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/Manuals#Math
322 \begin_layout Standard
323 \begin_inset Newpage newpage
329 \begin_layout Section
333 \begin_layout Standard
334 This document explains \SpecialChar LyX
335 's math features and is furthermore a collection
336 of \SpecialChar LaTeX
337 -commands used for mathematical characters and constructs.
338 The explanations are designed for the usage of commands.
339 It is therefore required that you have read the section
350 \begin_layout Standard
351 Most of the characters and many constructs explained in this manual are
352 also accessible via the menu
356 \SpecialChar menuseparator
372 But everybody who has to write lots of formulas will notice that it is
373 much faster to use commands instead of the math toolbar.
374 Therefore this manual is focused on commands but also mentions the correspondin
375 g toolbar buttons when available.
378 \begin_layout Standard
379 If not specially mentioned the commands are only available within formulas.
380 To be able to use all commands explained in this document, the option
384 must be checked in the document settings (menu
386 Document\SpecialChar menuseparator
387 Settings\SpecialChar menuseparator
398 \begin_layout Plain Layout
401 Use AMS math package automatically
407 \begin_layout Plain Layout
416 -math when math constructs are found that are supported by \SpecialChar LyX
425 \begin_layout Standard
426 This document doesn't list all
430 \begin_layout Plain Layout
443 \begin_layout Plain Layout
448 \begin_layout Plain Layout
457 -math commands is in the file
460 \begin_inset CommandInset href
463 target "ftp://ftp.ams.org/pub/tex/doc/amstex/amsguide.pdf"
469 , which is part of every \SpecialChar LaTeX
470 standard installation.
475 for lucidity reasons.
478 \begin_layout Section
482 \begin_layout Standard
483 To create an inline formula
484 \begin_inset Index idx
487 \begin_layout Plain Layout
493 that is embedded into a text line, use one of the shortcuts
499 or the toolbar button
506 \begin_inset Newline newline
509 To create a display style formula
510 \begin_inset Index idx
513 \begin_layout Plain Layout
514 Formula ! display style
519 which will appear bigger, has a different format, and will be in a separate
520 paragraph, use one of these shortcuts:
529 \begin_layout Standard
530 To change a display style formula to an inline formula, set the cursor into
531 the formula and use one of the shortcuts
539 Edit\SpecialChar menuseparator
540 Math\SpecialChar menuseparator
544 The same way is used to change an inline formula to a display style formula.
547 \begin_layout Standard
548 To display parts of an inline formula in the size of a display style formula,
556 \begin_inset Index idx
559 \begin_layout Plain Layout
568 Then a new blue box appears in which the desired formula part is inserted.
571 \begin_layout Standard
572 Only inline formulas are allowed inside tables.
575 \begin_layout Standard
580 can be turned on in the menu
582 View\SpecialChar menuseparator
586 When you click there on
587 \begin_inset Quotes eld
591 \begin_inset Quotes erd
594 the toolbar will be shown permanently at the bottom; this state is visualized
599 menu with a checkmark.
600 When you click in this state again on
601 \begin_inset Quotes eld
605 \begin_inset Quotes erd
616 is only shown when the cursor is within a formula; this state is visualized
617 by the renaming of the menu entry from
618 \begin_inset Quotes eld
622 \begin_inset Quotes erd
626 \begin_inset Quotes eld
634 \begin_inset Quotes erd
640 \begin_layout Standard
643 \begin_inset Index idx
646 \begin_layout Plain Layout
653 is invoked by pressing the toolbar button
661 Insert\SpecialChar menuseparator
673 \begin_layout Standard
674 To change the \SpecialChar LaTeX
676 \begin_inset Index idx
679 \begin_layout Plain Layout
688 Document\SpecialChar menuseparator
689 Settings\SpecialChar menuseparator
699 \begin_layout Standard
700 To edit matrices, case differentiations and multiline formulas subsequently,
703 Edit\SpecialChar menuseparator
708 Edit\SpecialChar menuseparator
710 \begin_inset space \thinspace{}
714 \begin_inset space \thinspace{}
724 When lines and columns are swapped via the menu, the column or line where
725 the cursor is in is exchanged with the column to the right or the line
727 Is the cursor in the last column or row, the exchange is done with the
728 column to the left or the line above.
731 \begin_layout Standard
732 To write text in formulas
736 \begin_layout Plain Layout
737 For multiline formulas the command
744 \begin_inset CommandInset ref
746 reference "subsec:Text-in-multiline"
760 \begin_inset Index idx
763 \begin_layout Plain Layout
770 \begin_inset Index idx
773 \begin_layout Plain Layout
780 This mode is invoked with the shortcut
786 or by the insertion of the command
793 \begin_inset Index idx
796 \begin_layout Plain Layout
805 The text appears black in \SpecialChar LyX
806 and can therefore be distinguished from the
807 other formula parts which appear blue.
808 In the output mathematical text is set upright, in contrary to other formula
812 \begin_layout Subsection*
816 \begin_layout Standard
817 Most of the \SpecialChar LaTeX
818 -commands for math constructs have the following scheme:
821 \begin_layout Standard
837 \begin_layout Standard
838 A command always starts with a backslash
839 \begin_inset Quotes gld
849 \begin_inset Quotes grd
853 To omit optional arguments, also omit the associated brackets.
854 The braces around the required arguments are named in this document as
857 \begin_inset Index idx
860 \begin_layout Plain Layout
868 If you add in a formula a left brace to a command name, \SpecialChar LyX
870 creates a \SpecialChar TeX
872 In all other cases \SpecialChar TeX
873 braces are created in formulas with the command
881 braces appear red in \SpecialChar LyX
882 , in contrary to normal braces which appear blue.
884 mode no command is needed to get \SpecialChar TeX
887 braces don't appear in the output.
890 \begin_layout Standard
891 When commands without arguments, like commands for symbols are entered in
893 mode, a space character must
897 be behind the command to end it.
898 This space doesn't appear in the output.
899 When the space should appear in the output, the space must be followed
900 by a protected space in normal text.
903 \begin_layout Standard
904 A protected space is inserted with
907 arg "command-alternatives space-insert protected ; math-space"
913 \begin_layout Subsection*
914 \begin_inset Newpage newpage
920 \begin_layout Itemize
922 \begin_inset space \textvisiblespace{}
925 denotes a space character to be input.
928 \begin_layout Itemize
930 \begin_inset Formula $\to$
933 denotes the usage of the corresponding arrow key on the keyboard.
