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"
1496 \begin_inset Separator parbreak
1502 \begin_layout Standard
1504 \begin_inset Tabular
1505 <lyxtabular version="3" rows="4" columns="2">
1506 <features booktabs="true" tabularvalignment="middle">
1507 <column alignment="center" valignment="top" width="0pt">
1508 <column alignment="center" valignment="top" width="0pt">
1510 <cell alignment="center" valignment="top" topline="true" bottomline="true" usebox="none">
1513 \begin_layout Plain Layout
1519 <cell alignment="center" valignment="top" topline="true" bottomline="true" usebox="none">
1522 \begin_layout Plain Layout
1530 <cell alignment="center" valignment="top" usebox="none">
1533 \begin_layout Plain Layout
1539 <cell alignment="center" valignment="top" usebox="none">
1542 \begin_layout Plain Layout
1543 \begin_inset Formula $B_{V}$
1552 <row topspace="1.5mm">
1553 <cell alignment="center" valignment="top" usebox="none">
1556 \begin_layout Plain Layout
1562 <cell alignment="center" valignment="top" usebox="none">
1565 \begin_layout Plain Layout
1566 \begin_inset Formula $B^{V}$
1575 <row topspace="1.5mm">
1576 <cell alignment="center" valignment="top" topline="true" bottomline="true" usebox="none">
1579 \begin_layout Plain Layout
1581 \begin_inset space \textvisiblespace{}
1589 <cell alignment="center" valignment="top" topline="true" bottomline="true" usebox="none">
1592 \begin_layout Plain Layout
1593 \begin_inset Formula $B^{A}$
1609 \begin_layout Standard
1610 As the caret is in some languages an accent, vowels will be accentuated
1611 in this case and not set as exponents
1615 \begin_layout Plain Layout
1616 Depending on the used keyboard settings this can also happen for characters
1623 To get exponents in this case, press
1627 after the caret as in the last example.
1630 \begin_layout Subsection
1632 \begin_inset CommandInset label
1634 name "subsec:Fractions"
1639 \begin_inset Index idx
1642 \begin_layout Plain Layout
1651 \begin_layout Standard
1652 Fractions are generated with the command
1659 \begin_inset Index idx
1662 \begin_layout Plain Layout
1670 or via the math toolbar button
1673 arg "math-insert \\frac"
1677 The font size is adjusted automatically, depending on whether the fraction
1678 is in an inline or display style formula.
1679 With the math toolbar button
1682 arg "math-insert \\frac-square"
1685 you can select different fraction types.
1688 \begin_layout Standard
1696 \begin_inset Index idx
1699 \begin_layout Plain Layout
1707 a fraction can be created that always has the size of a display style formula.
1715 \begin_inset Index idx
1718 \begin_layout Plain Layout
1726 the fraction appears always with the size of an inline formula.
1730 \begin_layout Standard
1731 A line with the fraction
1732 \begin_inset Formula $\frac{1}{2}$
1735 that was created with the command
1744 \begin_layout Standard
1745 A line with the fraction
1746 \begin_inset Formula $\dfrac{1}{2}$
1749 that was created with the command
1756 \begin_inset Separator parbreak
1762 \begin_layout Standard
1764 \begin_inset Tabular
1765 <lyxtabular version="3" rows="4" columns="2">
1766 <features booktabs="true" tabularvalignment="middle">
1767 <column alignment="center" valignment="top" width="0pt">
1768 <column alignment="center" valignment="top" width="0pt">
1770 <cell alignment="center" valignment="top" topline="true" bottomline="true" usebox="none">
1773 \begin_layout Plain Layout
1779 <cell alignment="center" valignment="top" topline="true" bottomline="true" usebox="none">
1782 \begin_layout Plain Layout
1789 <row topspace="1.5mm">
1790 <cell alignment="center" valignment="top" usebox="none">
1793 \begin_layout Plain Layout
1797 \begin_inset space \textvisiblespace{}
1801 \begin_inset Formula $\downarrow$
1809 <cell alignment="center" valignment="top" usebox="none">
1812 \begin_layout Plain Layout
1813 \begin_inset Formula $\frac{A}{B}$
1822 <row topspace="2mm">
1823 <cell alignment="center" valignment="top" usebox="none">
1826 \begin_layout Plain Layout
1830 \begin_inset space \textvisiblespace{}
1834 \begin_inset Formula $\downarrow$
1842 <cell alignment="center" valignment="top" usebox="none">
1845 \begin_layout Plain Layout
1846 \begin_inset Formula $\dfrac{A}{B}$
1855 <row topspace="2mm" bottomspace="1mm">
1856 <cell alignment="center" valignment="top" bottomline="true" usebox="none">
1859 \begin_layout Plain Layout
1863 \begin_inset space \textvisiblespace{}
1869 \begin_inset space \textvisiblespace{}
1873 \begin_inset Formula $\downarrow$
1877 \begin_inset Formula $\downarrow\downarrow$
1885 <cell alignment="center" valignment="top" bottomline="true" usebox="none">
1888 \begin_layout Plain Layout
1889 \begin_inset Formula $\dfrac{e^{\frac{1}{2}}}{3}$
1905 \begin_layout Standard
1906 \begin_inset VSpace bigskip
1910 \begin_inset Newpage newpage
1913 For nested fractions the command
1920 \begin_inset Index idx
1923 \begin_layout Plain Layout
1933 \begin_inset VSpace -3mm
1939 \begin_layout Standard
1940 \begin_inset Formula
1942 \textrm{created with \textbf{\textbackslash frac}} & & \textrm{created with \textbf{\textbackslash cfrac}}\\
1943 \frac{A}{B+\frac{C+\frac{E}{F}}{D}} & & \cfrac{A}{B+\cfrac{C+\cfrac{E}{F}}{D}}
1951 \begin_layout Standard
1952 The command for the example above is:
1955 \begin_layout Standard
1961 \begin_inset space \textvisiblespace{}
1965 \begin_inset Formula $\downarrow$
1971 \begin_inset space \textvisiblespace{}
1977 \begin_inset space \textvisiblespace{}
1981 \begin_inset Formula $\downarrow$
1985 \begin_inset Formula $\downarrow$
1991 \begin_layout Standard
1992 \begin_inset VSpace medskip
1998 \begin_layout Standard
2005 sets the fraction always in the size of a displayed formula, also when
2006 it is part of another fraction.
2009 \begin_layout Standard
2010 It is possible to specify the alignment of the numerator.
2017 is used to left align it, the command
2030 centers the numerator.
2031 These fractions demonstrate the different alignments:
2034 \begin_layout Standard
2037 \begin_inset Formula
2039 \cfrac[l]{A}{B+C}\,,\,\cfrac{A}{B+C}\,,\,\cfrac[r]{A}{B+C}
2047 \begin_layout Standard
2048 \begin_inset Note Greyedout
2051 \begin_layout Plain Layout
2068 are no real \SpecialChar LaTeX
2069 commands but represent the command
2073 cfrac[alignment]{numerator}{denominator}
2076 Therefore you cannot use them in \SpecialChar TeX
2085 \begin_layout Standard
2086 \begin_inset VSpace medskip
2089 It is often advantageous to combine
2102 \begin_inset Formula
2104 \cfrac{A}{B+\cfrac{C+\frac{E}{F}}{D}}
2112 \begin_layout Standard
2113 For inline fractions with a sloped fraction stroke you can use the command
2121 \begin_inset Index idx
2124 \begin_layout Plain Layout
2133 \begin_inset Formula $\nicefrac{5}{31}$
2143 \begin_inset Index idx
2146 \begin_layout Plain Layout
2155 \begin_inset Formula $\unitfrac{5}{31}$
2158 There is furthermore the command
2164 that offers to write a fraction in combination with a number:
2165 \begin_inset Formula $\unitfrac[2]{1}{3}$
2171 \begin_layout Standard
2172 \begin_inset Note Greyedout
2175 \begin_layout Plain Layout
2186 is not a real \SpecialChar LaTeX
2187 command but the command
2188 \begin_inset Newline newline
2195 unitfrac[number]{numerator}{denominator}
2198 Therefore you cannot use it in \SpecialChar TeX
2207 \begin_layout Standard
2208 How to define own fractions where the fraction stroke can be changed, is
2210 \begin_inset CommandInset ref
2212 reference "subsec:Self-defined-Fractions"
2219 \begin_layout Standard
2220 Multiline fractions are explained in
2221 \begin_inset CommandInset ref
2223 reference "subsec:Multiline-Fractions"
2230 \begin_layout Subsection
2232 \begin_inset Index idx
2235 \begin_layout Plain Layout
2244 \begin_layout Standard
2245 Square roots are created with
2252 \begin_inset Index idx
2255 \begin_layout Plain Layout
2263 or the math toolbar button
2266 arg "math-insert \\sqrt"
2269 , all other roots with the command
2276 \begin_inset Index idx
2279 \begin_layout Plain Layout
2287 or with the math toolbar button
2290 arg "math-insert \\root"
2294 \begin_inset Separator parbreak
2300 \begin_layout Standard
2302 \begin_inset Tabular
2303 <lyxtabular version="3" rows="3" columns="2">
2304 <features booktabs="true" tabularvalignment="middle">
2305 <column alignment="center" valignment="top" width="0pt">
2306 <column alignment="center" valignment="top" width="0pt">
2308 <cell alignment="center" valignment="top" topline="true" bottomline="true" usebox="none">
2311 \begin_layout Plain Layout
2317 <cell alignment="center" valignment="top" topline="true" bottomline="true" usebox="none">
2320 \begin_layout Plain Layout
2327 <row topspace="1mm">
2328 <cell alignment="center" valignment="top" usebox="none">
2331 \begin_layout Plain Layout
2335 \begin_inset space \textvisiblespace{}
2343 <cell alignment="center" valignment="top" usebox="none">
2346 \begin_layout Plain Layout
2347 \begin_inset Formula $\sqrt{A-B}$
2356 <row topspace="1mm">
2357 <cell alignment="center" valignment="top" bottomline="true" usebox="none">
2360 \begin_layout Plain Layout
2364 \begin_inset space \textvisiblespace{}
2368 \begin_inset Formula $\downarrow$
2376 <cell alignment="center" valignment="top" bottomline="true" usebox="none">
2379 \begin_layout Plain Layout
2380 \begin_inset Formula $\sqrt[3]{A-B}$
2396 \begin_layout Standard
2397 A square root can also be created with
2403 when the root index field is left empty.
2406 \begin_layout Standard
2407 With certain indices the distance to the root is too small, like in this
2409 \begin_inset Formula $\sqrt[\beta]{B}$
2413 \begin_inset Newline newline
2417 \begin_inset Formula $\beta$
2421 To avoid this, the commands
2428 \begin_inset Index idx
2431 \begin_layout Plain Layout
2446 \begin_inset Index idx
2449 \begin_layout Plain Layout
2457 are used with the following scheme:
2460 \begin_layout Standard
2474 \begin_layout Standard
2475 Distance is the number of Big Points (unit bp;
2476 \begin_inset Formula $\mathrm{72\,bp=1\,inch}$
2479 ), that the index should be moved to the left or top, resp..
2480 The commands are written to the index.
2481 This way the command
2482 \begin_inset Newline newline
2492 \begin_inset Formula $\to$
2498 \begin_inset Formula $\to$
2504 \begin_inset space \textvisiblespace{}
2508 \begin_inset Formula $\to$
2512 \begin_inset Newline newline
2517 produces a correct typeset formula:
2518 \begin_inset Formula $\sqrt[\leftroot{-1}\uproot{2}\beta]{B}$
2524 \begin_layout Subsection
2525 Binomial Coefficients
2526 \begin_inset Index idx
2529 \begin_layout Plain Layout
2530 Binomial coefficients
2538 \begin_layout Standard
2539 Binomial coefficients are inserted with the command
2546 \begin_inset Index idx
2549 \begin_layout Plain Layout
2557 or with the submenu of the math toolbar button
2560 arg "math-insert \\frac-square"
2576 there are the commands
2583 \begin_inset Index idx
2586 \begin_layout Plain Layout
2601 \begin_inset Index idx
2604 \begin_layout Plain Layout
2613 For other brackets around binomial coeficients there are the commands
2620 \begin_inset Index idx
2623 \begin_layout Plain Layout
2638 \begin_inset Index idx
2641 \begin_layout Plain Layout
2650 \begin_inset Separator parbreak
2656 \begin_layout Standard
2658 \begin_inset Tabular
2659 <lyxtabular version="3" rows="6" columns="2">
2660 <features booktabs="true" tabularvalignment="middle">
2661 <column alignment="center" valignment="top" width="0pt">
2662 <column alignment="center" valignment="top" width="0pt">
2664 <cell alignment="center" valignment="top" topline="true" bottomline="true" usebox="none">
2667 \begin_layout Plain Layout
2673 <cell alignment="center" valignment="top" topline="true" bottomline="true" usebox="none">
2676 \begin_layout Plain Layout
2683 <row topspace="1mm">
2684 <cell alignment="center" valignment="top" usebox="none">
2687 \begin_layout Plain Layout
2691 \begin_inset space \textvisiblespace{}
2695 \begin_inset Formula $\downarrow$
2703 <cell alignment="center" valignment="top" usebox="none">
2706 \begin_layout Plain Layout
2707 \begin_inset Formula $\binom{A}{B}$
2716 <row topspace="2mm">
2717 <cell alignment="center" valignment="top" usebox="none">
2720 \begin_layout Plain Layout
2724 \begin_inset space \textvisiblespace{}
2728 \begin_inset Formula $\downarrow$
2736 <cell alignment="center" valignment="top" usebox="none">
2739 \begin_layout Plain Layout
2740 \begin_inset Formula $\dbinom{A}{B}$
2749 <row topspace="2mm" bottomspace="0.5mm">
2750 <cell alignment="center" valignment="top" usebox="none">
2753 \begin_layout Plain Layout
2757 \begin_inset space \textvisiblespace{}
2761 \begin_inset Formula $\downarrow$
2769 <cell alignment="center" valignment="top" usebox="none">
2772 \begin_layout Plain Layout
2773 \begin_inset Formula $\tbinom{A}{B}$
2782 <row topspace="1mm">
2783 <cell alignment="center" valignment="top" topline="true" usebox="none">
2786 \begin_layout Plain Layout
2790 \begin_inset space \textvisiblespace{}
2794 \begin_inset Formula $\downarrow$
2802 <cell alignment="center" valignment="top" topline="true" usebox="none">
2805 \begin_layout Plain Layout
2806 \begin_inset Formula ${A \brack B}$
2815 <row topspace="2mm" bottomspace="0.5mm">
2816 <cell alignment="center" valignment="top" bottomline="true" usebox="none">
2819 \begin_layout Plain Layout
2823 \begin_inset space \textvisiblespace{}
2827 \begin_inset Formula $\downarrow$
2835 <cell alignment="center" valignment="top" bottomline="true" usebox="none">
2838 \begin_layout Plain Layout
2839 \begin_inset Formula ${A \brace B}$
2855 \begin_layout Subsection
2856 Case Differentiations
2857 \begin_inset Index idx
2860 \begin_layout Plain Layout
2861 Case differentiations
2869 \begin_layout Standard
2871 \begin_inset Tabular
2872 <lyxtabular version="3" rows="3" columns="2">
2873 <features booktabs="true" tabularvalignment="middle">
2874 <column alignment="center" valignment="top" width="0pt">
2875 <column alignment="center" valignment="top" width="0pt">
2877 <cell alignment="center" valignment="top" topline="true" bottomline="true" usebox="none">
2880 \begin_layout Plain Layout
2886 <cell alignment="center" valignment="top" topline="true" bottomline="true" usebox="none">
2889 \begin_layout Plain Layout
2897 <cell alignment="center" valignment="top" usebox="none">
2900 \begin_layout Plain Layout
2904 \begin_inset space \textvisiblespace{}
2908 \begin_inset Formula $\to$
2912 \begin_inset Index idx
2915 \begin_layout Plain Layout
2928 <cell alignment="center" valignment="top" usebox="none">
2931 \begin_layout Plain Layout
2932 \begin_inset Formula $\begin{cases}
2942 <row topspace="1.5mm">
2943 <cell alignment="center" valignment="top" bottomline="true" usebox="none">
2946 \begin_layout Plain Layout
2950 \begin_inset space \textvisiblespace{}
2956 arg "newline-insert newline"
2964 <cell alignment="center" valignment="top" bottomline="true" usebox="none">
2967 \begin_layout Plain Layout
2968 \begin_inset Formula $\begin{cases}
2969 A & \textrm{for }x>0\\
2970 B & \textrm{for }x=0
2987 \begin_layout Standard
2994 or pressing the math toolbar button
2997 arg "math-insert \\cases"
3000 you can create new lines with the shortcut
3003 arg "newline-insert newline"
3006 or the table toolbar button
3009 arg "tabular-feature append-row"
3015 \begin_layout Standard
3022 is also available via the menu
3024 Insert\SpecialChar menuseparator
3025 Math\SpecialChar menuseparator
3031 \begin_layout Subsection
3033 \begin_inset Index idx
3036 \begin_layout Plain Layout
3045 \begin_layout Standard
3053 \begin_inset Index idx
3056 \begin_layout Plain Layout
3064 every character can be displayed canceled.
3065 The characters are quasi accentuated by a slash.
3066 \begin_inset Separator parbreak
3072 \begin_layout Standard
3074 \begin_inset Tabular
3075 <lyxtabular version="3" rows="4" columns="2">
3076 <features booktabs="true" tabularvalignment="middle">
3077 <column alignment="center" valignment="top" width="0pt">
3078 <column alignment="center" valignment="top" width="0pt">
3080 <cell alignment="center" valignment="top" topline="true" bottomline="true" usebox="none">
3083 \begin_layout Plain Layout
3089 <cell alignment="center" valignment="top" topline="true" bottomline="true" usebox="none">
3092 \begin_layout Plain Layout
3100 <cell alignment="center" valignment="top" usebox="none">
3103 \begin_layout Plain Layout
3111 <cell alignment="center" valignment="top" usebox="none">
3114 \begin_layout Plain Layout
3115 \begin_inset Formula $\not=$
3125 <cell alignment="center" valignment="top" usebox="none">
3128 \begin_layout Plain Layout
3138 <cell alignment="center" valignment="top" usebox="none">
3141 \begin_layout Plain Layout
3142 \begin_inset Formula $\not\le$
3152 <cell alignment="center" valignment="top" topline="true" bottomline="true" usebox="none">
3155 \begin_layout Plain Layout
3165 <cell alignment="center" valignment="top" topline="true" bottomline="true" usebox="none">
3168 \begin_layout Plain Layout
3169 \begin_inset Formula $\not\parallel$
3185 \begin_layout Standard
3186 The last example shows that not all negations look good.
3187 Therefore there are special commands for some negations (see
3188 \begin_inset CommandInset ref
3190 reference "subsec:Mathematical-Symbols"
3195 \begin_inset CommandInset ref
3197 reference "sec:Relations"
3204 \begin_layout Subsection
3206 \begin_inset CommandInset label
3208 name "subsec:Placeholders"
3213 \begin_inset Index idx
3216 \begin_layout Plain Layout
3223 \begin_inset Index idx
3226 \begin_layout Plain Layout
3227 Chemical characters ! Isotopes
3233 \begin_inset Index idx
3236 \begin_layout Plain Layout
3241 \begin_layout Plain Layout
3252 \begin_layout Plain Layout
3267 \begin_layout Standard
3269 \begin_inset space \thinspace{}
3273 \begin_inset space \space{}
3280 \begin_layout Plain Layout
3281 Typesetting isotopes and chemical symbols is described in
3282 \begin_inset CommandInset ref
3284 reference "subsec:Chemical-Symbols-and"
3293 the following problem occurs:
3294 \begin_inset Separator parbreak
3300 \begin_layout Standard
3302 \begin_inset Tabular
3303 <lyxtabular version="3" rows="2" columns="2">
3304 <features booktabs="true" tabularvalignment="middle">
3305 <column alignment="center" valignment="top" width="0pt">
3306 <column alignment="center" valignment="top" width="0pt">
3308 <cell alignment="center" valignment="top" usebox="none">
3311 \begin_layout Plain Layout
3312 Indices created with sub- and superscripts:
3317 <cell alignment="center" valignment="top" usebox="none">
3320 \begin_layout Plain Layout
3321 \begin_inset Formula $_{9}^{19}\mathrm{F}$
3330 <row topspace="1.5mm">
3331 <cell alignment="center" valignment="top" usebox="none">
3334 \begin_layout Plain Layout
3340 <cell alignment="center" valignment="top" usebox="none">
3343 \begin_layout Plain Layout
3344 \begin_inset Formula $_{\phantom{1}9}^{19}\mathrm{F}$
3360 \begin_layout Standard
3361 The shorter index is by default placed below or above the first character
3362 of the longer index.
3363 To avoid this there is the command
3370 \begin_inset Index idx
3373 \begin_layout Plain Layout
3381 or the math toolbar button
3382 \begin_inset space \thinspace{}
3389 \begin_layout Plain Layout
3390 can be found in the submenu of the toolbar button
3393 arg "math-insert \\space"
3407 that creates one or more phantom characters.
3414 a small blue box appears that is superposed with two red arrows.
3415 The arrows indicate that the complete width and height of the box content
3416 will be created as placeholder.
3417 Phantom characters are accordingly placeholders with the size of the characters.
3418 \begin_inset Separator parbreak
3424 \begin_layout Standard
3426 \begin_inset Tabular
3427 <lyxtabular version="3" rows="4" columns="2">
3428 <features booktabs="true" tabularvalignment="middle">
3429 <column alignment="center" valignment="top" width="0pt">
3430 <column alignment="center" valignment="top" width="0pt">
3432 <cell alignment="center" valignment="top" topline="true" bottomline="true" usebox="none">
3435 \begin_layout Plain Layout
3441 <cell alignment="center" valignment="top" topline="true" bottomline="true" usebox="none">
3444 \begin_layout Plain Layout
3451 <row topspace="1.5mm">
3452 <cell alignment="center" valignment="top" usebox="none">
3455 \begin_layout Plain Layout
3457 \begin_inset space \textvisiblespace{}
3463 \begin_inset space \textvisiblespace{}
3467 \begin_inset Formula $\to$
3471 \begin_inset space \textvisiblespace{}
3479 <cell alignment="center" valignment="top" usebox="none">
3482 \begin_layout Plain Layout
3483 \begin_inset Formula $_{\phantom{1}9}^{19}\mathrm{F}$
3492 <row topspace="1.5mm" bottomspace="0.5mm">
3493 <cell alignment="center" valignment="top" usebox="none">
3496 \begin_layout Plain Layout
3498 \begin_inset space \textvisiblespace{}
3504 \begin_inset space \textvisiblespace{}
3508 \begin_inset Formula $\to$
3512 \begin_inset space \textvisiblespace{}
3520 <cell alignment="center" valignment="top" usebox="none">
3523 \begin_layout Plain Layout
3524 \begin_inset Formula $_{\phantom{23}9}^{235}\mathrm{F}$
3533 <row topspace="1.5mm" bottomspace="0.5mm">
3534 <cell alignment="center" valignment="top" topline="true" bottomline="true" usebox="none">
3537 \begin_layout Plain Layout
3541 \begin_inset space \textvisiblespace{}
3547 \begin_inset space \textvisiblespace{}
3551 \begin_inset Formula $\to$
3555 \begin_inset space \textvisiblespace{}
3563 <cell alignment="center" valignment="top" topline="true" bottomline="true" usebox="none">
3566 \begin_layout Plain Layout
3567 \begin_inset Formula $\Lambda_{MMt}^{\phantom{ii}t}$
3583 \begin_layout Standard
3584 Furthermore there are the commands
3591 \begin_inset Index idx
3594 \begin_layout Plain Layout
3615 \begin_inset Index idx
3618 \begin_layout Plain Layout
3639 creates only space for the maximal height of the characters in the box
3640 but not for its width.
3647 creates only space for the width of the box content.
3648 Therefore the boxes of both commands have only one red arrow.
3651 \begin_layout Standard
3652 For example the command
3657 \begin_inset space \textvisiblespace{}
3664 creates space for the height of the integral sign,
3668 \begin_layout Plain Layout
3675 creates an integral sign, see
3676 \begin_inset CommandInset ref
3678 reference "subsec:Big-Operators"
3687 because this is the larger character.
3688 An example application is in
3689 \begin_inset CommandInset ref
3691 reference "subsec:Multiline-Brackets"
3698 \begin_layout Standard
3699 Placeholders can also be used for text when they are inserted via the menu
3702 Insert\SpecialChar menuseparator
3703 Formatting\SpecialChar menuseparator
3709 \begin_layout Standard
3711 \begin_inset Newline newline
3715 \begin_inset Phantom Phantom
3718 \begin_layout Plain Layout
3727 \begin_layout Subsection
3729 \begin_inset Index idx
3732 \begin_layout Plain Layout
3739 \begin_inset Index idx
3742 \begin_layout Plain Layout
3743 Formula ! underlined
3751 \begin_layout Standard
3753 \begin_inset Tabular
3754 <lyxtabular version="3" rows="4" columns="2">
3755 <features booktabs="true" tabularvalignment="middle">
3756 <column alignment="center" valignment="top" width="0pt">
3757 <column alignment="center" valignment="top" width="0pt">
3759 <cell alignment="center" valignment="top" topline="true" bottomline="true" usebox="none">
3762 \begin_layout Plain Layout
3768 <cell alignment="center" valignment="top" topline="true" bottomline="true" usebox="none">
3771 \begin_layout Plain Layout
3778 <row topspace="2mm">
3779 <cell alignment="center" valignment="top" usebox="none">
3782 \begin_layout Plain Layout
3786 \begin_inset space \textvisiblespace{}
3790 \begin_inset Index idx
3793 \begin_layout Plain Layout
3806 <cell alignment="center" valignment="top" usebox="none">
3809 \begin_layout Plain Layout
3810 \begin_inset Formula $\overline{A+B}$
3819 <row bottomspace="1mm">
3820 <cell alignment="center" valignment="top" usebox="none">
3823 \begin_layout Plain Layout
3827 \begin_inset space \textvisiblespace{}
3831 \begin_inset Index idx
3834 \begin_layout Plain Layout
3847 <cell alignment="center" valignment="top" usebox="none">
3850 \begin_layout Plain Layout
3851 \begin_inset Formula $\underline{A+B}$
3860 <row topspace="2mm" bottomspace="1mm">
3861 <cell alignment="center" valignment="top" topline="true" bottomline="true" usebox="none">
3864 \begin_layout Plain Layout
3868 \begin_inset space \textvisiblespace{}
3874 \begin_inset space \textvisiblespace{}
3882 <cell alignment="center" valignment="top" topline="true" bottomline="true" usebox="none">
3885 \begin_layout Plain Layout
3886 \begin_inset Formula $\overline{\underline{A+B}}$
3902 \begin_layout Standard
3903 In the last example it doesn't matter if first
3918 \begin_layout Standard
3919 To double underline use
3928 \begin_layout Standard
3929 It is possible to place up to 6 lines above or below characters.
3932 \begin_layout Standard
3933 \begin_inset VSpace bigskip
3936 Custom lines can be created using the command
3943 \begin_inset Index idx
3946 \begin_layout Plain Layout
3954 which has the following scheme:
3957 \begin_layout Standard
3962 rule[vertical offset]{length}{thickness}
3965 \begin_layout Standard
3966 The optional vertical offset shifts the line upwards (or downwards, when
3967 the value is negative).
3969 \begin_inset CommandInset ref
3971 reference "tab:Available-units"
3975 can be used for the values.
3976 Here are two example lines created with the commands
3977 \begin_inset Newline newline
3984 rule[-2ex]{3cm}{2pt}
3995 \begin_layout Standard
3997 \begin_inset Formula $\rule[-2ex]{3cm}{2pt}\rule{2cm}{1pt}$
4003 \begin_layout Standard
4010 can also be used for text when a line is inserted via the menu
4012 Insert\SpecialChar menuseparator
4013 Formatting\SpecialChar menuseparator
4015 \begin_inset space ~
4023 \begin_layout Standard
4025 \begin_inset CommandInset line
4036 \begin_layout Subsection
4038 \begin_inset CommandInset label
4040 name "subsec:Ellipses"
4045 \begin_inset Index idx
4048 \begin_layout Plain Layout
4057 \begin_layout Standard
4058 There are different types of ellipses available.
4062 \begin_layout Plain Layout
4063 In the math toolbar in the submenu of the button
4066 arg "math-insert \\ldots"
4074 For listings dots at the baseline are used (
4081 \begin_inset Index idx
4084 \begin_layout Plain Layout
4092 ), while for operations dots are needed that are on the same height as the
4100 \begin_inset Index idx
4103 \begin_layout Plain Layout
4112 When using the command
4119 \begin_inset Index idx
4122 \begin_layout Plain Layout
4130 , \SpecialChar LaTeX
4131 decides on the basis of the next character what type is used.
4132 \begin_inset Separator parbreak
4138 \begin_layout Standard
4140 \begin_inset Tabular
4141 <lyxtabular version="3" rows="9" columns="2">
4142 <features booktabs="true" tabularvalignment="middle">
4143 <column alignment="center" valignment="top" width="0pt">
4144 <column alignment="center" valignment="top" width="0pt">
4146 <cell alignment="center" valignment="top" topline="true" bottomline="true" usebox="none">
4149 \begin_layout Plain Layout
4155 <cell alignment="center" valignment="top" topline="true" bottomline="true" usebox="none">
4158 \begin_layout Plain Layout
4166 <cell alignment="center" valignment="top" usebox="none">
4169 \begin_layout Plain Layout
4171 \begin_inset space \textvisiblespace{}
4177 \begin_inset space \textvisiblespace{}
4185 <cell alignment="center" valignment="top" usebox="none">
4188 \begin_layout Plain Layout
4189 \begin_inset Formula $A_{1},\dots,A_{n}$
4199 <cell alignment="center" valignment="top" usebox="none">
4202 \begin_layout Plain Layout
4204 \begin_inset space \textvisiblespace{}
4210 \begin_inset space \textvisiblespace{}
4218 <cell alignment="center" valignment="top" usebox="none">
4221 \begin_layout Plain Layout
4222 \begin_inset Formula $A_{1}+\dots+A_{n}$
4232 <cell alignment="center" valignment="top" usebox="none">
4235 \begin_layout Plain Layout
4237 \begin_inset space \textvisiblespace{}
4243 \begin_inset space \textvisiblespace{}
4251 <cell alignment="center" valignment="top" usebox="none">
4254 \begin_layout Plain Layout
4255 \begin_inset Formula $A_{1},\ldots,A_{n}$
4265 <cell alignment="center" valignment="top" bottomline="true" usebox="none">
4268 \begin_layout Plain Layout
4270 \begin_inset space \textvisiblespace{}
4276 \begin_inset space \textvisiblespace{}
4284 <cell alignment="center" valignment="top" bottomline="true" usebox="none">
4287 \begin_layout Plain Layout
4288 \begin_inset Formula $A_{1}+\cdots+A_{n}$
4298 <cell alignment="center" valignment="top" usebox="none">
4301 \begin_layout Plain Layout
4309 <cell alignment="center" valignment="top" usebox="none">
4312 \begin_layout Plain Layout
4313 \begin_inset Formula $\vdots$
4323 <cell alignment="center" valignment="top" usebox="none">
4326 \begin_layout Plain Layout
4334 <cell alignment="center" valignment="top" usebox="none">
4337 \begin_layout Plain Layout
4338 \begin_inset Formula $\ddots$
4348 <cell alignment="center" valignment="top" usebox="none">
4351 \begin_layout Plain Layout
4359 <cell alignment="center" valignment="top" usebox="none">
4362 \begin_layout Plain Layout
4363 \begin_inset Formula $\iddots$
4373 <cell alignment="center" valignment="top" topline="true" bottomline="true" usebox="none">
4376 \begin_layout Plain Layout
4378 \begin_inset space \thinspace{}
4381 matrix with the different dots
4386 <cell alignment="center" valignment="top" topline="true" bottomline="true" usebox="none">
4389 \begin_layout Plain Layout
4390 \begin_inset Formula $\begin{array}{ccc}
4391 A_{11} & \cdots & A_{1m}\\
4392 \vdots & \ddots & \vdots\\
4393 A_{n1} & \cdots & A_{nm}
4410 \begin_layout Standard
4411 The ellipses available in menu
4413 Insert\SpecialChar menuseparator
4415 \begin_inset space ~
4429 \begin_layout Standard
4430 \begin_inset VSpace medskip
4439 , one of the options
4441 Use mathdots package (automatically)
4443 must be set in the document settings under
4446 \begin_inset space ~
4452 \begin_inset Newline newline
4457 Use mathdots package
4459 will improve the appearance of all dots in the documents if their font
4460 style or size is not the default.
4463 \begin_layout Standard
4464 \begin_inset VSpace medskip
4467 Specially for matrices there are ellipses that span over several columns.
4468 They are created with the command
4475 \begin_inset Index idx
4478 \begin_layout Plain Layout
4486 , that has the following scheme:
4489 \begin_layout Standard
4494 hdotsfor[distance]{number of columns}
4497 \begin_layout Standard
4498 The number of columns specifies how many columns should be spanned.
4499 Distance is a factor for the distance between the dots.
4502 \begin_layout Standard
4503 In the following matrix the command
4509 was inserted in the first box of the second line, to get an ellipsis with
4510 a dot distance twice as long as with the command
4517 \begin_inset Formula
4519 \left(\begin{array}{cccc}
4528 Note that the matrix fields that should be spanned must be empty, otherwise
4529 you get \SpecialChar LaTeX
4533 \begin_layout Standard
4534 \begin_inset VSpace bigskip
4537 Furthermore you can fill with the command
4544 \begin_inset Index idx
4547 \begin_layout Plain Layout
4555 the rest of a line with dots.
4556 The effect of these commands is the same as with
4563 \begin_inset CommandInset ref
4565 reference "subsec:Variable-Space"
4572 \begin_layout Standard
4573 For example the command
4578 \begin_inset space \textvisiblespace{}
4586 \begin_layout Standard
4587 \begin_inset Formula $A\dotfill B$
4593 \begin_layout Standard
4600 there is for a line the command
4607 \begin_inset Index idx
4610 \begin_layout Plain Layout
4621 \begin_layout Standard
4622 \begin_inset Formula $A\hrulefill B$
4628 \begin_layout Standard
4629 To use the commands for text, they have to be inserted in \SpecialChar TeX
4633 \begin_layout Section
4635 \begin_inset CommandInset label
4642 \begin_inset Index idx
4645 \begin_layout Plain Layout
4654 \begin_layout Standard
4655 Matrices can be inserted via the math toolbar button
4658 arg "dialog-show mathmatrix"
4663 Insert\SpecialChar menuseparator
4664 Math\SpecialChar menuseparator
4668 In the matrix dialog you can specify the number of columns and rows, the
4669 alignment and the decoration.
4670 The vertical alignment is only of importance for matrices in inline formulas:
4673 \begin_layout Standard
4674 The first matrix is top
4675 \begin_inset Formula $\begin{array}[t]{cccc}
4683 \begin_inset Formula $\begin{array}{cccc}
4690 and the third bottom
4691 \begin_inset Formula $\begin{array}[b]{cccc}
4701 \begin_layout Standard
4702 The horizontal alignment specifies how the column entries should be aligned.
4703 It is set by entering a letter for every column.
4708 denotes left aligned,
4717 To create for example a 4
4722 \begin_inset space ~
4725 matrix where the first column is left aligned, the second and third are
4726 centered and the last one is right aligned, one enters for the horizontal
4732 Normally in a matrix all columns are centered, therefore the default for
4740 \begin_layout Standard
4741 Horizontal alignment:
4744 \begin_layout Standard
4750 \begin_inset Formula $\begin{array}{lll}
4762 \begin_inset Formula $\begin{array}{ccc}
4774 \begin_inset Formula $\begin{array}{rrr}
4784 \begin_layout Standard
4785 To add or delete rows and columns subsequently, the math toolbar buttons
4789 arg "tabular-feature append-row"
4795 arg "tabular-feature delete-row"
4799 \begin_inset space \thinspace{}
4804 Edit\SpecialChar menuseparator
4808 New rows can also be created with
4811 arg "newline-insert newline"
4817 \begin_layout Standard
4818 \begin_inset VSpace bigskip
4825 adds parentheses in the selected style around the matrix.
4826 Alternatively, parentheses can can either be created with the commands
4834 \begin_inset Index idx
4837 \begin_layout Plain Layout
4852 \begin_inset Index idx
4855 \begin_layout Plain Layout
4866 \begin_inset space ~
4872 \begin_inset CommandInset ref
4874 reference "subsec:Automatic-Bracket-Size"
4878 , or by using the following commands:
4879 \begin_inset VSpace medskip
4885 \begin_layout Standard
4886 \begin_inset space \hfill{}
4890 \begin_inset Tabular
4891 <lyxtabular version="3" rows="4" columns="2">
4892 <features booktabs="true" tabularvalignment="middle">
4893 <column alignment="center" valignment="top" width="0pt">
4894 <column alignment="center" valignment="top">
4896 <cell alignment="center" valignment="top" topline="true" bottomline="true" usebox="none">
4899 \begin_layout Plain Layout
4905 <cell alignment="center" valignment="top" topline="true" bottomline="true" usebox="none">
4908 \begin_layout Plain Layout
4915 <row topspace="1.5mm">
4916 <cell alignment="center" valignment="top" usebox="none">
4919 \begin_layout Plain Layout
4923 \begin_inset space \textvisiblespace{}
4931 \begin_inset space \thinspace{}
4939 <cell alignment="center" valignment="top" usebox="none">
4942 \begin_layout Plain Layout
4943 \begin_inset Formula $\begin{bmatrix}\begin{array}{cc}
4944 0 & \textrm{-}\mathrm{i}\\
4946 \end{array}\end{bmatrix}$
4955 <row topspace="1.5mm" bottomspace="0.5mm">
4956 <cell alignment="center" valignment="top" usebox="none">
4959 \begin_layout Plain Layout
4963 \begin_inset space \textvisiblespace{}
4971 \begin_inset space \thinspace{}
4979 <cell alignment="center" valignment="top" usebox="none">
4982 \begin_layout Plain Layout
4983 \begin_inset Formula $\begin{Bmatrix}\begin{array}{cc}
4984 0 & \textrm{-}\mathrm{i}\\
4986 \end{array}\end{Bmatrix}$
4996 <cell alignment="center" valignment="top" bottomline="true" usebox="none">
4999 \begin_layout Plain Layout
5003 \begin_inset space \textvisiblespace{}
5011 \begin_inset space \thinspace{}
5019 <cell alignment="center" valignment="top" bottomline="true" usebox="none">
5022 \begin_layout Plain Layout
5023 \begin_inset Formula $\begin{pmatrix}\begin{array}{cc}
5024 0 & \textrm{-}\mathrm{i}\\
5026 \end{array}\end{pmatrix}$
5040 \begin_inset space \hfill{}
5044 \begin_inset Tabular
5045 <lyxtabular version="3" rows="4" columns="2">
5046 <features booktabs="true" tabularvalignment="middle">
5047 <column alignment="center" valignment="top" width="0pt">
5048 <column alignment="center" valignment="top">
5050 <cell alignment="center" valignment="top" topline="true" bottomline="true" usebox="none">
5053 \begin_layout Plain Layout
5059 <cell alignment="center" valignment="top" topline="true" bottomline="true" usebox="none">
5062 \begin_layout Plain Layout
5069 <row topspace="1.5mm">
5070 <cell alignment="center" valignment="top" usebox="none">
5073 \begin_layout Plain Layout
5077 \begin_inset space \textvisiblespace{}
5085 \begin_inset space \thinspace{}
5093 <cell alignment="center" valignment="top" usebox="none">
5096 \begin_layout Plain Layout
5097 \begin_inset Formula $\begin{vmatrix}\begin{array}{cc}
5098 0 & \textrm{-}\mathrm{i}\\
5100 \end{array}\end{vmatrix}$
5109 <row topspace="1.5mm" bottomspace="0.5mm">
5110 <cell alignment="center" valignment="top" usebox="none">
5113 \begin_layout Plain Layout
5117 \begin_inset space \textvisiblespace{}
5125 \begin_inset space \thinspace{}
5133 <cell alignment="center" valignment="top" usebox="none">
5136 \begin_layout Plain Layout
5137 \begin_inset Formula $\begin{Vmatrix}\begin{array}{cc}
5138 0 & \textrm{-}\mathrm{i}\\
5140 \end{array}\end{Vmatrix}$
5150 <cell alignment="center" valignment="top" bottomline="true" usebox="none">
5153 \begin_layout Plain Layout
5157 \begin_inset space \textvisiblespace{}
5165 \begin_inset space \thinspace{}
5173 <cell alignment="center" valignment="top" bottomline="true" usebox="none">
5176 \begin_layout Plain Layout
5177 \begin_inset Formula $\begin{matrix}\begin{array}{cc}
5178 0 & \textrm{-}\mathrm{i}\\
5180 \end{array}\end{matrix}$
5194 \begin_inset space \hfill{}
5200 \begin_layout Standard
5201 \begin_inset VSpace medskip
5205 \begin_inset space \thinspace{}
5209 \begin_inset space \space{}
5218 is inserted, a blue box appears between two vertical lines where the matrix
5220 \begin_inset Newline newline
5223 Note that decorated matrices ignore the vertical alignment.
5226 \begin_layout Standard
5227 \begin_inset VSpace bigskip
5230 As all multiline formulas are matrices, the length
5237 \begin_inset Index idx
5240 \begin_layout Plain Layout
5248 that is described in
5249 \begin_inset CommandInset ref
5251 reference "subsec:Column-Separation"
5255 can also be used to change the column separation of matrices.
5258 \begin_layout Standard
5259 To change the row separation, the command
5266 \begin_inset Index idx
5269 \begin_layout Plain Layout
5278 It is used as follows:
5281 \begin_layout Standard
5288 arraystretch}{stretch factor}
5289 \begin_inset Index idx
5292 \begin_layout Plain Layout
5303 \begin_layout Standard
5310 assigns the stretch factor to the predefined command
5318 \begin_inset space \thinspace{}
5322 \begin_inset space \space{}
5325 the row separation, use the factor 2.
