblespace{}
1969 \begin_inset space \textvisiblespace{}
1973 \begin_inset Formula $\downarrow$
1977 \begin_inset Formula $\downarrow$
1983 \begin_layout Standard
1984 \begin_inset VSpace medskip
1990 \begin_layout Standard
1997 sets the fraction always in the size of a displayed formula, also when
1998 it is part of another fraction.
2001 \begin_layout Standard
2002 It is possible to specify the alignment of the numerator.
2009 is used to left align it, the command
2022 centers the numerator.
2023 These fractions demonstrate the different alignments:
2026 \begin_layout Standard
2029 \begin_inset Formula
2031 \cfrac[l]{A}{B+C}\,,\,\cfrac{A}{B+C}\,,\,\cfrac[r]{A}{B+C}
2039 \begin_layout Standard
2040 \begin_inset Note Greyedout
2043 \begin_layout Plain Layout
2060 are no real \SpecialChar LaTeX
2061 commands but represent the command
2065 cfrac[alignment]{numerator}{denominator}
2068 Therefore you cannot use them in \SpecialChar TeX
2077 \begin_layout Standard
2078 \begin_inset VSpace medskip
2081 It is often advantageous to combine
2094 \begin_inset Formula
2096 \cfrac{A}{B+\cfrac{C+\frac{E}{F}}{D}}
2104 \begin_layout Standard
2105 For inline fractions with a sloped fraction stroke you can use the command
2113 \begin_inset Index idx
2116 \begin_layout Plain Layout
2125 \begin_inset Formula $\nicefrac{5}{31}$
2135 \begin_inset Index idx
2138 \begin_layout Plain Layout
2147 \begin_inset Formula $\unitfrac{5}{31}$
2150 There is furthermore the command
2156 that offers to write a fraction in combination with a number:
2157 \begin_inset Formula $\unitfrac[2]{1}{3}$
2163 \begin_layout Standard
2164 \begin_inset Note Greyedout
2167 \begin_layout Plain Layout
2178 is not a real \SpecialChar LaTeX
2179 command but the command
2180 \begin_inset Newline newline
2187 unitfrac[number]{numerator}{denominator}
2190 Therefore you cannot use it in \SpecialChar TeX
2199 \begin_layout Standard
2200 How to define own fractions where the fraction stroke can be changed, is
2202 \begin_inset CommandInset ref
2204 reference "subsec:Self-defined-Fractions"
2211 \begin_layout Standard
2212 Multiline fractions are explained in
2213 \begin_inset CommandInset ref
2215 reference "subsec:Multiline-Fractions"
2222 \begin_layout Subsection
2224 \begin_inset Index idx
2227 \begin_layout Plain Layout
2236 \begin_layout Standard
2237 Square roots are created with
2244 \begin_inset Index idx
2247 \begin_layout Plain Layout
2255 or the math toolbar button
2258 arg "math-insert \\sqrt"
2261 , all other roots with the command
2268 \begin_inset Index idx
2271 \begin_layout Plain Layout
2279 or with the math toolbar button
2282 arg "math-insert \\root"
2288 \begin_layout Standard
2290 \begin_inset Tabular
2291 <lyxtabular version="3" rows="3" columns="2">
2292 <features booktabs="true" tabularvalignment="middle">
2293 <column alignment="center" valignment="top" width="0pt">
2294 <column alignment="center" valignment="top" width="0pt">
2296 <cell alignment="center" valignment="top" topline="true" bottomline="true" usebox="none">
2299 \begin_layout Plain Layout
2305 <cell alignment="center" valignment="top" topline="true" bottomline="true" usebox="none">
2308 \begin_layout Plain Layout
2315 <row topspace="1mm">
2316 <cell alignment="center" valignment="top" usebox="none">
2319 \begin_layout Plain Layout
2323 \begin_inset space \textvisiblespace{}
2331 <cell alignment="center" valignment="top" usebox="none">
2334 \begin_layout Plain Layout
2335 \begin_inset Formula $\sqrt{A-B}$
2344 <row topspace="1mm">
2345 <cell alignment="center" valignment="top" bottomline="true" usebox="none">
2348 \begin_layout Plain Layout
2352 \begin_inset space \textvisiblespace{}
2356 \begin_inset Formula $\downarrow$
2364 <cell alignment="center" valignment="top" bottomline="true" usebox="none">
2367 \begin_layout Plain Layout
2368 \begin_inset Formula $\sqrt[3]{A-B}$
2384 \begin_layout Standard
2385 A square root can also be created with
2391 when the root index field is left empty.
2394 \begin_layout Standard
2395 With certain indices the distance to the root is too small, like in this
2397 \begin_inset Formula $\sqrt[\beta]{B}$
2401 \begin_inset Newline newline
2405 \begin_inset Formula $\beta$
2409 To avoid this, the commands
2416 \begin_inset Index idx
2419 \begin_layout Plain Layout
2434 \begin_inset Index idx
2437 \begin_layout Plain Layout
2445 are used with the following scheme:
2448 \begin_layout Standard
2462 \begin_layout Standard
2463 Distance is the number of Big Points (unit bp;
2464 \begin_inset Formula $\mathrm{72\,bp=1\,inch}$
2467 ), that the index should be moved to the left or top, resp..
2468 The commands are written to the index.
2469 This way the command
2470 \begin_inset Newline newline
2480 \begin_inset Formula $\to$
2486 \begin_inset Formula $\to$
2492 \begin_inset space \textvisiblespace{}
2496 \begin_inset Formula $\to$
2500 \begin_inset Newline newline
2505 produces a correct typeset formula:
2506 \begin_inset Formula $\sqrt[\leftroot{-1}\uproot{2}\beta]{B}$
2512 \begin_layout Subsection
2513 Binomial Coefficients
2514 \begin_inset Index idx
2517 \begin_layout Plain Layout
2518 Binomial coefficients
2526 \begin_layout Standard
2527 Binomial coefficients are inserted with the command
2534 \begin_inset Index idx
2537 \begin_layout Plain Layout
2545 or with the submenu of the math toolbar button
2548 arg "math-insert \\frac-square"
2564 there are the commands
2571 \begin_inset Index idx
2574 \begin_layout Plain Layout
2589 \begin_inset Index idx
2592 \begin_layout Plain Layout
2601 For other brackets around binomial coeficients there are the commands
2608 \begin_inset Index idx
2611 \begin_layout Plain Layout
2626 \begin_inset Index idx
2629 \begin_layout Plain Layout
2640 \begin_layout Standard
2642 \begin_inset Tabular
2643 <lyxtabular version="3" rows="6" columns="2">
2644 <features booktabs="true" tabularvalignment="middle">
2645 <column alignment="center" valignment="top" width="0pt">
2646 <column alignment="center" valignment="top" width="0pt">
2648 <cell alignment="center" valignment="top" topline="true" bottomline="true" usebox="none">
2651 \begin_layout Plain Layout
2657 <cell alignment="center" valignment="top" topline="true" bottomline="true" usebox="none">
2660 \begin_layout Plain Layout
2667 <row topspace="1mm">
2668 <cell alignment="center" valignment="top" usebox="none">
2671 \begin_layout Plain Layout
2675 \begin_inset space \textvisiblespace{}
2679 \begin_inset Formula $\downarrow$
2687 <cell alignment="center" valignment="top" usebox="none">
2690 \begin_layout Plain Layout
2691 \begin_inset Formula $\binom{A}{B}$
2700 <row topspace="2mm">
2701 <cell alignment="center" valignment="top" usebox="none">
2704 \begin_layout Plain Layout
2708 \begin_inset space \textvisiblespace{}
2712 \begin_inset Formula $\downarrow$
2720 <cell alignment="center" valignment="top" usebox="none">
2723 \begin_layout Plain Layout
2724 \begin_inset Formula $\dbinom{A}{B}$
2733 <row topspace="2mm" bottomspace="0.5mm">
2734 <cell alignment="center" valignment="top" usebox="none">
2737 \begin_layout Plain Layout
2741 \begin_inset space \textvisiblespace{}
2745 \begin_inset Formula $\downarrow$
2753 <cell alignment="center" valignment="top" usebox="none">
2756 \begin_layout Plain Layout
2757 \begin_inset Formula $\tbinom{A}{B}$
2766 <row topspace="1mm">
2767 <cell alignment="center" valignment="top" topline="true" usebox="none">
2770 \begin_layout Plain Layout
2774 \begin_inset space \textvisiblespace{}
2778 \begin_inset Formula $\downarrow$
2786 <cell alignment="center" valignment="top" topline="true" usebox="none">
2789 \begin_layout Plain Layout
2790 \begin_inset Formula ${A \brack B}$
2799 <row topspace="2mm" bottomspace="0.5mm">
2800 <cell alignment="center" valignment="top" bottomline="true" usebox="none">
2803 \begin_layout Plain Layout
2807 \begin_inset space \textvisiblespace{}
2811 \begin_inset Formula $\downarrow$
2819 <cell alignment="center" valignment="top" bottomline="true" usebox="none">
2822 \begin_layout Plain Layout
2823 \begin_inset Formula ${A \brace B}$
2839 \begin_layout Subsection
2840 Case Differentiations
2841 \begin_inset Index idx
2844 \begin_layout Plain Layout
2845 Case differentiations
2853 \begin_layout Standard
2855 \begin_inset Tabular
2856 <lyxtabular version="3" rows="3" columns="2">
2857 <features booktabs="true" tabularvalignment="middle">
2858 <column alignment="center" valignment="top" width="0pt">
2859 <column alignment="center" valignment="top" width="0pt">
2861 <cell alignment="center" valignment="top" topline="true" bottomline="true" usebox="none">
2864 \begin_layout Plain Layout
2870 <cell alignment="center" valignment="top" topline="true" bottomline="true" usebox="none">
2873 \begin_layout Plain Layout
2881 <cell alignment="center" valignment="top" usebox="none">
2884 \begin_layout Plain Layout
2888 \begin_inset space \textvisiblespace{}
2892 \begin_inset Formula $\to$
2896 \begin_inset Index idx
2899 \begin_layout Plain Layout
2912 <cell alignment="center" valignment="top" usebox="none">
2915 \begin_layout Plain Layout
2916 \begin_inset Formula $\begin{cases}
2926 <row topspace="1.5mm">
2927 <cell alignment="center" valignment="top" bottomline="true" usebox="none">
2930 \begin_layout Plain Layout
2934 \begin_inset space \textvisiblespace{}
2940 arg "newline-insert newline"
2948 <cell alignment="center" valignment="top" bottomline="true" usebox="none">
2951 \begin_layout Plain Layout
2952 \begin_inset Formula $\begin{cases}
2953 A & \textrm{for }x>0\\
2954 B & \textrm{for }x=0
2971 \begin_layout Standard
2978 or pressing the math toolbar button
2981 arg "math-insert \\cases"
2984 you can create new lines with the shortcut
2987 arg "newline-insert newline"
2990 or the table toolbar button
2993 arg "tabular-feature append-row"
2999 \begin_layout Standard
3006 is also available via the menu
3008 Insert\SpecialChar menuseparator
3009 Math\SpecialChar menuseparator
3015 \begin_layout Subsection
3017 \begin_inset Index idx
3020 \begin_layout Plain Layout
3029 \begin_layout Standard
3037 \begin_inset Index idx
3040 \begin_layout Plain Layout
3048 every character can be displayed canceled.
3049 The characters are quasi accentuated by a slash.
3052 \begin_layout Standard
3054 \begin_inset Tabular
3055 <lyxtabular version="3" rows="4" columns="2">
3056 <features booktabs="true" tabularvalignment="middle">
3057 <column alignment="center" valignment="top" width="0pt">
3058 <column alignment="center" valignment="top" width="0pt">
3060 <cell alignment="center" valignment="top" topline="true" bottomline="true" usebox="none">
3063 \begin_layout Plain Layout
3069 <cell alignment="center" valignment="top" topline="true" bottomline="true" usebox="none">
3072 \begin_layout Plain Layout
3080 <cell alignment="center" valignment="top" usebox="none">
3083 \begin_layout Plain Layout
3091 <cell alignment="center" valignment="top" usebox="none">
3094 \begin_layout Plain Layout
3095 \begin_inset Formula $\not=$
3105 <cell alignment="center" valignment="top" usebox="none">
3108 \begin_layout Plain Layout
3118 <cell alignment="center" valignment="top" usebox="none">
3121 \begin_layout Plain Layout
3122 \begin_inset Formula $\not\le$
3132 <cell alignment="center" valignment="top" topline="true" bottomline="true" usebox="none">
3135 \begin_layout Plain Layout
3145 <cell alignment="center" valignment="top" topline="true" bottomline="true" usebox="none">
3148 \begin_layout Plain Layout
3149 \begin_inset Formula $\not\parallel$
3165 \begin_layout Standard
3166 The last example shows that not all negations look good.
3167 Therefore there are special commands for some negations (see
3168 \begin_inset CommandInset ref
3170 reference "subsec:Mathematical-Symbols"
3175 \begin_inset CommandInset ref
3177 reference "sec:Relations"
3184 \begin_layout Subsection
3186 \begin_inset CommandInset label
3188 name "subsec:Placeholders"
3193 \begin_inset Index idx
3196 \begin_layout Plain Layout
3203 \begin_inset Index idx
3206 \begin_layout Plain Layout
3207 Chemical characters ! Isotopes
3213 \begin_inset Index idx
3216 \begin_layout Plain Layout
3221 \begin_layout Plain Layout
3232 \begin_layout Plain Layout
3247 \begin_layout Standard
3249 \begin_inset space \thinspace{}
3253 \begin_inset space \space{}
3260 \begin_layout Plain Layout
3261 Typesetting isotopes and chemical symbols is described in
3262 \begin_inset CommandInset ref
3264 reference "subsec:Chemical-Symbols-and"
3273 the following problem occurs:
3276 \begin_layout Standard
3278 \begin_inset Tabular
3279 <lyxtabular version="3" rows="2" columns="2">
3280 <features booktabs="true" tabularvalignment="middle">
3281 <column alignment="center" valignment="top" width="0pt">
3282 <column alignment="center" valignment="top" width="0pt">
3284 <cell alignment="center" valignment="top" usebox="none">
3287 \begin_layout Plain Layout
3288 Indices created with sub- and superscripts:
3293 <cell alignment="center" valignment="top" usebox="none">
3296 \begin_layout Plain Layout
3297 \begin_inset Formula $_{9}^{19}\mathrm{F}$
3306 <row topspace="1.5mm">
3307 <cell alignment="center" valignment="top" usebox="none">
3310 \begin_layout Plain Layout
3316 <cell alignment="center" valignment="top" usebox="none">
3319 \begin_layout Plain Layout
3320 \begin_inset Formula $_{\phantom{1}9}^{19}\mathrm{F}$
3336 \begin_layout Standard
3337 The shorter index is by default placed below or above the first character
3338 of the longer index.
3339 To avoid this there is the command
3346 \begin_inset Index idx
3349 \begin_layout Plain Layout
3357 or the math toolbar button
3358 \begin_inset space \thinspace{}
3365 \begin_layout Plain Layout
3366 can be found in the submenu of the toolbar button
3369 arg "math-insert \\space"
3383 that creates one or more phantom characters.
3390 a small blue box appears that is superposed with two red arrows.
3391 The arrows indicate that the complete width and height of the box content
3392 will be created as placeholder.
3393 Phantom characters are accordingly placeholders with the size of the characters.
3396 \begin_layout Standard
3398 \begin_inset Tabular
3399 <lyxtabular version="3" rows="4" columns="2">
3400 <features booktabs="true" tabularvalignment="middle">
3401 <column alignment="center" valignment="top" width="0pt">
3402 <column alignment="center" valignment="top" width="0pt">
3404 <cell alignment="center" valignment="top" topline="true" bottomline="true" usebox="none">
3407 \begin_layout Plain Layout
3413 <cell alignment="center" valignment="top" topline="true" bottomline="true" usebox="none">
3416 \begin_layout Plain Layout
3423 <row topspace="1.5mm">
3424 <cell alignment="center" valignment="top" usebox="none">
3427 \begin_layout Plain Layout
3429 \begin_inset space \textvisiblespace{}
3435 \begin_inset space \textvisiblespace{}
3439 \begin_inset Formula $\to$
3443 \begin_inset space \textvisiblespace{}
3451 <cell alignment="center" valignment="top" usebox="none">
3454 \begin_layout Plain Layout
3455 \begin_inset Formula $_{\phantom{1}9}^{19}\mathrm{F}$
3464 <row topspace="1.5mm" bottomspace="0.5mm">
3465 <cell alignment="center" valignment="top" usebox="none">
3468 \begin_layout Plain Layout
3470 \begin_inset space \textvisiblespace{}
3476 \begin_inset space \textvisiblespace{}
3480 \begin_inset Formula $\to$
3484 \begin_inset space \textvisiblespace{}
3492 <cell alignment="center" valignment="top" usebox="none">
3495 \begin_layout Plain Layout
3496 \begin_inset Formula $_{\phantom{23}9}^{235}\mathrm{F}$
3505 <row topspace="1.5mm" bottomspace="0.5mm">
3506 <cell alignment="center" valignment="top" topline="true" bottomline="true" usebox="none">
3509 \begin_layout Plain Layout
3513 \begin_inset space \textvisiblespace{}
3519 \begin_inset space \textvisiblespace{}
3523 \begin_inset Formula $\to$
3527 \begin_inset space \textvisiblespace{}
3535 <cell alignment="center" valignment="top" topline="true" bottomline="true" usebox="none">
3538 \begin_layout Plain Layout
3539 \begin_inset Formula $\Lambda_{MMt}^{\phantom{ii}t}$
3555 \begin_layout Standard
3556 Furthermore there are the commands
3563 \begin_inset Index idx
3566 \begin_layout Plain Layout
3587 \begin_inset Index idx
3590 \begin_layout Plain Layout
3611 creates only space for the maximal height of the characters in the box
3612 but not for its width.
3619 creates only space for the width of the box content.
3620 Therefore the boxes of both commands have only one red arrow.
3623 \begin_layout Standard
3624 For example the command
3629 \begin_inset space \textvisiblespace{}
3636 creates space for the height of the integral sign,
3640 \begin_layout Plain Layout
3647 creates an integral sign, see
3648 \begin_inset CommandInset ref
3650 reference "subsec:Big-Operators"
3659 because this is the larger character.
3660 An example application is in
3661 \begin_inset CommandInset ref
3663 reference "subsec:Multiline-Brackets"
3670 \begin_layout Standard
3671 Placeholders can also be used for text when they are inserted via the menu
3674 Insert\SpecialChar menuseparator
3675 Formatting\SpecialChar menuseparator
3681 \begin_layout Standard
3683 \begin_inset Newline newline
3687 \begin_inset Phantom Phantom
3690 \begin_layout Plain Layout
3699 \begin_layout Subsection
3701 \begin_inset Index idx
3704 \begin_layout Plain Layout
3711 \begin_inset Index idx
3714 \begin_layout Plain Layout
3715 Formula ! underlined
3723 \begin_layout Standard
3725 \begin_inset Tabular
3726 <lyxtabular version="3" rows="4" columns="2">
3727 <features booktabs="true" tabularvalignment="middle">
3728 <column alignment="center" valignment="top" width="0pt">
3729 <column alignment="center" valignment="top" width="0pt">
3731 <cell alignment="center" valignment="top" topline="true" bottomline="true" usebox="none">
3734 \begin_layout Plain Layout
3740 <cell alignment="center" valignment="top" topline="true" bottomline="true" usebox="none">
3743 \begin_layout Plain Layout
3750 <row topspace="2mm">
3751 <cell alignment="center" valignment="top" usebox="none">
3754 \begin_layout Plain Layout
3758 \begin_inset space \textvisiblespace{}
3762 \begin_inset Index idx
3765 \begin_layout Plain Layout
3778 <cell alignment="center" valignment="top" usebox="none">
3781 \begin_layout Plain Layout
3782 \begin_inset Formula $\overline{A+B}$
3791 <row bottomspace="1mm">
3792 <cell alignment="center" valignment="top" usebox="none">
3795 \begin_layout Plain Layout
3799 \begin_inset space \textvisiblespace{}
3803 \begin_inset Index idx
3806 \begin_layout Plain Layout
3819 <cell alignment="center" valignment="top" usebox="none">
3822 \begin_layout Plain Layout
3823 \begin_inset Formula $\underline{A+B}$
3832 <row topspace="2mm" bottomspace="1mm">
3833 <cell alignment="center" valignment="top" topline="true" bottomline="true" usebox="none">
3836 \begin_layout Plain Layout
3840 \begin_inset space \textvisiblespace{}
3846 \begin_inset space \textvisiblespace{}
3854 <cell alignment="center" valignment="top" topline="true" bottomline="true" usebox="none">
3857 \begin_layout Plain Layout
3858 \begin_inset Formula $\overline{\underline{A+B}}$
3874 \begin_layout Standard
3875 In the last example it doesn't matter if first
3890 \begin_layout Standard
3891 To double underline use
3900 \begin_layout Standard
3901 It is possible to place up to 6 lines above or below characters.
3904 \begin_layout Standard
3905 \begin_inset VSpace bigskip
3908 Custom lines can be created using the command
3915 \begin_inset Index idx
3918 \begin_layout Plain Layout
3926 which has the following scheme:
3929 \begin_layout Standard
3934 rule[vertical offset]{length}{thickness}
3937 \begin_layout Standard
3938 The optional vertical offset shifts the line upwards (or downwards, when
3939 the value is negative).
3941 \begin_inset CommandInset ref
3943 reference "tab:Available-units"
3947 can be used for the values.
3948 Here are two example lines created with the commands
3949 \begin_inset Newline newline
3956 rule[-2ex]{3cm}{2pt}
3967 \begin_layout Standard
3969 \begin_inset Formula $\rule[-2ex]{3cm}{2pt}\rule{2cm}{1pt}$
3975 \begin_layout Standard
3982 can also be used for text when a line is inserted via the menu
3984 Insert\SpecialChar menuseparator
3985 Formatting\SpecialChar menuseparator
3987 \begin_inset space ~
3995 \begin_layout Standard
3997 \begin_inset CommandInset line
4008 \begin_layout Subsection
4010 \begin_inset CommandInset label
4012 name "subsec:Ellipses"
4017 \begin_inset Index idx
4020 \begin_layout Plain Layout
4029 \begin_layout Standard
4030 There are different types of ellipses available.
4034 \begin_layout Plain Layout
4035 In the math toolbar in the submenu of the button
4038 arg "math-insert \\ldots"
4046 For listings dots at the baseline are used (
4053 \begin_inset Index idx
4056 \begin_layout Plain Layout
4064 ), while for operations dots are needed that are on the same height as the
4072 \begin_inset Index idx
4075 \begin_layout Plain Layout
4084 When using the command
4091 \begin_inset Index idx
4094 \begin_layout Plain Layout
4102 , \SpecialChar LaTeX
4103 decides on the basis of the next character what type is used.
4106 \begin_layout Standard
4108 \begin_inset Tabular
4109 <lyxtabular version="3" rows="9" columns="2">
4110 <features booktabs="true" tabularvalignment="middle">
4111 <column alignment="center" valignment="top" width="0pt">
4112 <column alignment="center" valignment="top" width="0pt">
4114 <cell alignment="center" valignment="top" topline="true" bottomline="true" usebox="none">
4117 \begin_layout Plain Layout
4123 <cell alignment="center" valignment="top" topline="true" bottomline="true" usebox="none">
4126 \begin_layout Plain Layout
4134 <cell alignment="center" valignment="top" usebox="none">
4137 \begin_layout Plain Layout
4139 \begin_inset space \textvisiblespace{}
4145 \begin_inset space \textvisiblespace{}
4153 <cell alignment="center" valignment="top" usebox="none">
4156 \begin_layout Plain Layout
4157 \begin_inset Formula $A_{1},\dots,A_{n}$
4167 <cell alignment="center" valignment="top" usebox="none">
4170 \begin_layout Plain Layout
4172 \begin_inset space \textvisiblespace{}
4178 \begin_inset space \textvisiblespace{}
4186 <cell alignment="center" valignment="top" usebox="none">
4189 \begin_layout Plain Layout
4190 \begin_inset Formula $A_{1}+\dots+A_{n}$
4200 <cell alignment="center" valignment="top" usebox="none">
4203 \begin_layout Plain Layout
4205 \begin_inset space \textvisiblespace{}
4211 \begin_inset space \textvisiblespace{}
4219 <cell alignment="center" valignment="top" usebox="none">
4222 \begin_layout Plain Layout
4223 \begin_inset Formula $A_{1},\ldots,A_{n}$
4233 <cell alignment="center" valignment="top" bottomline="true" usebox="none">
4236 \begin_layout Plain Layout
4238 \begin_inset space \textvisiblespace{}
4244 \begin_inset space \textvisiblespace{}
4252 <cell alignment="center" valignment="top" bottomline="true" usebox="none">
4255 \begin_layout Plain Layout
4256 \begin_inset Formula $A_{1}+\cdots+A_{n}$
4266 <cell alignment="center" valignment="top" usebox="none">
4269 \begin_layout Plain Layout
4277 <cell alignment="center" valignment="top" usebox="none">
4280 \begin_layout Plain Layout
4281 \begin_inset Formula $\vdots$
4291 <cell alignment="center" valignment="top" usebox="none">
4294 \begin_layout Plain Layout
4302 <cell alignment="center" valignment="top" usebox="none">
4305 \begin_layout Plain Layout
4306 \begin_inset Formula $\ddots$
4316 <cell alignment="center" valignment="top" usebox="none">
4319 \begin_layout Plain Layout
4327 <cell alignment="center" valignment="top" usebox="none">
4330 \begin_layout Plain Layout
4331 \begin_inset Formula $\iddots$
4341 <cell alignment="center" valignment="top" topline="true" bottomline="true" usebox="none">
4344 \begin_layout Plain Layout
4346 \begin_inset space \thinspace{}
4349 matrix with the different dots
4354 <cell alignment="center" valignment="top" topline="true" bottomline="true" usebox="none">
4357 \begin_layout Plain Layout
4358 \begin_inset Formula $\begin{array}{ccc}
4359 A_{11} & \cdots & A_{1m}\\
4360 \vdots & \ddots & \vdots\\
4361 A_{n1} & \cdots & A_{nm}
4378 \begin_layout Standard
4379 The ellipses available in menu
4381 Insert\SpecialChar menuseparator
4383 \begin_inset space ~
4397 \begin_layout Standard
4398 \begin_inset VSpace medskip
4407 , one of the options
4409 Use mathdots package (automatically)
4411 must be set in the document settings under
4414 \begin_inset space ~
4420 \begin_inset Newline newline
4425 Use mathdots package
4427 will improve the appearance of all dots in the documents if their font
4428 style or size is not the default.
4431 \begin_layout Standard
4432 \begin_inset VSpace medskip
4435 Specially for matrices there are ellipses that span over several columns.
4436 They are created with the command
4443 \begin_inset Index idx
4446 \begin_layout Plain Layout
4454 , that has the following scheme:
4457 \begin_layout Standard
4462 hdotsfor[distance]{number of columns}
4465 \begin_layout Standard
4466 The number of columns specifies how many columns should be spanned.
4467 Distance is a factor for the distance between the dots.
4470 \begin_layout Standard
4471 In the following matrix the command
4477 was inserted in the first box of the second line, to get an ellipsis with
4478 a dot distance twice as long as with the command
4485 \begin_inset Formula
4487 \left(\begin{array}{cccc}
4496 Note that the matrix fields that should be spanned must be empty, otherwise
4497 you get \SpecialChar LaTeX
4501 \begin_layout Standard
4502 \begin_inset VSpace bigskip
4505 Furthermore you can fill with the command
4512 \begin_inset Index idx
4515 \begin_layout Plain Layout
4523 the rest of a line with dots.
4524 The effect of these commands is the same as with
4531 \begin_inset CommandInset ref
4533 reference "subsec:Variable-Space"
4540 \begin_layout Standard
4541 For example the command
4546 \begin_inset space \textvisiblespace{}
4554 \begin_layout Standard
4555 \begin_inset Formula $A\dotfill B$
4561 \begin_layout Standard
4568 there is for a line the command
4575 \begin_inset Index idx
4578 \begin_layout Plain Layout
4589 \begin_layout Standard
4590 \begin_inset Formula $A\hrulefill B$
4596 \begin_layout Standard
4597 To use the commands for text, they have to be inserted in \SpecialChar TeX
4601 \begin_layout Section
4603 \begin_inset CommandInset label
4610 \begin_inset Index idx
4613 \begin_layout Plain Layout
4622 \begin_layout Standard
4623 Matrices can be inserted via the math toolbar button
4626 arg "dialog-show mathmatrix"
4631 Insert\SpecialChar menuseparator
4632 Math\SpecialChar menuseparator
4636 In the matrix dialog you can specify the number of columns and rows, the
4637 alignment and the decoration.
4638 The vertical alignment is only of importance for matrices in inline formulas:
4641 \begin_layout Standard
4642 The first matrix is top
4643 \begin_inset Formula $\begin{array}[t]{cccc}
4651 \begin_inset Formula $\begin{array}{cccc}
4658 and the third bottom
4659 \begin_inset Formula $\begin{array}[b]{cccc}
4669 \begin_layout Standard
4670 The horizontal alignment specifies how the column entries should be aligned.
4671 It is set by entering a letter for every column.
4676 denotes left aligned,
4685 To create for example a 4
4690 \begin_inset space ~
4693 matrix where the first column is left aligned, the second and third are
4694 centered and the last one is right aligned, one enters for the horizontal
4700 Normally in a matrix all columns are centered, therefore the default for
4708 \begin_layout Standard
4709 Horizontal alignment:
4712 \begin_layout Standard
4718 \begin_inset Formula $\begin{array}{lll}
4730 \begin_inset Formula $\begin{array}{ccc}
4742 \begin_inset Formula $\begin{array}{rrr}
4752 \begin_layout Standard
4753 To add or delete rows and columns subsequently, the math toolbar buttons
4757 arg "tabular-feature append-row"
4763 arg "tabular-feature delete-row"
4767 \begin_inset space \thinspace{}
4772 Edit\SpecialChar menuseparator
4776 New rows can also be created with
4779 arg "newline-insert newline"
4785 \begin_layout Standard
4786 \begin_inset VSpace bigskip
4793 adds parentheses in the selected style around the matrix.
4794 Alternatively, parentheses can can either be created with the commands
4802 \begin_inset Index idx
4805 \begin_layout Plain Layout
4820 \begin_inset Index idx
4823 \begin_layout Plain Layout
4834 \begin_inset space ~
4840 \begin_inset CommandInset ref
4842 reference "subsec:Automatic-Bracket-Size"
4846 , or by using the following commands:
4847 \begin_inset VSpace medskip
4853 \begin_layout Standard
4854 \begin_inset space \hfill{}
4858 \begin_inset Tabular
4859 <lyxtabular version="3" rows="4" columns="2">
4860 <features booktabs="true" tabularvalignment="middle">
4861 <column alignment="center" valignment="top" width="0pt">
4862 <column alignment="center" valignment="top">
4864 <cell alignment="center" valignment="top" topline="true" bottomline="true" usebox="none">
4867 \begin_layout Plain Layout
4873 <cell alignment="center" valignment="top" topline="true" bottomline="true" usebox="none">
4876 \begin_layout Plain Layout
4883 <row topspace="1.5mm">
4884 <cell alignment="center" valignment="top" usebox="none">
4887 \begin_layout Plain Layout
4891 \begin_inset space \textvisiblespace{}
4899 \begin_inset space \thinspace{}
4907 <cell alignment="center" valignment="top" usebox="none">
4910 \begin_layout Plain Layout
4911 \begin_inset Formula $\begin{bmatrix}\begin{array}{cc}
4912 0 & \textrm{-}\mathrm{i}\\
4914 \end{array}\end{bmatrix}$
4923 <row topspace="1.5mm" bottomspace="0.5mm">
4924 <cell alignment="center" valignment="top" usebox="none">
4927 \begin_layout Plain Layout
4931 \begin_inset space \textvisiblespace{}
4939 \begin_inset space \thinspace{}
4947 <cell alignment="center" valignment="top" usebox="none">
4950 \begin_layout Plain Layout
4951 \begin_inset Formula $\begin{Bmatrix}\begin{array}{cc}
4952 0 & \textrm{-}\mathrm{i}\\
4954 \end{array}\end{Bmatrix}$
4964 <cell alignment="center" valignment="top" bottomline="true" usebox="none">
4967 \begin_layout Plain Layout
4971 \begin_inset space \textvisiblespace{}
4979 \begin_inset space \thinspace{}
4987 <cell alignment="center" valignment="top" bottomline="true" usebox="none">
4990 \begin_layout Plain Layout
4991 \begin_inset Formula $\begin{pmatrix}\begin{array}{cc}
4992 0 & \textrm{-}\mathrm{i}\\
4994 \end{array}\end{pmatrix}$
5008 \begin_inset space \hfill{}
5012 \begin_inset Tabular
5013 <lyxtabular version="3" rows="4" columns="2">
5014 <features booktabs="true" tabularvalignment="middle">
5015 <column alignment="center" valignment="top" width="0pt">
5016 <column alignment="center" valignment="top">
5018 <cell alignment="center" valignment="top" topline="true" bottomline="true" usebox="none">
5021 \begin_layout Plain Layout
5027 <cell alignment="center" valignment="top" topline="true" bottomline="true" usebox="none">
5030 \begin_layout Plain Layout
5037 <row topspace="1.5mm">
5038 <cell alignment="center" valignment="top" usebox="none">
5041 \begin_layout Plain Layout
5045 \begin_inset space \textvisiblespace{}
5053 \begin_inset space \thinspace{}
5061 <cell alignment="center" valignment="top" usebox="none">
5064 \begin_layout Plain Layout
5065 \begin_inset Formula $\begin{vmatrix}\begin{array}{cc}
5066 0 & \textrm{-}\mathrm{i}\\
5068 \end{array}\end{vmatrix}$
5077 <row topspace="1.5mm" bottomspace="0.5mm">
5078 <cell alignment="center" valignment="top" usebox="none">
5081 \begin_layout Plain Layout
5085 \begin_inset space \textvisiblespace{}
5093 \begin_inset space \thinspace{}
5101 <cell alignment="center" valignment="top" usebox="none">
5104 \begin_layout Plain Layout
5105 \begin_inset Formula $\begin{Vmatrix}\begin{array}{cc}
5106 0 & \textrm{-}\mathrm{i}\\
5108 \end{array}\end{Vmatrix}$
5118 <cell alignment="center" valignment="top" bottomline="true" usebox="none">
5121 \begin_layout Plain Layout
5125 \begin_inset space \textvisiblespace{}
5133 \begin_inset space \thinspace{}
5141 <cell alignment="center" valignment="top" bottomline="true" usebox="none">
5144 \begin_layout Plain Layout
5145 \begin_inset Formula $\begin{matrix}\begin{array}{cc}
5146 0 & \textrm{-}\mathrm{i}\\
5148 \end{array}\end{matrix}$
5162 \begin_inset space \hfill{}
5168 \begin_layout Standard
5169 \begin_inset VSpace medskip
5173 \begin_inset space \thinspace{}
5177 \begin_inset space \space{}
5186 is inserted, a blue box appears between two vertical lines where the matrix
5188 \begin_inset Newline newline
5191 Note that decorated matrices ignore the vertical alignment.
5194 \begin_layout Standard
5195 \begin_inset VSpace bigskip
5198 As all multiline formulas are matrices, the length
5205 \begin_inset Index idx
5208 \begin_layout Plain Layout
5216 that is described in
5217 \begin_inset CommandInset ref
5219 reference "subsec:Column-Separation"
5223 can also be used to change the column separation of matrices.
5226 \begin_layout Standard
5227 To change the row separation, the command
5234 \begin_inset Index idx
5237 \begin_layout Plain Layout
5246 It is used as follows:
5249 \begin_layout Standard
5256 arraystretch}{stretch factor}
5257 \begin_inset Index idx
5260 \begin_layout Plain Layout
5271 \begin_layout Standard
5278 assigns the stretch factor to the predefined command
5286 \begin_inset space \thinspace{}
5290 \begin_inset space \space{}
5293 the row separation, use the factor 2.
5294 This is then used for all following matrices.
5295 To go back to the original separation, assign the factor 1 to
5304 \begin_layout Standard
5305 To set matrices into a text line, the command
5312 \begin_inset Index idx
5315 \begin_layout Plain Layout
5324 When it is inserted a blue box with two dashed lines appears.
5325 In this box the matrix is inserted.
5328 \begin_layout Standard
5330 \begin_inset Formula $\left(\begin{smallmatrix}A & B\\
5332 \end{smallmatrix}\right)$
5338 \begin_layout Section
5339 Brackets and Delimiters
5340 \begin_inset Index idx
5343 \begin_layout Plain Layout
5350 \begin_inset Index idx
5353 \begin_layout Plain Layout
5362 \begin_layout Subsection
5363 Vertical Brackets and Delimiters
5364 \begin_inset Index idx
5367 \begin_layout Plain Layout
5376 \begin_layout Standard
5377 \begin_inset space \hfill{}
5381 \begin_inset Tabular
5382 <lyxtabular version="3" rows="9" columns="2">
5383 <features booktabs="true" tabularvalignment="middle">
5384 <column alignment="center" valignment="top" width="0pt">
5385 <column alignment="center" valignment="top" width="0pt">
5387 <cell alignment="center" valignment="top" topline="true" bottomline="true" usebox="none">
5390 \begin_layout Plain Layout
5396 <cell alignment="center" valignment="top" topline="true" bottomline="true" usebox="none">
5399 \begin_layout Plain Layout
5407 <cell alignment="center" valignment="top" usebox="none">
5410 \begin_layout Plain Layout
5416 <cell alignment="center" valignment="top" usebox="none">
5419 \begin_layout Plain Layout
5420 \begin_inset Formula $($
5430 <cell alignment="center" valignment="top" usebox="none">
5433 \begin_layout Plain Layout
5439 <cell alignment="center" valignment="top" usebox="none">
5442 \begin_layout Plain Layout
5443 \begin_inset Formula $\{$
5453 <cell alignment="center" valignment="top" usebox="none">
5456 \begin_layout Plain Layout
5462 <cell alignment="center" valignment="top" usebox="none">
5465 \begin_layout Plain Layout
5466 \begin_inset Formula $[$
5476 <cell alignment="center" valignment="top" usebox="none">
5479 \begin_layout Plain Layout
5487 <cell alignment="center" valignment="top" usebox="none">
5490 \begin_layout Plain Layout
5491 \begin_inset Formula $\langle$
5501 <cell alignment="center" valignment="top" usebox="none">
5504 \begin_layout Plain Layout
5512 <cell alignment="center" valignment="top" usebox="none">
5515 \begin_layout Plain Layout
5516 \begin_inset Formula $\lceil$
5526 <cell alignment="center" valignment="top" usebox="none">
5529 \begin_layout Plain Layout
5537 <cell alignment="center" valignment="top" usebox="none">
5540 \begin_layout Plain Layout
5541 \begin_inset Formula $\lfloor$
5551 <cell alignment="center" valignment="top" usebox="none">
5554 \begin_layout Plain Layout
5560 <cell alignment="center" valignment="top" usebox="none">
5563 \begin_layout Plain Layout
5564 \begin_inset Formula $/$
5574 <cell alignment="center" valignment="top" bottomline="true" usebox="none">
5577 \begin_layout Plain Layout
5583 <cell alignment="center" valignment="top" bottomline="true" usebox="none">
5586 \begin_layout Plain Layout
5587 \begin_inset Formula $|$
5601 \begin_inset space \hfill{}
5605 \begin_inset Tabular
5606 <lyxtabular version="3" rows="9" columns="2">
5607 <features booktabs="true" tabularvalignment="middle">
5608 <column alignment="center" valignment="top" width="0pt">
5609 <column alignment="center" valignment="top" width="0pt">
5611 <cell alignment="center" valignment="top" topline="true" bottomline="true" usebox="none">
5614 \begin_layout Plain Layout
5620 <cell alignment="center" valignment="top" topline="true" bottomline="true" usebox="none">
5623 \begin_layout Plain Layout
5631 <cell alignment="center" valignment="top" usebox="none">
5634 \begin_layout Plain Layout
5640 <cell alignment="center" valignment="top" usebox="none">
5643 \begin_layout Plain Layout
5644 \begin_inset Formula $)$
5654 <cell alignment="center" valignment="top" usebox="none">
5657 \begin_layout Plain Layout
5663 <cell alignment="center" valignment="top" usebox="none">
5666 \begin_layout Plain Layout
5667 \begin_inset Formula $\}$
5677 <cell alignment="center" valignment="top" usebox="none">
5680 \begin_layout Plain Layout
5686 <cell alignment="center" valignment="top" usebox="none">
5689 \begin_layout Plain Layout
5690 \begin_inset Formula $]$
5700 <cell alignment="center" valignment="top" usebox="none">
5703 \begin_layout Plain Layout
5711 <cell alignment="center" valignment="top" usebox="none">
5714 \begin_layout Plain Layout
5715 \begin_inset Formula $\rangle$
5725 <cell alignment="center" valignment="top" usebox="none">
5728 \begin_layout Plain Layout
5736 <cell alignment="center" valignment="top" usebox="none">
5739 \begin_layout Plain Layout
5740 \begin_inset Formula $\rceil$
5750 <cell alignment="center" valignment="top" usebox="none">
5753 \begin_layout Plain Layout
5761 <cell alignment="center" valignment="top" usebox="none">
5764 \begin_layout Plain Layout
5765 \begin_inset Formula $\rfloor$
5775 <cell alignment="center" valignment="top" usebox="none">
5778 \begin_layout Plain Layout
5788 <cell alignment="center" valignment="top" usebox="none">
5791 \begin_layout Plain Layout
5792 \begin_inset Formula $\backslash$
5802 <cell alignment="center" valignment="top" bottomline="true" usebox="none">
5805 \begin_layout Plain Layout
5813 <cell alignment="center" valignment="top" bottomline="true" usebox="none">
5816 \begin_layout Plain Layout
5817 \begin_inset Formula $\|$
5831 \begin_inset space \hfill{}
5837 \begin_layout Standard
5840 \begin_inset Note Greyedout
5843 \begin_layout Plain Layout
5856 \begin_inset Index idx
5859 \begin_layout Plain Layout
5867 must be used for the backslash, because the command
5875 produces a line break there.
5883 \begin_layout Standard
5884 For all characters listed above the size can be adjusted with the commands
5885 described in the following two subsections.
5886 When using these commands, the characters < and > can directly be used
5887 instead of the commands
5902 \begin_layout Subsubsection
5904 \begin_inset CommandInset label
5906 name "subsec:Manual-Bracket-Size"
5911 \begin_inset Index idx
5914 \begin_layout Plain Layout
5915 Bracket size ! manual
5923 \begin_layout Standard
5924 The bracket size can be specified manually by the \SpecialChar LaTeX
5932 \begin_inset Index idx
5935 \begin_layout Plain Layout
5968 denotes the smallest and
5974 the largest bracket size.
5977 \begin_layout Standard
5978 These commands are used to emphasize levels of brackets:
5981 \begin_layout Standard
5983 \begin_inset Tabular
5984 <lyxtabular version="3" rows="2" columns="2">
5985 <features booktabs="true" tabularvalignment="middle">
5986 <column alignment="center" valignment="top" width="0pt">
5987 <column alignment="center" valignment="top" width="0pt">
5989 <cell alignment="center" valignment="top" usebox="none">
5992 \begin_layout Plain Layout
5993 all brackets in the same size:
5998 <cell alignment="center" valignment="top" usebox="none">
6001 \begin_layout Plain Layout
6002 \begin_inset Formula $((A+B)(A-B))^{C}$
6011 <row topspace="2mm">
6012 <cell alignment="center" valignment="top" usebox="none">
6015 \begin_layout Plain Layout
6021 <cell alignment="center" valignment="top" usebox="none">
6024 \begin_layout Plain Layout
6025 \begin_inset Formula $\Big((A+B)(A-B)\Big)^{C}$
6041 \begin_layout Standard
6042 For the second formula the command
6049 \begin_inset space \textvisiblespace{}
6057 \begin_layout Standard
6058 Here is an overview about all bracket sizes:
6061 \begin_layout Standard
6078 \begin_inset space \textvisiblespace{}
6086 \begin_inset space \textvisiblespace{}
6090 \begin_inset space \textvisiblespace{}
6100 \begin_layout Standard
6102 \begin_inset Formula $\Bigg(\exp\bigg<\Big[\big\{\ln(3x)\big\}^{2}\sin(x)\Big]^{A}\bigg>\Bigg)^{0,5}$
6108 \begin_layout Standard
6115 -commands there is the variant
6122 \begin_inset Index idx
6125 \begin_layout Plain Layout
6133 that adds a bit more space between the bracket and its content, and the
6147 \begin_inset Index idx
6150 \begin_layout Plain Layout
6160 , that don't add additional space.