938 key can often be used instead of
939 \begin_inset Formula $\to$
943 \begin_inset Formula $\downarrow$
951 \begin_inset Formula $\leftarrow$
955 \begin_inset Formula $\uparrow$
961 \begin_layout Subsection*
965 \begin_layout Standard
967 \begin_inset Float table
973 \begin_layout Plain Layout
975 \begin_inset Caption Standard
977 \begin_layout Plain Layout
978 \begin_inset CommandInset label
980 name "tab:Available-units"
992 \begin_layout Plain Layout
995 <lyxtabular version="3" rows="13" columns="2">
996 <features booktabs="true" tabularvalignment="middle">
997 <column alignment="center" valignment="top">
998 <column alignment="center" valignment="top" width="0pt">
1000 <cell alignment="center" valignment="top" topline="true" bottomline="true" usebox="none">
1003 \begin_layout Plain Layout
1009 <cell alignment="center" valignment="top" topline="true" bottomline="true" usebox="none">
1012 \begin_layout Plain Layout
1020 <cell alignment="center" valignment="top" leftline="true" usebox="none">
1023 \begin_layout Plain Layout
1029 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
1032 \begin_layout Plain Layout
1040 <cell alignment="center" valignment="top" leftline="true" usebox="none">
1043 \begin_layout Plain Layout
1049 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
1052 \begin_layout Plain Layout
1060 <cell alignment="center" valignment="top" leftline="true" usebox="none">
1063 \begin_layout Plain Layout
1069 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
1072 \begin_layout Plain Layout
1074 \begin_inset space \thinspace{}
1078 \begin_inset space \thinspace{}
1088 <cell alignment="center" valignment="top" leftline="true" usebox="none">
1091 \begin_layout Plain Layout
1097 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
1100 \begin_layout Plain Layout
1102 \begin_inset space \thinspace{}
1106 \begin_inset space \thinspace{}
1116 <cell alignment="center" valignment="top" leftline="true" usebox="none">
1119 \begin_layout Plain Layout
1125 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
1128 \begin_layout Plain Layout
1130 \begin_inset space \thinspace{}
1134 \begin_inset space \thinspace{}
1144 <cell alignment="center" valignment="top" leftline="true" usebox="none">
1147 \begin_layout Plain Layout
1153 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
1156 \begin_layout Plain Layout
1158 \begin_inset space \thinspace{}
1162 \begin_inset space \thinspace{}
1172 <cell alignment="center" valignment="top" leftline="true" usebox="none">
1175 \begin_layout Plain Layout
1181 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
1184 \begin_layout Plain Layout
1186 \begin_inset space \thinspace{}
1190 \begin_inset space \thinspace{}
1200 <cell alignment="center" valignment="top" leftline="true" usebox="none">
1203 \begin_layout Plain Layout
1209 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
1212 \begin_layout Plain Layout
1214 \begin_inset space \thinspace{}
1218 \begin_inset Formula $\approx$
1222 \begin_inset space \thinspace{}
1232 <cell alignment="center" valignment="top" leftline="true" usebox="none">
1235 \begin_layout Plain Layout
1241 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
1244 \begin_layout Plain Layout
1246 \begin_inset space \thinspace{}
1250 \begin_inset space \thinspace{}
1260 <cell alignment="center" valignment="top" leftline="true" usebox="none">
1263 \begin_layout Plain Layout
1269 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
1272 \begin_layout Plain Layout
1276 \begin_inset Quotes eld
1282 \begin_inset Quotes erd
1292 <cell alignment="center" valignment="top" leftline="true" usebox="none">
1295 \begin_layout Plain Layout
1301 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
1304 \begin_layout Plain Layout
1306 \begin_inset Quotes eld
1314 \begin_inset Quotes erd
1324 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
1327 \begin_layout Plain Layout
1333 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
1336 \begin_layout Plain Layout
1338 \begin_inset space \thinspace{}
1342 \begin_inset Formula $\nicefrac{1}{18}$
1346 \begin_inset space \thinspace{}
1367 \begin_layout Standard
1368 \begin_inset Newpage newpage
1374 \begin_layout Section
1378 \begin_layout Subsection
1380 \begin_inset Index idx
1383 \begin_layout Plain Layout
1390 \begin_inset Index idx
1393 \begin_layout Plain Layout
1400 \begin_inset Index idx
1403 \begin_layout Plain Layout
1408 \begin_layout Plain Layout
1419 \begin_layout Plain Layout
1432 \begin_inset Index idx
1435 \begin_layout Plain Layout
1440 \begin_layout Plain Layout
1451 \begin_layout Plain Layout
1466 \begin_layout Standard
1467 Indices are created with an underscore
1468 \begin_inset Quotes eld
1472 \begin_inset Quotes erd
1475 or via the math toolbar button
1478 arg "math-subscript"
1481 , exponents with a caret
1482 \begin_inset Quotes eld
1486 \begin_inset Quotes erd
1489 or via the math toolbar button
1492 arg "math-superscript"
1498 \begin_layout Standard
1500 \begin_inset Tabular
1501 <lyxtabular version="3" rows="4" columns="2">
1502 <features booktabs="true" tabularvalignment="middle">
1503 <column alignment="center" valignment="top" width="0pt">
1504 <column alignment="center" valignment="top" width="0pt">
1506 <cell alignment="center" valignment="top" topline="true" bottomline="true" usebox="none">
1509 \begin_layout Plain Layout
1515 <cell alignment="center" valignment="top" topline="true" bottomline="true" usebox="none">
1518 \begin_layout Plain Layout
1526 <cell alignment="center" valignment="top" usebox="none">
1529 \begin_layout Plain Layout
1535 <cell alignment="center" valignment="top" usebox="none">
1538 \begin_layout Plain Layout
1539 \begin_inset Formula $B_{V}$
1548 <row topspace="1.5mm">
1549 <cell alignment="center" valignment="top" usebox="none">
1552 \begin_layout Plain Layout
1558 <cell alignment="center" valignment="top" usebox="none">
1561 \begin_layout Plain Layout
1562 \begin_inset Formula $B^{V}$
1571 <row topspace="1.5mm">
1572 <cell alignment="center" valignment="top" topline="true" bottomline="true" usebox="none">
1575 \begin_layout Plain Layout
1577 \begin_inset space \textvisiblespace{}
1585 <cell alignment="center" valignment="top" topline="true" bottomline="true" usebox="none">
1588 \begin_layout Plain Layout
1589 \begin_inset Formula $B^{A}$
1605 \begin_layout Standard
1606 As the caret is in some languages an accent, vowels will be accentuated
1607 in this case and not set as exponents
1611 \begin_layout Plain Layout
1612 Depending on the used keyboard settings this can also happen for characters
1619 To get exponents in this case, press
1623 after the caret as in the last example.
1626 \begin_layout Subsection
1628 \begin_inset CommandInset label
1630 name "subsec:Fractions"
1635 \begin_inset Index idx
1638 \begin_layout Plain Layout
1647 \begin_layout Standard
1648 Fractions are generated with the command
1655 \begin_inset Index idx
1658 \begin_layout Plain Layout
1666 or via the math toolbar button
1669 arg "math-insert \\frac"
1673 The font size is adjusted automatically, depending on whether the fraction
1674 is in an inline or display style formula.
1675 With the math toolbar button
1678 arg "math-insert \\frac-square"
1681 you can select different fraction types.
1684 \begin_layout Standard
1692 \begin_inset Index idx
1695 \begin_layout Plain Layout
1703 a fraction can be created that always has the size of a display style formula.
1711 \begin_inset Index idx
1714 \begin_layout Plain Layout
1722 the fraction appears always with the size of an inline formula.