5326 This is then used for all following matrices.
5327 To go back to the original separation, assign the factor 1 to
5336 \begin_layout Standard
5337 To set matrices into a text line, the command
5344 \begin_inset Index idx
5347 \begin_layout Plain Layout
5356 When it is inserted a blue box with two dashed lines appears.
5357 In this box the matrix is inserted.
5360 \begin_layout Standard
5362 \begin_inset Formula $\left(\begin{smallmatrix}A & B\\
5364 \end{smallmatrix}\right)$
5370 \begin_layout Section
5371 Brackets and Delimiters
5372 \begin_inset Index idx
5375 \begin_layout Plain Layout
5382 \begin_inset Index idx
5385 \begin_layout Plain Layout
5394 \begin_layout Subsection
5395 Vertical Brackets and Delimiters
5396 \begin_inset Index idx
5399 \begin_layout Plain Layout
5408 \begin_layout Standard
5409 \begin_inset space \hfill{}
5413 \begin_inset Tabular
5414 <lyxtabular version="3" rows="9" columns="2">
5415 <features booktabs="true" tabularvalignment="middle">
5416 <column alignment="center" valignment="top" width="0pt">
5417 <column alignment="center" valignment="top" width="0pt">
5419 <cell alignment="center" valignment="top" topline="true" bottomline="true" usebox="none">
5422 \begin_layout Plain Layout
5428 <cell alignment="center" valignment="top" topline="true" bottomline="true" usebox="none">
5431 \begin_layout Plain Layout
5439 <cell alignment="center" valignment="top" usebox="none">
5442 \begin_layout Plain Layout
5448 <cell alignment="center" valignment="top" usebox="none">
5451 \begin_layout Plain Layout
5452 \begin_inset Formula $($
5462 <cell alignment="center" valignment="top" usebox="none">
5465 \begin_layout Plain Layout
5471 <cell alignment="center" valignment="top" usebox="none">
5474 \begin_layout Plain Layout
5475 \begin_inset Formula $\{$
5485 <cell alignment="center" valignment="top" usebox="none">
5488 \begin_layout Plain Layout
5494 <cell alignment="center" valignment="top" usebox="none">
5497 \begin_layout Plain Layout
5498 \begin_inset Formula $[$
5508 <cell alignment="center" valignment="top" usebox="none">
5511 \begin_layout Plain Layout
5519 <cell alignment="center" valignment="top" usebox="none">
5522 \begin_layout Plain Layout
5523 \begin_inset Formula $\langle$
5533 <cell alignment="center" valignment="top" usebox="none">
5536 \begin_layout Plain Layout
5544 <cell alignment="center" valignment="top" usebox="none">
5547 \begin_layout Plain Layout
5548 \begin_inset Formula $\lceil$
5558 <cell alignment="center" valignment="top" usebox="none">
5561 \begin_layout Plain Layout
5569 <cell alignment="center" valignment="top" usebox="none">
5572 \begin_layout Plain Layout
5573 \begin_inset Formula $\lfloor$
5583 <cell alignment="center" valignment="top" usebox="none">
5586 \begin_layout Plain Layout
5592 <cell alignment="center" valignment="top" usebox="none">
5595 \begin_layout Plain Layout
5596 \begin_inset Formula $/$
5606 <cell alignment="center" valignment="top" bottomline="true" usebox="none">
5609 \begin_layout Plain Layout
5615 <cell alignment="center" valignment="top" bottomline="true" usebox="none">
5618 \begin_layout Plain Layout
5619 \begin_inset Formula $|$
5633 \begin_inset space \hfill{}
5637 \begin_inset Tabular
5638 <lyxtabular version="3" rows="9" columns="2">
5639 <features booktabs="true" tabularvalignment="middle">
5640 <column alignment="center" valignment="top" width="0pt">
5641 <column alignment="center" valignment="top" width="0pt">
5643 <cell alignment="center" valignment="top" topline="true" bottomline="true" usebox="none">
5646 \begin_layout Plain Layout
5652 <cell alignment="center" valignment="top" topline="true" bottomline="true" usebox="none">
5655 \begin_layout Plain Layout
5663 <cell alignment="center" valignment="top" usebox="none">
5666 \begin_layout Plain Layout
5672 <cell alignment="center" valignment="top" usebox="none">
5675 \begin_layout Plain Layout
5676 \begin_inset Formula $)$
5686 <cell alignment="center" valignment="top" usebox="none">
5689 \begin_layout Plain Layout
5695 <cell alignment="center" valignment="top" usebox="none">
5698 \begin_layout Plain Layout
5699 \begin_inset Formula $\}$
5709 <cell alignment="center" valignment="top" usebox="none">
5712 \begin_layout Plain Layout
5718 <cell alignment="center" valignment="top" usebox="none">
5721 \begin_layout Plain Layout
5722 \begin_inset Formula $]$
5732 <cell alignment="center" valignment="top" usebox="none">
5735 \begin_layout Plain Layout
5743 <cell alignment="center" valignment="top" usebox="none">
5746 \begin_layout Plain Layout
5747 \begin_inset Formula $\rangle$
5757 <cell alignment="center" valignment="top" usebox="none">
5760 \begin_layout Plain Layout
5768 <cell alignment="center" valignment="top" usebox="none">
5771 \begin_layout Plain Layout
5772 \begin_inset Formula $\rceil$
5782 <cell alignment="center" valignment="top" usebox="none">
5785 \begin_layout Plain Layout
5793 <cell alignment="center" valignment="top" usebox="none">
5796 \begin_layout Plain Layout
5797 \begin_inset Formula $\rfloor$
5807 <cell alignment="center" valignment="top" usebox="none">
5810 \begin_layout Plain Layout
5820 <cell alignment="center" valignment="top" usebox="none">
5823 \begin_layout Plain Layout
5824 \begin_inset Formula $\backslash$
5834 <cell alignment="center" valignment="top" bottomline="true" usebox="none">
5837 \begin_layout Plain Layout
5845 <cell alignment="center" valignment="top" bottomline="true" usebox="none">
5848 \begin_layout Plain Layout
5849 \begin_inset Formula $\|$
5863 \begin_inset space \hfill{}
5869 \begin_layout Standard
5872 \begin_inset Note Greyedout
5875 \begin_layout Plain Layout
5888 \begin_inset Index idx
5891 \begin_layout Plain Layout
5899 must be used for the backslash, because the command
5907 produces a line break there.
5915 \begin_layout Standard
5916 For all characters listed above the size can be adjusted with the commands
5917 described in the following two subsections.
5918 When using these commands, the characters < and > can directly be used
5919 instead of the commands
5934 \begin_layout Subsubsection
5936 \begin_inset CommandInset label
5938 name "subsec:Manual-Bracket-Size"
5943 \begin_inset Index idx
5946 \begin_layout Plain Layout
5947 Bracket size ! manual
5955 \begin_layout Standard
5956 The bracket size can be specified manually by the \SpecialChar LaTeX
5964 \begin_inset Index idx
5967 \begin_layout Plain Layout
6000 denotes the smallest and
6006 the largest bracket size.
6009 \begin_layout Standard
6010 These commands are used to emphasize levels of brackets:
6011 \begin_inset Separator parbreak
6017 \begin_layout Standard
6019 \begin_inset Tabular
6020 <lyxtabular version="3" rows="2" columns="2">
6021 <features booktabs="true" tabularvalignment="middle">
6022 <column alignment="center" valignment="top" width="0pt">
6023 <column alignment="center" valignment="top" width="0pt">
6025 <cell alignment="center" valignment="top" usebox="none">
6028 \begin_layout Plain Layout
6029 all brackets in the same size:
6034 <cell alignment="center" valignment="top" usebox="none">
6037 \begin_layout Plain Layout
6038 \begin_inset Formula $((A+B)(A-B))^{C}$
6047 <row topspace="2mm">
6048 <cell alignment="center" valignment="top" usebox="none">
6051 \begin_layout Plain Layout
6057 <cell alignment="center" valignment="top" usebox="none">
6060 \begin_layout Plain Layout
6061 \begin_inset Formula $\Big((A+B)(A-B)\Big)^{C}$
6077 \begin_layout Standard
6078 For the second formula the command
6085 \begin_inset space \textvisiblespace{}
6093 \begin_layout Standard
6094 Here is an overview about all bracket sizes:
6095 \begin_inset Separator parbreak
6101 \begin_layout Standard
6118 \begin_inset space \textvisiblespace{}
6126 \begin_inset space \textvisiblespace{}
6130 \begin_inset space \textvisiblespace{}
6140 \begin_layout Standard
6142 \begin_inset Formula $\Bigg(\exp\bigg<\Big[\big\{\ln(3x)\big\}^{2}\sin(x)\Big]^{A}\bigg>\Bigg)^{0,5}$
6148 \begin_layout Standard
6155 -commands there is the variant
6162 \begin_inset Index idx
6165 \begin_layout Plain Layout
6173 that adds a bit more space between the bracket and its content, and the
6187 \begin_inset Index idx
6190 \begin_layout Plain Layout
6200 , that don't add additional space.
6205 at the end of the command
6211 is for a left bracket; for a right bracket this will be replaced by an
6217 A left or right bracket can each be an opening or closing bracket.
6220 \begin_layout Standard
6221 In the following table is a comparison of the variants:
6222 \begin_inset Separator parbreak
6228 \begin_layout Standard
6230 \begin_inset Tabular
6231 <lyxtabular version="3" rows="5" columns="2">
6232 <features booktabs="true" tabularvalignment="middle">
6233 <column alignment="center" valignment="top" width="0pt">
6234 <column alignment="center" valignment="middle">
6236 <cell alignment="center" valignment="top" topline="true" bottomline="true" usebox="none">
6239 \begin_layout Plain Layout
6245 <cell alignment="center" valignment="top" topline="true" bottomline="true" usebox="none">
6248 \begin_layout Plain Layout
6255 <row topspace="2mm">
6256 <cell alignment="center" valignment="top" usebox="none">
6259 \begin_layout Plain Layout
6269 \begin_inset space \textvisiblespace{}
6279 <cell alignment="center" valignment="top" usebox="none">
6282 \begin_layout Plain Layout
6283 \begin_inset Formula $\Bigm(\bigm(\ln(3x)\bigm)^{2}\Bigm)$
6292 <row topspace="2mm">
6293 <cell alignment="center" valignment="top" usebox="none">
6296 \begin_layout Plain Layout
6306 \begin_inset space \textvisiblespace{}
6316 <cell alignment="center" valignment="top" usebox="none">
6319 \begin_layout Plain Layout
6320 \begin_inset Formula $\Big(\big(\ln(3x)\big)^{2}\Big)$
6329 <row topspace="2mm" bottomspace="0.5mm">
6330 <cell alignment="center" valignment="top" usebox="none">
6333 \begin_layout Plain Layout
6343 \begin_inset space \textvisiblespace{}
6353 <cell alignment="center" valignment="top" usebox="none">
6356 \begin_layout Plain Layout
6357 \begin_inset Formula $\Bigl(\bigl(\ln(3x)\bigr)^{2}\Bigr)$
6366 <row topspace="1.5mm" bottomspace="0.5mm">
6367 <cell alignment="center" valignment="top" topline="true" bottomline="true" usebox="none">
6370 \begin_layout Plain Layout
6382 <cell alignment="center" valignment="top" topline="true" bottomline="true" usebox="none">
6385 \begin_layout Plain Layout
6386 \begin_inset Formula $\bigl)\ln(3x)\bigr($
6402 \begin_layout Subsubsection
6403 Automatic Bracket Size
6404 \begin_inset CommandInset label
6406 name "subsec:Automatic-Bracket-Size"
6411 \begin_inset Index idx
6414 \begin_layout Plain Layout
6415 Bracket size ! automatic
6423 \begin_layout Standard
6424 Brackets with variable size can be inserted with the commands
6431 \begin_inset Index idx
6434 \begin_layout Plain Layout
6449 \begin_inset Index idx
6452 \begin_layout Plain Layout
6460 or via the math toolbar button
6463 arg "dialog-show mathdelimiter"
6479 the wanted bracket must be inserted.
6480 The bracket size will then automatically be calculated for the output.
6481 \begin_inset Separator parbreak
6487 \begin_layout Standard
6489 normal bracket: The command
6496 \begin_inset space \textvisiblespace{}
6500 \begin_inset Formula $\downarrow$
6504 \begin_inset space \textvisiblespace{}
6510 \begin_inset Formula
6520 \begin_layout Standard
6522 multiline bracket: The command
6531 \begin_inset space \textvisiblespace{}
6535 \begin_inset Formula $\downarrow$
6539 \begin_inset space \textvisiblespace{}
6547 \begin_inset Formula
6549 \ln\left(\frac{A}{C}\right)
6557 \begin_layout Standard
6573 \begin_inset space ~
6579 This has the advantage that you can see in \SpecialChar LyX
6580 immediately the real bracket
6581 size and that the matching right bracket will be created too.
6582 \begin_inset Newline newline
6585 The command for the last example would then be:
6596 \begin_inset space \textvisiblespace{}
6600 \begin_inset Formula $\downarrow$
6606 \begin_layout Standard
6607 To omit a left or right bracket, a dot is inserted for the omitted bracket.
6608 For example the command
6615 \begin_inset space \textvisiblespace{}
6619 \begin_inset Formula $\downarrow$
6623 \begin_inset space \textvisiblespace{}
6633 \begin_inset Formula
6635 \left.\frac{A}{B}\right\}
6654 will be converted by \SpecialChar LyX
6655 to brackets in the right size when the document is
6656 reloaded and an omitted bracket will appear as dashed line.
6659 \begin_layout Standard
6660 \begin_inset VSpace bigskip
6663 Because all popular \SpecialChar LaTeX
6664 distributions use e\SpecialChar TeX
6665 , an extension to \SpecialChar LaTeX
6674 \begin_inset Index idx
6677 \begin_layout Plain Layout
6685 is additionally available for all brackets and limits.
6686 With this command the height of the following character is adapted to the
6687 one of the surrounding brackets, what is e.
6688 \begin_inset space \thinspace{}
6692 \begin_inset space \space{}
6695 needed for physical vectors:
6696 \begin_inset Formula
6698 \left\langle \phi\:\middle|\:J=\frac{3}{2}\,,\,M_{J}\right\rangle
6703 For physical vectors there is a special \SpecialChar LaTeX
6704 -package, described in
6705 \begin_inset CommandInset ref
6707 reference "subsec:Physical-Vectors"
6714 \begin_layout Subsection
6716 \begin_inset Index idx
6719 \begin_layout Plain Layout
6720 Brackets ! horizontal
6728 \begin_layout Standard
6730 \begin_inset Tabular
6731 <lyxtabular version="3" rows="4" columns="2">
6732 <features booktabs="true" tabularvalignment="middle">
6733 <column alignment="center" valignment="top" width="0pt">
6734 <column alignment="center" valignment="top" width="0pt">
6736 <cell alignment="center" valignment="top" topline="true" bottomline="true" usebox="none">
6739 \begin_layout Plain Layout
6745 <cell alignment="center" valignment="top" topline="true" bottomline="true" usebox="none">
6748 \begin_layout Plain Layout
6756 <cell alignment="center" valignment="top" usebox="none">
6759 \begin_layout Plain Layout
6763 \begin_inset space \textvisiblespace{}
6767 \begin_inset space \textvisiblespace{}
6771 \begin_inset Index idx
6774 \begin_layout Plain Layout
6787 <cell alignment="center" valignment="top" usebox="none">
6790 \begin_layout Plain Layout
6791 \begin_inset Formula $\overbrace{A+B}^{3}$
6800 <row topspace="2mm">
6801 <cell alignment="center" valignment="top" usebox="none">
6804 \begin_layout Plain Layout
6808 \begin_inset space \textvisiblespace{}
6812 \begin_inset space \textvisiblespace{}
6816 \begin_inset Index idx
6819 \begin_layout Plain Layout
6832 <cell alignment="center" valignment="top" usebox="none">
6835 \begin_layout Plain Layout
6836 \begin_inset Formula $\underbrace{A+B}_{5}$
6846 <cell alignment="center" valignment="top" topline="true" bottomline="true" usebox="none">
6849 \begin_layout Plain Layout
6853 \begin_inset space \textvisiblespace{}
6859 \begin_inset space \textvisiblespace{}
6863 \begin_inset space \textvisiblespace{}
6867 \begin_inset space \textvisiblespace{}
6871 \begin_inset space \textvisiblespace{}
6875 \begin_inset space \textvisiblespace{}
6879 \begin_inset space \textvisiblespace{}
6887 <cell alignment="center" valignment="top" topline="true" bottomline="true" usebox="none">
6890 \begin_layout Plain Layout
6891 \begin_inset Formula $\overbrace{\underbrace{A+B_{w}}_{7}}^{C}$
6907 \begin_layout Standard
6908 In the last example it doesn't matter if
6920 is inserted at first.
6923 \begin_layout Standard
6924 \begin_inset VSpace medskip
6930 \begin_layout Standard
6931 If you set in the document settings under
6934 \begin_inset space ~
6944 \begin_inset Index idx
6947 \begin_layout Plain Layout
6948 Packages ! mathtools
6956 \begin_inset space ~
6961 , you have access to square backets:
6962 \begin_inset Separator parbreak
6968 \begin_layout Standard
6970 \begin_inset Tabular
6971 <lyxtabular version="3" rows="4" columns="2">
6972 <features booktabs="true" tabularvalignment="middle">
6973 <column alignment="center" valignment="top" width="0pt">
6974 <column alignment="center" valignment="top" width="0pt">
6976 <cell alignment="center" valignment="top" topline="true" bottomline="true" usebox="none">
6979 \begin_layout Plain Layout
6985 <cell alignment="center" valignment="top" topline="true" bottomline="true" usebox="none">
6988 \begin_layout Plain Layout
6996 <cell alignment="center" valignment="top" usebox="none">
6999 \begin_layout Plain Layout
7027 \begin_inset space \textvisiblespace{}
7031 \begin_inset Index idx
7034 \begin_layout Plain Layout
7047 <cell alignment="center" valignment="top" usebox="none">
7050 \begin_layout Plain Layout
7051 \begin_inset Formula $\overbracket{A+B}^{3}$
7060 <row topspace="2mm">
7061 <cell alignment="center" valignment="top" usebox="none">
7064 \begin_layout Plain Layout
7092 \begin_inset space \textvisiblespace{}
7096 \begin_inset Index idx
7099 \begin_layout Plain Layout
7124 <cell alignment="center" valignment="top" usebox="none">
7127 \begin_layout Plain Layout
7128 \begin_inset Formula $\underbracket{A+B}_{5}$
7138 <cell alignment="center" valignment="top" topline="true" bottomline="true" usebox="none">
7141 \begin_layout Plain Layout
7147 \begin_inset space \textvisiblespace{}
7151 \begin_inset space \textvisiblespace{}
7155 \begin_inset space \textvisiblespace{}
7159 \begin_inset space \textvisiblespace{}
7163 \begin_inset space \textvisiblespace{}
7171 <cell alignment="center" valignment="top" topline="true" bottomline="true" usebox="none">
7174 \begin_layout Plain Layout
7175 \begin_inset Formula $\overbracket{\underbracket{A+B_{w}}_{7}}^{C}$
7191 \begin_layout Standard
7204 you can change the thickness of the bracket's stroke by specifying the
7205 desired thickness in square brackets behind the command:
7206 \begin_inset Separator parbreak
7212 \begin_layout Standard
7214 \begin_inset Tabular
7215 <lyxtabular version="3" rows="3" columns="2">
7216 <features booktabs="true" tabularvalignment="middle">
7217 <column alignment="center" valignment="top" width="0pt">
7218 <column alignment="center" valignment="top" width="0pt">
7220 <cell alignment="center" valignment="top" topline="true" bottomline="true" usebox="none">
7223 \begin_layout Plain Layout
7229 <cell alignment="center" valignment="top" topline="true" bottomline="true" usebox="none">
7232 \begin_layout Plain Layout
7240 <cell alignment="center" valignment="top" usebox="none">
7243 \begin_layout Plain Layout
7273 \begin_inset space \textvisiblespace{}
7281 <cell alignment="center" valignment="top" usebox="none">
7284 \begin_layout Plain Layout
7285 \begin_inset Formula $\overbracket[3pt]{A+B}^{3}$
7294 <row topspace="2mm">
7295 <cell alignment="center" valignment="top" bottomline="true" usebox="none">
7298 \begin_layout Plain Layout
7328 \begin_inset space \textvisiblespace{}
7336 <cell alignment="center" valignment="top" bottomline="true" usebox="none">
7339 \begin_layout Plain Layout
7340 \begin_inset Formula $\underbracket[1pt]{A+B}_{5}$
7356 \begin_layout Standard
7357 \begin_inset VSpace bigskip
7360 When brackets should overlap each other, multiline formulas, as described
7362 \begin_inset CommandInset ref
7364 reference "sec:Multiline-Formulas"
7369 \begin_inset Formula
7371 A & = & \underbrace{gggg+bbqq}_{r}+\:dddd\\
7372 & & \hphantom{gggg+\:}\underbrace{\hphantom{bbqq+dddd}}_{s}
7377 In the first row the formula is inserted together with the first brace.
7378 It is hereby important that the space command
7382 \begin_layout Plain Layout
7383 Space commands are explained in
7384 \begin_inset CommandInset ref
7386 reference "subsec:Predefined-Space"
7401 is inserted before the first
7402 \begin_inset Formula $d$
7405 , because the brace that ends behind the
7406 \begin_inset Formula $q$
7409 prevents that the following
7410 \begin_inset Quotes eld
7414 \begin_inset Quotes erd
7417 is surrounded by space.
7421 \begin_layout Plain Layout
7422 because a bracket is not handled as a character, see
7423 \begin_inset CommandInset ref
7425 reference "subsec:Binary-Operators"
7434 In the second row the second brace is inserted.
7435 As it should begin before the
7436 \begin_inset Formula $b$
7451 \begin_layout Plain Layout
7459 \begin_inset CommandInset ref
7461 reference "subsec:Placeholders"
7470 This space is needed because the
7471 \begin_inset Quotes eld
7475 \begin_inset Quotes erd
7478 is also surrounded by space in the formula.
7479 The brace is placed under the command
7488 \begin_layout Standard
7489 It gets more complicated when brackets overlap each other above and under
7490 the formula, like in the following example:
7494 \begin_layout Plain Layout
7506 \begin_inset Formula
7508 & & \hphantom{gggg+\:}\overbrace{\hphantom{bbqq+dddd}}^{s}\\
7509 A & = & \underbrace{gggg+bbqq}_{r}+\:dddd
7518 \begin_layout Plain Layout
7529 The first formula row is the same as the second row of the previous example,
7530 with the difference that the brace is above.
7531 The second row contains the formula together with the second brace.
7532 To avoid that there is space between the upper brace in the first row and
7533 the formula, the row spacing needs to be reduced.
7534 This is not easily possible due to a bug in \SpecialChar LyX
7539 \begin_layout Plain Layout
7540 \begin_inset CommandInset href
7542 name "LyX-bug #1505"
7543 target "http://www.lyx.org/trac/ticket/1505"
7552 As a solution for the problem, the global formula row separation
7559 \begin_inset Index idx
7562 \begin_layout Plain Layout
7570 must be changed to -6
7571 \begin_inset space \thinspace{}
7574 pt before the formula with the command
7590 is set back after the formula to the standard value of 3
7591 \begin_inset space \thinspace{}
7594 pt using the same command.
7595 More about the row separation in formulas is explained in
7596 \begin_inset CommandInset ref
7598 reference "subsec:Line-Separation"
7605 \begin_layout Section
7607 \begin_inset Index idx
7610 \begin_layout Plain Layout
7619 \begin_layout Standard
7620 Arrows can be inserted via the math toolbar button
7623 arg "math-insert \\leftarrow"
7626 or the commands listed in the following subsections.
7629 \begin_layout Subsection
7631 \begin_inset Index idx
7634 \begin_layout Plain Layout
7643 \begin_layout Standard
7644 \begin_inset space \hfill{}
7648 \begin_inset Tabular
7649 <lyxtabular version="3" rows="8" columns="2">
7650 <features booktabs="true" tabularvalignment="middle">
7651 <column alignment="center" valignment="top" width="0pt">
7652 <column alignment="center" valignment="top" width="0pt">
7654 <cell alignment="center" valignment="top" topline="true" bottomline="true" usebox="none">
7657 \begin_layout Plain Layout
7663 <cell alignment="center" valignment="top" topline="true" bottomline="true" usebox="none">
7666 \begin_layout Plain Layout
7674 <cell alignment="center" valignment="top" usebox="none">
7677 \begin_layout Plain Layout
7685 <cell alignment="center" valignment="top" usebox="none">
7688 \begin_layout Plain Layout
7689 \begin_inset Formula $\gets$
7699 <cell alignment="center" valignment="top" usebox="none">
7702 \begin_layout Plain Layout
7710 <cell alignment="center" valignment="top" usebox="none">
7713 \begin_layout Plain Layout
7714 \begin_inset Formula $\Leftarrow$
7724 <cell alignment="center" valignment="top" usebox="none">
7727 \begin_layout Plain Layout
7735 <cell alignment="center" valignment="top" usebox="none">
7738 \begin_layout Plain Layout
7739 \begin_inset Formula $\longleftarrow$
7749 <cell alignment="center" valignment="top" usebox="none">
7752 \begin_layout Plain Layout
7760 <cell alignment="center" valignment="top" usebox="none">
7763 \begin_layout Plain Layout
7764 \begin_inset Formula $\Longleftarrow$
7774 <cell alignment="center" valignment="top" usebox="none">
7777 \begin_layout Plain Layout
7785 <cell alignment="center" valignment="top" usebox="none">
7788 \begin_layout Plain Layout
7789 \begin_inset Formula $\leftharpoonup$
7799 <cell alignment="center" valignment="top" usebox="none">
7802 \begin_layout Plain Layout
7810 <cell alignment="center" valignment="top" usebox="none">
7813 \begin_layout Plain Layout
7814 \begin_inset Formula $\leftharpoondown$
7824 <cell alignment="center" valignment="top" bottomline="true" usebox="none">
7827 \begin_layout Plain Layout
7835 <cell alignment="center" valignment="top" bottomline="true" usebox="none">
7838 \begin_layout Plain Layout
7839 \begin_inset Formula $\hookleftarrow$
7853 \begin_inset space \hfill{}
7857 \begin_inset Tabular
7858 <lyxtabular version="3" rows="8" columns="2">
7859 <features booktabs="true" tabularvalignment="middle">
7860 <column alignment="center" valignment="top" width="0pt">
7861 <column alignment="center" valignment="top" width="0pt">
7863 <cell alignment="center" valignment="top" topline="true" bottomline="true" usebox="none">
7866 \begin_layout Plain Layout
7872 <cell alignment="center" valignment="top" topline="true" bottomline="true" usebox="none">
7875 \begin_layout Plain Layout
7883 <cell alignment="center" valignment="top" usebox="none">
7886 \begin_layout Plain Layout
7894 <cell alignment="center" valignment="top" usebox="none">
7897 \begin_layout Plain Layout
7898 \begin_inset Formula $\to$
7908 <cell alignment="center" valignment="top" usebox="none">
7911 \begin_layout Plain Layout
7919 <cell alignment="center" valignment="top" usebox="none">
7922 \begin_layout Plain Layout
7923 \begin_inset Formula $\Rightarrow$
7933 <cell alignment="center" valignment="top" usebox="none">
7936 \begin_layout Plain Layout
7944 <cell alignment="center" valignment="top" usebox="none">
7947 \begin_layout Plain Layout
7948 \begin_inset Formula $\longrightarrow$
7958 <cell alignment="center" valignment="top" usebox="none">
7961 \begin_layout Plain Layout
7969 <cell alignment="center" valignment="top" usebox="none">
7972 \begin_layout Plain Layout
7973 \begin_inset Formula $\Longrightarrow$
7983 <cell alignment="center" valignment="top" usebox="none">
7986 \begin_layout Plain Layout
7994 <cell alignment="center" valignment="top" usebox="none">
7997 \begin_layout Plain Layout
7998 \begin_inset Formula $\rightharpoonup$
8008 <cell alignment="center" valignment="top" usebox="none">
8011 \begin_layout Plain Layout
8019 <cell alignment="center" valignment="top" usebox="none">
8022 \begin_layout Plain Layout
8023 \begin_inset Formula $\rightharpoondown$
8033 <cell alignment="center" valignment="top" bottomline="true" usebox="none">
8036 \begin_layout Plain Layout
8044 <cell alignment="center" valignment="top" bottomline="true" usebox="none">
8047 \begin_layout Plain Layout
8048 \begin_inset Formula $\hookrightarrow$
8062 \begin_inset space \hfill{}
8068 \begin_layout Standard
8069 \begin_inset space \hfill{}
8073 \begin_inset Tabular
8074 <lyxtabular version="3" rows="6" columns="2">
8075 <features booktabs="true" tabularvalignment="middle">
8076 <column alignment="center" valignment="top" width="0pt">
8077 <column alignment="center" valignment="top" width="0pt">
8079 <cell alignment="center" valignment="top" topline="true" bottomline="true" usebox="none">
8082 \begin_layout Plain Layout
8088 <cell alignment="center" valignment="top" topline="true" bottomline="true" usebox="none">
8091 \begin_layout Plain Layout
8099 <cell alignment="center" valignment="top" usebox="none">
8102 \begin_layout Plain Layout
8110 <cell alignment="center" valignment="top" usebox="none">
8113 \begin_layout Plain Layout
8114 \begin_inset Formula $\leftrightarrow$
8124 <cell alignment="center" valignment="top" usebox="none">
8127 \begin_layout Plain Layout
8135 <cell alignment="center" valignment="top" usebox="none">
8138 \begin_layout Plain Layout
8139 \begin_inset Formula $\Leftrightarrow$
8149 <cell alignment="center" valignment="top" usebox="none">
8152 \begin_layout Plain Layout
8160 <cell alignment="center" valignment="top" usebox="none">
8163 \begin_layout Plain Layout
8164 \begin_inset Formula $\longleftrightarrow$
8174 <cell alignment="center" valignment="top" usebox="none">
8177 \begin_layout Plain Layout
8185 <cell alignment="center" valignment="top" usebox="none">
8188 \begin_layout Plain Layout
8189 \begin_inset Formula $\Longleftrightarrow$
8199 <cell alignment="center" valignment="top" bottomline="true" usebox="none">
8202 \begin_layout Plain Layout
8210 <cell alignment="center" valignment="top" bottomline="true" usebox="none">
8213 \begin_layout Plain Layout
8214 \begin_inset Formula $\rightleftharpoons$
8228 \begin_inset space \hspace{}
8233 \begin_inset space \hfill{}
8237 \begin_inset Tabular
8238 <lyxtabular version="3" rows="5" columns="2">
8239 <features booktabs="true" tabularvalignment="middle">
8240 <column alignment="center" valignment="top" width="0pt">
8241 <column alignment="center" valignment="top" width="0pt">
8243 <cell alignment="center" valignment="top" topline="true" bottomline="true" usebox="none">
8246 \begin_layout Plain Layout
8252 <cell alignment="center" valignment="top" topline="true" bottomline="true" usebox="none">
8255 \begin_layout Plain Layout
8263 <cell alignment="center" valignment="top" usebox="none">
8266 \begin_layout Plain Layout
8274 <cell alignment="center" valignment="top" usebox="none">
8277 \begin_layout Plain Layout
8278 \begin_inset Formula $\mapsto$
8288 <cell alignment="center" valignment="top" usebox="none">
8291 \begin_layout Plain Layout
8299 <cell alignment="center" valignment="top" usebox="none">
8302 \begin_layout Plain Layout
8303 \begin_inset Formula $\longmapsto$
8313 <cell alignment="center" valignment="top" usebox="none">
8316 \begin_layout Plain Layout
8324 <cell alignment="center" valignment="top" usebox="none">
8327 \begin_layout Plain Layout
8328 \begin_inset Formula $\leadsto$
8338 <cell alignment="center" valignment="top" bottomline="true" usebox="none">
8341 \begin_layout Plain Layout
8349 <cell alignment="center" valignment="top" bottomline="true" usebox="none">
8352 \begin_layout Plain Layout
8353 \begin_inset Formula $\dasharrow$
8367 \begin_inset space \hfill{}
8373 \begin_layout Standard
8374 \begin_inset VSpace medskip
8377 Arrows used as accents like e.
8378 \begin_inset space \thinspace{}
8382 \begin_inset space \space{}
8385 vector arrows are listed in
8386 \begin_inset CommandInset ref
8388 reference "sec:Accents"
8395 \begin_layout Standard
8396 \begin_inset VSpace bigskip
8399 Furthermore there are the labeled arrows
8400 \begin_inset Index idx
8403 \begin_layout Plain Layout
8416 \begin_inset Index idx
8419 \begin_layout Plain Layout
8434 \begin_inset Index idx
8437 \begin_layout Plain Layout
8444 \begin_layout Plain Layout
8459 When inserting one of these commands in a formula, an arrow with two blue
8460 boxes appear where the label can be inserted.
8461 The length of the arrow adapts to the label width.
8464 \begin_layout Standard
8466 \begin_inset Tabular
8467 <lyxtabular version="3" rows="3" columns="2">
8468 <features booktabs="true" tabularvalignment="middle">
8469 <column alignment="center" valignment="top" width="0pt">
8470 <column alignment="center" valignment="top" width="0pt">
8472 <cell alignment="center" valignment="top" topline="true" bottomline="true" usebox="none">
8475 \begin_layout Plain Layout
8481 <cell alignment="center" valignment="top" topline="true" bottomline="true" usebox="none">
8484 \begin_layout Plain Layout
8492 <cell alignment="center" valignment="top" usebox="none">
8495 \begin_layout Plain Layout
8499 \begin_inset space \textvisiblespace{}
8503 \begin_inset Formula $\downarrow$
8507 \begin_inset Formula $\to$
8515 <cell alignment="center" valignment="top" usebox="none">
8518 \begin_layout Plain Layout
8519 \begin_inset Formula $F(a)\xleftarrow[x>0]{x=a}F(x)$
8528 <row topspace="2mm">
8529 <cell alignment="center" valignment="top" bottomline="true" usebox="none">
8532 \begin_layout Plain Layout
8536 \begin_inset space \textvisiblespace{}
8540 \begin_inset Formula $\downarrow$
8544 \begin_inset Formula $\to$
8552 <cell alignment="center" valignment="top" bottomline="true" usebox="none">
8555 \begin_layout Plain Layout
8556 \begin_inset Formula $F(x)\xrightarrow[x>0]{x=a}F(a)$
8572 \begin_layout Standard
8573 \begin_inset VSpace medskip
8579 \begin_layout Standard
8580 If you set in the document settings under
8583 \begin_inset space ~
8593 \begin_inset Index idx
8596 \begin_layout Plain Layout
8597 Packages ! mathtools
8605 \begin_inset space ~
8610 , you have access to the following labeled arrows:
8613 \begin_layout Standard
8614 \begin_inset Newpage newpage
8618 \begin_inset Separator parbreak
8624 \begin_layout Standard
8626 \begin_inset space \hspace*{\fill}
8630 \begin_inset Tabular
8631 <lyxtabular version="3" rows="7" columns="2">
8632 <features booktabs="true" tabularvalignment="middle">
8633 <column alignment="center" valignment="top" width="0pt">
8634 <column alignment="center" valignment="top" width="0pt">
8636 <cell alignment="center" valignment="top" topline="true" bottomline="true" usebox="none">
8639 \begin_layout Plain Layout
8645 <cell alignment="center" valignment="top" topline="true" bottomline="true" usebox="none">
8648 \begin_layout Plain Layout
8656 <cell alignment="center" valignment="top" usebox="none">
8659 \begin_layout Plain Layout
8679 <cell alignment="center" valignment="top" usebox="none">
8682 \begin_layout Plain Layout
8683 \begin_inset Formula $\xleftrightarrow[x=a]{x>0}$
8692 <row topspace="2mm">
8693 <cell alignment="center" valignment="top" usebox="none">
8696 \begin_layout Plain Layout
8716 <cell alignment="center" valignment="top" usebox="none">
8719 \begin_layout Plain Layout
8720 \begin_inset Formula $\xLeftarrow[x=a]{x>0}$
8729 <row topspace="2mm">
8730 <cell alignment="center" valignment="top" usebox="none">
8733 \begin_layout Plain Layout
8753 <cell alignment="center" valignment="top" usebox="none">
8756 \begin_layout Plain Layout
8757 \begin_inset Formula $\xRightarrow[x=a]{x>0}$
8766 <row topspace="2mm">
8767 <cell alignment="center" valignment="top" usebox="none">
8770 \begin_layout Plain Layout
8790 <cell alignment="center" valignment="top" usebox="none">
8793 \begin_layout Plain Layout
8794 \begin_inset Formula $\xLeftrightarrow[x=a]{x>0}$
8803 <row topspace="2mm">
8804 <cell alignment="center" valignment="top" usebox="none">
8807 \begin_layout Plain Layout
8827 <cell alignment="center" valignment="top" usebox="none">
8830 \begin_layout Plain Layout
8831 \begin_inset Formula $\xhookleftarrow[x=a]{x>0}$
8840 <row topspace="2mm">
8841 <cell alignment="center" valignment="top" bottomline="true" usebox="none">
8844 \begin_layout Plain Layout
8864 <cell alignment="center" valignment="top" bottomline="true" usebox="none">
8867 \begin_layout Plain Layout
8868 \begin_inset Formula $\xhookrightarrow[x=a]{x>0}$
8882 \begin_inset space \hspace*{\fill}
8886 \begin_inset Tabular
8887 <lyxtabular version="3" rows="7" columns="2">
8888 <features booktabs="true" tabularvalignment="middle">
8889 <column alignment="center" valignment="top" width="0pt">
8890 <column alignment="center" valignment="top" width="0pt">
8892 <cell alignment="center" valignment="top" topline="true" bottomline="true" usebox="none">
8895 \begin_layout Plain Layout
8901 <cell alignment="center" valignment="top" topline="true" bottomline="true" usebox="none">
8904 \begin_layout Plain Layout
8912 <cell alignment="center" valignment="top" usebox="none">
8915 \begin_layout Plain Layout
8935 <cell alignment="center" valignment="top" usebox="none">
8938 \begin_layout Plain Layout
8939 \begin_inset Formula $\xleftharpoondown[x=a]{x>0}$
8948 <row topspace="2mm">
8949 <cell alignment="center" valignment="top" usebox="none">
8952 \begin_layout Plain Layout
8972 <cell alignment="center" valignment="top" usebox="none">
8975 \begin_layout Plain Layout
8976 \begin_inset Formula $\xleftharpoonup[x=a]{x>0}$
8985 <row topspace="2mm">
8986 <cell alignment="center" valignment="top" usebox="none">
8989 \begin_layout Plain Layout
9009 <cell alignment="center" valignment="top" usebox="none">
9012 \begin_layout Plain Layout
9013 \begin_inset Formula $\xrightharpoondown[x=a]{x>0}$
9022 <row topspace="2mm">
9023 <cell alignment="center" valignment="top" usebox="none">
9026 \begin_layout Plain Layout
9046 <cell alignment="center" valignment="top" usebox="none">
9049 \begin_layout Plain Layout
9050 \begin_inset Formula $\xrightharpoonup[x=a]{x>0}$
9059 <row topspace="2mm">
9060 <cell alignment="center" valignment="top" usebox="none">
9063 \begin_layout Plain Layout
9083 <cell alignment="center" valignment="top" usebox="none">
9086 \begin_layout Plain Layout
9087 \begin_inset Formula $\xleftrightharpoons[x=a]{x>0}$
9096 <row topspace="2mm">
9097 <cell alignment="center" valignment="top" bottomline="true" usebox="none">
9100 \begin_layout Plain Layout
9120 <cell alignment="center" valignment="top" bottomline="true" usebox="none">
9123 \begin_layout Plain Layout
9124 \begin_inset Formula $\xrightleftharpoons[x=a]{x>0}$
9138 \begin_inset space \hspace*{\fill}
9144 \begin_layout Standard
9145 The command scheme is for all these arrows:
9146 \begin_inset Separator parbreak
9152 \begin_layout Standard
9154 \begin_inset Tabular
9155 <lyxtabular version="3" rows="2" columns="2">
9156 <features booktabs="true" tabularvalignment="middle">
9157 <column alignment="center" valignment="top" width="0pt">
9158 <column alignment="center" valignment="top" width="0pt">
9160 <cell alignment="center" valignment="top" topline="true" bottomline="true" usebox="none">
9163 \begin_layout Plain Layout
9169 <cell alignment="center" valignment="top" topline="true" bottomline="true" usebox="none">
9172 \begin_layout Plain Layout
9179 <row bottomspace="0.5mm">
9180 <cell alignment="center" valignment="top" bottomline="true" usebox="none">
9183 \begin_layout Plain Layout
9186 xleftrightarrow[x=a]
9189 \begin_inset Formula $\to$
9197 <cell alignment="center" valignment="top" bottomline="true" usebox="none">
9200 \begin_layout Plain Layout
9201 \begin_inset Formula $F(a)\xleftrightarrow[x=a]{x>0}F(x)$
9217 \begin_layout Subsection
9218 Vertical and diagonal Arrows
9219 \begin_inset Index idx
9222 \begin_layout Plain Layout
9229 \begin_inset Index idx
9232 \begin_layout Plain Layout
9241 \begin_layout Standard
9242 \begin_inset space \hfill{}
9246 \begin_inset Tabular
9247 <lyxtabular version="3" rows="7" columns="2">
9248 <features booktabs="true" tabularvalignment="middle">
9249 <column alignment="center" valignment="top" width="0pt">
9250 <column alignment="center" valignment="top" width="0pt">
9252 <cell alignment="center" valignment="top" topline="true" bottomline="true" usebox="none">
9255 \begin_layout Plain Layout
9261 <cell alignment="center" valignment="top" topline="true" bottomline="true" usebox="none">
9264 \begin_layout Plain Layout
9272 <cell alignment="center" valignment="top" usebox="none">
9275 \begin_layout Plain Layout
9283 <cell alignment="center" valignment="top" usebox="none">
9286 \begin_layout Plain Layout
9287 \begin_inset Formula $\uparrow$
9297 <cell alignment="center" valignment="top" usebox="none">
9300 \begin_layout Plain Layout
9308 <cell alignment="center" valignment="top" usebox="none">
9311 \begin_layout Plain Layout
9312 \begin_inset Formula $\Uparrow$
9322 <cell alignment="center" valignment="top" usebox="none">
9325 \begin_layout Plain Layout
9333 <cell alignment="center" valignment="top" usebox="none">
9336 \begin_layout Plain Layout
9337 \begin_inset Formula $\updownarrow$
9347 <cell alignment="center" valignment="top" usebox="none">
9350 \begin_layout Plain Layout
9358 <cell alignment="center" valignment="top" usebox="none">
9361 \begin_layout Plain Layout
9362 \begin_inset Formula $\Updownarrow$
9372 <cell alignment="center" valignment="top" usebox="none">
9375 \begin_layout Plain Layout
9383 <cell alignment="center" valignment="top" usebox="none">
9386 \begin_layout Plain Layout
9387 \begin_inset Formula $\Downarrow$
9397 <cell alignment="center" valignment="top" bottomline="true" usebox="none">
9400 \begin_layout Plain Layout
9408 <cell alignment="center" valignment="top" bottomline="true" usebox="none">
9411 \begin_layout Plain Layout
9412 \begin_inset Formula $\downarrow$
9426 \begin_inset space \hfill{}
9430 \begin_inset Tabular
9431 <lyxtabular version="3" rows="5" columns="2">
9432 <features booktabs="true" tabularvalignment="middle">
9433 <column alignment="center" valignment="top" width="0pt">
9434 <column alignment="center" valignment="top" width="0pt">
9436 <cell alignment="center" valignment="top" topline="true" bottomline="true" usebox="none">
9439 \begin_layout Plain Layout
9445 <cell alignment="center" valignment="top" topline="true" bottomline="true" usebox="none">
9448 \begin_layout Plain Layout
9456 <cell alignment="center" valignment="top" usebox="none">
9459 \begin_layout Plain Layout
9467 <cell alignment="center" valignment="top" usebox="none">
9470 \begin_layout Plain Layout
9471 \begin_inset Formula $\nearrow$
9481 <cell alignment="center" valignment="top" usebox="none">
9484 \begin_layout Plain Layout
9492 <cell alignment="center" valignment="top" usebox="none">
9495 \begin_layout Plain Layout
9496 \begin_inset Formula $\searrow$
9506 <cell alignment="center" valignment="top" usebox="none">
9509 \begin_layout Plain Layout
9517 <cell alignment="center" valignment="top" usebox="none">
9520 \begin_layout Plain Layout
9521 \begin_inset Formula $\swarrow$
9531 <cell alignment="center" valignment="top" bottomline="true" usebox="none">
9534 \begin_layout Plain Layout
9542 <cell alignment="center" valignment="top" bottomline="true" usebox="none">
9545 \begin_layout Plain Layout
9546 \begin_inset Formula $\nwarrow$
9560 \begin_inset space \hfill{}
9566 \begin_layout Standard
9567 \begin_inset VSpace medskip
9570 Vertical arrows can be used also as delimiters together with the commands
9572 \begin_inset CommandInset ref
9574 reference "subsec:Manual-Bracket-Size"
9579 \begin_inset CommandInset ref
9581 reference "subsec:Automatic-Bracket-Size"
9588 \begin_layout Section
9590 \begin_inset CommandInset label
9597 \begin_inset Index idx
9600 \begin_layout Plain Layout
9609 \begin_layout Standard
9610 Accents can be inserted via the math toolbar button
9613 arg "math-insert \\hat"
9616 or the commands listed in the following subsections.
9619 \begin_layout Subsection
9620 Accents for one Character
9624 \begin_layout Plain Layout
9637 \begin_layout Plain Layout
9639 \begin_inset CommandInset ref
9641 reference "subsec:Accents-in-Text"
9654 \begin_layout Plain Layout
9662 \begin_inset Note Note
9665 \begin_layout Plain Layout
9672 is used to avoid that the footnote appears in the PDF-bookmark.