6165 at the end of the command
6171 is for a left bracket; for a right bracket this will be replaced by an
6177 A left or right bracket can each be an opening or closing bracket.
6180 \begin_layout Standard
6181 In the following table is a comparison of the variants:
6184 \begin_layout Standard
6186 \begin_inset Tabular
6187 <lyxtabular version="3" rows="5" columns="2">
6188 <features booktabs="true" tabularvalignment="middle">
6189 <column alignment="center" valignment="top" width="0pt">
6190 <column alignment="center" valignment="middle">
6192 <cell alignment="center" valignment="top" topline="true" bottomline="true" usebox="none">
6195 \begin_layout Plain Layout
6201 <cell alignment="center" valignment="top" topline="true" bottomline="true" usebox="none">
6204 \begin_layout Plain Layout
6211 <row topspace="2mm">
6212 <cell alignment="center" valignment="top" usebox="none">
6215 \begin_layout Plain Layout
6225 \begin_inset space \textvisiblespace{}
6235 <cell alignment="center" valignment="top" usebox="none">
6238 \begin_layout Plain Layout
6239 \begin_inset Formula $\Bigm(\bigm(\ln(3x)\bigm)^{2}\Bigm)$
6248 <row topspace="2mm">
6249 <cell alignment="center" valignment="top" usebox="none">
6252 \begin_layout Plain Layout
6262 \begin_inset space \textvisiblespace{}
6272 <cell alignment="center" valignment="top" usebox="none">
6275 \begin_layout Plain Layout
6276 \begin_inset Formula $\Big(\big(\ln(3x)\big)^{2}\Big)$
6285 <row topspace="2mm" bottomspace="0.5mm">
6286 <cell alignment="center" valignment="top" usebox="none">
6289 \begin_layout Plain Layout
6299 \begin_inset space \textvisiblespace{}
6309 <cell alignment="center" valignment="top" usebox="none">
6312 \begin_layout Plain Layout
6313 \begin_inset Formula $\Bigl(\bigl(\ln(3x)\bigr)^{2}\Bigr)$
6322 <row topspace="1.5mm" bottomspace="0.5mm">
6323 <cell alignment="center" valignment="top" topline="true" bottomline="true" usebox="none">
6326 \begin_layout Plain Layout
6338 <cell alignment="center" valignment="top" topline="true" bottomline="true" usebox="none">
6341 \begin_layout Plain Layout
6342 \begin_inset Formula $\bigl)\ln(3x)\bigr($
6358 \begin_layout Subsubsection
6359 Automatic Bracket Size
6360 \begin_inset CommandInset label
6362 name "subsec:Automatic-Bracket-Size"
6367 \begin_inset Index idx
6370 \begin_layout Plain Layout
6371 Bracket size ! automatic
6379 \begin_layout Standard
6380 Brackets with variable size can be inserted with the commands
6387 \begin_inset Index idx
6390 \begin_layout Plain Layout
6405 \begin_inset Index idx
6408 \begin_layout Plain Layout
6416 or via the math toolbar button
6419 arg "dialog-show mathdelimiter"
6435 the wanted bracket must be inserted.
6436 The bracket size will then automatically be calculated for the output.
6439 \begin_layout Standard
6441 normal bracket: The command
6448 \begin_inset space \textvisiblespace{}
6452 \begin_inset Formula $\downarrow$
6456 \begin_inset space \textvisiblespace{}
6462 \begin_inset Formula
6472 \begin_layout Standard
6474 multiline bracket: The command
6483 \begin_inset space \textvisiblespace{}
6487 \begin_inset Formula $\downarrow$
6491 \begin_inset space \textvisiblespace{}
6499 \begin_inset Formula
6501 \ln\left(\frac{A}{C}\right)
6509 \begin_layout Standard
6525 \begin_inset space ~
6531 This has the advantage that you can see in \SpecialChar LyX
6532 immediately the real bracket
6533 size and that the matching right bracket will be created too.
6534 \begin_inset Newline newline
6537 The command for the last example would then be:
6548 \begin_inset space \textvisiblespace{}
6552 \begin_inset Formula $\downarrow$
6558 \begin_layout Standard
6559 To omit a left or right bracket, a dot is inserted for the omitted bracket.
6560 For example the command
6567 \begin_inset space \textvisiblespace{}
6571 \begin_inset Formula $\downarrow$
6575 \begin_inset space \textvisiblespace{}
6585 \begin_inset Formula
6587 \left.\frac{A}{B}\right\}
6606 will be converted by \SpecialChar LyX
6607 to brackets in the right size when the document is
6608 reloaded and an omitted bracket will appear as dashed line.
6611 \begin_layout Standard
6612 \begin_inset VSpace bigskip
6615 Because all popular \SpecialChar LaTeX
6616 distributions use e\SpecialChar TeX
6617 , an extension to \SpecialChar LaTeX
6626 \begin_inset Index idx
6629 \begin_layout Plain Layout
6637 is additionally available for all brackets and limits.
6638 With this command the height of the following character is adapted to the
6639 one of the surrounding brackets, what is e.
6640 \begin_inset space \thinspace{}
6644 \begin_inset space \space{}
6647 needed for physical vectors:
6648 \begin_inset Formula
6650 \left\langle \phi\:\middle|\:J=\frac{3}{2}\,,\,M_{J}\right\rangle
6655 For physical vectors there is a special \SpecialChar LaTeX
6656 -package, described in
6657 \begin_inset CommandInset ref
6659 reference "subsec:Physical-Vectors"
6666 \begin_layout Subsection
6668 \begin_inset Index idx
6671 \begin_layout Plain Layout
6672 Brackets ! horizontal
6680 \begin_layout Standard
6682 \begin_inset Tabular
6683 <lyxtabular version="3" rows="4" columns="2">
6684 <features booktabs="true" tabularvalignment="middle">
6685 <column alignment="center" valignment="top" width="0pt">
6686 <column alignment="center" valignment="top" width="0pt">
6688 <cell alignment="center" valignment="top" topline="true" bottomline="true" usebox="none">
6691 \begin_layout Plain Layout
6697 <cell alignment="center" valignment="top" topline="true" bottomline="true" usebox="none">
6700 \begin_layout Plain Layout
6708 <cell alignment="center" valignment="top" usebox="none">
6711 \begin_layout Plain Layout
6715 \begin_inset space \textvisiblespace{}
6719 \begin_inset space \textvisiblespace{}
6723 \begin_inset Index idx
6726 \begin_layout Plain Layout
6739 <cell alignment="center" valignment="top" usebox="none">
6742 \begin_layout Plain Layout
6743 \begin_inset Formula $\overbrace{A+B}^{3}$
6752 <row topspace="2mm">
6753 <cell alignment="center" valignment="top" usebox="none">
6756 \begin_layout Plain Layout
6760 \begin_inset space \textvisiblespace{}
6764 \begin_inset space \textvisiblespace{}
6768 \begin_inset Index idx
6771 \begin_layout Plain Layout
6784 <cell alignment="center" valignment="top" usebox="none">
6787 \begin_layout Plain Layout
6788 \begin_inset Formula $\underbrace{A+B}_{5}$
6798 <cell alignment="center" valignment="top" topline="true" bottomline="true" usebox="none">
6801 \begin_layout Plain Layout
6805 \begin_inset space \textvisiblespace{}
6811 \begin_inset space \textvisiblespace{}
6815 \begin_inset space \textvisiblespace{}
6819 \begin_inset space \textvisiblespace{}
6823 \begin_inset space \textvisiblespace{}
6827 \begin_inset space \textvisiblespace{}
6831 \begin_inset space \textvisiblespace{}
6839 <cell alignment="center" valignment="top" topline="true" bottomline="true" usebox="none">
6842 \begin_layout Plain Layout
6843 \begin_inset Formula $\overbrace{\underbrace{A+B_{w}}_{7}}^{C}$
6859 \begin_layout Standard
6860 In the last example it doesn't matter if
6872 is inserted at first.
6875 \begin_layout Standard
6876 \begin_inset VSpace medskip
6882 \begin_layout Standard
6883 If you set in the document settings under
6886 \begin_inset space ~
6896 \begin_inset Index idx
6899 \begin_layout Plain Layout
6900 Packages ! mathtools
6908 \begin_inset space ~
6913 , you have access to square backets:
6916 \begin_layout Standard
6918 \begin_inset Tabular
6919 <lyxtabular version="3" rows="4" columns="2">
6920 <features booktabs="true" tabularvalignment="middle">
6921 <column alignment="center" valignment="top" width="0pt">
6922 <column alignment="center" valignment="top" width="0pt">
6924 <cell alignment="center" valignment="top" topline="true" bottomline="true" usebox="none">
6927 \begin_layout Plain Layout
6933 <cell alignment="center" valignment="top" topline="true" bottomline="true" usebox="none">
6936 \begin_layout Plain Layout
6944 <cell alignment="center" valignment="top" usebox="none">
6947 \begin_layout Plain Layout
6975 \begin_inset space \textvisiblespace{}
6979 \begin_inset Index idx
6982 \begin_layout Plain Layout
6995 <cell alignment="center" valignment="top" usebox="none">
6998 \begin_layout Plain Layout
6999 \begin_inset Formula $\overbracket{A+B}^{3}$
7008 <row topspace="2mm">
7009 <cell alignment="center" valignment="top" usebox="none">
7012 \begin_layout Plain Layout
7040 \begin_inset space \textvisiblespace{}
7044 \begin_inset Index idx
7047 \begin_layout Plain Layout
7072 <cell alignment="center" valignment="top" usebox="none">
7075 \begin_layout Plain Layout
7076 \begin_inset Formula $\underbracket{A+B}_{5}$
7086 <cell alignment="center" valignment="top" topline="true" bottomline="true" usebox="none">
7089 \begin_layout Plain Layout
7095 \begin_inset space \textvisiblespace{}
7099 \begin_inset space \textvisiblespace{}
7103 \begin_inset space \textvisiblespace{}
7107 \begin_inset space \textvisiblespace{}
7111 \begin_inset space \textvisiblespace{}
7119 <cell alignment="center" valignment="top" topline="true" bottomline="true" usebox="none">
7122 \begin_layout Plain Layout
7123 \begin_inset Formula $\overbracket{\underbracket{A+B_{w}}_{7}}^{C}$
7139 \begin_layout Standard
7152 you can change the thickness of the bracket's stroke by specifying the
7153 desired thickness in square brackets behind the command:
7156 \begin_layout Standard
7158 \begin_inset Tabular
7159 <lyxtabular version="3" rows="3" columns="2">
7160 <features booktabs="true" tabularvalignment="middle">
7161 <column alignment="center" valignment="top" width="0pt">
7162 <column alignment="center" valignment="top" width="0pt">
7164 <cell alignment="center" valignment="top" topline="true" bottomline="true" usebox="none">
7167 \begin_layout Plain Layout
7173 <cell alignment="center" valignment="top" topline="true" bottomline="true" usebox="none">
7176 \begin_layout Plain Layout
7184 <cell alignment="center" valignment="top" usebox="none">
7187 \begin_layout Plain Layout
7217 \begin_inset space \textvisiblespace{}
7225 <cell alignment="center" valignment="top" usebox="none">
7228 \begin_layout Plain Layout
7229 \begin_inset Formula $\overbracket[3pt]{A+B}^{3}$
7238 <row topspace="2mm">
7239 <cell alignment="center" valignment="top" bottomline="true" usebox="none">
7242 \begin_layout Plain Layout
7272 \begin_inset space \textvisiblespace{}
7280 <cell alignment="center" valignment="top" bottomline="true" usebox="none">
7283 \begin_layout Plain Layout
7284 \begin_inset Formula $\underbracket[1pt]{A+B}_{5}$
7300 \begin_layout Standard
7301 \begin_inset VSpace bigskip
7304 When brackets should overlap each other, multiline formulas, as described
7306 \begin_inset CommandInset ref
7308 reference "sec:Multiline-Formulas"
7313 \begin_inset Formula
7315 A & = & \underbrace{gggg+bbqq}_{r}+\:dddd\\
7316 & & \hphantom{gggg+\:}\underbrace{\hphantom{bbqq+dddd}}_{s}
7321 In the first row the formula is inserted together with the first brace.
7322 It is hereby important that the space command
7326 \begin_layout Plain Layout
7327 Space commands are explained in
7328 \begin_inset CommandInset ref
7330 reference "subsec:Predefined-Space"
7345 is inserted before the first
7346 \begin_inset Formula $d$
7349 , because the brace that ends behind the
7350 \begin_inset Formula $q$
7353 prevents that the following
7354 \begin_inset Quotes eld
7358 \begin_inset Quotes erd
7361 is surrounded by space.
7365 \begin_layout Plain Layout
7366 because a bracket is not handled as a character, see
7367 \begin_inset CommandInset ref
7369 reference "subsec:Binary-Operators"
7378 In the second row the second brace is inserted.
7379 As it should begin before the
7380 \begin_inset Formula $b$
7395 \begin_layout Plain Layout
7403 \begin_inset CommandInset ref
7405 reference "subsec:Placeholders"
7414 This space is needed because the
7415 \begin_inset Quotes eld
7419 \begin_inset Quotes erd
7422 is also surrounded by space in the formula.
7423 The brace is placed under the command
7432 \begin_layout Standard
7433 It gets more complicated when brackets overlap each other above and under
7434 the formula, like in the following example:
7438 \begin_layout Plain Layout
7450 \begin_inset Formula
7452 & & \hphantom{gggg+\:}\overbrace{\hphantom{bbqq+dddd}}^{s}\\
7453 A & = & \underbrace{gggg+bbqq}_{r}+\:dddd
7462 \begin_layout Plain Layout
7473 The first formula row is the same as the second row of the previous example,
7474 with the difference that the brace is above.
7475 The second row contains the formula together with the second brace.
7476 To avoid that there is space between the upper brace in the first row and
7477 the formula, the row spacing needs to be reduced.
7478 This is not easily possible due to a bug in \SpecialChar LyX
7483 \begin_layout Plain Layout
7484 \begin_inset CommandInset href
7486 name "LyX-bug #1505"
7487 target "http://www.lyx.org/trac/ticket/1505"
7496 As a solution for the problem, the global formula row separation
7503 \begin_inset Index idx
7506 \begin_layout Plain Layout
7514 must be changed to -6
7515 \begin_inset space \thinspace{}
7518 pt before the formula with the command
7534 is set back after the formula to the standard value of 3
7535 \begin_inset space \thinspace{}
7538 pt using the same command.
7539 More about the row separation in formulas is explained in
7540 \begin_inset CommandInset ref
7542 reference "subsec:Line-Separation"
7549 \begin_layout Section
7551 \begin_inset Index idx
7554 \begin_layout Plain Layout
7563 \begin_layout Standard
7564 Arrows can be inserted via the math toolbar button
7567 arg "math-insert \\leftarrow"
7570 or the commands listed in the following subsections.
7573 \begin_layout Subsection
7575 \begin_inset Index idx
7578 \begin_layout Plain Layout
7587 \begin_layout Standard
7588 \begin_inset space \hfill{}
7592 \begin_inset Tabular
7593 <lyxtabular version="3" rows="8" columns="2">
7594 <features booktabs="true" tabularvalignment="middle">
7595 <column alignment="center" valignment="top" width="0pt">
7596 <column alignment="center" valignment="top" width="0pt">
7598 <cell alignment="center" valignment="top" topline="true" bottomline="true" usebox="none">
7601 \begin_layout Plain Layout
7607 <cell alignment="center" valignment="top" topline="true" bottomline="true" usebox="none">
7610 \begin_layout Plain Layout
7618 <cell alignment="center" valignment="top" usebox="none">
7621 \begin_layout Plain Layout
7629 <cell alignment="center" valignment="top" usebox="none">
7632 \begin_layout Plain Layout
7633 \begin_inset Formula $\gets$
7643 <cell alignment="center" valignment="top" usebox="none">
7646 \begin_layout Plain Layout
7654 <cell alignment="center" valignment="top" usebox="none">
7657 \begin_layout Plain Layout
7658 \begin_inset Formula $\Leftarrow$
7668 <cell alignment="center" valignment="top" usebox="none">
7671 \begin_layout Plain Layout
7679 <cell alignment="center" valignment="top" usebox="none">
7682 \begin_layout Plain Layout
7683 \begin_inset Formula $\longleftarrow$
7693 <cell alignment="center" valignment="top" usebox="none">
7696 \begin_layout Plain Layout
7704 <cell alignment="center" valignment="top" usebox="none">
7707 \begin_layout Plain Layout
7708 \begin_inset Formula $\Longleftarrow$
7718 <cell alignment="center" valignment="top" usebox="none">
7721 \begin_layout Plain Layout
7729 <cell alignment="center" valignment="top" usebox="none">
7732 \begin_layout Plain Layout
7733 \begin_inset Formula $\leftharpoonup$
7743 <cell alignment="center" valignment="top" usebox="none">
7746 \begin_layout Plain Layout
7754 <cell alignment="center" valignment="top" usebox="none">
7757 \begin_layout Plain Layout
7758 \begin_inset Formula $\leftharpoondown$
7768 <cell alignment="center" valignment="top" bottomline="true" usebox="none">
7771 \begin_layout Plain Layout
7779 <cell alignment="center" valignment="top" bottomline="true" usebox="none">
7782 \begin_layout Plain Layout
7783 \begin_inset Formula $\hookleftarrow$
7797 \begin_inset space \hfill{}
7801 \begin_inset Tabular
7802 <lyxtabular version="3" rows="8" columns="2">
7803 <features booktabs="true" tabularvalignment="middle">
7804 <column alignment="center" valignment="top" width="0pt">
7805 <column alignment="center" valignment="top" width="0pt">
7807 <cell alignment="center" valignment="top" topline="true" bottomline="true" usebox="none">
7810 \begin_layout Plain Layout
7816 <cell alignment="center" valignment="top" topline="true" bottomline="true" usebox="none">
7819 \begin_layout Plain Layout
7827 <cell alignment="center" valignment="top" usebox="none">
7830 \begin_layout Plain Layout
7838 <cell alignment="center" valignment="top" usebox="none">
7841 \begin_layout Plain Layout
7842 \begin_inset Formula $\to$
7852 <cell alignment="center" valignment="top" usebox="none">
7855 \begin_layout Plain Layout
7863 <cell alignment="center" valignment="top" usebox="none">
7866 \begin_layout Plain Layout
7867 \begin_inset Formula $\Rightarrow$
7877 <cell alignment="center" valignment="top" usebox="none">
7880 \begin_layout Plain Layout
7888 <cell alignment="center" valignment="top" usebox="none">
7891 \begin_layout Plain Layout
7892 \begin_inset Formula $\longrightarrow$
7902 <cell alignment="center" valignment="top" usebox="none">
7905 \begin_layout Plain Layout
7913 <cell alignment="center" valignment="top" usebox="none">
7916 \begin_layout Plain Layout
7917 \begin_inset Formula $\Longrightarrow$
7927 <cell alignment="center" valignment="top" usebox="none">
7930 \begin_layout Plain Layout
7938 <cell alignment="center" valignment="top" usebox="none">
7941 \begin_layout Plain Layout
7942 \begin_inset Formula $\rightharpoonup$
7952 <cell alignment="center" valignment="top" usebox="none">
7955 \begin_layout Plain Layout
7963 <cell alignment="center" valignment="top" usebox="none">
7966 \begin_layout Plain Layout
7967 \begin_inset Formula $\rightharpoondown$
7977 <cell alignment="center" valignment="top" bottomline="true" usebox="none">
7980 \begin_layout Plain Layout
7988 <cell alignment="center" valignment="top" bottomline="true" usebox="none">
7991 \begin_layout Plain Layout
7992 \begin_inset Formula $\hookrightarrow$
8006 \begin_inset space \hfill{}
8012 \begin_layout Standard
8013 \begin_inset space \hfill{}
8017 \begin_inset Tabular
8018 <lyxtabular version="3" rows="6" columns="2">
8019 <features booktabs="true" tabularvalignment="middle">
8020 <column alignment="center" valignment="top" width="0pt">
8021 <column alignment="center" valignment="top" width="0pt">
8023 <cell alignment="center" valignment="top" topline="true" bottomline="true" usebox="none">
8026 \begin_layout Plain Layout
8032 <cell alignment="center" valignment="top" topline="true" bottomline="true" usebox="none">
8035 \begin_layout Plain Layout
8043 <cell alignment="center" valignment="top" usebox="none">
8046 \begin_layout Plain Layout
8054 <cell alignment="center" valignment="top" usebox="none">
8057 \begin_layout Plain Layout
8058 \begin_inset Formula $\leftrightarrow$
8068 <cell alignment="center" valignment="top" usebox="none">
8071 \begin_layout Plain Layout
8079 <cell alignment="center" valignment="top" usebox="none">
8082 \begin_layout Plain Layout
8083 \begin_inset Formula $\Leftrightarrow$
8093 <cell alignment="center" valignment="top" usebox="none">
8096 \begin_layout Plain Layout
8104 <cell alignment="center" valignment="top" usebox="none">
8107 \begin_layout Plain Layout
8108 \begin_inset Formula $\longleftrightarrow$
8118 <cell alignment="center" valignment="top" usebox="none">
8121 \begin_layout Plain Layout
8129 <cell alignment="center" valignment="top" usebox="none">
8132 \begin_layout Plain Layout
8133 \begin_inset Formula $\Longleftrightarrow$
8143 <cell alignment="center" valignment="top" bottomline="true" usebox="none">
8146 \begin_layout Plain Layout
8154 <cell alignment="center" valignment="top" bottomline="true" usebox="none">
8157 \begin_layout Plain Layout
8158 \begin_inset Formula $\rightleftharpoons$
8172 \begin_inset space \hspace{}
8177 \begin_inset space \hfill{}
8181 \begin_inset Tabular
8182 <lyxtabular version="3" rows="5" columns="2">
8183 <features booktabs="true" tabularvalignment="middle">
8184 <column alignment="center" valignment="top" width="0pt">
8185 <column alignment="center" valignment="top" width="0pt">
8187 <cell alignment="center" valignment="top" topline="true" bottomline="true" usebox="none">
8190 \begin_layout Plain Layout
8196 <cell alignment="center" valignment="top" topline="true" bottomline="true" usebox="none">
8199 \begin_layout Plain Layout
8207 <cell alignment="center" valignment="top" usebox="none">
8210 \begin_layout Plain Layout
8218 <cell alignment="center" valignment="top" usebox="none">
8221 \begin_layout Plain Layout
8222 \begin_inset Formula $\mapsto$
8232 <cell alignment="center" valignment="top" usebox="none">
8235 \begin_layout Plain Layout
8243 <cell alignment="center" valignment="top" usebox="none">
8246 \begin_layout Plain Layout
8247 \begin_inset Formula $\longmapsto$
8257 <cell alignment="center" valignment="top" usebox="none">
8260 \begin_layout Plain Layout
8268 <cell alignment="center" valignment="top" usebox="none">
8271 \begin_layout Plain Layout
8272 \begin_inset Formula $\leadsto$
8282 <cell alignment="center" valignment="top" bottomline="true" usebox="none">
8285 \begin_layout Plain Layout
8293 <cell alignment="center" valignment="top" bottomline="true" usebox="none">
8296 \begin_layout Plain Layout
8297 \begin_inset Formula $\dasharrow$
8311 \begin_inset space \hfill{}
8317 \begin_layout Standard
8318 \begin_inset VSpace medskip
8321 Arrows used as accents like e.
8322 \begin_inset space \thinspace{}
8326 \begin_inset space \space{}
8329 vector arrows are listed in
8330 \begin_inset CommandInset ref
8332 reference "sec:Accents"
8339 \begin_layout Standard
8340 \begin_inset VSpace bigskip
8343 Furthermore there are the labeled arrows
8344 \begin_inset Index idx
8347 \begin_layout Plain Layout
8360 \begin_inset Index idx
8363 \begin_layout Plain Layout
8378 \begin_inset Index idx
8381 \begin_layout Plain Layout
8388 \begin_layout Plain Layout
8403 When inserting one of these commands in a formula, an arrow with two blue
8404 boxes appear where the label can be inserted.
8405 The length of the arrow adapts to the label width.
8408 \begin_layout Standard
8410 \begin_inset Tabular
8411 <lyxtabular version="3" rows="3" columns="2">
8412 <features booktabs="true" tabularvalignment="middle">
8413 <column alignment="center" valignment="top" width="0pt">
8414 <column alignment="center" valignment="top" width="0pt">
8416 <cell alignment="center" valignment="top" topline="true" bottomline="true" usebox="none">
8419 \begin_layout Plain Layout
8425 <cell alignment="center" valignment="top" topline="true" bottomline="true" usebox="none">
8428 \begin_layout Plain Layout
8436 <cell alignment="center" valignment="top" usebox="none">
8439 \begin_layout Plain Layout
8443 \begin_inset space \textvisiblespace{}
8447 \begin_inset Formula $\downarrow$
8451 \begin_inset Formula $\to$
8459 <cell alignment="center" valignment="top" usebox="none">
8462 \begin_layout Plain Layout
8463 \begin_inset Formula $F(a)\xleftarrow[x>0]{x=a}F(x)$
8472 <row topspace="2mm">
8473 <cell alignment="center" valignment="top" bottomline="true" usebox="none">
8476 \begin_layout Plain Layout
8480 \begin_inset space \textvisiblespace{}
8484 \begin_inset Formula $\downarrow$
8488 \begin_inset Formula $\to$
8496 <cell alignment="center" valignment="top" bottomline="true" usebox="none">
8499 \begin_layout Plain Layout
8500 \begin_inset Formula $F(x)\xrightarrow[x>0]{x=a}F(a)$
8516 \begin_layout Standard
8517 \begin_inset VSpace medskip
8523 \begin_layout Standard
8524 If you set in the document settings under
8527 \begin_inset space ~
8537 \begin_inset Index idx
8540 \begin_layout Plain Layout
8541 Packages ! mathtools
8549 \begin_inset space ~
8554 , you have access to the following labeled arrows:
8557 \begin_layout Standard
8558 \begin_inset Newpage newpage
8564 \begin_layout Standard
8566 \begin_inset space \hspace*{\fill}
8570 \begin_inset Tabular
8571 <lyxtabular version="3" rows="7" columns="2">
8572 <features booktabs="true" tabularvalignment="middle">
8573 <column alignment="center" valignment="top" width="0pt">
8574 <column alignment="center" valignment="top" width="0pt">
8576 <cell alignment="center" valignment="top" topline="true" bottomline="true" usebox="none">
8579 \begin_layout Plain Layout
8585 <cell alignment="center" valignment="top" topline="true" bottomline="true" usebox="none">
8588 \begin_layout Plain Layout
8596 <cell alignment="center" valignment="top" usebox="none">
8599 \begin_layout Plain Layout
8619 <cell alignment="center" valignment="top" usebox="none">
8622 \begin_layout Plain Layout
8623 \begin_inset Formula $\xleftrightarrow[x=a]{x>0}$
8632 <row topspace="2mm">
8633 <cell alignment="center" valignment="top" usebox="none">
8636 \begin_layout Plain Layout
8656 <cell alignment="center" valignment="top" usebox="none">
8659 \begin_layout Plain Layout
8660 \begin_inset Formula $\xLeftarrow[x=a]{x>0}$
8669 <row topspace="2mm">
8670 <cell alignment="center" valignment="top" usebox="none">
8673 \begin_layout Plain Layout
8693 <cell alignment="center" valignment="top" usebox="none">
8696 \begin_layout Plain Layout
8697 \begin_inset Formula $\xRightarrow[x=a]{x>0}$
8706 <row topspace="2mm">
8707 <cell alignment="center" valignment="top" usebox="none">
8710 \begin_layout Plain Layout
8730 <cell alignment="center" valignment="top" usebox="none">
8733 \begin_layout Plain Layout
8734 \begin_inset Formula $\xLeftrightarrow[x=a]{x>0}$
8743 <row topspace="2mm">
8744 <cell alignment="center" valignment="top" usebox="none">
8747 \begin_layout Plain Layout
8767 <cell alignment="center" valignment="top" usebox="none">
8770 \begin_layout Plain Layout
8771 \begin_inset Formula $\xhookleftarrow[x=a]{x>0}$
8780 <row topspace="2mm">
8781 <cell alignment="center" valignment="top" bottomline="true" usebox="none">
8784 \begin_layout Plain Layout
8804 <cell alignment="center" valignment="top" bottomline="true" usebox="none">
8807 \begin_layout Plain Layout
8808 \begin_inset Formula $\xhookrightarrow[x=a]{x>0}$
8822 \begin_inset space \hspace*{\fill}
8826 \begin_inset Tabular
8827 <lyxtabular version="3" rows="7" columns="2">
8828 <features booktabs="true" tabularvalignment="middle">
8829 <column alignment="center" valignment="top" width="0pt">
8830 <column alignment="center" valignment="top" width="0pt">
8832 <cell alignment="center" valignment="top" topline="true" bottomline="true" usebox="none">
8835 \begin_layout Plain Layout
8841 <cell alignment="center" valignment="top" topline="true" bottomline="true" usebox="none">
8844 \begin_layout Plain Layout
8852 <cell alignment="center" valignment="top" usebox="none">
8855 \begin_layout Plain Layout
8875 <cell alignment="center" valignment="top" usebox="none">
8878 \begin_layout Plain Layout
8879 \begin_inset Formula $\xleftharpoondown[x=a]{x>0}$
8888 <row topspace="2mm">
8889 <cell alignment="center" valignment="top" usebox="none">
8892 \begin_layout Plain Layout
8912 <cell alignment="center" valignment="top" usebox="none">
8915 \begin_layout Plain Layout
8916 \begin_inset Formula $\xleftharpoonup[x=a]{x>0}$
8925 <row topspace="2mm">
8926 <cell alignment="center" valignment="top" usebox="none">
8929 \begin_layout Plain Layout
8949 <cell alignment="center" valignment="top" usebox="none">
8952 \begin_layout Plain Layout
8953 \begin_inset Formula $\xrightharpoondown[x=a]{x>0}$
8962 <row topspace="2mm">
8963 <cell alignment="center" valignment="top" usebox="none">
8966 \begin_layout Plain Layout
8986 <cell alignment="center" valignment="top" usebox="none">
8989 \begin_layout Plain Layout
8990 \begin_inset Formula $\xrightharpoonup[x=a]{x>0}$
8999 <row topspace="2mm">
9000 <cell alignment="center" valignment="top" usebox="none">
9003 \begin_layout Plain Layout
9023 <cell alignment="center" valignment="top" usebox="none">
9026 \begin_layout Plain Layout
9027 \begin_inset Formula $\xleftrightharpoons[x=a]{x>0}$
9036 <row topspace="2mm">
9037 <cell alignment="center" valignment="top" bottomline="true" usebox="none">
9040 \begin_layout Plain Layout
9060 <cell alignment="center" valignment="top" bottomline="true" usebox="none">
9063 \begin_layout Plain Layout
9064 \begin_inset Formula $\xrightleftharpoons[x=a]{x>0}$
9078 \begin_inset space \hspace*{\fill}
9084 \begin_layout Standard
9085 The command scheme is for all these arrows:
9088 \begin_layout Standard
9090 \begin_inset Tabular
9091 <lyxtabular version="3" rows="2" columns="2">
9092 <features booktabs="true" tabularvalignment="middle">
9093 <column alignment="center" valignment="top" width="0pt">
9094 <column alignment="center" valignment="top" width="0pt">
9096 <cell alignment="center" valignment="top" topline="true" bottomline="true" usebox="none">
9099 \begin_layout Plain Layout
9105 <cell alignment="center" valignment="top" topline="true" bottomline="true" usebox="none">
9108 \begin_layout Plain Layout
9115 <row bottomspace="0.5mm">
9116 <cell alignment="center" valignment="top" bottomline="true" usebox="none">
9119 \begin_layout Plain Layout
9122 xleftrightarrow[x=a]
9125 \begin_inset Formula $\to$
9133 <cell alignment="center" valignment="top" bottomline="true" usebox="none">
9136 \begin_layout Plain Layout
9137 \begin_inset Formula $F(a)\xleftrightarrow[x=a]{x>0}F(x)$
9153 \begin_layout Subsection
9154 Vertical and diagonal Arrows
9155 \begin_inset Index idx
9158 \begin_layout Plain Layout
9165 \begin_inset Index idx
9168 \begin_layout Plain Layout
9177 \begin_layout Standard
9178 \begin_inset space \hfill{}
9182 \begin_inset Tabular
9183 <lyxtabular version="3" rows="7" columns="2">
9184 <features booktabs="true" tabularvalignment="middle">
9185 <column alignment="center" valignment="top" width="0pt">
9186 <column alignment="center" valignment="top" width="0pt">
9188 <cell alignment="center" valignment="top" topline="true" bottomline="true" usebox="none">
9191 \begin_layout Plain Layout
9197 <cell alignment="center" valignment="top" topline="true" bottomline="true" usebox="none">
9200 \begin_layout Plain Layout
9208 <cell alignment="center" valignment="top" usebox="none">
9211 \begin_layout Plain Layout
9219 <cell alignment="center" valignment="top" usebox="none">
9222 \begin_layout Plain Layout
9223 \begin_inset Formula $\uparrow$
9233 <cell alignment="center" valignment="top" usebox="none">
9236 \begin_layout Plain Layout
9244 <cell alignment="center" valignment="top" usebox="none">
9247 \begin_layout Plain Layout
9248 \begin_inset Formula $\Uparrow$
9258 <cell alignment="center" valignment="top" usebox="none">
9261 \begin_layout Plain Layout
9269 <cell alignment="center" valignment="top" usebox="none">
9272 \begin_layout Plain Layout
9273 \begin_inset Formula $\updownarrow$
9283 <cell alignment="center" valignment="top" usebox="none">
9286 \begin_layout Plain Layout
9294 <cell alignment="center" valignment="top" usebox="none">
9297 \begin_layout Plain Layout
9298 \begin_inset Formula $\Updownarrow$
9308 <cell alignment="center" valignment="top" usebox="none">
9311 \begin_layout Plain Layout
9319 <cell alignment="center" valignment="top" usebox="none">
9322 \begin_layout Plain Layout
9323 \begin_inset Formula $\Downarrow$
9333 <cell alignment="center" valignment="top" bottomline="true" usebox="none">
9336 \begin_layout Plain Layout
9344 <cell alignment="center" valignment="top" bottomline="true" usebox="none">
9347 \begin_layout Plain Layout
9348 \begin_inset Formula $\downarrow$
9362 \begin_inset space \hfill{}
9366 \begin_inset Tabular
9367 <lyxtabular version="3" rows="5" columns="2">
9368 <features booktabs="true" tabularvalignment="middle">
9369 <column alignment="center" valignment="top" width="0pt">
9370 <column alignment="center" valignment="top" width="0pt">
9372 <cell alignment="center" valignment="top" topline="true" bottomline="true" usebox="none">
9375 \begin_layout Plain Layout
9381 <cell alignment="center" valignment="top" topline="true" bottomline="true" usebox="none">
9384 \begin_layout Plain Layout
9392 <cell alignment="center" valignment="top" usebox="none">
9395 \begin_layout Plain Layout
9403 <cell alignment="center" valignment="top" usebox="none">
9406 \begin_layout Plain Layout
9407 \begin_inset Formula $\nearrow$
9417 <cell alignment="center" valignment="top" usebox="none">
9420 \begin_layout Plain Layout
9428 <cell alignment="center" valignment="top" usebox="none">
9431 \begin_layout Plain Layout
9432 \begin_inset Formula $\searrow$
9442 <cell alignment="center" valignment="top" usebox="none">
9445 \begin_layout Plain Layout
9453 <cell alignment="center" valignment="top" usebox="none">
9456 \begin_layout Plain Layout
9457 \begin_inset Formula $\swarrow$
9467 <cell alignment="center" valignment="top" bottomline="true" usebox="none">
9470 \begin_layout Plain Layout
9478 <cell alignment="center" valignment="top" bottomline="true" usebox="none">
9481 \begin_layout Plain Layout
9482 \begin_inset Formula $\nwarrow$
9496 \begin_inset space \hfill{}
9502 \begin_layout Standard
9503 \begin_inset VSpace medskip
9506 Vertical arrows can be used also as delimiters together with the commands
9508 \begin_inset CommandInset ref
9510 reference "subsec:Manual-Bracket-Size"
9515 \begin_inset CommandInset ref
9517 reference "subsec:Automatic-Bracket-Size"
9524 \begin_layout Section
9526 \begin_inset CommandInset label
9533 \begin_inset Index idx
9536 \begin_layout Plain Layout
9545 \begin_layout Standard
9546 Accents can be inserted via the math toolbar button
9549 arg "math-insert \\hat"
9552 or the commands listed in the following subsections.
9555 \begin_layout Subsection
9556 Accents for one Character
9560 \begin_layout Plain Layout
9573 \begin_layout Plain Layout
9575 \begin_inset CommandInset ref
9577 reference "subsec:Accents-in-Text"
9590 \begin_layout Plain Layout
9598 \begin_inset Note Note
9601 \begin_layout Plain Layout
9608 is used to avoid that the footnote appears in the PDF-bookmark.
9611 \begin_layout Plain Layout
9619 \begin_inset CommandInset ref
9621 reference "subsec:Formulas-in-Section"
9631 \begin_inset CommandInset label
9633 name "subsec:Accents-for-one"
9638 \begin_inset Index idx
9641 \begin_layout Plain Layout
9642 Accents ! for one character
9650 \begin_layout Standard
9651 \begin_inset space \hfill{}
9655 \begin_inset Tabular
9656 <lyxtabular version="3" rows="8" columns="2">
9657 <features booktabs="true" tabularvalignment="middle">
9658 <column alignment="center" valignment="top" width="0pt">
9659 <column alignment="center" valignment="top" width="0pt">
9661 <cell alignment="center" valignment="top" topline="true" bottomline="true" usebox="none">
9664 \begin_layout Plain Layout
9670 <cell alignment="center" valignment="top" topline="true" bottomline="true" usebox="none">
9673 \begin_layout Plain Layout
9680 <row topspace="1.5mm">
9681 <cell alignment="center" valignment="top" usebox="none">
9684 \begin_layout Plain Layout
9688 \begin_inset space \textvisiblespace{}
9696 <cell alignment="center" valignment="top" usebox="none">
9699 \begin_layout Plain Layout
9700 \begin_inset Formula $\dot{A}$
9709 <row topspace="1.5mm">
9710 <cell alignment="center" valignment="top" usebox="none">
9713 \begin_layout Plain Layout
9717 \begin_inset space \textvisiblespace{}
9725 <cell alignment="center" valignment="top" usebox="none">
9728 \begin_layout Plain Layout
9729 \begin_inset Formula $\ddot{A}$
9738 <row topspace="1.5mm">
9739 <cell alignment="center" valignment="top" usebox="none">
9742 \begin_layout Plain Layout
9746 \begin_inset space \textvisiblespace{}
9754 <cell alignment="center" valignment="top" usebox="none">
9757 \begin_layout Plain Layout
9758 \begin_inset Formula $\dddot{A}$
9767 <row topspace="1.5mm">
9768 <cell alignment="center" valignment="top" usebox="none">
9771 \begin_layout Plain Layout
9775 \begin_inset space \textvisiblespace{}
9783 <cell alignment="center" valignment="top" usebox="none">
9786 \begin_layout Plain Layout
9787 \begin_inset Formula $\ddddot{A}$
9796 <row topspace="1.5mm">
9797 <cell alignment="center" valignment="top" usebox="none">
9800 \begin_layout Plain Layout
9804 \begin_inset space \textvisiblespace{}
9808 \begin_inset Index idx
9811 \begin_layout Plain Layout
9822 <cell alignment="center" valignment="top" usebox="none">
9825 \begin_layout Plain Layout
9826 \begin_inset Formula $\vec{A}$
9835 <row topspace="1.5mm">
9836 <cell alignment="center" valignment="top" usebox="none">
9839 \begin_layout Plain Layout
9843 \begin_inset space \textvisiblespace{}
9851 <cell alignment="center" valignment="top" usebox="none">
9854 \begin_layout Plain Layout
9855 \begin_inset Formula $\bar{A}$
9864 <row topspace="1.5mm">
9865 <cell alignment="center" valignment="top" bottomline="true" usebox="none">
9868 \begin_layout Plain Layout
9872 \begin_inset space \textvisiblespace{}
9880 <cell alignment="center" valignment="top" bottomline="true" usebox="none">
9883 \begin_layout Plain Layout
9884 \begin_inset Formula $\mathring{A}$
9898 \begin_inset space \hfill{}
9902 \begin_inset Tabular
9903 <lyxtabular version="3" rows="7" columns="2">
9904 <features booktabs="true" tabularvalignment="middle">
9905 <column alignment="center" valignment="top" width="0pt">
9906 <column alignment="center" valignment="top" width="0pt">
9908 <cell alignment="center" valignment="top" topline="true" bottomline="true" usebox="none">
9911 \begin_layout Plain Layout
9917 <cell alignment="center" valignment="top" topline="true" bottomline="true" usebox="none">
9920 \begin_layout Plain Layout
9927 <row topspace="1.5mm">
9928 <cell alignment="center" valignment="top" usebox="none">
9931 \begin_layout Plain Layout
9935 \begin_inset space \textvisiblespace{}
9943 <cell alignment="center" valignment="top" usebox="none">
9946 \begin_layout Plain Layout
9947 \begin_inset Formula $\tilde{A}$
9956 <row topspace="1.5mm">
9957 <cell alignment="center" valignment="top" usebox="none">
9960 \begin_layout Plain Layout
9964 \begin_inset space \textvisiblespace{}
9972 <cell alignment="center" valignment="top" usebox="none">
9975 \begin_layout Plain Layout
9976 \begin_inset Formula $\hat{A}$
9985 <row topspace="1.5mm">
9986 <cell alignment="center" valignment="top" usebox="none">
9989 \begin_layout Plain Layout
9993 \begin_inset space \textvisiblespace{}
10001 <cell alignment="center" valignment="top" usebox="none">
10004 \begin_layout Plain Layout
10005 \begin_inset Formula $\check{A}$
10014 <row topspace="1.5mm">
10015 <cell alignment="center" valignment="top" usebox="none">
10018 \begin_layout Plain Layout
10022 \begin_inset space \textvisiblespace{}
10030 <cell alignment="center" valignment="top" usebox="none">
10033 \begin_layout Plain Layout
10034 \begin_inset Formula $\acute{A}$
10043 <row topspace="1.5mm">
10044 <cell alignment="center" valignment="top" usebox="none">
10047 \begin_layout Plain Layout
10051 \begin_inset space \textvisiblespace{}
10059 <cell alignment="center" valignment="top" usebox="none">
10062 \begin_layout Plain Layout
10063 \begin_inset Formula $\grave{A}$
10072 <row topspace="1.5mm">
10073 <cell alignment="center" valignment="top" bottomline="true" usebox="none">
10076 \begin_layout Plain Layout
10080 \begin_inset space \textvisiblespace{}
10088 <cell alignment="center" valignment="top" bottomline="true" usebox="none">
10091 \begin_layout Plain Layout
10092 \begin_inset Formula $\breve{A}$
10106 \begin_inset space \hfill{}
10112 \begin_layout Standard
10113 \begin_inset VSpace bigskip
10119 \begin_layout Standard
10120 You can directly insert accents like é to formulas.
10122 will transform them to the corresponding accent command.
10124 \begin_inset Index idx
10127 \begin_layout Plain Layout
10133 it is better to insert a quotation mark before the vowel.
10134 These two characters are then treated by \SpecialChar LaTeX
10139 character when the formula part with the umlaut is marked as German.