1726 \begin_layout Standard
1727 A line with the fraction
1728 \begin_inset Formula $\frac{1}{2}$
1731 that was created with the command
1740 \begin_layout Standard
1741 A line with the fraction
1742 \begin_inset Formula $\dfrac{1}{2}$
1745 that was created with the command
1754 \begin_layout Standard
1756 \begin_inset Tabular
1757 <lyxtabular version="3" rows="4" columns="2">
1758 <features booktabs="true" tabularvalignment="middle">
1759 <column alignment="center" valignment="top" width="0pt">
1760 <column alignment="center" valignment="top" width="0pt">
1762 <cell alignment="center" valignment="top" topline="true" bottomline="true" usebox="none">
1765 \begin_layout Plain Layout
1771 <cell alignment="center" valignment="top" topline="true" bottomline="true" usebox="none">
1774 \begin_layout Plain Layout
1781 <row topspace="1.5mm">
1782 <cell alignment="center" valignment="top" usebox="none">
1785 \begin_layout Plain Layout
1789 \begin_inset space \textvisiblespace{}
1793 \begin_inset Formula $\downarrow$
1801 <cell alignment="center" valignment="top" usebox="none">
1804 \begin_layout Plain Layout
1805 \begin_inset Formula $\frac{A}{B}$
1814 <row topspace="2mm">
1815 <cell alignment="center" valignment="top" usebox="none">
1818 \begin_layout Plain Layout
1822 \begin_inset space \textvisiblespace{}
1826 \begin_inset Formula $\downarrow$
1834 <cell alignment="center" valignment="top" usebox="none">
1837 \begin_layout Plain Layout
1838 \begin_inset Formula $\dfrac{A}{B}$
1847 <row topspace="2mm" bottomspace="1mm">
1848 <cell alignment="center" valignment="top" bottomline="true" usebox="none">
1851 \begin_layout Plain Layout
1855 \begin_inset space \textvisiblespace{}
1861 \begin_inset space \textvisiblespace{}
1865 \begin_inset Formula $\downarrow$
1869 \begin_inset Formula $\downarrow\downarrow$
1877 <cell alignment="center" valignment="top" bottomline="true" usebox="none">
1880 \begin_layout Plain Layout
1881 \begin_inset Formula $\dfrac{e^{\frac{1}{2}}}{3}$
1897 \begin_layout Standard
1898 \begin_inset VSpace bigskip
1902 \begin_inset Newpage newpage
1905 For nested fractions the command
1912 \begin_inset Index idx
1915 \begin_layout Plain Layout
1925 \begin_inset VSpace -3mm
1931 \begin_layout Standard
1932 \begin_inset Formula
1934 \textrm{created with \textbf{\textbackslash frac}} & & \textrm{created with \textbf{\textbackslash cfrac}}\\
1935 \frac{A}{B+\frac{C+\frac{E}{F}}{D}} & & \cfrac{A}{B+\cfrac{C+\cfrac{E}{F}}{D}}
1943 \begin_layout Standard
1944 The command for the example above is:
1947 \begin_layout Standard
1953 \begin_inset space \textvisiblespace{}
1957 \begin_inset Formula $\downarrow$
1963 \begin_inset space \textvisiblespace{}
1969 \begin_inset space \textvisiblespace{}
1973 \begin_inset Formula $\downarrow$
1977 \begin_inset Formula $\downarrow$
1983 \begin_layout Standard
1984 \begin_inset VSpace medskip
1990 \begin_layout Standard
1997 sets the fraction always in the size of a displayed formula, also when
1998 it is part of another fraction.
2001 \begin_layout Standard
2002 It is possible to specify the alignment of the numerator.
2009 is used to left align it, the command
2022 centers the numerator.
2023 These fractions demonstrate the different alignments:
2026 \begin_layout Standard
2029 \begin_inset Formula
2031 \cfrac[l]{A}{B+C}\,,\,\cfrac{A}{B+C}\,,\,\cfrac[r]{A}{B+C}
2039 \begin_layout Standard
2040 \begin_inset Note Greyedout
2043 \begin_layout Plain Layout
2060 are no real \SpecialChar LaTeX
2061 commands but represent the command
2065 cfrac[alignment]{numerator}{denominator}
2068 Therefore you cannot use them in \SpecialChar TeX
2077 \begin_layout Standard
2078 \begin_inset VSpace medskip
2081 It is often advantageous to combine
2094 \begin_inset Formula
2096 \cfrac{A}{B+\cfrac{C+\frac{E}{F}}{D}}
2104 \begin_layout Standard
2105 For inline fractions with a sloped fraction stroke you can use the command
2113 \begin_inset Index idx
2116 \begin_layout Plain Layout
2125 \begin_inset Formula $\nicefrac{5}{31}$
2135 \begin_inset Index idx
2138 \begin_layout Plain Layout
2147 \begin_inset Formula $\unitfrac{5}{31}$
2150 There is furthermore the command
2156 that offers to write a fraction in combination with a number:
2157 \begin_inset Formula $\unitfrac[2]{1}{3}$
2163 \begin_layout Standard
2164 \begin_inset Note Greyedout
2167 \begin_layout Plain Layout
2178 is not a real \SpecialChar LaTeX
2179 command but the command
2180 \begin_inset Newline newline
2187 unitfrac[number]{numerator}{denominator}
2190 Therefore you cannot use it in \SpecialChar TeX
2199 \begin_layout Standard
2200 How to define own fractions where the fraction stroke can be changed, is
2202 \begin_inset CommandInset ref
2204 reference "subsec:Self-defined-Fractions"
2211 \begin_layout Standard
2212 Multiline fractions are explained in
2213 \begin_inset CommandInset ref
2215 reference "subsec:Multiline-Fractions"
2222 \begin_layout Subsection
2224 \begin_inset Index idx
2227 \begin_layout Plain Layout
2236 \begin_layout Standard
2237 Square roots are created with
2244 \begin_inset Index idx
2247 \begin_layout Plain Layout
2255 or the math toolbar button
2258 arg "math-insert \\sqrt"
2261 , all other roots with the command
2268 \begin_inset Index idx
2271 \begin_layout Plain Layout
2279 or with the math toolbar button
2282 arg "math-insert \\root"
2288 \begin_layout Standard
2290 \begin_inset Tabular
2291 <lyxtabular version="3" rows="3" columns="2">
2292 <features booktabs="true" tabularvalignment="middle">
2293 <column alignment="center" valignment="top" width="0pt">
2294 <column alignment="center" valignment="top" width="0pt">
2296 <cell alignment="center" valignment="top" topline="true" bottomline="true" usebox="none">
2299 \begin_layout Plain Layout
2305 <cell alignment="center" valignment="top" topline="true" bottomline="true" usebox="none">
2308 \begin_layout Plain Layout
2315 <row topspace="1mm">
2316 <cell alignment="center" valignment="top" usebox="none">
2319 \begin_layout Plain Layout
2323 \begin_inset space \textvisiblespace{}
2331 <cell alignment="center" valignment="top" usebox="none">
2334 \begin_layout Plain Layout
2335 \begin_inset Formula $\sqrt{A-B}$
2344 <row topspace="1mm">
2345 <cell alignment="center" valignment="top" bottomline="true" usebox="none">
2348 \begin_layout Plain Layout
2352 \begin_inset space \textvisiblespace{}
2356 \begin_inset Formula $\downarrow$
2364 <cell alignment="center" valignment="top" bottomline="true" usebox="none">
2367 \begin_layout Plain Layout
2368 \begin_inset Formula $\sqrt[3]{A-B}$
2384 \begin_layout Standard
2385 A square root can also be created with
2391 when the root index field is left empty.
2394 \begin_layout Standard
2395 With certain indices the distance to the root is too small, like in this
2397 \begin_inset Formula $\sqrt[\beta]{B}$
2401 \begin_inset Newline newline
2405 \begin_inset Formula $\beta$
2409 To avoid this, the commands
2416 \begin_inset Index idx
2419 \begin_layout Plain Layout
2434 \begin_inset Index idx
2437 \begin_layout Plain Layout
2445 are used with the following scheme:
2448 \begin_layout Standard
2462 \begin_layout Standard
2463 Distance is the number of Big Points (unit bp;
2464 \begin_inset Formula $\mathrm{72\,bp=1\,inch}$
2467 ), that the index should be moved to the left or top, resp..