9675 \begin_layout Plain Layout
9683 \begin_inset CommandInset ref
9685 reference "subsec:Formulas-in-Section"
9695 \begin_inset CommandInset label
9697 name "subsec:Accents-for-one"
9702 \begin_inset Index idx
9705 \begin_layout Plain Layout
9706 Accents ! for one character
9714 \begin_layout Standard
9715 \begin_inset space \hfill{}
9719 \begin_inset Tabular
9720 <lyxtabular version="3" rows="8" columns="2">
9721 <features booktabs="true" tabularvalignment="middle">
9722 <column alignment="center" valignment="top" width="0pt">
9723 <column alignment="center" valignment="top" width="0pt">
9725 <cell alignment="center" valignment="top" topline="true" bottomline="true" usebox="none">
9728 \begin_layout Plain Layout
9734 <cell alignment="center" valignment="top" topline="true" bottomline="true" usebox="none">
9737 \begin_layout Plain Layout
9744 <row topspace="1.5mm">
9745 <cell alignment="center" valignment="top" usebox="none">
9748 \begin_layout Plain Layout
9752 \begin_inset space \textvisiblespace{}
9760 <cell alignment="center" valignment="top" usebox="none">
9763 \begin_layout Plain Layout
9764 \begin_inset Formula $\dot{A}$
9773 <row topspace="1.5mm">
9774 <cell alignment="center" valignment="top" usebox="none">
9777 \begin_layout Plain Layout
9781 \begin_inset space \textvisiblespace{}
9789 <cell alignment="center" valignment="top" usebox="none">
9792 \begin_layout Plain Layout
9793 \begin_inset Formula $\ddot{A}$
9802 <row topspace="1.5mm">
9803 <cell alignment="center" valignment="top" usebox="none">
9806 \begin_layout Plain Layout
9810 \begin_inset space \textvisiblespace{}
9818 <cell alignment="center" valignment="top" usebox="none">
9821 \begin_layout Plain Layout
9822 \begin_inset Formula $\dddot{A}$
9831 <row topspace="1.5mm">
9832 <cell alignment="center" valignment="top" usebox="none">
9835 \begin_layout Plain Layout
9839 \begin_inset space \textvisiblespace{}
9847 <cell alignment="center" valignment="top" usebox="none">
9850 \begin_layout Plain Layout
9851 \begin_inset Formula $\ddddot{A}$
9860 <row topspace="1.5mm">
9861 <cell alignment="center" valignment="top" usebox="none">
9864 \begin_layout Plain Layout
9868 \begin_inset space \textvisiblespace{}
9872 \begin_inset Index idx
9875 \begin_layout Plain Layout
9886 <cell alignment="center" valignment="top" usebox="none">
9889 \begin_layout Plain Layout
9890 \begin_inset Formula $\vec{A}$
9899 <row topspace="1.5mm">
9900 <cell alignment="center" valignment="top" usebox="none">
9903 \begin_layout Plain Layout
9907 \begin_inset space \textvisiblespace{}
9915 <cell alignment="center" valignment="top" usebox="none">
9918 \begin_layout Plain Layout
9919 \begin_inset Formula $\bar{A}$
9928 <row topspace="1.5mm">
9929 <cell alignment="center" valignment="top" bottomline="true" usebox="none">
9932 \begin_layout Plain Layout
9936 \begin_inset space \textvisiblespace{}
9944 <cell alignment="center" valignment="top" bottomline="true" usebox="none">
9947 \begin_layout Plain Layout
9948 \begin_inset Formula $\mathring{A}$
9962 \begin_inset space \hfill{}
9966 \begin_inset Tabular
9967 <lyxtabular version="3" rows="7" columns="2">
9968 <features booktabs="true" tabularvalignment="middle">
9969 <column alignment="center" valignment="top" width="0pt">
9970 <column alignment="center" valignment="top" width="0pt">
9972 <cell alignment="center" valignment="top" topline="true" bottomline="true" usebox="none">
9975 \begin_layout Plain Layout
9981 <cell alignment="center" valignment="top" topline="true" bottomline="true" usebox="none">
9984 \begin_layout Plain Layout
9991 <row topspace="1.5mm">
9992 <cell alignment="center" valignment="top" usebox="none">
9995 \begin_layout Plain Layout
9999 \begin_inset space \textvisiblespace{}
10007 <cell alignment="center" valignment="top" usebox="none">
10010 \begin_layout Plain Layout
10011 \begin_inset Formula $\tilde{A}$
10020 <row topspace="1.5mm">
10021 <cell alignment="center" valignment="top" usebox="none">
10024 \begin_layout Plain Layout
10028 \begin_inset space \textvisiblespace{}
10036 <cell alignment="center" valignment="top" usebox="none">
10039 \begin_layout Plain Layout
10040 \begin_inset Formula $\hat{A}$
10049 <row topspace="1.5mm">
10050 <cell alignment="center" valignment="top" usebox="none">
10053 \begin_layout Plain Layout
10057 \begin_inset space \textvisiblespace{}
10065 <cell alignment="center" valignment="top" usebox="none">
10068 \begin_layout Plain Layout
10069 \begin_inset Formula $\check{A}$
10078 <row topspace="1.5mm">
10079 <cell alignment="center" valignment="top" usebox="none">
10082 \begin_layout Plain Layout
10086 \begin_inset space \textvisiblespace{}
10094 <cell alignment="center" valignment="top" usebox="none">
10097 \begin_layout Plain Layout
10098 \begin_inset Formula $\acute{A}$
10107 <row topspace="1.5mm">
10108 <cell alignment="center" valignment="top" usebox="none">
10111 \begin_layout Plain Layout
10115 \begin_inset space \textvisiblespace{}
10123 <cell alignment="center" valignment="top" usebox="none">
10126 \begin_layout Plain Layout
10127 \begin_inset Formula $\grave{A}$
10136 <row topspace="1.5mm">
10137 <cell alignment="center" valignment="top" bottomline="true" usebox="none">
10140 \begin_layout Plain Layout
10144 \begin_inset space \textvisiblespace{}
10152 <cell alignment="center" valignment="top" bottomline="true" usebox="none">
10155 \begin_layout Plain Layout
10156 \begin_inset Formula $\breve{A}$
10170 \begin_inset space \hfill{}
10176 \begin_layout Standard
10177 \begin_inset VSpace bigskip
10183 \begin_layout Standard
10184 You can directly insert accents like é to formulas.
10186 will transform them to the corresponding accent command.
10188 \begin_inset Index idx
10191 \begin_layout Plain Layout
10197 it is better to insert a quotation mark before the vowel.
10198 These two characters are then treated by \SpecialChar LaTeX
10203 character when the formula part with the umlaut is marked as German.
10211 \begin_inset Quotes eld
10215 \begin_inset Quotes erd
10218 umlauts are created as demonstrated in the following example:
10221 \begin_layout Standard
10222 \begin_inset VSpace -2mm
10228 \begin_layout Standard
10230 \begin_inset Tabular
10231 <lyxtabular version="3" rows="3" columns="2">
10232 <features booktabs="true" tabularvalignment="middle">
10233 <column alignment="center" valignment="top" width="0pt">
10234 <column alignment="center" valignment="top">
10236 <cell alignment="center" valignment="top" topline="true" bottomline="true" usebox="none">
10239 \begin_layout Plain Layout
10245 <cell alignment="center" valignment="top" topline="true" bottomline="true" usebox="none">
10248 \begin_layout Plain Layout
10256 <cell alignment="center" valignment="top" usebox="none">
10259 \begin_layout Plain Layout
10260 \begin_inset Quotes grd
10268 <cell alignment="center" valignment="top" usebox="none">
10271 \begin_layout Plain Layout
10272 \begin_inset space \hspace{}
10279 \begin_inset Formula $"i$
10288 <row topspace="1.5mm">
10289 <cell alignment="center" valignment="top" bottomline="true" usebox="none">
10292 \begin_layout Plain Layout
10296 \begin_inset space \textvisiblespace{}
10304 <cell alignment="center" valignment="top" bottomline="true" usebox="none">
10307 \begin_layout Plain Layout
10308 \begin_inset Formula $\ddot{i}$
10324 \begin_layout Standard
10325 Another advantage to
10331 is that umlauts can directly be converted to mathematical text because
10332 the accent commands above are
10338 in mathematical text
10341 To convert an accented character to mathematical text, only the character
10342 under the accent may be converted.
10343 This applies also for all other conversions, e.
10344 \begin_inset space \thinspace{}
10348 \begin_inset space \space{}
10354 \begin_layout Standard
10355 In mathematical text, umlauts and other accented characters can directly
10359 \begin_layout Standard
10360 \begin_inset VSpace bigskip
10366 \begin_layout Standard
10368 also supports a tilde under the character if the \SpecialChar LaTeX
10374 \begin_inset Index idx
10377 \begin_layout Plain Layout
10378 Packages ! undertilde
10383 is installed on your system:
10386 \begin_layout Standard
10390 \begin_layout Plain Layout
10400 \begin_inset Note Note
10403 \begin_layout Plain Layout
10404 The following table will only be displayed when the \SpecialChar LaTeX
10415 \begin_inset Separator parbreak
10421 \begin_layout Standard
10424 \begin_inset Tabular
10425 <lyxtabular version="3" rows="2" columns="2">
10426 <features booktabs="true" tabularvalignment="middle">
10427 <column alignment="center" valignment="top" width="0pt">
10428 <column alignment="center" valignment="top" width="0pt">
10430 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
10433 \begin_layout Plain Layout
10439 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
10442 \begin_layout Plain Layout
10450 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
10453 \begin_layout Plain Layout
10457 \begin_inset space \textvisiblespace{}
10465 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
10468 \begin_layout Plain Layout
10469 \begin_inset Formula $\utilde{A}$
10485 \begin_layout Standard
10489 \begin_layout Plain Layout
10499 \begin_inset Note Note
10502 \begin_layout Plain Layout
10503 The following will be displayed when the \SpecialChar LaTeX
10516 \begin_layout Standard
10517 You need to install the \SpecialChar LaTeX
10522 to see the rest of this subsection in the output.
10525 \begin_layout Standard
10529 \begin_layout Plain Layout
10541 \begin_layout Standard
10542 \begin_inset Newpage newpage
10548 \begin_layout Subsection
10549 Accents for several Characters
10550 \begin_inset Index idx
10553 \begin_layout Plain Layout
10554 Accents ! for several characters
10562 \begin_layout Standard
10563 \begin_inset space \hfill{}
10567 \begin_inset Tabular
10568 <lyxtabular version="3" rows="5" columns="2">
10569 <features booktabs="true" tabularvalignment="middle">
10570 <column alignment="center" valignment="top" width="0pt">
10571 <column alignment="center" valignment="top" width="0pt">
10573 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
10576 \begin_layout Plain Layout
10582 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
10585 \begin_layout Plain Layout
10592 <row topspace="1.5mm">
10593 <cell alignment="center" valignment="top" usebox="none">
10596 \begin_layout Plain Layout
10600 \begin_inset space \textvisiblespace{}
10608 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
10611 \begin_layout Plain Layout
10612 \begin_inset Formula $\overleftarrow{A=B}$
10621 <row topspace="1.5mm">
10622 <cell alignment="center" valignment="top" usebox="none">
10625 \begin_layout Plain Layout
10629 \begin_inset space \textvisiblespace{}
10637 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
10640 \begin_layout Plain Layout
10641 \begin_inset Formula $\underleftarrow{A=B}$
10650 <row topspace="1.5mm">
10651 <cell alignment="center" valignment="top" usebox="none">
10654 \begin_layout Plain Layout
10658 \begin_inset space \textvisiblespace{}
10666 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
10669 \begin_layout Plain Layout
10670 \begin_inset Formula $\overleftrightarrow{A=B}$
10679 <row topspace="1.5mm" bottomspace="1mm">
10680 <cell alignment="center" valignment="top" bottomline="true" usebox="none">
10683 \begin_layout Plain Layout
10686 underleftrightarrow
10687 \begin_inset space \textvisiblespace{}
10695 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
10698 \begin_layout Plain Layout
10699 \begin_inset Formula $\underleftrightarrow{A=B}$
10713 \begin_inset space \hfill{}
10717 \begin_inset Tabular
10718 <lyxtabular version="3" rows="5" columns="2">
10719 <features booktabs="true" tabularvalignment="middle">
10720 <column alignment="center" valignment="top" width="0pt">
10721 <column alignment="center" valignment="top" width="0pt">
10723 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
10726 \begin_layout Plain Layout
10732 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
10735 \begin_layout Plain Layout
10742 <row topspace="1.5mm">
10743 <cell alignment="center" valignment="top" usebox="none">
10746 \begin_layout Plain Layout
10750 \begin_inset space \textvisiblespace{}
10758 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
10761 \begin_layout Plain Layout
10762 \begin_inset Formula $\overrightarrow{A=B}$
10771 <row topspace="1.5mm">
10772 <cell alignment="center" valignment="top" usebox="none">
10775 \begin_layout Plain Layout
10779 \begin_inset space \textvisiblespace{}
10787 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
10790 \begin_layout Plain Layout
10791 \begin_inset Formula $\underrightarrow{A=B}$
10800 <row topspace="1.5mm">
10801 <cell alignment="center" valignment="top" usebox="none">
10804 \begin_layout Plain Layout
10808 \begin_inset space \textvisiblespace{}
10816 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
10819 \begin_layout Plain Layout
10820 \begin_inset Formula $\widetilde{A=B}$
10829 <row topspace="1.5mm" bottomspace="1mm">
10830 <cell alignment="center" valignment="top" bottomline="true" usebox="none">
10833 \begin_layout Plain Layout
10837 \begin_inset space \textvisiblespace{}
10845 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
10848 \begin_layout Plain Layout
10849 \begin_inset Formula $\widehat{A=B}$
10863 \begin_inset space \hfill{}
10869 \begin_layout Standard
10870 \begin_inset VSpace medskip
10873 With these commands as many characters as you like can be accented.
10886 will only be set in the output with a length of three characters, as shown
10887 in the following example:
10888 \begin_inset Formula
10890 \widetilde{A+B=C-D}
10898 \begin_layout Standard
10906 \begin_inset Index idx
10909 \begin_layout Plain Layout
10924 \begin_inset Index idx
10927 \begin_layout Plain Layout
10935 described in the previous subsection it is also possible to accent several
10942 \begin_inset space \textvisiblespace{}
10946 \begin_inset Formula $\downarrow$
10952 \begin_inset Formula
10954 \underset{***}{A=B}
10962 \begin_layout Section
10964 \begin_inset CommandInset label
10966 name "subsec:Space"
10971 \begin_inset Index idx
10974 \begin_layout Plain Layout
10983 \begin_layout Subsection
10985 \begin_inset CommandInset label
10987 name "subsec:Predefined-Space"
10992 \begin_inset Index idx
10995 \begin_layout Plain Layout
10996 Space ! horizontal ! predefined
11004 \begin_layout Standard
11005 Sometimes it is necessary to insert horizontal space into a formula.
11006 This is done by inserting a protected space (shortcut
11009 arg "command-alternatives space-insert protected ; math-space"
11014 \begin_inset Quotes eld
11020 \begin_inset space \textvisiblespace{}
11026 \begin_inset Quotes erd
11029 appears and by pressing
11033 several times one can select one of eight different space sizes.
11034 The spaces can also be inserted using the math toolbar button
11037 arg "math-insert \\space"
11040 or special commands.
11041 Independent from the inserted command, one can select the size again by
11047 \begin_inset Separator parbreak
11053 \begin_layout Standard
11056 \begin_inset Tabular
11057 <lyxtabular version="3" rows="6" columns="3">
11058 <features booktabs="true" tabularvalignment="middle">
11059 <column alignment="center" valignment="top">
11060 <column alignment="center" valignment="top" width="15col%">
11061 <column alignment="center" valignment="top">
11063 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
11066 \begin_layout Plain Layout
11072 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
11075 \begin_layout Plain Layout
11085 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
11088 \begin_layout Plain Layout
11096 <cell alignment="center" valignment="top" leftline="true" usebox="none">
11099 \begin_layout Plain Layout
11107 <cell alignment="center" valignment="top" leftline="true" usebox="none">
11110 \begin_layout Plain Layout
11116 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
11119 \begin_layout Plain Layout
11120 \begin_inset Formula $A\,B$
11130 <cell alignment="center" valignment="top" leftline="true" usebox="none">
11133 \begin_layout Plain Layout
11141 <cell alignment="center" valignment="top" leftline="true" usebox="none">
11144 \begin_layout Plain Layout
11150 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
11153 \begin_layout Plain Layout
11154 \begin_inset Formula $A\:B$
11164 <cell alignment="center" valignment="top" leftline="true" usebox="none">
11167 \begin_layout Plain Layout
11175 <cell alignment="center" valignment="top" leftline="true" usebox="none">
11178 \begin_layout Plain Layout
11184 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
11187 \begin_layout Plain Layout
11188 \begin_inset Formula $A\;B$
11198 <cell alignment="center" valignment="top" leftline="true" usebox="none">
11201 \begin_layout Plain Layout
11209 <cell alignment="center" valignment="top" leftline="true" usebox="none">
11212 \begin_layout Plain Layout
11218 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
11221 \begin_layout Plain Layout
11222 \begin_inset Formula $A\quad B$
11232 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
11235 \begin_layout Plain Layout
11243 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
11246 \begin_layout Plain Layout
11252 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
11255 \begin_layout Plain Layout
11256 \begin_inset Formula $A\qquad B$
11270 \begin_inset space \hfill{}
11274 \begin_inset Tabular
11275 <lyxtabular version="3" rows="6" columns="3">
11276 <features booktabs="true" tabularvalignment="middle">
11277 <column alignment="center" valignment="top">
11278 <column alignment="center" valignment="top" width="15col%">
11279 <column alignment="center" valignment="top">
11281 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
11284 \begin_layout Plain Layout
11290 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
11293 \begin_layout Plain Layout
11303 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
11306 \begin_layout Plain Layout
11314 <cell alignment="center" valignment="top" leftline="true" usebox="none">
11317 \begin_layout Plain Layout
11325 <cell alignment="center" valignment="top" leftline="true" usebox="none">
11328 \begin_layout Plain Layout
11334 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
11337 \begin_layout Plain Layout
11338 \begin_inset Formula $A\hfill B$
11348 <cell alignment="center" valignment="top" leftline="true" usebox="none">
11351 \begin_layout Plain Layout
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 $A\hspace*{1em}B$
11382 <cell alignment="center" valignment="top" leftline="true" usebox="none">
11385 \begin_layout Plain Layout
11393 <cell alignment="center" valignment="top" leftline="true" usebox="none">
11396 \begin_layout Plain Layout
11402 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
11405 \begin_layout Plain Layout
11406 \begin_inset Formula $A\hspace{1em}B$
11416 <cell alignment="center" valignment="top" leftline="true" usebox="none">
11419 \begin_layout Plain Layout
11423 \begin_inset space \textvisiblespace{}
11431 <cell alignment="center" valignment="top" leftline="true" usebox="none">
11434 \begin_layout Plain Layout
11440 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
11443 \begin_layout Plain Layout
11444 \begin_inset Formula $A\ B$
11454 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
11457 \begin_layout Plain Layout
11465 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
11468 \begin_layout Plain Layout
11474 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
11477 \begin_layout Plain Layout
11478 \begin_inset Formula $A\!B$
11494 \begin_layout Standard
11496 \begin_inset space ~
11500 \begin_inset space \thinspace{}
11504 \begin_inset space \thinspace{}
11507 7 are variable spaces which are explained in
11508 \begin_inset CommandInset ref
11510 reference "subsec:Variable-Space"
11516 \begin_inset space ~
11519 9 seems to produce no space.
11520 It is displayed red in \SpecialChar LyX
11521 contrary to the other sizes, because it is a negative
11523 There are two more negative spaces:
11524 \begin_inset Separator parbreak
11530 \begin_layout Standard
11532 \begin_inset Tabular
11533 <lyxtabular version="3" rows="3" columns="3">
11534 <features booktabs="true" tabularvalignment="middle">
11535 <column alignment="center" valignment="middle" width="6.8cm">
11536 <column alignment="center" valignment="top" width="0pt">
11537 <column alignment="center" valignment="top" width="0pt">
11539 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
11542 \begin_layout Plain Layout
11548 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
11551 \begin_layout Plain Layout
11559 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
11562 \begin_layout Plain Layout
11572 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
11575 \begin_layout Plain Layout
11580 keystrokes after inserting the protected space
11585 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
11588 \begin_layout Plain Layout
11594 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
11597 \begin_layout Plain Layout
11605 <cell multicolumn="1" alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
11608 \begin_layout Plain Layout
11614 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
11617 \begin_layout Plain Layout
11618 \begin_inset Formula $A\negmedspace B$
11626 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
11629 \begin_layout Plain Layout
11630 \begin_inset Formula $A\negthickspace B$
11646 \begin_layout Standard
11647 Negative spaces can lead to characters overlapping each other.
11648 Thus they can be used to enforce ligatures, which are e.
11649 \begin_inset space \thinspace{}
11653 \begin_inset space \space{}
11656 useful for summation operators:
11657 \begin_inset Separator parbreak
11663 \begin_layout Standard
11665 \begin_inset Tabular
11666 <lyxtabular version="3" rows="3" columns="2">
11667 <features booktabs="true" tabularvalignment="middle">
11668 <column alignment="center" valignment="top" width="0pt">
11669 <column alignment="center" valignment="top">
11671 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
11674 \begin_layout Plain Layout
11680 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
11683 \begin_layout Plain Layout
11691 <cell alignment="center" valignment="top" leftline="true" usebox="none">
11694 \begin_layout Plain Layout
11700 \begin_inset space \textvisiblespace{}
11708 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
11711 \begin_layout Plain Layout
11712 \begin_inset Formula $\sum\sum f_{kl}$
11722 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
11725 \begin_layout Plain Layout
11733 \begin_inset space \textvisiblespace{}
11741 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
11744 \begin_layout Plain Layout
11745 \begin_inset Formula $\sum\negmedspace\sum f_{kl}$
11761 \begin_layout Standard
11763 \begin_inset VSpace medskip
11769 \begin_layout Standard
11771 Relations like for example equal signs, are always surrounded by space.
11772 To suppress this, the equal sign is placed into a \SpecialChar TeX
11774 The following example demonstrates this:
11775 \begin_inset Separator parbreak
11781 \begin_layout Standard
11783 \begin_inset Tabular
11784 <lyxtabular version="3" rows="2" columns="2">
11785 <features tabularvalignment="middle">
11786 <column alignment="center" valignment="top" width="0pt">
11787 <column alignment="center" valignment="top" width="0pt">
11789 <cell alignment="center" valignment="top" usebox="none">
11792 \begin_layout Plain Layout
11798 <cell alignment="center" valignment="top" usebox="none">
11801 \begin_layout Plain Layout
11802 \begin_inset Formula $A=B$
11812 <cell alignment="center" valignment="top" usebox="none">
11815 \begin_layout Plain Layout
11816 equation without space
11821 <cell multicolumn="1" alignment="center" valignment="top" usebox="none">
11824 \begin_layout Plain Layout
11825 \begin_inset Formula $A{=}B$
11841 \begin_layout Standard
11843 The command for the last formula is:
11848 \begin_inset Formula $\to$
11854 \begin_layout Standard
11855 \begin_inset VSpace bigskip
11861 \begin_layout Standard
11862 Spaces are needed for physical units, because the space between the value
11863 and the unit is the smallest one and not a normal space.
11864 For units in text, the smallest space is inserted via the menu
11866 Insert\SpecialChar menuseparator
11867 Formatting\SpecialChar menuseparator
11869 \begin_inset space ~
11877 arg "space-insert thin"
11883 \begin_layout Standard
11884 An example to visualize the difference:
11887 \begin_layout Standard
11888 \begin_inset Tabular
11889 <lyxtabular version="3" rows="2" columns="2">
11890 <features tabularvalignment="middle">
11891 <column alignment="left" valignment="top">
11892 <column alignment="left" valignment="top">
11894 <cell alignment="center" valignment="top" usebox="none">
11897 \begin_layout Plain Layout
11899 \begin_inset Formula $\cdot$
11907 <cell alignment="center" valignment="top" usebox="none">
11910 \begin_layout Plain Layout
11911 space between value and unit
11918 <cell alignment="center" valignment="top" usebox="none">
11921 \begin_layout Plain Layout
11923 \begin_inset space \thinspace{}
11927 \begin_inset Formula $\cdot$
11935 <cell alignment="center" valignment="top" usebox="none">
11938 \begin_layout Plain Layout
11939 smallest space between value and unit
11952 \begin_layout Subsection
11957 \begin_layout Plain Layout
11970 \begin_layout Plain Layout
11971 for vertical space in formulas see
11972 \begin_inset CommandInset ref
11974 reference "subsec:Line-Separation"
11987 \begin_layout Plain Layout
11995 \begin_inset Note Note
11998 \begin_layout Plain Layout
12001 texorpdfstring is used to avoid that the footnote appears in the PDF-bookmark.
12004 \begin_layout Plain Layout
12007 texorpdfstring is in section
12008 \begin_inset CommandInset ref
12010 reference "subsec:Formulas-in-Section"
12020 \begin_inset CommandInset label
12022 name "subsec:Variable-Space"
12027 \begin_inset Index idx
12030 \begin_layout Plain Layout
12031 Space ! horizontal ! variable
12039 \begin_layout Standard
12040 Space with a defined length can be inserted with the command
12047 \begin_inset Index idx
12050 \begin_layout Plain Layout
12060 \begin_inset Quotes eld
12066 \begin_inset space \textvisiblespace{}
12072 \begin_inset Quotes erd
12076 The length can be specified by left-clicking on the
12077 \begin_inset Quotes eld
12083 \begin_inset space \textvisiblespace{}
12089 \begin_inset Quotes erd
12093 The length may also be negative.
12094 When a space would be the first character in a line it would be omitted.
12095 To force its output use the command
12107 or left-click on the
12108 \begin_inset Quotes eld
12114 \begin_inset space \textvisiblespace{}
12120 \begin_inset Quotes erd
12123 and check the option
12128 \begin_inset Newline newline
12131 To insert as much space as is available, the command
12138 \begin_inset Index idx
12141 \begin_layout Plain Layout
12152 \begin_layout Standard
12154 \begin_inset Tabular
12155 <lyxtabular version="3" rows="4" columns="2">
12156 <features booktabs="true" tabularvalignment="middle">
12157 <column alignment="center" valignment="top" width="0pt">
12158 <column alignment="center" valignment="top">
12160 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
12163 \begin_layout Plain Layout
12171 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
12174 \begin_layout Plain Layout
12182 <cell alignment="center" valignment="top" leftline="true" usebox="none">
12185 \begin_layout Plain Layout
12189 \begin_inset space \textvisiblespace{}
12195 \begin_inset space \thinspace{}
12203 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
12206 \begin_layout Plain Layout
12207 \begin_inset Formula $A=B\hspace{3cm}A\not=C$
12217 <cell alignment="center" valignment="top" leftline="true" usebox="none">
12220 \begin_layout Plain Layout
12224 \begin_inset space \textvisiblespace{}
12230 \begin_inset space \thinspace{}
12238 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
12241 \begin_layout Plain Layout
12242 \begin_inset Formula $A\hspace{-1mm}A\not=A$
12252 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
12255 \begin_layout Plain Layout
12259 \begin_inset space \textvisiblespace{}
12267 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
12270 \begin_layout Plain Layout
12271 \begin_inset Formula $A=A\hfill B=B$
12287 \begin_layout Standard
12288 In the last example the available space is given by the longest column entry
12290 In an inline formula the space depends on the length of the line in which
12298 Thus, when the line uses the full width, no space will be created.
12305 only has an effect on displayed formulas when the formula style
12310 (Formula styles are explained in
12311 \begin_inset CommandInset ref
12313 reference "sec:Formula-Styles"
12320 \begin_layout Standard
12327 , there are the commands
12339 that fill the space with a pattern, see
12340 \begin_inset CommandInset ref
12342 reference "subsec:Ellipses"
12349 \begin_layout Standard
12350 For text, variable space can be inserted via the menu
12352 Insert\SpecialChar menuseparator
12353 Formatting\SpecialChar menuseparator
12355 \begin_inset space ~
12363 \begin_layout Standard
12364 This is a line with
12365 \begin_inset space \hspace{}
12370 \begin_inset space \thinspace{}
12376 \begin_layout Standard
12377 This is a line with
12378 \begin_inset space \hfill{}
12384 \begin_layout Subsection
12385 Space besides inline Formulas
12386 \begin_inset Index idx
12389 \begin_layout Plain Layout
12390 Space ! besides inline formulas
12398 \begin_layout Standard
12399 The space that surrounds inline formulas can be adjusted with the length
12407 \begin_inset Index idx
12410 \begin_layout Plain Layout
12419 The value of a length is set with the command
12426 \begin_inset Index idx
12429 \begin_layout Plain Layout
12437 which has the following scheme:
12440 \begin_layout Standard
12445 setlength{length name}{value}
12448 \begin_layout Standard
12456 \begin_inset space \thinspace{}
12462 \begin_layout Standard
12472 \begin_layout Standard
12473 is inserted in \SpecialChar TeX
12476 \begin_inset space \thinspace{}
12479 mm space will now be set around all inline formulas:
12483 \begin_layout Plain Layout
12497 \begin_layout Standard
12498 This is a line with an inline formula
12499 \begin_inset Formula $A=B$
12503 \begin_inset space \thinspace{}
12506 mm surrounding space.
12510 \begin_layout Plain Layout
12524 \begin_layout Standard
12525 To return to the predefined value,
12531 is set to the value 0
12532 \begin_inset space \thinspace{}
12538 \begin_layout Standard
12539 \begin_inset Newpage newpage
12545 \begin_layout Section
12547 \begin_inset Index idx
12550 \begin_layout Plain Layout
12557 \begin_inset Index idx
12560 \begin_layout Plain Layout
12565 \begin_layout Plain Layout
12576 \begin_layout Plain Layout
12591 \begin_layout Standard
12592 Boxes for text are described in chapter
12599 \begin_inset space ~
12607 \begin_layout Subsection
12609 \begin_inset CommandInset label
12611 name "subsec:Boxes-with-Frame"
12616 \begin_inset Index idx
12619 \begin_layout Plain Layout
12628 \begin_layout Standard
12629 It is possible to frame a formula or part of one with the commands
12636 \begin_inset Index idx
12639 \begin_layout Plain Layout
12654 \begin_inset Index idx
12657 \begin_layout Plain Layout
12668 \begin_layout Standard
12669 When one of these commands is inserted in a formula, a blue box appears
12670 within a frame to enter formula parts.
12677 an additional formula has to be created by
12681 within this box, because the box content will otherwise be treated as mathemati
12689 is used, a new formula is automatically created inside the frame.
12692 \begin_layout Standard
12699 is not suitable to frame displayed formulas because the formula will always
12700 be set in the size of the text.
12707 is in contrary not suitable to frame inline formulas, because the formula
12708 will always be set in the size of a displayed formula.
12711 \begin_layout Standard
12725 \begin_inset Index idx
12728 \begin_layout Plain Layout
12736 where additionally the frame width and the alignment can be specified.
12743 is used in the following scheme:
12746 \begin_layout Standard
12751 framebox[frame width][position]{box content}
12754 \begin_layout Standard
12755 The position can either be
12772 right aligns the formula in the box.
12773 When no position is given, the formula will be centered.
12774 \begin_inset Newline newline
12777 If no width is given, also no position can be given.
12778 In this case the frame width is adjusted to the box content like for
12787 \begin_layout Standard
12794 is inserted, a box appears containing three blue boxes.
12795 The first two boxes are surrounded by brackets and denote the two optional
12797 The third box is for formula parts like for
12804 \begin_inset Separator parbreak
12810 \begin_layout Standard
12812 \begin_inset Tabular
12813 <lyxtabular version="3" rows="5" columns="2">
12814 <features booktabs="true" tabularvalignment="middle">
12815 <column alignment="center" valignment="top" width="0pt">
12816 <column alignment="center" valignment="top">
12818 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
12821 \begin_layout Plain Layout
12827 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
12830 \begin_layout Plain Layout
12837 <row topspace="1.5mm">
12838 <cell alignment="center" valignment="top" usebox="none">
12841 \begin_layout Plain Layout
12845 \begin_inset space \textvisiblespace{}
12855 \begin_inset space \textvisiblespace{}
12863 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
12866 \begin_layout Plain Layout
12867 \begin_inset Formula $\fbox{\ensuremath{\int A=B}}$
12876 <row topspace="1.5mm">
12877 <cell alignment="center" valignment="top" usebox="none">
12880 \begin_layout Plain Layout
12884 \begin_inset space \textvisiblespace{}
12890 \begin_inset space \textvisiblespace{}
12898 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
12901 \begin_layout Plain Layout
12902 \begin_inset Formula $\boxed{\int A=B}$
12911 <row topspace="1.5mm">
12912 <cell alignment="center" valignment="top" usebox="none">
12915 \begin_layout Plain Layout
12919 \begin_inset space \textvisiblespace{}
12927 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
12930 \begin_layout Plain Layout
12931 \begin_inset Formula $A+\fbox{B}$
12940 <row topspace="1.5mm" bottomspace="1mm">
12941 <cell alignment="center" valignment="top" bottomline="true" usebox="none">
12944 \begin_layout Plain Layout
12948 \begin_inset space \textvisiblespace{}
12952 \begin_inset Formula $\to$
12956 \begin_inset Formula $\to$
12966 \begin_inset space \textvisiblespace{}
12970 \begin_inset Formula $\downarrow$
12978 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
12981 \begin_layout Plain Layout
12982 \begin_inset Formula $\framebox[20mm][]{\ensuremath{\frac{A}{B}}}$
12998 \begin_layout Standard
12999 The frame thickness can also be adjusted.
13000 To do this the following commands have to be inserted in \SpecialChar TeX
13005 \begin_layout Standard
13015 \begin_inset Quotes eld
13019 \begin_inset Quotes erd
13033 \begin_inset Quotes eld
13037 \begin_inset Quotes erd
13043 \begin_layout Standard
13044 \begin_inset Quotes eld
13048 \begin_inset Quotes erd
13051 specifies the minimal distance between the frame and the first character
13053 An example for this is the following framed formula:
13057 \begin_layout Plain Layout
13069 \begin_inset Formula
13076 Before this formula the commands
13079 \begin_layout Standard
13101 \begin_layout Standard
13102 were inserted in \SpecialChar TeX
13104 The given values are used for all following boxes.
13107 \begin_layout Standard
13108 To return to the standard frame size, the command
13111 \begin_layout Standard
13136 \begin_layout Plain Layout
13150 \begin_layout Standard
13151 is inserted in \SpecialChar TeX
13152 mode before the next formula.
13155 \begin_layout Subsection
13156 Boxes without Frame
13157 \begin_inset CommandInset label
13159 name "subsec:Boxes-without-Frame"
13164 \begin_inset Index idx
13167 \begin_layout Plain Layout
13168 Boxes ! without frame
13176 \begin_layout Standard
13177 For boxes without a frame there are the following box commands:
13184 \begin_inset Index idx
13187 \begin_layout Plain Layout
13202 \begin_inset Index idx
13205 \begin_layout Plain Layout
13220 \begin_inset Index idx
13223 \begin_layout Plain Layout
13234 \begin_layout Standard
13241 a box can be super- or subscripted.
13242 But in contrary to normal super- and subscripting, the characters in the
13243 box keep their font size.
13250 is used in the following scheme:
13253 \begin_layout Standard
13258 raisebox{height}{box content}
13261 \begin_layout Standard
13262 When the box should contain a formula, an extra formula is needed like for
13273 \begin_inset Note Greyedout
13276 \begin_layout Plain Layout
13287 this extra formula is created by pressing
13291 twice instead of once because \SpecialChar LyX
13292 doesn't yet support
13306 \begin_inset Separator parbreak
13312 \begin_layout Standard
13314 \begin_inset Tabular
13315 <lyxtabular version="3" rows="4" columns="2">
13316 <features booktabs="true" tabularvalignment="middle">
13317 <column alignment="center" valignment="top" width="0pt">
13318 <column alignment="center" valignment="top">
13320 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
13323 \begin_layout Plain Layout
13329 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
13332 \begin_layout Plain Layout
13340 <cell alignment="center" valignment="top" leftline="true" usebox="none">
13343 \begin_layout Plain Layout
13347 \begin_inset Formula $\to$
13353 \begin_inset Formula $\to$
13361 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
13364 \begin_layout Plain Layout
13365 \begin_inset Formula $H\raisebox{2mm}{al}lo$
13375 <cell alignment="center" valignment="top" leftline="true" usebox="none">
13378 \begin_layout Plain Layout
13382 \begin_inset Formula $\to$
13388 \begin_inset Formula $\to$
13396 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
13399 \begin_layout Plain Layout
13400 \begin_inset Formula $H\raisebox{-2mm}{al}lo$
13410 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
13413 \begin_layout Plain Layout
13417 \begin_inset Formula $\to$
13433 \begin_inset space \textvisiblespace{}
13441 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
13444 \begin_layout Plain Layout
13445 \begin_inset Formula $A=\raisebox{-2mm}{\mbox{\ensuremath{\sqrt{B}}}}$
13461 \begin_layout Standard
13486 , with the difference that there is no frame.
13489 \begin_layout Subsection
13491 \begin_inset CommandInset label
13493 name "subsec:Colored-Boxes"
13498 \begin_inset Index idx
13501 \begin_layout Plain Layout
13510 \begin_layout Standard
13511 To be able to use all commands explained in this section, the \SpecialChar LaTeX
13520 \begin_layout Plain Layout
13521 The \SpecialChar LaTeX
13526 is part of every \SpecialChar LaTeX
13527 standard installation.
13533 \begin_inset Index idx
13536 \begin_layout Plain Layout
13542 has to be loaded in the \SpecialChar LaTeX
13543 -preamble with the line
13547 \begin_layout Plain Layout
13548 When text is colored somewhere in the document with a predefined color,
13550 loads the \SpecialChar LaTeX
13556 Thus it is possible that the package is loaded twice, but this does not
13563 \begin_inset Note Note
13566 \begin_layout Plain Layout
13567 To avoid that the package is loaded twice, a macro was inserted to the \SpecialChar LaTeX
13576 \begin_layout Standard
13584 \begin_layout Standard
13585 \begin_inset VSpace medskip
13588 To color boxes, the command
13595 \begin_inset Index idx
13598 \begin_layout Plain Layout
13606 is used in the following scheme:
13609 \begin_layout Standard
13614 colorbox{color}{box content}
13617 \begin_layout Standard
13618 The box content can also be a box and a
13624 can also be part of another box (see the 2nd and 3rd example).
13625 When the box should contain a formula, an extra formula has to be created,
13626 the same way as for
13636 \begin_layout Plain Layout
13637 This also applies for the command
13651 \begin_layout Standard
13652 One of the following predefined colors can be chosen:
13655 \begin_layout Standard
13689 \begin_inset Separator parbreak
13695 \begin_layout Standard
13697 \begin_inset Tabular
13698 <lyxtabular version="3" rows="4" columns="2">
13699 <features booktabs="true" tabularvalignment="middle">
13700 <column alignment="center" valignment="top" width="0pt">
13701 <column alignment="center" valignment="top">
13703 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
13706 \begin_layout Plain Layout
13712 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
13715 \begin_layout Plain Layout
13723 <cell alignment="center" valignment="top" leftline="true" usebox="none">
13726 \begin_layout Plain Layout
13730 \begin_inset Formula $\to$
13740 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
13743 \begin_layout Plain Layout
13744 \begin_inset Formula $\colorbox{yellow}{A=B}$
13753 <row topspace="1.5mm">
13754 <cell alignment="center" valignment="top" usebox="none">
13757 \begin_layout Plain Layout
13761 \begin_inset Formula $\to$
13769 \begin_inset space \textvisiblespace{}
13777 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
13780 \begin_layout Plain Layout
13781 \begin_inset Formula $\colorbox{green}{\fbox{A=B}}$
13790 <row topspace="1.5mm" bottomspace="1mm">
13791 <cell alignment="center" valignment="top" bottomline="true" usebox="none">
13794 \begin_layout Plain Layout
13798 \begin_inset space \textvisiblespace{}
13804 \begin_inset Formula $\to$
13820 \begin_inset space \textvisiblespace{}
13828 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
13831 \begin_layout Plain Layout
13832 \begin_inset Formula $\fbox{\colorbox{green}{\mbox{\ensuremath{\int C=D}}}}$
13848 \begin_layout Standard
13855 only colors the box but not the characters in the box.
13856 To color all characters, the whole formula is highlighted and the desired
13857 color is chosen in the
13860 \begin_inset space ~
13866 The dialog can be called with the toolbar button
13869 arg "dialog-show character"
13874 Edit\SpecialChar menuseparator
13876 \begin_inset space ~
13879 Style\SpecialChar menuseparator
13883 The formula number then has the same color as the formula.
13884 When the formula number should get another color than the formula characters,
13885 the color must be changed within the formula.
13888 \begin_layout Standard
13892 \begin_layout Standard
13895 \begin_inset Formula
13897 \int A=B\label{eq:red}
13905 \begin_inset Formula
13907 \textcolor{red}{\int A=B}\label{eq:redgreen}
13915 \begin_layout Standard
13917 \begin_inset CommandInset ref
13923 is completely colored red.
13924 \begin_inset Newline newline
13928 \begin_inset CommandInset ref
13930 reference "eq:redgreen"
13934 was first completely colored green to set the color for the formula number.
13935 Subsequently the formula characters were colored red.
13938 \begin_layout Standard
13939 \begin_inset VSpace bigskip
13942 To color the frame different than the rest of the box, the command
13949 \begin_inset Index idx
13952 \begin_layout Plain Layout
13960 is used in the following scheme:
13963 \begin_layout Standard
13968 fcolorbox{frame color}{color}{box content}
13971 \begin_layout Standard
13978 is an extension of the command
13985 The frame width is set, like for
14008 \begin_layout Plain Layout
14020 \begin_inset Formula
14022 \fcolorbox{cyan}{magenta}{A=B}
14031 \begin_layout Plain Layout
14045 \begin_layout Standard
14046 This formula was created with the command
14047 \begin_inset Newline newline
14055 \begin_inset Formula $\to$
14061 \begin_inset Formula $\to$
14071 \begin_layout Standard
14072 \begin_inset VSpace bigskip
14075 To use other colors than the predefined ones, they have to be defined first.
14078 \begin_layout Standard
14079 One can for example define the color
14080 \begin_inset Quotes eld
14088 \begin_inset Quotes erd
14091 with the \SpecialChar LaTeX
14095 \begin_layout Standard
14100 definecolor{darkgreen}{cmyk}{0.5,
14115 \begin_inset Index idx
14118 \begin_layout Plain Layout
14129 \begin_layout Standard
14134 is the color space that denotes the colors
14151 The four comma separated numbers are the portion factor for the corresponding
14152 colors of the color space.
14153 The factors can be in the range of 0
14154 \begin_inset space \thinspace{}
14158 \begin_inset space \thinspace{}
14166 also the color space
14170 can be used for definitions.
14187 , so that there are in this case three portion factors for the corresponding
14189 Furthermore there is the color space
14193 with one portion factor for the gray value.
14196 \begin_layout Standard
14197 As example a framed box with the new defined color
14201 where the characters have been colored
14206 \begin_inset Formula
14208 \colorbox{darkgreen}{\color{yellow}\boxed{\int A\,\mathrm{d}x=\frac{\sqrt[5]{B}}{\ln\left(\frac{1}{3}\right)}}}
14216 \begin_layout Standard
14217 Self-defined colors can also be used for text with the help of the command
14225 \begin_inset Index idx
14228 \begin_layout Plain Layout
14237 \begin_layout Standard
14241 \begin_layout Plain Layout
14245 textcolor{darkgreen}{
14251 \begin_inset Quotes eld
14255 \begin_inset Quotes erd
14262 \begin_layout Plain Layout
14272 \begin_layout Standard
14280 \begin_inset Index idx
14283 \begin_layout Plain Layout
14291 is used in the scheme
14295 textcolor{color}{characters to color}
14300 \begin_layout Subsection
14302 \begin_inset CommandInset label
14304 name "subsec:Paragraph-Boxes"
14309 \begin_inset Index idx
14312 \begin_layout Plain Layout
14313 Boxes ! as paragraph
14321 \begin_layout Standard
14322 A box that can contain several lines and paragraphs, a so-called paragraph
14323 box (parbox), can be created with the menu
14325 Insert\SpecialChar menuseparator
14328 or the toolbar button
14337 \begin_layout Standard
14338 The following example shows a framed parbox in a line:
14341 \begin_layout Standard
14342 \begin_inset VSpace medskip
14346 \begin_inset Box Boxed
14356 height_special "totalheight"
14361 backgroundcolor "none"
14364 \begin_layout Plain Layout
14365 This is a paragraph box.
14367 \begin_inset space \thinspace{}
14370 cm long and can also contain formulas:
14371 \begin_inset Formula $\int A\,\mathrm{d}s=C$
14382 \begin_layout Standard
14383 \begin_inset VSpace medskip
14389 \begin_layout Standard
14390 Such a box is created by right-clicking on the gray box inset.
14391 A dialog pops up showing the box properties.
14405 \begin_inset space \thinspace{}
14410 Vertical Box Alignment
14415 \begin_layout Standard
14416 \begin_inset VSpace medskip
14419 In \SpecialChar LaTeX
14420 a parbox is created with the command
14427 \begin_inset Index idx
14430 \begin_layout Plain Layout
14438 which has the following scheme:
14441 \begin_layout Standard
14446 parbox[position]{width}{box content}
14449 \begin_layout Standard
14464 \begin_inset Quotes eld
14468 \begin_inset Quotes erd
14471 means that the box is aligned within the surrounding text with its last
14478 \begin_inset Quotes eld
14482 \begin_inset Quotes erd
14485 this is done with the first line.