10147 \begin_inset Quotes eld
10151 \begin_inset Quotes erd
10154 umlauts are created as demonstrated in the following example:
10157 \begin_layout Standard
10158 \begin_inset VSpace -2mm
10164 \begin_layout Standard
10166 \begin_inset Tabular
10167 <lyxtabular version="3" rows="3" columns="2">
10168 <features booktabs="true" tabularvalignment="middle">
10169 <column alignment="center" valignment="top" width="0pt">
10170 <column alignment="center" valignment="top">
10172 <cell alignment="center" valignment="top" topline="true" bottomline="true" usebox="none">
10175 \begin_layout Plain Layout
10181 <cell alignment="center" valignment="top" topline="true" bottomline="true" usebox="none">
10184 \begin_layout Plain Layout
10192 <cell alignment="center" valignment="top" usebox="none">
10195 \begin_layout Plain Layout
10196 \begin_inset Quotes grd
10204 <cell alignment="center" valignment="top" usebox="none">
10207 \begin_layout Plain Layout
10208 \begin_inset space \hspace{}
10215 \begin_inset Formula $"i$
10224 <row topspace="1.5mm">
10225 <cell alignment="center" valignment="top" bottomline="true" usebox="none">
10228 \begin_layout Plain Layout
10232 \begin_inset space \textvisiblespace{}
10240 <cell alignment="center" valignment="top" bottomline="true" usebox="none">
10243 \begin_layout Plain Layout
10244 \begin_inset Formula $\ddot{i}$
10260 \begin_layout Standard
10261 Another advantage to
10267 is that umlauts can directly be converted to mathematical text because
10268 the accent commands above are
10274 in mathematical text
10277 To convert an accented character to mathematical text, only the character
10278 under the accent may be converted.
10279 This applies also for all other conversions, e.
10280 \begin_inset space \thinspace{}
10284 \begin_inset space \space{}
10290 \begin_layout Standard
10291 In mathematical text, umlauts and other accented characters can directly
10295 \begin_layout Standard
10296 \begin_inset VSpace bigskip
10302 \begin_layout Standard
10304 also supports a tilde under the character if the \SpecialChar LaTeX
10310 \begin_inset Index idx
10313 \begin_layout Plain Layout
10314 Packages ! undertilde
10319 is installed on your system:
10322 \begin_layout Standard
10326 \begin_layout Plain Layout
10336 \begin_inset Note Note
10339 \begin_layout Plain Layout
10340 The following table will only be displayed when the \SpecialChar LaTeX
10353 \begin_layout Standard
10356 \begin_inset Tabular
10357 <lyxtabular version="3" rows="2" columns="2">
10358 <features booktabs="true" tabularvalignment="middle">
10359 <column alignment="center" valignment="top" width="0pt">
10360 <column alignment="center" valignment="top" width="0pt">
10362 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
10365 \begin_layout Plain Layout
10371 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
10374 \begin_layout Plain Layout
10382 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
10385 \begin_layout Plain Layout
10389 \begin_inset space \textvisiblespace{}
10397 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
10400 \begin_layout Plain Layout
10401 \begin_inset Formula $\utilde{A}$
10417 \begin_layout Standard
10421 \begin_layout Plain Layout
10431 \begin_inset Note Note
10434 \begin_layout Plain Layout
10435 The following will be displayed when the \SpecialChar LaTeX
10448 \begin_layout Standard
10449 You need to install the \SpecialChar LaTeX
10454 to see the rest of this subsection in the output.
10457 \begin_layout Standard
10461 \begin_layout Plain Layout
10473 \begin_layout Standard
10474 \begin_inset Newpage newpage
10480 \begin_layout Subsection
10481 Accents for several Characters
10482 \begin_inset Index idx
10485 \begin_layout Plain Layout
10486 Accents ! for several characters
10494 \begin_layout Standard
10495 \begin_inset space \hfill{}
10499 \begin_inset Tabular
10500 <lyxtabular version="3" rows="5" columns="2">
10501 <features booktabs="true" tabularvalignment="middle">
10502 <column alignment="center" valignment="top" width="0pt">
10503 <column alignment="center" valignment="top" width="0pt">
10505 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
10508 \begin_layout Plain Layout
10514 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
10517 \begin_layout Plain Layout
10524 <row topspace="1.5mm">
10525 <cell alignment="center" valignment="top" usebox="none">
10528 \begin_layout Plain Layout
10532 \begin_inset space \textvisiblespace{}
10540 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
10543 \begin_layout Plain Layout
10544 \begin_inset Formula $\overleftarrow{A=B}$
10553 <row topspace="1.5mm">
10554 <cell alignment="center" valignment="top" usebox="none">
10557 \begin_layout Plain Layout
10561 \begin_inset space \textvisiblespace{}
10569 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
10572 \begin_layout Plain Layout
10573 \begin_inset Formula $\underleftarrow{A=B}$
10582 <row topspace="1.5mm">
10583 <cell alignment="center" valignment="top" usebox="none">
10586 \begin_layout Plain Layout
10590 \begin_inset space \textvisiblespace{}
10598 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
10601 \begin_layout Plain Layout
10602 \begin_inset Formula $\overleftrightarrow{A=B}$
10611 <row topspace="1.5mm" bottomspace="1mm">
10612 <cell alignment="center" valignment="top" bottomline="true" usebox="none">
10615 \begin_layout Plain Layout
10618 underleftrightarrow
10619 \begin_inset space \textvisiblespace{}
10627 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
10630 \begin_layout Plain Layout
10631 \begin_inset Formula $\underleftrightarrow{A=B}$
10645 \begin_inset space \hfill{}
10649 \begin_inset Tabular
10650 <lyxtabular version="3" rows="5" columns="2">
10651 <features booktabs="true" tabularvalignment="middle">
10652 <column alignment="center" valignment="top" width="0pt">
10653 <column alignment="center" valignment="top" width="0pt">
10655 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
10658 \begin_layout Plain Layout
10664 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
10667 \begin_layout Plain Layout
10674 <row topspace="1.5mm">
10675 <cell alignment="center" valignment="top" usebox="none">
10678 \begin_layout Plain Layout
10682 \begin_inset space \textvisiblespace{}
10690 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
10693 \begin_layout Plain Layout
10694 \begin_inset Formula $\overrightarrow{A=B}$
10703 <row topspace="1.5mm">
10704 <cell alignment="center" valignment="top" usebox="none">
10707 \begin_layout Plain Layout
10711 \begin_inset space \textvisiblespace{}
10719 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
10722 \begin_layout Plain Layout
10723 \begin_inset Formula $\underrightarrow{A=B}$
10732 <row topspace="1.5mm">
10733 <cell alignment="center" valignment="top" usebox="none">
10736 \begin_layout Plain Layout
10740 \begin_inset space \textvisiblespace{}
10748 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
10751 \begin_layout Plain Layout
10752 \begin_inset Formula $\widetilde{A=B}$
10761 <row topspace="1.5mm" bottomspace="1mm">
10762 <cell alignment="center" valignment="top" bottomline="true" usebox="none">
10765 \begin_layout Plain Layout
10769 \begin_inset space \textvisiblespace{}
10777 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
10780 \begin_layout Plain Layout
10781 \begin_inset Formula $\widehat{A=B}$
10795 \begin_inset space \hfill{}
10801 \begin_layout Standard
10802 \begin_inset VSpace medskip
10805 With these commands as many characters as you like can be accented.
10818 will only be set in the output with a length of three characters, as shown
10819 in the following example:
10820 \begin_inset Formula
10822 \widetilde{A+B=C-D}
10830 \begin_layout Standard
10838 \begin_inset Index idx
10841 \begin_layout Plain Layout
10856 \begin_inset Index idx
10859 \begin_layout Plain Layout
10867 described in the previous subsection it is also possible to accent several
10874 \begin_inset space \textvisiblespace{}
10878 \begin_inset Formula $\downarrow$
10884 \begin_inset Formula
10886 \underset{***}{A=B}
10894 \begin_layout Section
10896 \begin_inset CommandInset label
10898 name "subsec:Space"
10903 \begin_inset Index idx
10906 \begin_layout Plain Layout
10915 \begin_layout Subsection
10917 \begin_inset CommandInset label
10919 name "subsec:Predefined-Space"
10924 \begin_inset Index idx
10927 \begin_layout Plain Layout
10928 Space ! horizontal ! predefined
10936 \begin_layout Standard
10937 Sometimes it is necessary to insert horizontal space into a formula.
10938 This is done by inserting a protected space (shortcut
10941 arg "command-alternatives space-insert protected ; math-space"
10946 \begin_inset Quotes eld
10952 \begin_inset space \textvisiblespace{}
10958 \begin_inset Quotes erd
10961 appears and by pressing
10965 several times one can select one of eight different space sizes.
10966 The spaces can also be inserted using the math toolbar button
10969 arg "math-insert \\space"
10972 or special commands.
10973 Independent from the inserted command, one can select the size again by
10981 \begin_layout Standard
10984 \begin_inset Tabular
10985 <lyxtabular version="3" rows="6" columns="3">
10986 <features booktabs="true" tabularvalignment="middle">
10987 <column alignment="center" valignment="top">
10988 <column alignment="center" valignment="top" width="15col%">
10989 <column alignment="center" valignment="top">
10991 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
10994 \begin_layout Plain Layout
11000 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
11003 \begin_layout Plain Layout
11013 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
11016 \begin_layout Plain Layout
11024 <cell alignment="center" valignment="top" leftline="true" usebox="none">
11027 \begin_layout Plain Layout
11035 <cell alignment="center" valignment="top" leftline="true" usebox="none">
11038 \begin_layout Plain Layout
11044 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
11047 \begin_layout Plain Layout
11048 \begin_inset Formula $A\,B$
11058 <cell alignment="center" valignment="top" leftline="true" usebox="none">
11061 \begin_layout Plain Layout
11069 <cell alignment="center" valignment="top" leftline="true" usebox="none">
11072 \begin_layout Plain Layout
11078 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
11081 \begin_layout Plain Layout
11082 \begin_inset Formula $A\:B$
11092 <cell alignment="center" valignment="top" leftline="true" usebox="none">
11095 \begin_layout Plain Layout
11103 <cell alignment="center" valignment="top" leftline="true" usebox="none">
11106 \begin_layout Plain Layout
11112 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
11115 \begin_layout Plain Layout
11116 \begin_inset Formula $A\;B$
11126 <cell alignment="center" valignment="top" leftline="true" usebox="none">
11129 \begin_layout Plain Layout
11137 <cell alignment="center" valignment="top" leftline="true" usebox="none">
11140 \begin_layout Plain Layout
11146 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
11149 \begin_layout Plain Layout
11150 \begin_inset Formula $A\quad B$
11160 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
11163 \begin_layout Plain Layout
11171 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
11174 \begin_layout Plain Layout
11180 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
11183 \begin_layout Plain Layout
11184 \begin_inset Formula $A\qquad B$
11198 \begin_inset space \hfill{}
11202 \begin_inset Tabular
11203 <lyxtabular version="3" rows="6" columns="3">
11204 <features booktabs="true" tabularvalignment="middle">
11205 <column alignment="center" valignment="top">
11206 <column alignment="center" valignment="top" width="15col%">
11207 <column alignment="center" valignment="top">
11209 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
11212 \begin_layout Plain Layout
11218 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
11221 \begin_layout Plain Layout
11231 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
11234 \begin_layout Plain Layout
11242 <cell alignment="center" valignment="top" leftline="true" usebox="none">
11245 \begin_layout Plain Layout
11253 <cell alignment="center" valignment="top" leftline="true" usebox="none">
11256 \begin_layout Plain Layout
11262 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
11265 \begin_layout Plain Layout
11266 \begin_inset Formula $A\hfill B$
11276 <cell alignment="center" valignment="top" leftline="true" usebox="none">
11279 \begin_layout Plain Layout
11287 <cell alignment="center" valignment="top" leftline="true" usebox="none">
11290 \begin_layout Plain Layout
11296 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
11299 \begin_layout Plain Layout
11300 \begin_inset Formula $A\hspace*{1em}B$
11310 <cell alignment="center" valignment="top" leftline="true" usebox="none">
11313 \begin_layout Plain Layout
11321 <cell alignment="center" valignment="top" leftline="true" usebox="none">
11324 \begin_layout Plain Layout
11330 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
11333 \begin_layout Plain Layout
11334 \begin_inset Formula $A\hspace{1em}B$
11344 <cell alignment="center" valignment="top" leftline="true" usebox="none">
11347 \begin_layout Plain Layout
11351 \begin_inset space \textvisiblespace{}
11359 <cell alignment="center" valignment="top" leftline="true" usebox="none">
11362 \begin_layout Plain Layout
11368 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
11371 \begin_layout Plain Layout
11372 \begin_inset Formula $A\ B$
11382 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
11385 \begin_layout Plain Layout
11393 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
11396 \begin_layout Plain Layout
11402 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
11405 \begin_layout Plain Layout
11406 \begin_inset Formula $A\!B$
11422 \begin_layout Standard
11424 \begin_inset space ~
11428 \begin_inset space \thinspace{}
11432 \begin_inset space \thinspace{}
11435 7 are variable spaces which are explained in
11436 \begin_inset CommandInset ref
11438 reference "subsec:Variable-Space"
11444 \begin_inset space ~
11447 9 seems to produce no space.
11448 It is displayed red in \SpecialChar LyX
11449 contrary to the other sizes, because it is a negative
11451 There are two more negative spaces:
11454 \begin_layout Standard
11456 \begin_inset Tabular
11457 <lyxtabular version="3" rows="3" columns="3">
11458 <features booktabs="true" tabularvalignment="middle">
11459 <column alignment="center" valignment="middle" width="6.8cm">
11460 <column alignment="center" valignment="top" width="0pt">
11461 <column alignment="center" valignment="top" width="0pt">
11463 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
11466 \begin_layout Plain Layout
11472 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
11475 \begin_layout Plain Layout
11483 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
11486 \begin_layout Plain Layout
11496 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
11499 \begin_layout Plain Layout
11504 keystrokes after inserting the protected space
11509 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
11512 \begin_layout Plain Layout
11518 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
11521 \begin_layout Plain Layout
11529 <cell multicolumn="1" alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
11532 \begin_layout Plain Layout
11538 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
11541 \begin_layout Plain Layout
11542 \begin_inset Formula $A\negmedspace B$
11550 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
11553 \begin_layout Plain Layout
11554 \begin_inset Formula $A\negthickspace B$
11570 \begin_layout Standard
11571 Negative spaces can lead to characters overlapping each other.
11572 Thus they can be used to enforce ligatures, which are e.
11573 \begin_inset space \thinspace{}
11577 \begin_inset space \space{}
11580 useful for summation operators:
11583 \begin_layout Standard
11585 \begin_inset Tabular
11586 <lyxtabular version="3" rows="3" columns="2">
11587 <features booktabs="true" tabularvalignment="middle">
11588 <column alignment="center" valignment="top" width="0pt">
11589 <column alignment="center" valignment="top">
11591 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
11594 \begin_layout Plain Layout
11600 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
11603 \begin_layout Plain Layout
11611 <cell alignment="center" valignment="top" leftline="true" usebox="none">
11614 \begin_layout Plain Layout
11620 \begin_inset space \textvisiblespace{}
11628 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
11631 \begin_layout Plain Layout
11632 \begin_inset Formula $\sum\sum f_{kl}$
11642 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
11645 \begin_layout Plain Layout
11653 \begin_inset space \textvisiblespace{}
11661 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
11664 \begin_layout Plain Layout
11665 \begin_inset Formula $\sum\negmedspace\sum f_{kl}$
11681 \begin_layout Standard
11683 \begin_inset VSpace medskip
11689 \begin_layout Standard
11691 Relations like for example equal signs, are always surrounded by space.
11692 To suppress this, the equal sign is placed into a \SpecialChar TeX
11694 The following example demonstrates this:
11697 \begin_layout Standard
11699 \begin_inset Tabular
11700 <lyxtabular version="3" rows="2" columns="2">
11701 <features tabularvalignment="middle">
11702 <column alignment="center" valignment="top" width="0pt">
11703 <column alignment="center" valignment="top" width="0pt">
11705 <cell alignment="center" valignment="top" usebox="none">
11708 \begin_layout Plain Layout
11714 <cell alignment="center" valignment="top" usebox="none">
11717 \begin_layout Plain Layout
11718 \begin_inset Formula $A=B$
11728 <cell alignment="center" valignment="top" usebox="none">
11731 \begin_layout Plain Layout
11732 equation without space
11737 <cell multicolumn="1" alignment="center" valignment="top" usebox="none">
11740 \begin_layout Plain Layout
11741 \begin_inset Formula $A{=}B$
11757 \begin_layout Standard
11759 The command for the last formula is:
11764 \begin_inset Formula $\to$
11770 \begin_layout Standard
11771 \begin_inset VSpace bigskip
11777 \begin_layout Standard
11778 Spaces are needed for physical units, because the space between the value
11779 and the unit is the smallest one and not a normal space.
11780 For units in text, the smallest space is inserted via the menu
11782 Insert\SpecialChar menuseparator
11783 Formatting\SpecialChar menuseparator
11785 \begin_inset space ~
11793 arg "space-insert thin"
11799 \begin_layout Standard
11800 An example to visualize the difference:
11803 \begin_layout Standard
11804 \begin_inset Tabular
11805 <lyxtabular version="3" rows="2" columns="2">
11806 <features tabularvalignment="middle">
11807 <column alignment="left" valignment="top">
11808 <column alignment="left" valignment="top">
11810 <cell alignment="center" valignment="top" usebox="none">
11813 \begin_layout Plain Layout
11815 \begin_inset Formula $\cdot$
11823 <cell alignment="center" valignment="top" usebox="none">
11826 \begin_layout Plain Layout
11827 space between value and unit
11834 <cell alignment="center" valignment="top" usebox="none">
11837 \begin_layout Plain Layout
11839 \begin_inset space \thinspace{}
11843 \begin_inset Formula $\cdot$
11851 <cell alignment="center" valignment="top" usebox="none">
11854 \begin_layout Plain Layout
11855 smallest space between value and unit
11868 \begin_layout Subsection
11873 \begin_layout Plain Layout
11886 \begin_layout Plain Layout
11887 for vertical space in formulas see
11888 \begin_inset CommandInset ref
11890 reference "subsec:Line-Separation"
11903 \begin_layout Plain Layout
11911 \begin_inset Note Note
11914 \begin_layout Plain Layout
11917 texorpdfstring is used to avoid that the footnote appears in the PDF-bookmark.
11920 \begin_layout Plain Layout
11923 texorpdfstring is in section
11924 \begin_inset CommandInset ref
11926 reference "subsec:Formulas-in-Section"
11936 \begin_inset CommandInset label
11938 name "subsec:Variable-Space"
11943 \begin_inset Index idx
11946 \begin_layout Plain Layout
11947 Space ! horizontal ! variable
11955 \begin_layout Standard
11956 Space with a defined length can be inserted with the command
11963 \begin_inset Index idx
11966 \begin_layout Plain Layout
11976 \begin_inset Quotes eld
11982 \begin_inset space \textvisiblespace{}
11988 \begin_inset Quotes erd
11992 The length can be specified by left-clicking on the
11993 \begin_inset Quotes eld
11999 \begin_inset space \textvisiblespace{}
12005 \begin_inset Quotes erd
12009 The length may also be negative.
12010 When a space would be the first character in a line it would be omitted.
12011 To force its output use the command
12023 or left-click on the
12024 \begin_inset Quotes eld
12030 \begin_inset space \textvisiblespace{}
12036 \begin_inset Quotes erd
12039 and check the option
12044 \begin_inset Newline newline
12047 To insert as much space as is available, the command
12054 \begin_inset Index idx
12057 \begin_layout Plain Layout
12068 \begin_layout Standard
12070 \begin_inset Tabular
12071 <lyxtabular version="3" rows="4" columns="2">
12072 <features booktabs="true" tabularvalignment="middle">
12073 <column alignment="center" valignment="top" width="0pt">
12074 <column alignment="center" valignment="top">
12076 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
12079 \begin_layout Plain Layout
12087 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
12090 \begin_layout Plain Layout
12098 <cell alignment="center" valignment="top" leftline="true" usebox="none">
12101 \begin_layout Plain Layout
12105 \begin_inset space \textvisiblespace{}
12111 \begin_inset space \thinspace{}
12119 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
12122 \begin_layout Plain Layout
12123 \begin_inset Formula $A=B\hspace{3cm}A\not=C$
12133 <cell alignment="center" valignment="top" leftline="true" usebox="none">
12136 \begin_layout Plain Layout
12140 \begin_inset space \textvisiblespace{}
12146 \begin_inset space \thinspace{}
12154 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
12157 \begin_layout Plain Layout
12158 \begin_inset Formula $A\hspace{-1mm}A\not=A$
12168 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
12171 \begin_layout Plain Layout
12175 \begin_inset space \textvisiblespace{}
12183 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
12186 \begin_layout Plain Layout
12187 \begin_inset Formula $A=A\hfill B=B$
12203 \begin_layout Standard
12204 In the last example the available space is given by the longest column entry
12206 In an inline formula the space depends on the length of the line in which
12214 Thus, when the line uses the full width, no space will be created.
12221 only has an effect on displayed formulas when the formula style
12226 (Formula styles are explained in
12227 \begin_inset CommandInset ref
12229 reference "sec:Formula-Styles"
12236 \begin_layout Standard
12243 , there are the commands
12255 that fill the space with a pattern, see
12256 \begin_inset CommandInset ref
12258 reference "subsec:Ellipses"
12265 \begin_layout Standard
12266 For text, variable space can be inserted via the menu
12268 Insert\SpecialChar menuseparator
12269 Formatting\SpecialChar menuseparator
12271 \begin_inset space ~
12279 \begin_layout Standard
12280 This is a line with
12281 \begin_inset space \hspace{}
12286 \begin_inset space \thinspace{}
12292 \begin_layout Standard
12293 This is a line with
12294 \begin_inset space \hfill{}
12300 \begin_layout Subsection
12301 Space besides inline Formulas
12302 \begin_inset Index idx
12305 \begin_layout Plain Layout
12306 Space ! besides inline formulas
12314 \begin_layout Standard
12315 The space that surrounds inline formulas can be adjusted with the length
12323 \begin_inset Index idx
12326 \begin_layout Plain Layout
12335 The value of a length is set with the command
12342 \begin_inset Index idx
12345 \begin_layout Plain Layout
12353 which has the following scheme:
12356 \begin_layout Standard
12361 setlength{length name}{value}
12364 \begin_layout Standard
12372 \begin_inset space \thinspace{}
12378 \begin_layout Standard
12388 \begin_layout Standard
12389 is inserted in \SpecialChar TeX
12392 \begin_inset space \thinspace{}
12395 mm space will now be set around all inline formulas:
12399 \begin_layout Plain Layout
12413 \begin_layout Standard
12414 This is a line with an inline formula
12415 \begin_inset Formula $A=B$
12419 \begin_inset space \thinspace{}
12422 mm surrounding space.
12426 \begin_layout Plain Layout
12440 \begin_layout Standard
12441 To return to the predefined value,
12447 is set to the value 0
12448 \begin_inset space \thinspace{}
12454 \begin_layout Standard
12455 \begin_inset Newpage newpage
12461 \begin_layout Section
12463 \begin_inset Index idx
12466 \begin_layout Plain Layout
12473 \begin_inset Index idx
12476 \begin_layout Plain Layout
12481 \begin_layout Plain Layout
12492 \begin_layout Plain Layout
12507 \begin_layout Standard
12508 Boxes for text are described in chapter
12515 \begin_inset space ~
12523 \begin_layout Subsection
12525 \begin_inset CommandInset label
12527 name "subsec:Boxes-with-Frame"
12532 \begin_inset Index idx
12535 \begin_layout Plain Layout
12544 \begin_layout Standard
12545 It is possible to frame a formula or part of one with the commands
12552 \begin_inset Index idx
12555 \begin_layout Plain Layout
12570 \begin_inset Index idx
12573 \begin_layout Plain Layout
12584 \begin_layout Standard
12585 When one of these commands is inserted in a formula, a blue box appears
12586 within a frame to enter formula parts.
12593 an additional formula has to be created by
12597 within this box, because the box content will otherwise be treated as mathemati
12605 is used, a new formula is automatically created inside the frame.
12608 \begin_layout Standard
12615 is not suitable to frame displayed formulas because the formula will always
12616 be set in the size of the text.
12623 is in contrary not suitable to frame inline formulas, because the formula
12624 will always be set in the size of a displayed formula.
12627 \begin_layout Standard
12641 \begin_inset Index idx
12644 \begin_layout Plain Layout
12652 where additionally the frame width and the alignment can be specified.
12659 is used in the following scheme:
12662 \begin_layout Standard
12667 framebox[frame width][position]{box content}
12670 \begin_layout Standard
12671 The position can either be
12688 right aligns the formula in the box.
12689 When no position is given, the formula will be centered.
12690 \begin_inset Newline newline
12693 If no width is given, also no position can be given.
12694 In this case the frame width is adjusted to the box content like for
12703 \begin_layout Standard
12710 is inserted, a box appears containing three blue boxes.
12711 The first two boxes are surrounded by brackets and denote the two optional
12713 The third box is for formula parts like for
12722 \begin_layout Standard
12724 \begin_inset Tabular
12725 <lyxtabular version="3" rows="5" columns="2">
12726 <features booktabs="true" tabularvalignment="middle">
12727 <column alignment="center" valignment="top" width="0pt">
12728 <column alignment="center" valignment="top">
12730 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
12733 \begin_layout Plain Layout
12739 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
12742 \begin_layout Plain Layout
12749 <row topspace="1.5mm">
12750 <cell alignment="center" valignment="top" usebox="none">
12753 \begin_layout Plain Layout
12757 \begin_inset space \textvisiblespace{}
12767 \begin_inset space \textvisiblespace{}
12775 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
12778 \begin_layout Plain Layout
12779 \begin_inset Formula $\fbox{\ensuremath{\int A=B}}$
12788 <row topspace="1.5mm">
12789 <cell alignment="center" valignment="top" usebox="none">
12792 \begin_layout Plain Layout
12796 \begin_inset space \textvisiblespace{}
12802 \begin_inset space \textvisiblespace{}
12810 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
12813 \begin_layout Plain Layout
12814 \begin_inset Formula $\boxed{\int A=B}$
12823 <row topspace="1.5mm">
12824 <cell alignment="center" valignment="top" usebox="none">
12827 \begin_layout Plain Layout
12831 \begin_inset space \textvisiblespace{}
12839 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
12842 \begin_layout Plain Layout
12843 \begin_inset Formula $A+\fbox{B}$
12852 <row topspace="1.5mm" bottomspace="1mm">
12853 <cell alignment="center" valignment="top" bottomline="true" usebox="none">
12856 \begin_layout Plain Layout
12860 \begin_inset space \textvisiblespace{}
12864 \begin_inset Formula $\to$
12868 \begin_inset Formula $\to$
12878 \begin_inset space \textvisiblespace{}
12882 \begin_inset Formula $\downarrow$
12890 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
12893 \begin_layout Plain Layout
12894 \begin_inset Formula $\framebox[20mm][]{\ensuremath{\frac{A}{B}}}$
12910 \begin_layout Standard
12911 The frame thickness can also be adjusted.
12912 To do this the following commands have to be inserted in \SpecialChar TeX
12917 \begin_layout Standard
12927 \begin_inset Quotes eld
12931 \begin_inset Quotes erd
12945 \begin_inset Quotes eld
12949 \begin_inset Quotes erd
12955 \begin_layout Standard
12956 \begin_inset Quotes eld
12960 \begin_inset Quotes erd
12963 specifies the minimal distance between the frame and the first character
12965 An example for this is the following framed formula:
12969 \begin_layout Plain Layout
12981 \begin_inset Formula
12988 Before this formula the commands
12991 \begin_layout Standard
13013 \begin_layout Standard
13014 were inserted in \SpecialChar TeX
13016 The given values are used for all following boxes.
13019 \begin_layout Standard
13020 To return to the standard frame size, the command
13023 \begin_layout Standard
13048 \begin_layout Plain Layout
13062 \begin_layout Standard
13063 is inserted in \SpecialChar TeX
13064 mode before the next formula.
13067 \begin_layout Subsection
13068 Boxes without Frame
13069 \begin_inset CommandInset label
13071 name "subsec:Boxes-without-Frame"
13076 \begin_inset Index idx
13079 \begin_layout Plain Layout
13080 Boxes ! without frame
13088 \begin_layout Standard
13089 For boxes without a frame there are the following box commands:
13096 \begin_inset Index idx
13099 \begin_layout Plain Layout
13114 \begin_inset Index idx
13117 \begin_layout Plain Layout
13132 \begin_inset Index idx
13135 \begin_layout Plain Layout
13146 \begin_layout Standard
13153 a box can be super- or subscripted.
13154 But in contrary to normal super- and subscripting, the characters in the
13155 box keep their font size.
13162 is used in the following scheme:
13165 \begin_layout Standard
13170 raisebox{height}{box content}
13173 \begin_layout Standard
13174 When the box should contain a formula, an extra formula is needed like for
13185 \begin_inset Note Greyedout
13188 \begin_layout Plain Layout
13199 this extra formula is created by pressing
13203 twice instead of once because \SpecialChar LyX
13204 doesn't yet support
13220 \begin_layout Standard
13222 \begin_inset Tabular
13223 <lyxtabular version="3" rows="4" columns="2">
13224 <features booktabs="true" tabularvalignment="middle">
13225 <column alignment="center" valignment="top" width="0pt">
13226 <column alignment="center" valignment="top">
13228 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
13231 \begin_layout Plain Layout
13237 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
13240 \begin_layout Plain Layout
13248 <cell alignment="center" valignment="top" leftline="true" usebox="none">
13251 \begin_layout Plain Layout
13255 \begin_inset Formula $\to$
13261 \begin_inset Formula $\to$
13269 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
13272 \begin_layout Plain Layout
13273 \begin_inset Formula $H\raisebox{2mm}{al}lo$
13283 <cell alignment="center" valignment="top" leftline="true" usebox="none">
13286 \begin_layout Plain Layout
13290 \begin_inset Formula $\to$
13296 \begin_inset Formula $\to$
13304 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
13307 \begin_layout Plain Layout
13308 \begin_inset Formula $H\raisebox{-2mm}{al}lo$
13318 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
13321 \begin_layout Plain Layout
13325 \begin_inset Formula $\to$
13341 \begin_inset space \textvisiblespace{}
13349 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
13352 \begin_layout Plain Layout
13353 \begin_inset Formula $A=\raisebox{-2mm}{\mbox{\ensuremath{\sqrt{B}}}}$
13369 \begin_layout Standard
13394 , with the difference that there is no frame.
13397 \begin_layout Subsection
13399 \begin_inset CommandInset label
13401 name "subsec:Colored-Boxes"
13406 \begin_inset Index idx
13409 \begin_layout Plain Layout
13418 \begin_layout Standard
13419 To be able to use all commands explained in this section, the \SpecialChar LaTeX
13428 \begin_layout Plain Layout
13429 The \SpecialChar LaTeX
13434 is part of every \SpecialChar LaTeX
13435 standard installation.
13441 \begin_inset Index idx
13444 \begin_layout Plain Layout
13450 has to be loaded in the \SpecialChar LaTeX
13451 -preamble with the line
13455 \begin_layout Plain Layout
13456 When text is colored somewhere in the document with a predefined color,
13458 loads the \SpecialChar LaTeX
13464 Thus it is possible that the package is loaded twice, but this does not
13471 \begin_inset Note Note
13474 \begin_layout Plain Layout
13475 To avoid that the package is loaded twice, a macro was inserted to the \SpecialChar LaTeX
13484 \begin_layout Standard
13492 \begin_layout Standard
13493 \begin_inset VSpace medskip
13496 To color boxes, the command
13503 \begin_inset Index idx
13506 \begin_layout Plain Layout
13514 is used in the following scheme:
13517 \begin_layout Standard
13522 colorbox{color}{box content}
13525 \begin_layout Standard
13526 The box content can also be a box and a
13532 can also be part of another box (see the 2nd and 3rd example).
13533 When the box should contain a formula, an extra formula has to be created,
13534 the same way as for
13544 \begin_layout Plain Layout
13545 This also applies for the command
13559 \begin_layout Standard
13560 One of the following predefined colors can be chosen:
13563 \begin_layout Standard
13599 \begin_layout Standard
13601 \begin_inset Tabular
13602 <lyxtabular version="3" rows="4" columns="2">
13603 <features booktabs="true" tabularvalignment="middle">
13604 <column alignment="center" valignment="top" width="0pt">
13605 <column alignment="center" valignment="top">
13607 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
13610 \begin_layout Plain Layout
13616 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
13619 \begin_layout Plain Layout
13627 <cell alignment="center" valignment="top" leftline="true" usebox="none">
13630 \begin_layout Plain Layout
13634 \begin_inset Formula $\to$
13644 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
13647 \begin_layout Plain Layout
13648 \begin_inset Formula $\colorbox{yellow}{A=B}$
13657 <row topspace="1.5mm">
13658 <cell alignment="center" valignment="top" usebox="none">
13661 \begin_layout Plain Layout
13665 \begin_inset Formula $\to$
13673 \begin_inset space \textvisiblespace{}
13681 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
13684 \begin_layout Plain Layout
13685 \begin_inset Formula $\colorbox{green}{\fbox{A=B}}$
13694 <row topspace="1.5mm" bottomspace="1mm">
13695 <cell alignment="center" valignment="top" bottomline="true" usebox="none">
13698 \begin_layout Plain Layout
13702 \begin_inset space \textvisiblespace{}
13708 \begin_inset Formula $\to$
13724 \begin_inset space \textvisiblespace{}
13732 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
13735 \begin_layout Plain Layout
13736 \begin_inset Formula $\fbox{\colorbox{green}{\mbox{\ensuremath{\int C=D}}}}$
13752 \begin_layout Standard
13759 only colors the box but not the characters in the box.
13760 To color all characters, the whole formula is highlighted and the desired
13761 color is chosen in the
13764 \begin_inset space ~
13770 The dialog can be called with the toolbar button
13773 arg "dialog-show character"
13778 Edit\SpecialChar menuseparator
13780 \begin_inset space ~
13783 Style\SpecialChar menuseparator
13787 The formula number then has the same color as the formula.
13788 When the formula number should get another color than the formula characters,
13789 the color must be changed within the formula.
13792 \begin_layout Standard
13796 \begin_layout Standard
13799 \begin_inset Formula
13801 \int A=B\label{eq:red}
13809 \begin_inset Formula
13811 \textcolor{red}{\int A=B}\label{eq:redgreen}
13819 \begin_layout Standard
13821 \begin_inset CommandInset ref
13827 is completely colored red.
13828 \begin_inset Newline newline
13832 \begin_inset CommandInset ref
13834 reference "eq:redgreen"
13838 was first completely colored green to set the color for the formula number.
13839 Subsequently the formula characters were colored red.
13842 \begin_layout Standard
13843 \begin_inset VSpace bigskip
13846 To color the frame different than the rest of the box, the command
13853 \begin_inset Index idx
13856 \begin_layout Plain Layout
13864 is used in the following scheme:
13867 \begin_layout Standard
13872 fcolorbox{frame color}{color}{box content}
13875 \begin_layout Standard
13882 is an extension of the command
13889 The frame width is set, like for
13912 \begin_layout Plain Layout
13924 \begin_inset Formula
13926 \fcolorbox{cyan}{magenta}{A=B}
13935 \begin_layout Plain Layout
13949 \begin_layout Standard
13950 This formula was created with the command
13951 \begin_inset Newline newline
13959 \begin_inset Formula $\to$
13965 \begin_inset Formula $\to$
13975 \begin_layout Standard
13976 \begin_inset VSpace bigskip
13979 To use other colors than the predefined ones, they have to be defined first.
13982 \begin_layout Standard
13983 One can for example define the color
13984 \begin_inset Quotes eld
13992 \begin_inset Quotes erd
13995 with the \SpecialChar LaTeX
13999 \begin_layout Standard
14004 definecolor{darkgreen}{cmyk}{0.5,
14019 \begin_inset Index idx
14022 \begin_layout Plain Layout
14033 \begin_layout Standard
14038 is the color space that denotes the colors
14055 The four comma separated numbers are the portion factor for the corresponding
14056 colors of the color space.
14057 The factors can be in the range of 0
14058 \begin_inset space \thinspace{}
14062 \begin_inset space \thinspace{}
14070 also the color space
14074 can be used for definitions.
14091 , so that there are in this case three portion factors for the corresponding
14093 Furthermore there is the color space
14097 with one portion factor for the gray value.
14100 \begin_layout Standard
14101 As example a framed box with the new defined color
14105 where the characters have been colored
14110 \begin_inset Formula
14112 \colorbox{darkgreen}{\color{yellow}\boxed{\int A\,\mathrm{d}x=\frac{\sqrt[5]{B}}{\ln\left(\frac{1}{3}\right)}}}
14120 \begin_layout Standard
14121 Self-defined colors can also be used for text with the help of the command
14129 \begin_inset Index idx
14132 \begin_layout Plain Layout
14141 \begin_layout Standard
14145 \begin_layout Plain Layout
14149 textcolor{darkgreen}{
14155 \begin_inset Quotes eld
14159 \begin_inset Quotes erd
14166 \begin_layout Plain Layout
14176 \begin_layout Standard
14184 \begin_inset Index idx
14187 \begin_layout Plain Layout
14195 is used in the scheme
14199 textcolor{color}{characters to color}
14204 \begin_layout Subsection
14206 \begin_inset CommandInset label
14208 name "subsec:Paragraph-Boxes"
14213 \begin_inset Index idx
14216 \begin_layout Plain Layout
14217 Boxes ! as paragraph
14225 \begin_layout Standard
14226 A box that can contain several lines and paragraphs, a so-called paragraph
14227 box (parbox), can be created with the menu
14229 Insert\SpecialChar menuseparator
14232 or the toolbar button
14241 \begin_layout Standard
14242 The following example shows a framed parbox in a line:
14245 \begin_layout Standard
14246 \begin_inset VSpace medskip
14250 \begin_inset Box Boxed
14260 height_special "totalheight"
14265 backgroundcolor "none"
14268 \begin_layout Plain Layout
14269 This is a paragraph box.
14271 \begin_inset space \thinspace{}
14274 cm long and can also contain formulas:
14275 \begin_inset Formula $\int A\,\mathrm{d}s=C$
14286 \begin_layout Standard
14287 \begin_inset VSpace medskip
14293 \begin_layout Standard
14294 Such a box is created by right-clicking on the gray box inset.
14295 A dialog pops up showing the box properties.
14309 \begin_inset space \thinspace{}
14314 Vertical Box Alignment
14319 \begin_layout Standard
14320 \begin_inset VSpace medskip
14323 In \SpecialChar LaTeX
14324 a parbox is created with the command
14331 \begin_inset Index idx
14334 \begin_layout Plain Layout
14342 which has the following scheme:
14345 \begin_layout Standard
14350 parbox[position]{width}{box content}
14353 \begin_layout Standard
14368 \begin_inset Quotes eld
14372 \begin_inset Quotes erd
14375 means that the box is aligned within the surrounding text with its last
14382 \begin_inset Quotes eld
14386 \begin_inset Quotes erd
14389 this is done with the first line.
14390 When no position is given, the box will be vertically centered, see section
14398 \begin_inset space ~
14403 manual for examples.
14406 \begin_layout Standard
14407 \begin_inset VSpace bigskip
14410 To frame formulas completely, including the formula number, the formula
14411 must be set into a parbox.
14412 To do this, the command
14426 is inserted in \SpecialChar TeX
14427 mode before the formula.
14435 \begin_inset Index idx
14438 \begin_layout Plain Layout
14446 is hereby the line width set for the document.
14447 Because the frame is outside the parbox, 2
14448 \begin_inset space \thinspace{}
14451 times the frame separation and the frame thickness must be subtracted from
14453 To be able to multiply and subtract in arguments, the \SpecialChar LaTeX
14462 \begin_layout Plain Layout
14467 is part of every \SpecialChar LaTeX
14468 standard installation.
14474 \begin_inset Index idx
14477 \begin_layout Plain Layout
14483 must be loaded in the \SpecialChar LaTeX
14484 -preamble with the line
14487 \begin_layout Standard
14495 \begin_layout Standard
14496 Behind the formula both boxes are closed by entering
14500 in \SpecialChar TeX
14502 Here is an example:
14506 \begin_layout Plain Layout
14520 \begin_layout Standard
14524 \begin_layout Plain Layout
14542 \begin_inset Formula
14544 \int A\,\mathrm{d}x=\frac{\sqrt[5]{B}}{\ln\left(\frac{1}{3}\right)}
14553 \begin_layout Plain Layout
14564 \begin_layout Plain Layout
14578 \begin_layout Standard
14579 \begin_inset VSpace medskip
14582 As a parbox is used as the argument of
14588 , there is in this case no difference between
14603 \begin_layout Standard
14604 \begin_inset VSpace bigskip
14607 Paragraph boxes are very useful to comment formulas directly.
14614 is used in combination with the command
14628 \begin_inset CommandInset ref
14630 reference "subsec:User-defined-Numbering"
14637 \begin_layout Standard
14638 An example of a formula commented with
14647 \begin_layout Standard
14651 \begin_layout Plain Layout
14664 This is a description.
14665 It is distinctly separated from the formula and multiline.
14669 \begin_layout Plain Layout
14681 \begin_layout Standard
14682 Such a formula must be inserted completely in \SpecialChar TeX
14683 mode because \SpecialChar LyX
14685 support the command
14692 The formula is created with the following command sequence:
14695 \begin_layout Standard
14708 is inserted in \SpecialChar TeX
14713 \begin_layout Plain Layout
14714 When the formula style
14726 can also be replaced by
14733 (formula styles see
14734 \begin_inset CommandInset ref
14736 reference "sec:Formula-Styles"
14745 Then the description follows as normal text and finally
14751 is inserted in \SpecialChar TeX
14765 hereby create a displayed formula.