2468 The commands are written to the index.
2469 This way the command
2470 \begin_inset Newline newline
2480 \begin_inset Formula $\to$
2486 \begin_inset Formula $\to$
2492 \begin_inset space \textvisiblespace{}
2496 \begin_inset Formula $\to$
2500 \begin_inset Newline newline
2505 produces a correct typeset formula:
2506 \begin_inset Formula $\sqrt[\leftroot{-1}\uproot{2}\beta]{B}$
2512 \begin_layout Subsection
2513 Binomial Coefficients
2514 \begin_inset Index idx
2517 \begin_layout Plain Layout
2518 Binomial coefficients
2526 \begin_layout Standard
2527 Binomial coefficients are inserted with the command
2534 \begin_inset Index idx
2537 \begin_layout Plain Layout
2545 or with the submenu of the math toolbar button
2548 arg "math-insert \\frac-square"
2564 there are the commands
2571 \begin_inset Index idx
2574 \begin_layout Plain Layout
2589 \begin_inset Index idx
2592 \begin_layout Plain Layout
2601 For other brackets around binomial coeficients there are the commands
2608 \begin_inset Index idx
2611 \begin_layout Plain Layout
2626 \begin_inset Index idx
2629 \begin_layout Plain Layout
2640 \begin_layout Standard
2642 \begin_inset Tabular
2643 <lyxtabular version="3" rows="6" columns="2">
2644 <features booktabs="true" tabularvalignment="middle">
2645 <column alignment="center" valignment="top" width="0pt">
2646 <column alignment="center" valignment="top" width="0pt">
2648 <cell alignment="center" valignment="top" topline="true" bottomline="true" usebox="none">
2651 \begin_layout Plain Layout
2657 <cell alignment="center" valignment="top" topline="true" bottomline="true" usebox="none">
2660 \begin_layout Plain Layout
2667 <row topspace="1mm">
2668 <cell alignment="center" valignment="top" usebox="none">
2671 \begin_layout Plain Layout
2675 \begin_inset space \textvisiblespace{}
2679 \begin_inset Formula $\downarrow$
2687 <cell alignment="center" valignment="top" usebox="none">
2690 \begin_layout Plain Layout
2691 \begin_inset Formula $\binom{A}{B}$
2700 <row topspace="2mm">
2701 <cell alignment="center" valignment="top" usebox="none">
2704 \begin_layout Plain Layout
2708 \begin_inset space \textvisiblespace{}
2712 \begin_inset Formula $\downarrow$
2720 <cell alignment="center" valignment="top" usebox="none">
2723 \begin_layout Plain Layout
2724 \begin_inset Formula $\dbinom{A}{B}$
2733 <row topspace="2mm" bottomspace="0.5mm">
2734 <cell alignment="center" valignment="top" usebox="none">
2737 \begin_layout Plain Layout
2741 \begin_inset space \textvisiblespace{}
2745 \begin_inset Formula $\downarrow$
2753 <cell alignment="center" valignment="top" usebox="none">
2756 \begin_layout Plain Layout
2757 \begin_inset Formula $\tbinom{A}{B}$
2766 <row topspace="1mm">
2767 <cell alignment="center" valignment="top" topline="true" usebox="none">
2770 \begin_layout Plain Layout
2774 \begin_inset space \textvisiblespace{}
2778 \begin_inset Formula $\downarrow$
2786 <cell alignment="center" valignment="top" topline="true" usebox="none">
2789 \begin_layout Plain Layout
2790 \begin_inset Formula ${A \brack B}$
2799 <row topspace="2mm" bottomspace="0.5mm">
2800 <cell alignment="center" valignment="top" bottomline="true" usebox="none">
2803 \begin_layout Plain Layout
2807 \begin_inset space \textvisiblespace{}
2811 \begin_inset Formula $\downarrow$
2819 <cell alignment="center" valignment="top" bottomline="true" usebox="none">
2822 \begin_layout Plain Layout
2823 \begin_inset Formula ${A \brace B}$
2839 \begin_layout Subsection
2840 Case Differentiations
2841 \begin_inset Index idx
2844 \begin_layout Plain Layout
2845 Case differentiations
2853 \begin_layout Standard
2855 \begin_inset Tabular
2856 <lyxtabular version="3" rows="3" columns="2">
2857 <features booktabs="true" tabularvalignment="middle">
2858 <column alignment="center" valignment="top" width="0pt">
2859 <column alignment="center" valignment="top" width="0pt">
2861 <cell alignment="center" valignment="top" topline="true" bottomline="true" usebox="none">
2864 \begin_layout Plain Layout
2870 <cell alignment="center" valignment="top" topline="true" bottomline="true" usebox="none">
2873 \begin_layout Plain Layout
2881 <cell alignment="center" valignment="top" usebox="none">
2884 \begin_layout Plain Layout
2888 \begin_inset space \textvisiblespace{}
2892 \begin_inset Formula $\to$
2896 \begin_inset Index idx
2899 \begin_layout Plain Layout
2912 <cell alignment="center" valignment="top" usebox="none">
2915 \begin_layout Plain Layout
2916 \begin_inset Formula $\begin{cases}
2926 <row topspace="1.5mm">
2927 <cell alignment="center" valignment="top" bottomline="true" usebox="none">
2930 \begin_layout Plain Layout
2934 \begin_inset space \textvisiblespace{}
2940 arg "newline-insert newline"
2948 <cell alignment="center" valignment="top" bottomline="true" usebox="none">
2951 \begin_layout Plain Layout
2952 \begin_inset Formula $\begin{cases}
2953 A & \textrm{for }x>0\\
2954 B & \textrm{for }x=0
2971 \begin_layout Standard
2978 or pressing the math toolbar button
2981 arg "math-insert \\cases"
2984 you can create new lines with the shortcut
2987 arg "newline-insert newline"
2990 or the table toolbar button
2993 arg "tabular-feature append-row"
2999 \begin_layout Standard
3006 is also available via the menu
3008 Insert\SpecialChar menuseparator
3009 Math\SpecialChar menuseparator
3015 \begin_layout Subsection
3017 \begin_inset Index idx
3020 \begin_layout Plain Layout
3029 \begin_layout Standard
3037 \begin_inset Index idx
3040 \begin_layout Plain Layout
3048 every character can be displayed canceled.
3049 The characters are quasi accentuated by a slash.
3052 \begin_layout Standard
3054 \begin_inset Tabular
3055 <lyxtabular version="3" rows="4" columns="2">
3056 <features booktabs="true" tabularvalignment="middle">
3057 <column alignment="center" valignment="top" width="0pt">
3058 <column alignment="center" valignment="top" width="0pt">
3060 <cell alignment="center" valignment="top" topline="true" bottomline="true" usebox="none">
3063 \begin_layout Plain Layout
3069 <cell alignment="center" valignment="top" topline="true" bottomline="true" usebox="none">
3072 \begin_layout Plain Layout
3080 <cell alignment="center" valignment="top" usebox="none">
3083 \begin_layout Plain Layout
3091 <cell alignment="center" valignment="top" usebox="none">
3094 \begin_layout Plain Layout
3095 \begin_inset Formula $\not=$
3105 <cell alignment="center" valignment="top" usebox="none">
3108 \begin_layout Plain Layout
3118 <cell alignment="center" valignment="top" usebox="none">
3121 \begin_layout Plain Layout
3122 \begin_inset Formula $\not\le$
3132 <cell alignment="center" valignment="top" topline="true" bottomline="true" usebox="none">
3135 \begin_layout Plain Layout
3145 <cell alignment="center" valignment="top" topline="true" bottomline="true" usebox="none">
3148 \begin_layout Plain Layout
3149 \begin_inset Formula $\not\parallel$
3165 \begin_layout Standard
3166 The last example shows that not all negations look good.
3167 Therefore there are special commands for some negations (see
3168 \begin_inset CommandInset ref
3170 reference "subsec:Mathematical-Symbols"
3175 \begin_inset CommandInset ref
3177 reference "sec:Relations"
3184 \begin_layout Subsection
3186 \begin_inset CommandInset label
3188 name "subsec:Placeholders"
3193 \begin_inset Index idx
3196 \begin_layout Plain Layout
3203 \begin_inset Index idx
3206 \begin_layout Plain Layout
3207 Chemical characters ! Isotopes
3213 \begin_inset Index idx
3216 \begin_layout Plain Layout
3221 \begin_layout Plain Layout
3232 \begin_layout Plain Layout
3247 \begin_layout Standard
3249 \begin_inset space \thinspace{}
3253 \begin_inset space \space{}
3260 \begin_layout Plain Layout
3261 Typesetting isotopes and chemical symbols is described in
3262 \begin_inset CommandInset ref
3264 reference "subsec:Chemical-Symbols-and"
3273 the following problem occurs:
3276 \begin_layout Standard
3278 \begin_inset Tabular
3279 <lyxtabular version="3" rows="2" columns="2">
3280 <features booktabs="true" tabularvalignment="middle">
3281 <column alignment="center" valignment="top" width="0pt">
3282 <column alignment="center" valignment="top" width="0pt">
3284 <cell alignment="center" valignment="top" usebox="none">
3287 \begin_layout Plain Layout
3288 Indices created with sub- and superscripts:
3293 <cell alignment="center" valignment="top" usebox="none">
3296 \begin_layout Plain Layout
3297 \begin_inset Formula $_{9}^{19}\mathrm{F}$
3306 <row topspace="1.5mm">
3307 <cell alignment="center" valignment="top" usebox="none">
3310 \begin_layout Plain Layout
3316 <cell alignment="center" valignment="top" usebox="none">
3319 \begin_layout Plain Layout
3320 \begin_inset Formula $_{\phantom{1}9}^{19}\mathrm{F}$
3336 \begin_layout Standard
3337 The shorter index is by default placed below or above the first character
3338 of the longer index.