14486 When no position is given, the box will be vertically centered, see section
14494 \begin_inset space ~
14499 manual for examples.
14502 \begin_layout Standard
14503 \begin_inset VSpace bigskip
14506 To frame formulas completely, including the formula number, the formula
14507 must be set into a parbox.
14508 To do this, the command
14522 is inserted in \SpecialChar TeX
14523 mode before the formula.
14531 \begin_inset Index idx
14534 \begin_layout Plain Layout
14542 is hereby the line width set for the document.
14543 Because the frame is outside the parbox, 2
14544 \begin_inset space \thinspace{}
14547 times the frame separation and the frame thickness must be subtracted from
14549 To be able to multiply and subtract in arguments, the \SpecialChar LaTeX
14558 \begin_layout Plain Layout
14563 is part of every \SpecialChar LaTeX
14564 standard installation.
14570 \begin_inset Index idx
14573 \begin_layout Plain Layout
14579 must be loaded in the \SpecialChar LaTeX
14580 -preamble with the line
14583 \begin_layout Standard
14591 \begin_layout Standard
14592 Behind the formula both boxes are closed by entering
14596 in \SpecialChar TeX
14598 Here is an example:
14602 \begin_layout Plain Layout
14616 \begin_layout Standard
14620 \begin_layout Plain Layout
14638 \begin_inset Formula
14640 \int A\,\mathrm{d}x=\frac{\sqrt[5]{B}}{\ln\left(\frac{1}{3}\right)}
14649 \begin_layout Plain Layout
14660 \begin_layout Plain Layout
14674 \begin_layout Standard
14675 \begin_inset VSpace medskip
14678 As a parbox is used as the argument of
14684 , there is in this case no difference between
14699 \begin_layout Standard
14700 \begin_inset VSpace bigskip
14703 Paragraph boxes are very useful to comment formulas directly.
14710 is used in combination with the command
14724 \begin_inset CommandInset ref
14726 reference "subsec:User-defined-Numbering"
14733 \begin_layout Standard
14734 An example of a formula commented with
14743 \begin_layout Standard
14747 \begin_layout Plain Layout
14760 This is a description.
14761 It is distinctly separated from the formula and multiline.
14765 \begin_layout Plain Layout
14777 \begin_layout Standard
14778 Such a formula must be inserted completely in \SpecialChar TeX
14779 mode because \SpecialChar LyX
14781 support the command
14788 The formula is created with the following command sequence:
14791 \begin_layout Standard
14804 is inserted in \SpecialChar TeX
14809 \begin_layout Plain Layout
14810 When the formula style
14822 can also be replaced by
14829 (formula styles see
14830 \begin_inset CommandInset ref
14832 reference "sec:Formula-Styles"
14841 Then the description follows as normal text and finally
14847 is inserted in \SpecialChar TeX
14861 hereby create a displayed formula.
14864 \begin_layout Standard
14871 can be seen in this example that was
14872 \begin_inset Quotes eld
14876 \begin_inset Quotes erd
14879 using the mathematical textmode:
14880 \begin_inset Formula
14882 5x-7b=3b\textrm{This is a description. It is not separated from the formula ...}
14890 \begin_layout Section
14892 \begin_inset Index idx
14895 \begin_layout Plain Layout
14904 \begin_layout Subsection
14906 \begin_inset CommandInset label
14908 name "subsec:Big-Operators"
14913 \begin_inset Index idx
14916 \begin_layout Plain Layout
14923 \begin_inset Index idx
14926 \begin_layout Plain Layout
14933 \begin_inset Index idx
14936 \begin_layout Plain Layout
14945 \begin_layout Standard
14946 To be able to use all integral operators listed here, the option
14948 Use esint package automatically
14950 must be set in the document settings under
14953 \begin_inset space ~
14961 \begin_layout Standard
14962 \begin_inset space \hfill{}
14966 \begin_inset Tabular
14967 <lyxtabular version="3" rows="11" columns="2">
14968 <features booktabs="true" tabularvalignment="middle">
14969 <column alignment="center" valignment="top" width="0pt">
14970 <column alignment="center" valignment="top" width="0pt">
14972 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
14975 \begin_layout Plain Layout
14981 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
14984 \begin_layout Plain Layout
14992 <cell alignment="center" valignment="top" leftline="true" usebox="none">
14995 \begin_layout Plain Layout
14999 \begin_inset Index idx
15002 \begin_layout Plain Layout
15015 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
15018 \begin_layout Plain Layout
15019 \begin_inset Formula $\int$
15029 <cell alignment="center" valignment="top" leftline="true" usebox="none">
15032 \begin_layout Plain Layout
15040 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
15043 \begin_layout Plain Layout
15044 \begin_inset Formula $\oint$
15054 <cell alignment="center" valignment="top" leftline="true" usebox="none">
15057 \begin_layout Plain Layout
15065 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
15068 \begin_layout Plain Layout
15069 \begin_inset Formula $\ointctrclockwise$
15079 <cell alignment="center" valignment="top" leftline="true" usebox="none">
15082 \begin_layout Plain Layout
15090 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
15093 \begin_layout Plain Layout
15094 \begin_inset Formula $\ointclockwise$
15104 <cell alignment="center" valignment="top" leftline="true" usebox="none">
15107 \begin_layout Plain Layout
15115 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
15118 \begin_layout Plain Layout
15119 \begin_inset Formula $\sqint$
15129 <cell alignment="center" valignment="top" leftline="true" usebox="none">
15132 \begin_layout Plain Layout
15140 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
15143 \begin_layout Plain Layout
15145 \begin_inset Formula $\fint$
15155 <cell alignment="center" valignment="top" leftline="true" usebox="none">
15158 \begin_layout Plain Layout
15166 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
15169 \begin_layout Plain Layout
15171 \begin_inset Formula $\landupint$
15181 <cell alignment="center" valignment="top" leftline="true" usebox="none">
15184 \begin_layout Plain Layout
15192 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
15195 \begin_layout Plain Layout
15197 \begin_inset Formula $\landdownint$
15207 <cell alignment="center" valignment="top" leftline="true" usebox="none">
15210 \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 $\bigcap$
15232 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
15235 \begin_layout Plain Layout
15243 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
15246 \begin_layout Plain Layout
15247 \begin_inset Formula $\bigcup$
15261 \begin_inset space \hfill{}
15265 \begin_inset Tabular
15266 <lyxtabular version="3" rows="11" columns="2">
15267 <features booktabs="true" tabularvalignment="middle">
15268 <column alignment="center" valignment="top" width="0pt">
15269 <column alignment="center" valignment="top" width="0pt">
15271 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
15274 \begin_layout Plain Layout
15280 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
15283 \begin_layout Plain Layout
15291 <cell alignment="center" valignment="top" leftline="true" usebox="none">
15294 \begin_layout Plain Layout
15298 \begin_inset Index idx
15301 \begin_layout Plain Layout
15314 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
15317 \begin_layout Plain Layout
15318 \begin_inset Formula $\sum$
15328 <cell alignment="center" valignment="top" leftline="true" usebox="none">
15331 \begin_layout Plain Layout
15335 \begin_inset Index idx
15338 \begin_layout Plain Layout
15345 \begin_layout Plain Layout
15364 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
15367 \begin_layout Plain Layout
15368 \begin_inset Formula $\prod$
15378 <cell alignment="center" valignment="top" leftline="true" usebox="none">
15381 \begin_layout Plain Layout
15389 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
15392 \begin_layout Plain Layout
15393 \begin_inset Formula $\coprod$
15403 <cell alignment="center" valignment="top" leftline="true" usebox="none">
15406 \begin_layout Plain Layout
15414 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
15417 \begin_layout Plain Layout
15418 \begin_inset Formula $\bigodot$
15428 <cell alignment="center" valignment="top" leftline="true" usebox="none">
15431 \begin_layout Plain Layout
15439 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
15442 \begin_layout Plain Layout
15443 \begin_inset Formula $\bigotimes$
15453 <cell alignment="center" valignment="top" leftline="true" usebox="none">
15456 \begin_layout Plain Layout
15464 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
15467 \begin_layout Plain Layout
15468 \begin_inset Formula $\bigoplus$
15478 <cell alignment="center" valignment="top" leftline="true" usebox="none">
15481 \begin_layout Plain Layout
15489 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
15492 \begin_layout Plain Layout
15493 \begin_inset Formula $\bigwedge$
15503 <cell alignment="center" valignment="top" leftline="true" usebox="none">
15506 \begin_layout Plain Layout
15514 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
15517 \begin_layout Plain Layout
15518 \begin_inset Formula $\bigvee$
15528 <cell alignment="center" valignment="top" leftline="true" usebox="none">
15531 \begin_layout Plain Layout
15539 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
15542 \begin_layout Plain Layout
15543 \begin_inset Formula $\bigsqcup$
15553 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
15556 \begin_layout Plain Layout
15564 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
15567 \begin_layout Plain Layout
15568 \begin_inset Formula $\biguplus$
15582 \begin_inset space \hfill{}
15588 \begin_layout Standard
15589 All big operators can also be inserted via the math toolbar button
15592 arg "math-insert \\intop"
15598 \begin_layout Standard
15599 The operators are called big because they are bigger than the sometimes
15600 equal looking binary operators.
15601 All big operators can have limits as described in the next subsection.
15604 \begin_layout Standard
15605 For all integral operators there is a second version available, ending in
15623 These operators are different from
15630 \begin_inset space \space{}
15633 in the style the operator limits are displayed, see
15634 \begin_inset CommandInset ref
15636 reference "subsec:Operator-Limits"
15644 \begin_layout Subsubsection*
15645 Advice for Integrals
15648 \begin_layout Standard
15653 in an integral is an operator, that therefore has to be set upright.
15654 This is done by highlighting the
15658 and using the keyboard shortcut
15668 \begin_layout Plain Layout
15674 \begin_inset CommandInset ref
15676 reference "subsec:Font-Styles"
15686 Finally the smallest space is inserted before the
15690 , as this is usual for operators.
15694 \begin_layout Standard
15696 \begin_inset Formula $\int A(x)dx$
15700 \begin_inset Newline newline
15704 \begin_inset Phantom HPhantom
15707 \begin_layout Plain Layout
15714 \begin_inset Formula $\int A(x)\,\mathrm{d}x$
15720 \begin_layout Standard
15721 For multiple integrals there are the following commands:
15722 \begin_inset VSpace medskip
15728 \begin_layout Standard
15729 \begin_inset space \hfill{}
15733 \begin_inset Tabular
15734 <lyxtabular version="3" rows="4" columns="2">
15735 <features booktabs="true" tabularvalignment="middle">
15736 <column alignment="center" valignment="top" width="0pt">
15737 <column alignment="center" valignment="top" width="0pt">
15739 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
15742 \begin_layout Plain Layout
15748 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
15751 \begin_layout Plain Layout
15758 <row bottomspace="1mm">
15759 <cell alignment="center" valignment="top" usebox="none">
15762 \begin_layout Plain Layout
15770 <cell alignment="center" valignment="top" usebox="none">
15773 \begin_layout Plain Layout
15774 \begin_inset Formula $\iint$
15783 <row bottomspace="1mm">
15784 <cell alignment="center" valignment="top" usebox="none">
15787 \begin_layout Plain Layout
15795 <cell alignment="center" valignment="top" usebox="none">
15798 \begin_layout Plain Layout
15799 \begin_inset Formula $\oiint$
15808 <row bottomspace="1mm">
15809 <cell alignment="center" valignment="top" bottomline="true" usebox="none">
15812 \begin_layout Plain Layout
15820 <cell alignment="center" valignment="top" bottomline="true" usebox="none">
15823 \begin_layout Plain Layout
15824 \begin_inset Formula $\sqiint$
15838 \begin_inset space \hfill{}
15842 \begin_inset Tabular
15843 <lyxtabular version="3" rows="4" columns="2">
15844 <features booktabs="true" tabularvalignment="middle">
15845 <column alignment="center" valignment="top" width="0pt">
15846 <column alignment="center" valignment="top" width="0pt">
15848 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
15851 \begin_layout Plain Layout
15857 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
15860 \begin_layout Plain Layout
15867 <row bottomspace="1mm">
15868 <cell alignment="center" valignment="top" usebox="none">
15871 \begin_layout Plain Layout
15879 <cell alignment="center" valignment="top" usebox="none">
15882 \begin_layout Plain Layout
15883 \begin_inset Formula $\iiint$
15892 <row bottomspace="1mm">
15893 <cell alignment="center" valignment="top" usebox="none">
15896 \begin_layout Plain Layout
15904 <cell alignment="center" valignment="top" usebox="none">
15907 \begin_layout Plain Layout
15908 \begin_inset Formula $\iiiint$
15917 <row bottomspace="1mm">
15918 <cell alignment="center" valignment="top" bottomline="true" usebox="none">
15921 \begin_layout Plain Layout
15929 <cell alignment="center" valignment="top" bottomline="true" usebox="none">
15932 \begin_layout Plain Layout
15933 \begin_inset Formula $\dotsint$
15947 \begin_inset space \hfill{}
15953 \begin_layout Subsection
15955 \begin_inset CommandInset label
15957 name "subsec:Operator-Limits"
15962 \begin_inset Index idx
15965 \begin_layout Plain Layout
15974 \begin_layout Standard
15975 Limits are created by super- and subscripts:
15976 \begin_inset Separator parbreak
15982 \begin_layout Standard
15984 \begin_inset Tabular
15985 <lyxtabular version="3" rows="2" columns="2">
15986 <features booktabs="true" tabularvalignment="middle">
15987 <column alignment="center" valignment="top" width="0pt">
15988 <column alignment="center" valignment="top" width="0pt">
15990 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
15993 \begin_layout Plain Layout
15999 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
16002 \begin_layout Plain Layout
16010 <cell alignment="center" valignment="top" bottomline="true" usebox="none">
16013 \begin_layout Plain Layout
16019 \begin_inset space \textvisiblespace{}
16023 \begin_inset Formula $\to$
16027 \begin_inset Formula $\to$
16035 <cell alignment="center" valignment="top" bottomline="true" usebox="none">
16038 \begin_layout Plain Layout
16039 \begin_inset Formula $\prod_{0}^{\infty}A(x)$
16055 \begin_layout Standard
16056 Limits of inline formulas are set right beside the operator.
16057 Limits in displayed formulas are set above or below the operator, except
16058 for integral limits.
16061 \begin_layout Standard
16062 To force that the limits are set beside the operator, the cursor is set
16063 directly behind the operator and the limits type is changed with the menu
16066 Edit\SpecialChar menuseparator
16067 Math\SpecialChar menuseparator
16086 \begin_layout Standard
16087 The default limits type is this:
16088 \begin_inset Formula
16090 \sum_{x=0}^{\infty}\frac{1}{x^{2}}
16095 This is how it looks when the limits type was changed to
16102 \begin_inset Formula
16104 \sum\nolimits _{x=0}^{\infty}\frac{1}{x^{2}}
16109 For integrals, except those ending with
16125 etc., the limits are by default set beside the operator.
16126 But for multiple integrals the limits are often set below the operator.
16127 In the following example the limits type was therefore set to
16131 and so set below the integrals:
16132 \begin_inset Formula
16134 \iiint\limits _{V}X\,\mathrm{d}V=U\label{eq:VolInt}
16142 \begin_layout Standard
16143 \begin_inset VSpace medskip
16146 To specify conditions for limits, the commands
16153 \begin_inset Index idx
16156 \begin_layout Plain Layout
16171 \begin_inset Index idx
16174 \begin_layout Plain Layout
16183 To create for example this expression
16184 \begin_inset Formula
16186 \sum_{\begin{subarray}{c}
16190 \end{subarray}}^{n}k^{-2}\label{eq:substack}
16198 \begin_layout Standard
16199 the following has to be done:
16200 \begin_inset Newline newline
16212 \begin_inset space \textvisiblespace{}
16218 One is now in a blue box under the summation operator and insert there
16224 \begin_inset space \textvisiblespace{}
16230 The blue box is now within a purple box and now several lines can be written
16232 A new line is created by inserting a line break (
16235 arg "newline-insert newline"
16240 \begin_inset Newline newline
16245 0<k<1000 Ctrl+Return
16246 \begin_inset Newline newline
16251 is typed in, a new box appears below for the new line.
16254 \begin_layout Standard
16255 The alignment of the lines can be changed to left aligned with the
16265 Edit\SpecialChar menuseparator
16269 To get right alignment,
16274 \begin_inset space \textvisiblespace{}
16279 is inserted at the beginning of the line.
16282 \begin_layout Standard
16295 with the difference that the lines are always centered.
16298 \begin_layout Standard
16299 \begin_inset VSpace bigskip
16303 \begin_inset CommandInset ref
16305 reference "eq:substack"
16309 there can be too much space beside an operator, because the characters
16310 following the operator are set beside the limits.
16311 To avoid this the command
16318 \begin_inset Index idx
16321 \begin_layout Plain Layout
16330 To activate it, set in the document settings under
16333 \begin_inset space ~
16343 \begin_inset Index idx
16346 \begin_layout Plain Layout
16347 Packages ! mathtools
16355 \begin_inset space ~
16367 sets the space besides the operator to 0
16368 \begin_inset space \thinspace{}
16372 \begin_inset Newline newline
16376 \begin_inset CommandInset ref
16378 reference "eq:substack"
16382 , one uses the command
16385 \begin_layout Standard
16393 \begin_layout Standard
16394 and inserts the operator with its limits into the braces.
16395 Behind the brace one continues the formula:
16396 \begin_inset Formula
16398 \smashoperator{\sum_{\begin{subarray}{c}
16402 \end{subarray}}^{n}}k^{-2}
16410 \begin_layout Standard
16411 It is possible to set the space of only one side of the operator to 0
16412 \begin_inset space \thinspace{}
16416 To do this write either
16435 stands for the left and
16439 for the right side of the operator.
16440 Here is an example of the possible
16449 \begin_layout Standard
16450 \begin_inset Formula
16452 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}
16460 \begin_layout Standard
16461 \begin_inset VSpace bigskip
16467 \begin_layout Standard
16468 When several consecutive operators have limits the typesetting of the limits
16469 looks often imperfect in the output, see this example:
16470 \begin_inset Formula
16472 \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}
16477 To improve the typesetting set in the document settings under
16480 \begin_inset space ~
16490 \begin_inset Index idx
16493 \begin_layout Plain Layout
16494 Packages ! mathtools
16502 \begin_inset space ~
16508 Then insert into your formula the command
16515 \begin_inset Index idx
16518 \begin_layout Plain Layout
16526 directly before the first operator.
16527 The example will then look like this:
16528 \begin_inset Formula
16530 \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}
16538 \begin_layout Standard
16539 \begin_inset VSpace bigskip
16542 How to use one limit for several operators is described in
16543 \begin_inset CommandInset ref
16545 reference "subsec:Self-defined-Operators"
16552 \begin_layout Subsection
16553 Decoration for Operators
16554 \begin_inset Index idx
16557 \begin_layout Plain Layout
16558 Operators ! Decoration
16566 \begin_layout Standard
16574 \begin_inset Index idx
16577 \begin_layout Plain Layout
16592 \begin_inset Index idx
16595 \begin_layout Plain Layout
16603 characters can be placed above or below an operator, respectively.
16611 \begin_inset Index idx
16614 \begin_layout Plain Layout
16622 characters can be set before and behind a big operator.
16625 \begin_layout Standard
16627 \begin_inset space ~
16639 \begin_layout Itemize
16646 is used to set characters at the corners of the operator
16649 \begin_layout Itemize
16656 is used to set characters before and/or behind the operator (this variant
16657 represents \SpecialChar LaTeX
16667 \begin_layout Itemize
16674 is used to set characters at the left corners and/or behind the operator
16677 \begin_layout Itemize
16684 is used to set characters at the right corners and/or before the operator
16687 \begin_layout Standard
16688 For example the command
16693 \begin_inset space \textvisiblespace{}
16699 \begin_inset space \textvisiblespace{}
16703 \begin_inset Formula $\to$
16707 \begin_inset Formula $\to$
16711 \begin_inset space \textvisiblespace{}
16721 \begin_inset Formula
16723 \sideset{}{'}\sum_{k=1}^{n}
16731 \begin_layout Standard
16732 \begin_inset Note Greyedout
16735 \begin_layout Plain Layout
16742 can only be used to decorate big operators, binary operators are not allowed.
16750 \begin_layout Standard
16763 can also be used to decorate symbols and characters.
16764 For example, the command
16769 \begin_inset space \textvisiblespace{}
16775 \begin_inset space \textvisiblespace{}
16781 \begin_inset Formula $\uparrow$
16789 \begin_inset Formula
16791 \overset{a}{\maltese}
16799 \begin_layout Subsection
16801 \begin_inset CommandInset label
16803 name "subsec:Binary-Operators"
16808 \begin_inset Index idx
16811 \begin_layout Plain Layout
16820 \begin_layout Standard
16821 Binary operators are surrounded by space when there is a character before
16823 \begin_inset VSpace medskip
16829 \begin_layout Standard
16830 \begin_inset Tabular
16831 <lyxtabular version="3" rows="13" columns="2">
16832 <features booktabs="true" tabularvalignment="middle">
16833 <column alignment="center" valignment="top" width="0pt">
16834 <column alignment="center" valignment="top" width="0pt">
16836 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
16839 \begin_layout Plain Layout
16841 \begin_inset Note Note
16844 \begin_layout Plain Layout
16851 is only used as spacer.
16861 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
16864 \begin_layout Plain Layout
16872 <cell alignment="center" valignment="top" leftline="true" usebox="none">
16875 \begin_layout Plain Layout
16881 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
16884 \begin_layout Plain Layout
16885 \begin_inset Formula $+$
16895 <cell alignment="center" valignment="top" leftline="true" usebox="none">
16898 \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 $-$
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 $\pm$
16943 <cell alignment="center" valignment="top" leftline="true" usebox="none">
16946 \begin_layout Plain Layout
16954 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
16957 \begin_layout Plain Layout
16958 \begin_inset Formula $\mp$
16968 <cell alignment="center" valignment="top" leftline="true" usebox="none">
16971 \begin_layout Plain Layout
16979 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
16982 \begin_layout Plain Layout
16983 \begin_inset Formula $\cdot$
16993 <cell alignment="center" valignment="top" leftline="true" usebox="none">
16996 \begin_layout Plain Layout
17004 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
17007 \begin_layout Plain Layout
17008 \begin_inset Formula $\times$
17018 <cell alignment="center" valignment="top" leftline="true" usebox="none">
17021 \begin_layout Plain Layout
17029 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
17032 \begin_layout Plain Layout
17033 \begin_inset Formula $\div$
17043 <cell alignment="center" valignment="top" leftline="true" usebox="none">
17046 \begin_layout Plain Layout
17050 \begin_layout Plain Layout
17063 \begin_layout Plain Layout
17075 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
17078 \begin_layout Plain Layout
17079 \begin_inset Formula $*$
17089 <cell alignment="center" valignment="top" leftline="true" usebox="none">
17092 \begin_layout Plain Layout
17100 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
17103 \begin_layout Plain Layout
17104 \begin_inset Formula $\star$
17114 <cell alignment="center" valignment="top" leftline="true" usebox="none">
17117 \begin_layout Plain Layout
17125 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
17128 \begin_layout Plain Layout
17129 \begin_inset Formula $\circ$
17139 <cell alignment="center" valignment="top" leftline="true" usebox="none">
17142 \begin_layout Plain Layout
17150 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
17153 \begin_layout Plain Layout
17154 \begin_inset Formula $\diamond$
17164 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
17167 \begin_layout Plain Layout
17175 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
17178 \begin_layout Plain Layout
17179 \begin_inset Formula $\bullet$
17193 \begin_inset space \hfill{}
17197 \begin_inset Tabular
17198 <lyxtabular version="3" rows="13" columns="2">
17199 <features booktabs="true" tabularvalignment="middle">
17200 <column alignment="center" valignment="top" width="0pt">
17201 <column alignment="center" valignment="top" width="0pt">
17203 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
17206 \begin_layout Plain Layout
17212 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
17215 \begin_layout Plain Layout
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 $\nabla$
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 $\bigtriangledown$
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 $\bigtriangleup$
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 $\Box$
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 $\cap$
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 $\cup$
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 $\dagger$
17398 <cell alignment="center" valignment="top" leftline="true" usebox="none">
17401 \begin_layout Plain Layout
17409 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
17412 \begin_layout Plain Layout
17413 \begin_inset Formula $\ddagger$
17423 <cell alignment="center" valignment="top" leftline="true" usebox="none">
17426 \begin_layout Plain Layout
17434 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
17437 \begin_layout Plain Layout
17438 \begin_inset Formula $\wr$
17448 <cell alignment="center" valignment="top" leftline="true" usebox="none">
17451 \begin_layout Plain Layout
17459 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
17462 \begin_layout Plain Layout
17463 \begin_inset Formula $\bigcirc$
17473 <cell alignment="center" valignment="top" leftline="true" usebox="none">
17476 \begin_layout Plain Layout
17484 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
17487 \begin_layout Plain Layout
17488 \begin_inset Formula $\wedge$
17498 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
17501 \begin_layout Plain Layout
17509 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
17512 \begin_layout Plain Layout
17513 \begin_inset Formula $\vee$
17527 \begin_inset space \hfill{}
17531 \begin_inset Tabular
17532 <lyxtabular version="3" rows="13" columns="2">
17533 <features booktabs="true" tabularvalignment="middle">
17534 <column alignment="center" valignment="top" width="0pt">
17535 <column alignment="center" valignment="top" width="0pt">
17537 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
17540 \begin_layout Plain Layout
17546 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
17549 \begin_layout Plain Layout
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 $\oplus$
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 $\ominus$
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 $\otimes$
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 $\oslash$
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 $\odot$
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 $\amalg$
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 $\uplus$
17732 <cell alignment="center" valignment="top" leftline="true" usebox="none">
17735 \begin_layout Plain Layout
17743 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
17746 \begin_layout Plain Layout
17747 \begin_inset Formula $\setminus$
17757 <cell alignment="center" valignment="top" leftline="true" usebox="none">
17760 \begin_layout Plain Layout
17768 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
17771 \begin_layout Plain Layout
17772 \begin_inset Formula $\sqcap$
17782 <cell alignment="center" valignment="top" leftline="true" usebox="none">
17785 \begin_layout Plain Layout
17793 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
17796 \begin_layout Plain Layout
17797 \begin_inset Formula $\sqcup$
17807 <cell alignment="center" valignment="top" leftline="true" usebox="none">
17810 \begin_layout Plain Layout
17818 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
17821 \begin_layout Plain Layout
17822 \begin_inset Formula $\triangleleft$
17832 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
17835 \begin_layout Plain Layout
17843 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
17846 \begin_layout Plain Layout
17847 \begin_inset Formula $\triangleright$
17863 \begin_layout Standard
17864 All binary operators can also be inserted via the math toolbar button
17867 arg "math-insert \\pm"
17873 \begin_layout Standard
17874 To typeset the Laplace operator also
17891 \begin_inset Formula $\nabla^{2}$
17894 ) can be used instead of
17903 \begin_layout Standard
17910 Insert\SpecialChar menuseparator
17922 \begin_layout Subsection
17923 Self-defined Operators
17924 \begin_inset CommandInset label
17926 name "subsec:Self-defined-Operators"
17931 \begin_inset Index idx
17934 \begin_layout Plain Layout
17935 Operators ! self-defined
17943 \begin_layout Standard
17944 With the help of the command
17948 DeclareMathOperator
17951 \begin_inset Index idx
17954 \begin_layout Plain Layout
17959 DeclareMathOperator
17964 custom operators can be defined in the \SpecialChar LaTeX
17966 Its command scheme is:
17969 \begin_layout Standard
17974 DeclareMathOperator{new command}{display}
17977 \begin_layout Standard
17978 Display can be characters or symbols that define how the operator looks
17980 To define a big operator a * is set behind the command.
17981 All self-defined big operators can have limits as described in
17982 \begin_inset CommandInset ref
17984 reference "subsec:Operator-Limits"
17991 \begin_layout Standard
17992 For example the \SpecialChar LaTeX
17996 \begin_layout Standard
18001 DeclareMathOperator*{
18008 \begin_layout Standard
18009 defines the command
18015 , that inserts a big operator consisting of the lozenge symbol from
18016 \begin_inset CommandInset ref
18018 reference "subsec:Miscellaneous-Symbols"
18023 \begin_inset Formula
18025 \Lozenge_{n=1}^{\infty}
18030 The command for this formula is:
18041 \begin_inset Formula $\to$
18047 \begin_layout Standard
18048 \begin_inset VSpace bigskip
18051 When self-defined operators are not used several times in the document,
18052 they can also be defined with the commands
18059 \begin_inset Index idx
18062 \begin_layout Plain Layout
18077 \begin_inset Index idx
18080 \begin_layout Plain Layout
18088 , which have the following scheme:
18091 \begin_layout Standard
18105 \begin_layout Standard
18112 defines big operators,
18121 \begin_layout Standard
18129 \begin_inset space \thinspace{}
18133 \begin_inset space \space{}
18136 be used to use one limit for several operators:
18139 \begin_layout Standard
18140 \begin_inset Formula
18142 \mathop{\sum\negmedspace\sum}_{i,j=1}^{N}
18150 \begin_layout Standard
18151 The command for the formula above is:
18152 \begin_inset Newline newline
18168 \begin_inset space \textvisiblespace{}
18174 \begin_inset Formula $\to$
18180 \begin_inset space \textvisiblespace{}
18188 \begin_layout Section
18190 \begin_inset Index idx
18193 \begin_layout Plain Layout
18202 \begin_layout Subsection
18204 \begin_inset CommandInset label
18206 name "subsec:Font-Styles"
18211 \begin_inset Index idx
18214 \begin_layout Plain Layout
18223 \begin_layout Standard
18224 Latin letters in formulas can be set in one of the following font styles:
18227 \begin_layout Standard
18229 \begin_inset space \hfill{}
18233 \begin_inset Tabular
18234 <lyxtabular version="3" rows="6" columns="2">
18235 <features booktabs="true" tabularvalignment="middle">
18236 <column alignment="center" valignment="top" width="0pt">
18237 <column alignment="center" valignment="top">
18239 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
18242 \begin_layout Plain Layout
18248 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
18251 \begin_layout Plain Layout
18259 <cell alignment="center" valignment="top" leftline="true" usebox="none">
18262 \begin_layout Plain Layout
18268 \begin_inset space \textvisiblespace{}
18278 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
18281 \begin_layout Plain Layout
18282 \begin_inset Formula $\mathbb{ABC}$
18292 <cell alignment="center" valignment="top" leftline="true" usebox="none">
18295 \begin_layout Plain Layout
18301 \begin_inset space \textvisiblespace{}
18311 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
18314 \begin_layout Plain Layout
18315 \begin_inset Formula $\mathbf{AbC}$
18325 <cell alignment="center" valignment="top" leftline="true" usebox="none">
18328 \begin_layout Plain Layout
18334 \begin_inset space \textvisiblespace{}
18344 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
18347 \begin_layout Plain Layout
18348 \begin_inset Formula $\boldsymbol{AbC}$
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 $\mathcal{ABC}$
18391 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
18394 \begin_layout Plain Layout
18400 \begin_inset space \textvisiblespace{}
18410 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
18413 \begin_layout Plain Layout
18414 \begin_inset Formula $\mathfrak{AbC}$
18428 \begin_inset space \hfill{}
18432 \begin_inset Tabular
18433 <lyxtabular version="3" rows="6" columns="2">
18434 <features booktabs="true" tabularvalignment="middle">
18435 <column alignment="center" valignment="top" width="0pt">
18436 <column alignment="center" valignment="top">
18438 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
18441 \begin_layout Plain Layout
18447 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
18450 \begin_layout Plain Layout
18458 <cell alignment="center" valignment="top" leftline="true" usebox="none">
18461 \begin_layout Plain Layout
18467 \begin_inset space \textvisiblespace{}
18477 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
18480 \begin_layout Plain Layout
18481 \begin_inset Formula $\mathit{AbC}$
18491 <cell alignment="center" valignment="top" leftline="true" usebox="none">
18494 \begin_layout Plain Layout
18500 \begin_inset space \textvisiblespace{}
18510 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
18513 \begin_layout Plain Layout
18514 \begin_inset Formula $\mathrm{AbC}$
18524 <cell alignment="center" valignment="top" leftline="true" usebox="none">
18527 \begin_layout Plain Layout
18533 \begin_inset space \textvisiblespace{}
18543 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
18546 \begin_layout Plain Layout
18547 \begin_inset Formula $\mathsf{AbC}$
18557 <cell alignment="center" valignment="top" leftline="true" usebox="none">
18560 \begin_layout Plain Layout
18566 \begin_inset space \textvisiblespace{}
18576 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
18579 \begin_layout Plain Layout
18580 \begin_inset Formula $\mathtt{AbC}$
18590 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
18593 \begin_layout Plain Layout
18599 \begin_inset space \textvisiblespace{}
18609 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
18612 \begin_layout Plain Layout
18613 \begin_inset Formula $\mathscr{ABC}$
18627 \begin_inset space \hfill{}
18633 \begin_layout Standard
18634 \begin_inset Note Greyedout
18637 \begin_layout Plain Layout
18660 can only be used for big letters.
18668 \begin_layout Standard
18669 Predefined is the style
18678 \begin_layout Standard
18679 The style commands work also for letters in mathematical constructs:
18680 \begin_inset Formula
18682 \mathfrak{A=\frac{b}{C}}
18690 \begin_layout Standard
18691 Characters in mathematical text don't appear in a math font style but in
18692 the text font style
18699 That their style can't be set correctly via the text style dialog is a
18700 bug in \SpecialChar LyX
18705 \begin_layout Plain Layout
18706 \begin_inset CommandInset href
18708 name "LyX-bug #4629"
18709 target "http://www.lyx.org/trac/ticket/4629"
18721 \begin_layout Standard
18722 Instead of the style commands the dialog
18724 Edit\SpecialChar menuseparator
18725 Math\SpecialChar menuseparator
18728 or the toolbar button
18731 arg "math-insert \\font"
18737 \begin_layout Subsection
18739 \begin_inset CommandInset label
18741 name "subsec:Bold-Formulas"
18746 \begin_inset Index idx
18749 \begin_layout Plain Layout
18758 \begin_layout Standard
18759 To make a complete formula bold, the command
18765 from the previous subsection cannot be used, because it doesn't work for
18766 small Greek letters.
18767 Furthermore it prints Latin letters always upright, like in the following
18771 \begin_layout Standard
18772 \begin_inset Formula
18774 \mathbf{\int_{n}^{2}f(\theta)=\Gamma}\qquad\textrm{equation with \textbackslash mathbf}
18782 \begin_layout Standard
18783 To display the formula correctly, the command
18790 \begin_inset Formula
18792 \boldsymbol{\int_{n}^{2}f(\theta)=\Gamma\qquad\textrm{equation with \textbackslash boldsymbol}}
18797 It is also possible to set the formula in a
18799 boldmath environment
18802 This environment is created by inserting the command
18809 \begin_inset Index idx
18812 \begin_layout Plain Layout
18820 in \SpecialChar TeX
18822 To end the environment, the command
18829 \begin_inset Index idx
18832 \begin_layout Plain Layout
18840 is inserted in \SpecialChar TeX
18845 \begin_layout Plain Layout
18855 \begin_inset Formula
18857 \int_{n}^{2}f(\theta)=\Gamma\qquad\textrm{equation in a boldmath environment}
18866 \begin_layout Plain Layout
18878 \begin_layout Subsection
18880 \begin_inset Index idx
18883 \begin_layout Plain Layout
18892 \begin_layout Standard
18893 Formulas can be colored like normal text: Highlight a formula or a formula
18899 Here is a formula in magenta:
18900 \begin_inset Formula
18902 {\color{magenta}\int A\,\mathrm{d}x=\frac{\sqrt[5]{B}}{\ln\left(\frac{1}{3}\right)}}
18910 \begin_layout Standard
18911 You can also define your own colors as described in
18912 \begin_inset CommandInset ref
18914 reference "subsec:Colored-Boxes"
18919 They can be used with the \SpecialChar TeX
18927 \begin_inset Index idx
18930 \begin_layout Plain Layout
18941 \begin_layout Standard
18946 textcolor{color}{characters or formula}
18949 \begin_layout Standard
18950 The following example was colored completely dark green and partly red:
18953 \begin_layout Standard
18957 \begin_layout Plain Layout
18961 textcolor{darkgreen}{
18967 \begin_inset Formula
18969 \int A\,\mathrm{d}x=\frac{{\color{red}\sqrt[5]{B}}}{\ln\left(\frac{1}{3}\right)}
18978 \begin_layout Plain Layout
18988 \begin_layout Standard
18989 Due to a bug in \SpecialChar LyX
18990 only complete formulas can be colored with self-defined
18995 \begin_layout Plain Layout
18996 \begin_inset CommandInset href
18998 name "LyX-bug #5269"
18999 target "http://www.lyx.org/trac/ticket/5269"
19011 \begin_layout Subsection
19013 \begin_inset CommandInset label
19015 name "subsec:Font-Sizes"
19020 \begin_inset Index idx
19023 \begin_layout Plain Layout
19032 \begin_layout Standard
19033 For characters in formulas there are, analog to characters in text, the
19034 following size commands:
19037 \begin_layout Standard
19081 \begin_inset Newline newline
19103 \begin_layout Standard
19104 The size produced by the commands depends on the document font size, which
19105 corresponds to the command
19112 The other commands produce smaller or larger sizes than
19119 The font size can however not exceed a certain value.
19120 Is for example the document font size 12
19121 \begin_inset space \thinspace{}
19130 switches to the same size as
19140 \begin_layout Standard
19141 A size command is inserted in \SpecialChar TeX
19142 mode before the formula and sets the size
19143 for all following formula and text characters.
19144 To switch back to the initial size, the command
19150 is inserted behind the formula in \SpecialChar TeX
19154 \begin_layout Standard
19155 Within a formula the size can be changed using the following size commands
19156 or the toolbar button
19159 arg "math-insert \\style"
19163 \begin_inset Separator parbreak
19169 \begin_layout Standard
19172 \begin_inset Tabular
19173 <lyxtabular version="3" rows="5" columns="2">
19174 <features booktabs="true" tabularvalignment="middle">
19175 <column alignment="center" valignment="top" width="0pt">
19176 <column alignment="center" valignment="top">
19178 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
19181 \begin_layout Plain Layout
19187 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
19190 \begin_layout Plain Layout
19198 <cell alignment="center" valignment="top" leftline="true" usebox="none">
19201 \begin_layout Plain Layout
19205 \begin_inset Index idx
19208 \begin_layout Plain Layout
19221 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
19224 \begin_layout Plain Layout
19225 \begin_inset Formula ${\displaystyle E_{\mathrm{pot_{1}}}=\frac{K}{l+\frac{m}{n_{2}}}}$
19234 <row topspace="1mm">
19235 <cell alignment="center" valignment="top" usebox="none">
19238 \begin_layout Plain Layout
19246 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
19249 \begin_layout Plain Layout
19250 \begin_inset Formula ${\textstyle E_{\mathrm{pot_{1}}}=\frac{K}{l+\frac{m}{n_{2}}}}$
19260 <cell alignment="center" valignment="top" leftline="true" usebox="none">
19263 \begin_layout Plain Layout
19271 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
19274 \begin_layout Plain Layout
19275 \begin_inset Formula ${\scriptstyle E_{\mathrm{pot_{1}}}=\frac{K}{l+\frac{m}{n_{2}}}}$
19285 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
19288 \begin_layout Plain Layout
19296 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
19299 \begin_layout Plain Layout
19300 \begin_inset Formula ${\scriptscriptstyle E_{\mathrm{pot_{1}}}=\frac{K}{l+\frac{m}{n_{2}}}}$
19316 \begin_layout Standard
19317 After entering these commands, a blue box appears in which the formula parts
19321 \begin_layout Standard
19322 There is a further method to change the font size, that though only works
19323 for symbols or letters in mathematical text.
19324 To use it, one of the above text size commands is inserted in mathematical
19326 All following characters until the end of the mathematical text or until
19327 another size command will have the selected size.
19329 \begin_inset VSpace -2mm
19335 \begin_layout Standard
19339 \begin_layout Plain Layout
19349 \begin_inset Formula
19351 A=\frac{B}{c}\cdot\maltese
19357 \begin_inset Formula
19359 \maltese A\textrm{\Large\maltese\textit{A}}\textrm{\tiny\maltese\textit{A}}
19368 \begin_layout Plain Layout
19380 \begin_layout Standard
19381 \begin_inset VSpace medskip
19384 Before both formulas the command
19391 The command for the second formula is:
19392 \begin_inset Newline newline
19400 \begin_inset space \textvisiblespace{}
19406 \begin_inset space \textvisiblespace{}
19412 \begin_inset space \textvisiblespace{}
19418 \begin_inset space \textvisiblespace{}
19422 \begin_inset Formula $\to$
19426 \begin_inset Formula $\to$
19430 \begin_inset Newline newline
19434 \begin_inset space \hspace*{}
19445 \begin_inset space \textvisiblespace{}
19451 \begin_inset space \textvisiblespace{}
19457 \begin_inset space \textvisiblespace{}
19463 \begin_layout Standard
19464 If a symbol cannot be displayed in different sizes, it will always be displayed
19465 in the default size.
19468 \begin_layout Section
19470 \begin_inset Index idx
19473 \begin_layout Plain Layout
19482 \begin_layout Standard
19483 Greek letters can also be inserted via the toolbar button
19486 arg "math-insert \\alpha"
19490 All international typesetting norms purport that Greek letters in math
19491 have to be typeset italic/slanted.