14768 \begin_layout Standard
14775 can be seen in this example that was
14776 \begin_inset Quotes eld
14780 \begin_inset Quotes erd
14783 using the mathematical textmode:
14784 \begin_inset Formula
14786 5x-7b=3b\textrm{This is a description. It is not separated from the formula ...}
14794 \begin_layout Section
14796 \begin_inset Index idx
14799 \begin_layout Plain Layout
14808 \begin_layout Subsection
14810 \begin_inset CommandInset label
14812 name "subsec:Big-Operators"
14817 \begin_inset Index idx
14820 \begin_layout Plain Layout
14827 \begin_inset Index idx
14830 \begin_layout Plain Layout
14837 \begin_inset Index idx
14840 \begin_layout Plain Layout
14849 \begin_layout Standard
14850 To be able to use all integral operators listed here, the option
14852 Use esint package automatically
14854 must be set in the document settings under
14857 \begin_inset space ~
14865 \begin_layout Standard
14866 \begin_inset space \hfill{}
14870 \begin_inset Tabular
14871 <lyxtabular version="3" rows="11" columns="2">
14872 <features booktabs="true" tabularvalignment="middle">
14873 <column alignment="center" valignment="top" width="0pt">
14874 <column alignment="center" valignment="top" width="0pt">
14876 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
14879 \begin_layout Plain Layout
14885 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
14888 \begin_layout Plain Layout
14896 <cell alignment="center" valignment="top" leftline="true" usebox="none">
14899 \begin_layout Plain Layout
14903 \begin_inset Index idx
14906 \begin_layout Plain Layout
14919 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
14922 \begin_layout Plain Layout
14923 \begin_inset Formula $\int$
14933 <cell alignment="center" valignment="top" leftline="true" usebox="none">
14936 \begin_layout Plain Layout
14944 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
14947 \begin_layout Plain Layout
14948 \begin_inset Formula $\oint$
14958 <cell alignment="center" valignment="top" leftline="true" usebox="none">
14961 \begin_layout Plain Layout
14969 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
14972 \begin_layout Plain Layout
14973 \begin_inset Formula $\ointctrclockwise$
14983 <cell alignment="center" valignment="top" leftline="true" usebox="none">
14986 \begin_layout Plain Layout
14994 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
14997 \begin_layout Plain Layout
14998 \begin_inset Formula $\ointclockwise$
15008 <cell alignment="center" valignment="top" leftline="true" usebox="none">
15011 \begin_layout Plain Layout
15019 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
15022 \begin_layout Plain Layout
15023 \begin_inset Formula $\sqint$
15033 <cell alignment="center" valignment="top" leftline="true" usebox="none">
15036 \begin_layout Plain Layout
15044 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
15047 \begin_layout Plain Layout
15049 \begin_inset Formula $\fint$
15059 <cell alignment="center" valignment="top" leftline="true" usebox="none">
15062 \begin_layout Plain Layout
15070 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
15073 \begin_layout Plain Layout
15075 \begin_inset Formula $\landupint$
15085 <cell alignment="center" valignment="top" leftline="true" usebox="none">
15088 \begin_layout Plain Layout
15096 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
15099 \begin_layout Plain Layout
15101 \begin_inset Formula $\landdownint$
15111 <cell alignment="center" valignment="top" leftline="true" usebox="none">
15114 \begin_layout Plain Layout
15122 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
15125 \begin_layout Plain Layout
15126 \begin_inset Formula $\bigcap$
15136 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
15139 \begin_layout Plain Layout
15147 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
15150 \begin_layout Plain Layout
15151 \begin_inset Formula $\bigcup$
15165 \begin_inset space \hfill{}
15169 \begin_inset Tabular
15170 <lyxtabular version="3" rows="11" columns="2">
15171 <features booktabs="true" tabularvalignment="middle">
15172 <column alignment="center" valignment="top" width="0pt">
15173 <column alignment="center" valignment="top" width="0pt">
15175 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
15178 \begin_layout Plain Layout
15184 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
15187 \begin_layout Plain Layout
15195 <cell alignment="center" valignment="top" leftline="true" usebox="none">
15198 \begin_layout Plain Layout
15202 \begin_inset Index idx
15205 \begin_layout Plain Layout
15218 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
15221 \begin_layout Plain Layout
15222 \begin_inset Formula $\sum$
15232 <cell alignment="center" valignment="top" leftline="true" usebox="none">
15235 \begin_layout Plain Layout
15239 \begin_inset Index idx
15242 \begin_layout Plain Layout
15249 \begin_layout Plain Layout
15268 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
15271 \begin_layout Plain Layout
15272 \begin_inset Formula $\prod$
15282 <cell alignment="center" valignment="top" leftline="true" usebox="none">
15285 \begin_layout Plain Layout
15293 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
15296 \begin_layout Plain Layout
15297 \begin_inset Formula $\coprod$
15307 <cell alignment="center" valignment="top" leftline="true" usebox="none">
15310 \begin_layout Plain Layout
15318 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
15321 \begin_layout Plain Layout
15322 \begin_inset Formula $\bigodot$
15332 <cell alignment="center" valignment="top" leftline="true" usebox="none">
15335 \begin_layout Plain Layout
15343 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
15346 \begin_layout Plain Layout
15347 \begin_inset Formula $\bigotimes$
15357 <cell alignment="center" valignment="top" leftline="true" usebox="none">
15360 \begin_layout Plain Layout
15368 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
15371 \begin_layout Plain Layout
15372 \begin_inset Formula $\bigoplus$
15382 <cell alignment="center" valignment="top" leftline="true" usebox="none">
15385 \begin_layout Plain Layout
15393 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
15396 \begin_layout Plain Layout
15397 \begin_inset Formula $\bigwedge$
15407 <cell alignment="center" valignment="top" leftline="true" usebox="none">
15410 \begin_layout Plain Layout
15418 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
15421 \begin_layout Plain Layout
15422 \begin_inset Formula $\bigvee$
15432 <cell alignment="center" valignment="top" leftline="true" usebox="none">
15435 \begin_layout Plain Layout
15443 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
15446 \begin_layout Plain Layout
15447 \begin_inset Formula $\bigsqcup$
15457 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
15460 \begin_layout Plain Layout
15468 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
15471 \begin_layout Plain Layout
15472 \begin_inset Formula $\biguplus$
15486 \begin_inset space \hfill{}
15492 \begin_layout Standard
15493 All big operators can also be inserted via the math toolbar button
15496 arg "math-insert \\intop"
15502 \begin_layout Standard
15503 The operators are called big because they are bigger than the sometimes
15504 equal looking binary operators.
15505 All big operators can have limits as described in the next subsection.
15508 \begin_layout Standard
15509 For all integral operators there is a second version available, ending in
15527 These operators are different from
15534 \begin_inset space \space{}
15537 in the style the operator limits are displayed, see
15538 \begin_inset CommandInset ref
15540 reference "subsec:Operator-Limits"
15548 \begin_layout Subsubsection*
15549 Advice for Integrals
15552 \begin_layout Standard
15557 in an integral is an operator, that therefore has to be set upright.
15558 This is done by highlighting the
15562 and using the keyboard shortcut
15572 \begin_layout Plain Layout
15578 \begin_inset CommandInset ref
15580 reference "subsec:Font-Styles"
15590 Finally the smallest space is inserted before the
15594 , as this is usual for operators.
15598 \begin_layout Standard
15600 \begin_inset Formula $\int A(x)dx$
15604 \begin_inset Newline newline
15608 \begin_inset Phantom HPhantom
15611 \begin_layout Plain Layout
15618 \begin_inset Formula $\int A(x)\,\mathrm{d}x$
15624 \begin_layout Standard
15625 For multiple integrals there are the following commands:
15626 \begin_inset VSpace medskip
15632 \begin_layout Standard
15633 \begin_inset space \hfill{}
15637 \begin_inset Tabular
15638 <lyxtabular version="3" rows="4" columns="2">
15639 <features booktabs="true" tabularvalignment="middle">
15640 <column alignment="center" valignment="top" width="0pt">
15641 <column alignment="center" valignment="top" width="0pt">
15643 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
15646 \begin_layout Plain Layout
15652 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
15655 \begin_layout Plain Layout
15662 <row bottomspace="1mm">
15663 <cell alignment="center" valignment="top" usebox="none">
15666 \begin_layout Plain Layout
15674 <cell alignment="center" valignment="top" usebox="none">
15677 \begin_layout Plain Layout
15678 \begin_inset Formula $\iint$
15687 <row bottomspace="1mm">
15688 <cell alignment="center" valignment="top" usebox="none">
15691 \begin_layout Plain Layout
15699 <cell alignment="center" valignment="top" usebox="none">
15702 \begin_layout Plain Layout
15703 \begin_inset Formula $\oiint$
15712 <row bottomspace="1mm">
15713 <cell alignment="center" valignment="top" bottomline="true" usebox="none">
15716 \begin_layout Plain Layout
15724 <cell alignment="center" valignment="top" bottomline="true" usebox="none">
15727 \begin_layout Plain Layout
15728 \begin_inset Formula $\sqiint$
15742 \begin_inset space \hfill{}
15746 \begin_inset Tabular
15747 <lyxtabular version="3" rows="4" columns="2">
15748 <features booktabs="true" tabularvalignment="middle">
15749 <column alignment="center" valignment="top" width="0pt">
15750 <column alignment="center" valignment="top" width="0pt">
15752 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
15755 \begin_layout Plain Layout
15761 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
15764 \begin_layout Plain Layout
15771 <row bottomspace="1mm">
15772 <cell alignment="center" valignment="top" usebox="none">
15775 \begin_layout Plain Layout
15783 <cell alignment="center" valignment="top" usebox="none">
15786 \begin_layout Plain Layout
15787 \begin_inset Formula $\iiint$
15796 <row bottomspace="1mm">
15797 <cell alignment="center" valignment="top" usebox="none">
15800 \begin_layout Plain Layout
15808 <cell alignment="center" valignment="top" usebox="none">
15811 \begin_layout Plain Layout
15812 \begin_inset Formula $\iiiint$
15821 <row bottomspace="1mm">
15822 <cell alignment="center" valignment="top" bottomline="true" usebox="none">
15825 \begin_layout Plain Layout
15833 <cell alignment="center" valignment="top" bottomline="true" usebox="none">
15836 \begin_layout Plain Layout
15837 \begin_inset Formula $\dotsint$
15851 \begin_inset space \hfill{}
15857 \begin_layout Subsection
15859 \begin_inset CommandInset label
15861 name "subsec:Operator-Limits"
15866 \begin_inset Index idx
15869 \begin_layout Plain Layout
15878 \begin_layout Standard
15879 Limits are created by super- and subscripts:
15882 \begin_layout Standard
15884 \begin_inset Tabular
15885 <lyxtabular version="3" rows="2" columns="2">
15886 <features booktabs="true" tabularvalignment="middle">
15887 <column alignment="center" valignment="top" width="0pt">
15888 <column alignment="center" valignment="top" width="0pt">
15890 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
15893 \begin_layout Plain Layout
15899 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
15902 \begin_layout Plain Layout
15910 <cell alignment="center" valignment="top" bottomline="true" usebox="none">
15913 \begin_layout Plain Layout
15919 \begin_inset space \textvisiblespace{}
15923 \begin_inset Formula $\to$
15927 \begin_inset Formula $\to$
15935 <cell alignment="center" valignment="top" bottomline="true" usebox="none">
15938 \begin_layout Plain Layout
15939 \begin_inset Formula $\prod_{0}^{\infty}A(x)$
15955 \begin_layout Standard
15956 Limits of inline formulas are set right beside the operator.
15957 Limits in displayed formulas are set above or below the operator, except
15958 for integral limits.
15961 \begin_layout Standard
15962 To force that the limits are set beside the operator, the cursor is set
15963 directly behind the operator and the limits type is changed with the menu
15966 Edit\SpecialChar menuseparator
15967 Math\SpecialChar menuseparator
15986 \begin_layout Standard
15987 The default limits type is this:
15988 \begin_inset Formula
15990 \sum_{x=0}^{\infty}\frac{1}{x^{2}}
15995 This is how it looks when the limits type was changed to
16002 \begin_inset Formula
16004 \sum\nolimits _{x=0}^{\infty}\frac{1}{x^{2}}
16009 For integrals, except those ending with
16025 etc., the limits are by default set beside the operator.
16026 But for multiple integrals the limits are often set below the operator.
16027 In the following example the limits type was therefore set to
16031 and so set below the integrals:
16032 \begin_inset Formula
16034 \iiint\limits _{V}X\,\mathrm{d}V=U\label{eq:VolInt}
16042 \begin_layout Standard
16043 \begin_inset VSpace medskip
16046 To specify conditions for limits, the commands
16053 \begin_inset Index idx
16056 \begin_layout Plain Layout
16071 \begin_inset Index idx
16074 \begin_layout Plain Layout
16083 To create for example this expression
16084 \begin_inset Formula
16086 \sum_{\begin{subarray}{c}
16090 \end{subarray}}^{n}k^{-2}\label{eq:substack}
16098 \begin_layout Standard
16099 the following has to be done:
16100 \begin_inset Newline newline
16112 \begin_inset space \textvisiblespace{}
16118 One is now in a blue box under the summation operator and insert there
16124 \begin_inset space \textvisiblespace{}
16130 The blue box is now within a purple box and now several lines can be written
16132 A new line is created by inserting a line break (
16135 arg "newline-insert newline"
16140 \begin_inset Newline newline
16145 0<k<1000 Ctrl+Return
16146 \begin_inset Newline newline
16151 is typed in, a new box appears below for the new line.
16154 \begin_layout Standard
16155 The alignment of the lines can be changed to left aligned with the
16165 Edit\SpecialChar menuseparator
16169 To get right alignment,
16174 \begin_inset space \textvisiblespace{}
16179 is inserted at the beginning of the line.
16182 \begin_layout Standard
16195 with the difference that the lines are always centered.
16198 \begin_layout Standard
16199 \begin_inset VSpace bigskip
16203 \begin_inset CommandInset ref
16205 reference "eq:substack"
16209 there can be too much space beside an operator, because the characters
16210 following the operator are set beside the limits.
16211 To avoid this the command
16218 \begin_inset Index idx
16221 \begin_layout Plain Layout
16230 To activate it, set in the document settings under
16233 \begin_inset space ~
16243 \begin_inset Index idx
16246 \begin_layout Plain Layout
16247 Packages ! mathtools
16255 \begin_inset space ~
16267 sets the space besides the operator to 0
16268 \begin_inset space \thinspace{}
16272 \begin_inset Newline newline
16276 \begin_inset CommandInset ref
16278 reference "eq:substack"
16282 , one uses the command
16285 \begin_layout Standard
16293 \begin_layout Standard
16294 and inserts the operator with its limits into the braces.
16295 Behind the brace one continues the formula:
16296 \begin_inset Formula
16298 \smashoperator{\sum_{\begin{subarray}{c}
16302 \end{subarray}}^{n}}k^{-2}
16310 \begin_layout Standard
16311 It is possible to set the space of only one side of the operator to 0
16312 \begin_inset space \thinspace{}
16316 To do this write either
16335 stands for the left and
16339 for the right side of the operator.
16340 Here is an example of the possible
16349 \begin_layout Standard
16350 \begin_inset Formula
16352 Y\smashoperator{\sum_{1\le i\le j\le n}^{n=3456}}X_{ij}=Y\smashoperator[l]{\sum_{1\le i\le j\le n}^{n=3456}}X_{ij}=Y\smashoperator[r]{\sum_{1\le i\le j\le n}^{n=3456}}X_{ij}
16360 \begin_layout Standard
16361 \begin_inset VSpace bigskip
16367 \begin_layout Standard
16368 When several consecutive operators have limits the typesetting of the limits
16369 looks often imperfect in the output, see this example:
16370 \begin_inset Formula
16372 \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}
16377 To improve the typesetting set in the document settings under
16380 \begin_inset space ~
16390 \begin_inset Index idx
16393 \begin_layout Plain Layout
16394 Packages ! mathtools
16402 \begin_inset space ~
16408 Then insert into your formula the command
16415 \begin_inset Index idx
16418 \begin_layout Plain Layout
16426 directly before the first operator.
16427 The example will then look like this:
16428 \begin_inset Formula
16430 \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}
16438 \begin_layout Standard
16439 \begin_inset VSpace bigskip
16442 How to use one limit for several operators is described in
16443 \begin_inset CommandInset ref
16445 reference "subsec:Self-defined-Operators"
16452 \begin_layout Subsection
16453 Decoration for Operators
16454 \begin_inset Index idx
16457 \begin_layout Plain Layout
16458 Operators ! Decoration
16466 \begin_layout Standard
16474 \begin_inset Index idx
16477 \begin_layout Plain Layout
16492 \begin_inset Index idx
16495 \begin_layout Plain Layout
16503 characters can be placed above or below an operator, respectively.
16511 \begin_inset Index idx
16514 \begin_layout Plain Layout
16522 characters can be set before and behind a big operator.
16525 \begin_layout Standard
16527 \begin_inset space ~
16539 \begin_layout Itemize
16546 is used to set characters at the corners of the operator
16549 \begin_layout Itemize
16556 is used to set characters before and/or behind the operator (this variant
16557 represents \SpecialChar LaTeX
16567 \begin_layout Itemize
16574 is used to set characters at the left corners and/or behind the operator
16577 \begin_layout Itemize
16584 is used to set characters at the right corners and/or before the operator
16587 \begin_layout Standard
16588 For example the command
16593 \begin_inset space \textvisiblespace{}
16599 \begin_inset space \textvisiblespace{}
16603 \begin_inset Formula $\to$
16607 \begin_inset Formula $\to$
16611 \begin_inset space \textvisiblespace{}
16621 \begin_inset Formula
16623 \sideset{}{'}\sum_{k=1}^{n}
16631 \begin_layout Standard
16632 \begin_inset Note Greyedout
16635 \begin_layout Plain Layout
16642 can only be used to decorate big operators, binary operators are not allowed.
16650 \begin_layout Standard
16663 can also be used to decorate symbols and characters.
16664 For example, the command
16669 \begin_inset space \textvisiblespace{}
16675 \begin_inset space \textvisiblespace{}
16681 \begin_inset Formula $\uparrow$
16689 \begin_inset Formula
16691 \overset{a}{\maltese}
16699 \begin_layout Subsection
16701 \begin_inset CommandInset label
16703 name "subsec:Binary-Operators"
16708 \begin_inset Index idx
16711 \begin_layout Plain Layout
16720 \begin_layout Standard
16721 Binary operators are surrounded by space when there is a character before
16723 \begin_inset VSpace medskip
16729 \begin_layout Standard
16730 \begin_inset Tabular
16731 <lyxtabular version="3" rows="13" columns="2">
16732 <features booktabs="true" tabularvalignment="middle">
16733 <column alignment="center" valignment="top" width="0pt">
16734 <column alignment="center" valignment="top" width="0pt">
16736 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
16739 \begin_layout Plain Layout
16741 \begin_inset Note Note
16744 \begin_layout Plain Layout
16751 is only used as spacer.
16761 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
16764 \begin_layout Plain Layout
16772 <cell alignment="center" valignment="top" leftline="true" usebox="none">
16775 \begin_layout Plain Layout
16781 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
16784 \begin_layout Plain Layout
16785 \begin_inset Formula $+$
16795 <cell alignment="center" valignment="top" leftline="true" usebox="none">
16798 \begin_layout Plain Layout
16804 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
16807 \begin_layout Plain Layout
16808 \begin_inset Formula $-$
16818 <cell alignment="center" valignment="top" leftline="true" usebox="none">
16821 \begin_layout Plain Layout
16829 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
16832 \begin_layout Plain Layout
16833 \begin_inset Formula $\pm$
16843 <cell alignment="center" valignment="top" leftline="true" usebox="none">
16846 \begin_layout Plain Layout
16854 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
16857 \begin_layout Plain Layout
16858 \begin_inset Formula $\mp$
16868 <cell alignment="center" valignment="top" leftline="true" usebox="none">
16871 \begin_layout Plain Layout
16879 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
16882 \begin_layout Plain Layout
16883 \begin_inset Formula $\cdot$
16893 <cell alignment="center" valignment="top" leftline="true" usebox="none">
16896 \begin_layout Plain Layout
16904 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
16907 \begin_layout Plain Layout
16908 \begin_inset Formula $\times$
16918 <cell alignment="center" valignment="top" leftline="true" usebox="none">
16921 \begin_layout Plain Layout
16929 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
16932 \begin_layout Plain Layout
16933 \begin_inset Formula $\div$
16943 <cell alignment="center" valignment="top" leftline="true" usebox="none">
16946 \begin_layout Plain Layout
16950 \begin_layout Plain Layout
16963 \begin_layout Plain Layout
16975 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
16978 \begin_layout Plain Layout
16979 \begin_inset Formula $*$
16989 <cell alignment="center" valignment="top" leftline="true" usebox="none">
16992 \begin_layout Plain Layout
17000 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
17003 \begin_layout Plain Layout
17004 \begin_inset Formula $\star$
17014 <cell alignment="center" valignment="top" leftline="true" usebox="none">
17017 \begin_layout Plain Layout
17025 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
17028 \begin_layout Plain Layout
17029 \begin_inset Formula $\circ$
17039 <cell alignment="center" valignment="top" leftline="true" usebox="none">
17042 \begin_layout Plain Layout
17050 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
17053 \begin_layout Plain Layout
17054 \begin_inset Formula $\diamond$
17064 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
17067 \begin_layout Plain Layout
17075 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
17078 \begin_layout Plain Layout
17079 \begin_inset Formula $\bullet$
17093 \begin_inset space \hfill{}
17097 \begin_inset Tabular
17098 <lyxtabular version="3" rows="13" columns="2">
17099 <features booktabs="true" tabularvalignment="middle">
17100 <column alignment="center" valignment="top" width="0pt">
17101 <column alignment="center" valignment="top" width="0pt">
17103 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
17106 \begin_layout Plain Layout
17112 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
17115 \begin_layout Plain Layout
17123 <cell alignment="center" valignment="top" leftline="true" usebox="none">
17126 \begin_layout Plain Layout
17134 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
17137 \begin_layout Plain Layout
17138 \begin_inset Formula $\nabla$
17148 <cell alignment="center" valignment="top" leftline="true" usebox="none">
17151 \begin_layout Plain Layout
17159 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
17162 \begin_layout Plain Layout
17163 \begin_inset Formula $\bigtriangledown$
17173 <cell alignment="center" valignment="top" leftline="true" usebox="none">
17176 \begin_layout Plain Layout
17184 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
17187 \begin_layout Plain Layout
17188 \begin_inset Formula $\bigtriangleup$
17198 <cell alignment="center" valignment="top" leftline="true" usebox="none">
17201 \begin_layout Plain Layout
17209 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
17212 \begin_layout Plain Layout
17213 \begin_inset Formula $\Box$
17223 <cell alignment="center" valignment="top" leftline="true" usebox="none">
17226 \begin_layout Plain Layout
17234 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
17237 \begin_layout Plain Layout
17238 \begin_inset Formula $\cap$
17248 <cell alignment="center" valignment="top" leftline="true" usebox="none">
17251 \begin_layout Plain Layout
17259 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
17262 \begin_layout Plain Layout
17263 \begin_inset Formula $\cup$
17273 <cell alignment="center" valignment="top" leftline="true" usebox="none">
17276 \begin_layout Plain Layout
17284 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
17287 \begin_layout Plain Layout
17288 \begin_inset Formula $\dagger$
17298 <cell alignment="center" valignment="top" leftline="true" usebox="none">
17301 \begin_layout Plain Layout
17309 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
17312 \begin_layout Plain Layout
17313 \begin_inset Formula $\ddagger$
17323 <cell alignment="center" valignment="top" leftline="true" usebox="none">
17326 \begin_layout Plain Layout
17334 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
17337 \begin_layout Plain Layout
17338 \begin_inset Formula $\wr$
17348 <cell alignment="center" valignment="top" leftline="true" usebox="none">
17351 \begin_layout Plain Layout
17359 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
17362 \begin_layout Plain Layout
17363 \begin_inset Formula $\bigcirc$
17373 <cell alignment="center" valignment="top" leftline="true" usebox="none">
17376 \begin_layout Plain Layout
17384 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
17387 \begin_layout Plain Layout
17388 \begin_inset Formula $\wedge$
17398 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
17401 \begin_layout Plain Layout
17409 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
17412 \begin_layout Plain Layout
17413 \begin_inset Formula $\vee$
17427 \begin_inset space \hfill{}
17431 \begin_inset Tabular
17432 <lyxtabular version="3" rows="13" columns="2">
17433 <features booktabs="true" tabularvalignment="middle">
17434 <column alignment="center" valignment="top" width="0pt">
17435 <column alignment="center" valignment="top" width="0pt">
17437 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
17440 \begin_layout Plain Layout
17446 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
17449 \begin_layout Plain Layout
17457 <cell alignment="center" valignment="top" leftline="true" usebox="none">
17460 \begin_layout Plain Layout
17468 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
17471 \begin_layout Plain Layout
17472 \begin_inset Formula $\oplus$
17482 <cell alignment="center" valignment="top" leftline="true" usebox="none">
17485 \begin_layout Plain Layout
17493 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
17496 \begin_layout Plain Layout
17497 \begin_inset Formula $\ominus$
17507 <cell alignment="center" valignment="top" leftline="true" usebox="none">
17510 \begin_layout Plain Layout
17518 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
17521 \begin_layout Plain Layout
17522 \begin_inset Formula $\otimes$
17532 <cell alignment="center" valignment="top" leftline="true" usebox="none">
17535 \begin_layout Plain Layout
17543 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
17546 \begin_layout Plain Layout
17547 \begin_inset Formula $\oslash$
17557 <cell alignment="center" valignment="top" leftline="true" usebox="none">
17560 \begin_layout Plain Layout
17568 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
17571 \begin_layout Plain Layout
17572 \begin_inset Formula $\odot$
17582 <cell alignment="center" valignment="top" leftline="true" usebox="none">
17585 \begin_layout Plain Layout
17593 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
17596 \begin_layout Plain Layout
17597 \begin_inset Formula $\amalg$
17607 <cell alignment="center" valignment="top" leftline="true" usebox="none">
17610 \begin_layout Plain Layout
17618 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
17621 \begin_layout Plain Layout
17622 \begin_inset Formula $\uplus$
17632 <cell alignment="center" valignment="top" leftline="true" usebox="none">
17635 \begin_layout Plain Layout
17643 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
17646 \begin_layout Plain Layout
17647 \begin_inset Formula $\setminus$
17657 <cell alignment="center" valignment="top" leftline="true" usebox="none">
17660 \begin_layout Plain Layout
17668 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
17671 \begin_layout Plain Layout
17672 \begin_inset Formula $\sqcap$
17682 <cell alignment="center" valignment="top" leftline="true" usebox="none">
17685 \begin_layout Plain Layout
17693 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
17696 \begin_layout Plain Layout
17697 \begin_inset Formula $\sqcup$
17707 <cell alignment="center" valignment="top" leftline="true" usebox="none">
17710 \begin_layout Plain Layout
17718 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
17721 \begin_layout Plain Layout
17722 \begin_inset Formula $\triangleleft$
17732 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
17735 \begin_layout Plain Layout
17743 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
17746 \begin_layout Plain Layout
17747 \begin_inset Formula $\triangleright$
17763 \begin_layout Standard
17764 All binary operators can also be inserted via the math toolbar button
17767 arg "math-insert \\pm"
17773 \begin_layout Standard
17774 To typeset the Laplace operator also
17791 \begin_inset Formula $\nabla^{2}$
17794 ) can be used instead of
17803 \begin_layout Standard
17810 Insert\SpecialChar menuseparator
17822 \begin_layout Subsection
17823 Self-defined Operators
17824 \begin_inset CommandInset label
17826 name "subsec:Self-defined-Operators"
17831 \begin_inset Index idx
17834 \begin_layout Plain Layout
17835 Operators ! self-defined
17843 \begin_layout Standard
17844 With the help of the command
17848 DeclareMathOperator
17851 \begin_inset Index idx
17854 \begin_layout Plain Layout
17859 DeclareMathOperator
17864 custom operators can be defined in the \SpecialChar LaTeX
17866 Its command scheme is:
17869 \begin_layout Standard
17874 DeclareMathOperator{new command}{display}
17877 \begin_layout Standard
17878 Display can be characters or symbols that define how the operator looks
17880 To define a big operator a * is set behind the command.
17881 All self-defined big operators can have limits as described in
17882 \begin_inset CommandInset ref
17884 reference "subsec:Operator-Limits"
17891 \begin_layout Standard
17892 For example the \SpecialChar LaTeX
17896 \begin_layout Standard
17901 DeclareMathOperator*{
17908 \begin_layout Standard
17909 defines the command
17915 , that inserts a big operator consisting of the lozenge symbol from
17916 \begin_inset CommandInset ref
17918 reference "subsec:Miscellaneous-Symbols"
17923 \begin_inset Formula
17925 \Lozenge_{n=1}^{\infty}
17930 The command for this formula is:
17941 \begin_inset Formula $\to$
17947 \begin_layout Standard
17948 \begin_inset VSpace bigskip
17951 When self-defined operators are not used several times in the document,
17952 they can also be defined with the commands
17959 \begin_inset Index idx
17962 \begin_layout Plain Layout
17977 \begin_inset Index idx
17980 \begin_layout Plain Layout
17988 , which have the following scheme:
17991 \begin_layout Standard
18005 \begin_layout Standard
18012 defines big operators,
18021 \begin_layout Standard
18029 \begin_inset space \thinspace{}
18033 \begin_inset space \space{}
18036 be used to use one limit for several operators:
18039 \begin_layout Standard
18040 \begin_inset Formula
18042 \mathop{\sum\negmedspace\sum}_{i,j=1}^{N}
18050 \begin_layout Standard
18051 The command for the formula above is:
18052 \begin_inset Newline newline
18068 \begin_inset space \textvisiblespace{}
18074 \begin_inset Formula $\to$
18080 \begin_inset space \textvisiblespace{}
18088 \begin_layout Section
18090 \begin_inset Index idx
18093 \begin_layout Plain Layout
18102 \begin_layout Subsection
18104 \begin_inset CommandInset label
18106 name "subsec:Font-Styles"
18111 \begin_inset Index idx
18114 \begin_layout Plain Layout
18123 \begin_layout Standard
18124 Latin letters in formulas can be set in one of the following font styles:
18127 \begin_layout Standard
18129 \begin_inset space \hfill{}
18133 \begin_inset Tabular
18134 <lyxtabular version="3" rows="6" columns="2">
18135 <features booktabs="true" tabularvalignment="middle">
18136 <column alignment="center" valignment="top" width="0pt">
18137 <column alignment="center" valignment="top">
18139 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
18142 \begin_layout Plain Layout
18148 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
18151 \begin_layout Plain Layout
18159 <cell alignment="center" valignment="top" leftline="true" usebox="none">
18162 \begin_layout Plain Layout
18168 \begin_inset space \textvisiblespace{}
18178 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
18181 \begin_layout Plain Layout
18182 \begin_inset Formula $\mathbb{ABC}$
18192 <cell alignment="center" valignment="top" leftline="true" usebox="none">
18195 \begin_layout Plain Layout
18201 \begin_inset space \textvisiblespace{}
18211 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
18214 \begin_layout Plain Layout
18215 \begin_inset Formula $\mathbf{AbC}$
18225 <cell alignment="center" valignment="top" leftline="true" usebox="none">
18228 \begin_layout Plain Layout
18234 \begin_inset space \textvisiblespace{}
18244 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
18247 \begin_layout Plain Layout
18248 \begin_inset Formula $\boldsymbol{AbC}$
18258 <cell alignment="center" valignment="top" leftline="true" usebox="none">
18261 \begin_layout Plain Layout
18267 \begin_inset space \textvisiblespace{}
18277 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
18280 \begin_layout Plain Layout
18281 \begin_inset Formula $\mathcal{ABC}$
18291 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
18294 \begin_layout Plain Layout
18300 \begin_inset space \textvisiblespace{}
18310 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
18313 \begin_layout Plain Layout
18314 \begin_inset Formula $\mathfrak{AbC}$
18328 \begin_inset space \hfill{}
18332 \begin_inset Tabular
18333 <lyxtabular version="3" rows="6" columns="2">
18334 <features booktabs="true" tabularvalignment="middle">
18335 <column alignment="center" valignment="top" width="0pt">
18336 <column alignment="center" valignment="top">
18338 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
18341 \begin_layout Plain Layout
18347 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
18350 \begin_layout Plain Layout
18358 <cell alignment="center" valignment="top" leftline="true" usebox="none">
18361 \begin_layout Plain Layout
18367 \begin_inset space \textvisiblespace{}
18377 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
18380 \begin_layout Plain Layout
18381 \begin_inset Formula $\mathit{AbC}$
18391 <cell alignment="center" valignment="top" leftline="true" usebox="none">
18394 \begin_layout Plain Layout
18400 \begin_inset space \textvisiblespace{}
18410 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
18413 \begin_layout Plain Layout
18414 \begin_inset Formula $\mathrm{AbC}$
18424 <cell alignment="center" valignment="top" leftline="true" usebox="none">
18427 \begin_layout Plain Layout
18433 \begin_inset space \textvisiblespace{}
18443 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
18446 \begin_layout Plain Layout
18447 \begin_inset Formula $\mathsf{AbC}$
18457 <cell alignment="center" valignment="top" leftline="true" usebox="none">
18460 \begin_layout Plain Layout
18466 \begin_inset space \textvisiblespace{}
18476 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
18479 \begin_layout Plain Layout
18480 \begin_inset Formula $\mathtt{AbC}$
18490 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
18493 \begin_layout Plain Layout
18499 \begin_inset space \textvisiblespace{}
18509 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
18512 \begin_layout Plain Layout
18513 \begin_inset Formula $\mathscr{ABC}$
18527 \begin_inset space \hfill{}
18533 \begin_layout Standard
18534 \begin_inset Note Greyedout
18537 \begin_layout Plain Layout
18560 can only be used for big letters.
18568 \begin_layout Standard
18569 Predefined is the style
18578 \begin_layout Standard
18579 The style commands work also for letters in mathematical constructs:
18580 \begin_inset Formula
18582 \mathfrak{A=\frac{b}{C}}
18590 \begin_layout Standard
18591 Characters in mathematical text don't appear in a math font style but in
18592 the text font style
18599 That their style can't be set correctly via the text style dialog is a
18600 bug in \SpecialChar LyX
18605 \begin_layout Plain Layout
18606 \begin_inset CommandInset href
18608 name "LyX-bug #4629"
18609 target "http://www.lyx.org/trac/ticket/4629"
18621 \begin_layout Standard
18622 Instead of the style commands the dialog
18624 Edit\SpecialChar menuseparator
18625 Math\SpecialChar menuseparator
18628 or the toolbar button
18631 arg "math-insert \\font"
18637 \begin_layout Subsection
18639 \begin_inset CommandInset label
18641 name "subsec:Bold-Formulas"
18646 \begin_inset Index idx
18649 \begin_layout Plain Layout
18658 \begin_layout Standard
18659 To make a complete formula bold, the command
18665 from the previous subsection cannot be used, because it doesn't work for
18666 small Greek letters.
18667 Furthermore it prints Latin letters always upright, like in the following
18671 \begin_layout Standard
18672 \begin_inset Formula
18674 \mathbf{\int_{n}^{2}f(\theta)=\Gamma}\qquad\textrm{equation with \textbackslash mathbf}
18682 \begin_layout Standard
18683 To display the formula correctly, the command
18690 \begin_inset Formula
18692 \boldsymbol{\int_{n}^{2}f(\theta)=\Gamma\qquad\textrm{equation with \textbackslash boldsymbol}}
18697 It is also possible to set the formula in a
18699 boldmath environment
18702 This environment is created by inserting the command
18709 \begin_inset Index idx
18712 \begin_layout Plain Layout
18720 in \SpecialChar TeX
18722 To end the environment, the command
18729 \begin_inset Index idx
18732 \begin_layout Plain Layout
18740 is inserted in \SpecialChar TeX
18745 \begin_layout Plain Layout
18755 \begin_inset Formula
18757 \int_{n}^{2}f(\theta)=\Gamma\qquad\textrm{equation in a boldmath environment}
18766 \begin_layout Plain Layout
18778 \begin_layout Subsection
18780 \begin_inset Index idx
18783 \begin_layout Plain Layout
18792 \begin_layout Standard
18793 Formulas can be colored like normal text: Highlight a formula or a formula
18799 Here is a formula in magenta:
18800 \begin_inset Formula
18802 {\color{magenta}\int A\,\mathrm{d}x=\frac{\sqrt[5]{B}}{\ln\left(\frac{1}{3}\right)}}
18810 \begin_layout Standard
18811 You can also define your own colors as described in
18812 \begin_inset CommandInset ref
18814 reference "subsec:Colored-Boxes"
18819 They can be used with the \SpecialChar TeX
18827 \begin_inset Index idx
18830 \begin_layout Plain Layout
18841 \begin_layout Standard
18846 textcolor{color}{characters or formula}
18849 \begin_layout Standard
18850 The following example was colored completely dark green and partly red:
18853 \begin_layout Standard
18857 \begin_layout Plain Layout
18861 textcolor{darkgreen}{
18867 \begin_inset Formula
18869 \int A\,\mathrm{d}x=\frac{{\color{red}\sqrt[5]{B}}}{\ln\left(\frac{1}{3}\right)}
18878 \begin_layout Plain Layout
18888 \begin_layout Standard
18889 Due to a bug in \SpecialChar LyX
18890 only complete formulas can be colored with self-defined
18895 \begin_layout Plain Layout
18896 \begin_inset CommandInset href
18898 name "LyX-bug #5269"
18899 target "http://www.lyx.org/trac/ticket/5269"
18911 \begin_layout Subsection
18913 \begin_inset CommandInset label
18915 name "subsec:Font-Sizes"
18920 \begin_inset Index idx
18923 \begin_layout Plain Layout
18932 \begin_layout Standard
18933 For characters in formulas there are, analog to characters in text, the
18934 following size commands:
18937 \begin_layout Standard
18981 \begin_inset Newline newline
19003 \begin_layout Standard
19004 The size produced by the commands depends on the document font size, which
19005 corresponds to the command
19012 The other commands produce smaller or larger sizes than
19019 The font size can however not exceed a certain value.
19020 Is for example the document font size 12
19021 \begin_inset space \thinspace{}
19030 switches to the same size as
19040 \begin_layout Standard
19041 A size command is inserted in \SpecialChar TeX
19042 mode before the formula and sets the size
19043 for all following formula and text characters.
19044 To switch back to the initial size, the command
19050 is inserted behind the formula in \SpecialChar TeX
19054 \begin_layout Standard
19055 Within a formula the size can be changed using the following size commands
19056 or the toolbar button
19059 arg "math-insert \\style"
19065 \begin_layout Standard
19068 \begin_inset Tabular
19069 <lyxtabular version="3" rows="5" columns="2">
19070 <features booktabs="true" tabularvalignment="middle">
19071 <column alignment="center" valignment="top" width="0pt">
19072 <column alignment="center" valignment="top">
19074 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
19077 \begin_layout Plain Layout
19083 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
19086 \begin_layout Plain Layout
19094 <cell alignment="center" valignment="top" leftline="true" usebox="none">
19097 \begin_layout Plain Layout
19101 \begin_inset Index idx
19104 \begin_layout Plain Layout
19117 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
19120 \begin_layout Plain Layout
19121 \begin_inset Formula ${\displaystyle E_{\mathrm{pot_{1}}}=\frac{K}{l+\frac{m}{n_{2}}}}$
19130 <row topspace="1mm">
19131 <cell alignment="center" valignment="top" usebox="none">
19134 \begin_layout Plain Layout
19142 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
19145 \begin_layout Plain Layout
19146 \begin_inset Formula ${\textstyle E_{\mathrm{pot_{1}}}=\frac{K}{l+\frac{m}{n_{2}}}}$
19156 <cell alignment="center" valignment="top" leftline="true" usebox="none">
19159 \begin_layout Plain Layout
19167 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
19170 \begin_layout Plain Layout
19171 \begin_inset Formula ${\scriptstyle E_{\mathrm{pot_{1}}}=\frac{K}{l+\frac{m}{n_{2}}}}$
19181 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
19184 \begin_layout Plain Layout
19192 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
19195 \begin_layout Plain Layout
19196 \begin_inset Formula ${\scriptscriptstyle E_{\mathrm{pot_{1}}}=\frac{K}{l+\frac{m}{n_{2}}}}$
19212 \begin_layout Standard
19213 After entering these commands, a blue box appears in which the formula parts
19217 \begin_layout Standard
19218 There is a further method to change the font size, that though only works
19219 for symbols or letters in mathematical text.
19220 To use it, one of the above text size commands is inserted in mathematical
19222 All following characters until the end of the mathematical text or until
19223 another size command will have the selected size.
19225 \begin_inset VSpace -2mm
19231 \begin_layout Standard
19235 \begin_layout Plain Layout
19245 \begin_inset Formula
19247 A=\frac{B}{c}\cdot\maltese
19253 \begin_inset Formula
19255 \maltese A\textrm{\Large\maltese\textit{A}}\textrm{\tiny\maltese\textit{A}}
19264 \begin_layout Plain Layout
19276 \begin_layout Standard
19277 \begin_inset VSpace medskip
19280 Before both formulas the command
19287 The command for the second formula is:
19288 \begin_inset Newline newline
19296 \begin_inset space \textvisiblespace{}
19302 \begin_inset space \textvisiblespace{}
19308 \begin_inset space \textvisiblespace{}
19314 \begin_inset space \textvisiblespace{}
19318 \begin_inset Formula $\to$
19322 \begin_inset Formula $\to$
19326 \begin_inset Newline newline
19330 \begin_inset space \hspace*{}
19341 \begin_inset space \textvisiblespace{}
19347 \begin_inset space \textvisiblespace{}
19353 \begin_inset space \textvisiblespace{}
19359 \begin_layout Standard
19360 If a symbol cannot be displayed in different sizes, it will always be displayed
19361 in the default size.
19364 \begin_layout Section
19366 \begin_inset Index idx
19369 \begin_layout Plain Layout
19378 \begin_layout Standard
19379 Greek letters can also be inserted via the toolbar button
19382 arg "math-insert \\alpha"
19386 All international typesetting norms purport that Greek letters in math
19387 have to be typeset italic/slanted.