3339 To avoid this there is the command
3346 \begin_inset Index idx
3349 \begin_layout Plain Layout
3357 or the math toolbar button
3358 \begin_inset space \thinspace{}
3365 \begin_layout Plain Layout
3366 can be found in the submenu of the toolbar button
3369 arg "math-insert \\space"
3383 that creates one or more phantom characters.
3390 a small blue box appears that is superposed with two red arrows.
3391 The arrows indicate that the complete width and height of the box content
3392 will be created as placeholder.
3393 Phantom characters are accordingly placeholders with the size of the characters.
3396 \begin_layout Standard
3398 \begin_inset Tabular
3399 <lyxtabular version="3" rows="4" columns="2">
3400 <features booktabs="true" tabularvalignment="middle">
3401 <column alignment="center" valignment="top" width="0pt">
3402 <column alignment="center" valignment="top" width="0pt">
3404 <cell alignment="center" valignment="top" topline="true" bottomline="true" usebox="none">
3407 \begin_layout Plain Layout
3413 <cell alignment="center" valignment="top" topline="true" bottomline="true" usebox="none">
3416 \begin_layout Plain Layout
3423 <row topspace="1.5mm">
3424 <cell alignment="center" valignment="top" usebox="none">
3427 \begin_layout Plain Layout
3429 \begin_inset space \textvisiblespace{}
3435 \begin_inset space \textvisiblespace{}
3439 \begin_inset Formula $\to$
3443 \begin_inset space \textvisiblespace{}
3451 <cell alignment="center" valignment="top" usebox="none">
3454 \begin_layout Plain Layout
3455 \begin_inset Formula $_{\phantom{1}9}^{19}\mathrm{F}$
3464 <row topspace="1.5mm" bottomspace="0.5mm">
3465 <cell alignment="center" valignment="top" usebox="none">
3468 \begin_layout Plain Layout
3470 \begin_inset space \textvisiblespace{}
3476 \begin_inset space \textvisiblespace{}
3480 \begin_inset Formula $\to$
3484 \begin_inset space \textvisiblespace{}
3492 <cell alignment="center" valignment="top" usebox="none">
3495 \begin_layout Plain Layout
3496 \begin_inset Formula $_{\phantom{23}9}^{235}\mathrm{F}$
3505 <row topspace="1.5mm" bottomspace="0.5mm">
3506 <cell alignment="center" valignment="top" topline="true" bottomline="true" usebox="none">
3509 \begin_layout Plain Layout
3513 \begin_inset space \textvisiblespace{}
3519 \begin_inset space \textvisiblespace{}
3523 \begin_inset Formula $\to$
3527 \begin_inset space \textvisiblespace{}
3535 <cell alignment="center" valignment="top" topline="true" bottomline="true" usebox="none">
3538 \begin_layout Plain Layout
3539 \begin_inset Formula $\Lambda_{MMt}^{\phantom{ii}t}$
3555 \begin_layout Standard
3556 Furthermore there are the commands
3563 \begin_inset Index idx
3566 \begin_layout Plain Layout
3587 \begin_inset Index idx
3590 \begin_layout Plain Layout
3611 creates only space for the maximal height of the characters in the box
3612 but not for its width.
3619 creates only space for the width of the box content.
3620 Therefore the boxes of both commands have only one red arrow.
3623 \begin_layout Standard
3624 For example the command
3629 \begin_inset space \textvisiblespace{}
3636 creates space for the height of the integral sign,
3640 \begin_layout Plain Layout
3647 creates an integral sign, see
3648 \begin_inset CommandInset ref
3650 reference "subsec:Big-Operators"
3659 because this is the larger character.
3660 An example application is in
3661 \begin_inset CommandInset ref
3663 reference "subsec:Multiline-Brackets"
3670 \begin_layout Standard
3671 Placeholders can also be used for text when they are inserted via the menu
3674 Insert\SpecialChar menuseparator
3675 Formatting\SpecialChar menuseparator
3681 \begin_layout Standard
3683 \begin_inset Newline newline
3687 \begin_inset Phantom Phantom
3690 \begin_layout Plain Layout
3699 \begin_layout Subsection
3701 \begin_inset Index idx
3704 \begin_layout Plain Layout
3711 \begin_inset Index idx
3714 \begin_layout Plain Layout
3715 Formula ! underlined
3723 \begin_layout Standard
3725 \begin_inset Tabular
3726 <lyxtabular version="3" rows="4" columns="2">
3727 <features booktabs="true" tabularvalignment="middle">
3728 <column alignment="center" valignment="top" width="0pt">
3729 <column alignment="center" valignment="top" width="0pt">
3731 <cell alignment="center" valignment="top" topline="true" bottomline="true" usebox="none">
3734 \begin_layout Plain Layout
3740 <cell alignment="center" valignment="top" topline="true" bottomline="true" usebox="none">
3743 \begin_layout Plain Layout
3750 <row topspace="2mm">
3751 <cell alignment="center" valignment="top" usebox="none">
3754 \begin_layout Plain Layout
3758 \begin_inset space \textvisiblespace{}
3762 \begin_inset Index idx
3765 \begin_layout Plain Layout
3778 <cell alignment="center" valignment="top" usebox="none">
3781 \begin_layout Plain Layout
3782 \begin_inset Formula $\overline{A+B}$
3791 <row bottomspace="1mm">
3792 <cell alignment="center" valignment="top" usebox="none">
3795 \begin_layout Plain Layout
3799 \begin_inset space \textvisiblespace{}
3803 \begin_inset Index idx
3806 \begin_layout Plain Layout
3819 <cell alignment="center" valignment="top" usebox="none">
3822 \begin_layout Plain Layout
3823 \begin_inset Formula $\underline{A+B}$
3832 <row topspace="2mm" bottomspace="1mm">
3833 <cell alignment="center" valignment="top" topline="true" bottomline="true" usebox="none">
3836 \begin_layout Plain Layout
3840 \begin_inset space \textvisiblespace{}
3846 \begin_inset space \textvisiblespace{}
3854 <cell alignment="center" valignment="top" topline="true" bottomline="true" usebox="none">
3857 \begin_layout Plain Layout
3858 \begin_inset Formula $\overline{\underline{A+B}}$
3874 \begin_layout Standard
3875 In the last example it doesn't matter if first
3890 \begin_layout Standard
3891 To double underline use
3900 \begin_layout Standard
3901 It is possible to place up to 6 lines above or below characters.
3904 \begin_layout Standard
3905 \begin_inset VSpace bigskip
3908 Custom lines can be created using the command
3915 \begin_inset Index idx
3918 \begin_layout Plain Layout
3926 which has the following scheme:
3929 \begin_layout Standard
3934 rule[vertical offset]{length}{thickness}
3937 \begin_layout Standard
3938 The optional vertical offset shifts the line upwards (or downwards, when
3939 the value is negative).