19492 In some languages, like French or Russian, they are nevertheless sometimes
19496 \begin_layout Subsection
19498 \begin_inset Index idx
19501 \begin_layout Plain Layout
19502 Greek letters ! small
19510 \begin_layout Standard
19511 \begin_inset space \hfill{}
19515 \begin_inset Tabular
19516 <lyxtabular version="3" rows="11" columns="2">
19517 <features booktabs="true" tabularvalignment="middle">
19518 <column alignment="center" valignment="top" width="0pt">
19519 <column alignment="center" valignment="top" width="0pt">
19521 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
19524 \begin_layout Plain Layout
19530 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
19533 \begin_layout Plain Layout
19541 <cell alignment="center" valignment="top" leftline="true" usebox="none">
19544 \begin_layout Plain Layout
19552 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
19555 \begin_layout Plain Layout
19556 \begin_inset Formula $\alpha$
19566 <cell alignment="center" valignment="top" leftline="true" usebox="none">
19569 \begin_layout Plain Layout
19577 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
19580 \begin_layout Plain Layout
19581 \begin_inset Formula $\beta$
19591 <cell alignment="center" valignment="top" leftline="true" usebox="none">
19594 \begin_layout Plain Layout
19602 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
19605 \begin_layout Plain Layout
19606 \begin_inset Formula $\gamma$
19616 <cell alignment="center" valignment="top" leftline="true" usebox="none">
19619 \begin_layout Plain Layout
19627 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
19630 \begin_layout Plain Layout
19631 \begin_inset Formula $\delta$
19641 <cell alignment="center" valignment="top" leftline="true" usebox="none">
19644 \begin_layout Plain Layout
19652 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
19655 \begin_layout Plain Layout
19656 \begin_inset Formula $\epsilon$
19666 <cell alignment="center" valignment="top" leftline="true" usebox="none">
19669 \begin_layout Plain Layout
19677 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
19680 \begin_layout Plain Layout
19681 \begin_inset Formula $\varepsilon$
19691 <cell alignment="center" valignment="top" leftline="true" usebox="none">
19694 \begin_layout Plain Layout
19702 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
19705 \begin_layout Plain Layout
19706 \begin_inset Formula $\zeta$
19716 <cell alignment="center" valignment="top" leftline="true" usebox="none">
19719 \begin_layout Plain Layout
19727 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
19730 \begin_layout Plain Layout
19731 \begin_inset Formula $\eta$
19741 <cell alignment="center" valignment="top" leftline="true" usebox="none">
19744 \begin_layout Plain Layout
19752 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
19755 \begin_layout Plain Layout
19756 \begin_inset Formula $\theta$
19766 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
19769 \begin_layout Plain Layout
19777 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
19780 \begin_layout Plain Layout
19781 \begin_inset Formula $\vartheta$
19795 \begin_inset space \hfill{}
19799 \begin_inset Tabular
19800 <lyxtabular version="3" rows="12" columns="2">
19801 <features booktabs="true" tabularvalignment="middle">
19802 <column alignment="center" valignment="top" width="0pt">
19803 <column alignment="center" valignment="top" width="0pt">
19805 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
19808 \begin_layout Plain Layout
19814 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
19817 \begin_layout Plain Layout
19825 <cell alignment="center" valignment="top" leftline="true" usebox="none">
19828 \begin_layout Plain Layout
19836 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
19839 \begin_layout Plain Layout
19840 \begin_inset Formula $\iota$
19850 <cell alignment="center" valignment="top" leftline="true" usebox="none">
19853 \begin_layout Plain Layout
19861 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
19864 \begin_layout Plain Layout
19865 \begin_inset Formula $\kappa$
19875 <cell alignment="center" valignment="top" leftline="true" usebox="none">
19878 \begin_layout Plain Layout
19886 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
19889 \begin_layout Plain Layout
19890 \begin_inset Formula $\varkappa$
19900 <cell alignment="center" valignment="top" leftline="true" usebox="none">
19903 \begin_layout Plain Layout
19911 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
19914 \begin_layout Plain Layout
19915 \begin_inset Formula $\lambda$
19925 <cell alignment="center" valignment="top" leftline="true" usebox="none">
19928 \begin_layout Plain Layout
19936 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
19939 \begin_layout Plain Layout
19940 \begin_inset Formula $\mu$
19950 <cell alignment="center" valignment="top" leftline="true" usebox="none">
19953 \begin_layout Plain Layout
19961 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
19964 \begin_layout Plain Layout
19965 \begin_inset Formula $\nu$
19975 <cell alignment="center" valignment="top" leftline="true" usebox="none">
19978 \begin_layout Plain Layout
19986 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
19989 \begin_layout Plain Layout
19990 \begin_inset Formula $\xi$
20000 <cell alignment="center" valignment="top" leftline="true" usebox="none">
20003 \begin_layout Plain Layout
20009 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
20012 \begin_layout Plain Layout
20013 \begin_inset Formula $o$
20023 <cell alignment="center" valignment="top" leftline="true" usebox="none">
20026 \begin_layout Plain Layout
20034 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
20037 \begin_layout Plain Layout
20038 \begin_inset Formula $\pi$
20048 <cell alignment="center" valignment="top" leftline="true" usebox="none">
20051 \begin_layout Plain Layout
20059 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
20062 \begin_layout Plain Layout
20063 \begin_inset Formula $\varpi$
20073 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
20076 \begin_layout Plain Layout
20084 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
20087 \begin_layout Plain Layout
20088 \begin_inset Formula $\rho$
20102 \begin_inset space \hfill{}
20106 \begin_inset Tabular
20107 <lyxtabular version="3" rows="11" columns="2">
20108 <features booktabs="true" tabularvalignment="middle">
20109 <column alignment="center" valignment="top" width="0pt">
20110 <column alignment="center" valignment="top" width="0pt">
20112 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
20115 \begin_layout Plain Layout
20121 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
20124 \begin_layout Plain Layout
20132 <cell alignment="center" valignment="top" leftline="true" usebox="none">
20135 \begin_layout Plain Layout
20143 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
20146 \begin_layout Plain Layout
20147 \begin_inset Formula $\varrho$
20157 <cell alignment="center" valignment="top" leftline="true" usebox="none">
20160 \begin_layout Plain Layout
20168 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
20171 \begin_layout Plain Layout
20172 \begin_inset Formula $\sigma$
20182 <cell alignment="center" valignment="top" leftline="true" usebox="none">
20185 \begin_layout Plain Layout
20193 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
20196 \begin_layout Plain Layout
20197 \begin_inset Formula $\varsigma$
20207 <cell alignment="center" valignment="top" leftline="true" usebox="none">
20210 \begin_layout Plain Layout
20218 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
20221 \begin_layout Plain Layout
20222 \begin_inset Formula $\tau$
20232 <cell alignment="center" valignment="top" leftline="true" usebox="none">
20235 \begin_layout Plain Layout
20243 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
20246 \begin_layout Plain Layout
20247 \begin_inset Formula $\upsilon$
20257 <cell alignment="center" valignment="top" leftline="true" usebox="none">
20260 \begin_layout Plain Layout
20268 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
20271 \begin_layout Plain Layout
20272 \begin_inset Formula $\phi$
20282 <cell alignment="center" valignment="top" leftline="true" usebox="none">
20285 \begin_layout Plain Layout
20293 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
20296 \begin_layout Plain Layout
20297 \begin_inset Formula $\varphi$
20307 <cell alignment="center" valignment="top" leftline="true" usebox="none">
20310 \begin_layout Plain Layout
20318 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
20321 \begin_layout Plain Layout
20322 \begin_inset Formula $\chi$
20332 <cell alignment="center" valignment="top" leftline="true" usebox="none">
20335 \begin_layout Plain Layout
20343 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
20346 \begin_layout Plain Layout
20347 \begin_inset Formula $\psi$
20357 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
20360 \begin_layout Plain Layout
20368 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
20371 \begin_layout Plain Layout
20372 \begin_inset Formula $\omega$
20386 \begin_inset space \hfill{}
20392 \begin_layout Standard
20393 \begin_inset VSpace medskip
20399 \begin_layout Standard
20400 How to create special upright Greek letters is explained in
20401 \begin_inset CommandInset ref
20403 reference "subsec:Upright-small-Greek"
20410 \begin_layout Subsection
20412 \begin_inset Index idx
20415 \begin_layout Plain Layout
20416 Greek letters ! big
20424 \begin_layout Standard
20425 \begin_inset space \hfill{}
20429 \begin_inset Tabular
20430 <lyxtabular version="3" rows="7" columns="2">
20431 <features booktabs="true" tabularvalignment="middle">
20432 <column alignment="center" valignment="top" width="0pt">
20433 <column alignment="center" valignment="top" width="0pt">
20435 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
20438 \begin_layout Plain Layout
20444 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
20447 \begin_layout Plain Layout
20455 <cell alignment="center" valignment="top" leftline="true" usebox="none">
20458 \begin_layout Plain Layout
20466 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
20469 \begin_layout Plain Layout
20470 \begin_inset Formula $\Gamma$
20480 <cell alignment="center" valignment="top" leftline="true" usebox="none">
20483 \begin_layout Plain Layout
20491 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
20494 \begin_layout Plain Layout
20495 \begin_inset Formula $\Delta$
20505 <cell alignment="center" valignment="top" leftline="true" usebox="none">
20508 \begin_layout Plain Layout
20516 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
20519 \begin_layout Plain Layout
20520 \begin_inset Formula $\Theta$
20530 <cell alignment="center" valignment="top" leftline="true" usebox="none">
20533 \begin_layout Plain Layout
20541 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
20544 \begin_layout Plain Layout
20545 \begin_inset Formula $\Lambda$
20555 <cell alignment="center" valignment="top" leftline="true" usebox="none">
20558 \begin_layout Plain Layout
20566 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
20569 \begin_layout Plain Layout
20570 \begin_inset Formula $\Xi$
20580 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
20583 \begin_layout Plain Layout
20591 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
20594 \begin_layout Plain Layout
20595 \begin_inset Formula $\Pi$
20609 \begin_inset space \hfill{}
20613 \begin_inset Tabular
20614 <lyxtabular version="3" rows="6" columns="2">
20615 <features booktabs="true" tabularvalignment="middle">
20616 <column alignment="center" valignment="top" width="0pt">
20617 <column alignment="center" valignment="top" width="0pt">
20619 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
20622 \begin_layout Plain Layout
20628 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
20631 \begin_layout Plain Layout
20639 <cell alignment="center" valignment="top" leftline="true" usebox="none">
20642 \begin_layout Plain Layout
20650 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
20653 \begin_layout Plain Layout
20654 \begin_inset Formula $\Sigma$
20664 <cell alignment="center" valignment="top" leftline="true" usebox="none">
20667 \begin_layout Plain Layout
20675 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
20678 \begin_layout Plain Layout
20679 \begin_inset Formula $\Upsilon$
20689 <cell alignment="center" valignment="top" leftline="true" usebox="none">
20692 \begin_layout Plain Layout
20700 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
20703 \begin_layout Plain Layout
20704 \begin_inset Formula $\Phi$
20714 <cell alignment="center" valignment="top" leftline="true" usebox="none">
20717 \begin_layout Plain Layout
20725 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
20728 \begin_layout Plain Layout
20729 \begin_inset Formula $\Psi$
20739 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
20742 \begin_layout Plain Layout
20750 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
20753 \begin_layout Plain Layout
20754 \begin_inset Formula $\Omega$
20768 \begin_inset space \hfill{}
20774 \begin_layout Standard
20775 \begin_inset VSpace medskip
20778 That the big Greek letters appear upright is caused by a design bug when
20781 To get correct italic big letters, begin every command with
20786 For example the command
20793 \begin_inset Formula $\varGamma$
20797 Another way is to load the package
20805 \begin_layout Plain Layout
20810 is part of the \SpecialChar LaTeX
20816 \begin_inset Index idx
20819 \begin_layout Plain Layout
20824 \begin_layout Plain Layout
20844 \begin_inset Index idx
20847 \begin_layout Plain Layout
20853 with the \SpecialChar LaTeX
20857 \begin_layout Standard
20862 usepackage{fixmath}
20865 \begin_layout Standard
20866 Then all big Greek letters in a document will automatically be typeset italic.
20869 \begin_layout Subsection
20871 \begin_inset Index idx
20874 \begin_layout Plain Layout
20875 Greek letters ! bold
20883 \begin_layout Standard
20884 Greek letters cannot be set with different font styles like Latin letters.
20885 They can only be made bold with the command
20892 \begin_inset Index idx
20895 \begin_layout Plain Layout
20904 \begin_inset Separator parbreak
20910 \begin_layout Standard
20912 \begin_inset Tabular
20913 <lyxtabular version="3" rows="3" columns="2">
20914 <features booktabs="true" tabularvalignment="middle">
20915 <column alignment="center" valignment="top" width="0pt">
20916 <column alignment="center" valignment="top">
20918 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
20921 \begin_layout Plain Layout
20927 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
20930 \begin_layout Plain Layout
20938 <cell alignment="center" valignment="top" leftline="true" usebox="none">
20941 \begin_layout Plain Layout
20953 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
20956 \begin_layout Plain Layout
20957 \begin_inset Formula $\Upsilon\boldsymbol{\Upsilon}$
20967 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
20970 \begin_layout Plain Layout
20982 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
20985 \begin_layout Plain Layout
20986 \begin_inset Formula $\theta\boldsymbol{\theta}$
21002 \begin_layout Section
21007 \begin_layout Plain Layout
21020 \begin_layout Plain Layout
21021 A list with all symbols of most of the \SpecialChar LaTeX
21022 -packages can be found in
21023 \begin_inset CommandInset citation
21038 \begin_layout Plain Layout
21046 \begin_inset Note Note
21049 \begin_layout Plain Layout
21052 texorpdfstring is used to avoid that the footnote appears in the PDF-bookmark.
21055 \begin_layout Plain Layout
21058 texorpdfstring is in section
21059 \begin_inset CommandInset ref
21061 reference "subsec:Formulas-in-Section"
21071 \begin_inset Index idx
21074 \begin_layout Plain Layout
21083 \begin_layout Standard
21084 Many of the symbols listed in this section can also be inserted via the
21088 arg "math-insert \\nabla"
21094 arg "math-insert \\digamma"
21100 \begin_layout Subsection
21101 Mathematical Symbols
21102 \begin_inset CommandInset label
21104 name "subsec:Mathematical-Symbols"
21109 \begin_inset Index idx
21112 \begin_layout Plain Layout
21113 Symbols ! mathematical
21121 \begin_layout Standard
21122 \begin_inset Tabular
21123 <lyxtabular version="3" rows="10" columns="2">
21124 <features booktabs="true" tabularvalignment="middle">
21125 <column alignment="center" valignment="top" width="0pt">
21126 <column alignment="center" valignment="top" width="0pt">
21128 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
21131 \begin_layout Plain Layout
21137 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
21140 \begin_layout Plain Layout
21148 <cell alignment="center" valignment="top" leftline="true" usebox="none">
21151 \begin_layout Plain Layout
21159 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
21162 \begin_layout Plain Layout
21163 \begin_inset Formula $\neg$
21173 <cell alignment="center" valignment="top" leftline="true" usebox="none">
21176 \begin_layout Plain Layout
21184 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
21187 \begin_layout Plain Layout
21188 \begin_inset Formula $\Im$
21198 <cell alignment="center" valignment="top" leftline="true" usebox="none">
21201 \begin_layout Plain Layout
21209 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
21212 \begin_layout Plain Layout
21213 \begin_inset Formula $\Re$
21223 <cell alignment="center" valignment="top" leftline="true" usebox="none">
21226 \begin_layout Plain Layout
21234 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
21237 \begin_layout Plain Layout
21238 \begin_inset Formula $\aleph$
21248 <cell alignment="center" valignment="top" leftline="true" usebox="none">
21251 \begin_layout Plain Layout
21259 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
21262 \begin_layout Plain Layout
21263 \begin_inset Formula $\partial$
21273 <cell alignment="center" valignment="top" leftline="true" usebox="none">
21276 \begin_layout Plain Layout
21284 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
21287 \begin_layout Plain Layout
21288 \begin_inset Formula $\infty$
21298 <cell alignment="center" valignment="top" leftline="true" usebox="none">
21301 \begin_layout Plain Layout
21309 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
21312 \begin_layout Plain Layout
21313 \begin_inset Formula $\wp$
21323 <cell alignment="center" valignment="top" leftline="true" usebox="none">
21326 \begin_layout Plain Layout
21334 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
21337 \begin_layout Plain Layout
21338 \begin_inset Formula $\imath$
21348 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
21351 \begin_layout Plain Layout
21359 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
21362 \begin_layout Plain Layout
21363 \begin_inset Formula $\jmath$
21377 \begin_inset space \hfill{}
21381 \begin_inset Tabular
21382 <lyxtabular version="3" rows="10" columns="2">
21383 <features booktabs="true" tabularvalignment="middle">
21384 <column alignment="center" valignment="top" width="0pt">
21385 <column alignment="center" valignment="top" width="0pt">
21387 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
21390 \begin_layout Plain Layout
21396 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
21399 \begin_layout Plain Layout
21401 \begin_inset Note Note
21404 \begin_layout Plain Layout
21411 is only used as spacer.
21423 <cell alignment="center" valignment="top" leftline="true" usebox="none">
21426 \begin_layout Plain Layout
21434 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
21437 \begin_layout Plain Layout
21438 \begin_inset Formula $\forall$
21448 <cell alignment="center" valignment="top" leftline="true" usebox="none">
21451 \begin_layout Plain Layout
21459 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
21462 \begin_layout Plain Layout
21463 \begin_inset Formula $\exists$
21473 <cell alignment="center" valignment="top" leftline="true" usebox="none">
21476 \begin_layout Plain Layout
21484 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
21487 \begin_layout Plain Layout
21488 \begin_inset Formula $\nexists$
21498 <cell alignment="center" valignment="top" leftline="true" usebox="none">
21501 \begin_layout Plain Layout
21509 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
21512 \begin_layout Plain Layout
21513 \begin_inset Formula $\emptyset$
21523 <cell alignment="center" valignment="top" leftline="true" usebox="none">
21526 \begin_layout Plain Layout
21534 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
21537 \begin_layout Plain Layout
21538 \begin_inset Formula $\varnothing$
21548 <cell alignment="center" valignment="top" leftline="true" usebox="none">
21551 \begin_layout Plain Layout
21559 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
21562 \begin_layout Plain Layout
21563 \begin_inset Formula $\dag$
21573 <cell alignment="center" valignment="top" leftline="true" usebox="none">
21576 \begin_layout Plain Layout
21584 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
21587 \begin_layout Plain Layout
21588 \begin_inset Formula $\ddag$
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
21616 \begin_layout Plain Layout
21626 \begin_inset Formula $\complement$
21633 \begin_layout Plain Layout
21647 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
21650 \begin_layout Plain Layout
21658 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
21661 \begin_layout Plain Layout
21662 \begin_inset Formula $\Bbbk$
21676 \begin_inset space \hfill{}
21680 \begin_inset Tabular
21681 <lyxtabular version="3" rows="10" columns="2">
21682 <features booktabs="true" tabularvalignment="middle">
21683 <column alignment="center" valignment="top" width="0pt">
21684 <column alignment="center" valignment="top" width="0pt">
21686 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
21689 \begin_layout Plain Layout
21695 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
21698 \begin_layout Plain Layout
21706 <cell alignment="center" valignment="top" leftline="true" usebox="none">
21709 \begin_layout Plain Layout
21717 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
21720 \begin_layout Plain Layout
21721 \begin_inset Formula $\prime$
21731 <cell alignment="center" valignment="top" leftline="true" usebox="none">
21734 \begin_layout Plain Layout
21742 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
21745 \begin_layout Plain Layout
21746 \begin_inset Formula $\backprime$
21756 <cell alignment="center" valignment="top" leftline="true" usebox="none">
21759 \begin_layout Plain Layout
21767 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
21770 \begin_layout Plain Layout
21771 \begin_inset Formula $\mho$
21781 <cell alignment="center" valignment="top" leftline="true" usebox="none">
21784 \begin_layout Plain Layout
21792 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
21795 \begin_layout Plain Layout
21796 \begin_inset Formula $\triangle$
21806 <cell alignment="center" valignment="top" leftline="true" usebox="none">
21809 \begin_layout Plain Layout
21817 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
21820 \begin_layout Plain Layout
21821 \begin_inset Formula $\angle$
21831 <cell alignment="center" valignment="top" leftline="true" usebox="none">
21834 \begin_layout Plain Layout
21842 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
21845 \begin_layout Plain Layout
21846 \begin_inset Formula $\measuredangle$
21856 <cell alignment="center" valignment="top" leftline="true" usebox="none">
21859 \begin_layout Plain Layout
21867 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
21870 \begin_layout Plain Layout
21871 \begin_inset Formula $\sphericalangle$
21881 <cell alignment="center" valignment="top" leftline="true" usebox="none">
21884 \begin_layout Plain Layout
21892 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
21895 \begin_layout Plain Layout
21896 \begin_inset Formula $\top$
21906 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
21909 \begin_layout Plain Layout
21917 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
21920 \begin_layout Plain Layout
21921 \begin_inset Formula $\bot$
21937 \begin_layout Standard
21938 \begin_inset Newpage newpage
21944 \begin_layout Subsection
21945 Miscellaneous Symbols
21946 \begin_inset CommandInset label
21948 name "subsec:Miscellaneous-Symbols"
21953 \begin_inset Index idx
21956 \begin_layout Plain Layout
21957 Symbols ! miscellaneous
21965 \begin_layout Standard
21968 \begin_inset Tabular
21969 <lyxtabular version="3" rows="10" columns="2">
21970 <features booktabs="true" tabularvalignment="middle">
21971 <column alignment="center" valignment="top" width="0pt">
21972 <column alignment="center" valignment="top" width="0pt">
21974 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
21977 \begin_layout Plain Layout
21983 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
21986 \begin_layout Plain Layout
21994 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
21997 \begin_layout Plain Layout
22005 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
22008 \begin_layout Plain Layout
22009 \begin_inset Formula $\flat$
22019 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
22022 \begin_layout Plain Layout
22030 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
22033 \begin_layout Plain Layout
22034 \begin_inset Formula $\natural$
22044 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
22047 \begin_layout Plain Layout
22055 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
22058 \begin_layout Plain Layout
22059 \begin_inset Formula $\sharp$
22069 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
22072 \begin_layout Plain Layout
22080 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
22083 \begin_layout Plain Layout
22084 \begin_inset Formula $\surd$
22094 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
22097 \begin_layout Plain Layout
22105 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
22108 \begin_layout Plain Layout
22109 \begin_inset Formula $\checkmark$
22119 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
22122 \begin_layout Plain Layout
22130 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
22133 \begin_layout Plain Layout
22134 \begin_inset Formula $\yen$
22144 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
22147 \begin_layout Plain Layout
22155 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
22158 \begin_layout Plain Layout
22159 \begin_inset Formula $\pounds$
22169 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
22172 \begin_layout Plain Layout
22178 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
22181 \begin_layout Plain Layout
22182 \begin_inset Formula $\$$
22192 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
22195 \begin_layout Plain Layout
22201 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
22204 \begin_layout Plain Layout
22205 \begin_inset Formula $§$
22219 \begin_inset space \hfill{}
22223 \begin_inset Tabular
22224 <lyxtabular version="3" rows="10" columns="2">
22225 <features booktabs="true" tabularvalignment="middle">
22226 <column alignment="center" valignment="top" width="0pt">
22227 <column alignment="center" valignment="top">
22229 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
22232 \begin_layout Plain Layout
22238 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
22241 \begin_layout Plain Layout
22249 <cell alignment="center" valignment="top" leftline="true" usebox="none">
22252 \begin_layout Plain Layout
22260 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
22263 \begin_layout Plain Layout
22264 \begin_inset Formula $\hbar$
22274 <cell alignment="center" valignment="top" leftline="true" usebox="none">
22277 \begin_layout Plain Layout
22285 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
22288 \begin_layout Plain Layout
22289 \begin_inset Formula $\hslash$
22299 <cell alignment="center" valignment="top" leftline="true" usebox="none">
22302 \begin_layout Plain Layout
22310 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
22313 \begin_layout Plain Layout
22314 \begin_inset Formula $\clubsuit$
22324 <cell alignment="center" valignment="top" leftline="true" usebox="none">
22327 \begin_layout Plain Layout
22335 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
22338 \begin_layout Plain Layout
22339 \begin_inset Formula $\spadesuit$
22349 <cell alignment="center" valignment="top" leftline="true" usebox="none">
22352 \begin_layout Plain Layout
22360 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
22363 \begin_layout Plain Layout
22364 \begin_inset Formula $\bigstar$
22374 <cell alignment="center" valignment="top" leftline="true" usebox="none">
22377 \begin_layout Plain Layout
22385 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
22388 \begin_layout Plain Layout
22389 \begin_inset Formula $\blacklozenge$
22399 <cell alignment="center" valignment="top" leftline="true" usebox="none">
22402 \begin_layout Plain Layout
22410 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
22413 \begin_layout Plain Layout
22414 \begin_inset Formula $\blacktriangle$
22424 <cell alignment="center" valignment="top" leftline="true" usebox="none">
22427 \begin_layout Plain Layout
22435 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
22438 \begin_layout Plain Layout
22439 \begin_inset Formula $\blacktriangledown$
22449 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
22452 \begin_layout Plain Layout
22460 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
22463 \begin_layout Plain Layout
22464 \begin_inset Formula $\bullet$
22478 \begin_inset space \hfill{}
22482 \begin_inset Tabular
22483 <lyxtabular version="3" rows="10" columns="2">
22484 <features booktabs="true" tabularvalignment="middle">
22485 <column alignment="center" valignment="top" width="0pt">
22486 <column alignment="center" valignment="top" width="0pt">
22488 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
22491 \begin_layout Plain Layout
22497 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
22500 \begin_layout Plain Layout
22508 <cell alignment="center" valignment="top" leftline="true" usebox="none">
22511 \begin_layout Plain Layout
22519 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
22522 \begin_layout Plain Layout
22523 \begin_inset Formula $\diamondsuit$
22533 <cell alignment="center" valignment="top" rightline="true" usebox="none">
22536 \begin_layout Plain Layout
22544 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
22547 \begin_layout Plain Layout
22548 \begin_inset Formula $\Diamond$
22558 <cell alignment="center" valignment="top" leftline="true" usebox="none">
22561 \begin_layout Plain Layout
22569 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
22572 \begin_layout Plain Layout
22573 \begin_inset Formula $\heartsuit$
22583 <cell alignment="center" valignment="top" leftline="true" usebox="none">
22586 \begin_layout Plain Layout
22594 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
22597 \begin_layout Plain Layout
22598 \begin_inset Formula $\P$
22608 <cell alignment="center" valignment="top" leftline="true" usebox="none">
22611 \begin_layout Plain Layout
22619 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
22622 \begin_layout Plain Layout
22623 \begin_inset Formula $\copyright$
22633 <cell alignment="center" valignment="top" leftline="true" usebox="none">
22636 \begin_layout Plain Layout
22644 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
22647 \begin_layout Plain Layout
22648 \begin_inset Formula $\circledR$
22658 <cell alignment="center" valignment="top" leftline="true" usebox="none">
22661 \begin_layout Plain Layout
22669 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
22672 \begin_layout Plain Layout
22673 \begin_inset Formula $\maltese$
22683 <cell alignment="center" valignment="top" leftline="true" usebox="none">
22686 \begin_layout Plain Layout
22694 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
22697 \begin_layout Plain Layout
22698 \begin_inset Formula $\diagup$
22708 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
22711 \begin_layout Plain Layout
22719 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
22722 \begin_layout Plain Layout
22723 \begin_inset Formula $\diagdown$
22739 \begin_layout Standard
22740 \begin_inset VSpace medskip
22746 \begin_layout Standard
22747 Some symbols can be displayed in different sizes, see
22748 \begin_inset CommandInset ref
22750 reference "subsec:Font-Sizes"
22757 \begin_layout Subsection
22759 \begin_inset Index idx
22762 \begin_layout Plain Layout
22763 Symbols ! Euro-symbol
22769 \begin_inset Index idx
22772 \begin_layout Plain Layout
22779 \begin_layout Plain Layout
22796 \begin_layout Standard
22797 To use the Euro symbol in formulas, the \SpecialChar LaTeX
22803 \begin_inset Index idx
22806 \begin_layout Plain Layout
22812 must be installed and loaded with the \SpecialChar LaTeX
22816 \begin_layout Standard
22821 usepackage[gennarrow]{eurosym}
22824 \begin_layout Standard
22825 The Euro symbol can now be inserted with the command
22832 \begin_inset Index idx
22835 \begin_layout Plain Layout
22846 \begin_layout Standard
22847 The Euro symbol can directly be inserted with the € key in mathematical
22848 text, without having
22863 can also be inserted in \SpecialChar TeX
22865 The official currency symbol can then be inserted with the command
22872 \begin_inset Index idx
22875 \begin_layout Plain Layout
22883 , that is only available in \SpecialChar TeX
22887 \begin_layout Standard
22891 \begin_layout Plain Layout
22901 \begin_inset Note Note
22904 \begin_layout Plain Layout
22905 The following table will only be displayed when the \SpecialChar LaTeX
22918 \begin_layout Standard
22919 An overview about the different Euro symbols:
22920 \begin_inset Separator parbreak
22926 \begin_layout Standard
22928 \begin_inset Tabular
22929 <lyxtabular version="3" rows="4" columns="3">
22930 <features booktabs="true" tabularvalignment="middle">
22931 <column alignment="center" valignment="top" width="0pt">
22932 <column alignment="center" valignment="top" width="0pt">
22933 <column alignment="center" valignment="top" width="0pt">
22935 <cell alignment="center" valignment="top" bottomline="true" usebox="none">
22938 \begin_layout Plain Layout
22942 \begin_layout Plain Layout
22946 cmidrule[0.08em]{2-3}
22956 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
22959 \begin_layout Plain Layout
22965 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
22968 \begin_layout Plain Layout
22976 <cell alignment="center" valignment="top" leftline="true" usebox="none">
22979 \begin_layout Plain Layout
22985 <cell alignment="center" valignment="top" leftline="true" usebox="none">
22988 \begin_layout Plain Layout
22996 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
22999 \begin_layout Plain Layout
23000 \begin_inset Formula $\euro$
23010 <cell alignment="center" valignment="top" leftline="true" usebox="none">
23013 \begin_layout Plain Layout
23019 <cell alignment="center" valignment="top" leftline="true" usebox="none">
23022 \begin_layout Plain Layout
23028 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
23031 \begin_layout Plain Layout
23032 \begin_inset Formula $\mbox{€}$
23042 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
23045 \begin_layout Plain Layout
23052 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
23055 \begin_layout Plain Layout
23063 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
23066 \begin_layout Plain Layout
23070 \begin_layout Plain Layout
23090 \begin_inset Note Note
23093 \begin_layout Plain Layout
23100 is used here only for table borders.
23110 manual for details.
23118 \begin_layout Standard
23122 \begin_layout Plain Layout
23132 \begin_inset Note Note
23135 \begin_layout Plain Layout
23136 The following will be displayed when the \SpecialChar LaTeX
23149 \begin_layout Standard
23150 You need to install the \SpecialChar LaTeX
23155 to see the rest of this subsection in the output.
23158 \begin_layout Standard
23162 \begin_layout Plain Layout
23174 \begin_layout Standard
23175 \begin_inset Newpage newpage
23181 \begin_layout Section
23183 \begin_inset CommandInset label
23185 name "sec:Relations"
23190 \begin_inset Index idx
23193 \begin_layout Plain Layout
23200 \begin_inset Index idx
23203 \begin_layout Plain Layout
23208 \begin_layout Plain Layout
23219 \begin_layout Plain Layout
23234 \begin_layout Standard
23235 All following relations can also be inserted via the toolbar button
23238 arg "math-insert \\leq"
23244 \begin_layout Standard
23245 \begin_inset Tabular
23246 <lyxtabular version="3" rows="17" columns="2">
23247 <features booktabs="true" tabularvalignment="middle">
23248 <column alignment="center" valignment="top" width="0pt">
23249 <column alignment="center" valignment="top" width="0pt">
23251 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
23254 \begin_layout Plain Layout
23260 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
23263 \begin_layout Plain Layout
23271 <cell alignment="center" valignment="top" leftline="true" usebox="none">
23274 \begin_layout Plain Layout
23280 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
23283 \begin_layout Plain Layout
23284 \begin_inset Formula $<$
23294 <cell alignment="center" valignment="top" leftline="true" usebox="none">
23297 \begin_layout Plain Layout
23305 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
23308 \begin_layout Plain Layout
23309 \begin_inset Formula $\le$
23319 <cell alignment="center" valignment="top" leftline="true" usebox="none">
23322 \begin_layout Plain Layout
23330 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
23333 \begin_layout Plain Layout
23334 \begin_inset Formula $\ll$
23344 <cell alignment="center" valignment="top" leftline="true" usebox="none">
23347 \begin_layout Plain Layout
23355 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
23358 \begin_layout Plain Layout
23359 \begin_inset Formula $\prec$
23369 <cell alignment="center" valignment="top" leftline="true" usebox="none">
23372 \begin_layout Plain Layout
23380 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
23383 \begin_layout Plain Layout
23384 \begin_inset Formula $\preceq$
23394 <cell alignment="center" valignment="top" leftline="true" usebox="none">
23397 \begin_layout Plain Layout
23405 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
23408 \begin_layout Plain Layout
23409 \begin_inset Formula $\subset$
23419 <cell alignment="center" valignment="top" leftline="true" usebox="none">
23422 \begin_layout Plain Layout
23430 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
23433 \begin_layout Plain Layout
23434 \begin_inset Formula $\subseteq$
23444 <cell alignment="center" valignment="top" leftline="true" usebox="none">
23447 \begin_layout Plain Layout
23455 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
23458 \begin_layout Plain Layout
23459 \begin_inset Formula $\sqsubseteq$
23469 <cell alignment="center" valignment="top" leftline="true" usebox="none">
23472 \begin_layout Plain Layout
23480 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
23483 \begin_layout Plain Layout
23484 \begin_inset Formula $\in$
23494 <cell alignment="center" valignment="top" leftline="true" usebox="none">
23497 \begin_layout Plain Layout
23505 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
23508 \begin_layout Plain Layout
23509 \begin_inset Formula $\vdash$
23519 <cell alignment="center" valignment="top" leftline="true" usebox="none">
23522 \begin_layout Plain Layout
23530 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
23533 \begin_layout Plain Layout
23534 \begin_inset Formula $\smile$
23544 <cell alignment="center" valignment="top" leftline="true" usebox="none">
23547 \begin_layout Plain Layout
23555 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
23558 \begin_layout Plain Layout
23559 \begin_inset Formula $\lhd$
23569 <cell alignment="center" valignment="top" leftline="true" usebox="none">
23572 \begin_layout Plain Layout
23580 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
23583 \begin_layout Plain Layout
23584 \begin_inset Formula $\unlhd$
23594 <cell alignment="center" valignment="top" leftline="true" usebox="none">
23597 \begin_layout Plain Layout
23605 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
23608 \begin_layout Plain Layout
23609 \begin_inset Formula $\gtrless$
23619 <cell alignment="center" valignment="top" leftline="true" usebox="none">
23622 \begin_layout Plain Layout
23630 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
23633 \begin_layout Plain Layout
23634 \begin_inset Formula $\mid$
23644 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
23647 \begin_layout Plain Layout
23655 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
23658 \begin_layout Plain Layout
23659 \begin_inset Formula $\nmid$
23673 \begin_inset space \hfill{}
23677 \begin_inset Tabular
23678 <lyxtabular version="3" rows="17" columns="2">
23679 <features booktabs="true" tabularvalignment="middle">
23680 <column alignment="center" valignment="top" width="0pt">
23681 <column alignment="center" valignment="top" width="0pt">
23683 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
23686 \begin_layout Plain Layout
23692 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
23695 \begin_layout Plain Layout
23703 <cell alignment="center" valignment="top" leftline="true" usebox="none">
23706 \begin_layout Plain Layout
23712 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
23715 \begin_layout Plain Layout
23716 \begin_inset Formula $=$
23726 <cell alignment="center" valignment="top" leftline="true" usebox="none">
23729 \begin_layout Plain Layout
23737 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
23740 \begin_layout Plain Layout
23741 \begin_inset Formula $\not=$
23751 <cell alignment="center" valignment="top" leftline="true" usebox="none">
23754 \begin_layout Plain Layout
23762 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
23765 \begin_layout Plain Layout
23766 \begin_inset Formula $\equiv$
23776 <cell alignment="center" valignment="top" leftline="true" usebox="none">
23779 \begin_layout Plain Layout
23787 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
23790 \begin_layout Plain Layout
23791 \begin_inset Formula $\sim$
23801 <cell alignment="center" valignment="top" leftline="true" usebox="none">
23804 \begin_layout Plain Layout
23812 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
23815 \begin_layout Plain Layout
23816 \begin_inset Formula $\simeq$
23826 <cell alignment="center" valignment="top" leftline="true" usebox="none">
23829 \begin_layout Plain Layout
23837 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
23840 \begin_layout Plain Layout
23841 \begin_inset Formula $\approx$
23851 <cell alignment="center" valignment="top" leftline="true" usebox="none">
23854 \begin_layout Plain Layout
23862 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
23865 \begin_layout Plain Layout
23866 \begin_inset Formula $\cong$
23876 <cell alignment="center" valignment="top" leftline="true" usebox="none">
23879 \begin_layout Plain Layout
23887 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
23890 \begin_layout Plain Layout
23891 \begin_inset Formula $\bowtie$
23901 <cell alignment="center" valignment="top" leftline="true" usebox="none">
23904 \begin_layout Plain Layout
23912 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
23915 \begin_layout Plain Layout
23916 \begin_inset Formula $\notin$
23926 <cell alignment="center" valignment="top" leftline="true" usebox="none">
23929 \begin_layout Plain Layout
23937 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
23940 \begin_layout Plain Layout
23941 \begin_inset Formula $\perp$
23951 <cell alignment="center" valignment="top" leftline="true" usebox="none">
23954 \begin_layout Plain Layout
23962 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
23965 \begin_layout Plain Layout
23966 \begin_inset Formula $\propto$
23976 <cell alignment="center" valignment="top" leftline="true" usebox="none">
23979 \begin_layout Plain Layout
23987 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
23990 \begin_layout Plain Layout
23991 \begin_inset Formula $\asymp$
24001 <cell alignment="center" valignment="top" leftline="true" usebox="none">
24004 \begin_layout Plain Layout
24012 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
24015 \begin_layout Plain Layout
24016 \begin_inset Formula $\doteq$
24026 <cell alignment="center" valignment="top" leftline="true" usebox="none">
24029 \begin_layout Plain Layout
24037 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
24040 \begin_layout Plain Layout
24041 \begin_inset Formula $\circeq$
24051 <cell alignment="center" valignment="top" leftline="true" usebox="none">
24054 \begin_layout Plain Layout
24062 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
24065 \begin_layout Plain Layout
24066 \begin_inset Formula $\models$
24076 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
24079 \begin_layout Plain Layout
24087 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
24090 \begin_layout Plain Layout
24091 \begin_inset Formula $\widehat{=}$
24105 \begin_inset space \hfill{}
24109 \begin_inset Tabular
24110 <lyxtabular version="3" rows="17" columns="2">
24111 <features booktabs="true" tabularvalignment="middle">
24112 <column alignment="center" valignment="top" width="0pt">
24113 <column alignment="center" valignment="top" width="0pt">
24115 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
24118 \begin_layout Plain Layout
24124 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
24127 \begin_layout Plain Layout
24135 <cell alignment="center" valignment="top" leftline="true" usebox="none">
24138 \begin_layout Plain Layout
24144 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
24147 \begin_layout Plain Layout
24148 \begin_inset Formula $>$
24158 <cell alignment="center" valignment="top" leftline="true" usebox="none">
24161 \begin_layout Plain Layout
24169 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
24172 \begin_layout Plain Layout
24173 \begin_inset Formula $\ge$
24183 <cell alignment="center" valignment="top" leftline="true" usebox="none">
24186 \begin_layout Plain Layout
24194 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
24197 \begin_layout Plain Layout
24198 \begin_inset Formula $\gg$
24208 <cell alignment="center" valignment="top" leftline="true" usebox="none">
24211 \begin_layout Plain Layout
24219 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
24222 \begin_layout Plain Layout
24223 \begin_inset Formula $\succ$
24233 <cell alignment="center" valignment="top" leftline="true" usebox="none">
24236 \begin_layout Plain Layout
24244 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
24247 \begin_layout Plain Layout
24248 \begin_inset Formula $\succeq$
24258 <cell alignment="center" valignment="top" leftline="true" usebox="none">
24261 \begin_layout Plain Layout
24269 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
24272 \begin_layout Plain Layout
24273 \begin_inset Formula $\supset$
24283 <cell alignment="center" valignment="top" leftline="true" usebox="none">
24286 \begin_layout Plain Layout
24294 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
24297 \begin_layout Plain Layout
24298 \begin_inset Formula $\supseteq$
24308 <cell alignment="center" valignment="top" leftline="true" usebox="none">
24311 \begin_layout Plain Layout
24319 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
24322 \begin_layout Plain Layout
24323 \begin_inset Formula $\sqsupseteq$
24333 <cell alignment="center" valignment="top" leftline="true" usebox="none">
24336 \begin_layout Plain Layout
24344 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
24347 \begin_layout Plain Layout
24348 \begin_inset Formula $\ni$
24358 <cell alignment="center" valignment="top" leftline="true" usebox="none">
24361 \begin_layout Plain Layout
24369 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
24372 \begin_layout Plain Layout
24373 \begin_inset Formula $\dashv$
24383 <cell alignment="center" valignment="top" leftline="true" usebox="none">
24386 \begin_layout Plain Layout
24394 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
24397 \begin_layout Plain Layout
24398 \begin_inset Formula $\frown$
24408 <cell alignment="center" valignment="top" leftline="true" usebox="none">
24411 \begin_layout Plain Layout
24419 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
24422 \begin_layout Plain Layout
24423 \begin_inset Formula $\rhd$
24433 <cell alignment="center" valignment="top" leftline="true" usebox="none">
24436 \begin_layout Plain Layout
24444 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
24447 \begin_layout Plain Layout
24448 \begin_inset Formula $\unrhd$
24458 <cell alignment="center" valignment="top" leftline="true" usebox="none">
24461 \begin_layout Plain Layout
24469 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
24472 \begin_layout Plain Layout
24473 \begin_inset Formula $\lessgtr$
24483 <cell alignment="center" valignment="top" leftline="true" usebox="none">
24486 \begin_layout Plain Layout
24494 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
24497 \begin_layout Plain Layout
24498 \begin_inset Formula $\parallel$
24508 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
24511 \begin_layout Plain Layout
24519 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
24522 \begin_layout Plain Layout
24523 \begin_inset Formula $\nparallel$
24539 \begin_layout Standard
24540 \begin_inset VSpace medskip
24555 are bigger than the equal looking operators
24570 \begin_layout Standard
24572 supports also many special relations.
24573 Use the toolbar button
24576 arg "math-insert \\leqq"
24579 to see a list of these relations.