19388 In some languages, like French or Russian, they are nevertheless sometimes
19392 \begin_layout Subsection
19394 \begin_inset Index idx
19397 \begin_layout Plain Layout
19398 Greek letters ! small
19406 \begin_layout Standard
19407 \begin_inset space \hfill{}
19411 \begin_inset Tabular
19412 <lyxtabular version="3" rows="11" columns="2">
19413 <features booktabs="true" tabularvalignment="middle">
19414 <column alignment="center" valignment="top" width="0pt">
19415 <column alignment="center" valignment="top" width="0pt">
19417 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
19420 \begin_layout Plain Layout
19426 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
19429 \begin_layout Plain Layout
19437 <cell alignment="center" valignment="top" leftline="true" usebox="none">
19440 \begin_layout Plain Layout
19448 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
19451 \begin_layout Plain Layout
19452 \begin_inset Formula $\alpha$
19462 <cell alignment="center" valignment="top" leftline="true" usebox="none">
19465 \begin_layout Plain Layout
19473 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
19476 \begin_layout Plain Layout
19477 \begin_inset Formula $\beta$
19487 <cell alignment="center" valignment="top" leftline="true" usebox="none">
19490 \begin_layout Plain Layout
19498 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
19501 \begin_layout Plain Layout
19502 \begin_inset Formula $\gamma$
19512 <cell alignment="center" valignment="top" leftline="true" usebox="none">
19515 \begin_layout Plain Layout
19523 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
19526 \begin_layout Plain Layout
19527 \begin_inset Formula $\delta$
19537 <cell alignment="center" valignment="top" leftline="true" usebox="none">
19540 \begin_layout Plain Layout
19548 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
19551 \begin_layout Plain Layout
19552 \begin_inset Formula $\epsilon$
19562 <cell alignment="center" valignment="top" leftline="true" usebox="none">
19565 \begin_layout Plain Layout
19573 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
19576 \begin_layout Plain Layout
19577 \begin_inset Formula $\varepsilon$
19587 <cell alignment="center" valignment="top" leftline="true" usebox="none">
19590 \begin_layout Plain Layout
19598 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
19601 \begin_layout Plain Layout
19602 \begin_inset Formula $\zeta$
19612 <cell alignment="center" valignment="top" leftline="true" usebox="none">
19615 \begin_layout Plain Layout
19623 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
19626 \begin_layout Plain Layout
19627 \begin_inset Formula $\eta$
19637 <cell alignment="center" valignment="top" leftline="true" usebox="none">
19640 \begin_layout Plain Layout
19648 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
19651 \begin_layout Plain Layout
19652 \begin_inset Formula $\theta$
19662 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
19665 \begin_layout Plain Layout
19673 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
19676 \begin_layout Plain Layout
19677 \begin_inset Formula $\vartheta$
19691 \begin_inset space \hfill{}
19695 \begin_inset Tabular
19696 <lyxtabular version="3" rows="12" columns="2">
19697 <features booktabs="true" tabularvalignment="middle">
19698 <column alignment="center" valignment="top" width="0pt">
19699 <column alignment="center" valignment="top" width="0pt">
19701 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
19704 \begin_layout Plain Layout
19710 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
19713 \begin_layout Plain Layout
19721 <cell alignment="center" valignment="top" leftline="true" usebox="none">
19724 \begin_layout Plain Layout
19732 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
19735 \begin_layout Plain Layout
19736 \begin_inset Formula $\iota$
19746 <cell alignment="center" valignment="top" leftline="true" usebox="none">
19749 \begin_layout Plain Layout
19757 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
19760 \begin_layout Plain Layout
19761 \begin_inset Formula $\kappa$
19771 <cell alignment="center" valignment="top" leftline="true" usebox="none">
19774 \begin_layout Plain Layout
19782 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
19785 \begin_layout Plain Layout
19786 \begin_inset Formula $\varkappa$
19796 <cell alignment="center" valignment="top" leftline="true" usebox="none">
19799 \begin_layout Plain Layout
19807 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
19810 \begin_layout Plain Layout
19811 \begin_inset Formula $\lambda$
19821 <cell alignment="center" valignment="top" leftline="true" usebox="none">
19824 \begin_layout Plain Layout
19832 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
19835 \begin_layout Plain Layout
19836 \begin_inset Formula $\mu$
19846 <cell alignment="center" valignment="top" leftline="true" usebox="none">
19849 \begin_layout Plain Layout
19857 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
19860 \begin_layout Plain Layout
19861 \begin_inset Formula $\nu$
19871 <cell alignment="center" valignment="top" leftline="true" usebox="none">
19874 \begin_layout Plain Layout
19882 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
19885 \begin_layout Plain Layout
19886 \begin_inset Formula $\xi$
19896 <cell alignment="center" valignment="top" leftline="true" usebox="none">
19899 \begin_layout Plain Layout
19905 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
19908 \begin_layout Plain Layout
19909 \begin_inset Formula $o$
19919 <cell alignment="center" valignment="top" leftline="true" usebox="none">
19922 \begin_layout Plain Layout
19930 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
19933 \begin_layout Plain Layout
19934 \begin_inset Formula $\pi$
19944 <cell alignment="center" valignment="top" leftline="true" usebox="none">
19947 \begin_layout Plain Layout
19955 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
19958 \begin_layout Plain Layout
19959 \begin_inset Formula $\varpi$
19969 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
19972 \begin_layout Plain Layout
19980 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
19983 \begin_layout Plain Layout
19984 \begin_inset Formula $\rho$
19998 \begin_inset space \hfill{}
20002 \begin_inset Tabular
20003 <lyxtabular version="3" rows="11" columns="2">
20004 <features booktabs="true" tabularvalignment="middle">
20005 <column alignment="center" valignment="top" width="0pt">
20006 <column alignment="center" valignment="top" width="0pt">
20008 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
20011 \begin_layout Plain Layout
20017 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
20020 \begin_layout Plain Layout
20028 <cell alignment="center" valignment="top" leftline="true" usebox="none">
20031 \begin_layout Plain Layout
20039 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
20042 \begin_layout Plain Layout
20043 \begin_inset Formula $\varrho$
20053 <cell alignment="center" valignment="top" leftline="true" usebox="none">
20056 \begin_layout Plain Layout
20064 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
20067 \begin_layout Plain Layout
20068 \begin_inset Formula $\sigma$
20078 <cell alignment="center" valignment="top" leftline="true" usebox="none">
20081 \begin_layout Plain Layout
20089 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
20092 \begin_layout Plain Layout
20093 \begin_inset Formula $\varsigma$
20103 <cell alignment="center" valignment="top" leftline="true" usebox="none">
20106 \begin_layout Plain Layout
20114 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
20117 \begin_layout Plain Layout
20118 \begin_inset Formula $\tau$
20128 <cell alignment="center" valignment="top" leftline="true" usebox="none">
20131 \begin_layout Plain Layout
20139 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
20142 \begin_layout Plain Layout
20143 \begin_inset Formula $\upsilon$
20153 <cell alignment="center" valignment="top" leftline="true" usebox="none">
20156 \begin_layout Plain Layout
20164 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
20167 \begin_layout Plain Layout
20168 \begin_inset Formula $\phi$
20178 <cell alignment="center" valignment="top" leftline="true" usebox="none">
20181 \begin_layout Plain Layout
20189 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
20192 \begin_layout Plain Layout
20193 \begin_inset Formula $\varphi$
20203 <cell alignment="center" valignment="top" leftline="true" usebox="none">
20206 \begin_layout Plain Layout
20214 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
20217 \begin_layout Plain Layout
20218 \begin_inset Formula $\chi$
20228 <cell alignment="center" valignment="top" leftline="true" usebox="none">
20231 \begin_layout Plain Layout
20239 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
20242 \begin_layout Plain Layout
20243 \begin_inset Formula $\psi$
20253 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
20256 \begin_layout Plain Layout
20264 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
20267 \begin_layout Plain Layout
20268 \begin_inset Formula $\omega$
20282 \begin_inset space \hfill{}
20288 \begin_layout Standard
20289 \begin_inset VSpace medskip
20295 \begin_layout Standard
20296 How to create special upright Greek letters is explained in
20297 \begin_inset CommandInset ref
20299 reference "subsec:Upright-small-Greek"
20306 \begin_layout Subsection
20308 \begin_inset Index idx
20311 \begin_layout Plain Layout
20312 Greek letters ! big
20320 \begin_layout Standard
20321 \begin_inset space \hfill{}
20325 \begin_inset Tabular
20326 <lyxtabular version="3" rows="7" columns="2">
20327 <features booktabs="true" tabularvalignment="middle">
20328 <column alignment="center" valignment="top" width="0pt">
20329 <column alignment="center" valignment="top" width="0pt">
20331 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
20334 \begin_layout Plain Layout
20340 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
20343 \begin_layout Plain Layout
20351 <cell alignment="center" valignment="top" leftline="true" usebox="none">
20354 \begin_layout Plain Layout
20362 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
20365 \begin_layout Plain Layout
20366 \begin_inset Formula $\Gamma$
20376 <cell alignment="center" valignment="top" leftline="true" usebox="none">
20379 \begin_layout Plain Layout
20387 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
20390 \begin_layout Plain Layout
20391 \begin_inset Formula $\Delta$
20401 <cell alignment="center" valignment="top" leftline="true" usebox="none">
20404 \begin_layout Plain Layout
20412 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
20415 \begin_layout Plain Layout
20416 \begin_inset Formula $\Theta$
20426 <cell alignment="center" valignment="top" leftline="true" usebox="none">
20429 \begin_layout Plain Layout
20437 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
20440 \begin_layout Plain Layout
20441 \begin_inset Formula $\Lambda$
20451 <cell alignment="center" valignment="top" leftline="true" usebox="none">
20454 \begin_layout Plain Layout
20462 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
20465 \begin_layout Plain Layout
20466 \begin_inset Formula $\Xi$
20476 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
20479 \begin_layout Plain Layout
20487 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
20490 \begin_layout Plain Layout
20491 \begin_inset Formula $\Pi$
20505 \begin_inset space \hfill{}
20509 \begin_inset Tabular
20510 <lyxtabular version="3" rows="6" columns="2">
20511 <features booktabs="true" tabularvalignment="middle">
20512 <column alignment="center" valignment="top" width="0pt">
20513 <column alignment="center" valignment="top" width="0pt">
20515 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
20518 \begin_layout Plain Layout
20524 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
20527 \begin_layout Plain Layout
20535 <cell alignment="center" valignment="top" leftline="true" usebox="none">
20538 \begin_layout Plain Layout
20546 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
20549 \begin_layout Plain Layout
20550 \begin_inset Formula $\Sigma$
20560 <cell alignment="center" valignment="top" leftline="true" usebox="none">
20563 \begin_layout Plain Layout
20571 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
20574 \begin_layout Plain Layout
20575 \begin_inset Formula $\Upsilon$
20585 <cell alignment="center" valignment="top" leftline="true" usebox="none">
20588 \begin_layout Plain Layout
20596 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
20599 \begin_layout Plain Layout
20600 \begin_inset Formula $\Phi$
20610 <cell alignment="center" valignment="top" leftline="true" usebox="none">
20613 \begin_layout Plain Layout
20621 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
20624 \begin_layout Plain Layout
20625 \begin_inset Formula $\Psi$
20635 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
20638 \begin_layout Plain Layout
20646 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
20649 \begin_layout Plain Layout
20650 \begin_inset Formula $\Omega$
20664 \begin_inset space \hfill{}
20670 \begin_layout Standard
20671 \begin_inset VSpace medskip
20674 That the big Greek letters appear upright is caused by a design bug when
20677 To get correct italic big letters, begin every command with
20682 For example the command
20689 \begin_inset Formula $\varGamma$
20693 Another way is to load the package
20701 \begin_layout Plain Layout
20706 is part of the \SpecialChar LaTeX
20712 \begin_inset Index idx
20715 \begin_layout Plain Layout
20720 \begin_layout Plain Layout
20740 \begin_inset Index idx
20743 \begin_layout Plain Layout
20749 with the \SpecialChar LaTeX
20753 \begin_layout Standard
20758 usepackage{fixmath}
20761 \begin_layout Standard
20762 Then all big Greek letters in a document will automatically be typeset italic.
20765 \begin_layout Subsection
20767 \begin_inset Index idx
20770 \begin_layout Plain Layout
20771 Greek letters ! bold
20779 \begin_layout Standard
20780 Greek letters cannot be set with different font styles like Latin letters.
20781 They can only be made bold with the command
20788 \begin_inset Index idx
20791 \begin_layout Plain Layout
20802 \begin_layout Standard
20804 \begin_inset Tabular
20805 <lyxtabular version="3" rows="3" columns="2">
20806 <features booktabs="true" tabularvalignment="middle">
20807 <column alignment="center" valignment="top" width="0pt">
20808 <column alignment="center" valignment="top">
20810 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
20813 \begin_layout Plain Layout
20819 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
20822 \begin_layout Plain Layout
20830 <cell alignment="center" valignment="top" leftline="true" usebox="none">
20833 \begin_layout Plain Layout
20845 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
20848 \begin_layout Plain Layout
20849 \begin_inset Formula $\Upsilon\boldsymbol{\Upsilon}$
20859 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
20862 \begin_layout Plain Layout
20874 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
20877 \begin_layout Plain Layout
20878 \begin_inset Formula $\theta\boldsymbol{\theta}$
20894 \begin_layout Section
20899 \begin_layout Plain Layout
20912 \begin_layout Plain Layout
20913 A list with all symbols of most of the \SpecialChar LaTeX
20914 -packages can be found in
20915 \begin_inset CommandInset citation
20930 \begin_layout Plain Layout
20938 \begin_inset Note Note
20941 \begin_layout Plain Layout
20944 texorpdfstring is used to avoid that the footnote appears in the PDF-bookmark.
20947 \begin_layout Plain Layout
20950 texorpdfstring is in section
20951 \begin_inset CommandInset ref
20953 reference "subsec:Formulas-in-Section"
20963 \begin_inset Index idx
20966 \begin_layout Plain Layout
20975 \begin_layout Standard
20976 Many of the symbols listed in this section can also be inserted via the
20980 arg "math-insert \\nabla"
20986 arg "math-insert \\digamma"
20992 \begin_layout Subsection
20993 Mathematical Symbols
20994 \begin_inset CommandInset label
20996 name "subsec:Mathematical-Symbols"
21001 \begin_inset Index idx
21004 \begin_layout Plain Layout
21005 Symbols ! mathematical
21013 \begin_layout Standard
21014 \begin_inset Tabular
21015 <lyxtabular version="3" rows="10" columns="2">
21016 <features booktabs="true" tabularvalignment="middle">
21017 <column alignment="center" valignment="top" width="0pt">
21018 <column alignment="center" valignment="top" width="0pt">
21020 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
21023 \begin_layout Plain Layout
21029 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
21032 \begin_layout Plain Layout
21040 <cell alignment="center" valignment="top" leftline="true" usebox="none">
21043 \begin_layout Plain Layout
21051 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
21054 \begin_layout Plain Layout
21055 \begin_inset Formula $\neg$
21065 <cell alignment="center" valignment="top" leftline="true" usebox="none">
21068 \begin_layout Plain Layout
21076 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
21079 \begin_layout Plain Layout
21080 \begin_inset Formula $\Im$
21090 <cell alignment="center" valignment="top" leftline="true" usebox="none">
21093 \begin_layout Plain Layout
21101 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
21104 \begin_layout Plain Layout
21105 \begin_inset Formula $\Re$
21115 <cell alignment="center" valignment="top" leftline="true" usebox="none">
21118 \begin_layout Plain Layout
21126 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
21129 \begin_layout Plain Layout
21130 \begin_inset Formula $\aleph$
21140 <cell alignment="center" valignment="top" leftline="true" usebox="none">
21143 \begin_layout Plain Layout
21151 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
21154 \begin_layout Plain Layout
21155 \begin_inset Formula $\partial$
21165 <cell alignment="center" valignment="top" leftline="true" usebox="none">
21168 \begin_layout Plain Layout
21176 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
21179 \begin_layout Plain Layout
21180 \begin_inset Formula $\infty$
21190 <cell alignment="center" valignment="top" leftline="true" usebox="none">
21193 \begin_layout Plain Layout
21201 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
21204 \begin_layout Plain Layout
21205 \begin_inset Formula $\wp$
21215 <cell alignment="center" valignment="top" leftline="true" usebox="none">
21218 \begin_layout Plain Layout
21226 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
21229 \begin_layout Plain Layout
21230 \begin_inset Formula $\imath$
21240 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
21243 \begin_layout Plain Layout
21251 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
21254 \begin_layout Plain Layout
21255 \begin_inset Formula $\jmath$
21269 \begin_inset space \hfill{}
21273 \begin_inset Tabular
21274 <lyxtabular version="3" rows="10" columns="2">
21275 <features booktabs="true" tabularvalignment="middle">
21276 <column alignment="center" valignment="top" width="0pt">
21277 <column alignment="center" valignment="top" width="0pt">
21279 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
21282 \begin_layout Plain Layout
21288 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
21291 \begin_layout Plain Layout
21293 \begin_inset Note Note
21296 \begin_layout Plain Layout
21303 is only used as spacer.
21315 <cell alignment="center" valignment="top" leftline="true" usebox="none">
21318 \begin_layout Plain Layout
21326 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
21329 \begin_layout Plain Layout
21330 \begin_inset Formula $\forall$
21340 <cell alignment="center" valignment="top" leftline="true" usebox="none">
21343 \begin_layout Plain Layout
21351 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
21354 \begin_layout Plain Layout
21355 \begin_inset Formula $\exists$
21365 <cell alignment="center" valignment="top" leftline="true" usebox="none">
21368 \begin_layout Plain Layout
21376 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
21379 \begin_layout Plain Layout
21380 \begin_inset Formula $\nexists$
21390 <cell alignment="center" valignment="top" leftline="true" usebox="none">
21393 \begin_layout Plain Layout
21401 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
21404 \begin_layout Plain Layout
21405 \begin_inset Formula $\emptyset$
21415 <cell alignment="center" valignment="top" leftline="true" usebox="none">
21418 \begin_layout Plain Layout
21426 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
21429 \begin_layout Plain Layout
21430 \begin_inset Formula $\varnothing$
21440 <cell alignment="center" valignment="top" leftline="true" usebox="none">
21443 \begin_layout Plain Layout
21451 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
21454 \begin_layout Plain Layout
21455 \begin_inset Formula $\dag$
21465 <cell alignment="center" valignment="top" leftline="true" usebox="none">
21468 \begin_layout Plain Layout
21476 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
21479 \begin_layout Plain Layout
21480 \begin_inset Formula $\ddag$
21490 <cell alignment="center" valignment="top" leftline="true" usebox="none">
21493 \begin_layout Plain Layout
21501 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
21504 \begin_layout Plain Layout
21508 \begin_layout Plain Layout
21518 \begin_inset Formula $\complement$
21525 \begin_layout Plain Layout
21539 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
21542 \begin_layout Plain Layout
21550 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
21553 \begin_layout Plain Layout
21554 \begin_inset Formula $\Bbbk$
21568 \begin_inset space \hfill{}
21572 \begin_inset Tabular
21573 <lyxtabular version="3" rows="10" columns="2">
21574 <features booktabs="true" tabularvalignment="middle">
21575 <column alignment="center" valignment="top" width="0pt">
21576 <column alignment="center" valignment="top" width="0pt">
21578 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
21581 \begin_layout Plain Layout
21587 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
21590 \begin_layout Plain Layout
21598 <cell alignment="center" valignment="top" leftline="true" usebox="none">
21601 \begin_layout Plain Layout
21609 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
21612 \begin_layout Plain Layout
21613 \begin_inset Formula $\prime$
21623 <cell alignment="center" valignment="top" leftline="true" usebox="none">
21626 \begin_layout Plain Layout
21634 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
21637 \begin_layout Plain Layout
21638 \begin_inset Formula $\backprime$
21648 <cell alignment="center" valignment="top" leftline="true" usebox="none">
21651 \begin_layout Plain Layout
21659 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
21662 \begin_layout Plain Layout
21663 \begin_inset Formula $\mho$
21673 <cell alignment="center" valignment="top" leftline="true" usebox="none">
21676 \begin_layout Plain Layout
21684 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
21687 \begin_layout Plain Layout
21688 \begin_inset Formula $\triangle$
21698 <cell alignment="center" valignment="top" leftline="true" usebox="none">
21701 \begin_layout Plain Layout
21709 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
21712 \begin_layout Plain Layout
21713 \begin_inset Formula $\angle$
21723 <cell alignment="center" valignment="top" leftline="true" usebox="none">
21726 \begin_layout Plain Layout
21734 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
21737 \begin_layout Plain Layout
21738 \begin_inset Formula $\measuredangle$
21748 <cell alignment="center" valignment="top" leftline="true" usebox="none">
21751 \begin_layout Plain Layout
21759 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
21762 \begin_layout Plain Layout
21763 \begin_inset Formula $\sphericalangle$
21773 <cell alignment="center" valignment="top" leftline="true" usebox="none">
21776 \begin_layout Plain Layout
21784 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
21787 \begin_layout Plain Layout
21788 \begin_inset Formula $\top$
21798 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
21801 \begin_layout Plain Layout
21809 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
21812 \begin_layout Plain Layout
21813 \begin_inset Formula $\bot$
21829 \begin_layout Standard
21830 \begin_inset Newpage newpage
21836 \begin_layout Subsection
21837 Miscellaneous Symbols
21838 \begin_inset CommandInset label
21840 name "subsec:Miscellaneous-Symbols"
21845 \begin_inset Index idx
21848 \begin_layout Plain Layout
21849 Symbols ! miscellaneous
21857 \begin_layout Standard
21860 \begin_inset Tabular
21861 <lyxtabular version="3" rows="10" columns="2">
21862 <features booktabs="true" tabularvalignment="middle">
21863 <column alignment="center" valignment="top" width="0pt">
21864 <column alignment="center" valignment="top" width="0pt">
21866 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
21869 \begin_layout Plain Layout
21875 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
21878 \begin_layout Plain Layout
21886 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
21889 \begin_layout Plain Layout
21897 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
21900 \begin_layout Plain Layout
21901 \begin_inset Formula $\flat$
21911 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
21914 \begin_layout Plain Layout
21922 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
21925 \begin_layout Plain Layout
21926 \begin_inset Formula $\natural$
21936 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
21939 \begin_layout Plain Layout
21947 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
21950 \begin_layout Plain Layout
21951 \begin_inset Formula $\sharp$
21961 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
21964 \begin_layout Plain Layout
21972 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
21975 \begin_layout Plain Layout
21976 \begin_inset Formula $\surd$
21986 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
21989 \begin_layout Plain Layout
21997 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
22000 \begin_layout Plain Layout
22001 \begin_inset Formula $\checkmark$
22011 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
22014 \begin_layout Plain Layout
22022 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
22025 \begin_layout Plain Layout
22026 \begin_inset Formula $\yen$
22036 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
22039 \begin_layout Plain Layout
22047 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
22050 \begin_layout Plain Layout
22051 \begin_inset Formula $\pounds$
22061 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
22064 \begin_layout Plain Layout
22070 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
22073 \begin_layout Plain Layout
22074 \begin_inset Formula $\$$
22084 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
22087 \begin_layout Plain Layout
22093 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
22096 \begin_layout Plain Layout
22097 \begin_inset Formula $§$
22111 \begin_inset space \hfill{}
22115 \begin_inset Tabular
22116 <lyxtabular version="3" rows="10" columns="2">
22117 <features booktabs="true" tabularvalignment="middle">
22118 <column alignment="center" valignment="top" width="0pt">
22119 <column alignment="center" valignment="top">
22121 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
22124 \begin_layout Plain Layout
22130 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
22133 \begin_layout Plain Layout
22141 <cell alignment="center" valignment="top" leftline="true" usebox="none">
22144 \begin_layout Plain Layout
22152 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
22155 \begin_layout Plain Layout
22156 \begin_inset Formula $\hbar$
22166 <cell alignment="center" valignment="top" leftline="true" usebox="none">
22169 \begin_layout Plain Layout
22177 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
22180 \begin_layout Plain Layout
22181 \begin_inset Formula $\hslash$
22191 <cell alignment="center" valignment="top" leftline="true" usebox="none">
22194 \begin_layout Plain Layout
22202 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
22205 \begin_layout Plain Layout
22206 \begin_inset Formula $\clubsuit$
22216 <cell alignment="center" valignment="top" leftline="true" usebox="none">
22219 \begin_layout Plain Layout
22227 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
22230 \begin_layout Plain Layout
22231 \begin_inset Formula $\spadesuit$
22241 <cell alignment="center" valignment="top" leftline="true" usebox="none">
22244 \begin_layout Plain Layout
22252 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
22255 \begin_layout Plain Layout
22256 \begin_inset Formula $\bigstar$
22266 <cell alignment="center" valignment="top" leftline="true" usebox="none">
22269 \begin_layout Plain Layout
22277 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
22280 \begin_layout Plain Layout
22281 \begin_inset Formula $\blacklozenge$
22291 <cell alignment="center" valignment="top" leftline="true" usebox="none">
22294 \begin_layout Plain Layout
22302 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
22305 \begin_layout Plain Layout
22306 \begin_inset Formula $\blacktriangle$
22316 <cell alignment="center" valignment="top" leftline="true" usebox="none">
22319 \begin_layout Plain Layout
22327 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
22330 \begin_layout Plain Layout
22331 \begin_inset Formula $\blacktriangledown$
22341 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
22344 \begin_layout Plain Layout
22352 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
22355 \begin_layout Plain Layout
22356 \begin_inset Formula $\bullet$
22370 \begin_inset space \hfill{}
22374 \begin_inset Tabular
22375 <lyxtabular version="3" rows="10" columns="2">
22376 <features booktabs="true" tabularvalignment="middle">
22377 <column alignment="center" valignment="top" width="0pt">
22378 <column alignment="center" valignment="top" width="0pt">
22380 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
22383 \begin_layout Plain Layout
22389 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
22392 \begin_layout Plain Layout
22400 <cell alignment="center" valignment="top" leftline="true" usebox="none">
22403 \begin_layout Plain Layout
22411 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
22414 \begin_layout Plain Layout
22415 \begin_inset Formula $\diamondsuit$
22425 <cell alignment="center" valignment="top" rightline="true" usebox="none">
22428 \begin_layout Plain Layout
22436 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
22439 \begin_layout Plain Layout
22440 \begin_inset Formula $\Diamond$
22450 <cell alignment="center" valignment="top" leftline="true" usebox="none">
22453 \begin_layout Plain Layout
22461 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
22464 \begin_layout Plain Layout
22465 \begin_inset Formula $\heartsuit$
22475 <cell alignment="center" valignment="top" leftline="true" usebox="none">
22478 \begin_layout Plain Layout
22486 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
22489 \begin_layout Plain Layout
22490 \begin_inset Formula $\P$
22500 <cell alignment="center" valignment="top" leftline="true" usebox="none">
22503 \begin_layout Plain Layout
22511 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
22514 \begin_layout Plain Layout
22515 \begin_inset Formula $\copyright$
22525 <cell alignment="center" valignment="top" leftline="true" usebox="none">
22528 \begin_layout Plain Layout
22536 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
22539 \begin_layout Plain Layout
22540 \begin_inset Formula $\circledR$
22550 <cell alignment="center" valignment="top" leftline="true" usebox="none">
22553 \begin_layout Plain Layout
22561 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
22564 \begin_layout Plain Layout
22565 \begin_inset Formula $\maltese$
22575 <cell alignment="center" valignment="top" leftline="true" usebox="none">
22578 \begin_layout Plain Layout
22586 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
22589 \begin_layout Plain Layout
22590 \begin_inset Formula $\diagup$
22600 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
22603 \begin_layout Plain Layout
22611 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
22614 \begin_layout Plain Layout
22615 \begin_inset Formula $\diagdown$
22631 \begin_layout Standard
22632 \begin_inset VSpace medskip
22638 \begin_layout Standard
22639 Some symbols can be displayed in different sizes, see
22640 \begin_inset CommandInset ref
22642 reference "subsec:Font-Sizes"
22649 \begin_layout Subsection
22651 \begin_inset Index idx
22654 \begin_layout Plain Layout
22655 Symbols ! Euro-symbol
22661 \begin_inset Index idx
22664 \begin_layout Plain Layout
22671 \begin_layout Plain Layout
22688 \begin_layout Standard
22689 To use the Euro symbol in formulas, the \SpecialChar LaTeX
22695 \begin_inset Index idx
22698 \begin_layout Plain Layout
22704 must be installed and loaded with the \SpecialChar LaTeX
22708 \begin_layout Standard
22713 usepackage[gennarrow]{eurosym}
22716 \begin_layout Standard
22717 The Euro symbol can now be inserted with the command
22724 \begin_inset Index idx
22727 \begin_layout Plain Layout
22738 \begin_layout Standard
22739 The Euro symbol can directly be inserted with the € key in mathematical
22740 text, without having
22755 can also be inserted in \SpecialChar TeX
22757 The official currency symbol can then be inserted with the command
22764 \begin_inset Index idx
22767 \begin_layout Plain Layout
22775 , that is only available in \SpecialChar TeX
22779 \begin_layout Standard
22783 \begin_layout Plain Layout
22793 \begin_inset Note Note
22796 \begin_layout Plain Layout
22797 The following table will only be displayed when the \SpecialChar LaTeX
22810 \begin_layout Standard
22811 An overview about the different Euro symbols:
22814 \begin_layout Standard
22816 \begin_inset Tabular
22817 <lyxtabular version="3" rows="4" columns="3">
22818 <features booktabs="true" tabularvalignment="middle">
22819 <column alignment="center" valignment="top" width="0pt">
22820 <column alignment="center" valignment="top" width="0pt">
22821 <column alignment="center" valignment="top" width="0pt">
22823 <cell alignment="center" valignment="top" bottomline="true" usebox="none">
22826 \begin_layout Plain Layout
22830 \begin_layout Plain Layout
22834 cmidrule[0.08em]{2-3}
22844 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
22847 \begin_layout Plain Layout
22853 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
22856 \begin_layout Plain Layout
22864 <cell alignment="center" valignment="top" leftline="true" usebox="none">
22867 \begin_layout Plain Layout
22873 <cell alignment="center" valignment="top" leftline="true" usebox="none">
22876 \begin_layout Plain Layout
22884 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
22887 \begin_layout Plain Layout
22888 \begin_inset Formula $\euro$
22898 <cell alignment="center" valignment="top" leftline="true" usebox="none">
22901 \begin_layout Plain Layout
22907 <cell alignment="center" valignment="top" leftline="true" usebox="none">
22910 \begin_layout Plain Layout
22916 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
22919 \begin_layout Plain Layout
22920 \begin_inset Formula $\mbox{€}$
22930 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
22933 \begin_layout Plain Layout
22940 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
22943 \begin_layout Plain Layout
22951 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
22954 \begin_layout Plain Layout
22958 \begin_layout Plain Layout
22978 \begin_inset Note Note
22981 \begin_layout Plain Layout
22988 is used here only for table borders.
22998 manual for details.
23006 \begin_layout Standard
23010 \begin_layout Plain Layout
23020 \begin_inset Note Note
23023 \begin_layout Plain Layout
23024 The following will be displayed when the \SpecialChar LaTeX
23037 \begin_layout Standard
23038 You need to install the \SpecialChar LaTeX
23043 to see the rest of this subsection in the output.
23046 \begin_layout Standard
23050 \begin_layout Plain Layout
23062 \begin_layout Standard
23063 \begin_inset Newpage newpage
23069 \begin_layout Section
23071 \begin_inset CommandInset label
23073 name "sec:Relations"
23078 \begin_inset Index idx
23081 \begin_layout Plain Layout
23088 \begin_inset Index idx
23091 \begin_layout Plain Layout
23096 \begin_layout Plain Layout
23107 \begin_layout Plain Layout
23122 \begin_layout Standard
23123 All following relations can also be inserted via the toolbar button
23126 arg "math-insert \\leq"
23132 \begin_layout Standard
23133 \begin_inset Tabular
23134 <lyxtabular version="3" rows="17" columns="2">
23135 <features booktabs="true" tabularvalignment="middle">
23136 <column alignment="center" valignment="top" width="0pt">
23137 <column alignment="center" valignment="top" width="0pt">
23139 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
23142 \begin_layout Plain Layout
23148 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
23151 \begin_layout Plain Layout
23159 <cell alignment="center" valignment="top" leftline="true" usebox="none">
23162 \begin_layout Plain Layout
23168 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
23171 \begin_layout Plain Layout
23172 \begin_inset Formula $<$
23182 <cell alignment="center" valignment="top" leftline="true" usebox="none">
23185 \begin_layout Plain Layout
23193 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
23196 \begin_layout Plain Layout
23197 \begin_inset Formula $\le$
23207 <cell alignment="center" valignment="top" leftline="true" usebox="none">
23210 \begin_layout Plain Layout
23218 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
23221 \begin_layout Plain Layout
23222 \begin_inset Formula $\ll$
23232 <cell alignment="center" valignment="top" leftline="true" usebox="none">
23235 \begin_layout Plain Layout
23243 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
23246 \begin_layout Plain Layout
23247 \begin_inset Formula $\prec$
23257 <cell alignment="center" valignment="top" leftline="true" usebox="none">
23260 \begin_layout Plain Layout
23268 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
23271 \begin_layout Plain Layout
23272 \begin_inset Formula $\preceq$
23282 <cell alignment="center" valignment="top" leftline="true" usebox="none">
23285 \begin_layout Plain Layout
23293 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
23296 \begin_layout Plain Layout
23297 \begin_inset Formula $\subset$
23307 <cell alignment="center" valignment="top" leftline="true" usebox="none">
23310 \begin_layout Plain Layout
23318 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
23321 \begin_layout Plain Layout
23322 \begin_inset Formula $\subseteq$
23332 <cell alignment="center" valignment="top" leftline="true" usebox="none">
23335 \begin_layout Plain Layout
23343 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
23346 \begin_layout Plain Layout
23347 \begin_inset Formula $\sqsubseteq$
23357 <cell alignment="center" valignment="top" leftline="true" usebox="none">
23360 \begin_layout Plain Layout
23368 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
23371 \begin_layout Plain Layout
23372 \begin_inset Formula $\in$
23382 <cell alignment="center" valignment="top" leftline="true" usebox="none">
23385 \begin_layout Plain Layout
23393 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
23396 \begin_layout Plain Layout
23397 \begin_inset Formula $\vdash$
23407 <cell alignment="center" valignment="top" leftline="true" usebox="none">
23410 \begin_layout Plain Layout
23418 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
23421 \begin_layout Plain Layout
23422 \begin_inset Formula $\smile$
23432 <cell alignment="center" valignment="top" leftline="true" usebox="none">
23435 \begin_layout Plain Layout
23443 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
23446 \begin_layout Plain Layout
23447 \begin_inset Formula $\lhd$
23457 <cell alignment="center" valignment="top" leftline="true" usebox="none">
23460 \begin_layout Plain Layout
23468 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
23471 \begin_layout Plain Layout
23472 \begin_inset Formula $\unlhd$
23482 <cell alignment="center" valignment="top" leftline="true" usebox="none">
23485 \begin_layout Plain Layout
23493 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
23496 \begin_layout Plain Layout
23497 \begin_inset Formula $\gtrless$
23507 <cell alignment="center" valignment="top" leftline="true" usebox="none">
23510 \begin_layout Plain Layout
23518 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
23521 \begin_layout Plain Layout
23522 \begin_inset Formula $\mid$
23532 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
23535 \begin_layout Plain Layout
23543 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
23546 \begin_layout Plain Layout
23547 \begin_inset Formula $\nmid$
23561 \begin_inset space \hfill{}
23565 \begin_inset Tabular
23566 <lyxtabular version="3" rows="17" columns="2">
23567 <features booktabs="true" tabularvalignment="middle">
23568 <column alignment="center" valignment="top" width="0pt">
23569 <column alignment="center" valignment="top" width="0pt">
23571 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
23574 \begin_layout Plain Layout
23580 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
23583 \begin_layout Plain Layout
23591 <cell alignment="center" valignment="top" leftline="true" usebox="none">
23594 \begin_layout Plain Layout
23600 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
23603 \begin_layout Plain Layout
23604 \begin_inset Formula $=$
23614 <cell alignment="center" valignment="top" leftline="true" usebox="none">
23617 \begin_layout Plain Layout
23625 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
23628 \begin_layout Plain Layout
23629 \begin_inset Formula $\not=$
23639 <cell alignment="center" valignment="top" leftline="true" usebox="none">
23642 \begin_layout Plain Layout
23650 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
23653 \begin_layout Plain Layout
23654 \begin_inset Formula $\equiv$
23664 <cell alignment="center" valignment="top" leftline="true" usebox="none">
23667 \begin_layout Plain Layout
23675 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
23678 \begin_layout Plain Layout
23679 \begin_inset Formula $\sim$
23689 <cell alignment="center" valignment="top" leftline="true" usebox="none">
23692 \begin_layout Plain Layout
23700 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
23703 \begin_layout Plain Layout
23704 \begin_inset Formula $\simeq$
23714 <cell alignment="center" valignment="top" leftline="true" usebox="none">
23717 \begin_layout Plain Layout
23725 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
23728 \begin_layout Plain Layout
23729 \begin_inset Formula $\approx$
23739 <cell alignment="center" valignment="top" leftline="true" usebox="none">
23742 \begin_layout Plain Layout
23750 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
23753 \begin_layout Plain Layout
23754 \begin_inset Formula $\cong$
23764 <cell alignment="center" valignment="top" leftline="true" usebox="none">
23767 \begin_layout Plain Layout
23775 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
23778 \begin_layout Plain Layout
23779 \begin_inset Formula $\bowtie$
23789 <cell alignment="center" valignment="top" leftline="true" usebox="none">
23792 \begin_layout Plain Layout
23800 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
23803 \begin_layout Plain Layout
23804 \begin_inset Formula $\notin$
23814 <cell alignment="center" valignment="top" leftline="true" usebox="none">
23817 \begin_layout Plain Layout
23825 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
23828 \begin_layout Plain Layout
23829 \begin_inset Formula $\perp$
23839 <cell alignment="center" valignment="top" leftline="true" usebox="none">
23842 \begin_layout Plain Layout
23850 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
23853 \begin_layout Plain Layout
23854 \begin_inset Formula $\propto$
23864 <cell alignment="center" valignment="top" leftline="true" usebox="none">
23867 \begin_layout Plain Layout
23875 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
23878 \begin_layout Plain Layout
23879 \begin_inset Formula $\asymp$
23889 <cell alignment="center" valignment="top" leftline="true" usebox="none">
23892 \begin_layout Plain Layout
23900 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
23903 \begin_layout Plain Layout
23904 \begin_inset Formula $\doteq$
23914 <cell alignment="center" valignment="top" leftline="true" usebox="none">
23917 \begin_layout Plain Layout
23925 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
23928 \begin_layout Plain Layout
23929 \begin_inset Formula $\circeq$
23939 <cell alignment="center" valignment="top" leftline="true" usebox="none">
23942 \begin_layout Plain Layout
23950 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
23953 \begin_layout Plain Layout
23954 \begin_inset Formula $\models$
23964 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
23967 \begin_layout Plain Layout
23975 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
23978 \begin_layout Plain Layout
23979 \begin_inset Formula $\widehat{=}$
23993 \begin_inset space \hfill{}
23997 \begin_inset Tabular
23998 <lyxtabular version="3" rows="17" columns="2">
23999 <features booktabs="true" tabularvalignment="middle">
24000 <column alignment="center" valignment="top" width="0pt">
24001 <column alignment="center" valignment="top" width="0pt">
24003 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
24006 \begin_layout Plain Layout
24012 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
24015 \begin_layout Plain Layout
24023 <cell alignment="center" valignment="top" leftline="true" usebox="none">
24026 \begin_layout Plain Layout
24032 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
24035 \begin_layout Plain Layout
24036 \begin_inset Formula $>$
24046 <cell alignment="center" valignment="top" leftline="true" usebox="none">
24049 \begin_layout Plain Layout
24057 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
24060 \begin_layout Plain Layout
24061 \begin_inset Formula $\ge$
24071 <cell alignment="center" valignment="top" leftline="true" usebox="none">
24074 \begin_layout Plain Layout
24082 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
24085 \begin_layout Plain Layout
24086 \begin_inset Formula $\gg$
24096 <cell alignment="center" valignment="top" leftline="true" usebox="none">
24099 \begin_layout Plain Layout
24107 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
24110 \begin_layout Plain Layout
24111 \begin_inset Formula $\succ$
24121 <cell alignment="center" valignment="top" leftline="true" usebox="none">
24124 \begin_layout Plain Layout
24132 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
24135 \begin_layout Plain Layout
24136 \begin_inset Formula $\succeq$
24146 <cell alignment="center" valignment="top" leftline="true" usebox="none">
24149 \begin_layout Plain Layout
24157 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
24160 \begin_layout Plain Layout
24161 \begin_inset Formula $\supset$
24171 <cell alignment="center" valignment="top" leftline="true" usebox="none">
24174 \begin_layout Plain Layout
24182 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
24185 \begin_layout Plain Layout
24186 \begin_inset Formula $\supseteq$
24196 <cell alignment="center" valignment="top" leftline="true" usebox="none">
24199 \begin_layout Plain Layout
24207 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
24210 \begin_layout Plain Layout
24211 \begin_inset Formula $\sqsupseteq$
24221 <cell alignment="center" valignment="top" leftline="true" usebox="none">
24224 \begin_layout Plain Layout
24232 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
24235 \begin_layout Plain Layout
24236 \begin_inset Formula $\ni$
24246 <cell alignment="center" valignment="top" leftline="true" usebox="none">
24249 \begin_layout Plain Layout
24257 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
24260 \begin_layout Plain Layout
24261 \begin_inset Formula $\dashv$
24271 <cell alignment="center" valignment="top" leftline="true" usebox="none">
24274 \begin_layout Plain Layout
24282 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
24285 \begin_layout Plain Layout
24286 \begin_inset Formula $\frown$
24296 <cell alignment="center" valignment="top" leftline="true" usebox="none">
24299 \begin_layout Plain Layout
24307 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
24310 \begin_layout Plain Layout
24311 \begin_inset Formula $\rhd$
24321 <cell alignment="center" valignment="top" leftline="true" usebox="none">
24324 \begin_layout Plain Layout
24332 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
24335 \begin_layout Plain Layout
24336 \begin_inset Formula $\unrhd$
24346 <cell alignment="center" valignment="top" leftline="true" usebox="none">
24349 \begin_layout Plain Layout
24357 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
24360 \begin_layout Plain Layout
24361 \begin_inset Formula $\lessgtr$
24371 <cell alignment="center" valignment="top" leftline="true" usebox="none">
24374 \begin_layout Plain Layout
24382 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
24385 \begin_layout Plain Layout
24386 \begin_inset Formula $\parallel$
24396 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
24399 \begin_layout Plain Layout
24407 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
24410 \begin_layout Plain Layout
24411 \begin_inset Formula $\nparallel$
24427 \begin_layout Standard
24428 \begin_inset VSpace medskip
24443 are bigger than the equal looking operators
24458 \begin_layout Standard
24460 supports also many special relations.
24461 Use the toolbar button
24464 arg "math-insert \\leqq"
24467 to see a list of these relations.
24470 \begin_layout Standard
24471 Relations are, in contrary to symbols, always surrounded by space.
24474 \begin_layout Standard
24475 Relations with labels can be created with the command
24482 \begin_inset Index idx
24485 \begin_layout Plain Layout
24496 \begin_layout Standard
24498 \begin_inset Tabular
24499 <lyxtabular version="3" rows="2" columns="2">
24500 <features booktabs="true" tabularvalignment="middle">
24501 <column alignment="center" valignment="top" width="0pt">
24502 <column alignment="center" valignment="top">
24504 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
24507 \begin_layout Plain Layout
24513 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
24516 \begin_layout Plain Layout
24523 <row topspace="1.5mm">
24524 <cell alignment="center" valignment="top" bottomline="true" usebox="none">
24527 \begin_layout Plain Layout
24531 \begin_inset space \textvisiblespace{}
24539 \begin_inset space \textvisiblespace{}
24543 \begin_inset Formula $\downarrow$
24549 \begin_inset space \textvisiblespace{}
24553 \begin_inset space \textvisiblespace{}
24561 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
24564 \begin_layout Plain Layout
24565 \begin_inset Formula $A(r)\stackrel{r\to\infty}{\approx}B$
24581 \begin_layout Section
24585 \begin_layout Subsection
24586 Predefined Functions
24587 \begin_inset CommandInset label
24589 name "subsec:Predefined-Functions"
24594 \begin_inset Index idx
24597 \begin_layout Plain Layout
24598 Functions ! predefined
24606 \begin_layout Standard
24607 In general, variables are set
24611 in mathematical expressions, but not function names, because
24612 \begin_inset Formula $sin$
24615 could be misunderstood as
24616 \begin_inset Formula $s\cdot i\cdot n$
24620 Therefore there are predefined functions which are additionally a bit separated
24622 They are inserted as commands starting with a backslash before their name.
24625 \begin_layout Standard
24627 \begin_inset Tabular
24628 <lyxtabular version="3" rows="2" columns="2">
24629 <features booktabs="true" tabularvalignment="middle">
24630 <column alignment="center" valignment="top" width="0pt">
24631 <column alignment="center" valignment="top" width="0pt">
24633 <cell alignment="center" valignment="top" topline="true" bottomline="true" usebox="none">
24636 \begin_layout Plain Layout
24642 <cell alignment="center" valignment="top" topline="true" bottomline="true" rightline="true" usebox="none">
24645 \begin_layout Plain Layout
24653 <cell alignment="center" valignment="top" bottomline="true" usebox="none">
24656 \begin_layout Plain Layout
24662 <cell alignment="center" valignment="top" bottomline="true" rightline="true" usebox="none">
24665 \begin_layout Plain Layout
24666 \begin_inset Formula $Asin(x)+B$
24680 \begin_inset space \quad{}
24684 \begin_inset Tabular
24685 <lyxtabular version="3" rows="2" columns="2">
24686 <features booktabs="true" tabularvalignment="middle">
24687 <column alignment="center" valignment="top" width="0pt">
24688 <column alignment="center" valignment="top" width="0pt">
24690 <cell alignment="center" valignment="top" topline="true" bottomline="true" usebox="none">
24693 \begin_layout Plain Layout
24699 <cell alignment="center" valignment="top" topline="true" bottomline="true" usebox="none">
24702 \begin_layout Plain Layout
24710 <cell alignment="center" valignment="top" bottomline="true" usebox="none">
24713 \begin_layout Plain Layout
24721 <cell alignment="center" valignment="top" bottomline="true" usebox="none">
24724 \begin_layout Plain Layout
24725 \begin_inset Formula $A\sin(x)+B$
24741 \begin_layout Standard
24742 The following functions are predefined:
24745 \begin_layout Standard
24746 \begin_inset VSpace -2mm
24752 \begin_layout Standard
24754 \begin_inset Tabular
24755 <lyxtabular version="3" rows="9" columns="4">
24756 <features booktabs="true" tabularvalignment="middle">
24757 <column alignment="center" valignment="top" width="0pt">
24758 <column alignment="center" valignment="top" width="0pt">
24759 <column alignment="center" valignment="top" width="0pt">
24760 <column alignment="center" valignment="top" width="0pt">
24762 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
24765 \begin_layout Plain Layout
24771 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
24774 \begin_layout Plain Layout
24780 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
24783 \begin_layout Plain Layout
24789 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
24792 \begin_layout Plain Layout
24800 <cell alignment="center" valignment="top" leftline="true" usebox="none">
24803 \begin_layout Plain Layout
24811 <cell alignment="center" valignment="top" leftline="true" usebox="none">
24814 \begin_layout Plain Layout
24822 <cell alignment="center" valignment="top" leftline="true" usebox="none">
24825 \begin_layout Plain Layout
24833 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
24836 \begin_layout Plain Layout
24846 <cell alignment="center" valignment="top" leftline="true" usebox="none">
24849 \begin_layout Plain Layout
24857 <cell alignment="center" valignment="top" leftline="true" usebox="none">
24860 \begin_layout Plain Layout
24868 <cell alignment="center" valignment="top" leftline="true" usebox="none">
24871 \begin_layout Plain Layout
24879 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
24882 \begin_layout Plain Layout
24892 <cell alignment="center" valignment="top" leftline="true" usebox="none">
24895 \begin_layout Plain Layout
24903 <cell alignment="center" valignment="top" leftline="true" usebox="none">
24906 \begin_layout Plain Layout
24914 <cell alignment="center" valignment="top" leftline="true" usebox="none">
24917 \begin_layout Plain Layout
24925 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
24928 \begin_layout Plain Layout
24938 <cell alignment="center" valignment="top" leftline="true" usebox="none">
24941 \begin_layout Plain Layout
24949 <cell alignment="center" valignment="top" leftline="true" usebox="none">
24952 \begin_layout Plain Layout
24960 <cell alignment="center" valignment="top" leftline="true" usebox="none">
24963 \begin_layout Plain Layout
24971 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
24974 \begin_layout Plain Layout
24984 <cell alignment="center" valignment="top" leftline="true" usebox="none">
24987 \begin_layout Plain Layout
24995 <cell alignment="center" valignment="top" leftline="true" usebox="none">
24998 \begin_layout Plain Layout
25006 <cell alignment="center" valignment="top" leftline="true" usebox="none">
25009 \begin_layout Plain Layout
25017 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
25020 \begin_layout Plain Layout
25030 <cell alignment="center" valignment="top" leftline="true" usebox="none">
25033 \begin_layout Plain Layout
25041 <cell alignment="center" valignment="top" leftline="true" usebox="none">
25044 \begin_layout Plain Layout
25052 <cell alignment="center" valignment="top" leftline="true" usebox="none">
25055 \begin_layout Plain Layout
25063 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
25066 \begin_layout Plain Layout
25076 <cell alignment="center" valignment="top" leftline="true" usebox="none">
25079 \begin_layout Plain Layout
25087 <cell alignment="center" valignment="top" leftline="true" usebox="none">
25090 \begin_layout Plain Layout
25098 <cell alignment="center" valignment="top" leftline="true" usebox="none">
25101 \begin_layout Plain Layout
25109 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
25112 \begin_layout Plain Layout
25122 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
25125 \begin_layout Plain Layout
25133 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
25136 \begin_layout Plain Layout
25144 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
25147 \begin_layout Plain Layout
25155 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
25158 \begin_layout Plain Layout
25174 \begin_layout Standard
25175 They can also be inserted with the math toolbar button
25178 arg "math-insert \\functions"
25184 \begin_layout Subsection
25185 Self-defined Functions
25186 \begin_inset Index idx
25189 \begin_layout Plain Layout
25190 Functions ! self-defined
25198 \begin_layout Standard
25199 To use a function that is not predefined, like for example the sign function
25200 sgn(x), there are two possibilities:
25203 \begin_layout Itemize
25204 Define the function by inserting the following line to the \SpecialChar LaTeX
25209 \begin_layout Plain Layout
25214 DeclareMathOperator
25217 \begin_inset CommandInset ref
25219 reference "subsec:Self-defined-Operators"
25229 \begin_inset Newline newline
25233 \begin_inset VSpace -3mm
25237 \begin_inset Newline newline
25244 DeclareMathOperator{
25249 \begin_inset Index idx
25252 \begin_layout Plain Layout
25257 DeclareMathOperator
25263 \begin_inset Newline newline
25267 \begin_inset VSpace -2mm
25271 \begin_inset Newline newline
25274 Now the new defined function can be called with the command
25283 \begin_layout Itemize
25284 Write the formula as usual, mark the formula name, in our example the letters
25289 , and change it to mathematical text.