3941 \begin_inset CommandInset ref
3943 reference "tab:Available-units"
3947 can be used for the values.
3948 Here are two example lines created with the commands
3949 \begin_inset Newline newline
3956 rule[-2ex]{3cm}{2pt}
3967 \begin_layout Standard
3969 \begin_inset Formula $\rule[-2ex]{3cm}{2pt}\rule{2cm}{1pt}$
3975 \begin_layout Standard
3982 can also be used for text when a line is inserted via the menu
3984 Insert\SpecialChar menuseparator
3985 Formatting\SpecialChar menuseparator
3987 \begin_inset space ~
3995 \begin_layout Standard
3997 \begin_inset CommandInset line
4008 \begin_layout Subsection
4010 \begin_inset CommandInset label
4012 name "subsec:Ellipses"
4017 \begin_inset Index idx
4020 \begin_layout Plain Layout
4029 \begin_layout Standard
4030 There are different types of ellipses available.
4034 \begin_layout Plain Layout
4035 In the math toolbar in the submenu of the button
4038 arg "math-insert \\ldots"
4046 For listings dots at the baseline are used (
4053 \begin_inset Index idx
4056 \begin_layout Plain Layout
4064 ), while for operations dots are needed that are on the same height as the
4072 \begin_inset Index idx
4075 \begin_layout Plain Layout
4084 When using the command
4091 \begin_inset Index idx
4094 \begin_layout Plain Layout
4102 , \SpecialChar LaTeX
4103 decides on the basis of the next character what type is used.
4106 \begin_layout Standard
4108 \begin_inset Tabular
4109 <lyxtabular version="3" rows="9" columns="2">
4110 <features booktabs="true" tabularvalignment="middle">
4111 <column alignment="center" valignment="top" width="0pt">
4112 <column alignment="center" valignment="top" width="0pt">
4114 <cell alignment="center" valignment="top" topline="true" bottomline="true" usebox="none">
4117 \begin_layout Plain Layout
4123 <cell alignment="center" valignment="top" topline="true" bottomline="true" usebox="none">
4126 \begin_layout Plain Layout
4134 <cell alignment="center" valignment="top" usebox="none">
4137 \begin_layout Plain Layout
4139 \begin_inset space \textvisiblespace{}
4145 \begin_inset space \textvisiblespace{}
4153 <cell alignment="center" valignment="top" usebox="none">
4156 \begin_layout Plain Layout
4157 \begin_inset Formula $A_{1},\dots,A_{n}$
4167 <cell alignment="center" valignment="top" usebox="none">
4170 \begin_layout Plain Layout
4172 \begin_inset space \textvisiblespace{}
4178 \begin_inset space \textvisiblespace{}
4186 <cell alignment="center" valignment="top" usebox="none">
4189 \begin_layout Plain Layout
4190 \begin_inset Formula $A_{1}+\dots+A_{n}$
4200 <cell alignment="center" valignment="top" usebox="none">
4203 \begin_layout Plain Layout
4205 \begin_inset space \textvisiblespace{}
4211 \begin_inset space \textvisiblespace{}
4219 <cell alignment="center" valignment="top" usebox="none">
4222 \begin_layout Plain Layout
4223 \begin_inset Formula $A_{1},\ldots,A_{n}$
4233 <cell alignment="center" valignment="top" bottomline="true" usebox="none">
4236 \begin_layout Plain Layout
4238 \begin_inset space \textvisiblespace{}
4244 \begin_inset space \textvisiblespace{}
4252 <cell alignment="center" valignment="top" bottomline="true" usebox="none">
4255 \begin_layout Plain Layout
4256 \begin_inset Formula $A_{1}+\cdots+A_{n}$
4266 <cell alignment="center" valignment="top" usebox="none">
4269 \begin_layout Plain Layout
4277 <cell alignment="center" valignment="top" usebox="none">
4280 \begin_layout Plain Layout
4281 \begin_inset Formula $\vdots$
4291 <cell alignment="center" valignment="top" usebox="none">
4294 \begin_layout Plain Layout
4302 <cell alignment="center" valignment="top" usebox="none">
4305 \begin_layout Plain Layout
4306 \begin_inset Formula $\ddots$
4316 <cell alignment="center" valignment="top" usebox="none">
4319 \begin_layout Plain Layout
4327 <cell alignment="center" valignment="top" usebox="none">
4330 \begin_layout Plain Layout
4331 \begin_inset Formula $\iddots$
4341 <cell alignment="center" valignment="top" topline="true" bottomline="true" usebox="none">
4344 \begin_layout Plain Layout
4346 \begin_inset space \thinspace{}
4349 matrix with the different dots
4354 <cell alignment="center" valignment="top" topline="true" bottomline="true" usebox="none">
4357 \begin_layout Plain Layout
4358 \begin_inset Formula $\begin{array}{ccc}
4359 A_{11} & \cdots & A_{1m}\\
4360 \vdots & \ddots & \vdots\\
4361 A_{n1} & \cdots & A_{nm}
4378 \begin_layout Standard
4379 The ellipses available in menu
4381 Insert\SpecialChar menuseparator
4383 \begin_inset space ~
4397 \begin_layout Standard
4398 \begin_inset VSpace medskip
4407 , one of the options
4409 Use mathdots package (automatically)
4411 must be set in the document settings under
4414 \begin_inset space ~
4420 \begin_inset Newline newline
4425 Use mathdots package
4427 will improve the appearance of all dots in the documents if their font
4428 style or size is not the default.
4431 \begin_layout Standard
4432 \begin_inset VSpace medskip
4435 Specially for matrices there are ellipses that span over several columns.
4436 They are created with the command
4443 \begin_inset Index idx
4446 \begin_layout Plain Layout
4454 , that has the following scheme:
4457 \begin_layout Standard
4462 hdotsfor[distance]{number of columns}
4465 \begin_layout Standard
4466 The number of columns specifies how many columns should be spanned.
4467 Distance is a factor for the distance between the dots.
4470 \begin_layout Standard
4471 In the following matrix the command
4477 was inserted in the first box of the second line, to get an ellipsis with
4478 a dot distance twice as long as with the command
4485 \begin_inset Formula
4487 \left(\begin{array}{cccc}
4496 Note that the matrix fields that should be spanned must be empty, otherwise
4497 you get \SpecialChar LaTeX
4501 \begin_layout Standard
4502 \begin_inset VSpace bigskip
4505 Furthermore you can fill with the command
4512 \begin_inset Index idx
4515 \begin_layout Plain Layout
4523 the rest of a line with dots.
4524 The effect of these commands is the same as with
4531 \begin_inset CommandInset ref
4533 reference "subsec:Variable-Space"
4540 \begin_layout Standard
4541 For example the command
4546 \begin_inset space \textvisiblespace{}
4554 \begin_layout Standard
4555 \begin_inset Formula $A\dotfill B$
4561 \begin_layout Standard
4568 there is for a line the command
4575 \begin_inset Index idx
4578 \begin_layout Plain Layout
4589 \begin_layout Standard
4590 \begin_inset Formula $A\hrulefill B$
4596 \begin_layout Standard
4597 To use the commands for text, they have to be inserted in \SpecialChar TeX
4601 \begin_layout Section
4603 \begin_inset CommandInset label
4610 \begin_inset Index idx
4613 \begin_layout Plain Layout
4622 \begin_layout Standard
4623 Matrices can be inserted via the math toolbar button
4626 arg "dialog-show mathmatrix"
4631 Insert\SpecialChar menuseparator
4632 Math\SpecialChar menuseparator
4636 In the matrix dialog you can specify the number of columns and rows, the
4637 alignment and the decoration.