24582 \begin_layout Standard
24583 Relations are, in contrary to symbols, always surrounded by space.
24586 \begin_layout Standard
24587 Relations with labels can be created with the command
24594 \begin_inset Index idx
24597 \begin_layout Plain Layout
24606 \begin_inset Separator parbreak
24612 \begin_layout Standard
24614 \begin_inset Tabular
24615 <lyxtabular version="3" rows="2" columns="2">
24616 <features booktabs="true" tabularvalignment="middle">
24617 <column alignment="center" valignment="top" width="0pt">
24618 <column alignment="center" valignment="top">
24620 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
24623 \begin_layout Plain Layout
24629 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
24632 \begin_layout Plain Layout
24639 <row topspace="1.5mm">
24640 <cell alignment="center" valignment="top" bottomline="true" usebox="none">
24643 \begin_layout Plain Layout
24647 \begin_inset space \textvisiblespace{}
24655 \begin_inset space \textvisiblespace{}
24659 \begin_inset Formula $\downarrow$
24665 \begin_inset space \textvisiblespace{}
24669 \begin_inset space \textvisiblespace{}
24677 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
24680 \begin_layout Plain Layout
24681 \begin_inset Formula $A(r)\stackrel{r\to\infty}{\approx}B$
24697 \begin_layout Section
24701 \begin_layout Subsection
24702 Predefined Functions
24703 \begin_inset CommandInset label
24705 name "subsec:Predefined-Functions"
24710 \begin_inset Index idx
24713 \begin_layout Plain Layout
24714 Functions ! predefined
24722 \begin_layout Standard
24723 In general, variables are set
24727 in mathematical expressions, but not function names, because
24728 \begin_inset Formula $sin$
24731 could be misunderstood as
24732 \begin_inset Formula $s\cdot i\cdot n$
24736 Therefore there are predefined functionswhich are additionally a bit separated
24738 They are inserted as commands starting with a backslash before their name.
24739 \begin_inset Separator parbreak
24745 \begin_layout Standard
24747 \begin_inset Tabular
24748 <lyxtabular version="3" rows="2" columns="2">
24749 <features booktabs="true" tabularvalignment="middle">
24750 <column alignment="center" valignment="top" width="0pt">
24751 <column alignment="center" valignment="top" width="0pt">
24753 <cell alignment="center" valignment="top" topline="true" bottomline="true" usebox="none">
24756 \begin_layout Plain Layout
24762 <cell alignment="center" valignment="top" topline="true" bottomline="true" rightline="true" usebox="none">
24765 \begin_layout Plain Layout
24773 <cell alignment="center" valignment="top" bottomline="true" usebox="none">
24776 \begin_layout Plain Layout
24782 <cell alignment="center" valignment="top" bottomline="true" rightline="true" usebox="none">
24785 \begin_layout Plain Layout
24786 \begin_inset Formula $Asin(x)+B$
24800 \begin_inset space \quad{}
24804 \begin_inset Tabular
24805 <lyxtabular version="3" rows="2" columns="2">
24806 <features booktabs="true" tabularvalignment="middle">
24807 <column alignment="center" valignment="top" width="0pt">
24808 <column alignment="center" valignment="top" width="0pt">
24810 <cell alignment="center" valignment="top" topline="true" bottomline="true" usebox="none">
24813 \begin_layout Plain Layout
24819 <cell alignment="center" valignment="top" topline="true" bottomline="true" usebox="none">
24822 \begin_layout Plain Layout
24830 <cell alignment="center" valignment="top" bottomline="true" usebox="none">
24833 \begin_layout Plain Layout
24841 <cell alignment="center" valignment="top" bottomline="true" usebox="none">
24844 \begin_layout Plain Layout
24845 \begin_inset Formula $A\sin(x)+B$
24861 \begin_layout Standard
24862 The following functions are predefined:
24865 \begin_layout Standard
24866 \begin_inset VSpace -2mm
24872 \begin_layout Standard
24874 \begin_inset Tabular
24875 <lyxtabular version="3" rows="9" columns="4">
24876 <features booktabs="true" tabularvalignment="middle">
24877 <column alignment="center" valignment="top" width="0pt">
24878 <column alignment="center" valignment="top" width="0pt">
24879 <column alignment="center" valignment="top" width="0pt">
24880 <column alignment="center" valignment="top" width="0pt">
24882 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
24885 \begin_layout Plain Layout
24891 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
24894 \begin_layout Plain Layout
24900 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
24903 \begin_layout Plain Layout
24909 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
24912 \begin_layout Plain Layout
24920 <cell alignment="center" valignment="top" leftline="true" usebox="none">
24923 \begin_layout Plain Layout
24931 <cell alignment="center" valignment="top" leftline="true" usebox="none">
24934 \begin_layout Plain Layout
24942 <cell alignment="center" valignment="top" leftline="true" usebox="none">
24945 \begin_layout Plain Layout
24953 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
24956 \begin_layout Plain Layout
24966 <cell alignment="center" valignment="top" leftline="true" usebox="none">
24969 \begin_layout Plain Layout
24977 <cell alignment="center" valignment="top" leftline="true" usebox="none">
24980 \begin_layout Plain Layout
24988 <cell alignment="center" valignment="top" leftline="true" usebox="none">
24991 \begin_layout Plain Layout
24999 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
25002 \begin_layout Plain Layout
25012 <cell alignment="center" valignment="top" leftline="true" usebox="none">
25015 \begin_layout Plain Layout
25023 <cell alignment="center" valignment="top" leftline="true" usebox="none">
25026 \begin_layout Plain Layout
25034 <cell alignment="center" valignment="top" leftline="true" usebox="none">
25037 \begin_layout Plain Layout
25045 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
25048 \begin_layout Plain Layout
25058 <cell alignment="center" valignment="top" leftline="true" usebox="none">
25061 \begin_layout Plain Layout
25069 <cell alignment="center" valignment="top" leftline="true" usebox="none">
25072 \begin_layout Plain Layout
25080 <cell alignment="center" valignment="top" leftline="true" usebox="none">
25083 \begin_layout Plain Layout
25091 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
25094 \begin_layout Plain Layout
25104 <cell alignment="center" valignment="top" leftline="true" usebox="none">
25107 \begin_layout Plain Layout
25115 <cell alignment="center" valignment="top" leftline="true" usebox="none">
25118 \begin_layout Plain Layout
25126 <cell alignment="center" valignment="top" leftline="true" usebox="none">
25129 \begin_layout Plain Layout
25137 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
25140 \begin_layout Plain Layout
25150 <cell alignment="center" valignment="top" leftline="true" usebox="none">
25153 \begin_layout Plain Layout
25161 <cell alignment="center" valignment="top" leftline="true" usebox="none">
25164 \begin_layout Plain Layout
25172 <cell alignment="center" valignment="top" leftline="true" usebox="none">
25175 \begin_layout Plain Layout
25183 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
25186 \begin_layout Plain Layout
25196 <cell alignment="center" valignment="top" leftline="true" usebox="none">
25199 \begin_layout Plain Layout
25207 <cell alignment="center" valignment="top" leftline="true" usebox="none">
25210 \begin_layout Plain Layout
25218 <cell alignment="center" valignment="top" leftline="true" usebox="none">
25221 \begin_layout Plain Layout
25229 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
25232 \begin_layout Plain Layout
25242 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
25245 \begin_layout Plain Layout
25253 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
25256 \begin_layout Plain Layout
25264 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
25267 \begin_layout Plain Layout
25275 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
25278 \begin_layout Plain Layout
25294 \begin_layout Standard
25295 They can also be inserted with the math toolbar button
25298 arg "math-insert \\functions"
25304 \begin_layout Subsection
25305 Self-defined Functions
25306 \begin_inset Index idx
25309 \begin_layout Plain Layout
25310 Functions ! self-defined
25318 \begin_layout Standard
25319 To use a function that is not predefined, like for example the sign function
25320 sgn(x), there are two possibilities:
25323 \begin_layout Itemize
25324 Define the function by inserting the following line to the \SpecialChar LaTeX
25329 \begin_layout Plain Layout
25334 DeclareMathOperator
25337 \begin_inset CommandInset ref
25339 reference "subsec:Self-defined-Operators"
25349 \begin_inset Newline newline
25353 \begin_inset VSpace -3mm
25357 \begin_inset Newline newline
25364 DeclareMathOperator{
25369 \begin_inset Index idx
25372 \begin_layout Plain Layout
25377 DeclareMathOperator
25383 \begin_inset Newline newline
25387 \begin_inset VSpace -2mm
25391 \begin_inset Newline newline
25394 Now the new defined function can be called with the command
25403 \begin_layout Itemize
25404 Write the formula as usual, mark the formula name, in our example the letters
25409 , and change it to mathematical text.
25410 Finally, a space is inserted between prefactor and function.
25413 \begin_layout Standard
25414 The result is the same with both methods as with a predefined function
25418 \begin_layout Plain Layout
25419 In \SpecialChar LyX
25420 self-defined functions are displayed red, predefined ones black.
25426 \begin_inset Separator parbreak
25432 \begin_layout Standard
25434 \begin_inset Tabular
25435 <lyxtabular version="3" rows="3" columns="2">
25436 <features booktabs="true" tabularvalignment="middle">
25437 <column alignment="center" valignment="top" width="0pt">
25438 <column alignment="center" valignment="top" width="0pt">
25440 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
25443 \begin_layout Plain Layout
25449 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
25452 \begin_layout Plain Layout
25460 <cell alignment="center" valignment="top" leftline="true" usebox="none">
25463 \begin_layout Plain Layout
25471 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
25474 \begin_layout Plain Layout
25475 \begin_inset Formula $A\sgn(x)+B$
25485 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
25488 \begin_layout Plain Layout
25492 \begin_inset Formula $\underbrace{\textrm{sgn}}_{\textrm{Alt+M}\,\textrm{M}}$
25500 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
25503 \begin_layout Plain Layout
25504 \begin_inset Formula $A\,\textrm{sgn}(x)+B$
25520 \begin_layout Standard
25521 The first method is more suitable when the self-defined function should
25522 be used several times.
25525 \begin_layout Subsection
25527 \begin_inset Index idx
25530 \begin_layout Plain Layout
25539 \begin_layout Standard
25540 For limits, in addition to the commands
25547 \begin_inset Index idx
25550 \begin_layout Plain Layout
25570 the following functions are defined:
25571 \begin_inset Separator parbreak
25577 \begin_layout Standard
25579 \begin_inset Tabular
25580 <lyxtabular version="3" rows="5" columns="2">
25581 <features booktabs="true" tabularvalignment="middle">
25582 <column alignment="center" valignment="top" width="0pt">
25583 <column alignment="center" valignment="top" width="0pt">
25585 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
25588 \begin_layout Plain Layout
25594 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
25597 \begin_layout Plain Layout
25605 <cell alignment="center" valignment="top" leftline="true" usebox="none">
25608 \begin_layout Plain Layout
25616 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
25619 \begin_layout Plain Layout
25620 \begin_inset Formula $\varliminf$
25629 <row topspace="1.5mm">
25630 <cell alignment="center" valignment="top" usebox="none">
25633 \begin_layout Plain Layout
25641 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
25644 \begin_layout Plain Layout
25645 \begin_inset Formula $\varlimsup$
25654 <row topspace="1.5mm">
25655 <cell alignment="center" valignment="top" usebox="none">
25658 \begin_layout Plain Layout
25666 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
25669 \begin_layout Plain Layout
25670 \begin_inset Formula $\varprojlim$
25679 <row topspace="1.5mm" bottomspace="1mm">
25680 <cell alignment="center" valignment="top" bottomline="true" usebox="none">
25683 \begin_layout Plain Layout
25691 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
25694 \begin_layout Plain Layout
25695 \begin_inset Formula $\varinjlim$
25711 \begin_layout Standard
25712 \begin_inset VSpace medskip
25715 The limit is created by inserting a subscript.
25716 It is set right beside the function in an inline formula:
25719 \begin_layout Standard
25721 \begin_inset Tabular
25722 <lyxtabular version="3" rows="2" columns="2">
25723 <features booktabs="true" tabularvalignment="middle">
25724 <column alignment="center" valignment="top" width="0pt">
25725 <column alignment="center" valignment="top" width="0pt">
25727 <cell alignment="center" valignment="top" bottomline="true" usebox="none">
25730 \begin_layout Plain Layout
25736 <cell alignment="center" valignment="top" bottomline="true" usebox="none">
25739 \begin_layout Plain Layout
25747 <cell alignment="center" valignment="top" usebox="none">
25750 \begin_layout Plain Layout
25756 \begin_inset space \textvisiblespace{}
25760 \begin_inset space \textvisiblespace{}
25768 <cell alignment="center" valignment="top" usebox="none">
25771 \begin_layout Plain Layout
25772 \begin_inset Formula $\lim_{x\to A}x=B$
25788 \begin_layout Standard
25789 In a displayed formula the limit is set below the formula, as usual:
25790 \begin_inset Formula
25800 \begin_layout Standard
25801 \begin_inset VSpace medskip
25807 \begin_layout Standard
25808 How to adjust the typesetting of the limits see
25809 \begin_inset CommandInset ref
25811 reference "subsec:Operator-Limits"
25818 \begin_layout Subsection
25820 \begin_inset Index idx
25823 \begin_layout Plain Layout
25824 Functions ! modulo-
25832 \begin_layout Standard
25833 The modulo-function is special, because it exists in four variants.
25834 The variants in a displayed formula are:
25835 \begin_inset Formula
25837 \underline{\textrm{Command}\raisebox{-0.9mm}{}} & & \underline{\textrm{Result}}\\
25838 \mathrm{a\backslash mod\textrm{␣}b} & & a\mod b\\
25839 \mathrm{a\backslash pmod\textrm{␣}b} & & a\pmod b\\
25840 \mathrm{a\backslash bmod\textrm{␣}b} & & a\bmod b\\
25841 \mathrm{a\backslash pod\textrm{␣}b} & & a\pod b
25849 \begin_layout Standard
25850 In an inline formula less space is set before the function names for all
25852 By default the modulo-functions take only the first following character
25854 To use more than one character, one has to put them into \SpecialChar TeX
25856 \begin_inset Formula
25858 \underline{\textrm{Command}\raisebox{-0.9mm}{}} & & \underline{\textrm{Result}}\\
25859 \mathrm{a\backslash pod\textrm{␣}bcd} & & a\pod bcd\\
25860 \mathrm{a\backslash pod\backslash\{bc\to d} & & a\pod{bc}d
25868 \begin_layout Section
25870 \begin_inset Index idx
25873 \begin_layout Plain Layout
25882 \begin_layout Standard
25883 The characters ^ and _ would normally create a superscript and subscript,
25885 To get these characters you have to insert them with a leading
25888 \begin_inset Separator parbreak
25894 \begin_layout Standard
25897 \begin_inset Tabular
25898 <lyxtabular version="3" rows="3" columns="2">
25899 <features booktabs="true" tabularvalignment="middle">
25900 <column alignment="left" valignment="top" width="0pt">
25901 <column alignment="block" valignment="top">
25903 <cell alignment="left" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
25906 \begin_layout Plain Layout
25912 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
25915 \begin_layout Plain Layout
25923 <cell alignment="left" valignment="top" leftline="true" usebox="none">
25926 \begin_layout Plain Layout
25930 \begin_inset space \textvisiblespace{}
25938 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
25941 \begin_layout Plain Layout
25942 \begin_inset Formula $\mathcircumflex$
25952 <cell alignment="left" valignment="top" bottomline="true" leftline="true" usebox="none">
25955 \begin_layout Plain Layout
25963 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
25966 \begin_layout Plain Layout
25967 \begin_inset Formula $\_$
25983 \begin_layout Subsection
25984 Special Characters in Mathematical Text
25987 \begin_layout Standard
25988 The following commands can only be used in mathematical text or in \SpecialChar TeX
25992 \begin_layout Standard
25993 \begin_inset space \hfill{}
25997 \begin_inset Tabular
25998 <lyxtabular version="3" rows="8" columns="2">
25999 <features booktabs="true" tabularvalignment="middle">
26000 <column alignment="left" valignment="top" width="0pt">
26001 <column alignment="block" valignment="top">
26003 <cell alignment="left" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
26006 \begin_layout Plain Layout
26012 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
26015 \begin_layout Plain Layout
26023 <cell alignment="left" valignment="top" leftline="true" usebox="none">
26026 \begin_layout Plain Layout
26034 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
26037 \begin_layout Plain Layout
26038 \begin_inset Formula $\textrm{œ}$
26048 <cell alignment="left" valignment="top" leftline="true" usebox="none">
26051 \begin_layout Plain Layout
26059 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
26062 \begin_layout Plain Layout
26063 \begin_inset Formula $\textrm{Œ}$
26073 <cell alignment="left" valignment="top" leftline="true" usebox="none">
26076 \begin_layout Plain Layout
26084 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
26087 \begin_layout Plain Layout
26088 \begin_inset Formula $\textrm{æ}$
26098 <cell alignment="left" valignment="top" leftline="true" usebox="none">
26101 \begin_layout Plain Layout
26109 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
26112 \begin_layout Plain Layout
26113 \begin_inset Formula $\textrm{Æ}$
26123 <cell alignment="left" valignment="top" leftline="true" usebox="none">
26126 \begin_layout Plain Layout
26134 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
26137 \begin_layout Plain Layout
26138 \begin_inset Formula $\textrm{å}$
26148 <cell alignment="left" valignment="top" leftline="true" usebox="none">
26151 \begin_layout Plain Layout
26155 \begin_inset Index idx
26158 \begin_layout Plain Layout
26165 \begin_layout Plain Layout
26186 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
26189 \begin_layout Plain Layout
26190 \begin_inset Formula $\textrm{Å}$
26200 <cell alignment="left" valignment="top" bottomline="true" leftline="true" usebox="none">
26203 \begin_layout Plain Layout
26211 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
26214 \begin_layout Plain Layout
26215 \begin_inset Formula $\textrm{ı}$
26229 \begin_inset space \hfill{}
26233 \begin_inset Tabular
26234 <lyxtabular version="3" rows="8" columns="2">
26235 <features booktabs="true" tabularvalignment="middle">
26236 <column alignment="left" valignment="top" width="0pt">
26237 <column alignment="center" valignment="top">
26239 <cell alignment="left" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
26242 \begin_layout Plain Layout
26244 \begin_inset Note Note
26247 \begin_layout Plain Layout
26249 \begin_inset space \thinspace{}
26252 mm is used for separation, because otherwise the output will be ¡ and ¿
26263 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
26266 \begin_layout Plain Layout
26274 <cell alignment="left" valignment="top" leftline="true" usebox="none">
26277 \begin_layout Plain Layout
26285 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
26288 \begin_layout Plain Layout
26289 \begin_inset Formula $\textrm{ø}$
26299 <cell alignment="left" valignment="top" leftline="true" usebox="none">
26302 \begin_layout Plain Layout
26310 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
26313 \begin_layout Plain Layout
26314 \begin_inset Formula $\textrm{Ø}$
26324 <cell alignment="left" valignment="top" leftline="true" usebox="none">
26327 \begin_layout Plain Layout
26335 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
26338 \begin_layout Plain Layout
26339 \begin_inset Formula $\textrm{ł}$
26349 <cell alignment="left" valignment="top" leftline="true" usebox="none">
26352 \begin_layout Plain Layout
26360 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
26363 \begin_layout Plain Layout
26364 \begin_inset Formula $\textrm{Ł}$
26374 <cell alignment="left" valignment="top" leftline="true" usebox="none">
26377 \begin_layout Plain Layout
26379 \begin_inset space \hspace{}
26384 \begin_inset space \textvisiblespace{}
26392 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
26395 \begin_layout Plain Layout
26396 \begin_inset Formula $\textrm{!`}$
26406 <cell alignment="left" valignment="top" leftline="true" usebox="none">
26409 \begin_layout Plain Layout
26411 \begin_inset space \hspace{}
26416 \begin_inset space \textvisiblespace{}
26424 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
26427 \begin_layout Plain Layout
26428 \begin_inset Formula $\textrm{?`}$
26438 <cell alignment="left" valignment="top" bottomline="true" leftline="true" usebox="none">
26441 \begin_layout Plain Layout
26449 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
26452 \begin_layout Plain Layout
26453 \begin_inset Formula $\textrm{ȷ}$
26467 \begin_inset space \hfill{}
26473 \begin_layout Standard
26475 \begin_inset Formula $\textrm{\textrm{Å}}$
26479 \begin_inset Formula $\textrm{\textrm{Ø}}$
26482 can also be inserted via the math toolbar button
26485 arg "math-insert \\digamma"
26491 \begin_layout Standard
26492 An exception are the commands
26495 \begin_inset space \hspace{}
26504 \begin_inset space \hspace{}
26510 , because they can be inserted in \SpecialChar LyX
26514 \begin_layout Subsection
26516 \begin_inset CommandInset label
26518 name "subsec:Accents-in-Text"
26523 \begin_inset Index idx
26526 \begin_layout Plain Layout
26535 \begin_layout Standard
26536 With the following commands all letters can be accented.
26537 The commands must be inserted in \SpecialChar TeX
26541 \begin_layout Standard
26542 \begin_inset space \hfill{}
26546 \begin_inset Tabular
26547 <lyxtabular version="3" rows="8" columns="2">
26548 <features booktabs="true" tabularvalignment="middle">
26549 <column alignment="left" valignment="top" width="0pt">
26550 <column alignment="block" valignment="top">
26552 <cell alignment="left" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
26555 \begin_layout Plain Layout
26561 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
26564 \begin_layout Plain Layout
26572 <cell alignment="left" valignment="top" leftline="true" usebox="none">
26575 \begin_layout Plain Layout
26579 \begin_inset Quotes grd
26587 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
26590 \begin_layout Plain Layout
26594 \begin_layout Plain Layout
26610 <cell alignment="left" valignment="top" leftline="true" usebox="none">
26613 \begin_layout Plain Layout
26621 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
26624 \begin_layout Plain Layout
26628 \begin_layout Plain Layout
26644 <cell alignment="left" valignment="top" leftline="true" usebox="none">
26647 \begin_layout Plain Layout
26651 \begin_inset space \textvisiblespace{}
26659 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
26662 \begin_layout Plain Layout
26666 \begin_layout Plain Layout
26682 <cell alignment="left" valignment="top" leftline="true" usebox="none">
26685 \begin_layout Plain Layout
26693 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
26696 \begin_layout Plain Layout
26700 \begin_layout Plain Layout
26716 <cell alignment="left" valignment="top" leftline="true" usebox="none">
26719 \begin_layout Plain Layout
26723 \begin_inset space \textvisiblespace{}
26731 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
26734 \begin_layout Plain Layout
26738 \begin_layout Plain Layout
26754 <cell alignment="left" valignment="top" leftline="true" usebox="none">
26757 \begin_layout Plain Layout
26761 \begin_inset space \textvisiblespace{}
26769 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
26772 \begin_layout Plain Layout
26776 \begin_layout Plain Layout
26792 <cell alignment="left" valignment="top" bottomline="true" leftline="true" usebox="none">
26795 \begin_layout Plain Layout
26799 \begin_inset space \textvisiblespace{}
26807 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
26810 \begin_layout Plain Layout
26814 \begin_layout Plain Layout
26834 \begin_inset space \hfill{}
26838 \begin_inset Tabular
26839 <lyxtabular version="3" rows="8" columns="2">
26840 <features booktabs="true" tabularvalignment="middle">
26841 <column alignment="left" valignment="top" width="0pt">
26842 <column alignment="center" valignment="top">
26844 <cell alignment="left" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
26847 \begin_layout Plain Layout
26853 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
26856 \begin_layout Plain Layout
26864 <cell alignment="left" valignment="top" leftline="true" usebox="none">
26867 \begin_layout Plain Layout
26871 \begin_inset space \textvisiblespace{}
26879 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
26882 \begin_layout Plain Layout
26886 \begin_layout Plain Layout
26902 <cell alignment="left" valignment="top" leftline="true" usebox="none">
26905 \begin_layout Plain Layout
26913 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
26916 \begin_layout Plain Layout
26920 \begin_layout Plain Layout
26936 <cell alignment="left" valignment="top" leftline="true" usebox="none">
26939 \begin_layout Plain Layout
26943 \begin_inset Index idx
26946 \begin_layout Plain Layout
26957 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
26960 \begin_layout Plain Layout
26964 \begin_layout Plain Layout
26980 <cell alignment="left" valignment="top" leftline="true" usebox="none">
26983 \begin_layout Plain Layout
26991 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
26994 \begin_layout Plain Layout
26998 \begin_layout Plain Layout
27014 <cell alignment="left" valignment="top" leftline="true" usebox="none">
27017 \begin_layout Plain Layout
27021 \begin_inset space \textvisiblespace{}
27029 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
27032 \begin_layout Plain Layout
27036 \begin_layout Plain Layout
27052 <cell alignment="left" valignment="top" leftline="true" usebox="none">
27055 \begin_layout Plain Layout
27059 \begin_inset space \textvisiblespace{}
27067 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
27070 \begin_layout Plain Layout
27074 \begin_layout Plain Layout
27090 <cell alignment="left" valignment="top" leftline="true" usebox="none">
27093 \begin_layout Plain Layout
27097 \begin_inset space \textvisiblespace{}
27105 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
27108 \begin_layout Plain Layout
27112 \begin_layout Plain Layout
27132 \begin_inset space \hfill{}
27138 \begin_layout Standard
27139 \begin_inset VSpace medskip
27148 also two different characters can be accented.
27154 \begin_inset space \textvisiblespace{}
27163 \begin_layout Plain Layout
27175 \begin_layout Standard
27188 can in combination with vowels directly be inserted with the keyboard without
27189 using \SpecialChar TeX
27191 The same applies for the tilde
27195 \begin_layout Plain Layout
27196 This only applies for keyboards where the tilde is defined as accent.
27205 in combination with
27220 \begin_layout Standard
27263 and accents that are inserted directly with the keyboard are also available
27264 in mathematical text.
27265 For the other accents there are special math commands to be used in formulas,
27267 \begin_inset CommandInset ref
27269 reference "subsec:Accents-for-one"
27276 \begin_layout Standard
27277 \begin_inset VSpace bigskip
27280 Furthermore, with the command
27287 \begin_inset Index idx
27290 \begin_layout Plain Layout
27298 all numbers and letters can be set into a circle, quasi accented with a
27299 circle, similar to the copyright symbol.
27302 \begin_layout Standard
27304 \begin_inset Tabular
27305 <lyxtabular version="3" rows="3" columns="2">
27306 <features booktabs="true" tabularvalignment="middle">
27307 <column alignment="center" valignment="top" width="0pt">
27308 <column alignment="center" valignment="top">
27310 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
27313 \begin_layout Plain Layout
27319 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
27322 \begin_layout Plain Layout
27330 <cell alignment="center" valignment="top" leftline="true" usebox="none">
27333 \begin_layout Plain Layout
27341 <cell multicolumn="1" alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
27344 \begin_layout Plain Layout
27348 \begin_layout Plain Layout
27363 <row topspace="1mm">
27364 <cell alignment="center" valignment="top" bottomline="true" usebox="none">
27367 \begin_layout Plain Layout
27378 raisebox{-1.5pt}{W}}
27383 <cell multicolumn="1" alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
27386 \begin_layout Plain Layout
27390 \begin_layout Plain Layout
27420 \begin_layout Standard
27421 One has to take care that the character fits in the circle.
27432 \begin_layout Plain Layout
27434 \begin_inset CommandInset ref
27436 reference "subsec:Font-Sizes"
27445 specifies thereby the size of the circle.
27456 \begin_layout Plain Layout
27458 \begin_inset CommandInset ref
27460 reference "subsec:Boxes-without-Frame"
27469 the character can be centered.
27472 \begin_layout Subsection
27474 \begin_inset Index idx
27477 \begin_layout Plain Layout
27486 \begin_layout Standard
27487 Old-style figures (also known as old-style numerals) are created with the
27495 \begin_inset Index idx
27498 \begin_layout Plain Layout
27507 The command can be used in formulas and in \SpecialChar TeX
27509 The command scheme is:
27512 \begin_layout Standard
27517 oldstylenums{number}
27520 \begin_layout Standard
27525 oldstylenums{0123456789
27528 \begin_inset Formula $\oldstylenums{0123456789}$
27534 \begin_layout Section
27536 \begin_inset CommandInset label
27538 name "sec:Formula-Styles"
27543 \begin_inset Index idx
27546 \begin_layout Plain Layout
27555 \begin_layout Itemize
27556 There are two different alignment styles:
27557 \begin_inset Separator parbreak
27564 \begin_layout Description
27565 Centered is the predefined standard
27568 \begin_layout Description
27569 Indented for this the option
27573 must be inserted in the menu
27575 Document\SpecialChar menuseparator
27581 \begin_inset space ~
27587 \begin_layout Standard
27592 is used, the indentation can be adjusted with the length
27599 \begin_inset Index idx
27602 \begin_layout Plain Layout
27611 Should the distance be 15
27612 \begin_inset space \thinspace{}
27615 mm, the following command line is inserted in the \SpecialChar LaTeX
27619 \begin_layout Standard
27629 \begin_layout Standard
27630 When no length is specified, the predefined value of 30
27631 \begin_inset space \thinspace{}
27638 \begin_layout Itemize
27639 And two different numbering styles:
27640 \begin_inset Separator parbreak
27647 \begin_layout Description
27648 Right is the predefined standard
27651 \begin_layout Description
27652 Left for this the option
27656 must be inserted in the menu
27658 Document\SpecialChar menuseparator
27664 \begin_inset space ~
27671 \begin_layout Standard
27680 can also be used together.
27681 In this case both options are inserted, separated by a comma.
27684 \begin_layout Standard
27685 The chosen styles are used for all displayed formulas of the document.
27686 When both, centered and indented formulas should be created in a document,
27692 The indented formulas are then set in a flalign environment, see
27693 \begin_inset CommandInset ref
27695 reference "subsec:Flalign-Environment"
27702 \begin_layout Section
27704 \begin_inset CommandInset label
27706 name "sec:Multiline-Formulas"
27711 \begin_inset Index idx
27714 \begin_layout Plain Layout
27715 Formula ! multiline
27723 \begin_layout Subsection
27727 \begin_layout Standard
27728 In \SpecialChar LyX
27729 multiline formulas are created by pressing
27732 arg "newline-insert newline"
27736 This creates either an
27740 that is described in
27741 \begin_inset CommandInset ref
27743 reference "subsec:Standard-align-Environment"
27747 or, when automatically loading the package
27751 is disabled in the document settings, an
27753 eqnarray environment
27755 that is described in
27756 \begin_inset CommandInset ref
27758 reference "subsec:Eqnarray-Environment"
27763 The align environment is recommended because it provides in any case a
27764 typographically correct output.
27767 \begin_layout Standard
27768 There are other multiline formula environments that can be created via the
27771 Insert\SpecialChar menuseparator
27775 These environments are described in the following sections.
27778 \begin_layout Standard
27779 In all multiline formula environments a new line is created by pressing
27783 arg "newline-insert newline"
27787 To add or delete lines, the math toolbar buttons
27790 arg "tabular-feature append-row"
27796 arg "tabular-feature delete-row"
27799 , respectively, or the menu
27801 Edit\SpecialChar menuseparator
27807 \begin_layout Subsubsection
27809 \begin_inset CommandInset label
27811 name "subsec:Line-Separation"
27816 \begin_inset Index idx
27819 \begin_layout Plain Layout
27820 Formula ! multiline ! Line separation
27828 \begin_layout Standard
27829 There is sometimes not enough space in multiline formulas between the lines:
27830 \begin_inset Formula
27832 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}\\
27833 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
27841 \begin_layout Standard
27842 In \SpecialChar LaTeX
27843 additional line space is specified as optional argument of the new line
27845 This is not yet possible in \SpecialChar LyX
27850 \begin_layout Plain Layout
27852 \begin_inset CommandInset href
27854 name "LyX-bug #1505"
27855 target "http://www.lyx.org/trac/ticket/1505"
27864 , therefore the whole formula must be inserted in \SpecialChar TeX
27866 To add in our example space, the command
27874 is inserted at the end of the first line.
27879 \begin_layout Plain Layout
27886 \begin_layout Plain Layout
27888 B^{2}(B^{2}-2r_{g}^{2}+2x_{0}^{2}-2r_{k}^{2})+4x_{0}^{2}x^{2}+4x_{0}xD &
27891 textrm{-}4x^{2}B^{2}+4x_{0}xB^{2}
27898 \begin_layout Plain Layout
27902 left(B^{2}+x_{0}^{2}
27910 left(B^{2}-2r_{g}^{2}+2x_{0}^{2}-2r_{k}^{2}
27915 \begin_layout Plain Layout
27927 \begin_layout Standard
27928 \begin_inset VSpace bigskip
27931 To set the line separation for all lines in a formula, the length
27938 \begin_inset Index idx
27941 \begin_layout Plain Layout
27951 \begin_inset Formula $\mbox{line separation}=\mathrm{6\,pt+\backslash jot}$
27962 \begin_inset space \thinspace{}
27967 \begin_inset space \thinspace{}
27970 mm additional line separation as in the previous example, the command
27973 \begin_layout Standard
27983 \begin_layout Standard
27984 is inserted in \SpecialChar TeX
27985 mode before the formula.
27986 This requires that the \SpecialChar LaTeX
27995 \begin_layout Plain Layout
28000 is part of every \SpecialChar LaTeX
28001 standard installation.
28007 \begin_inset Index idx
28010 \begin_layout Plain Layout
28016 was loaded in \SpecialChar LaTeX
28017 -preamble with the line
28020 \begin_layout Standard
28028 \begin_layout Standard
28033 \begin_layout Plain Layout
28045 \begin_inset Formula
28047 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}\\
28048 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
28056 \begin_layout Standard
28060 \begin_layout Plain Layout
28071 To get back to the predefined distance,
28077 is set to the value 3
28078 \begin_inset space \thinspace{}
28084 \begin_layout Subsubsection
28086 \begin_inset CommandInset label
28088 name "subsec:Column-Separation"
28093 \begin_inset Index idx
28096 \begin_layout Plain Layout
28097 Formula ! multiline ! Column separation
28105 \begin_layout Standard
28106 Multiline formulas form a matrix.
28107 A formula in the eqnarray environment is for example a matrix with three
28109 By changing the column separation in this environment, the space beside
28110 the relation sign can be changed.
28113 \begin_layout Standard
28114 The column separation is specified with the length
28121 \begin_inset Index idx
28124 \begin_layout Plain Layout
28133 \begin_inset Newline newline
28136 column separation = 2
28137 \begin_inset space \thinspace{}
28147 \begin_inset Newline newline
28153 \begin_layout Standard
28163 \begin_layout Standard
28164 inserted in \SpecialChar TeX
28165 mode, sets for all following formulas a column separation of
28167 \begin_inset space \thinspace{}
28171 To get back to the predefined distance,
28178 \begin_inset space \thinspace{}
28184 \begin_layout Standard
28186 \begin_inset space \thinspace{}
28189 cm column separation:
28193 \begin_layout Plain Layout
28205 \begin_inset Formula
28213 A formula with the predefined column separation for matrices of 10
28214 \begin_inset space \thinspace{}
28221 \begin_layout Plain Layout
28233 \begin_inset Formula
28244 \begin_layout Subsubsection
28246 \begin_inset Index idx
28249 \begin_layout Plain Layout
28258 \begin_layout Standard
28259 Long formulas can be typeset using these methods:
28262 \begin_layout Itemize
28263 When one side of the equation is much shorter than the line width, this
28264 one is chosen for the left side and the right side is typeset over two
28266 \begin_inset Formula
28268 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 \\
28269 & & -\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}
28274 The minus sign at the beginning of the second line does normally not appear
28275 as an operator because it is the first character of the line.
28276 Thus it would not be surrounded by space and could not be distinguished
28277 from the fraction bar.
28279 \begin_inset space \thinspace{}
28282 pt space was inserted behind the minus sign with the command
28292 \begin_layout Plain Layout
28300 \begin_inset CommandInset ref
28302 reference "subsec:Variable-Space"
28312 \begin_inset Index idx
28315 \begin_layout Plain Layout
28326 \begin_layout Itemize
28327 When both sides of the equation are too long, the command
28334 \begin_inset Index idx
28337 \begin_layout Plain Layout
28346 It is inserted in the first column of the first line and causes all further
28347 insertions to overwrite the following columns:
28348 \begin_inset Formula
28350 \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 \\
28351 & & -\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 \\
28352 & & =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}
28357 After the insertion of
28363 , the cursor is in a purple box that is a bit shifted to the left from the
28365 In this the formula is inserted.
28366 \begin_inset Newline newline
28369 The content of the further lines is inserted to the second or another formula
28371 The greater the column number where it was inserted, the larger the indentation.
28372 \begin_inset VSpace medskip
28376 \begin_inset Newline newline
28380 \begin_inset Note Greyedout
28383 \begin_layout Plain Layout
28384 Note the following when using
28393 \begin_layout Itemize
28394 The formula doesn't use the full page width.
28396 \begin_inset space \thinspace{}
28400 \begin_inset space \space{}
28404 \begin_inset Formula $-B^{2}$
28407 is added to the first line in the above example, it would have been outside
28409 To better use the width, negative space can be inserted at the beginning
28413 \begin_layout Itemize
28414 Due to a bug in \SpecialChar LyX
28415 the cursor cannot be set with the mouse into the first
28420 \begin_layout Plain Layout
28421 \begin_inset CommandInset href
28423 name "LyX-bug #1429"
28424 target "http://www.lyx.org/trac/ticket/1429"
28433 One can only set the cursor at the beginning of the line and move it with
28442 \begin_layout Itemize
28443 Other methods to set long formulas are offered by the environments described
28445 \begin_inset CommandInset ref
28447 reference "subsec:Multline-Environment"
28452 \begin_inset CommandInset ref
28454 reference "subsec:Multiline-Formula-Parts"
28461 \begin_layout Subsubsection
28462 Multiline Fractions
28463 \begin_inset CommandInset label
28465 name "subsec:Multiline-Fractions"
28470 \begin_inset Index idx
28473 \begin_layout Plain Layout
28474 Fractions ! multiline
28482 \begin_layout Standard
28483 There are cases where the denominator and/or the numerator of a fraction
28484 is so long that the fraction does not fit into one line.
28485 It is then necessary to add a line break within the fraction.
28486 This can be done using the command
28493 \begin_inset Index idx
28496 \begin_layout Plain Layout
28505 To activate it, set in the document settings under
28508 \begin_inset space ~
28518 \begin_inset Index idx
28521 \begin_layout Plain Layout
28522 Packages ! mathtools
28530 \begin_inset space ~
28545 \begin_layout Standard
28550 splitfrac{first line}{second line}
28553 \begin_layout Standard
28554 and is used as denominator and/or numerator:
28557 \begin_layout Standard
28558 \begin_inset Formula
28560 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}
28565 The command for the first numerator above is:
28568 \begin_layout Standard
28573 splitfrac{xy+xy+xy+xy+xy
28574 \begin_inset space \textvisiblespace{}
28582 \begin_layout Subsubsection
28584 \begin_inset CommandInset label
28586 name "subsec:Multiline-Brackets"
28591 \begin_inset Index idx
28594 \begin_layout Plain Layout
28595 Brackets ! for multiline expressions
28603 \begin_layout Standard
28604 For brackets spanning multiple lines the following problem occurs:
28605 \begin_inset Formula
28607 A & = & \sin(x)\left[\prod_{R=1}^{\infty}\frac{1}{R}+\cdots\right.\\
28608 & & \left.\cdots+B-D\right]
28616 \begin_layout Standard
28617 The closing bracket is smaller than the opening bracket because brackets
28618 with variable size may not span multiple lines.
28621 \begin_layout Standard
28622 To set the bracket size for the second line correctly, the first line is
28630 \begin_inset Index idx
28633 \begin_layout Plain Layout
28641 and the second line with
28649 \begin_layout Plain Layout
28663 \begin_inset CommandInset ref
28665 reference "subsec:Automatic-Bracket-Size"
28677 \begin_inset Index idx
28680 \begin_layout Plain Layout
28703 \begin_inset space \textvisiblespace{}
28713 \begin_inset space \textvisiblespace{}
28723 \begin_inset space \textvisiblespace{}
28729 \begin_inset Formula $\downarrow$
28735 \begin_inset Index idx
28738 \begin_layout Plain Layout
28746 is inserted, because the multiplication operator with its limits is the
28747 largest symbol in the first line and this should be the size for the bracket
28748 in the second line.
28751 \begin_layout Standard
28752 The result is this:
28753 \begin_inset Formula
28755 A & = & \sin(x)\left[\prod_{R=1}^{\infty}\frac{1}{R}+\cdots\right.\\
28756 & & \left.\vphantom{\prod_{R=1}^{\infty}}\cdots+B-D\right]
28764 \begin_layout Subsection
28768 \begin_layout Standard
28769 Align environments can be used for every kind of multiline formulas.
28770 They are especially useful to set several formulas side by side.
28773 \begin_layout Standard
28774 Align environments consist of columns.
28775 The odd columns are right aligned, the even ones left aligned.
28776 Every line in an Align environment can be numbered.
28779 \begin_layout Standard
28780 Align environments are created via the menu
28782 Insert\SpecialChar menuseparator
28788 Edit\SpecialChar menuseparator
28789 Math\SpecialChar menuseparator
28790 Change Formula Type
28792 already existing formulas can be converted to Align environments.
28795 \begin_layout Standard
28796 To add or delete columns, the math toolbar buttons
28799 arg "tabular-feature append-column"
28805 arg "tabular-feature delete-column"
28808 , respectively, or the menu
28810 Edit\SpecialChar menuseparator
28816 \begin_layout Subsubsection
28817 Standard align Environment
28818 \begin_inset CommandInset label
28820 name "subsec:Standard-align-Environment"
28825 \begin_inset Index idx
28828 \begin_layout Plain Layout
28829 Formula ! multiline ! align environment
28837 \begin_layout Standard
28838 This Align environment is created by pressing
28841 arg "newline-insert newline"
28844 in a formula or by the menu
28846 Insert\SpecialChar menuseparator
28847 Math\SpecialChar menuseparator
28848 AMS align Environment
28853 \begin_layout Standard
28854 An example for two formulas set side by side, that are created with a four
28855 column align environment:
28856 \begin_inset Formula
28858 A & =\sin(B) & C & =D\\
28859 C & \ne A & B & \ne D
28864 As it can be seen, the formulas in this environment are placed so as if
28873 \begin_layout Plain Layout
28881 \begin_inset CommandInset ref
28883 reference "subsec:Variable-Space"
28894 before the first and after every even column.
28895 When the formula style
28901 \begin_layout Plain Layout
28903 \begin_inset CommandInset ref
28905 reference "sec:Formula-Styles"
28916 is used, the formula is set without the
28922 before the first column.
28925 \begin_layout Subsubsection
28926 Alignat Environment
28927 \begin_inset Index idx
28930 \begin_layout Plain Layout
28931 Formula ! multiline ! alignat environment
28939 \begin_layout Standard
28940 The alignat environment has no predefined column separation.
28941 It can be inserted manually with the spaces that are described
28942 \begin_inset CommandInset ref
28944 reference "subsec:Space"
28951 \begin_layout Standard
28952 The above example in the alignat environment where 1
28953 \begin_inset space \thinspace{}
28956 cm space was inserted at the beginning of the second formula:
28957 \begin_inset Formula
28958 \begin{alignat*}{2}
28959 A & =\sin(B) & \hspace{1cm}C & =D\\
28960 C & \ne A & B & \ne D
28965 Because the column separation can be set separately for every column, this
28966 environment is especially suitable to set three and more formulas side
28970 \begin_layout Subsubsection
28971 Flalign Environment
28972 \begin_inset CommandInset label
28974 name "subsec:Flalign-Environment"
28979 \begin_inset Index idx
28982 \begin_layout Plain Layout
28983 Formula ! multiline ! flalign environment
28991 \begin_layout Standard
28992 In this environment the first two columns are always set as much as possible
28993 to the left and the last two ones to the right.
28995 \begin_inset Formula
28997 A & =1 & B & =2 & C & =3\\
28998 X & =\textrm{-}1 & Y & =\textrm{-}2 & Z & =4
29006 \begin_layout Standard
29007 By creating a flalign environment with an odd number of columns where an
29008 empty \SpecialChar TeX
29009 brace is inserted to the last column, several formulas in a document
29010 can be set to the left, although the formula style
29015 As example the indented formula
29016 \begin_inset CommandInset ref
29018 reference "eq:VolInt"
29023 \begin_inset Formula
29025 \hspace{30pt}\iiint\limits _{V}X\,\mathrm{d}V & =U & {}
29030 The first two columns contain the formula.
29031 To indent it as with the formula style
29036 \begin_inset space \thinspace{}
29039 pt space was inserted at the beginning of the first column.
29042 \begin_layout Subsection
29043 Eqnarray Environment
29044 \begin_inset CommandInset label
29046 name "subsec:Eqnarray-Environment"
29051 \begin_inset Index idx
29054 \begin_layout Plain Layout
29055 Formula ! multiline ! eqnarray environment
29063 \begin_layout Standard
29064 When this environment has been created, three blue boxes appear.
29065 The content of the first box is right aligned, the content of the last
29067 The content of the middle box appears centered and a bit smaller, because
29068 it is designed to insert there only relation characters.
29069 \begin_inset Formula
29071 \frac{ABC}{D} & \frac{ABC}{D} & \frac{ABC}{D}\\
29081 \begin_layout Subsection
29083 \begin_inset Index idx
29086 \begin_layout Plain Layout
29087 Formula ! multiline ! gather environment
29095 \begin_layout Standard
29096 This environment consists of only one centered column.
29097 Every line can be numbered.
29098 \begin_inset Formula
29109 \begin_layout Subsection
29110 Multline Environment
29111 \begin_inset CommandInset label
29113 name "subsec:Multline-Environment"
29118 \begin_inset Index idx
29121 \begin_layout Plain Layout
29122 Formula ! multiline ! multline environment
29130 \begin_layout Standard
29131 The multline environment consists, like the gather environment, of only
29133 But the first line is left aligned, the last one right aligned.
29134 All other lines are centered.
29135 Therefore this environment is suitable for long formulas.
29137 \begin_inset CommandInset ref
29139 reference "eq:lefteqn"
29143 in the multline environment:
29144 \begin_inset Formula
29146 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}\\
29147 -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}\\
29148 =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}}
29156 \begin_layout Standard
29157 In the output only the last (first) line of a multline environment appears
29158 numbered when the document numbering is right (left).
29162 \begin_layout Plain Layout
29163 numbering styles see
29164 \begin_inset CommandInset ref
29166 reference "sec:Formula-Styles"
29178 \begin_layout Standard
29186 \begin_inset Index idx
29189 \begin_layout Plain Layout
29204 \begin_inset Index idx
29207 \begin_layout Plain Layout
29215 a centered line can be right or left aligned, respectively.
29216 The commands are used as follows:
29219 \begin_layout Standard
29224 shoveright{line content}
29230 shoveleft{line content}
29233 \begin_layout Standard
29234 \begin_inset VSpace medskip
29244 \begin_inset Index idx
29247 \begin_layout Plain Layout
29255 specifies the distance of the first line from the left page margin.
29256 Predefined is the length 0
29257 \begin_inset space \thinspace{}
29263 \begin_layout Standard
29264 As example the above formula where the command
29267 \begin_layout Standard
29277 \begin_layout Standard
29278 was inserted in \SpecialChar TeX
29283 \begin_layout Plain Layout
29295 \begin_inset Formula
29297 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}\\
29298 \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}}\\
29299 =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}}
29308 \begin_layout Plain Layout
29319 The second line was left aligned using
29328 \begin_layout Subsection
29329 Multiline Formula Parts
29330 \begin_inset CommandInset label
29332 name "subsec:Multiline-Formula-Parts"
29337 \begin_inset Index idx
29340 \begin_layout Plain Layout
29341 Formula ! multiline ! formula parts
29349 \begin_layout Standard
29350 To display only parts of a formula with multiple lines, one of the following
29351 environments is used:
29368 They can be inserted via the menu
29370 Insert\SpecialChar menuseparator
29373 or by using the commands described in this section.