25290 Finally, a space is inserted between prefactor and function.
25293 \begin_layout Standard
25294 The result is the same with both methods as with a predefined function
25298 \begin_layout Plain Layout
25299 In \SpecialChar LyX
25300 self-defined functions are displayed red, predefined ones black.
25308 \begin_layout Standard
25310 \begin_inset Tabular
25311 <lyxtabular version="3" rows="3" columns="2">
25312 <features booktabs="true" tabularvalignment="middle">
25313 <column alignment="center" valignment="top" width="0pt">
25314 <column alignment="center" valignment="top" width="0pt">
25316 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
25319 \begin_layout Plain Layout
25325 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
25328 \begin_layout Plain Layout
25336 <cell alignment="center" valignment="top" leftline="true" usebox="none">
25339 \begin_layout Plain Layout
25347 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
25350 \begin_layout Plain Layout
25351 \begin_inset Formula $A\sgn(x)+B$
25361 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
25364 \begin_layout Plain Layout
25368 \begin_inset Formula $\underbrace{\textrm{sgn}}_{\textrm{Alt+M}\,\textrm{M}}$
25376 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
25379 \begin_layout Plain Layout
25380 \begin_inset Formula $A\,\textrm{sgn}(x)+B$
25396 \begin_layout Standard
25397 The first method is more suitable when the self-defined function should
25398 be used several times.
25401 \begin_layout Subsection
25403 \begin_inset Index idx
25406 \begin_layout Plain Layout
25415 \begin_layout Standard
25416 For limits, in addition to the commands
25423 \begin_inset Index idx
25426 \begin_layout Plain Layout
25446 the following functions are defined:
25449 \begin_layout Standard
25451 \begin_inset Tabular
25452 <lyxtabular version="3" rows="5" columns="2">
25453 <features booktabs="true" tabularvalignment="middle">
25454 <column alignment="center" valignment="top" width="0pt">
25455 <column alignment="center" valignment="top" width="0pt">
25457 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
25460 \begin_layout Plain Layout
25466 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
25469 \begin_layout Plain Layout
25477 <cell alignment="center" valignment="top" leftline="true" usebox="none">
25480 \begin_layout Plain Layout
25488 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
25491 \begin_layout Plain Layout
25492 \begin_inset Formula $\varliminf$
25501 <row topspace="1.5mm">
25502 <cell alignment="center" valignment="top" usebox="none">
25505 \begin_layout Plain Layout
25513 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
25516 \begin_layout Plain Layout
25517 \begin_inset Formula $\varlimsup$
25526 <row topspace="1.5mm">
25527 <cell alignment="center" valignment="top" usebox="none">
25530 \begin_layout Plain Layout
25538 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
25541 \begin_layout Plain Layout
25542 \begin_inset Formula $\varprojlim$
25551 <row topspace="1.5mm" bottomspace="1mm">
25552 <cell alignment="center" valignment="top" bottomline="true" usebox="none">
25555 \begin_layout Plain Layout
25563 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
25566 \begin_layout Plain Layout
25567 \begin_inset Formula $\varinjlim$
25583 \begin_layout Standard
25584 \begin_inset VSpace medskip
25587 The limit is created by inserting a subscript.
25588 It is set right beside the function in an inline formula:
25591 \begin_layout Standard
25593 \begin_inset Tabular
25594 <lyxtabular version="3" rows="2" columns="2">
25595 <features booktabs="true" tabularvalignment="middle">
25596 <column alignment="center" valignment="top" width="0pt">
25597 <column alignment="center" valignment="top" width="0pt">
25599 <cell alignment="center" valignment="top" bottomline="true" usebox="none">
25602 \begin_layout Plain Layout
25608 <cell alignment="center" valignment="top" bottomline="true" usebox="none">
25611 \begin_layout Plain Layout
25619 <cell alignment="center" valignment="top" usebox="none">
25622 \begin_layout Plain Layout
25628 \begin_inset space \textvisiblespace{}
25632 \begin_inset space \textvisiblespace{}
25640 <cell alignment="center" valignment="top" usebox="none">
25643 \begin_layout Plain Layout
25644 \begin_inset Formula $\lim_{x\to A}x=B$
25660 \begin_layout Standard
25661 In a displayed formula the limit is set below the formula, as usual:
25662 \begin_inset Formula
25672 \begin_layout Standard
25673 \begin_inset VSpace medskip
25679 \begin_layout Standard
25680 How to adjust the typesetting of the limits see
25681 \begin_inset CommandInset ref
25683 reference "subsec:Operator-Limits"
25690 \begin_layout Subsection
25692 \begin_inset Index idx
25695 \begin_layout Plain Layout
25696 Functions ! modulo-
25704 \begin_layout Standard
25705 The modulo-function is special, because it exists in four variants.
25706 The variants in a displayed formula are:
25707 \begin_inset Formula
25709 \underline{\textrm{Command}\raisebox{-0.9mm}{}} & & \underline{\textrm{Result}}\\
25710 \mathrm{a\backslash mod\textrm{␣}b} & & a\mod b\\
25711 \mathrm{a\backslash pmod\textrm{␣}b} & & a\pmod b\\
25712 \mathrm{a\backslash bmod\textrm{␣}b} & & a\bmod b\\
25713 \mathrm{a\backslash pod\textrm{␣}b} & & a\pod b
25721 \begin_layout Standard
25722 In an inline formula less space is set before the function names for all
25724 By default the modulo-functions take only the first following character
25726 To use more than one character, one has to put them into \SpecialChar TeX
25728 \begin_inset Formula
25730 \underline{\textrm{Command}\raisebox{-0.9mm}{}} & & \underline{\textrm{Result}}\\
25731 \mathrm{a\backslash pod\textrm{␣}bcd} & & a\pod bcd\\
25732 \mathrm{a\backslash pod\backslash\{bc\to d} & & a\pod{bc}d
25740 \begin_layout Section
25742 \begin_inset Index idx
25745 \begin_layout Plain Layout
25754 \begin_layout Standard
25755 The characters ^ and _ would normally create a superscript and subscript,
25757 To get these characters you have to insert them with a leading
25762 \begin_layout Standard
25765 \begin_inset Tabular
25766 <lyxtabular version="3" rows="3" columns="2">
25767 <features booktabs="true" tabularvalignment="middle">
25768 <column alignment="left" valignment="top" width="0pt">
25769 <column alignment="block" valignment="top">
25771 <cell alignment="left" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
25774 \begin_layout Plain Layout
25780 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
25783 \begin_layout Plain Layout
25791 <cell alignment="left" valignment="top" leftline="true" usebox="none">
25794 \begin_layout Plain Layout
25798 \begin_inset space \textvisiblespace{}
25806 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
25809 \begin_layout Plain Layout
25810 \begin_inset Formula $\mathcircumflex$
25820 <cell alignment="left" valignment="top" bottomline="true" leftline="true" usebox="none">
25823 \begin_layout Plain Layout
25831 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
25834 \begin_layout Plain Layout
25835 \begin_inset Formula $\_$
25851 \begin_layout Subsection
25852 Special Characters in Mathematical Text
25855 \begin_layout Standard
25856 The following commands can only be used in mathematical text or in \SpecialChar TeX
25860 \begin_layout Standard
25861 \begin_inset space \hfill{}
25865 \begin_inset Tabular
25866 <lyxtabular version="3" rows="8" columns="2">
25867 <features booktabs="true" tabularvalignment="middle">
25868 <column alignment="left" valignment="top" width="0pt">
25869 <column alignment="block" valignment="top">
25871 <cell alignment="left" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
25874 \begin_layout Plain Layout
25880 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
25883 \begin_layout Plain Layout
25891 <cell alignment="left" valignment="top" leftline="true" usebox="none">
25894 \begin_layout Plain Layout
25902 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
25905 \begin_layout Plain Layout
25906 \begin_inset Formula $\textrm{œ}$
25916 <cell alignment="left" valignment="top" leftline="true" usebox="none">
25919 \begin_layout Plain Layout
25927 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
25930 \begin_layout Plain Layout
25931 \begin_inset Formula $\textrm{Œ}$
25941 <cell alignment="left" valignment="top" leftline="true" usebox="none">
25944 \begin_layout Plain Layout
25952 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
25955 \begin_layout Plain Layout
25956 \begin_inset Formula $\textrm{æ}$
25966 <cell alignment="left" valignment="top" leftline="true" usebox="none">
25969 \begin_layout Plain Layout
25977 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
25980 \begin_layout Plain Layout
25981 \begin_inset Formula $\textrm{Æ}$
25991 <cell alignment="left" valignment="top" leftline="true" usebox="none">
25994 \begin_layout Plain Layout
26002 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
26005 \begin_layout Plain Layout
26006 \begin_inset Formula $\textrm{å}$
26016 <cell alignment="left" valignment="top" leftline="true" usebox="none">
26019 \begin_layout Plain Layout
26023 \begin_inset Index idx
26026 \begin_layout Plain Layout
26033 \begin_layout Plain Layout
26054 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
26057 \begin_layout Plain Layout
26058 \begin_inset Formula $\textrm{Å}$
26068 <cell alignment="left" valignment="top" bottomline="true" leftline="true" usebox="none">
26071 \begin_layout Plain Layout
26079 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
26082 \begin_layout Plain Layout
26083 \begin_inset Formula $\textrm{ı}$
26097 \begin_inset space \hfill{}
26101 \begin_inset Tabular
26102 <lyxtabular version="3" rows="8" columns="2">
26103 <features booktabs="true" tabularvalignment="middle">
26104 <column alignment="left" valignment="top" width="0pt">
26105 <column alignment="center" valignment="top">
26107 <cell alignment="left" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
26110 \begin_layout Plain Layout
26112 \begin_inset Note Note
26115 \begin_layout Plain Layout
26117 \begin_inset space \thinspace{}
26120 mm is used for separation, because otherwise the output will be ¡ and ¿
26131 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
26134 \begin_layout Plain Layout
26142 <cell alignment="left" valignment="top" leftline="true" usebox="none">
26145 \begin_layout Plain Layout
26153 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
26156 \begin_layout Plain Layout
26157 \begin_inset Formula $\textrm{ø}$
26167 <cell alignment="left" valignment="top" leftline="true" usebox="none">
26170 \begin_layout Plain Layout
26178 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
26181 \begin_layout Plain Layout
26182 \begin_inset Formula $\textrm{Ø}$
26192 <cell alignment="left" valignment="top" leftline="true" usebox="none">
26195 \begin_layout Plain Layout
26203 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
26206 \begin_layout Plain Layout
26207 \begin_inset Formula $\textrm{ł}$
26217 <cell alignment="left" valignment="top" leftline="true" usebox="none">
26220 \begin_layout Plain Layout
26228 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
26231 \begin_layout Plain Layout
26232 \begin_inset Formula $\textrm{Ł}$
26242 <cell alignment="left" valignment="top" leftline="true" usebox="none">
26245 \begin_layout Plain Layout
26247 \begin_inset space \hspace{}
26252 \begin_inset space \textvisiblespace{}
26260 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
26263 \begin_layout Plain Layout
26264 \begin_inset Formula $\textrm{!`}$
26274 <cell alignment="left" valignment="top" leftline="true" usebox="none">
26277 \begin_layout Plain Layout
26279 \begin_inset space \hspace{}
26284 \begin_inset space \textvisiblespace{}
26292 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
26295 \begin_layout Plain Layout
26296 \begin_inset Formula $\textrm{?`}$
26306 <cell alignment="left" valignment="top" bottomline="true" leftline="true" usebox="none">
26309 \begin_layout Plain Layout
26317 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
26320 \begin_layout Plain Layout
26321 \begin_inset Formula $\textrm{ȷ}$
26335 \begin_inset space \hfill{}
26341 \begin_layout Standard
26343 \begin_inset Formula $\textrm{\textrm{Å}}$
26347 \begin_inset Formula $\textrm{\textrm{Ø}}$
26350 can also be inserted via the math toolbar button
26353 arg "math-insert \\digamma"
26359 \begin_layout Standard
26360 An exception are the commands
26363 \begin_inset space \hspace{}
26372 \begin_inset space \hspace{}
26378 , because they can be inserted in \SpecialChar LyX
26382 \begin_layout Subsection
26384 \begin_inset CommandInset label
26386 name "subsec:Accents-in-Text"
26391 \begin_inset Index idx
26394 \begin_layout Plain Layout
26403 \begin_layout Standard
26404 With the following commands all letters can be accented.
26405 The commands must be inserted in \SpecialChar TeX
26409 \begin_layout Standard
26410 \begin_inset space \hfill{}
26414 \begin_inset Tabular
26415 <lyxtabular version="3" rows="8" columns="2">
26416 <features booktabs="true" tabularvalignment="middle">
26417 <column alignment="left" valignment="top" width="0pt">
26418 <column alignment="block" valignment="top">
26420 <cell alignment="left" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
26423 \begin_layout Plain Layout
26429 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
26432 \begin_layout Plain Layout
26440 <cell alignment="left" valignment="top" leftline="true" usebox="none">
26443 \begin_layout Plain Layout
26447 \begin_inset Quotes grd
26455 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
26458 \begin_layout Plain Layout
26462 \begin_layout Plain Layout
26478 <cell alignment="left" valignment="top" leftline="true" usebox="none">
26481 \begin_layout Plain Layout
26489 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
26492 \begin_layout Plain Layout
26496 \begin_layout Plain Layout
26512 <cell alignment="left" valignment="top" leftline="true" usebox="none">
26515 \begin_layout Plain Layout
26519 \begin_inset space \textvisiblespace{}
26527 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
26530 \begin_layout Plain Layout
26534 \begin_layout Plain Layout
26550 <cell alignment="left" valignment="top" leftline="true" usebox="none">
26553 \begin_layout Plain Layout
26561 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
26564 \begin_layout Plain Layout
26568 \begin_layout Plain Layout
26584 <cell alignment="left" valignment="top" leftline="true" usebox="none">
26587 \begin_layout Plain Layout
26591 \begin_inset space \textvisiblespace{}
26599 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
26602 \begin_layout Plain Layout
26606 \begin_layout Plain Layout
26622 <cell alignment="left" valignment="top" leftline="true" usebox="none">
26625 \begin_layout Plain Layout
26629 \begin_inset space \textvisiblespace{}
26637 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
26640 \begin_layout Plain Layout
26644 \begin_layout Plain Layout
26660 <cell alignment="left" valignment="top" bottomline="true" leftline="true" usebox="none">
26663 \begin_layout Plain Layout
26667 \begin_inset space \textvisiblespace{}
26675 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
26678 \begin_layout Plain Layout
26682 \begin_layout Plain Layout
26702 \begin_inset space \hfill{}
26706 \begin_inset Tabular
26707 <lyxtabular version="3" rows="8" columns="2">
26708 <features booktabs="true" tabularvalignment="middle">
26709 <column alignment="left" valignment="top" width="0pt">
26710 <column alignment="center" valignment="top">
26712 <cell alignment="left" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
26715 \begin_layout Plain Layout
26721 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
26724 \begin_layout Plain Layout
26732 <cell alignment="left" valignment="top" leftline="true" usebox="none">
26735 \begin_layout Plain Layout
26739 \begin_inset space \textvisiblespace{}
26747 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
26750 \begin_layout Plain Layout
26754 \begin_layout Plain Layout
26770 <cell alignment="left" valignment="top" leftline="true" usebox="none">
26773 \begin_layout Plain Layout
26781 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
26784 \begin_layout Plain Layout
26788 \begin_layout Plain Layout
26804 <cell alignment="left" valignment="top" leftline="true" usebox="none">
26807 \begin_layout Plain Layout
26811 \begin_inset Index idx
26814 \begin_layout Plain Layout
26825 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
26828 \begin_layout Plain Layout
26832 \begin_layout Plain Layout
26848 <cell alignment="left" valignment="top" leftline="true" usebox="none">
26851 \begin_layout Plain Layout
26859 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
26862 \begin_layout Plain Layout
26866 \begin_layout Plain Layout
26882 <cell alignment="left" valignment="top" leftline="true" usebox="none">
26885 \begin_layout Plain Layout
26889 \begin_inset space \textvisiblespace{}
26897 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
26900 \begin_layout Plain Layout
26904 \begin_layout Plain Layout
26920 <cell alignment="left" valignment="top" leftline="true" usebox="none">
26923 \begin_layout Plain Layout
26927 \begin_inset space \textvisiblespace{}
26935 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
26938 \begin_layout Plain Layout
26942 \begin_layout Plain Layout
26958 <cell alignment="left" valignment="top" leftline="true" usebox="none">
26961 \begin_layout Plain Layout
26965 \begin_inset space \textvisiblespace{}
26973 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
26976 \begin_layout Plain Layout
26980 \begin_layout Plain Layout
27000 \begin_inset space \hfill{}
27006 \begin_layout Standard
27007 \begin_inset VSpace medskip
27016 also two different characters can be accented.
27022 \begin_inset space \textvisiblespace{}
27031 \begin_layout Plain Layout
27043 \begin_layout Standard
27056 can in combination with vowels directly be inserted with the keyboard without
27057 using \SpecialChar TeX
27059 The same applies for the tilde
27063 \begin_layout Plain Layout
27064 This only applies for keyboards where the tilde is defined as accent.
27073 in combination with
27088 \begin_layout Standard
27131 and accents that are inserted directly with the keyboard are also available
27132 in mathematical text.
27133 For the other accents there are special math commands to be used in formulas,
27135 \begin_inset CommandInset ref
27137 reference "subsec:Accents-for-one"
27144 \begin_layout Standard
27145 \begin_inset VSpace bigskip
27148 Furthermore, with the command
27155 \begin_inset Index idx
27158 \begin_layout Plain Layout
27166 all numbers and letters can be set into a circle, quasi accented with a
27167 circle, similar to the copyright symbol.
27170 \begin_layout Standard
27172 \begin_inset Tabular
27173 <lyxtabular version="3" rows="3" columns="2">
27174 <features booktabs="true" tabularvalignment="middle">
27175 <column alignment="center" valignment="top" width="0pt">
27176 <column alignment="center" valignment="top">
27178 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
27181 \begin_layout Plain Layout
27187 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
27190 \begin_layout Plain Layout
27198 <cell alignment="center" valignment="top" leftline="true" usebox="none">
27201 \begin_layout Plain Layout
27209 <cell multicolumn="1" alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
27212 \begin_layout Plain Layout
27216 \begin_layout Plain Layout
27231 <row topspace="1mm">
27232 <cell alignment="center" valignment="top" bottomline="true" usebox="none">
27235 \begin_layout Plain Layout
27246 raisebox{-1.5pt}{W}}
27251 <cell multicolumn="1" alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
27254 \begin_layout Plain Layout
27258 \begin_layout Plain Layout
27288 \begin_layout Standard
27289 One has to take care that the character fits in the circle.
27300 \begin_layout Plain Layout
27302 \begin_inset CommandInset ref
27304 reference "subsec:Font-Sizes"
27313 specifies thereby the size of the circle.
27324 \begin_layout Plain Layout
27326 \begin_inset CommandInset ref
27328 reference "subsec:Boxes-without-Frame"
27337 the character can be centered.
27340 \begin_layout Subsection
27342 \begin_inset Index idx
27345 \begin_layout Plain Layout
27354 \begin_layout Standard
27355 Old-style figures (also known as old-style numerals) are created with the
27363 \begin_inset Index idx
27366 \begin_layout Plain Layout
27375 The command can be used in formulas and in \SpecialChar TeX
27377 The command scheme is:
27380 \begin_layout Standard
27385 oldstylenums{number}
27388 \begin_layout Standard
27393 oldstylenums{0123456789
27396 \begin_inset Formula $\oldstylenums{0123456789}$
27402 \begin_layout Section
27404 \begin_inset CommandInset label
27406 name "sec:Formula-Styles"
27411 \begin_inset Index idx
27414 \begin_layout Plain Layout
27423 \begin_layout Itemize
27424 There are two different alignment styles:
27428 \begin_layout Description
27429 Centered is the predefined standard
27432 \begin_layout Description
27433 Indented for this the option
27437 must be inserted in the menu
27439 Document\SpecialChar menuseparator
27445 \begin_inset space ~
27451 \begin_layout Standard
27456 is used, the indentation can be adjusted with the length
27463 \begin_inset Index idx
27466 \begin_layout Plain Layout
27475 Should the distance be 15
27476 \begin_inset space \thinspace{}
27479 mm, the following command line is inserted in the \SpecialChar LaTeX
27483 \begin_layout Standard
27493 \begin_layout Standard
27494 When no length is specified, the predefined value of 30
27495 \begin_inset space \thinspace{}
27502 \begin_layout Itemize
27503 And two different numbering styles:
27507 \begin_layout Description
27508 Right is the predefined standard
27511 \begin_layout Description
27512 Left for this the option
27516 must be inserted in the menu
27518 Document\SpecialChar menuseparator
27524 \begin_inset space ~
27531 \begin_layout Standard
27540 can also be used together.
27541 In this case both options are inserted, separated by a comma.
27544 \begin_layout Standard
27545 The chosen styles are used for all displayed formulas of the document.
27546 When both, centered and indented formulas should be created in a document,
27552 The indented formulas are then set in a flalign environment, see
27553 \begin_inset CommandInset ref
27555 reference "subsec:Flalign-Environment"
27562 \begin_layout Section
27564 \begin_inset CommandInset label
27566 name "sec:Multiline-Formulas"
27571 \begin_inset Index idx
27574 \begin_layout Plain Layout
27575 Formula ! multiline
27583 \begin_layout Subsection
27587 \begin_layout Standard
27588 In \SpecialChar LyX
27589 multiline formulas are created by pressing
27592 arg "newline-insert newline"
27596 This creates either an
27600 that is described in
27601 \begin_inset CommandInset ref
27603 reference "subsec:Standard-align-Environment"
27607 or, when automatically loading the package
27611 is disabled in the document settings, an
27613 eqnarray environment
27615 that is described in
27616 \begin_inset CommandInset ref
27618 reference "subsec:Eqnarray-Environment"
27623 The align environment is recommended because it provides in any case a
27624 typographically correct output.
27627 \begin_layout Standard
27628 There are other multiline formula environments that can be created via the
27631 Insert\SpecialChar menuseparator
27635 These environments are described in the following sections.
27638 \begin_layout Standard
27639 In all multiline formula environments a new line is created by pressing
27643 arg "newline-insert newline"
27647 To add or delete lines, the math toolbar buttons
27650 arg "tabular-feature append-row"
27656 arg "tabular-feature delete-row"
27659 , respectively, or the menu
27661 Edit\SpecialChar menuseparator
27667 \begin_layout Subsubsection
27669 \begin_inset CommandInset label
27671 name "subsec:Line-Separation"
27676 \begin_inset Index idx
27679 \begin_layout Plain Layout
27680 Formula ! multiline ! Line separation
27688 \begin_layout Standard
27689 There is sometimes not enough space in multiline formulas between the lines:
27690 \begin_inset Formula
27692 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}\\
27693 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
27701 \begin_layout Standard
27702 In \SpecialChar LaTeX
27703 additional line space is specified as optional argument of the new line
27705 This is not yet possible in \SpecialChar LyX
27710 \begin_layout Plain Layout
27712 \begin_inset CommandInset href
27714 name "LyX-bug #1505"
27715 target "http://www.lyx.org/trac/ticket/1505"
27724 , therefore the whole formula must be inserted in \SpecialChar TeX
27726 To add in our example space, the command
27734 is inserted at the end of the first line.
27739 \begin_layout Plain Layout
27746 \begin_layout Plain Layout
27748 B^{2}(B^{2}-2r_{g}^{2}+2x_{0}^{2}-2r_{k}^{2})+4x_{0}^{2}x^{2}+4x_{0}xD &
27751 textrm{-}4x^{2}B^{2}+4x_{0}xB^{2}
27758 \begin_layout Plain Layout
27762 left(B^{2}+x_{0}^{2}
27770 left(B^{2}-2r_{g}^{2}+2x_{0}^{2}-2r_{k}^{2}
27775 \begin_layout Plain Layout
27787 \begin_layout Standard
27788 \begin_inset VSpace bigskip
27791 To set the line separation for all lines in a formula, the length
27798 \begin_inset Index idx
27801 \begin_layout Plain Layout
27811 \begin_inset Formula $\mbox{line separation}=\mathrm{6\,pt+\backslash jot}$
27822 \begin_inset space \thinspace{}
27827 \begin_inset space \thinspace{}
27830 mm additional line separation as in the previous example, the command
27833 \begin_layout Standard
27843 \begin_layout Standard
27844 is inserted in \SpecialChar TeX
27845 mode before the formula.
27846 This requires that the \SpecialChar LaTeX
27855 \begin_layout Plain Layout
27860 is part of every \SpecialChar LaTeX
27861 standard installation.
27867 \begin_inset Index idx
27870 \begin_layout Plain Layout
27876 was loaded in \SpecialChar LaTeX
27877 -preamble with the line
27880 \begin_layout Standard
27888 \begin_layout Standard
27893 \begin_layout Plain Layout
27905 \begin_inset Formula
27907 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}\\
27908 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
27916 \begin_layout Standard
27920 \begin_layout Plain Layout
27931 To get back to the predefined distance,
27937 is set to the value 3
27938 \begin_inset space \thinspace{}
27944 \begin_layout Subsubsection
27946 \begin_inset CommandInset label
27948 name "subsec:Column-Separation"
27953 \begin_inset Index idx
27956 \begin_layout Plain Layout
27957 Formula ! multiline ! Column separation
27965 \begin_layout Standard
27966 Multiline formulas form a matrix.
27967 A formula in the eqnarray environment is for example a matrix with three
27969 By changing the column separation in this environment, the space beside
27970 the relation sign can be changed.
27973 \begin_layout Standard
27974 The column separation is specified with the length
27981 \begin_inset Index idx
27984 \begin_layout Plain Layout
27993 \begin_inset Newline newline
27996 column separation = 2
27997 \begin_inset space \thinspace{}
28007 \begin_inset Newline newline
28013 \begin_layout Standard
28023 \begin_layout Standard
28024 inserted in \SpecialChar TeX
28025 mode, sets for all following formulas a column separation of
28027 \begin_inset space \thinspace{}
28031 To get back to the predefined distance,
28038 \begin_inset space \thinspace{}
28044 \begin_layout Standard
28046 \begin_inset space \thinspace{}
28049 cm column separation:
28053 \begin_layout Plain Layout
28065 \begin_inset Formula
28073 A formula with the predefined column separation for matrices of 10
28074 \begin_inset space \thinspace{}
28081 \begin_layout Plain Layout
28093 \begin_inset Formula
28104 \begin_layout Subsubsection
28106 \begin_inset Index idx
28109 \begin_layout Plain Layout
28118 \begin_layout Standard
28119 Long formulas can be typeset using these methods:
28122 \begin_layout Itemize
28123 When one side of the equation is much shorter than the line width, this
28124 one is chosen for the left side and the right side is typeset over two
28126 \begin_inset Formula
28128 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 \\
28129 & & -\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}
28134 The minus sign at the beginning of the second line does normally not appear
28135 as an operator because it is the first character of the line.
28136 Thus it would not be surrounded by space and could not be distinguished
28137 from the fraction bar.
28139 \begin_inset space \thinspace{}
28142 pt space was inserted behind the minus sign with the command
28152 \begin_layout Plain Layout
28160 \begin_inset CommandInset ref
28162 reference "subsec:Variable-Space"
28172 \begin_inset Index idx
28175 \begin_layout Plain Layout
28186 \begin_layout Itemize
28187 When both sides of the equation are too long, the command
28194 \begin_inset Index idx
28197 \begin_layout Plain Layout
28206 It is inserted in the first column of the first line and causes all further
28207 insertions to overwrite the following columns:
28208 \begin_inset Formula
28210 \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 \\
28211 & & -\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 \\
28212 & & =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}
28217 After the insertion of
28223 , the cursor is in a purple box that is a bit shifted to the left from the
28225 In this the formula is inserted.
28226 \begin_inset Newline newline
28229 The content of the further lines is inserted to the second or another formula
28231 The greater the column number where it was inserted, the larger the indentation.
28232 \begin_inset VSpace medskip
28236 \begin_inset Newline newline
28240 \begin_inset Note Greyedout
28243 \begin_layout Plain Layout
28244 Note the following when using
28253 \begin_layout Itemize
28254 The formula doesn't use the full page width.
28256 \begin_inset space \thinspace{}
28260 \begin_inset space \space{}
28264 \begin_inset Formula $-B^{2}$
28267 is added to the first line in the above example, it would have been outside
28269 To better use the width, negative space can be inserted at the beginning
28273 \begin_layout Itemize
28274 Due to a bug in \SpecialChar LyX
28275 the cursor cannot be set with the mouse into the first
28280 \begin_layout Plain Layout
28281 \begin_inset CommandInset href
28283 name "LyX-bug #1429"
28284 target "http://www.lyx.org/trac/ticket/1429"
28293 One can only set the cursor at the beginning of the line and move it with
28302 \begin_layout Itemize
28303 Other methods to set long formulas are offered by the environments described
28305 \begin_inset CommandInset ref
28307 reference "subsec:Multline-Environment"
28312 \begin_inset CommandInset ref
28314 reference "subsec:Multiline-Formula-Parts"
28321 \begin_layout Subsubsection
28322 Multiline Fractions
28323 \begin_inset CommandInset label
28325 name "subsec:Multiline-Fractions"
28330 \begin_inset Index idx
28333 \begin_layout Plain Layout
28334 Fractions ! multiline
28342 \begin_layout Standard
28343 There are cases where the denominator and/or the numerator of a fraction
28344 is so long that the fraction does not fit into one line.
28345 It is then necessary to add a line break within the fraction.
28346 This can be done using the command
28353 \begin_inset Index idx
28356 \begin_layout Plain Layout
28365 To activate it, set in the document settings under
28368 \begin_inset space ~
28378 \begin_inset Index idx
28381 \begin_layout Plain Layout
28382 Packages ! mathtools
28390 \begin_inset space ~
28405 \begin_layout Standard
28410 splitfrac{first line}{second line}
28413 \begin_layout Standard
28414 and is used as denominator and/or numerator:
28417 \begin_layout Standard
28418 \begin_inset Formula
28420 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}
28425 The command for the first numerator above is:
28428 \begin_layout Standard
28433 splitfrac{xy+xy+xy+xy+xy
28434 \begin_inset space \textvisiblespace{}
28442 \begin_layout Subsubsection
28444 \begin_inset CommandInset label
28446 name "subsec:Multiline-Brackets"
28451 \begin_inset Index idx
28454 \begin_layout Plain Layout
28455 Brackets ! for multiline expressions
28463 \begin_layout Standard
28464 For brackets spanning multiple lines the following problem occurs:
28465 \begin_inset Formula
28467 A & = & \sin(x)\left[\prod_{R=1}^{\infty}\frac{1}{R}+\cdots\right.\\
28468 & & \left.\cdots+B-D\right]
28476 \begin_layout Standard
28477 The closing bracket is smaller than the opening bracket because brackets
28478 with variable size may not span multiple lines.
28481 \begin_layout Standard
28482 To set the bracket size for the second line correctly, the first line is
28490 \begin_inset Index idx
28493 \begin_layout Plain Layout
28501 and the second line with
28509 \begin_layout Plain Layout
28523 \begin_inset CommandInset ref
28525 reference "subsec:Automatic-Bracket-Size"
28537 \begin_inset Index idx
28540 \begin_layout Plain Layout
28563 \begin_inset space \textvisiblespace{}
28573 \begin_inset space \textvisiblespace{}
28583 \begin_inset space \textvisiblespace{}
28589 \begin_inset Formula $\downarrow$
28595 \begin_inset Index idx
28598 \begin_layout Plain Layout
28606 is inserted, because the multiplication operator with its limits is the
28607 largest symbol in the first line and this should be the size for the bracket
28608 in the second line.
28611 \begin_layout Standard
28612 The result is this:
28613 \begin_inset Formula
28615 A & = & \sin(x)\left[\prod_{R=1}^{\infty}\frac{1}{R}+\cdots\right.\\
28616 & & \left.\vphantom{\prod_{R=1}^{\infty}}\cdots+B-D\right]
28624 \begin_layout Subsection
28628 \begin_layout Standard
28629 Align environments can be used for every kind of multiline formulas.
28630 They are especially useful to set several formulas side by side.
28633 \begin_layout Standard
28634 Align environments consist of columns.
28635 The odd columns are right aligned, the even ones left aligned.
28636 Every line in an Align environment can be numbered.
28639 \begin_layout Standard
28640 Align environments are created via the menu
28642 Insert\SpecialChar menuseparator
28648 Edit\SpecialChar menuseparator
28649 Math\SpecialChar menuseparator
28650 Change Formula Type
28652 already existing formulas can be converted to Align environments.
28655 \begin_layout Standard
28656 To add or delete columns, the math toolbar buttons
28659 arg "tabular-feature append-column"
28665 arg "tabular-feature delete-column"
28668 , respectively, or the menu
28670 Edit\SpecialChar menuseparator
28676 \begin_layout Subsubsection
28677 Standard align Environment
28678 \begin_inset CommandInset label
28680 name "subsec:Standard-align-Environment"
28685 \begin_inset Index idx
28688 \begin_layout Plain Layout
28689 Formula ! multiline ! align environment
28697 \begin_layout Standard
28698 This Align environment is created by pressing
28701 arg "newline-insert newline"
28704 in a formula or by the menu
28706 Insert\SpecialChar menuseparator
28707 Math\SpecialChar menuseparator
28708 AMS align Environment
28713 \begin_layout Standard
28714 An example for two formulas set side by side, that are created with a four
28715 column align environment:
28716 \begin_inset Formula
28718 A & =\sin(B) & C & =D\\
28719 C & \ne A & B & \ne D
28724 As it can be seen, the formulas in this environment are placed so as if
28733 \begin_layout Plain Layout
28741 \begin_inset CommandInset ref
28743 reference "subsec:Variable-Space"
28754 before the first and after every even column.
28755 When the formula style
28761 \begin_layout Plain Layout
28763 \begin_inset CommandInset ref
28765 reference "sec:Formula-Styles"
28776 is used, the formula is set without the
28782 before the first column.
28785 \begin_layout Subsubsection
28786 Alignat Environment
28787 \begin_inset Index idx
28790 \begin_layout Plain Layout
28791 Formula ! multiline ! alignat environment
28799 \begin_layout Standard
28800 The alignat environment has no predefined column separation.
28801 It can be inserted manually with the spaces that are described
28802 \begin_inset CommandInset ref
28804 reference "subsec:Space"
28811 \begin_layout Standard
28812 The above example in the alignat environment where 1
28813 \begin_inset space \thinspace{}
28816 cm space was inserted at the beginning of the second formula:
28817 \begin_inset Formula
28818 \begin{alignat*}{2}
28819 A & =\sin(B) & \hspace{1cm}C & =D\\
28820 C & \ne A & B & \ne D
28825 Because the column separation can be set separately for every column, this
28826 environment is especially suitable to set three and more formulas side
28830 \begin_layout Subsubsection
28831 Flalign Environment
28832 \begin_inset CommandInset label
28834 name "subsec:Flalign-Environment"
28839 \begin_inset Index idx
28842 \begin_layout Plain Layout
28843 Formula ! multiline ! flalign environment
28851 \begin_layout Standard
28852 In this environment the first two columns are always set as much as possible
28853 to the left and the last two ones to the right.
28855 \begin_inset Formula
28857 A & =1 & B & =2 & C & =3\\
28858 X & =\textrm{-}1 & Y & =\textrm{-}2 & Z & =4
28866 \begin_layout Standard
28867 By creating a flalign environment with an odd number of columns where an
28868 empty \SpecialChar TeX
28869 brace is inserted to the last column, several formulas in a document
28870 can be set to the left, although the formula style
28875 As example the indented formula
28876 \begin_inset CommandInset ref
28878 reference "eq:VolInt"
28883 \begin_inset Formula
28885 \hspace{30pt}\iiint\limits _{V}X\,\mathrm{d}V & =U & {}
28890 The first two columns contain the formula.
28891 To indent it as with the formula style
28896 \begin_inset space \thinspace{}
28899 pt space was inserted at the beginning of the first column.
28902 \begin_layout Subsection
28903 Eqnarray Environment
28904 \begin_inset CommandInset label
28906 name "subsec:Eqnarray-Environment"
28911 \begin_inset Index idx
28914 \begin_layout Plain Layout
28915 Formula ! multiline ! eqnarray environment
28923 \begin_layout Standard
28924 When this environment has been created, three blue boxes appear.
28925 The content of the first box is right aligned, the content of the last
28927 The content of the middle box appears centered and a bit smaller, because
28928 it is designed to insert there only relation characters.
28929 \begin_inset Formula
28931 \frac{ABC}{D} & \frac{ABC}{D} & \frac{ABC}{D}\\
28941 \begin_layout Subsection
28943 \begin_inset Index idx
28946 \begin_layout Plain Layout
28947 Formula ! multiline ! gather environment
28955 \begin_layout Standard
28956 This environment consists of only one centered column.
28957 Every line can be numbered.
28958 \begin_inset Formula
28969 \begin_layout Subsection
28970 Multline Environment
28971 \begin_inset CommandInset label
28973 name "subsec:Multline-Environment"
28978 \begin_inset Index idx
28981 \begin_layout Plain Layout
28982 Formula ! multiline ! multline environment
28990 \begin_layout Standard
28991 The multline environment consists, like the gather environment, of only
28993 But the first line is left aligned, the last one right aligned.
28994 All other lines are centered.
28995 Therefore this environment is suitable for long formulas.
28997 \begin_inset CommandInset ref
28999 reference "eq:lefteqn"
29003 in the multline environment:
29004 \begin_inset Formula
29006 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}\\
29007 -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}\\
29008 =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}}
29016 \begin_layout Standard
29017 In the output only the last (first) line of a multline environment appears
29018 numbered when the document numbering is right (left).
29022 \begin_layout Plain Layout
29023 numbering styles see
29024 \begin_inset CommandInset ref
29026 reference "sec:Formula-Styles"
29038 \begin_layout Standard
29046 \begin_inset Index idx
29049 \begin_layout Plain Layout
29064 \begin_inset Index idx
29067 \begin_layout Plain Layout
29075 a centered line can be right or left aligned, respectively.
29076 The commands are used as follows:
29079 \begin_layout Standard
29084 shoveright{line content}
29090 shoveleft{line content}
29093 \begin_layout Standard
29094 \begin_inset VSpace medskip
29104 \begin_inset Index idx
29107 \begin_layout Plain Layout
29115 specifies the distance of the first line from the left page margin.
29116 Predefined is the length 0
29117 \begin_inset space \thinspace{}
29123 \begin_layout Standard
29124 As example the above formula where the command
29127 \begin_layout Standard
29137 \begin_layout Standard
29138 was inserted in \SpecialChar TeX
29143 \begin_layout Plain Layout
29155 \begin_inset Formula
29157 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}\\
29158 \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}}\\
29159 =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}}
29168 \begin_layout Plain Layout
29179 The second line was left aligned using
29188 \begin_layout Subsection
29189 Multiline Formula Parts
29190 \begin_inset CommandInset label
29192 name "subsec:Multiline-Formula-Parts"
29197 \begin_inset Index idx
29200 \begin_layout Plain Layout
29201 Formula ! multiline ! formula parts
29209 \begin_layout Standard
29210 To display only parts of a formula with multiple lines, one of the following
29211 environments is used:
29228 They can be inserted via the menu
29230 Insert\SpecialChar menuseparator
29233 or by using the commands described in this section.
29236 \begin_layout Standard
29237 The first three have the same properties as the corresponding multiline
29238 formula environments, but it is possible to set further formula parts beside
29241 \begin_inset Formula
29243 \left.\begin{aligned}\Delta x\Delta p & \ge\frac{\hbar}{2}\\
29244 \Delta E\Delta t & \ge\frac{\hbar}{2}
29246 \right\} \textrm{Uncertainty relations}
29254 \begin_layout Standard
29255 To get this formula, a displayed formula is created where the command
29262 \begin_inset Index idx
29265 \begin_layout Plain Layout
29274 A purple box appears around the blue formula box where now columns and
29275 lines can be added.
29276 Outside the multiline environment other formula parts can be set, like
29280 \begin_layout Standard
29281 The aligned environment is also suitable for long formulas whose lines are
29282 horizontally aligned.
29283 Using aligned in a displayed formula has the advantage that the formula
29284 number is vertically centered behind the lines.
29286 \begin_inset CommandInset ref
29288 reference "eq:shortlong"
29292 in the aligned environment:
29293 \begin_inset Formula
29295 \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}|}\\
29296 & -\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}|}
29305 \begin_layout Standard
29306 To use the environments
29325 \begin_inset Index idx
29328 \begin_layout Plain Layout
29343 \begin_inset Index idx
29346 \begin_layout Plain Layout
29361 \begin_inset Index idx
29364 \begin_layout Plain Layout
29372 are inserted, respectively.
29373 The split environment has the same properties as the aligned environment
29374 but it can only have two columns.
29377 \begin_layout Subsection
29378 Text in multiline Formulas
29379 \begin_inset CommandInset label
29381 name "subsec:Text-in-multiline"
29386 \begin_inset Index idx
29389 \begin_layout Plain Layout
29396 \begin_inset Index idx
29399 \begin_layout Plain Layout
29400 Formula ! multiline ! text
29408 \begin_layout Standard
29409 In the Align environments, and the multline and gather environment, text
29410 can be inserted that will appear in a separate line and doesn't affect
29411 the column alignment.
29412 To do this, the command
29419 \begin_inset Index idx
29422 \begin_layout Plain Layout
29430 is used in the following scheme:
29433 \begin_layout Standard
29441 \begin_layout Standard
29442 The text should not be longer than a line because it cannot be hyphenated.
29443 As \SpecialChar LyX
29444 doesn't yet support
29450 directly, the text is written as mathematical text.