4638 The vertical alignment is only of importance for matrices in inline formulas:
4641 \begin_layout Standard
4642 The first matrix is top
4643 \begin_inset Formula $\begin{array}[t]{cccc}
4651 \begin_inset Formula $\begin{array}{cccc}
4658 and the third bottom
4659 \begin_inset Formula $\begin{array}[b]{cccc}
4669 \begin_layout Standard
4670 The horizontal alignment specifies how the column entries should be aligned.
4671 It is set by entering a letter for every column.
4676 denotes left aligned,
4685 To create for example a 4
4690 \begin_inset space ~
4693 matrix where the first column is left aligned, the second and third are
4694 centered and the last one is right aligned, one enters for the horizontal
4700 Normally in a matrix all columns are centered, therefore the default for
4708 \begin_layout Standard
4709 Horizontal alignment:
4712 \begin_layout Standard
4718 \begin_inset Formula $\begin{array}{lll}
4730 \begin_inset Formula $\begin{array}{ccc}
4742 \begin_inset Formula $\begin{array}{rrr}
4752 \begin_layout Standard
4753 To add or delete rows and columns subsequently, the math toolbar buttons
4757 arg "tabular-feature append-row"
4763 arg "tabular-feature delete-row"
4767 \begin_inset space \thinspace{}
4772 Edit\SpecialChar menuseparator
4776 New rows can also be created with
4779 arg "newline-insert newline"
4785 \begin_layout Standard
4786 \begin_inset VSpace bigskip
4793 adds parentheses in the selected style around the matrix.
4794 Alternatively, parentheses can can either be created with the commands
4802 \begin_inset Index idx
4805 \begin_layout Plain Layout
4820 \begin_inset Index idx
4823 \begin_layout Plain Layout
4834 \begin_inset space ~
4840 \begin_inset CommandInset ref
4842 reference "subsec:Automatic-Bracket-Size"
4846 , or by using the following commands:
4847 \begin_inset VSpace medskip
4853 \begin_layout Standard
4854 \begin_inset space \hfill{}
4858 \begin_inset Tabular
4859 <lyxtabular version="3" rows="4" columns="2">
4860 <features booktabs="true" tabularvalignment="middle">
4861 <column alignment="center" valignment="top" width="0pt">
4862 <column alignment="center" valignment="top">
4864 <cell alignment="center" valignment="top" topline="true" bottomline="true" usebox="none">
4867 \begin_layout Plain Layout
4873 <cell alignment="center" valignment="top" topline="true" bottomline="true" usebox="none">
4876 \begin_layout Plain Layout
4883 <row topspace="1.5mm">
4884 <cell alignment="center" valignment="top" usebox="none">
4887 \begin_layout Plain Layout
4891 \begin_inset space \textvisiblespace{}
4899 \begin_inset space \thinspace{}
4907 <cell alignment="center" valignment="top" usebox="none">
4910 \begin_layout Plain Layout
4911 \begin_inset Formula $\begin{bmatrix}\begin{array}{cc}
4912 0 & \textrm{-}\mathrm{i}\\
4914 \end{array}\end{bmatrix}$
4923 <row topspace="1.5mm" bottomspace="0.5mm">
4924 <cell alignment="center" valignment="top" usebox="none">
4927 \begin_layout Plain Layout
4931 \begin_inset space \textvisiblespace{}
4939 \begin_inset space \thinspace{}
4947 <cell alignment="center" valignment="top" usebox="none">
4950 \begin_layout Plain Layout
4951 \begin_inset Formula $\begin{Bmatrix}\begin{array}{cc}
4952 0 & \textrm{-}\mathrm{i}\\
4954 \end{array}\end{Bmatrix}$
4964 <cell alignment="center" valignment="top" bottomline="true" usebox="none">
4967 \begin_layout Plain Layout
4971 \begin_inset space \textvisiblespace{}
4979 \begin_inset space \thinspace{}
4987 <cell alignment="center" valignment="top" bottomline="true" usebox="none">
4990 \begin_layout Plain Layout
4991 \begin_inset Formula $\begin{pmatrix}\begin{array}{cc}
4992 0 & \textrm{-}\mathrm{i}\\
4994 \end{array}\end{pmatrix}$
5008 \begin_inset space \hfill{}
5012 \begin_inset Tabular
5013 <lyxtabular version="3" rows="4" columns="2">
5014 <features booktabs="true" tabularvalignment="middle">
5015 <column alignment="center" valignment="top" width="0pt">
5016 <column alignment="center" valignment="top">
5018 <cell alignment="center" valignment="top" topline="true" bottomline="true" usebox="none">
5021 \begin_layout Plain Layout
5027 <cell alignment="center" valignment="top" topline="true" bottomline="true" usebox="none">
5030 \begin_layout Plain Layout
5037 <row topspace="1.5mm">
5038 <cell alignment="center" valignment="top" usebox="none">
5041 \begin_layout Plain Layout
5045 \begin_inset space \textvisiblespace{}
5053 \begin_inset space \thinspace{}
5061 <cell alignment="center" valignment="top" usebox="none">
5064 \begin_layout Plain Layout
5065 \begin_inset Formula $\begin{vmatrix}\begin{array}{cc}
5066 0 & \textrm{-}\mathrm{i}\\
5068 \end{array}\end{vmatrix}$
5077 <row topspace="1.5mm" bottomspace="0.5mm">
5078 <cell alignment="center" valignment="top" usebox="none">
5081 \begin_layout Plain Layout
5085 \begin_inset space \textvisiblespace{}
5093 \begin_inset space \thinspace{}
5101 <cell alignment="center" valignment="top" usebox="none">
5104 \begin_layout Plain Layout
5105 \begin_inset Formula $\begin{Vmatrix}\begin{array}{cc}
5106 0 & \textrm{-}\mathrm{i}\\
5108 \end{array}\end{Vmatrix}$
5118 <cell alignment="center" valignment="top" bottomline="true" usebox="none">
5121 \begin_layout Plain Layout
5125 \begin_inset space \textvisiblespace{}
5133 \begin_inset space \thinspace{}
5141 <cell alignment="center" valignment="top" bottomline="true" usebox="none">
5144 \begin_layout Plain Layout
5145 \begin_inset Formula $\begin{matrix}\begin{array}{cc}
5146 0 & \textrm{-}\mathrm{i}\\
5148 \end{array}\end{matrix}$
5162 \begin_inset space \hfill{}
5168 \begin_layout Standard
5169 \begin_inset VSpace medskip
5173 \begin_inset space \thinspace{}
5177 \begin_inset space \space{}
5186 is inserted, a blue box appears between two vertical lines where the matrix
5188 \begin_inset Newline newline
5191 Note that decorated matrices ignore the vertical alignment.
5194 \begin_layout Standard
5195 \begin_inset VSpace bigskip
5198 As all multiline formulas are matrices, the length
5205 \begin_inset Index idx
5208 \begin_layout Plain Layout
5216 that is described in
5217 \begin_inset CommandInset ref
5219 reference "subsec:Column-Separation"
5223 can also be used to change the column separation of matrices.
5226 \begin_layout Standard
5227 To change the row separation, the command
5234 \begin_inset Index idx
5237 \begin_layout Plain Layout
5246 It is used as follows:
5249 \begin_layout Standard
5256 arraystretch}{stretch factor}
5257 \begin_inset Index idx
5260 \begin_layout Plain Layout
5271 \begin_layout Standard
5278 assigns the stretch factor to the predefined command
5286 \begin_inset space \thinspace{}
5290 \begin_inset space \space{}
5293 the row separation, use the factor 2.