29376 \begin_layout Standard
29377 The first three have the same properties as the corresponding multiline
29378 formula environments, but it is possible to set further formula parts beside
29381 \begin_inset Formula
29383 \left.\begin{aligned}\Delta x\Delta p & \ge\frac{\hbar}{2}\\
29384 \Delta E\Delta t & \ge\frac{\hbar}{2}
29386 \right\} \textrm{Uncertainty relations}
29394 \begin_layout Standard
29395 To get this formula, a displayed formula is created where the command
29402 \begin_inset Index idx
29405 \begin_layout Plain Layout
29414 A purple box appears around the blue formula box where now columns and
29415 lines can be added.
29416 Outside the multiline environment other formula parts can be set, like
29420 \begin_layout Standard
29421 The aligned environment is also suitable for long formulas whose lines are
29422 horizontally aligned.
29423 Using aligned in a displayed formula has the advantage that the formula
29424 number is vertically centered behind the lines.
29426 \begin_inset CommandInset ref
29428 reference "eq:shortlong"
29432 in the aligned environment:
29433 \begin_inset Formula
29435 \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}|}\\
29436 & -\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}|}
29445 \begin_layout Standard
29446 To use the environments
29465 \begin_inset Index idx
29468 \begin_layout Plain Layout
29483 \begin_inset Index idx
29486 \begin_layout Plain Layout
29501 \begin_inset Index idx
29504 \begin_layout Plain Layout
29512 are inserted, respectively.
29513 The split environment has the same properties as the aligned environment
29514 but it can only have two columns.
29517 \begin_layout Subsection
29518 Text in multiline Formulas
29519 \begin_inset CommandInset label
29521 name "subsec:Text-in-multiline"
29526 \begin_inset Index idx
29529 \begin_layout Plain Layout
29536 \begin_inset Index idx
29539 \begin_layout Plain Layout
29540 Formula ! multiline ! text
29548 \begin_layout Standard
29549 In the Align environments, and the multline and gather environment, text
29550 can be inserted that will appear in a separate line and doesn't affect
29551 the column alignment.
29552 To do this, the command
29559 \begin_inset Index idx
29562 \begin_layout Plain Layout
29570 is used in the following scheme:
29573 \begin_layout Standard
29581 \begin_layout Standard
29582 The text should not be longer than a line because it cannot be hyphenated.
29583 As \SpecialChar LyX
29584 doesn't yet support
29590 directly, the text is written as mathematical text.
29597 must hereby be at the beginning of a line and appears in the output above
29599 An example where the text was inserted at the beginning of the second line:
29600 \begin_inset Formula
29602 I & =a\sqrt{2}\int_{0}^{2\pi}\sqrt{1+\cos(\phi)}\;\mathrm{d}\phi\\
29603 \intertext{\text{integrand is symmetric to \ensuremath{\phi=\pi}, therefore}} & =2a\sqrt{2}\int_{0}^{\pi}\sqrt{1+\cos(\phi)}\;\mathrm{d}\phi
29611 \begin_layout Standard
29618 always creates some vertical space between the text and the formula lines.
29619 To avoid this space, set in the document settings under
29622 \begin_inset space ~
29632 \begin_inset Index idx
29635 \begin_layout Plain Layout
29636 Packages ! mathtools
29644 \begin_inset space ~
29650 Then you can use the command
29657 \begin_inset Index idx
29660 \begin_layout Plain Layout
29677 \begin_layout Standard
29678 \begin_inset Formula
29680 I & =a\sqrt{2}\int_{0}^{2\pi}\sqrt{1+\cos(\phi)}\;\mathrm{d}\phi\\
29681 \shortintertext{\text{integrand is symmetric to \ensuremath{\phi=\pi}, therefore}} & =2a\sqrt{2}\int_{0}^{\pi}\sqrt{1+\cos(\phi)}\;\mathrm{d}\phi
29689 \begin_layout Section
29691 \begin_inset Index idx
29694 \begin_layout Plain Layout
29701 \begin_inset Index idx
29704 \begin_layout Plain Layout
29705 Formula ! numbering|see
29709 \begin_layout Plain Layout
29720 \begin_layout Plain Layout
29735 \begin_layout Subsection
29739 \begin_layout Standard
29740 Numbered formulas can be created with the menu
29742 Insert\SpecialChar menuseparator
29743 Math\SpecialChar menuseparator
29745 \begin_inset space ~
29753 \begin_inset space ~
29759 Existing formulas can be numbered with the menu
29761 Edit\SpecialChar menuseparator
29762 Math\SpecialChar menuseparator
29764 \begin_inset space ~
29772 arg "math-number-toggle"
29776 The formula number is displayed in \SpecialChar LyX
29777 behind the formula as a number sign
29779 The number sign is replaced in the output by the formula number.
29782 \begin_layout Standard
29783 When numbering is turned on in multiline formulas, all lines will be numbered.
29784 But the numbering can be controlled with the menu
29786 Edit\SpecialChar menuseparator
29787 Math\SpecialChar menuseparator
29789 \begin_inset space ~
29793 \begin_inset space ~
29797 \begin_inset space ~
29805 arg "math-number-line-toggle"
29811 \begin_layout Standard
29812 Except for inline formulas, all formulas can be numbered with two different
29814 \begin_inset CommandInset ref
29816 reference "sec:Formula-Styles"
29823 \begin_layout Subsection
29825 \begin_inset Index idx
29828 \begin_layout Plain Layout
29829 Cross-references ! to formulas
29837 \begin_layout Standard
29838 All labeled formulas can be cross-referenced.
29839 A label is added by the menu
29841 Insert\SpecialChar menuseparator
29844 or the toolbar button
29851 The cursor must hereby be inside a displayed formula.
29852 Alternatively you can right-click on the formula and choose
29857 A dialog pops up displaying the prefix
29862 The label is inserted there behind the prefix.
29863 The predefined prefix means
29864 \begin_inset Quotes eld
29868 \begin_inset Quotes erd
29871 and makes it easier to find labels in large documents because it marks
29872 it as formula label to divide it from e.
29873 \begin_inset space \thinspace{}
29877 \begin_inset space \space{}
29881 To change a label, the menu
29883 Insert\SpecialChar menuseparator
29886 is used again or you right-click on a formula and then on
29893 \begin_layout Standard
29894 The name of the label is displayed in \SpecialChar LyX
29895 within two parentheses behind formula.
29896 A formula with a label is always numbered.
29899 \begin_layout Standard
29900 Cross-references are inserted via the menu
29902 Insert\SpecialChar menuseparator
29905 or with the toolbar button
29908 arg "dialog-show-new-inset ref"
29912 A formula cross-reference appears in the output as formula number.
29913 When in the cross-reference dialog window the format
29917 is chosen, the cross-reference appears in the output as formula number
29919 \begin_inset Newline newline
29922 By right-clicking on a cross-reference in \SpecialChar LyX
29923 , one jumps to the formula that
29927 \begin_layout Standard
29928 Here are as examples cross-references to formulas of the following subsections:
29929 \begin_inset Note Note
29932 \begin_layout Plain Layout
29933 Note the different cross-reference types.
29941 \begin_layout Standard
29943 \begin_inset CommandInset ref
29950 \begin_inset CommandInset ref
29958 \begin_inset CommandInset ref
29964 ) big Latin letters are used for the numbering in contrary to (
29965 \begin_inset CommandInset ref
29974 \begin_layout Standard
29975 \begin_inset VSpace medskip
29978 When the argument of
29986 \begin_layout Plain Layout
29994 \begin_inset CommandInset ref
29996 reference "subsec:User-defined-Numbering"
30007 contains a box like in
30008 \begin_inset CommandInset ref
30010 reference "subsec:Paragraph-Boxes"
30014 , the formula cannot be referenced.
30017 \begin_layout Subsection
30019 \begin_inset Index idx
30022 \begin_layout Plain Layout
30023 Formula numbering ! subnumbering
30031 \begin_layout Standard
30032 With the help of the commands
30036 begin{subequations}
30044 formulas can be subnumbered.
30045 Both commands are inserted in \SpecialChar TeX
30049 \begin_layout Standard
30051 \begin_inset Formula
30062 \begin_layout Plain Layout
30066 begin{subequations}
30072 \begin_inset VSpace -5mm
30076 \begin_inset Formula
30084 \begin_inset Formula
30094 \begin_layout Standard
30098 \begin_layout Plain Layout
30110 \begin_layout Standard
30111 To create the example, the following is done:
30114 \begin_layout Enumerate
30115 first formula is inserted
30118 \begin_layout Enumerate
30123 begin{subequations}
30124 \begin_inset Newline newline
30129 is inserted after the first formula
30132 \begin_layout Enumerate
30133 second formula is inserted
30136 \begin_layout Enumerate
30137 third formula is inserted
30140 \begin_layout Enumerate
30147 is inserted after the third formula
30150 \begin_layout Standard
30151 Every formula between the commands
30163 will be subnumbered with a, b, c, \SpecialChar ldots
30165 For multiline formulas every line will be subnumbered.
30168 \begin_layout Standard
30169 Referencing subequations work like for normal equations:
30170 \begin_inset CommandInset ref
30177 \begin_inset CommandInset ref
30184 If you want to reference the subequations collectively, insert a label
30189 begin{subequations}
30193 \begin_inset CommandInset ref
30195 reference "eq:Here-is-an"
30202 \begin_layout Standard
30203 By inserting commands in \SpecialChar TeX
30204 mode, a space is created between the first two
30207 \begin_inset space \thinspace{}
30210 mm vertical space is inserted after the command
30214 begin{subequations}
30217 When the formula style
30223 \begin_layout Plain Layout
30225 \begin_inset CommandInset ref
30227 reference "sec:Formula-Styles"
30239 \begin_inset space \thinspace{}
30242 mm space is inserted instead.
30245 \begin_layout Standard
30246 To get another subnumber instead of small Latin letters, insert this command
30251 begin{subequations}
30256 \begin_layout Standard
30265 theparentequation -
30270 \begin_layout Standard
30277 creates hereby the parent number and
30283 adds a small Roman number as subnumber.
30284 For more information about the customization of the numbering, see
30285 \begin_inset CommandInset ref
30287 reference "subsec:Numbering-with-Roman"
30294 \begin_layout Standard
30295 Here is an example for a multiline formula where the numbering is customized
30296 and turned off for the second line:
30300 \begin_layout Plain Layout
30304 begin{subequations}
30310 \begin_inset CommandInset label
30312 name "eq:Here-is-an"
30320 \begin_layout Plain Layout
30328 theparentequation -
30336 \begin_inset Formula
30338 A & = & (B-Z)^{2}=(B-Z)(B-Z)\\
30339 & = & B^{2}-ZB-BZ+Z^{2}\nonumber \\
30340 & = & B^{2}-2BZ+Z^{2}
30349 \begin_layout Plain Layout
30361 \begin_layout Subsection
30362 User-defined Numbering
30363 \begin_inset CommandInset label
30365 name "subsec:User-defined-Numbering"
30370 \begin_inset Index idx
30373 \begin_layout Plain Layout
30374 Formula numbering ! user-defined
30382 \begin_layout Standard
30383 \begin_inset Index idx
30386 \begin_layout Plain Layout
30387 Formula numbering ! self-defined delimiters
30392 With the standard numbering parentheses are set around the formula number.
30393 To replace the parentheses for example by vertical bars, the following
30394 line is added to the \SpecialChar LaTeX
30398 \begin_layout Standard
30410 \begin_inset Note Note
30413 \begin_layout Plain Layout
30414 This macro is already declared in the \SpecialChar LaTeX
30415 -preamble for testing.
30416 To activate it, remove the percent sign at the beginning.
30424 \begin_layout Standard
30425 To use other characters, the vertical bars besides the
30429 are replaced by one ore more characters.
30430 To get only the formula number the vertical bars are omitted.
30433 \begin_layout Standard
30434 \begin_inset VSpace bigskip
30437 When there should be an expression of your choice instead of the consecutive
30438 formula number in parentheses behind the formula, the command
30445 \begin_inset Index idx
30448 \begin_layout Plain Layout
30457 \begin_inset Formula
30459 A+B=C\tag{something}\label{eq:tag}
30464 In this example the command
30469 \begin_inset space \textvisiblespace{}
30474 was inserted in the formula.
30477 \begin_layout Standard
30483 \begin_inset space \textvisiblespace{}
30488 is inserted instead, the star prevents the parentheses around the expression:
30489 \begin_inset Formula
30491 A+B=C\tag*{something}
30499 \begin_layout Standard
30500 \begin_inset VSpace bigskip
30503 To restart the formula numbering with new document parts or sections, the
30504 following command is used:
30507 \begin_layout Standard
30512 @addtoreset{equation}{part}
30515 \begin_inset Index idx
30518 \begin_layout Plain Layout
30523 \begin_layout Plain Layout
30534 \begin_layout Plain Layout
30547 \begin_layout Plain Layout
30558 \begin_layout Plain Layout
30571 \begin_inset Newline newline
30575 \begin_inset Newline newline
30582 @addtoreset{equation}{section}
30585 \begin_layout Standard
30586 To be able to use these commands in \SpecialChar TeX
30588 \begin_inset Quotes eld
30592 \begin_inset Quotes erd
30595 character has to be made
30596 \begin_inset Quotes eld
30600 \begin_inset Quotes erd
30603 for \SpecialChar LaTeX
30618 So the command sequence in \SpecialChar TeX
30622 \begin_layout Standard
30628 \begin_inset Newline newline
30633 @addtoreset{equation}{section}
30634 \begin_inset Newline newline
30642 \begin_layout Standard
30643 In the \SpecialChar LaTeX
30656 can be omitted as they are automatically internally inserted by \SpecialChar LyX
30660 \begin_layout Standard
30675 \begin_layout Plain Layout
30680 is part of the \SpecialChar LaTeX
30686 \begin_inset Index idx
30689 \begin_layout Plain Layout
30690 Packages ! carlisle
30695 that is part of every \SpecialChar LaTeX
30696 standard installation.
30702 \begin_inset Index idx
30705 \begin_layout Plain Layout
30706 Packages ! remreset
30711 has to be loaded in the \SpecialChar LaTeX
30712 -preamble with the line
30715 \begin_layout Standard
30720 usepackage{remreset}
30723 \begin_layout Standard
30731 \begin_inset Index idx
30734 \begin_layout Plain Layout
30739 \begin_layout Plain Layout
30750 \begin_layout Plain Layout
30763 \begin_layout Plain Layout
30774 \begin_layout Plain Layout
30786 can be used with the same scheme as
30795 \begin_layout Standard
30796 \begin_inset VSpace bigskip
30799 Sometimes formulas should be numbered in the following form:
30802 \begin_layout Standard
30805 (section number.formula number)
30808 \begin_layout Standard
30809 The formula number should start with every section with
30810 \begin_inset Quotes eld
30814 \begin_inset Quotes erd
30820 \begin_layout Standard
30821 For this case there is the command
30828 \begin_inset Index idx
30831 \begin_layout Plain Layout
30839 , which is used with the following scheme:
30842 \begin_layout Standard
30847 numberwithin{counter}{sectioning}
30850 \begin_layout Standard
30851 Counter denotes what kind of numbering is affected, sectioning denotes what
30852 number is before the dot.
30855 \begin_layout Standard
30856 Thus in our case the following \SpecialChar LaTeX
30857 preamble or \SpecialChar TeX
30861 \begin_layout Standard
30866 numberwithin{equation}{section}
30869 \begin_layout Standard
30870 This is the result:
30874 \begin_layout Plain Layout
30878 numberwithin{equation}{section}
30884 \begin_inset Formula
30894 \begin_layout Standard
30896 \begin_inset space \thinspace{}
30900 \begin_inset space \space{}
30903 tables so that the number of the part is the sectioning,
30904 \begin_inset Newline newline
30911 numberwithin{table}{part}
30916 \begin_layout Standard
30917 To go back to the standard numbering or to prevent this kind of numbering
30918 when it is defined by the document class, the following command is inserted
30919 as \SpecialChar TeX
30920 code or to the \SpecialChar LaTeX
30924 \begin_layout Standard
30934 \begin_inset Index idx
30937 \begin_layout Plain Layout
30951 \begin_layout Plain Layout
30967 \begin_inset Newline newline
30975 \begin_inset Newline newline
30987 \begin_layout Standard
30994 uses internally the command
31000 , described above, that also needs to be reverted.
31004 \begin_layout Plain Layout
31011 \begin_layout Plain Layout
31015 @removefromreset{equation}{section}
31018 \begin_layout Plain Layout
31030 \begin_layout Subsection
31031 Numbering with Roman Numbers and Letters
31032 \begin_inset CommandInset label
31034 name "subsec:Numbering-with-Roman"
31039 \begin_inset Index idx
31042 \begin_layout Plain Layout
31043 Formula numbering ! with letters
31049 \begin_inset Index idx
31052 \begin_layout Plain Layout
31053 Formula numbering ! with Roman numbers
31061 \begin_layout Standard
31062 Formulas can also be numbered with Roman numbers and Latin letters.
31063 To number for example with small Roman numbers, the command
31066 \begin_layout Standard
31078 \begin_layout Standard
31079 is inserted before the formula in \SpecialChar TeX
31088 \begin_inset Index idx
31091 \begin_layout Plain Layout
31099 redefines the predefined command
31115 \begin_layout Plain Layout
31122 has the same scheme like the command
31128 that is described in
31129 \begin_inset CommandInset ref
31131 reference "subsec:The-Command-newcommand"
31144 is the formula counter.
31151 is used as prefix for a counter, the value of the counter is output as
31153 When a formula is numbered, \SpecialChar LaTeX
31154 sets internally the command
31160 behind the formula.
31166 \begin_inset Index idx
31169 \begin_layout Plain Layout
31179 outputs the counter as small Roman number.
31182 \begin_layout Standard
31183 All formulas behind the command
31193 are now numbered Roman.
31194 To switch to numbering with big Roman numbers, the command is inserted
31208 \begin_inset Index idx
31211 \begin_layout Plain Layout
31223 \begin_inset Quotes eld
31227 \begin_inset Quotes erd
31230 with small Latin letters there is the command
31237 \begin_inset Index idx
31240 \begin_layout Plain Layout
31248 , for big ones there is the command
31255 \begin_inset Index idx
31258 \begin_layout Plain Layout
31271 \begin_layout Standard
31272 \begin_inset Note Greyedout
31275 \begin_layout Plain Layout
31282 \begin_inset space ~
31285 formulas can be numbered with Latin letters in one document.
31293 \begin_layout Standard
31297 \begin_layout Plain Layout
31313 \begin_layout Standard
31314 \begin_inset Formula
31316 A=\textrm{small roman}
31325 \begin_layout Plain Layout
31339 \begin_inset Formula
31341 B=\textrm{big Roman}\label{eq:Rom}
31350 \begin_layout Plain Layout
31364 \begin_inset Formula
31366 C=\textrm{small Latin}
31375 \begin_layout Plain Layout
31389 \begin_inset Formula
31391 D=\textrm{big Latin}\label{eq:Lat}
31399 \begin_layout Standard
31400 To switch back to the default numbering, insert the command:
31403 \begin_layout Standard
31413 \begin_inset Index idx
31416 \begin_layout Plain Layout
31427 \begin_layout Standard
31431 \begin_layout Plain Layout
31445 \begin_inset Formula
31455 \begin_layout Standard
31456 \begin_inset VSpace medskip
31459 As you see, formulas are numbered serially independent from the numbering
31461 When then numbering should start with
31462 \begin_inset Quotes eld
31466 \begin_inset Quotes erd
31469 when the style is changed, new equation counters have to be defined.
31470 A description about this can be found in the file
31471 \begin_inset CommandInset href
31473 name "Formula-numbering.lyx"
31474 target "run:Formula-numbering.lyx"
31481 \begin_layout Section
31482 Chemical Symbols and Equations
31483 \begin_inset CommandInset label
31485 name "subsec:Chemical-Symbols-and"
31490 \begin_inset Index idx
31493 \begin_layout Plain Layout
31494 Chemical characters ! Symbols
31500 \begin_inset Index idx
31503 \begin_layout Plain Layout
31510 \begin_inset Index idx
31513 \begin_layout Plain Layout
31522 \begin_layout Standard
31523 An example text from chemistry:
31526 \begin_layout Quote
31528 \begin_inset Formula $\mathrm{SO_{4}^{2-}}$
31531 -ion reacts with two
31532 \begin_inset Formula $\mathrm{Na^{+}}$
31535 -ions to sodium sulfate
31536 \begin_inset Formula $\left(\mathrm{Na_{2}SO_{4}}\right)$
31540 The chemical equation for this is:
31541 \begin_inset Formula
31543 \mathrm{2\,Na^{+}+SO_{4}^{2-}\longrightarrow Na_{2}SO_{4}}\label{eq:chem-reaction}
31551 \begin_layout Standard
31552 This chemical equation can directly be created as formula.
31553 To avoid that the symbols appear italic, everything is highlighted and
31554 changed by the shortcut
31560 to the upright font style.
31564 \begin_layout Plain Layout
31570 \begin_inset CommandInset ref
31572 reference "subsec:Font-Styles"
31584 \begin_layout Standard
31585 A more convenient way to typeset chemical formulas is to use the command
31593 \begin_inset Index idx
31596 \begin_layout Plain Layout
31604 that is available when the \SpecialChar LaTeX
31610 \begin_inset Index idx
31613 \begin_layout Plain Layout
31626 to a formula a new blue box appears where chemical formulas can be inserted
31627 in an intuitive way.
31628 \begin_inset Separator parbreak
31634 \begin_layout Standard
31636 \begin_inset Tabular
31637 <lyxtabular version="3" rows="10" columns="2">
31638 <features booktabs="true" tabularvalignment="middle">
31639 <column alignment="center" valignment="top" width="0pt">
31640 <column alignment="center" valignment="top">
31642 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
31645 \begin_layout Plain Layout
31651 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
31654 \begin_layout Plain Layout
31662 <cell alignment="center" valignment="top" leftline="true" usebox="none">
31665 \begin_layout Plain Layout
31669 \begin_inset space \textvisiblespace{}
31677 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
31680 \begin_layout Plain Layout
31681 \begin_inset Formula $\ce{H2CO3}$
31690 <row topspace="1.5mm">
31691 <cell alignment="center" valignment="top" usebox="none">
31694 \begin_layout Plain Layout
31698 \begin_inset space \textvisiblespace{}
31706 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
31709 \begin_layout Plain Layout
31710 \begin_inset Formula $\ce{SO4^{2-}}$
31719 <row topspace="1.5mm">
31720 <cell alignment="center" valignment="top" usebox="none">
31723 \begin_layout Plain Layout
31727 \begin_inset space \textvisiblespace{}
31735 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
31738 \begin_layout Plain Layout
31739 \begin_inset Formula $\ce{(NH4)2S}$
31748 <row topspace="1.5mm">
31749 <cell alignment="center" valignment="top" usebox="none">
31752 \begin_layout Plain Layout
31756 \begin_inset space \textvisiblespace{}
31764 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
31767 \begin_layout Plain Layout
31768 \begin_inset Formula $\ce{KCr(SO4)2.12H2O}$
31777 <row topspace="1.5mm">
31778 <cell alignment="center" valignment="top" usebox="none">
31781 \begin_layout Plain Layout
31785 \begin_inset space \textvisiblespace{}
31791 \begin_inset space \textvisiblespace{}
31797 \begin_inset space \textvisiblespace{}
31805 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
31808 \begin_layout Plain Layout
31809 \begin_inset Formula $\ce{A-B\dbond C\tbond D}$
31818 <row topspace="1.5mm">
31819 <cell alignment="center" valignment="top" usebox="none">
31822 \begin_layout Plain Layout
31826 \begin_inset space \textvisiblespace{}
31830 \begin_inset Formula $\downarrow$
31834 \begin_inset Formula $\to$
31842 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
31845 \begin_layout Plain Layout
31846 \begin_inset Formula $\ce{_{90}^{227}Th+}$
31856 <cell alignment="center" valignment="top" leftline="true" usebox="none">
31859 \begin_layout Plain Layout
31863 \begin_inset space \textvisiblespace{}
31869 \begin_inset space \textvisiblespace{}
31875 \begin_inset space \textvisiblespace{}
31883 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
31886 \begin_layout Plain Layout
31887 \begin_inset Formula $\ce{\ensuremath{\mu\hyphen}Cl}$
31897 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
31900 \begin_layout Plain Layout
31904 \begin_inset space \textvisiblespace{}
31908 \begin_inset space \textvisiblespace{}
31912 \begin_inset space \textvisiblespace{}
31916 \begin_inset space \textvisiblespace{}
31920 \begin_inset space \textvisiblespace{}
31928 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
31931 \begin_layout Plain Layout
31932 \begin_inset Formula $\ce{CO2 + C <=> 2CO}$
31941 <row topspace="1.5mm">
31942 <cell alignment="center" valignment="top" bottomline="true" usebox="none">
31945 \begin_layout Plain Layout
31949 \begin_inset space \textvisiblespace{}
31953 \begin_inset space \textvisiblespace{}
31957 \begin_inset space \textvisiblespace{}
31961 \begin_inset space \textvisiblespace{}
31969 \begin_inset space \textvisiblespace{}
31977 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
31980 \begin_layout Plain Layout
31981 \begin_inset Formula $\ce{CO2 + C ->[\alpha][\beta] 2CO}$
31997 \begin_layout Standard
31998 \begin_inset Note Greyedout
32001 \begin_layout Plain Layout
32007 It is not possible in \SpecialChar LyX
32008 to use the character ^ to get an up-arrow as described
32014 One instead uses a negative thin space followed by the command
32021 \begin_inset Formula $\ce{Fe + 2H+ -> Fe^{2+} + H2\negthinspace\uparrow}$
32032 \begin_layout Standard
32039 the command for equation
32040 \begin_inset space ~
32044 \begin_inset CommandInset ref
32046 reference "eq:chem-reaction"
32051 \begin_inset Newline newline
32059 \begin_inset space \textvisiblespace{}
32063 \begin_inset space \textvisiblespace{}
32067 \begin_inset space \textvisiblespace{}
32071 \begin_inset space \textvisiblespace{}
32075 \begin_inset space \textvisiblespace{}
32079 \begin_inset space \textvisiblespace{}
32085 \begin_layout Standard
32086 To create multiline chemical equations first a multiline formula is created
32088 \begin_inset CommandInset ref
32090 reference "sec:Multiline-Formulas"
32095 Afterwards the command
32101 is used in every small blue box of the formula.
32103 \begin_inset CommandInset ref
32105 reference "eq:TEOS-reaction-1"
32110 \begin_inset CommandInset ref
32112 reference "eq:TEOS-reaction-2"
32116 are an example of a multi-stage chemical reaction where every equation
32117 has its own number.
32118 \begin_inset Formula
32120 \ce{TEOS + 4O} & \ce{->} & \ce{Si(OH)4 + 4C2H4O}\label{eq:TEOS-reaction-1}\\
32121 \ce{Si(OH)4} & \ce{->} & \ce{SiO2 + 2H2O}\label{eq:TEOS-reaction-2}
32129 \begin_layout Standard
32140 package provides the command
32147 \begin_inset Index idx
32150 \begin_layout Plain Layout
32158 that has to be used for special cases.
32159 For more information about
32165 and more examples have a look at the documentation of
32170 \begin_inset CommandInset citation
32179 \begin_layout Section
32183 \begin_layout Standard
32185 supports two types of commutative diagrams:
32193 that are explained in the following.
32196 \begin_layout Subsection
32198 \begin_inset Index idx
32201 \begin_layout Plain Layout
32210 \begin_layout Standard
32211 Diagrams of this type visualize relations by vertical and horizontal lines
32213 \begin_inset Formula
32215 \begin{CD}A@>>>B@>>>C\\
32226 \begin_layout Standard
32227 To get them, the command
32232 \begin_inset Index idx
32235 \begin_layout Plain Layout
32245 is inserted to a formula.
32246 A blue box appears with two dashed lines where further commands can be
32251 arg "newline-insert newline"
32254 a new line is created.
32255 Horizontal relations are inserted in odd, vertical in even formula lines.
32258 \begin_layout Standard
32259 To create the relations there are the following commands:
32262 \begin_layout Itemize
32267 creates a left arrow,
32278 \begin_layout Itemize
32283 creates an up arrow,
32291 a vertical equal sign
32294 \begin_layout Itemize
32300 is a placeholder for non-existent relations
32303 \begin_layout Standard
32304 All arrows can be labeled as follows:
32307 \begin_layout Itemize
32308 If text inserted between the first and second < or >, resp., it is placed
32310 When it is inserted between the second and third one, it appears under
32314 \begin_layout Itemize
32315 When text for vertical arrows is inserted between the first and second A
32316 or V, resp., it is placed left beside the arrow.
32317 When it is inserted between the second and third one, it appears right
32319 If the text contains an A or V, these letters must be set into a \SpecialChar TeX
32323 \begin_layout Standard
32324 As example a diagram with all possible relations:
32327 \begin_layout Standard
32328 \begin_inset Formula
32330 \begin{CD}A@>j>>B@>>k>C@=F\\
32341 \begin_layout Standard
32342 The command for this is:
32343 \begin_inset Newline newline
32351 \begin_inset space \textvisiblespace{}
32354 A@>j>>B@>>k>C@=F Ctrl+Return
32355 \begin_inset Newline newline
32359 \begin_inset Phantom HPhantom
32362 \begin_layout Plain Layout
32368 \begin_inset space \textvisiblespace{}
32381 \begin_inset Formula $\to$
32387 \begin_inset Newline newline
32391 \begin_inset Phantom HPhantom
32394 \begin_layout Plain Layout
32400 \begin_inset space \textvisiblespace{}
32411 \begin_layout Subsection
32413 \begin_inset Index idx
32416 \begin_layout Plain Layout
32417 Diagrams ! xymatrix
32425 \begin_layout Standard
32426 To be able to use xymatrices, the \SpecialChar LaTeX
32432 A xymatrix is created by inserting the command
32439 Then you are able to add new matrix columns and rows like for normal matrices,
32441 \begin_inset CommandInset ref
32443 reference "sec:Matrices"
32450 \begin_layout Standard
32451 In contrary to amscd diagrams, xymatrices supports diagonal and curved arrows,
32453 All possibilities to create commutative diagrams and decorations are explained
32458 that you find in the menu
32460 Help\SpecialChar menuseparator
32462 \begin_inset space ~
32470 \begin_layout Subsection
32476 \begin_inset Index idx
32479 \begin_layout Plain Layout
32488 \begin_layout Standard
32493 -diagrams, the \SpecialChar LaTeX
32503 -diagram is created by inserting the command
32510 Then you are able to add new matrix columns and rows like for normal matrices,
32512 \begin_inset CommandInset ref
32514 reference "sec:Matrices"
32521 \begin_layout Standard
32522 Examples how to create
32526 diagrams in \SpecialChar LyX
32529 Feynman-diagram manual
32531 that you find in the menu
32533 Help\SpecialChar menuseparator
32535 \begin_inset space ~
32543 \begin_layout Section
32544 User-defined Commands
32545 \begin_inset Index idx
32548 \begin_layout Plain Layout
32549 User-defined commands
32557 \begin_layout Standard
32558 \begin_inset Note Greyedout
32561 \begin_layout Plain Layout
32566 The names of user-defined commands and macros may only consist of Latin
32575 \begin_layout Subsection
32579 \begin_inset CommandInset label
32581 name "subsec:The-Command-newcommand"
32586 \begin_inset Index idx
32589 \begin_layout Plain Layout
32590 User-defined commands !
32598 \begin_inset Index idx
32601 \begin_layout Plain Layout
32612 \begin_layout Standard
32613 Many \SpecialChar LaTeX
32614 -commands are too long to be used frequently.
32615 But it is possible to define with the command
32621 new shorter commands.
32624 \begin_layout Standard
32625 The command scheme of
32634 \begin_layout Standard
32639 newcommand{new command name}[number of arguments][optional
32644 \begin_inset Newline newline
32648 \begin_inset Phantom HPhantom
32651 \begin_layout Plain Layout
32661 {command definition}
32664 \begin_layout Standard
32665 \begin_inset Note Greyedout
32668 \begin_layout Plain Layout
32673 Assure that the name of the new command is not already used in your document
32674 or by \SpecialChar LaTeX
32675 -packages that you use.
32676 When you for example define the command
32688 , you get an error message because
32694 is already defined as command for
32695 \begin_inset Quotes eld
32699 \begin_inset Formula $\le$
32703 \begin_inset Quotes erd
32714 \begin_layout Standard
32715 The number of arguments is an integer in the range 0
32716 \begin_inset space \thinspace{}
32720 \begin_inset space \thinspace{}
32723 9 and specifies how many arguments the new command should have.
32724 With the optional value a value for an optional argument can be predefined.
32725 When this is done, the
32733 rgument of the new command is automatically an optional one.
32736 \begin_layout Standard
32737 Here are some examples:
32740 \begin_layout Itemize
32741 To define the command
32753 , the \SpecialChar LaTeX
32755 \begin_inset VSpace medskip
32759 \begin_inset Newline newline
32773 \begin_layout Itemize
32774 To define the command
32786 , the argument (that should be underlined) must be taken into account.
32787 For this the preamble line is:
32788 \begin_inset VSpace medskip
32792 \begin_inset Newline newline
32806 \begin_inset VSpace medskip
32810 \begin_inset Newline newline
32817 acts as argument placeholder, the
32821 behind it denotes that it is the placeholder for the first argument.
32824 \begin_layout Itemize
32832 \begin_inset space \thinspace{}
32836 \begin_inset space \space{}
32846 \begin_inset VSpace medskip
32850 \begin_inset Newline newline
32861 framebox#1#2{$#3$}}
32864 \begin_inset VSpace medskip
32868 \begin_inset Newline newline
32871 The two Dollar signs creates the extra formula needed for
32878 \begin_inset CommandInset ref
32880 reference "subsec:Boxes-with-Frame"
32887 \begin_layout Itemize
32888 To create a new command for
32894 where the color for the box need not be specified, the argument for the
32895 color is defined optional:
32896 \begin_inset VSpace medskip
32900 \begin_inset Newline newline
32911 fcolorbox{#2}{#1}{$#3$}}
32914 \begin_inset VSpace medskip
32918 \begin_inset Newline newline
32921 When the color is not specified when using
32927 , the predefined color
32934 \begin_layout Standard
32935 A test of the new defined commands:
32936 \begin_inset Separator parbreak
32942 \begin_layout Standard
32944 \begin_inset Tabular
32945 <lyxtabular version="3" rows="6" columns="2">
32946 <features booktabs="true" tabularvalignment="middle">
32947 <column alignment="center" valignment="top" width="0pt">
32948 <column alignment="center" valignment="top">
32950 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
32953 \begin_layout Plain Layout
32959 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
32962 \begin_layout Plain Layout
32970 <cell alignment="center" valignment="top" leftline="true" usebox="none">
32973 \begin_layout Plain Layout
32977 \begin_inset space \textvisiblespace{}
32985 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
32988 \begin_layout Plain Layout
32989 \begin_inset Formula $A\gr B$
32999 <cell alignment="center" valignment="top" leftline="true" usebox="none">
33002 \begin_layout Plain Layout
33010 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
33013 \begin_layout Plain Layout
33014 \begin_inset Formula $\us{ABcd}$
33023 <row topspace="1mm">
33024 <cell alignment="center" valignment="top" usebox="none">
33027 \begin_layout Plain Layout
33031 \begin_inset Formula $\to$
33037 \begin_inset Formula $\to$
33045 \begin_inset space \textvisiblespace{}
33053 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
33056 \begin_layout Plain Layout
33057 \begin_inset Formula $\fb{[2cm]}{}{\int A=B}$
33066 <row topspace="1.5mm">
33067 <cell alignment="center" valignment="top" usebox="none">
33070 \begin_layout Plain Layout
33074 \begin_inset Formula $\to$
33082 \begin_inset space \textvisiblespace{}
33090 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
33093 \begin_layout Plain Layout
33094 \begin_inset Formula $\cb{red}{\int A=B}$
33103 <row topspace="1.5mm" bottomspace="1mm">
33104 <cell alignment="center" valignment="top" bottomline="true" usebox="none">
33107 \begin_layout Plain Layout
33113 \begin_inset Formula $\to$
33121 \begin_inset space \textvisiblespace{}
33129 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
33132 \begin_layout Plain Layout
33133 \begin_inset Formula $\cb[green]{red}{\int A=B}$
33149 \begin_layout Subsection
33151 \begin_inset Index idx
33154 \begin_layout Plain Layout
33155 User-defined commands! Math macros
33161 \begin_inset Index idx
33164 \begin_layout Plain Layout
33173 \begin_layout Standard
33174 User-defined commands are especially convenient for complex expressions.
33175 When you are for example dealing with a document that has quadratic equations,
33176 the same solution type occurs several times.
33177 The general form of a quadratic equation is
33178 \begin_inset Formula
33180 0=\lambda^{2}+p\lambda+q
33185 The general form of the solution is
33186 \begin_inset Formula
33188 \lambda_{1,2}=-\frac{p}{2}\pm\sqrt{\frac{p²}{4}-q}
33196 \begin_layout Standard
33197 To define a command for the solution formula where only the three parameters
33199 \begin_inset Formula $\lambda$
33203 \begin_inset Formula $p$
33207 \begin_inset Formula $q$
33210 need to be specified and the index of
33211 \begin_inset Formula $\lambda$
33214 can be given optionally, the \SpecialChar LaTeX
33216 \begin_inset Newline newline
33232 \begin_inset Newline newline
33236 \begin_inset Phantom HPhantom
33239 \begin_layout Plain Layout
33253 frac{#3^{2}}{4}-#4}}
33256 \begin_layout Standard
33257 To create with this the solution formula, the command
33258 \begin_inset Newline newline
33268 \begin_inset Formula $\to$
33274 \begin_inset Formula $\to$
33281 is inserted to a formula
33286 \begin_layout Standard
33287 The definition of the new command is unintuitive because one has to know
33288 the schemes of all used \SpecialChar LaTeX
33290 \begin_inset space \thinspace{}
33294 \begin_inset space \space{}
33297 that a fraction is inserted in \SpecialChar LaTeX
33302 frac{numerator}{denominator}
33305 Furthermore one can easily forget a brace in the definition and cannot
33306 see in \SpecialChar LyX
33307 what the new command is doing.
33308 To avoid these problems \SpecialChar LyX
33309 offers the possibility to use math macros instead
33319 \begin_layout Standard
33320 A math macro is created by using the menu
33322 Insert\SpecialChar menuseparator
33323 Math\SpecialChar menuseparator
33326 or the toolbar button
33329 arg "math-macro newmacroname_newcommand"
33333 The math macro toolbar appears together with the following box where the
33335 \begin_inset Newline newline
33339 \begin_inset space \hspace*{\fill}
33343 \begin_inset Graphics
33344 filename clipart/macrobox.png
33350 \begin_inset space \hspace*{\fill}
33354 \begin_inset Newline newline
33358 \begin_inset FormulaMacro
33359 \newcommand{\qG}[4][1,\,2]{#2_{#1}=-\frac{#3}{2}\pm\sqrt{\frac{#3^{2}}{4}-#4}}
33364 newmacroname is the default name of the macro that should be changed to
33365 something sensible.
33366 The wanted formula is inserted in the first blue box.
33367 An argument placeholder is inserted with the command
33374 \begin_inset space \thinspace{}
33378 \begin_inset space \space{}
33387 or by using the macro toolbar button
33390 arg "math-macro-add-param"
33394 Argument placeholders are displayed red.
33396 \begin_inset space ~
33399 arguments are possible.
33400 Optional arguments are created with the toolbar button
33403 arg "math-macro-add-optional-param"
33407 The first non-optional argument can be transformed to an optional one with
33411 arg "math-macro-make-optional"
33415 In the second blue box the appearance of the macro in \SpecialChar LyX
33417 Normally you want to see it as it is defined, so the box is kept empty.
33418 But when you have created a macro that needs lot of space on the screen,
33419 you can insert in the box for example
33420 \begin_inset Newline newline
33450 \begin_inset Newline newline
33455 For the macro only the arguments with the macro name in front of them will
33456 then be displayed in \SpecialChar LyX
33457 , leading to a better overview.
33458 The formula appears in the output as defined in the first box.
33459 \begin_inset Newline newline
33462 The appearance of macros in formulas can furthermore be changed for single
33463 macros by setting the cursor in the macro and using the menu
33465 View\SpecialChar menuseparator
33467 \begin_inset space ~
33471 \begin_inset space ~
33479 \begin_layout Standard
33480 To use a macro, the macro name is inserted as command to a formula, in our
33488 Our macro looks in \SpecialChar LyX
33490 \begin_inset Newline newline
33494 \begin_inset space \hspace*{\fill}
33498 \begin_inset Graphics
33499 filename clipart/macrouse.png
33505 \begin_inset space \hspace*{\fill}
33509 \begin_inset Newline newline
33512 Here is our macro example with the arguments
33513 \begin_inset Formula $x$
33517 \begin_inset Formula $\ln(x)$
33521 \begin_inset Formula $B$
33527 \begin_layout Standard
33528 \begin_inset Formula
33538 \begin_layout Standard
33542 Tools\SpecialChar menuseparator
33543 Preferences\SpecialChar menuseparator
33544 Editing\SpecialChar menuseparator
33547 different styles to edit macros.
33548 To find the style that suits you the most, choose a style and set the cursor
33549 in a macro formula to see the difference.
33552 \begin_layout Standard
33553 A math macro is transformed internally to a
33559 command when exporting the document.
33566 command is not placed in the \SpecialChar LaTeX
33567 -preamble, therefore macros can only be used
33568 in formulas that are in the document below the macro definition box.
33571 \begin_layout Standard
33572 Math macros can also be directly created from a
33579 When writing for example the command
33582 \begin_inset Newline newline
33591 xleftarrow[#2]{#1}}
33592 \begin_inset Newline newline
33597 in \SpecialChar LyX
33598 as normal text, highlighting it completely and using then the shortcut
33603 , the command will be transformed to a math macro.
33604 Using this method you need to be careful that the
33610 command is typed correctly, otherwise you get a faulty macro leading to
33615 \begin_layout Standard
33616 Math macros currently have the problem that further formulas in macro definition
33617 s are handled wrongly.
33618 Therefore the example
33625 \begin_inset CommandInset ref
33627 reference "subsec:The-Command-newcommand"
33631 cannot be created as macro.