29457 must hereby be at the beginning of a line and appears in the output above
29459 An example where the text was inserted at the beginning of the second line:
29460 \begin_inset Formula
29462 I & =a\sqrt{2}\int_{0}^{2\pi}\sqrt{1+\cos(\phi)}\;\mathrm{d}\phi\\
29463 \intertext{\text{integrand is symmetric to \ensuremath{\phi=\pi}, therefore}} & =2a\sqrt{2}\int_{0}^{\pi}\sqrt{1+\cos(\phi)}\;\mathrm{d}\phi
29471 \begin_layout Standard
29478 always creates some vertical space between the text and the formula lines.
29479 To avoid this space, set in the document settings under
29482 \begin_inset space ~
29492 \begin_inset Index idx
29495 \begin_layout Plain Layout
29496 Packages ! mathtools
29504 \begin_inset space ~
29510 Then you can use the command
29517 \begin_inset Index idx
29520 \begin_layout Plain Layout
29537 \begin_layout Standard
29538 \begin_inset Formula
29540 I & =a\sqrt{2}\int_{0}^{2\pi}\sqrt{1+\cos(\phi)}\;\mathrm{d}\phi\\
29541 \shortintertext{\text{integrand is symmetric to \ensuremath{\phi=\pi}, therefore}} & =2a\sqrt{2}\int_{0}^{\pi}\sqrt{1+\cos(\phi)}\;\mathrm{d}\phi
29549 \begin_layout Section
29551 \begin_inset Index idx
29554 \begin_layout Plain Layout
29561 \begin_inset Index idx
29564 \begin_layout Plain Layout
29565 Formula ! numbering|see
29569 \begin_layout Plain Layout
29580 \begin_layout Plain Layout
29595 \begin_layout Subsection
29599 \begin_layout Standard
29600 Numbered formulas can be created with the menu
29602 Insert\SpecialChar menuseparator
29603 Math\SpecialChar menuseparator
29605 \begin_inset space ~
29613 \begin_inset space ~
29619 Existing formulas can be numbered with the menu
29621 Edit\SpecialChar menuseparator
29622 Math\SpecialChar menuseparator
29624 \begin_inset space ~
29632 arg "math-number-toggle"
29636 The formula number is displayed in \SpecialChar LyX
29637 behind the formula as a number sign
29639 The number sign is replaced in the output by the formula number.
29642 \begin_layout Standard
29643 When numbering is turned on in multiline formulas, all lines will be numbered.
29644 But the numbering can be controlled with the menu
29646 Edit\SpecialChar menuseparator
29647 Math\SpecialChar menuseparator
29649 \begin_inset space ~
29653 \begin_inset space ~
29657 \begin_inset space ~
29665 arg "math-number-line-toggle"
29671 \begin_layout Standard
29672 Except for inline formulas, all formulas can be numbered with two different
29674 \begin_inset CommandInset ref
29676 reference "sec:Formula-Styles"
29683 \begin_layout Subsection
29685 \begin_inset Index idx
29688 \begin_layout Plain Layout
29689 Cross-references ! to formulas
29697 \begin_layout Standard
29698 All labeled formulas can be cross-referenced.
29699 A label is added by the menu
29701 Insert\SpecialChar menuseparator
29704 or the toolbar button
29711 The cursor must hereby be inside a displayed formula.
29712 Alternatively you can right-click on the formula and choose
29717 A dialog pops up displaying the prefix
29722 The label is inserted there behind the prefix.
29723 The predefined prefix means
29724 \begin_inset Quotes eld
29728 \begin_inset Quotes erd
29731 and makes it easier to find labels in large documents because it marks
29732 it as formula label to divide it from e.
29733 \begin_inset space \thinspace{}
29737 \begin_inset space \space{}
29741 To change a label, the menu
29743 Insert\SpecialChar menuseparator
29746 is used again or you right-click on a formula and then on
29753 \begin_layout Standard
29754 The name of the label is displayed in \SpecialChar LyX
29755 within two parentheses behind formula.
29756 A formula with a label is always numbered.
29759 \begin_layout Standard
29760 Cross-references are inserted via the menu
29762 Insert\SpecialChar menuseparator
29765 or with the toolbar button
29768 arg "dialog-show-new-inset ref"
29772 A formula cross-reference appears in the output as formula number.
29773 When in the cross-reference dialog window the format
29777 is chosen, the cross-reference appears in the output as formula number
29779 \begin_inset Newline newline
29782 By right-clicking on a cross-reference in \SpecialChar LyX
29783 , one jumps to the formula that
29787 \begin_layout Standard
29788 Here are as examples cross-references to formulas of the following subsections:
29789 \begin_inset Note Note
29792 \begin_layout Plain Layout
29793 Note the different cross-reference types.
29801 \begin_layout Standard
29803 \begin_inset CommandInset ref
29810 \begin_inset CommandInset ref
29818 \begin_inset CommandInset ref
29824 ) big Latin letters are used for the numbering in contrary to (
29825 \begin_inset CommandInset ref
29834 \begin_layout Standard
29835 \begin_inset VSpace medskip
29838 When the argument of
29846 \begin_layout Plain Layout
29854 \begin_inset CommandInset ref
29856 reference "subsec:User-defined-Numbering"
29867 contains a box like in
29868 \begin_inset CommandInset ref
29870 reference "subsec:Paragraph-Boxes"
29874 , the formula cannot be referenced.
29877 \begin_layout Subsection
29879 \begin_inset Index idx
29882 \begin_layout Plain Layout
29883 Formula numbering ! subnumbering
29891 \begin_layout Standard
29892 With the help of the commands
29896 begin{subequations}
29904 formulas can be subnumbered.
29905 Both commands are inserted in \SpecialChar TeX
29909 \begin_layout Standard
29911 \begin_inset Formula
29922 \begin_layout Plain Layout
29926 begin{subequations}
29932 \begin_inset VSpace -5mm
29936 \begin_inset Formula
29944 \begin_inset Formula
29954 \begin_layout Standard
29958 \begin_layout Plain Layout
29970 \begin_layout Standard
29971 To create the example, the following is done:
29974 \begin_layout Enumerate
29975 first formula is inserted
29978 \begin_layout Enumerate
29983 begin{subequations}
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 will be subnumbered with a, b, c, \SpecialChar ldots
30025 For multiline formulas every line will be subnumbered.
30028 \begin_layout Standard
30029 Referencing subequations work like for normal equations:
30030 \begin_inset CommandInset ref
30037 \begin_inset CommandInset ref
30044 If you want to reference the subequations collectively, insert a label
30049 begin{subequations}
30053 \begin_inset CommandInset ref
30055 reference "eq:Here-is-an"
30062 \begin_layout Standard
30063 By inserting commands in \SpecialChar TeX
30064 mode, a space is created between the first two
30067 \begin_inset space \thinspace{}
30070 mm vertical space is inserted after the command
30074 begin{subequations}
30077 When the formula style
30083 \begin_layout Plain Layout
30085 \begin_inset CommandInset ref
30087 reference "sec:Formula-Styles"
30099 \begin_inset space \thinspace{}
30102 mm space is inserted instead.
30105 \begin_layout Standard
30106 To get another subnumber instead of small Latin letters, insert this command
30111 begin{subequations}
30116 \begin_layout Standard
30125 theparentequation -
30130 \begin_layout Standard
30137 creates hereby the parent number and
30143 adds a small Roman number as subnumber.
30144 For more information about the customization of the numbering, see
30145 \begin_inset CommandInset ref
30147 reference "subsec:Numbering-with-Roman"
30154 \begin_layout Standard
30155 Here is an example for a multiline formula where the numbering is customized
30156 and turned off for the second line:
30160 \begin_layout Plain Layout
30164 begin{subequations}
30170 \begin_inset CommandInset label
30172 name "eq:Here-is-an"
30180 \begin_layout Plain Layout
30188 theparentequation -
30196 \begin_inset Formula
30198 A & = & (B-Z)^{2}=(B-Z)(B-Z)\\
30199 & = & B^{2}-ZB-BZ+Z^{2}\nonumber \\
30200 & = & B^{2}-2BZ+Z^{2}
30209 \begin_layout Plain Layout
30221 \begin_layout Subsection
30222 User-defined Numbering
30223 \begin_inset CommandInset label
30225 name "subsec:User-defined-Numbering"
30230 \begin_inset Index idx
30233 \begin_layout Plain Layout
30234 Formula numbering ! user-defined
30242 \begin_layout Standard
30243 \begin_inset Index idx
30246 \begin_layout Plain Layout
30247 Formula numbering ! self-defined delimiters
30252 With the standard numbering parentheses are set around the formula number.
30253 To replace the parentheses for example by vertical bars, the following
30254 line is added to the \SpecialChar LaTeX
30258 \begin_layout Standard
30270 \begin_inset Note Note
30273 \begin_layout Plain Layout
30274 This macro is already declared in the \SpecialChar LaTeX
30275 -preamble for testing.
30276 To activate it, remove the percent sign at the beginning.
30284 \begin_layout Standard
30285 To use other characters, the vertical bars besides the
30289 are replaced by one ore more characters.
30290 To get only the formula number the vertical bars are omitted.
30293 \begin_layout Standard
30294 \begin_inset VSpace bigskip
30297 When there should be an expression of your choice instead of the consecutive
30298 formula number in parentheses behind the formula, the command
30305 \begin_inset Index idx
30308 \begin_layout Plain Layout
30317 \begin_inset Formula
30319 A+B=C\tag{something}\label{eq:tag}
30324 In this example the command
30329 \begin_inset space \textvisiblespace{}
30334 was inserted in the formula.
30337 \begin_layout Standard
30343 \begin_inset space \textvisiblespace{}
30348 is inserted instead, the star prevents the parentheses around the expression:
30349 \begin_inset Formula
30351 A+B=C\tag*{something}
30359 \begin_layout Standard
30360 \begin_inset VSpace bigskip
30363 To restart the formula numbering with new document parts or sections, the
30364 following command is used:
30367 \begin_layout Standard
30372 @addtoreset{equation}{part}
30375 \begin_inset Index idx
30378 \begin_layout Plain Layout
30383 \begin_layout Plain Layout
30394 \begin_layout Plain Layout
30407 \begin_layout Plain Layout
30418 \begin_layout Plain Layout
30431 \begin_inset Newline newline
30435 \begin_inset Newline newline
30442 @addtoreset{equation}{section}
30445 \begin_layout Standard
30446 To be able to use these commands in \SpecialChar TeX
30448 \begin_inset Quotes eld
30452 \begin_inset Quotes erd
30455 character has to be made
30456 \begin_inset Quotes eld
30460 \begin_inset Quotes erd
30463 for \SpecialChar LaTeX
30478 So the command sequence in \SpecialChar TeX
30482 \begin_layout Standard
30488 \begin_inset Newline newline
30493 @addtoreset{equation}{section}
30494 \begin_inset Newline newline
30502 \begin_layout Standard
30503 In the \SpecialChar LaTeX
30516 can be omitted as they are automatically internally inserted by \SpecialChar LyX
30520 \begin_layout Standard
30535 \begin_layout Plain Layout
30540 is part of the \SpecialChar LaTeX
30546 \begin_inset Index idx
30549 \begin_layout Plain Layout
30550 Packages ! carlisle
30555 that is part of every \SpecialChar LaTeX
30556 standard installation.
30562 \begin_inset Index idx
30565 \begin_layout Plain Layout
30566 Packages ! remreset
30571 has to be loaded in the \SpecialChar LaTeX
30572 -preamble with the line
30575 \begin_layout Standard
30580 usepackage{remreset}
30583 \begin_layout Standard
30591 \begin_inset Index idx
30594 \begin_layout Plain Layout
30599 \begin_layout Plain Layout
30610 \begin_layout Plain Layout
30623 \begin_layout Plain Layout
30634 \begin_layout Plain Layout
30646 can be used with the same scheme as
30655 \begin_layout Standard
30656 \begin_inset VSpace bigskip
30659 Sometimes formulas should be numbered in the following form:
30662 \begin_layout Standard
30665 (section number.formula number)
30668 \begin_layout Standard
30669 The formula number should start with every section with
30670 \begin_inset Quotes eld
30674 \begin_inset Quotes erd
30680 \begin_layout Standard
30681 For this case there is the command
30688 \begin_inset Index idx
30691 \begin_layout Plain Layout
30699 , which is used with the following scheme:
30702 \begin_layout Standard
30707 numberwithin{counter}{sectioning}
30710 \begin_layout Standard
30711 Counter denotes what kind of numbering is affected, sectioning denotes what
30712 number is before the dot.
30715 \begin_layout Standard
30716 Thus in our case the following \SpecialChar LaTeX
30717 preamble or \SpecialChar TeX
30721 \begin_layout Standard
30726 numberwithin{equation}{section}
30729 \begin_layout Standard
30730 This is the result:
30734 \begin_layout Plain Layout
30738 numberwithin{equation}{section}
30744 \begin_inset Formula
30754 \begin_layout Standard
30756 \begin_inset space \thinspace{}
30760 \begin_inset space \space{}
30763 tables so that the number of the part is the sectioning,
30764 \begin_inset Newline newline
30771 numberwithin{table}{part}
30776 \begin_layout Standard
30777 To go back to the standard numbering or to prevent this kind of numbering
30778 when it is defined by the document class, the following command is inserted
30779 as \SpecialChar TeX
30780 code or to the \SpecialChar LaTeX
30784 \begin_layout Standard
30794 \begin_inset Index idx
30797 \begin_layout Plain Layout
30811 \begin_layout Plain Layout
30827 \begin_inset Newline newline
30835 \begin_inset Newline newline
30847 \begin_layout Standard
30854 uses internally the command
30860 , described above, that also needs to be reverted.
30864 \begin_layout Plain Layout
30871 \begin_layout Plain Layout
30875 @removefromreset{equation}{section}
30878 \begin_layout Plain Layout
30890 \begin_layout Subsection
30891 Numbering with Roman Numbers and Letters
30892 \begin_inset CommandInset label
30894 name "subsec:Numbering-with-Roman"
30899 \begin_inset Index idx
30902 \begin_layout Plain Layout
30903 Formula numbering ! with letters
30909 \begin_inset Index idx
30912 \begin_layout Plain Layout
30913 Formula numbering ! with Roman numbers
30921 \begin_layout Standard
30922 Formulas can also be numbered with Roman numbers and Latin letters.
30923 To number for example with small Roman numbers, the command
30926 \begin_layout Standard
30938 \begin_layout Standard
30939 is inserted before the formula in \SpecialChar TeX
30948 \begin_inset Index idx
30951 \begin_layout Plain Layout
30959 redefines the predefined command
30975 \begin_layout Plain Layout
30982 has the same scheme like the command
30988 that is described in
30989 \begin_inset CommandInset ref
30991 reference "subsec:The-Command-newcommand"
31004 is the formula counter.
31011 is used as prefix for a counter, the value of the counter is output as
31013 When a formula is numbered, \SpecialChar LaTeX
31014 sets internally the command
31020 behind the formula.
31026 \begin_inset Index idx
31029 \begin_layout Plain Layout
31039 outputs the counter as small Roman number.
31042 \begin_layout Standard
31043 All formulas behind the command
31053 are now numbered Roman.
31054 To switch to numbering with big Roman numbers, the command is inserted
31068 \begin_inset Index idx
31071 \begin_layout Plain Layout
31083 \begin_inset Quotes eld
31087 \begin_inset Quotes erd
31090 with small Latin letters there is the command
31097 \begin_inset Index idx
31100 \begin_layout Plain Layout
31108 , for big ones there is the command
31115 \begin_inset Index idx
31118 \begin_layout Plain Layout
31131 \begin_layout Standard
31132 \begin_inset Note Greyedout
31135 \begin_layout Plain Layout
31142 \begin_inset space ~
31145 formulas can be numbered with Latin letters in one document.
31153 \begin_layout Standard
31157 \begin_layout Plain Layout
31173 \begin_layout Standard
31174 \begin_inset Formula
31176 A=\textrm{small roman}
31185 \begin_layout Plain Layout
31199 \begin_inset Formula
31201 B=\textrm{big Roman}\label{eq:Rom}
31210 \begin_layout Plain Layout
31224 \begin_inset Formula
31226 C=\textrm{small Latin}
31235 \begin_layout Plain Layout
31249 \begin_inset Formula
31251 D=\textrm{big Latin}\label{eq:Lat}
31259 \begin_layout Standard
31260 To switch back to the default numbering, insert the command:
31263 \begin_layout Standard
31273 \begin_inset Index idx
31276 \begin_layout Plain Layout
31287 \begin_layout Standard
31291 \begin_layout Plain Layout
31305 \begin_inset Formula
31315 \begin_layout Standard
31316 \begin_inset VSpace medskip
31319 As you see, formulas are numbered serially independent from the numbering
31321 When then numbering should start with
31322 \begin_inset Quotes eld
31326 \begin_inset Quotes erd
31329 when the style is changed, new equation counters have to be defined.
31330 A description about this can be found in the file
31331 \begin_inset CommandInset href
31333 name "Formula-numbering.lyx"
31334 target "run:Formula-numbering.lyx"
31341 \begin_layout Section
31342 Chemical Symbols and Equations
31343 \begin_inset CommandInset label
31345 name "subsec:Chemical-Symbols-and"
31350 \begin_inset Index idx
31353 \begin_layout Plain Layout
31354 Chemical characters ! Symbols
31360 \begin_inset Index idx
31363 \begin_layout Plain Layout
31370 \begin_inset Index idx
31373 \begin_layout Plain Layout
31382 \begin_layout Standard
31383 An example text from chemistry:
31386 \begin_layout Quote
31388 \begin_inset Formula $\mathrm{SO_{4}^{2-}}$
31391 -ion reacts with two
31392 \begin_inset Formula $\mathrm{Na^{+}}$
31395 -ions to sodium sulfate
31396 \begin_inset Formula $\left(\mathrm{Na_{2}SO_{4}}\right)$
31400 The chemical equation for this is:
31401 \begin_inset Formula
31403 \mathrm{2\,Na^{+}+SO_{4}^{2-}\longrightarrow Na_{2}SO_{4}}\label{eq:chem-reaction}
31411 \begin_layout Standard
31412 This chemical equation can directly be created as formula.
31413 To avoid that the symbols appear italic, everything is highlighted and
31414 changed by the shortcut
31420 to the upright font style.
31424 \begin_layout Plain Layout
31430 \begin_inset CommandInset ref
31432 reference "subsec:Font-Styles"
31444 \begin_layout Standard
31445 A more convenient way to typeset chemical formulas is to use the command
31453 \begin_inset Index idx
31456 \begin_layout Plain Layout
31464 that is available when the \SpecialChar LaTeX
31470 \begin_inset Index idx
31473 \begin_layout Plain Layout
31486 to a formula a new blue box appears where chemical formulas can be inserted
31487 in an intuitive way.
31490 \begin_layout Standard
31492 \begin_inset Tabular
31493 <lyxtabular version="3" rows="10" columns="2">
31494 <features booktabs="true" tabularvalignment="middle">
31495 <column alignment="center" valignment="top" width="0pt">
31496 <column alignment="center" valignment="top">
31498 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
31501 \begin_layout Plain Layout
31507 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
31510 \begin_layout Plain Layout
31518 <cell alignment="center" valignment="top" leftline="true" usebox="none">
31521 \begin_layout Plain Layout
31525 \begin_inset space \textvisiblespace{}
31533 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
31536 \begin_layout Plain Layout
31537 \begin_inset Formula $\ce{H2CO3}$
31546 <row topspace="1.5mm">
31547 <cell alignment="center" valignment="top" usebox="none">
31550 \begin_layout Plain Layout
31554 \begin_inset space \textvisiblespace{}
31562 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
31565 \begin_layout Plain Layout
31566 \begin_inset Formula $\ce{SO4^{2-}}$
31575 <row topspace="1.5mm">
31576 <cell alignment="center" valignment="top" usebox="none">
31579 \begin_layout Plain Layout
31583 \begin_inset space \textvisiblespace{}
31591 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
31594 \begin_layout Plain Layout
31595 \begin_inset Formula $\ce{(NH4)2S}$
31604 <row topspace="1.5mm">
31605 <cell alignment="center" valignment="top" usebox="none">
31608 \begin_layout Plain Layout
31612 \begin_inset space \textvisiblespace{}
31620 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
31623 \begin_layout Plain Layout
31624 \begin_inset Formula $\ce{KCr(SO4)2.12H2O}$
31633 <row topspace="1.5mm">
31634 <cell alignment="center" valignment="top" usebox="none">
31637 \begin_layout Plain Layout
31641 \begin_inset space \textvisiblespace{}
31647 \begin_inset space \textvisiblespace{}
31653 \begin_inset space \textvisiblespace{}
31661 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
31664 \begin_layout Plain Layout
31665 \begin_inset Formula $\ce{A-B\dbond C\tbond D}$
31674 <row topspace="1.5mm">
31675 <cell alignment="center" valignment="top" usebox="none">
31678 \begin_layout Plain Layout
31682 \begin_inset space \textvisiblespace{}
31686 \begin_inset Formula $\downarrow$
31690 \begin_inset Formula $\to$
31698 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
31701 \begin_layout Plain Layout
31702 \begin_inset Formula $\ce{_{90}^{227}Th+}$
31712 <cell alignment="center" valignment="top" leftline="true" usebox="none">
31715 \begin_layout Plain Layout
31719 \begin_inset space \textvisiblespace{}
31725 \begin_inset space \textvisiblespace{}
31731 \begin_inset space \textvisiblespace{}
31739 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
31742 \begin_layout Plain Layout
31743 \begin_inset Formula $\ce{\ensuremath{\mu\hyphen}Cl}$
31753 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
31756 \begin_layout Plain Layout
31760 \begin_inset space \textvisiblespace{}
31764 \begin_inset space \textvisiblespace{}
31768 \begin_inset space \textvisiblespace{}
31772 \begin_inset space \textvisiblespace{}
31776 \begin_inset space \textvisiblespace{}
31784 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
31787 \begin_layout Plain Layout
31788 \begin_inset Formula $\ce{CO2 + C <=> 2CO}$
31797 <row topspace="1.5mm">
31798 <cell alignment="center" valignment="top" bottomline="true" usebox="none">
31801 \begin_layout Plain Layout
31805 \begin_inset space \textvisiblespace{}
31809 \begin_inset space \textvisiblespace{}
31813 \begin_inset space \textvisiblespace{}
31817 \begin_inset space \textvisiblespace{}
31825 \begin_inset space \textvisiblespace{}
31833 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
31836 \begin_layout Plain Layout
31837 \begin_inset Formula $\ce{CO2 + C ->[\alpha][\beta] 2CO}$
31853 \begin_layout Standard
31854 \begin_inset Note Greyedout
31857 \begin_layout Plain Layout
31863 It is not possible in \SpecialChar LyX
31864 to use the character ^ to get an up-arrow as described
31870 One instead uses a negative thin space followed by the command
31877 \begin_inset Formula $\ce{Fe + 2H+ -> Fe^{2+} + H2\negthinspace\uparrow}$
31888 \begin_layout Standard
31895 the command for equation
31896 \begin_inset space ~
31900 \begin_inset CommandInset ref
31902 reference "eq:chem-reaction"
31907 \begin_inset Newline newline
31915 \begin_inset space \textvisiblespace{}
31919 \begin_inset space \textvisiblespace{}
31923 \begin_inset space \textvisiblespace{}
31927 \begin_inset space \textvisiblespace{}
31931 \begin_inset space \textvisiblespace{}
31935 \begin_inset space \textvisiblespace{}
31941 \begin_layout Standard
31942 To create multiline chemical equations first a multiline formula is created
31944 \begin_inset CommandInset ref
31946 reference "sec:Multiline-Formulas"
31951 Afterwards the command
31957 is used in every small blue box of the formula.
31959 \begin_inset CommandInset ref
31961 reference "eq:TEOS-reaction-1"
31966 \begin_inset CommandInset ref
31968 reference "eq:TEOS-reaction-2"
31972 are an example of a multi-stage chemical reaction where every equation
31973 has its own number.
31974 \begin_inset Formula
31976 \ce{TEOS + 4O} & \ce{->} & \ce{Si(OH)4 + 4C2H4O}\label{eq:TEOS-reaction-1}\\
31977 \ce{Si(OH)4} & \ce{->} & \ce{SiO2 + 2H2O}\label{eq:TEOS-reaction-2}
31985 \begin_layout Standard
31996 package provides the command
32003 \begin_inset Index idx
32006 \begin_layout Plain Layout
32014 that has to be used for special cases.
32015 For more information about
32021 and more examples have a look at the documentation of
32026 \begin_inset CommandInset citation
32035 \begin_layout Section
32039 \begin_layout Standard
32041 supports two types of commutative diagrams:
32049 that are explained in the following.
32052 \begin_layout Subsection
32054 \begin_inset Index idx
32057 \begin_layout Plain Layout
32066 \begin_layout Standard
32067 Diagrams of this type visualize relations by vertical and horizontal lines
32069 \begin_inset Formula
32071 \begin{CD}A@>>>B@>>>C\\
32082 \begin_layout Standard
32083 To get them, the command
32088 \begin_inset Index idx
32091 \begin_layout Plain Layout
32101 is inserted to a formula.
32102 A blue box appears with two dashed lines where further commands can be
32107 arg "newline-insert newline"
32110 a new line is created.
32111 Horizontal relations are inserted in odd, vertical in even formula lines.
32114 \begin_layout Standard
32115 To create the relations there are the following commands:
32118 \begin_layout Itemize
32123 creates a left arrow,
32134 \begin_layout Itemize
32139 creates an up arrow,
32147 a vertical equal sign
32150 \begin_layout Itemize
32156 is a placeholder for non-existent relations
32159 \begin_layout Standard
32160 All arrows can be labeled as follows:
32163 \begin_layout Itemize
32164 If text inserted between the first and second < or >, resp., it is placed
32166 When it is inserted between the second and third one, it appears under
32170 \begin_layout Itemize
32171 When text for vertical arrows is inserted between the first and second A
32172 or V, resp., it is placed left beside the arrow.
32173 When it is inserted between the second and third one, it appears right
32175 If the text contains an A or V, these letters must be set into a \SpecialChar TeX
32179 \begin_layout Standard
32180 As example a diagram with all possible relations:
32183 \begin_layout Standard
32184 \begin_inset Formula
32186 \begin{CD}A@>j>>B@>>k>C@=F\\
32197 \begin_layout Standard
32198 The command for this is:
32199 \begin_inset Newline newline
32207 \begin_inset space \textvisiblespace{}
32210 A@>j>>B@>>k>C@=F Ctrl+Return
32211 \begin_inset Newline newline
32215 \begin_inset Phantom HPhantom
32218 \begin_layout Plain Layout
32224 \begin_inset space \textvisiblespace{}
32237 \begin_inset Formula $\to$
32243 \begin_inset Newline newline
32247 \begin_inset Phantom HPhantom
32250 \begin_layout Plain Layout
32256 \begin_inset space \textvisiblespace{}
32267 \begin_layout Subsection
32269 \begin_inset Index idx
32272 \begin_layout Plain Layout
32273 Diagrams ! xymatrix
32281 \begin_layout Standard
32282 To be able to use xymatrices, the \SpecialChar LaTeX
32288 A xymatrix is created by inserting the command
32295 Then you are able to add new matrix columns and rows like for normal matrices,
32297 \begin_inset CommandInset ref
32299 reference "sec:Matrices"
32306 \begin_layout Standard
32307 In contrary to amscd diagrams, xymatrices supports diagonal and curved arrows,
32309 All possibilities to create commutative diagrams and decorations are explained
32314 that you find in the menu
32316 Help\SpecialChar menuseparator
32318 \begin_inset space ~
32326 \begin_layout Subsection
32332 \begin_inset Index idx
32335 \begin_layout Plain Layout
32344 \begin_layout Standard
32349 -diagrams, the \SpecialChar LaTeX
32359 -diagram is created by inserting the command
32366 Then you are able to add new matrix columns and rows like for normal matrices,
32368 \begin_inset CommandInset ref
32370 reference "sec:Matrices"
32377 \begin_layout Standard
32378 Examples how to create
32382 diagrams in \SpecialChar LyX
32385 Feynman-diagram manual
32387 that you find in the menu
32389 Help\SpecialChar menuseparator
32391 \begin_inset space ~
32399 \begin_layout Section
32400 User-defined Commands
32401 \begin_inset Index idx
32404 \begin_layout Plain Layout
32405 User-defined commands
32413 \begin_layout Standard
32414 \begin_inset Note Greyedout
32417 \begin_layout Plain Layout
32422 The names of user-defined commands and macros may only consist of Latin
32431 \begin_layout Subsection
32435 \begin_inset CommandInset label
32437 name "subsec:The-Command-newcommand"
32442 \begin_inset Index idx
32445 \begin_layout Plain Layout
32446 User-defined commands !
32454 \begin_inset Index idx
32457 \begin_layout Plain Layout
32468 \begin_layout Standard
32469 Many \SpecialChar LaTeX
32470 -commands are too long to be used frequently.
32471 But it is possible to define with the command
32477 new shorter commands.
32480 \begin_layout Standard
32481 The command scheme of
32490 \begin_layout Standard
32495 newcommand{new command name}[number of arguments][optional
32500 \begin_inset Newline newline
32504 \begin_inset Phantom HPhantom
32507 \begin_layout Plain Layout
32517 {command definition}
32520 \begin_layout Standard
32521 \begin_inset Note Greyedout
32524 \begin_layout Plain Layout
32529 Assure that the name of the new command is not already used in your document
32530 or by \SpecialChar LaTeX
32531 -packages that you use.
32532 When you for example define the command
32544 , you get an error message because
32550 is already defined as command for
32551 \begin_inset Quotes eld
32555 \begin_inset Formula $\le$
32559 \begin_inset Quotes erd
32570 \begin_layout Standard
32571 The number of arguments is an integer in the range 0
32572 \begin_inset space \thinspace{}
32576 \begin_inset space \thinspace{}
32579 9 and specifies how many arguments the new command should have.
32580 With the optional value a value for an optional argument can be predefined.
32581 When this is done, the
32589 rgument of the new command is automatically an optional one.
32592 \begin_layout Standard
32593 Here are some examples:
32596 \begin_layout Itemize
32597 To define the command
32609 , the \SpecialChar LaTeX
32611 \begin_inset VSpace medskip
32615 \begin_inset Newline newline
32629 \begin_layout Itemize
32630 To define the command
32642 , the argument (that should be underlined) must be taken into account.
32643 For this the preamble line is:
32644 \begin_inset VSpace medskip
32648 \begin_inset Newline newline
32662 \begin_inset VSpace medskip
32666 \begin_inset Newline newline
32673 acts as argument placeholder, the
32677 behind it denotes that it is the placeholder for the first argument.
32680 \begin_layout Itemize
32688 \begin_inset space \thinspace{}
32692 \begin_inset space \space{}
32702 \begin_inset VSpace medskip
32706 \begin_inset Newline newline
32717 framebox#1#2{$#3$}}
32720 \begin_inset VSpace medskip
32724 \begin_inset Newline newline
32727 The two Dollar signs creates the extra formula needed for
32734 \begin_inset CommandInset ref
32736 reference "subsec:Boxes-with-Frame"
32743 \begin_layout Itemize
32744 To create a new command for
32750 where the color for the box need not be specified, the argument for the
32751 color is defined optional:
32752 \begin_inset VSpace medskip
32756 \begin_inset Newline newline
32767 fcolorbox{#2}{#1}{$#3$}}
32770 \begin_inset VSpace medskip
32774 \begin_inset Newline newline
32777 When the color is not specified when using
32783 , the predefined color
32790 \begin_layout Standard
32791 A test of the new defined commands:
32794 \begin_layout Standard
32796 \begin_inset Tabular
32797 <lyxtabular version="3" rows="6" columns="2">
32798 <features booktabs="true" tabularvalignment="middle">
32799 <column alignment="center" valignment="top" width="0pt">
32800 <column alignment="center" valignment="top">
32802 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
32805 \begin_layout Plain Layout
32811 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
32814 \begin_layout Plain Layout
32822 <cell alignment="center" valignment="top" leftline="true" usebox="none">
32825 \begin_layout Plain Layout
32829 \begin_inset space \textvisiblespace{}
32837 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
32840 \begin_layout Plain Layout
32841 \begin_inset Formula $A\gr B$
32851 <cell alignment="center" valignment="top" leftline="true" usebox="none">
32854 \begin_layout Plain Layout
32862 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
32865 \begin_layout Plain Layout
32866 \begin_inset Formula $\us{ABcd}$
32875 <row topspace="1mm">
32876 <cell alignment="center" valignment="top" usebox="none">
32879 \begin_layout Plain Layout
32883 \begin_inset Formula $\to$
32889 \begin_inset Formula $\to$
32897 \begin_inset space \textvisiblespace{}
32905 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
32908 \begin_layout Plain Layout
32909 \begin_inset Formula $\fb{[2cm]}{}{\int A=B}$
32918 <row topspace="1.5mm">
32919 <cell alignment="center" valignment="top" usebox="none">
32922 \begin_layout Plain Layout
32926 \begin_inset Formula $\to$
32934 \begin_inset space \textvisiblespace{}
32942 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
32945 \begin_layout Plain Layout
32946 \begin_inset Formula $\cb{red}{\int A=B}$
32955 <row topspace="1.5mm" bottomspace="1mm">
32956 <cell alignment="center" valignment="top" bottomline="true" usebox="none">
32959 \begin_layout Plain Layout
32965 \begin_inset Formula $\to$
32973 \begin_inset space \textvisiblespace{}
32981 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
32984 \begin_layout Plain Layout
32985 \begin_inset Formula $\cb[green]{red}{\int A=B}$
33001 \begin_layout Subsection
33003 \begin_inset Index idx
33006 \begin_layout Plain Layout
33007 User-defined commands! Math macros
33013 \begin_inset Index idx
33016 \begin_layout Plain Layout
33025 \begin_layout Standard
33026 User-defined commands are especially convenient for complex expressions.
33027 When you are for example dealing with a document that has quadratic equations,
33028 the same solution type occurs several times.
33029 The general form of a quadratic equation is
33030 \begin_inset Formula
33032 0=\lambda^{2}+p\lambda+q
33037 The general form of the solution is
33038 \begin_inset Formula
33040 \lambda_{1,2}=-\frac{p}{2}\pm\sqrt{\frac{p²}{4}-q}
33048 \begin_layout Standard
33049 To define a command for the solution formula where only the three parameters
33051 \begin_inset Formula $\lambda$
33055 \begin_inset Formula $p$
33059 \begin_inset Formula $q$
33062 need to be specified and the index of
33063 \begin_inset Formula $\lambda$
33066 can be given optionally, the \SpecialChar LaTeX
33068 \begin_inset Newline newline
33084 \begin_inset Newline newline
33088 \begin_inset Phantom HPhantom
33091 \begin_layout Plain Layout
33105 frac{#3^{2}}{4}-#4}}
33108 \begin_layout Standard
33109 To create with this the solution formula, the command
33110 \begin_inset Newline newline
33120 \begin_inset Formula $\to$
33126 \begin_inset Formula $\to$
33133 is inserted to a formula
33138 \begin_layout Standard
33139 The definition of the new command is unintuitive because one has to know
33140 the schemes of all used \SpecialChar LaTeX
33142 \begin_inset space \thinspace{}
33146 \begin_inset space \space{}
33149 that a fraction is inserted in \SpecialChar LaTeX
33154 frac{numerator}{denominator}
33157 Furthermore one can easily forget a brace in the definition and cannot
33158 see in \SpecialChar LyX
33159 what the new command is doing.
33160 To avoid these problems \SpecialChar LyX
33161 offers the possibility to use math macros instead
33171 \begin_layout Standard
33172 A math macro is created by using the menu
33174 Insert\SpecialChar menuseparator
33175 Math\SpecialChar menuseparator
33178 or the toolbar button
33181 arg "math-macro newmacroname_newcommand"
33185 The math macro toolbar appears together with the following box where the
33187 \begin_inset Newline newline
33191 \begin_inset space \hspace*{\fill}
33195 \begin_inset Graphics
33196 filename clipart/macrobox.png
33202 \begin_inset space \hspace*{\fill}
33206 \begin_inset Newline newline
33210 \begin_inset FormulaMacro
33211 \newcommand{\qG}[4][1,\,2]{#2_{#1}=-\frac{#3}{2}\pm\sqrt{\frac{#3^{2}}{4}-#4}}
33216 newmacroname is the default name of the macro that should be changed to
33217 something sensible.
33218 The wanted formula is inserted in the first blue box.
33219 An argument placeholder is inserted with the command
33226 \begin_inset space \thinspace{}
33230 \begin_inset space \space{}
33239 or by using the macro toolbar button
33242 arg "math-macro-add-param"
33246 Argument placeholders are displayed red.
33248 \begin_inset space ~
33251 arguments are possible.
33252 Optional arguments are created with the toolbar button
33255 arg "math-macro-add-optional-param"
33259 The first non-optional argument can be transformed to an optional one with
33263 arg "math-macro-make-optional"
33267 In the second blue box the appearance of the macro in \SpecialChar LyX
33269 Normally you want to see it as it is defined, so the box is kept empty.
33270 But when you have created a macro that needs lot of space on the screen,
33271 you can insert in the box for example
33272 \begin_inset Newline newline
33302 \begin_inset Newline newline
33307 For the macro only the arguments with the macro name in front of them will
33308 then be displayed in \SpecialChar LyX
33309 , leading to a better overview.
33310 The formula appears in the output as defined in the first box.
33311 \begin_inset Newline newline
33314 The appearance of macros in formulas can furthermore be changed for single
33315 macros by setting the cursor in the macro and using the menu
33317 View\SpecialChar menuseparator
33319 \begin_inset space ~
33323 \begin_inset space ~
33331 \begin_layout Standard
33332 To use a macro, the macro name is inserted as command to a formula, in our
33340 Our macro looks in \SpecialChar LyX
33342 \begin_inset Newline newline
33346 \begin_inset space \hspace*{\fill}
33350 \begin_inset Graphics
33351 filename clipart/macrouse.png
33357 \begin_inset space \hspace*{\fill}
33361 \begin_inset Newline newline
33364 Here is our macro example with the arguments
33365 \begin_inset Formula $x$
33369 \begin_inset Formula $\ln(x)$
33373 \begin_inset Formula $B$
33379 \begin_layout Standard
33380 \begin_inset Formula
33390 \begin_layout Standard
33394 Tools\SpecialChar menuseparator
33395 Preferences\SpecialChar menuseparator
33396 Editing\SpecialChar menuseparator
33399 different styles to edit macros.
33400 To find the style that suits you the most, choose a style and set the cursor
33401 in a macro formula to see the difference.
33404 \begin_layout Standard
33405 A math macro is transformed internally to a
33411 command when exporting the document.
33418 command is not placed in the \SpecialChar LaTeX
33419 -preamble, therefore macros can only be used
33420 in formulas that are in the document below the macro definition box.
33423 \begin_layout Standard
33424 Math macros can also be directly created from a
33431 When writing for example the command
33434 \begin_inset Newline newline
33443 xleftarrow[#2]{#1}}
33444 \begin_inset Newline newline
33449 in \SpecialChar LyX
33450 as normal text, highlighting it completely and using then the shortcut
33455 , the command will be transformed to a math macro.
33456 Using this method you need to be careful that the
33462 command is typed correctly, otherwise you get a faulty macro leading to
33467 \begin_layout Standard
33468 Math macros currently have the problem that further formulas in macro definition
33469 s are handled wrongly.
33470 Therefore the example
33477 \begin_inset CommandInset ref
33479 reference "subsec:The-Command-newcommand"
33483 cannot be created as macro.
33486 \begin_layout Standard
33487 When the cursor is in a macro definition box, you will see the macro toolbar
33488 in \SpecialChar LyX
33492 \begin_layout Standard
33493 \begin_inset VSpace defskip
33499 \begin_layout Standard
33500 \begin_inset Graphics
33501 filename clipart/MacroToolbar.png
33506 \begin_inset Index idx
33509 \begin_layout Plain Layout
33518 \begin_layout Standard
33519 \begin_inset VSpace defskip
33525 \begin_layout Standard
33526 The macro toolbar contains from left to right the following buttons:
33529 \begin_layout Standard
33530 \begin_inset VSpace defskip
33536 \begin_layout Standard
33537 \begin_inset Tabular
33538 <lyxtabular version="3" rows="9" columns="2">
33539 <features islongtable="true" longtabularalignment="center">
33540 <column alignment="left" valignment="top">
33541 <column alignment="left" valignment="top" width="85col%">
33542 <row interlinespace="2.5mm">
33543 <cell alignment="center" valignment="top" usebox="none">
33546 \begin_layout Plain Layout
33549 arg "math-macro-remove-param"
33557 <cell alignment="center" valignment="top" usebox="none">
33560 \begin_layout Plain Layout
33563 Edit\SpecialChar menuseparator
33564 Math\SpecialChar menuseparator
33566 \begin_inset space ~
33569 Definition\SpecialChar menuseparator
33570 Remove Last Argument
33576 <row interlinespace="2.5mm">
33577 <cell alignment="center" valignment="top" usebox="none">
33580 \begin_layout Plain Layout
33583 arg "math-macro-add-param"
33591 <cell alignment="center" valignment="top" usebox="none">
33594 \begin_layout Plain Layout
33597 Edit\SpecialChar menuseparator
33598 Math\SpecialChar menuseparator
33600 \begin_inset space ~
33603 Definition\SpecialChar menuseparator
33610 <row interlinespace="2.5mm">
33611 <cell alignment="center" valignment="top" usebox="none">
33614 \begin_layout Plain Layout
33617 arg "math-macro-make-optional"
33625 <cell alignment="center" valignment="top" usebox="none">
33628 \begin_layout Plain Layout
33631 Edit\SpecialChar menuseparator
33632 Math\SpecialChar menuseparator
33634 \begin_inset space ~
33637 Definition\SpecialChar menuseparator
33638 Transform First Non-Optional to
33639 \begin_inset Newline newline
33643 \begin_inset Phantom HPhantom
33646 \begin_layout Plain Layout
33649 Edit\SpecialChar menuseparator
33650 Math\SpecialChar menuseparator
33652 \begin_inset space ~
33655 Definition\SpecialChar menuseparator
33667 <row interlinespace="2.5mm">
33668 <cell alignment="center" valignment="top" usebox="none">
33671 \begin_layout Plain Layout
33674 arg "math-macro-make-nonoptional"
33682 <cell alignment="center" valignment="top" usebox="none">
33685 \begin_layout Plain Layout
33688 Edit\SpecialChar menuseparator
33689 Math\SpecialChar menuseparator
33691 \begin_inset space ~
33694 Definition\SpecialChar menuseparator
33695 Transform Last Optional to
33696 \begin_inset Newline newline
33700 \begin_inset Phantom HPhantom
33703 \begin_layout Plain Layout
33706 Edit\SpecialChar menuseparator
33707 Math\SpecialChar menuseparator
33709 \begin_inset space ~
33712 Definition\SpecialChar menuseparator
33718 Non-Optional Argument
33724 <row interlinespace="2.5mm">
33725 <cell alignment="center" valignment="top" usebox="none">
33728 \begin_layout Plain Layout
33731 arg "math-macro-remove-optional-param"
33739 <cell alignment="center" valignment="top" usebox="none">
33742 \begin_layout Plain Layout
33745 Edit\SpecialChar menuseparator
33746 Math\SpecialChar menuseparator
33748 \begin_inset space ~
33751 Definition\SpecialChar menuseparator
33752 Remove Optional Argument
33758 <row interlinespace="2.5mm">
33759 <cell alignment="center" valignment="top" usebox="none">
33762 \begin_layout Plain Layout
33765 arg "math-macro-add-optional-param"
33773 <cell alignment="center" valignment="top" usebox="none">
33776 \begin_layout Plain Layout
33779 Edit\SpecialChar menuseparator
33780 Math\SpecialChar menuseparator
33782 \begin_inset space ~
33785 Definition\SpecialChar menuseparator
33786 Insert Optional Argument
33792 <row interlinespace="2.5mm">
33793 <cell alignment="center" valignment="top" usebox="none">
33796 \begin_layout Plain Layout
33799 arg "math-macro-remove-greedy-param"
33807 <cell alignment="center" valignment="top" usebox="none">
33810 \begin_layout Plain Layout
33813 Edit\SpecialChar menuseparator
33814 Math\SpecialChar menuseparator
33816 \begin_inset space ~
33819 Definition\SpecialChar menuseparator
33820 Remove Last Argument
33821 \begin_inset Newline newline
33825 \begin_inset Phantom HPhantom
33828 \begin_layout Plain Layout
33831 Edit\SpecialChar menuseparator
33832 Math\SpecialChar menuseparator
33834 \begin_inset space ~
33837 Definition\SpecialChar menuseparator
33843 Spitting Out To The Right
33849 <row interlinespace="2.5mm">
33850 <cell alignment="center" valignment="top" usebox="none">
33853 \begin_layout Plain Layout
33856 arg "math-macro-append-greedy-param"
33864 <cell alignment="center" valignment="top" usebox="none">
33867 \begin_layout Plain Layout
33870 Edit\SpecialChar menuseparator
33871 Math\SpecialChar menuseparator
33873 \begin_inset space ~
33876 Definition\SpecialChar menuseparator
33878 \begin_inset Newline newline
33882 \begin_inset Phantom HPhantom
33885 \begin_layout Plain Layout
33888 Edit\SpecialChar menuseparator
33889 Math\SpecialChar menuseparator
33891 \begin_inset space ~
33894 Definition\SpecialChar menuseparator
33900 Eating From The Right
33906 <row interlinespace="2.5mm">
33907 <cell alignment="center" valignment="top" usebox="none">
33910 \begin_layout Plain Layout
33913 arg "math-macro-add-greedy-optional-param"
33921 <cell alignment="center" valignment="top" usebox="none">
33924 \begin_layout Plain Layout
33927 Edit\SpecialChar menuseparator
33928 Math\SpecialChar menuseparator
33930 \begin_inset space ~
33933 Definition\SpecialChar menuseparator
33934 Append Optional Argument
33935 \begin_inset Newline newline
33939 \begin_inset Phantom HPhantom
33942 \begin_layout Plain Layout
33945 Edit\SpecialChar menuseparator
33946 Math\SpecialChar menuseparator
33948 \begin_inset space ~
33951 Definition\SpecialChar menuseparator
33957 Eating From The Right
33970 \begin_layout Section
33971 Computer Algebra Systems
33974 \begin_layout Standard
33976 offers the exchange between mathematical expressions written in \SpecialChar LyX
33978 editor and external applications or user defined scripts.
33979 Currently supported applications are
33996 Note that the set of supported mathematical constructs is limited only
33997 to very simple cases.
34000 \begin_layout Subsection
34004 \begin_layout Standard
34005 Write some expression in a formula, go to the
34007 Edit\SpecialChar menuseparator
34008 Math\SpecialChar menuseparator
34009 Use Computer Algebra System
34011 menu and choose the application you have installed on the computer.
34012 After that the result of computation should show on the right side of the
34013 expression together with the
34014 \begin_inset Quotes eld
34018 \begin_inset Quotes erd
34024 \begin_layout Standard
34025 Here are few simple examples (with results from
34029 ) to show what kind of computations can be performed:
34032 \begin_layout Itemize
34033 \begin_inset Formula $\frac{37}{3}*2-\sum_{i=1}^{3}i^{i}=-\frac{22}{3}$
34039 \begin_layout Itemize
34040 \begin_inset Formula $\frac{37.0}{3}=12.33333333333333$
34046 \begin_layout Itemize
34047 \begin_inset Formula $\int_{1}^{2}\sin(x)dx=\cos1-\cos2$
34053 \begin_layout Itemize
34054 \begin_inset Formula $\int\left(\frac{1}{1+x^{3}}\right)dx=-\frac{\log\left(x^{2}-x+1\right)}{6}+\frac{\arctan\left(\frac{2\,x-1}{\sqrt{3}}\right)}{\sqrt{3}}+\frac{\log\left(x+1\right)}{3}$
34058 \begin_inset Newline newline
34062 \begin_inset Note Greyedout
34065 \begin_layout Plain Layout
34070 One needs to use proper delimiter insets
34071 \begin_inset Formula $\left(\right)$
34074 instead of simple '(' ')' characters.
34082 \begin_layout Itemize
34083 \begin_inset Formula $\det\left[\begin{array}{ccc}
34087 \end{array}\right]=-56$
34093 \begin_layout Itemize
34094 \begin_inset Formula $\lim_{x\rightarrow0}\left(\frac{\sin(x)}{x}\right)=1$
34100 \begin_layout Itemize
34101 \begin_inset Formula $powerseries\left(-\log\left(5-x\right),x,1\right)=\sum_{{\mathit{i}_{2}}=0}^{\infty}{\frac{4^{-{\mathit{i}_{2}}-1}\,\left(x-1\right)^{{\mathit{i}_{2}}+1}}{{\mathit{i}_{2}}+1}}-\log4$
34107 \begin_layout Itemize
34108 \begin_inset Formula $solve\left(x_{1}+y_{1}^{3}=y_{1}+x_{1}^{2},x_{1}\right)=\left[x_{1}=-\frac{\sqrt{4\,y_{1}^{3}-4\,y_{1}+1}-1}{2},x_{1}=\frac{\sqrt{4\,y_{1}^{3}-4\,y_{1}+1}+1}{2}\right]$
34114 \begin_layout Subsection
34118 \begin_layout Standard
34119 Currently there is no keyboard shortcut for calling the algebra applications.
34120 One can easily bind a shortcut to the
34134 \begin_inset space \thinspace{}
34138 \begin_inset space \space{}
34145 key inside the math editor.
34150 one would use this shortcut definition command:
34153 \begin_layout Standard
34156 command-alternatives paragraph-break;math-extern maxima
34159 \begin_layout Section
34161 \begin_inset Index idx
34164 \begin_layout Plain Layout
34173 \begin_layout Subsection
34175 \begin_inset Index idx
34178 \begin_layout Plain Layout
34187 \begin_layout Standard
34188 Negative numbers often look ugly in formulas because the minus sign before
34189 the number is set with the same length as the minus operator sign.
34190 When writing the negative number in normal text, the minus sign appears
34194 \begin_layout Standard
34195 Thus, the problem disappears when converting the minus sign to mathematical
34199 \begin_layout Standard
34200 An example to visualize the problem:
34203 \begin_layout Standard
34205 \begin_inset Tabular
34206 <lyxtabular version="3" rows="3" columns="2">
34207 <features booktabs="true" tabularvalignment="middle">
34208 <column alignment="right" valignment="top" width="0pt">
34209 <column alignment="left" valignment="top">
34211 <cell alignment="right" valignment="top" topline="true" leftline="true" usebox="none">
34214 \begin_layout Plain Layout
34220 <cell alignment="center" valignment="top" topline="true" rightline="true" usebox="none">
34223 \begin_layout Plain Layout
34231 <cell alignment="right" valignment="top" leftline="true" usebox="none">
34234 \begin_layout Plain Layout
34240 <cell alignment="center" valignment="top" rightline="true" usebox="none">
34243 \begin_layout Plain Layout
34244 \begin_inset Formula $x=-2$
34254 <cell alignment="right" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
34257 \begin_layout Plain Layout
34263 <cell alignment="center" valignment="top" topline="true" bottomline="true" rightline="true" usebox="none">
34266 \begin_layout Plain Layout
34267 \begin_inset Formula $x=\textrm{-}2$
34283 \begin_layout Subsection
34284 Comma as decimal Separator
34285 \begin_inset Index idx
34288 \begin_layout Plain Layout
34297 \begin_layout Standard
34298 In \SpecialChar LaTeX
34299 a comma inside a formula is used, according to the English convention,
34300 as number group separator.
34301 So there will be space added behind all commas in formulas.
34304 \begin_layout Standard
34305 To avoid this, the comma is highlighted and changed to mathematical text
34315 \begin_layout Standard
34316 To use all formula commas in the document as decimal separator, the file
34325 \begin_layout Plain Layout
34330 is part of the \SpecialChar LaTeX
34336 \begin_inset Index idx
34339 \begin_layout Plain Layout
34344 \begin_layout Plain Layout
34364 \begin_inset Index idx
34367 \begin_layout Plain Layout
34373 is loaded with the \SpecialChar LaTeX
34377 \begin_layout Standard
34385 \begin_layout Subsection
34387 \begin_inset CommandInset label
34389 name "subsec:Physical-Vectors"
34394 \begin_inset Index idx
34397 \begin_layout Plain Layout
34406 \begin_layout Standard
34407 Predefined vectors are offered by the \SpecialChar LaTeX
34413 \begin_inset Index idx
34416 \begin_layout Plain Layout
34422 that is loaded with the \SpecialChar LaTeX
34426 \begin_layout Standard
34434 \begin_layout Standard
34438 \begin_layout Plain Layout
34448 \begin_inset Note Note
34451 \begin_layout Plain Layout
34452 The following table will only be displayed when the \SpecialChar LaTeX
34465 \begin_layout Standard
34466 The following commands are defined:
34469 \begin_layout Standard
34471 \begin_inset Tabular
34472 <lyxtabular version="3" rows="4" columns="2">
34473 <features booktabs="true" tabularvalignment="middle">
34474 <column alignment="center" valignment="top" width="0pt">
34475 <column alignment="center" valignment="top">
34477 <cell alignment="center" valignment="top" topline="true" bottomline="true" usebox="none">
34480 \begin_layout Plain Layout
34486 <cell alignment="center" valignment="top" topline="true" bottomline="true" usebox="none">
34489 \begin_layout Plain Layout
34497 <cell alignment="center" valignment="top" usebox="none">
34500 \begin_layout Plain Layout
34510 <cell alignment="center" valignment="top" usebox="none">
34513 \begin_layout Plain Layout
34514 \begin_inset Formula $\Bra{\psi}$
34524 <cell alignment="center" valignment="top" usebox="none">
34527 \begin_layout Plain Layout
34537 <cell alignment="center" valignment="top" usebox="none">
34540 \begin_layout Plain Layout
34541 \begin_inset Formula $\Ket{\psi}$
34551 <cell alignment="center" valignment="top" bottomline="true" usebox="none">
34554 \begin_layout Plain Layout
34566 <cell alignment="center" valignment="top" bottomline="true" usebox="none">
34569 \begin_layout Plain Layout
34570 \begin_inset Formula $\Braket{\psi|\phi}$
34586 \begin_layout Standard
34593 assures that all vertical bars are set in the size of the surrounding brackets:
34594 \begin_inset Formula
34596 \Braket{\phi|J=\frac{3}{2}\,,\,M_{J}}
34605 \begin_layout Plain Layout
34615 \begin_inset Note Note
34618 \begin_layout Plain Layout
34619 The following will be displayed when the \SpecialChar LaTeX
34632 \begin_layout Standard
34633 You need to install the \SpecialChar LaTeX
34638 to see the rest of this subsection in the output.
34641 \begin_layout Standard
34645 \begin_layout Plain Layout
34657 \begin_layout Standard
34664 can also be achieved using the command
34670 , that is described in
34671 \begin_inset CommandInset ref
34673 reference "subsec:Automatic-Bracket-Size"
34680 \begin_layout Subsection
34681 Self-defined Fractions
34682 \begin_inset CommandInset label
34684 name "subsec:Self-defined-Fractions"
34689 \begin_inset Index idx
34692 \begin_layout Plain Layout
34693 Fractions ! self-defined
34701 \begin_layout Standard
34702 To define custom commands for fractions, the command
34709 \begin_inset Index idx
34712 \begin_layout Plain Layout
34719 \begin_layout Plain Layout
34733 is used in the following scheme:
34736 \begin_layout Standard
34749 bracket}{fraction bar thickness}{style}
34750 \begin_inset Newline newline
34754 \begin_inset Phantom HPhantom
34757 \begin_layout Plain Layout
34767 {numerator}{denominator}
34770 \begin_layout Standard
34771 The style is a number in the range of 0
34772 \begin_inset space \thinspace{}
34776 \begin_inset space \thinspace{}
34782 \begin_layout Standard
34784 \begin_inset Tabular
34785 <lyxtabular version="3" rows="5" columns="2">
34786 <features booktabs="true" tabularvalignment="middle">
34787 <column alignment="center" valignment="top" width="0pt">
34788 <column alignment="center" valignment="top">
34790 <cell alignment="center" valignment="top" topline="true" bottomline="true" usebox="none">
34793 \begin_layout Plain Layout
34799 <cell alignment="center" valignment="top" topline="true" bottomline="true" usebox="none">
34802 \begin_layout Plain Layout
34810 <cell alignment="center" valignment="top" usebox="none">
34813 \begin_layout Plain Layout
34819 <cell alignment="center" valignment="top" usebox="none">
34822 \begin_layout Plain Layout
34823 display style formula
34830 <cell alignment="center" valignment="top" usebox="none">
34833 \begin_layout Plain Layout
34839 <cell alignment="center" valignment="top" usebox="none">
34842 \begin_layout Plain Layout
34850 <cell alignment="center" valignment="top" usebox="none">
34853 \begin_layout Plain Layout
34859 <cell alignment="center" valignment="top" usebox="none">
34862 \begin_layout Plain Layout
34870 <cell alignment="center" valignment="top" bottomline="true" usebox="none">
34873 \begin_layout Plain Layout
34879 <cell alignment="center" valignment="top" bottomline="true" usebox="none">
34882 \begin_layout Plain Layout
34896 \begin_layout Standard
34897 When no style is given, the size is adjusted to the surrounding environment
34898 like for the command
34907 \begin_layout Standard
34908 When no fraction bar thickness is given, the predefined value of 0.4
34909 \begin_inset space \thinspace{}
34915 \begin_layout Standard
34916 \begin_inset VSpace medskip
34919 For example, the commands
34932 \begin_inset CommandInset ref
34934 reference "subsec:Fractions"
34938 are defined with the commands
34941 \begin_layout Standard
34950 genfrac{}{}{}{0}{#1}{#2}}
34953 \begin_layout Standard
34957 \begin_layout Standard
34966 genfrac{(}{)}{0pt}{1}{#1}{#2}}
34969 \begin_layout Standard
34970 \begin_inset VSpace medskip
34973 To define a fraction where the fraction bar thickness can be given as optional
34974 argument, the following line is inserted to the \SpecialChar LaTeX
34978 \begin_layout Standard
34987 genfrac{}{}{#1}{}{#2}{#3}}
34990 \begin_layout Standard
34992 \begin_inset Formula
34994 \text{Command} & & \mathrm{\backslash fracS[1mm]\backslash\{A\to\backslash\{B} & & \mathrm{\backslash fracS[5mm]\backslash\{A\to\backslash\{B}\\
34995 \text{Result} & & \fracS[1mm]{A}{B} & & \fracS[5mm]{A}{B}
35000 As one can see, the distance of the numerator and the denominator to the
35001 fraction bar is round about three times the bar thickness.
35004 \begin_layout Standard
35005 \begin_inset Newpage newpage
35011 \begin_layout Subsection
35013 \begin_inset Index idx
35016 \begin_layout Plain Layout
35025 \begin_layout Standard
35026 There are four ways to cancel formulas or parts of formulas:
35029 \begin_layout Standard
35033 \begin_layout Plain Layout
35043 \begin_inset Note Note
35046 \begin_layout Plain Layout
35047 The following table will only be displayed when the \SpecialChar LaTeX
35060 \begin_layout Standard
35062 \begin_inset Tabular
35063 <lyxtabular version="3" rows="5" columns="2">
35064 <features booktabs="true" tabularvalignment="middle">
35065 <column alignment="center" valignment="top" width="0pt">
35066 <column alignment="center" valignment="top">
35068 <cell alignment="center" valignment="top" topline="true" bottomline="true" usebox="none">
35071 \begin_layout Plain Layout
35077 <cell alignment="center" valignment="top" topline="true" bottomline="true" usebox="none">
35080 \begin_layout Plain Layout
35088 <cell alignment="center" valignment="top" usebox="none">
35091 \begin_layout Plain Layout
35095 \begin_inset space \textvisiblespace{}
35101 \begin_inset space \textvisiblespace{}
35109 <cell alignment="center" valignment="top" usebox="none">
35112 \begin_layout Plain Layout
35113 \begin_inset Formula $\cancel{\int A=B}$
35122 <row topspace="1.5mm">
35123 <cell alignment="center" valignment="top" usebox="none">
35126 \begin_layout Plain Layout
35130 \begin_inset space \textvisiblespace{}
35136 \begin_inset space \textvisiblespace{}
35144 <cell alignment="center" valignment="top" usebox="none">
35147 \begin_layout Plain Layout
35148 \begin_inset Formula $\bcancel{\int A=B}$
35157 <row topspace="1.5mm">
35158 <cell alignment="center" valignment="top" usebox="none">
35161 \begin_layout Plain Layout
35165 \begin_inset space \textvisiblespace{}
35171 \begin_inset space \textvisiblespace{}
35179 <cell alignment="center" valignment="top" usebox="none">
35182 \begin_layout Plain Layout
35183 \begin_inset Formula $\xcancel{\int A=B}$
35193 <cell alignment="center" valignment="top" topline="true" bottomline="true" usebox="none">
35196 \begin_layout Plain Layout
35200 \begin_inset space \textvisiblespace{}
35206 \begin_inset space \textvisiblespace{}
35210 \begin_inset Formula $\to$
35218 <cell alignment="center" valignment="top" topline="true" bottomline="true" usebox="none">
35221 \begin_layout Plain Layout
35222 \begin_inset Formula $\cancelto{1}{\int A=B}\hspace{3mm}$
35238 \begin_layout Standard
35245 is especially suitable to visualize the reduction of fractions within formulas:
35246 \begin_inset Formula
35248 \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}}}
35256 \begin_layout Standard
35257 To change the size of
35264 \begin_inset Quotes eld
35268 \begin_inset Quotes erd
35271 value one can add the \SpecialChar LaTeX
35275 \begin_layout Standard
35280 PassOptionsToPackage{option}{cancel}
35283 \begin_layout Standard
35292 which leads to the same size as for the canceled value, or
35296 which makes is it a bit smaller than normal.
35299 \begin_layout Standard
35300 To color the cancellation bar one adds this command as \SpecialChar TeX
35304 \begin_layout Standard
35316 \begin_layout Standard
35321 can be replaced by a color of your choice.
35324 \begin_layout Standard
35328 \begin_layout Plain Layout
35344 \begin_layout Standard
35345 \begin_inset Formula
35347 \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}}}
35355 \begin_layout Standard
35359 \begin_layout Plain Layout
35373 \begin_inset Note Note
35376 \begin_layout Plain Layout
35385 \begin_layout Standard
35386 For further customizations, see the documentation of the package
35391 \begin_inset CommandInset citation
35398 \begin_inset Index idx
35401 \begin_layout Plain Layout
35410 \begin_layout Standard
35414 \begin_layout Plain Layout
35424 \begin_inset Note Note
35427 \begin_layout Plain Layout
35428 The following will be displayed when the \SpecialChar LaTeX
35441 \begin_layout Standard
35442 You need to install the \SpecialChar LaTeX
35447 to see the rest of this subsection in the output.
35450 \begin_layout Standard
35454 \begin_layout Plain Layout
35466 \begin_layout Subsection
35467 Formulas in Section Headings
35468 \begin_inset CommandInset label
35470 name "subsec:Formulas-in-Section"
35475 \begin_inset Index idx
35478 \begin_layout Plain Layout
35479 Formula ! in section headings
35487 \begin_layout Standard
35488 When formulas are used in section headings, the following has to be taken
35492 \begin_layout Standard
35493 \begin_inset Note Greyedout
35496 \begin_layout Plain Layout
35502 \begin_inset Index idx
35505 \begin_layout Plain Layout
35506 Packages ! hyperref
35511 support is enabled in the document settings dialog under
35514 \begin_inset space ~
35519 , PDF-bookmarks are created for every section heading in the table of contents.
35520 If a section heading contains formulas, they are incorrectly displayed
35521 in the bookmark text, because formulas in bookmarks infringe the PDF convention
35530 \begin_layout Standard
35531 Both problems can be solved by inserting at the end of the section heading
35532 a short title with the menu
35534 Insert\SpecialChar menuseparator
35536 \begin_inset space ~
35542 Short titles are used as alternative for multiline section headings to
35543 keep the table of contents clearly arranged.
35544 Only the short title appears in the table of contents and therefore also
35545 in the PDF-bookmark.
35548 \begin_layout Standard
35549 When formulas should be used in the table of contents but
35553 is used, one can use the following command in \SpecialChar TeX
35557 \begin_layout Standard
35562 texorpdfstring{part}{alternative}
35563 \begin_inset Index idx
35566 \begin_layout Plain Layout
35577 \begin_layout Standard
35578 Part is the part of the heading that shouldn't appear in the PDF-bookmark.
35579 This can be characters, formulas, footnotes, but also cross-references.
35580 The alternative is used instead of the part for the bookmark.
35583 \begin_layout Standard
35584 Here are two example headings:
35585 \begin_inset VSpace -3mm
35592 \begin_layout Plain Layout
35604 \begin_layout Subsubsection
35605 Heading without formula in table of contents
35606 \begin_inset Formula $\sqrt{-1}=\mathrm{i}$
35610 \begin_inset Argument 1
35613 \begin_layout Plain Layout
35614 Heading without formula in table of contents
35622 \begin_layout Subsubsection
35623 Heading with formula in table of contents
35627 \begin_layout Plain Layout
35637 \begin_inset Formula $\sqrt{-1}=\mathrm{i}$
35644 \begin_layout Plain Layout
35654 \begin_layout Standard
35658 \begin_layout Plain Layout
35667 In the first heading a short title was used, in the second one
35676 \begin_layout Standard
35677 To get the same formatting as for the other headings, the complete heading
35686 \begin_layout Plain Layout
35688 \begin_inset CommandInset ref
35690 reference "subsec:Bold-Formulas"
35702 \begin_layout Subsection
35703 Formulas in multi-column Text
35704 \begin_inset Index idx
35707 \begin_layout Plain Layout
35708 Formula ! in multi-column text
35716 \begin_layout Standard
35717 Formulas in multi-column text are often too wide to fit into a column and
35718 thus need to be set over the whole page width.
35719 This is done by using the \SpecialChar LaTeX
35728 \begin_layout Plain Layout
35733 is part of every \SpecialChar LaTeX
35734 standard installation.
35740 \begin_inset Index idx
35743 \begin_layout Plain Layout
35744 Packages ! multicol
35749 , that is loaded with the \SpecialChar LaTeX
35753 \begin_layout Standard
35758 usepackage{multicol}
35761 \begin_layout Standard
35762 \begin_inset Note Greyedout
35765 \begin_layout Plain Layout
35766 Note that in this case the setting
35769 \begin_inset space ~
35776 Document\SpecialChar menuseparator
35782 \begin_inset space ~
35802 \begin_layout Standard
35803 Before the multi-column text the command
35806 \begin_layout Standard
35811 begin{multicols}{column number}
35814 \begin_layout Standard
35815 is written in \SpecialChar TeX
35817 The column number is a number in the range of 2
35818 \begin_inset space \thinspace{}
35822 \begin_inset space \thinspace{}
35826 Before the formula the multi-column text is ended by inserting the command
35829 \begin_layout Standard
35837 \begin_layout Standard
35838 in \SpecialChar TeX
35842 \begin_layout Standard
35843 Due to the command some space is automatically added before the formula.
35845 \begin_inset space \thinspace{}
35848 mm vertical space is inserted before the formula.
35849 When the formula style
35855 \begin_layout Plain Layout
35857 \begin_inset CommandInset ref
35859 reference "sec:Formula-Styles"
35871 \begin_inset space \thinspace{}
35874 mm space is inserted instead.
35877 \begin_layout Standard
35878 As example a multi-column text with a displayed formula:
35881 \begin_layout Standard
35887 \begin_layout Plain Layout
35891 begin{multicols}{2}
35896 Das Spektrum wird fouriertransformiert.
35897 Die Fouriertransformation wird verwendet, um die überlagerten Signale (Netzwerk
35898 , Lösungsmittel) zu trennen.
35899 Nachdem wir die Phasenverschiebung bestimmen konnten, interessiert uns
35900 nun das Aussehen des Ausgangssignals.
35901 Im Experiment haben wir es mit sehr vielen Teilchen zu tun, so dass man
35902 über alle Phasen integrieren muss.
35904 \begin_inset Formula $S$
35907 unser normiertes Ausgangssignal und
35908 \begin_inset Formula $P$
35911 die Phasenverteilungsfunktion, so ergibt sich die Beziehung
35915 \begin_layout Plain Layout
35925 \begin_inset VSpace -6mm
35929 \begin_inset Formula
35931 S(t)=S_{0}(t)\int_{-\infty}^{\infty}P(\phi,t)\mathrm{e}^{\mathrm{i}\phi}\,\mathrm{d}\phi
35940 \begin_layout Plain Layout
35944 begin{multicols}{2}
35950 \begin_inset Formula $S_{0}$
35953 das Signal ohne Gradient ist und die Normierungsbedingung
35954 \begin_inset Formula $\int_{-\infty}^{\infty}P(\phi,t)\,\mathrm{d}\phi=1$
35958 Nun dürfen wir aber nicht den Relaxationsprozess außer Acht lassen.
35960 \begin_inset Formula $\nicefrac{\pi}{2}$
35964 \begin_inset space \thinspace{}
35967 -rf-Puls beginnt sich die Magnetisierung zu entfokussieren, wodurch sich
35968 das Signal zusätzlich abschwächt.
35969 Diese Abschwächung verläuft exponentiell in Abhängigkeit der so genannten
35971 \begin_inset Formula $T_{2}$
35977 \begin_layout Standard
35983 \begin_layout Plain Layout
35995 \begin_layout Subsection
35996 Formulas with Description of Variables
35997 \begin_inset Index idx
36000 \begin_layout Plain Layout
36001 Formula ! with description of variables
36009 \begin_layout Standard
36010 To describe variables within a formula, like in formula
36011 \begin_inset CommandInset ref
36013 reference "eq:within"
36022 \begin_inset Formula $n$
36026 \begin_inset space ~
36029 matrix is used with left aligned columns for the
36030 \begin_inset Formula $n$
36037 \begin_layout Plain Layout
36039 \begin_inset CommandInset ref
36041 reference "sec:Matrices"
36050 To set the description in a smaller size, before the matrix e.
36051 \begin_inset space \thinspace{}
36055 \begin_inset space \space{}
36068 \begin_layout Plain Layout
36070 \begin_inset CommandInset ref
36072 reference "subsec:Font-Sizes"
36084 \begin_layout Standard
36085 When the formula style
36091 \begin_layout Plain Layout
36093 \begin_inset CommandInset ref
36095 reference "sec:Formula-Styles"
36116 \begin_layout Plain Layout
36123 only works in formulas with the style
36128 \begin_inset CommandInset ref
36130 reference "subsec:Variable-Space"
36139 is inserted before and after the matrix to have the same separation of
36140 the matrix from the equation and the side margin.
36143 \begin_layout Standard
36144 When the formula style
36148 is used, the method described in
36149 \begin_inset CommandInset ref
36151 reference "subsec:Flalign-Environment"
36155 is used to indent formulas.
36157 \begin_inset CommandInset ref
36159 reference "eq:within"
36163 consists of five columns where in the first two columns contain the equation,
36164 the third the matrix and the last one an empty \SpecialChar TeX
36166 \begin_inset Formula
36168 \hspace{30pt}F_{A} & =\rho·V·g & \footnotesize\begin{array}{ll}
36169 \rho & \textrm{density}\\
36170 V & \textrm{volume}\\
36171 g & \textrm{gravitational acceleration}
36172 \end{array} & & {}\label{eq:within}
36180 \begin_layout Subsection
36181 Upright small Greek Letters
36182 \begin_inset CommandInset label
36184 name "subsec:Upright-small-Greek"
36189 \begin_inset Index idx
36192 \begin_layout Plain Layout
36193 Greek letters ! upright
36201 \begin_layout Standard
36202 Most of the math fonts only provide italic small Greek letters.
36203 But for symbols of elementary particles like pions and neutrinos, upright
36204 Greek letters are needed.
36213 \begin_layout Plain Layout
36218 is part of the \SpecialChar LaTeX
36224 \begin_inset Index idx
36227 \begin_layout Plain Layout
36232 \begin_layout Plain Layout
36252 \begin_inset Index idx
36255 \begin_layout Plain Layout
36261 that is loaded with the \SpecialChar LaTeX
36265 \begin_layout Standard
36270 usepackage{upgreek}
36273 \begin_layout Standard
36279 \begin_layout Plain Layout
36289 \begin_inset Note Note
36292 \begin_layout Plain Layout
36293 The following table will only be displayed when the \SpecialChar LaTeX
36303 They are created when the command for a small Greek letter is started with
36309 For example the command
36316 \begin_inset Formula $\uptau$
36322 \begin_layout Standard
36323 With these commands reactions of elementary particles can be typeset:
36324 \begin_inset Formula
36326 \uppi^{+}\to\upmu^{+}+\upnu_{\upmu}
36334 \begin_layout Standard
36335 The upright letters are more bold and wider than the italic ones.
36336 They should therefore not be used for units like
36337 \begin_inset Quotes eld
36341 \begin_inset Quotes erd
36347 \begin_layout Standard
36351 \begin_layout Plain Layout
36361 \begin_inset Note Note
36364 \begin_layout Plain Layout
36365 The following will be displayed when the \SpecialChar LaTeX
36378 \begin_layout Standard
36379 You need to install the \SpecialChar LaTeX
36384 to see the rest of this subsection in the output.
36387 \begin_layout Standard
36391 \begin_layout Plain Layout
36403 \begin_layout Subsection
36404 Text Characters in Formulas
36405 \begin_inset Index idx
36408 \begin_layout Plain Layout
36417 \begin_layout Standard
36418 In some cases you might want to insert text characters directly into formulas.
36419 When for example the centered dot · is often used in formulas like
36420 \begin_inset Formula $\nu=5·10^{5}\,\mathrm{Hz}$
36423 , one would have to insert the command
36433 \begin_layout Plain Layout
36435 \begin_inset CommandInset ref
36437 reference "subsec:Binary-Operators"
36446 all the time, because this character is defined in all encodings as text
36448 But the encoding can be changed by this \SpecialChar LaTeX
36452 \begin_layout Standard
36457 Declare Inputtext{183}{
36467 f\SpecialChar ligaturebreak
36471 \begin_layout Standard
36472 The character encoding (menu
36474 Document\SpecialChar menuseparator
36475 Settings\SpecialChar menuseparator
36478 ) specifies what character appears when a keyboard key is pressed.
36479 When the key for the character '·' is pressed, internally the command
36486 But this command is not available in a formula so that you would get \SpecialChar LaTeX
36488 With the changed encoding the right command is chosen automatically, depending
36489 on if the character was inserted into a formula or not.
36492 \begin_layout Standard
36493 The encoding of several characters is saved in definition files.
36494 For example the encoding
36498 is defined in the file
36502 which is in the installation folder of \SpecialChar LaTeX
36504 Encodings should only be changed via the \SpecialChar LaTeX
36505 -preamble and not in the definition
36507 Otherwise documents could not be edited by other \SpecialChar LyX
36508 users working on other
36512 \begin_layout Standard
36513 \begin_inset VSpace medskip
36516 Besides the centered dot, in this document the degree sign ° is defined
36517 with the following \SpecialChar LaTeX
36518 -preamble line so that it can be directly inserted into
36522 \begin_layout Standard
36527 DeclareInputtext{176}{
36537 f\SpecialChar ligaturebreak
36541 \begin_layout Subsection
36543 -comments in formulas
36544 \begin_inset Index idx
36547 \begin_layout Plain Layout
36557 \begin_layout Standard
36558 In text you can insert a comment that will only be visible in the \SpecialChar LaTeX
36560 code of your file with the menu
36562 Insert\SpecialChar menuseparator
36563 Note\SpecialChar menuseparator
36567 This is not possible in a formula but you can insert \SpecialChar LaTeX
36572 \begin_layout Standard
36580 \begin_layout Standard
36581 This creates a box in which you can write your comment.
36582 Due to a bug in \SpecialChar LyX
36587 \begin_layout Plain Layout
36588 \begin_inset CommandInset href
36590 name "LyX-bug #9002"
36591 target "http://www.lyx.org/trac/ticket/9002"
36600 you cannot write normal text inside the comment, even when you use mathematical
36601 text, you will see its \SpecialChar LaTeX
36602 -commands in the \SpecialChar LaTeX
36604 \begin_inset Newline newline
36607 This a formula with a \SpecialChar LaTeX
36609 \begin_inset Formula
36611 A=B%\text{This is the comment}
36619 \begin_layout Standard
36620 \begin_inset Newpage newpage
36626 \begin_layout Section
36629 \begin_inset Index idx
36632 \begin_layout Plain Layout
36641 \begin_layout Standard
36642 This section is a summary of the most important typographic rules, listed
36647 \begin_layout Plain Layout
36648 This collection was partly taken from the German semi-official dictionary
36650 \begin_inset Quotes eld
36654 \begin_inset Quotes erd
36658 \begin_inset CommandInset citation
36664 that lists some of the ISO rules.
36665 More rules are listed in
36666 \begin_inset CommandInset citation
36680 \begin_layout Itemize
36689 \begin_layout Plain Layout
36690 done with font styles, see
36691 \begin_inset CommandInset ref
36693 reference "subsec:Font-Styles"
36702 , no matter if they appear in italic text: 30
36703 \begin_inset space \thinspace{}
36707 \begin_inset Newline newline
36710 Between the value and the unit is the smallest space, see
36711 \begin_inset CommandInset ref
36713 reference "subsec:Predefined-Space"
36718 \begin_inset Newline newline
36721 This convention is automatically fulfilled when the command
36728 When it is entered to a formula, two boxes appear.
36729 In the first one the value is inserted, in the second one the unit, and
36731 \begin_inset Formula $\unit[30]{km/h}$
36735 \begin_inset space \thinspace{}
36745 is not a real \SpecialChar LaTeX
36746 command but the command
36752 , therefore you cannot use it in \SpecialChar TeX
36756 \begin_layout Itemize
36757 Percent and perthousand signs are set like physical units:
36758 \begin_inset Newline newline
36762 \begin_inset space \thinspace{}
36768 \begin_layout Itemize
36769 The degree sign follows directly on the value: 15°, but not when it is used
36771 \begin_inset space \thinspace{}
36777 \begin_layout Itemize
36778 In numbers with more than four digits the smallest space is inserted before
36779 every third digit to group them:
36789 \begin_inset space \thinspace{}
36793 \begin_inset space \thinspace{}
36799 \begin_layout Itemize
36800 For dimensions like 120×90×40
36801 \begin_inset space \thinspace{}
36804 cm the multiplication sign
36805 \begin_inset Quotes eld
36809 \begin_inset Quotes erd
36813 It is available either via the command
36821 Insert\SpecialChar menuseparator
36822 Special Character\SpecialChar menuseparator
36828 \begin_layout Itemize
36829 Functions with names consisting of several letters are set upright to avoid
36831 \begin_inset CommandInset ref
36833 reference "subsec:Predefined-Functions"
36840 \begin_layout Itemize
36841 Indices consisting of several letters, are set upright:
36842 \begin_inset Formula $E_{\mathrm{kin}}$
36846 \begin_inset Newline newline
36849 Components of matrices are set italic:
36850 \begin_inset Formula $\hat{H}_{kl}$
36856 \begin_layout Itemize
36857 The differentiation/integration operator 'd', the Euler's number 'e' and
36858 the imaginary unit 'i' should be set upright, to avoid mixing them up with
36862 \begin_layout Itemize
36863 The character that denotes a
36867 transformation is inserted either by the command
36872 \begin_inset space \textvisiblespace{}
36879 Insert\SpecialChar menuseparator
36880 Special Character\SpecialChar menuseparator
36881 Symbols\SpecialChar menuseparator
36883 \begin_inset space ~
36889 \begin_inset Formula $\mathscr{F}$
36895 \begin_layout Standard
36896 \begin_inset Newpage newpage
36902 \begin_layout Section
36904 \begin_inset Index idx
36907 \begin_layout Plain Layout
36916 \begin_layout Standard
36917 Some characters and symbols can be created with several commands.
36918 Here is a list of the synonym commands:
36921 \begin_layout Standard
36922 \begin_inset VSpace bigskip
36926 \begin_inset space \hfill{}
36930 \begin_inset Tabular
36931 <lyxtabular version="3" rows="12" columns="2">
36932 <features booktabs="true" tabularvalignment="middle">
36933 <column alignment="center" valignment="top" width="0pt">
36934 <column alignment="center" valignment="top" width="0pt">
36936 <cell alignment="center" valignment="top" topline="true" bottomline="true" usebox="none">
36939 \begin_layout Plain Layout
36945 <cell alignment="center" valignment="top" topline="true" bottomline="true" usebox="none">
36948 \begin_layout Plain Layout
36956 <cell alignment="center" valignment="top" usebox="none">
36959 \begin_layout Plain Layout
36967 <cell alignment="center" valignment="top" usebox="none">
36970 \begin_layout Plain Layout
36978 <cell alignment="center" valignment="top" usebox="none">
36981 \begin_layout Plain Layout
36989 <cell alignment="center" valignment="top" usebox="none">
36992 \begin_layout Plain Layout
37002 <cell alignment="center" valignment="top" usebox="none">
37005 \begin_layout Plain Layout
37013 <cell alignment="center" valignment="top" usebox="none">
37016 \begin_layout Plain Layout
37026 <cell alignment="center" valignment="top" usebox="none">
37029 \begin_layout Plain Layout
37037 <cell alignment="center" valignment="top" usebox="none">
37040 \begin_layout Plain Layout
37048 <cell alignment="center" valignment="top" usebox="none">
37051 \begin_layout Plain Layout
37059 <cell alignment="center" valignment="top" usebox="none">
37062 \begin_layout Plain Layout
37070 <cell alignment="center" valignment="top" usebox="none">
37073 \begin_layout Plain Layout
37081 <cell alignment="center" valignment="top" usebox="none">
37084 \begin_layout Plain Layout
37094 <cell alignment="center" valignment="top" usebox="none">
37097 \begin_layout Plain Layout
37105 <cell alignment="center" valignment="top" usebox="none">
37108 \begin_layout Plain Layout
37118 <cell alignment="center" valignment="top" usebox="none">
37121 \begin_layout Plain Layout
37129 <cell alignment="center" valignment="top" usebox="none">
37132 \begin_layout Plain Layout
37142 <cell alignment="center" valignment="top" usebox="none">
37145 \begin_layout Plain Layout
37153 <cell alignment="center" valignment="top" usebox="none">
37156 \begin_layout Plain Layout
37166 <cell alignment="center" valignment="top" usebox="none">
37169 \begin_layout Plain Layout
37177 <cell alignment="center" valignment="top" usebox="none">
37180 \begin_layout Plain Layout
37188 <cell alignment="center" valignment="top" bottomline="true" usebox="none">
37191 \begin_layout Plain Layout
37199 <cell alignment="center" valignment="top" bottomline="true" usebox="none">
37202 \begin_layout Plain Layout
37214 \begin_inset space \hfill{}
37218 \begin_inset Tabular
37219 <lyxtabular version="3" rows="12" columns="2">
37220 <features booktabs="true" tabularvalignment="middle">
37221 <column alignment="center" valignment="top" width="0pt">
37222 <column alignment="center" valignment="top" width="0pt">
37224 <cell alignment="center" valignment="top" topline="true" bottomline="true" usebox="none">
37227 \begin_layout Plain Layout
37233 <cell alignment="center" valignment="top" topline="true" bottomline="true" usebox="none">
37236 \begin_layout Plain Layout
37244 <cell alignment="center" valignment="top" usebox="none">
37247 \begin_layout Plain Layout
37255 <cell alignment="center" valignment="top" usebox="none">
37258 \begin_layout Plain Layout
37270 <cell alignment="center" valignment="top" usebox="none">
37273 \begin_layout Plain Layout
37281 <cell alignment="center" valignment="top" usebox="none">
37284 \begin_layout Plain Layout
37294 <cell alignment="center" valignment="top" usebox="none">
37297 \begin_layout Plain Layout
37305 <cell alignment="center" valignment="top" usebox="none">
37308 \begin_layout Plain Layout
37318 <cell alignment="center" valignment="top" usebox="none">
37321 \begin_layout Plain Layout
37329 <cell alignment="center" valignment="top" usebox="none">
37332 \begin_layout Plain Layout
37340 <cell alignment="center" valignment="top" usebox="none">
37343 \begin_layout Plain Layout
37351 <cell alignment="center" valignment="top" usebox="none">
37354 \begin_layout Plain Layout
37362 <cell alignment="center" valignment="top" usebox="none">
37365 \begin_layout Plain Layout
37373 <cell alignment="center" valignment="top" usebox="none">
37376 \begin_layout Plain Layout
37386 <cell alignment="center" valignment="top" usebox="none">
37389 \begin_layout Plain Layout
37397 <cell alignment="center" valignment="top" usebox="none">
37400 \begin_layout Plain Layout
37410 <cell alignment="center" valignment="top" usebox="none">
37413 \begin_layout Plain Layout
37421 <cell alignment="center" valignment="top" usebox="none">
37424 \begin_layout Plain Layout
37434 <cell alignment="center" valignment="top" usebox="none">
37437 \begin_layout Plain Layout
37445 <cell alignment="center" valignment="top" usebox="none">
37448 \begin_layout Plain Layout
37458 <cell alignment="center" valignment="top" usebox="none">
37461 \begin_layout Plain Layout
37469 <cell alignment="center" valignment="top" usebox="none">
37472 \begin_layout Plain Layout
37482 <cell alignment="center" valignment="top" bottomline="true" usebox="none">
37485 \begin_layout Plain Layout
37493 <cell alignment="center" valignment="top" bottomline="true" usebox="none">
37496 \begin_layout Plain Layout
37510 \begin_inset space \hfill{}
37516 \begin_layout Standard
37517 \begin_inset Newpage newpage
37523 \begin_layout Bibliography
37524 \begin_inset CommandInset bibitem
37525 LatexCommand bibitem
37537 The \SpecialChar LaTeX
37541 Addison Wesley, 2004
37544 \begin_layout Bibliography
37545 \begin_inset CommandInset bibitem
37546 LatexCommand bibitem
37552 \begin_inset CommandInset href
37555 target "ftp://ftp.dante.de/tex-archive/info/math/voss/mathmode/Mathmode.pdf"
37559 of \SpecialChar LaTeX
37563 \begin_layout Bibliography
37564 \begin_inset CommandInset bibitem
37565 LatexCommand bibitem
37571 \begin_inset CommandInset href
37574 target "http://mirrors.ctan.org/macros/latex/required/amslatex/math/amsldoc.pdf"
37582 \begin_layout Plain Layout
37591 -\SpecialChar LaTeX
37595 \begin_layout Bibliography
37596 \begin_inset CommandInset bibitem
37597 LatexCommand bibitem
37603 \begin_inset CommandInset href
37606 target "ftp://ftp.dante.de/tex-archive/info/symbols/comprehensive/symbols-a4.pdf"
37610 of all symbols available with \SpecialChar LaTeX
37614 \begin_layout Bibliography
37615 \begin_inset CommandInset bibitem
37616 LatexCommand bibitem
37622 \begin_inset CommandInset href
37624 name "Documentation"
37625 target "http://mirrors.ctan.org/macros/latex/contrib/cancel/cancel.pdf"
37629 of the \SpecialChar LaTeX
37635 \begin_inset Index idx
37638 \begin_layout Plain Layout
37647 \begin_layout Bibliography
37648 \begin_inset CommandInset bibitem
37649 LatexCommand bibitem
37655 \begin_inset CommandInset href
37657 name "Documentation"
37658 target "http://www.tug.org/applications/hyperref/ftp/doc/manual.pdf"
37662 of the \SpecialChar LaTeX
37668 \begin_inset Index idx
37671 \begin_layout Plain Layout
37672 Packages ! hyperref
37680 \begin_layout Bibliography
37681 \begin_inset CommandInset bibitem
37682 LatexCommand bibitem
37688 \begin_inset CommandInset href
37690 name "Documentation"
37691 target "http://www.ctan.org/tex-archive/macros/latex/contrib/mhchem/mhchem.pdf"
37695 of the \SpecialChar LaTeX
37701 \begin_inset Index idx
37704 \begin_layout Plain Layout
37713 \begin_layout Bibliography
37714 \begin_inset CommandInset bibitem
37715 LatexCommand bibitem
37726 Auflage, Duden 2001
37729 \begin_layout Bibliography
37730 \begin_inset CommandInset bibitem
37731 LatexCommand bibitem
37737 \begin_inset CommandInset href
37740 target "http://physics.nist.gov/Pubs/SP811/sec11.html"
37744 for reviewing manuscripts
37747 \begin_layout Standard
37748 \begin_inset CommandInset index_print
37749 LatexCommand printindex