33634 \begin_layout Standard
33635 When the cursor is in a macro definition box, you will see the macro toolbar
33636 in \SpecialChar LyX
33640 \begin_layout Standard
33641 \begin_inset VSpace defskip
33647 \begin_layout Standard
33648 \begin_inset Graphics
33649 filename clipart/MacroToolbar.png
33654 \begin_inset Index idx
33657 \begin_layout Plain Layout
33666 \begin_layout Standard
33667 \begin_inset VSpace defskip
33673 \begin_layout Standard
33674 The macro toolbar contains from left to right the following buttons:
33677 \begin_layout Standard
33678 \begin_inset VSpace defskip
33684 \begin_layout Standard
33685 \begin_inset Tabular
33686 <lyxtabular version="3" rows="9" columns="2">
33687 <features islongtable="true" longtabularalignment="center">
33688 <column alignment="left" valignment="top">
33689 <column alignment="left" valignment="top" width="85col%">
33690 <row interlinespace="2.5mm">
33691 <cell alignment="center" valignment="top" usebox="none">
33694 \begin_layout Plain Layout
33697 arg "math-macro-remove-param"
33705 <cell alignment="center" valignment="top" usebox="none">
33708 \begin_layout Plain Layout
33711 Edit\SpecialChar menuseparator
33712 Math\SpecialChar menuseparator
33714 \begin_inset space ~
33717 Definition\SpecialChar menuseparator
33718 Remove Last Argument
33724 <row interlinespace="2.5mm">
33725 <cell alignment="center" valignment="top" usebox="none">
33728 \begin_layout Plain Layout
33731 arg "math-macro-add-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
33758 <row interlinespace="2.5mm">
33759 <cell alignment="center" valignment="top" usebox="none">
33762 \begin_layout Plain Layout
33765 arg "math-macro-make-optional"
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 Transform First Non-Optional to
33787 \begin_inset Newline newline
33791 \begin_inset Phantom HPhantom
33794 \begin_layout Plain Layout
33797 Edit\SpecialChar menuseparator
33798 Math\SpecialChar menuseparator
33800 \begin_inset space ~
33803 Definition\SpecialChar menuseparator
33815 <row interlinespace="2.5mm">
33816 <cell alignment="center" valignment="top" usebox="none">
33819 \begin_layout Plain Layout
33822 arg "math-macro-make-nonoptional"
33830 <cell alignment="center" valignment="top" usebox="none">
33833 \begin_layout Plain Layout
33836 Edit\SpecialChar menuseparator
33837 Math\SpecialChar menuseparator
33839 \begin_inset space ~
33842 Definition\SpecialChar menuseparator
33843 Transform Last Optional to
33844 \begin_inset Newline newline
33848 \begin_inset Phantom HPhantom
33851 \begin_layout Plain Layout
33854 Edit\SpecialChar menuseparator
33855 Math\SpecialChar menuseparator
33857 \begin_inset space ~
33860 Definition\SpecialChar menuseparator
33866 Non-Optional Argument
33872 <row interlinespace="2.5mm">
33873 <cell alignment="center" valignment="top" usebox="none">
33876 \begin_layout Plain Layout
33879 arg "math-macro-remove-optional-param"
33887 <cell alignment="center" valignment="top" usebox="none">
33890 \begin_layout Plain Layout
33893 Edit\SpecialChar menuseparator
33894 Math\SpecialChar menuseparator
33896 \begin_inset space ~
33899 Definition\SpecialChar menuseparator
33900 Remove Optional Argument
33906 <row interlinespace="2.5mm">
33907 <cell alignment="center" valignment="top" usebox="none">
33910 \begin_layout Plain Layout
33913 arg "math-macro-add-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 Insert Optional Argument
33940 <row interlinespace="2.5mm">
33941 <cell alignment="center" valignment="top" usebox="none">
33944 \begin_layout Plain Layout
33947 arg "math-macro-remove-greedy-param"
33955 <cell alignment="center" valignment="top" usebox="none">
33958 \begin_layout Plain Layout
33961 Edit\SpecialChar menuseparator
33962 Math\SpecialChar menuseparator
33964 \begin_inset space ~
33967 Definition\SpecialChar menuseparator
33968 Remove Last Argument
33969 \begin_inset Newline newline
33973 \begin_inset Phantom HPhantom
33976 \begin_layout Plain Layout
33979 Edit\SpecialChar menuseparator
33980 Math\SpecialChar menuseparator
33982 \begin_inset space ~
33985 Definition\SpecialChar menuseparator
33991 Spitting Out To The Right
33997 <row interlinespace="2.5mm">
33998 <cell alignment="center" valignment="top" usebox="none">
34001 \begin_layout Plain Layout
34004 arg "math-macro-append-greedy-param"
34012 <cell alignment="center" valignment="top" usebox="none">
34015 \begin_layout Plain Layout
34018 Edit\SpecialChar menuseparator
34019 Math\SpecialChar menuseparator
34021 \begin_inset space ~
34024 Definition\SpecialChar menuseparator
34026 \begin_inset Newline newline
34030 \begin_inset Phantom HPhantom
34033 \begin_layout Plain Layout
34036 Edit\SpecialChar menuseparator
34037 Math\SpecialChar menuseparator
34039 \begin_inset space ~
34042 Definition\SpecialChar menuseparator
34048 Eating From The Right
34054 <row interlinespace="2.5mm">
34055 <cell alignment="center" valignment="top" usebox="none">
34058 \begin_layout Plain Layout
34061 arg "math-macro-add-greedy-optional-param"
34069 <cell alignment="center" valignment="top" usebox="none">
34072 \begin_layout Plain Layout
34075 Edit\SpecialChar menuseparator
34076 Math\SpecialChar menuseparator
34078 \begin_inset space ~
34081 Definition\SpecialChar menuseparator
34082 Append Optional Argument
34083 \begin_inset Newline newline
34087 \begin_inset Phantom HPhantom
34090 \begin_layout Plain Layout
34093 Edit\SpecialChar menuseparator
34094 Math\SpecialChar menuseparator
34096 \begin_inset space ~
34099 Definition\SpecialChar menuseparator
34105 Eating From The Right
34118 \begin_layout Section
34119 Computer Algebra Systems
34122 \begin_layout Standard
34124 offers the exchange between mathematical expressions written in \SpecialChar LyX
34126 editor and external applications or user defined scripts.
34127 Currently supported applications are
34144 Note that the set of supported mathematical constructs is limited only
34145 to very simple cases.
34148 \begin_layout Subsection
34152 \begin_layout Standard
34153 Write some expression in a formula, go to the
34155 Edit\SpecialChar menuseparator
34156 Math\SpecialChar menuseparator
34157 Use Computer Algebra System
34159 menu and choose the application you have installed on the computer.
34160 After that the result of computation should show on the right side of the
34161 expression together with the
34162 \begin_inset Quotes eld
34166 \begin_inset Quotes erd
34172 \begin_layout Standard
34173 Here are few simple examples (with results from
34177 ) to show what kind of computations can be performed:
34180 \begin_layout Itemize
34181 \begin_inset Formula $\frac{37}{3}*2-\sum_{i=1}^{3}i^{i}=-\frac{22}{3}$
34187 \begin_layout Itemize
34188 \begin_inset Formula $\frac{37.0}{3}=12.33333333333333$
34194 \begin_layout Itemize
34195 \begin_inset Formula $\int_{1}^{2}\sin(x)dx=\cos1-\cos2$
34201 \begin_layout Itemize
34202 \begin_inset Formula $\det\left[\begin{array}{ccc}
34206 \end{array}\right]=-56$
34212 \begin_layout Itemize
34213 \begin_inset Formula $\lim_{x\rightarrow0}\left(\frac{\sin(x)}{x}\right)=1$
34219 \begin_layout Subsection
34223 \begin_layout Standard
34224 Currently there is no keyboard shortcut for calling the algebra applications.
34225 One can easily bind a shortcut to the
34239 \begin_inset space \thinspace{}
34243 \begin_inset space \space{}
34250 key inside the math editor.
34255 one would use this shortcut definition command:
34258 \begin_layout Standard
34261 command-alternatives paragraph-break;math-extern maxima
34264 \begin_layout Section
34266 \begin_inset Index idx
34269 \begin_layout Plain Layout
34278 \begin_layout Subsection
34280 \begin_inset Index idx
34283 \begin_layout Plain Layout
34292 \begin_layout Standard
34293 Negative numbers often look ugly in formulas because the minus sign before
34294 the number is set with the same length as the minus operator sign.
34295 When writing the negative number in normal text, the minus sign appears
34299 \begin_layout Standard
34300 Thus, the problem disappears when converting the minus sign to mathematical
34304 \begin_layout Standard
34305 An example to visualize the problem:
34306 \begin_inset Separator parbreak
34312 \begin_layout Standard
34314 \begin_inset Tabular
34315 <lyxtabular version="3" rows="3" columns="2">
34316 <features booktabs="true" tabularvalignment="middle">
34317 <column alignment="right" valignment="top" width="0pt">
34318 <column alignment="left" valignment="top">
34320 <cell alignment="right" valignment="top" topline="true" leftline="true" usebox="none">
34323 \begin_layout Plain Layout
34329 <cell alignment="center" valignment="top" topline="true" rightline="true" usebox="none">
34332 \begin_layout Plain Layout
34340 <cell alignment="right" valignment="top" leftline="true" usebox="none">
34343 \begin_layout Plain Layout
34349 <cell alignment="center" valignment="top" rightline="true" usebox="none">
34352 \begin_layout Plain Layout
34353 \begin_inset Formula $x=-2$
34363 <cell alignment="right" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
34366 \begin_layout Plain Layout
34372 <cell alignment="center" valignment="top" topline="true" bottomline="true" rightline="true" usebox="none">
34375 \begin_layout Plain Layout
34376 \begin_inset Formula $x=\textrm{-}2$
34392 \begin_layout Subsection
34393 Comma as decimal Separator
34394 \begin_inset Index idx
34397 \begin_layout Plain Layout
34406 \begin_layout Standard
34407 In \SpecialChar LaTeX
34408 a comma inside a formula is used, according to the English convention,
34409 as number group separator.
34410 So there will be space added behind all commas in formulas.
34413 \begin_layout Standard
34414 To avoid this, the comma is highlighted and changed to mathematical text
34424 \begin_layout Standard
34425 To use all formula commas in the document as decimal separator, the file
34434 \begin_layout Plain Layout
34439 is part of the \SpecialChar LaTeX
34445 \begin_inset Index idx
34448 \begin_layout Plain Layout
34453 \begin_layout Plain Layout
34473 \begin_inset Index idx
34476 \begin_layout Plain Layout
34482 is loaded with the \SpecialChar LaTeX
34486 \begin_layout Standard
34494 \begin_layout Subsection
34496 \begin_inset CommandInset label
34498 name "subsec:Physical-Vectors"
34503 \begin_inset Index idx
34506 \begin_layout Plain Layout
34515 \begin_layout Standard
34516 Predefined vectors are offered by the \SpecialChar LaTeX
34522 \begin_inset Index idx
34525 \begin_layout Plain Layout
34531 that is loaded with the \SpecialChar LaTeX
34535 \begin_layout Standard
34543 \begin_layout Standard
34547 \begin_layout Plain Layout
34557 \begin_inset Note Note
34560 \begin_layout Plain Layout
34561 The following table will only be displayed when the \SpecialChar LaTeX
34574 \begin_layout Standard
34575 The following commands are defined:
34576 \begin_inset Separator parbreak
34582 \begin_layout Standard
34584 \begin_inset Tabular
34585 <lyxtabular version="3" rows="4" columns="2">
34586 <features booktabs="true" tabularvalignment="middle">
34587 <column alignment="center" valignment="top" width="0pt">
34588 <column alignment="center" valignment="top">
34590 <cell alignment="center" valignment="top" topline="true" bottomline="true" usebox="none">
34593 \begin_layout Plain Layout
34599 <cell alignment="center" valignment="top" topline="true" bottomline="true" usebox="none">
34602 \begin_layout Plain Layout
34610 <cell alignment="center" valignment="top" usebox="none">
34613 \begin_layout Plain Layout
34623 <cell alignment="center" valignment="top" usebox="none">
34626 \begin_layout Plain Layout
34627 \begin_inset Formula $\Bra{\psi}$
34637 <cell alignment="center" valignment="top" usebox="none">
34640 \begin_layout Plain Layout
34650 <cell alignment="center" valignment="top" usebox="none">
34653 \begin_layout Plain Layout
34654 \begin_inset Formula $\Ket{\psi}$
34664 <cell alignment="center" valignment="top" bottomline="true" usebox="none">
34667 \begin_layout Plain Layout
34679 <cell alignment="center" valignment="top" bottomline="true" usebox="none">
34682 \begin_layout Plain Layout
34683 \begin_inset Formula $\Braket{\psi|\phi}$
34699 \begin_layout Standard
34706 assures that all vertical bars are set in the size of the surrounding brackets:
34707 \begin_inset Formula
34709 \Braket{\phi|J=\frac{3}{2}\,,\,M_{J}}
34718 \begin_layout Plain Layout
34728 \begin_inset Note Note
34731 \begin_layout Plain Layout
34732 The following will be displayed when the \SpecialChar LaTeX
34745 \begin_layout Standard
34746 You need to install the \SpecialChar LaTeX
34751 to see the rest of this subsection in the output.
34754 \begin_layout Standard
34758 \begin_layout Plain Layout
34770 \begin_layout Standard
34777 can also be achieved using the command
34783 , that is described in
34784 \begin_inset CommandInset ref
34786 reference "subsec:Automatic-Bracket-Size"
34793 \begin_layout Subsection
34794 Self-defined Fractions
34795 \begin_inset CommandInset label
34797 name "subsec:Self-defined-Fractions"
34802 \begin_inset Index idx
34805 \begin_layout Plain Layout
34806 Fractions ! self-defined
34814 \begin_layout Standard
34815 To define custom commands for fractions, the command
34822 \begin_inset Index idx
34825 \begin_layout Plain Layout
34832 \begin_layout Plain Layout
34846 is used in the following scheme:
34849 \begin_layout Standard
34862 bracket}{fraction bar thickness}{style}
34863 \begin_inset Newline newline
34867 \begin_inset Phantom HPhantom
34870 \begin_layout Plain Layout
34880 {numerator}{denominator}
34883 \begin_layout Standard
34884 The style is a number in the range of 0
34885 \begin_inset space \thinspace{}
34889 \begin_inset space \thinspace{}
34893 \begin_inset Separator parbreak
34899 \begin_layout Standard
34901 \begin_inset Tabular
34902 <lyxtabular version="3" rows="5" columns="2">
34903 <features booktabs="true" tabularvalignment="middle">
34904 <column alignment="center" valignment="top" width="0pt">
34905 <column alignment="center" valignment="top">
34907 <cell alignment="center" valignment="top" topline="true" bottomline="true" usebox="none">
34910 \begin_layout Plain Layout
34916 <cell alignment="center" valignment="top" topline="true" bottomline="true" usebox="none">
34919 \begin_layout Plain Layout
34927 <cell alignment="center" valignment="top" usebox="none">
34930 \begin_layout Plain Layout
34936 <cell alignment="center" valignment="top" usebox="none">
34939 \begin_layout Plain Layout
34940 display style formula
34947 <cell alignment="center" valignment="top" usebox="none">
34950 \begin_layout Plain Layout
34956 <cell alignment="center" valignment="top" usebox="none">
34959 \begin_layout Plain Layout
34967 <cell alignment="center" valignment="top" usebox="none">
34970 \begin_layout Plain Layout
34976 <cell alignment="center" valignment="top" usebox="none">
34979 \begin_layout Plain Layout
34987 <cell alignment="center" valignment="top" bottomline="true" usebox="none">
34990 \begin_layout Plain Layout
34996 <cell alignment="center" valignment="top" bottomline="true" usebox="none">
34999 \begin_layout Plain Layout
35013 \begin_layout Standard
35014 When no style is given, the size is adjusted to the surrounding environment
35015 like for the command
35024 \begin_layout Standard
35025 When no fraction bar thickness is given, the predefined value of 0.4
35026 \begin_inset space \thinspace{}
35032 \begin_layout Standard
35033 \begin_inset VSpace medskip
35036 For example, the commands
35049 \begin_inset CommandInset ref
35051 reference "subsec:Fractions"
35055 are defined with the commands
35058 \begin_layout Standard
35067 genfrac{}{}{}{0}{#1}{#2}}
35070 \begin_layout Standard
35074 \begin_layout Standard
35083 genfrac{(}{)}{0pt}{1}{#1}{#2}}
35086 \begin_layout Standard
35087 \begin_inset VSpace medskip
35090 To define a fraction where the fraction bar thickness can be given as optional
35091 argument, the following line is inserted to the \SpecialChar LaTeX
35095 \begin_layout Standard
35104 genfrac{}{}{#1}{}{#2}{#3}}
35107 \begin_layout Standard
35109 \begin_inset Formula
35111 \text{Command} & & \mathrm{\backslash fracS[1mm]\backslash\{A\to\backslash\{B} & & \mathrm{\backslash fracS[5mm]\backslash\{A\to\backslash\{B}\\
35112 \text{Result} & & \fracS[1mm]{A}{B} & & \fracS[5mm]{A}{B}
35117 As one can see, the distance of the numerator and the denominator to the
35118 fraction bar is round about three times the bar thickness.
35121 \begin_layout Subsection
35123 \begin_inset Index idx
35126 \begin_layout Plain Layout
35135 \begin_layout Standard
35136 There are four ways to cancel formulas or parts of formulas:
35139 \begin_layout Standard
35143 \begin_layout Plain Layout
35153 \begin_inset Note Note
35156 \begin_layout Plain Layout
35157 The following table will only be displayed when the \SpecialChar LaTeX
35168 \begin_inset Separator parbreak
35174 \begin_layout Standard
35176 \begin_inset Tabular
35177 <lyxtabular version="3" rows="5" columns="2">
35178 <features booktabs="true" tabularvalignment="middle">
35179 <column alignment="center" valignment="top" width="0pt">
35180 <column alignment="center" valignment="top">
35182 <cell alignment="center" valignment="top" topline="true" bottomline="true" usebox="none">
35185 \begin_layout Plain Layout
35191 <cell alignment="center" valignment="top" topline="true" bottomline="true" usebox="none">
35194 \begin_layout Plain Layout
35202 <cell alignment="center" valignment="top" usebox="none">
35205 \begin_layout Plain Layout
35209 \begin_inset space \textvisiblespace{}
35215 \begin_inset space \textvisiblespace{}
35223 <cell alignment="center" valignment="top" usebox="none">
35226 \begin_layout Plain Layout
35227 \begin_inset Formula $\cancel{\int A=B}$
35236 <row topspace="1.5mm">
35237 <cell alignment="center" valignment="top" usebox="none">
35240 \begin_layout Plain Layout
35244 \begin_inset space \textvisiblespace{}
35250 \begin_inset space \textvisiblespace{}
35258 <cell alignment="center" valignment="top" usebox="none">
35261 \begin_layout Plain Layout
35262 \begin_inset Formula $\bcancel{\int A=B}$
35271 <row topspace="1.5mm">
35272 <cell alignment="center" valignment="top" usebox="none">
35275 \begin_layout Plain Layout
35279 \begin_inset space \textvisiblespace{}
35285 \begin_inset space \textvisiblespace{}
35293 <cell alignment="center" valignment="top" usebox="none">
35296 \begin_layout Plain Layout
35297 \begin_inset Formula $\xcancel{\int A=B}$
35307 <cell alignment="center" valignment="top" topline="true" bottomline="true" usebox="none">
35310 \begin_layout Plain Layout
35314 \begin_inset space \textvisiblespace{}
35320 \begin_inset space \textvisiblespace{}
35324 \begin_inset Formula $\to$
35332 <cell alignment="center" valignment="top" topline="true" bottomline="true" usebox="none">
35335 \begin_layout Plain Layout
35336 \begin_inset Formula $\cancelto{1}{\int A=B}\hspace{3mm}$
35352 \begin_layout Standard
35359 is especially suitable to visualize the reduction of fractions within formulas:
35360 \begin_inset Formula
35362 \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}}}
35370 \begin_layout Standard
35371 To change the size of
35378 \begin_inset Quotes eld
35382 \begin_inset Quotes erd
35385 value one can add the \SpecialChar LaTeX
35389 \begin_layout Standard
35394 PassOptionsToPackage{option}{cancel}
35397 \begin_layout Standard
35406 which leads to the same size as for the canceled value, or
35410 which makes is it a bit smaller than normal.
35413 \begin_layout Standard
35414 To color the cancellation bar one adds this command as \SpecialChar TeX
35418 \begin_layout Standard
35430 \begin_layout Standard
35435 can be replaced by a color of your choice.
35438 \begin_layout Standard
35442 \begin_layout Plain Layout
35458 \begin_layout Standard
35459 \begin_inset Formula
35461 \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}}}
35469 \begin_layout Standard
35473 \begin_layout Plain Layout
35487 \begin_inset Note Note
35490 \begin_layout Plain Layout
35499 \begin_layout Standard
35500 For further customizations, see the documentation of the package
35505 \begin_inset CommandInset citation
35512 \begin_inset Index idx
35515 \begin_layout Plain Layout
35524 \begin_layout Standard
35528 \begin_layout Plain Layout
35538 \begin_inset Note Note
35541 \begin_layout Plain Layout
35542 The following will be displayed when the \SpecialChar LaTeX
35555 \begin_layout Standard
35556 You need to install the \SpecialChar LaTeX
35561 to see the rest of this subsection in the output.
35564 \begin_layout Standard
35568 \begin_layout Plain Layout
35580 \begin_layout Subsection
35581 Formulas in Section Headings
35582 \begin_inset CommandInset label
35584 name "subsec:Formulas-in-Section"
35589 \begin_inset Index idx
35592 \begin_layout Plain Layout
35593 Formula ! in section headings
35601 \begin_layout Standard
35602 When formulas are used in section headings, the following has to be taken
35606 \begin_layout Standard
35607 \begin_inset Note Greyedout
35610 \begin_layout Plain Layout
35616 \begin_inset Index idx
35619 \begin_layout Plain Layout
35620 Packages ! hyperref
35625 support is enabled in the document settings dialog under
35628 \begin_inset space ~
35633 , PDF-bookmarks are created for every section heading in the table of contents.
35634 If a section heading contains formulas, they are incorrectly displayed
35635 in the bookmark text, because formulas in bookmarks infringe the PDF convention
35644 \begin_layout Standard
35645 Both problems can be solved by inserting at the end of the section heading
35646 a short title with the menu
35648 Insert\SpecialChar menuseparator
35650 \begin_inset space ~
35656 Short titles are used as alternative for multiline section headings to
35657 keep the table of contents clearly arranged.
35658 Only the short title appears in the table of contents and therefore also
35659 in the PDF-bookmark.
35662 \begin_layout Standard
35663 When formulas should be used in the table of contents but
35667 is used, one can use the following command in \SpecialChar TeX
35671 \begin_layout Standard
35676 texorpdfstring{part}{alternative}
35677 \begin_inset Index idx
35680 \begin_layout Plain Layout
35691 \begin_layout Standard
35692 Part is the part of the heading that shouldn't appear in the PDF-bookmark.
35693 This can be characters, formulas, footnotes, but also cross-references.
35694 The alternative is used instead of the part for the bookmark.
35697 \begin_layout Standard
35698 Here are two example headings:
35699 \begin_inset VSpace -3mm
35706 \begin_layout Plain Layout
35718 \begin_layout Subsubsection
35719 Heading without formula in table of contents
35720 \begin_inset Formula $\sqrt{-1}=\mathrm{i}$
35724 \begin_inset Argument 1
35727 \begin_layout Plain Layout
35728 Heading without formula in table of contents
35736 \begin_layout Subsubsection
35737 Heading with formula in table of contents
35741 \begin_layout Plain Layout
35751 \begin_inset Formula $\sqrt{-1}=\mathrm{i}$
35758 \begin_layout Plain Layout
35768 \begin_layout Standard
35772 \begin_layout Plain Layout
35781 In the first heading a short title was used, in the second one
35790 \begin_layout Standard
35791 To get the same formatting as for the other headings, the complete heading
35800 \begin_layout Plain Layout
35802 \begin_inset CommandInset ref
35804 reference "subsec:Bold-Formulas"
35816 \begin_layout Subsection
35817 Formulas in multi-column Text
35818 \begin_inset Index idx
35821 \begin_layout Plain Layout
35822 Formula ! in multi-column text
35830 \begin_layout Standard
35831 Formulas in multi-column text are often too wide to fit into a column and
35832 thus need to be set over the whole page width.
35833 This is done by using the \SpecialChar LaTeX
35842 \begin_layout Plain Layout
35847 is part of every \SpecialChar LaTeX
35848 standard installation.
35854 \begin_inset Index idx
35857 \begin_layout Plain Layout
35858 Packages ! multicol
35863 , that is loaded with the \SpecialChar LaTeX
35867 \begin_layout Standard
35872 usepackage{multicol}
35875 \begin_layout Standard
35876 \begin_inset Note Greyedout
35879 \begin_layout Plain Layout
35880 Note that in this case the setting
35883 \begin_inset space ~
35890 Document\SpecialChar menuseparator
35896 \begin_inset space ~
35916 \begin_layout Standard
35917 Before the multi-column text the command
35920 \begin_layout Standard
35925 begin{multicols}{column number}
35928 \begin_layout Standard
35929 is written in \SpecialChar TeX
35931 The column number is a number in the range of 2
35932 \begin_inset space \thinspace{}
35936 \begin_inset space \thinspace{}
35940 Before the formula the multi-column text is ended by inserting the command
35943 \begin_layout Standard
35951 \begin_layout Standard
35952 in \SpecialChar TeX
35956 \begin_layout Standard
35957 Due to the command some space is automatically added before the formula.
35959 \begin_inset space \thinspace{}
35962 mm vertical space is inserted before the formula.
35963 When the formula style
35969 \begin_layout Plain Layout
35971 \begin_inset CommandInset ref
35973 reference "sec:Formula-Styles"
35985 \begin_inset space \thinspace{}
35988 mm space is inserted instead.
35991 \begin_layout Standard
35992 As example a multi-column text with a displayed formula:
35995 \begin_layout Standard
36001 \begin_layout Plain Layout
36005 begin{multicols}{2}
36010 Das Spektrum wird fouriertransformiert.
36011 Die Fouriertransformation wird verwendet, um die überlagerten Signale (Netzwerk
36012 , Lösungsmittel) zu trennen.
36013 Nachdem wir die Phasenverschiebung bestimmen konnten, interessiert uns
36014 nun das Aussehen des Ausgangssignals.
36015 Im Experiment haben wir es mit sehr vielen Teilchen zu tun, so dass man
36016 über alle Phasen integrieren muss.
36018 \begin_inset Formula $S$
36021 unser normiertes Ausgangssignal und
36022 \begin_inset Formula $P$
36025 die Phasenverteilungsfunktion, so ergibt sich die Beziehung
36029 \begin_layout Plain Layout
36039 \begin_inset VSpace -6mm
36043 \begin_inset Formula
36045 S(t)=S_{0}(t)\int_{-\infty}^{\infty}P(\phi,t)\mathrm{e}^{\mathrm{i}\phi}\,\mathrm{d}\phi
36054 \begin_layout Plain Layout
36058 begin{multicols}{2}
36064 \begin_inset Formula $S_{0}$
36067 das Signal ohne Gradient ist und die Normierungsbedingung
36068 \begin_inset Formula $\int_{-\infty}^{\infty}P(\phi,t)\,\mathrm{d}\phi=1$
36072 Nun dürfen wir aber nicht den Relaxationsprozess außer Acht lassen.
36074 \begin_inset Formula $\nicefrac{\pi}{2}$
36078 \begin_inset space \thinspace{}
36081 -rf-Puls beginnt sich die Magnetisierung zu entfokussieren, wodurch sich
36082 das Signal zusätzlich abschwächt.
36083 Diese Abschwächung verläuft exponentiell in Abhängigkeit der so genannten
36085 \begin_inset Formula $T_{2}$
36091 \begin_layout Standard
36097 \begin_layout Plain Layout
36109 \begin_layout Subsection
36110 Formulas with Description of Variables
36111 \begin_inset Index idx
36114 \begin_layout Plain Layout
36115 Formula ! with description of variables
36123 \begin_layout Standard
36124 To describe variables within a formula, like in formula
36125 \begin_inset CommandInset ref
36127 reference "eq:within"
36136 \begin_inset Formula $n$
36140 \begin_inset space ~
36143 matrix is used with left aligned columns for the
36144 \begin_inset Formula $n$
36151 \begin_layout Plain Layout
36153 \begin_inset CommandInset ref
36155 reference "sec:Matrices"
36164 To set the description in a smaller size, before the matrix e.
36165 \begin_inset space \thinspace{}
36169 \begin_inset space \space{}
36182 \begin_layout Plain Layout
36184 \begin_inset CommandInset ref
36186 reference "subsec:Font-Sizes"
36198 \begin_layout Standard
36199 When the formula style
36205 \begin_layout Plain Layout
36207 \begin_inset CommandInset ref
36209 reference "sec:Formula-Styles"
36230 \begin_layout Plain Layout
36237 only works in formulas with the style
36242 \begin_inset CommandInset ref
36244 reference "subsec:Variable-Space"
36253 is inserted before and after the matrix to have the same separation of
36254 the matrix from the equation and the side margin.
36257 \begin_layout Standard
36258 When the formula style
36262 is used, the method described in
36263 \begin_inset CommandInset ref
36265 reference "subsec:Flalign-Environment"
36269 is used to indent formulas.
36271 \begin_inset CommandInset ref
36273 reference "eq:within"
36277 consists of five columns where in the first two columns contain the equation,
36278 the third the matrix and the last one an empty \SpecialChar TeX
36280 \begin_inset Formula
36282 \hspace{30pt}F_{A} & =\rho·V·g & \footnotesize\begin{array}{ll}
36283 \rho & \textrm{density}\\
36284 V & \textrm{volume}\\
36285 g & \textrm{gravitational acceleration}
36286 \end{array} & & {}\label{eq:within}
36294 \begin_layout Subsection
36295 Upright small Greek Letters
36296 \begin_inset CommandInset label
36298 name "subsec:Upright-small-Greek"
36303 \begin_inset Index idx
36306 \begin_layout Plain Layout
36307 Greek letters ! upright
36315 \begin_layout Standard
36316 Most of the math fonts only provide italic small Greek letters.
36317 But for symbols of elementary particles like pions and neutrinos, upright
36318 Greek letters are needed.
36327 \begin_layout Plain Layout
36332 is part of the \SpecialChar LaTeX
36338 \begin_inset Index idx
36341 \begin_layout Plain Layout
36346 \begin_layout Plain Layout
36366 \begin_inset Index idx
36369 \begin_layout Plain Layout
36375 that is loaded with the \SpecialChar LaTeX
36379 \begin_layout Standard
36384 usepackage{upgreek}
36387 \begin_layout Standard
36393 \begin_layout Plain Layout
36403 \begin_inset Note Note
36406 \begin_layout Plain Layout
36407 The following table will only be displayed when the \SpecialChar LaTeX
36417 They are created when the command for a small Greek letter is started with
36423 For example the command
36430 \begin_inset Formula $\uptau$
36436 \begin_layout Standard
36437 With these commands reactions of elementary particles can be typeset:
36438 \begin_inset Formula
36440 \uppi^{+}\to\upmu^{+}+\upnu_{\upmu}
36448 \begin_layout Standard
36449 The upright letters are more bold and wider than the italic ones.
36450 They should therefore not be used for units like
36451 \begin_inset Quotes eld
36455 \begin_inset Quotes erd
36461 \begin_layout Standard
36465 \begin_layout Plain Layout
36475 \begin_inset Note Note
36478 \begin_layout Plain Layout
36479 The following will be displayed when the \SpecialChar LaTeX
36492 \begin_layout Standard
36493 You need to install the \SpecialChar LaTeX
36498 to see the rest of this subsection in the output.
36501 \begin_layout Standard
36505 \begin_layout Plain Layout
36517 \begin_layout Subsection
36518 Text Characters in Formulas
36519 \begin_inset Index idx
36522 \begin_layout Plain Layout
36531 \begin_layout Standard
36532 In some cases you might want to insert text characters directly into formulas.
36533 When for example the centered dot · is often used in formulas like
36534 \begin_inset Formula $\nu=5·10^{5}\,\mathrm{Hz}$
36537 , one would have to insert the command
36547 \begin_layout Plain Layout
36549 \begin_inset CommandInset ref
36551 reference "subsec:Binary-Operators"
36560 all the time, because this character is defined in all encodings as text
36562 But the encoding can be changed by this \SpecialChar LaTeX
36566 \begin_layout Standard
36571 Declare Inputtext{183}{
36581 f\SpecialChar ligaturebreak
36585 \begin_layout Standard
36586 The character encoding (menu
36588 Document\SpecialChar menuseparator
36589 Settings\SpecialChar menuseparator
36592 ) specifies what character appears when a keyboard key is pressed.
36593 When the key for the character '·' is pressed, internally the command
36600 But this command is not available in a formula so that you would get \SpecialChar LaTeX
36602 With the changed encoding the right command is chosen automatically, depending
36603 on if the character was inserted into a formula or not.
36606 \begin_layout Standard
36607 The encoding of several characters is saved in definition files.
36608 For example the encoding
36612 is defined in the file
36616 which is in the installation folder of \SpecialChar LaTeX
36618 Encodings should only be changed via the \SpecialChar LaTeX
36619 -preamble and not in the definition
36621 Otherwise documents could not be edited by other \SpecialChar LyX
36622 users working on other
36626 \begin_layout Standard
36627 \begin_inset VSpace medskip
36630 Besides the centered dot, in this document the degree sign ° is defined
36631 with the following \SpecialChar LaTeX
36632 -preamble line so that it can be directly inserted into
36636 \begin_layout Standard
36641 DeclareInputtext{176}{
36651 f\SpecialChar ligaturebreak
36655 \begin_layout Subsection
36657 -comments in formulas
36658 \begin_inset Index idx
36661 \begin_layout Plain Layout
36671 \begin_layout Standard
36672 In text you can insert a comment that will only be visible in the \SpecialChar LaTeX
36674 code of your file with the menu
36676 Insert\SpecialChar menuseparator
36677 Note\SpecialChar menuseparator
36681 This is not possible in a formula but you can insert \SpecialChar LaTeX
36686 \begin_layout Standard
36694 \begin_layout Standard
36695 This creates a box in which you can write your comment.
36696 Due to a bug in \SpecialChar LyX
36701 \begin_layout Plain Layout
36702 \begin_inset CommandInset href
36704 name "LyX-bug #9002"
36705 target "http://www.lyx.org/trac/ticket/9002"
36714 you cannot write normal text inside the comment, even when you use mathematical
36715 text, you will see its \SpecialChar LaTeX
36716 -commands in the \SpecialChar LaTeX
36718 \begin_inset Newline newline
36721 This a formula with a \SpecialChar LaTeX
36723 \begin_inset Formula
36725 A=B%\text{This is the comment}
36733 \begin_layout Standard
36734 \begin_inset Newpage newpage
36740 \begin_layout Section
36743 \begin_inset Index idx
36746 \begin_layout Plain Layout
36755 \begin_layout Standard
36756 This section is a summary of the most important typographic rules, listed
36761 \begin_layout Plain Layout
36762 This collection was partly taken from the German semi-official dictionary
36764 \begin_inset Quotes eld
36768 \begin_inset Quotes erd
36772 \begin_inset CommandInset citation
36778 that lists some of the ISO rules.
36779 More rules are listed in
36780 \begin_inset CommandInset citation
36794 \begin_layout Itemize
36803 \begin_layout Plain Layout
36804 done with font styles, see
36805 \begin_inset CommandInset ref
36807 reference "subsec:Font-Styles"
36816 , no matter if they appear in italic text: 30
36817 \begin_inset space \thinspace{}
36821 \begin_inset Newline newline
36824 Between the value and the unit is the smallest space, see
36825 \begin_inset CommandInset ref
36827 reference "subsec:Predefined-Space"
36832 \begin_inset Newline newline
36835 This convention is automatically fulfilled when the command
36842 When it is entered to a formula, two boxes appear.
36843 In the first one the value is inserted, in the second one the unit, and
36845 \begin_inset Formula $\unit[30]{km/h}$
36849 \begin_inset space \thinspace{}
36859 is not a real \SpecialChar LaTeX
36860 command but the command
36866 , therefore you cannot use it in \SpecialChar TeX
36870 \begin_layout Itemize
36871 Percent and perthousand signs are set like physical units:
36872 \begin_inset Newline newline
36876 \begin_inset space \thinspace{}
36882 \begin_layout Itemize
36883 The degree sign follows directly on the value: 15°, but not when it is used
36885 \begin_inset space \thinspace{}
36891 \begin_layout Itemize
36892 In numbers with more than four digits the smallest space is inserted before
36893 every third digit to group them:
36903 \begin_inset space \thinspace{}
36907 \begin_inset space \thinspace{}
36913 \begin_layout Itemize
36914 For dimensions like 120×90×40
36915 \begin_inset space \thinspace{}
36918 cm the multiplication sign
36919 \begin_inset Quotes eld
36923 \begin_inset Quotes erd
36927 It is available either via the command
36935 Insert\SpecialChar menuseparator
36936 Special Character\SpecialChar menuseparator
36942 \begin_layout Itemize
36943 Functions with names consisting of several letters are set upright to avoid
36945 \begin_inset CommandInset ref
36947 reference "subsec:Predefined-Functions"
36954 \begin_layout Itemize
36955 Indices consisting of several letters, are set upright:
36956 \begin_inset Formula $E_{\mathrm{kin}}$
36960 \begin_inset Newline newline
36963 Components of matrices are set italic:
36964 \begin_inset Formula $\hat{H}_{kl}$
36970 \begin_layout Itemize
36971 The differentiation/integration operator 'd', the Euler's number 'e' and
36972 the imaginary unit 'i' should be set upright, to avoid mixing them up with
36976 \begin_layout Itemize
36977 The character that denotes a
36981 transformation is inserted either by the command
36986 \begin_inset space \textvisiblespace{}
36993 Insert\SpecialChar menuseparator
36994 Special Character\SpecialChar menuseparator
36995 Symbols\SpecialChar menuseparator
36997 \begin_inset space ~
37003 \begin_inset Formula $\mathscr{F}$
37009 \begin_layout Standard
37010 \begin_inset Newpage newpage
37016 \begin_layout Section
37018 \begin_inset Index idx
37021 \begin_layout Plain Layout
37030 \begin_layout Standard
37031 Some characters and symbols can be created with several commands.
37032 Here is a list of the synonym commands:
37035 \begin_layout Standard
37036 \begin_inset VSpace bigskip
37040 \begin_inset space \hfill{}
37044 \begin_inset Tabular
37045 <lyxtabular version="3" rows="12" columns="2">
37046 <features booktabs="true" tabularvalignment="middle">
37047 <column alignment="center" valignment="top" width="0pt">
37048 <column alignment="center" valignment="top" width="0pt">
37050 <cell alignment="center" valignment="top" topline="true" bottomline="true" usebox="none">
37053 \begin_layout Plain Layout
37059 <cell alignment="center" valignment="top" topline="true" bottomline="true" 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
37092 <cell alignment="center" valignment="top" usebox="none">
37095 \begin_layout Plain Layout
37103 <cell alignment="center" valignment="top" usebox="none">
37106 \begin_layout Plain Layout
37116 <cell alignment="center" valignment="top" usebox="none">
37119 \begin_layout Plain Layout
37127 <cell alignment="center" valignment="top" usebox="none">
37130 \begin_layout Plain Layout
37140 <cell alignment="center" valignment="top" usebox="none">
37143 \begin_layout Plain Layout
37151 <cell alignment="center" valignment="top" usebox="none">
37154 \begin_layout Plain Layout
37162 <cell alignment="center" valignment="top" usebox="none">
37165 \begin_layout Plain Layout
37173 <cell alignment="center" valignment="top" usebox="none">
37176 \begin_layout Plain Layout
37184 <cell alignment="center" valignment="top" usebox="none">
37187 \begin_layout Plain Layout
37195 <cell alignment="center" valignment="top" usebox="none">
37198 \begin_layout Plain Layout
37208 <cell alignment="center" valignment="top" usebox="none">
37211 \begin_layout Plain Layout
37219 <cell alignment="center" valignment="top" usebox="none">
37222 \begin_layout Plain Layout
37232 <cell alignment="center" valignment="top" usebox="none">
37235 \begin_layout Plain Layout
37243 <cell alignment="center" valignment="top" usebox="none">
37246 \begin_layout Plain Layout
37256 <cell alignment="center" valignment="top" usebox="none">
37259 \begin_layout Plain Layout
37267 <cell alignment="center" valignment="top" usebox="none">
37270 \begin_layout Plain Layout
37280 <cell alignment="center" valignment="top" usebox="none">
37283 \begin_layout Plain Layout
37291 <cell alignment="center" valignment="top" usebox="none">
37294 \begin_layout Plain Layout
37302 <cell alignment="center" valignment="top" bottomline="true" usebox="none">
37305 \begin_layout Plain Layout
37313 <cell alignment="center" valignment="top" bottomline="true" usebox="none">
37316 \begin_layout Plain Layout
37328 \begin_inset space \hfill{}
37332 \begin_inset Tabular
37333 <lyxtabular version="3" rows="12" columns="2">
37334 <features booktabs="true" tabularvalignment="middle">
37335 <column alignment="center" valignment="top" width="0pt">
37336 <column alignment="center" valignment="top" width="0pt">
37338 <cell alignment="center" valignment="top" topline="true" bottomline="true" usebox="none">
37341 \begin_layout Plain Layout
37347 <cell alignment="center" valignment="top" topline="true" bottomline="true" usebox="none">
37350 \begin_layout Plain Layout
37358 <cell alignment="center" valignment="top" usebox="none">
37361 \begin_layout Plain Layout
37369 <cell alignment="center" valignment="top" usebox="none">
37372 \begin_layout Plain Layout
37384 <cell alignment="center" valignment="top" usebox="none">
37387 \begin_layout Plain Layout
37395 <cell alignment="center" valignment="top" usebox="none">
37398 \begin_layout Plain Layout
37408 <cell alignment="center" valignment="top" usebox="none">
37411 \begin_layout Plain Layout
37419 <cell alignment="center" valignment="top" usebox="none">
37422 \begin_layout Plain Layout
37432 <cell alignment="center" valignment="top" usebox="none">
37435 \begin_layout Plain Layout
37443 <cell alignment="center" valignment="top" usebox="none">
37446 \begin_layout Plain Layout
37454 <cell alignment="center" valignment="top" usebox="none">
37457 \begin_layout Plain Layout
37465 <cell alignment="center" valignment="top" usebox="none">
37468 \begin_layout Plain Layout
37476 <cell alignment="center" valignment="top" usebox="none">
37479 \begin_layout Plain Layout
37487 <cell alignment="center" valignment="top" usebox="none">
37490 \begin_layout Plain Layout
37500 <cell alignment="center" valignment="top" usebox="none">
37503 \begin_layout Plain Layout
37511 <cell alignment="center" valignment="top" usebox="none">
37514 \begin_layout Plain Layout
37524 <cell alignment="center" valignment="top" usebox="none">
37527 \begin_layout Plain Layout
37535 <cell alignment="center" valignment="top" usebox="none">
37538 \begin_layout Plain Layout
37548 <cell alignment="center" valignment="top" usebox="none">
37551 \begin_layout Plain Layout
37559 <cell alignment="center" valignment="top" usebox="none">
37562 \begin_layout Plain Layout
37572 <cell alignment="center" valignment="top" usebox="none">
37575 \begin_layout Plain Layout
37583 <cell alignment="center" valignment="top" usebox="none">
37586 \begin_layout Plain Layout
37596 <cell alignment="center" valignment="top" bottomline="true" usebox="none">
37599 \begin_layout Plain Layout
37607 <cell alignment="center" valignment="top" bottomline="true" usebox="none">
37610 \begin_layout Plain Layout
37624 \begin_inset space \hfill{}
37630 \begin_layout Standard
37631 \begin_inset Newpage newpage
37637 \begin_layout Bibliography
37638 \begin_inset CommandInset bibitem
37639 LatexCommand bibitem
37651 The \SpecialChar LaTeX
37655 Addison Wesley, 2004
37658 \begin_layout Bibliography
37659 \begin_inset CommandInset bibitem
37660 LatexCommand bibitem
37666 \begin_inset CommandInset href
37669 target "ftp://ftp.dante.de/tex-archive/info/math/voss/mathmode/Mathmode.pdf"
37673 of \SpecialChar LaTeX
37677 \begin_layout Bibliography
37678 \begin_inset CommandInset bibitem
37679 LatexCommand bibitem
37685 \begin_inset CommandInset href
37688 target "http://mirrors.ctan.org/macros/latex/required/amslatex/math/amsldoc.pdf"
37696 \begin_layout Plain Layout
37705 -\SpecialChar LaTeX
37709 \begin_layout Bibliography
37710 \begin_inset CommandInset bibitem
37711 LatexCommand bibitem
37717 \begin_inset CommandInset href
37720 target "ftp://ftp.dante.de/tex-archive/info/symbols/comprehensive/symbols-a4.pdf"
37724 of all symbols available with \SpecialChar LaTeX
37728 \begin_layout Bibliography
37729 \begin_inset CommandInset bibitem
37730 LatexCommand bibitem
37736 \begin_inset CommandInset href
37738 name "Documentation"
37739 target "http://mirrors.ctan.org/macros/latex/contrib/cancel/cancel.pdf"
37743 of the \SpecialChar LaTeX
37749 \begin_inset Index idx
37752 \begin_layout Plain Layout
37761 \begin_layout Bibliography
37762 \begin_inset CommandInset bibitem
37763 LatexCommand bibitem
37769 \begin_inset CommandInset href
37771 name "Documentation"
37772 target "http://www.tug.org/applications/hyperref/ftp/doc/manual.pdf"
37776 of the \SpecialChar LaTeX
37782 \begin_inset Index idx
37785 \begin_layout Plain Layout
37786 Packages ! hyperref
37794 \begin_layout Bibliography
37795 \begin_inset CommandInset bibitem
37796 LatexCommand bibitem
37802 \begin_inset CommandInset href
37804 name "Documentation"
37805 target "http://www.ctan.org/tex-archive/macros/latex/contrib/mhchem/mhchem.pdf"
37809 of the \SpecialChar LaTeX
37815 \begin_inset Index idx
37818 \begin_layout Plain Layout
37827 \begin_layout Bibliography
37828 \begin_inset CommandInset bibitem
37829 LatexCommand bibitem
37840 Auflage, Duden 2001
37843 \begin_layout Bibliography
37844 \begin_inset CommandInset bibitem
37845 LatexCommand bibitem
37851 \begin_inset CommandInset href
37854 target "http://physics.nist.gov/Pubs/SP811/sec11.html"
37858 for reviewing manuscripts
37861 \begin_layout Standard
37862 \begin_inset CommandInset index_print
37863 LatexCommand printindex