5294 This is then used for all following matrices.
5295 To go back to the original separation, assign the factor 1 to
5304 \begin_layout Standard
5305 To set matrices into a text line, the command
5312 \begin_inset Index idx
5315 \begin_layout Plain Layout
5324 When it is inserted a blue box with two dashed lines appears.
5325 In this box the matrix is inserted.
5328 \begin_layout Standard
5330 \begin_inset Formula $\left(\begin{smallmatrix}A & B\\
5332 \end{smallmatrix}\right)$
5338 \begin_layout Section
5339 Brackets and Delimiters
5340 \begin_inset Index idx
5343 \begin_layout Plain Layout
5350 \begin_inset Index idx
5353 \begin_layout Plain Layout
5362 \begin_layout Subsection
5363 Vertical Brackets and Delimiters
5364 \begin_inset Index idx
5367 \begin_layout Plain Layout
5376 \begin_layout Standard
5377 \begin_inset space \hfill{}
5381 \begin_inset Tabular
5382 <lyxtabular version="3" rows="9" columns="2">
5383 <features booktabs="true" tabularvalignment="middle">
5384 <column alignment="center" valignment="top" width="0pt">
5385 <column alignment="center" valignment="top" width="0pt">
5387 <cell alignment="center" valignment="top" topline="true" bottomline="true" usebox="none">
5390 \begin_layout Plain Layout
5396 <cell alignment="center" valignment="top" topline="true" bottomline="true" usebox="none">
5399 \begin_layout Plain Layout
5407 <cell alignment="center" valignment="top" usebox="none">
5410 \begin_layout Plain Layout
5416 <cell alignment="center" valignment="top" usebox="none">
5419 \begin_layout Plain Layout
5420 \begin_inset Formula $($
5430 <cell alignment="center" valignment="top" usebox="none">
5433 \begin_layout Plain Layout
5439 <cell alignment="center" valignment="top" usebox="none">
5442 \begin_layout Plain Layout
5443 \begin_inset Formula $\{$
5453 <cell alignment="center" valignment="top" usebox="none">
5456 \begin_layout Plain Layout
5462 <cell alignment="center" valignment="top" usebox="none">
5465 \begin_layout Plain Layout
5466 \begin_inset Formula $[$
5476 <cell alignment="center" valignment="top" usebox="none">
5479 \begin_layout Plain Layout
5487 <cell alignment="center" valignment="top" usebox="none">
5490 \begin_layout Plain Layout
5491 \begin_inset Formula $\langle$
5501 <cell alignment="center" valignment="top" usebox="none">
5504 \begin_layout Plain Layout
5512 <cell alignment="center" valignment="top" usebox="none">
5515 \begin_layout Plain Layout
5516 \begin_inset Formula $\lceil$
5526 <cell alignment="center" valignment="top" usebox="none">
5529 \begin_layout Plain Layout
5537 <cell alignment="center" valignment="top" usebox="none">
5540 \begin_layout Plain Layout
5541 \begin_inset Formula $\lfloor$
5551 <cell alignment="center" valignment="top" usebox="none">
5554 \begin_layout Plain Layout
5560 <cell alignment="center" valignment="top" usebox="none">
5563 \begin_layout Plain Layout
5564 \begin_inset Formula $/$
5574 <cell alignment="center" valignment="top" bottomline="true" usebox="none">
5577 \begin_layout Plain Layout
5583 <cell alignment="center" valignment="top" bottomline="true" usebox="none">
5586 \begin_layout Plain Layout
5587 \begin_inset Formula $|$
5601 \begin_inset space \hfill{}
5605 \begin_inset Tabular
5606 <lyxtabular version="3" rows="9" columns="2">
5607 <features booktabs="true" tabularvalignment="middle">
5608 <column alignment="center" valignment="top" width="0pt">
5609 <column alignment="center" valignment="top" width="0pt">
5611 <cell alignment="center" valignment="top" topline="true" bottomline="true" usebox="none">
5614 \begin_layout Plain Layout
5620 <cell alignment="center" valignment="top" topline="true" bottomline="true" usebox="none">
5623 \begin_layout Plain Layout
5631 <cell alignment="center" valignment="top" usebox="none">
5634 \begin_layout Plain Layout
5640 <cell alignment="center" valignment="top" usebox="none">
5643 \begin_layout Plain Layout
5644 \begin_inset Formula $)$
5654 <cell alignment="center" valignment="top" usebox="none">
5657 \begin_layout Plain Layout
5663 <cell alignment="center" valignment="top" usebox="none">
5666 \begin_layout Plain Layout
5667 \begin_inset Formula $\}$
5677 <cell alignment="center" valignment="top" usebox="none">
5680 \begin_layout Plain Layout
5686 <cell alignment="center" valignment="top" usebox="none">
5689 \begin_layout Plain Layout
5690 \begin_inset Formula $]$
5700 <cell alignment="center" valignment="top" usebox="none">
5703 \begin_layout Plain Layout
5711 <cell alignment="center" valignment="top" usebox="none">
5714 \begin_layout Plain Layout
5715 \begin_inset Formula $\rangle$
5725 <cell alignment="center" valignment="top" usebox="none">
5728 \begin_layout Plain Layout
5736 <cell alignment="center" valignment="top" usebox="none">
5739 \begin_layout Plain Layout
5740 \begin_inset Formula $\rceil$
5750 <cell alignment="center" valignment="top" usebox="none">
5753 \begin_layout Plain Layout
5761 <cell alignment="center" valignment="top" usebox="none">
5764 \begin_layout Plain Layout
5765 \begin_inset Formula $\rfloor$
5775 <cell alignment="center" valignment="top" usebox="none">
5778 \begin_layout Plain Layout
5788 <cell alignment="center" valignment="top" usebox="none">
5791 \begin_layout Plain Layout
5792 \begin_inset Formula $\backslash$
5802 <cell alignment="center" valignment="top" bottomline="true" usebox="none">
5805 \begin_layout Plain Layout
5813 <cell alignment="center" valignment="top" bottomline="true" usebox="none">
5816 \begin_layout Plain Layout
5817 \begin_inset Formula $\|$
5831 \begin_inset space \hfill{}
5837 \begin_layout Standard
5840 \begin_inset Note Greyedout
5843 \begin_layout Plain Layout
5856 \begin_inset Index idx
5859 \begin_layout Plain Layout
5867 must be used for the backslash, because the command
5875 produces a line break there.
5883 \begin_layout Standard
5884 For all characters listed above the size can be adjusted with the commands
5885 described in the following two subsections.
5886 When using these commands, the characters < and > can directly be used
5887 instead of the commands
5902 \begin_layout Subsubsection
5904 \begin_inset CommandInset label
5906 name "subsec:Manual-Bracket-Size"
5911 \begin_inset Index idx
5914 \begin_layout Plain Layout
5915 Bracket size ! manual
5923 \begin_layout Standard
5924 The bracket size can be specified manually by the \SpecialChar LaTeX
5932 \begin_inset Index idx
5935 \begin_layout Plain Layout
5968 denotes the smallest and
5974 the largest bracket size.
5977 \begin_layout Standard
5978 These commands are used to emphasize levels of brackets:
5981 \begin_layout Standard
5983 \begin_inset Tabular
5984 <lyxtabular version="3" rows="2" columns="2">
5985 <features booktabs="true" tabularvalignment="middle">
5986 <column alignment="center" valignment="top" width="0pt">
5987 <column alignment="center" valignment="top" width="0pt">
5989 <cell alignment="center" valignment="top" usebox="none">
5992 \begin_layout Plain Layout
5993 all brackets in the same size:
5998 <cell alignment="center" valignment="top" usebox="none">
6001 \begin_layout Plain Layout
6002 \begin_inset Formula $((A+B)(A-B))^{C}$
6011 <row topspace="2mm">
6012 <cell alignment="center" valignment="top" usebox="none">
6015 \begin_layout Plain Layout
6021 <cell alignment="center" valignment="top" usebox="none">
6024 \begin_layout Plain Layout
6025 \begin_inset Formula $\Big((A+B)(A-B)\Big)^{C}$
6041 \begin_layout Standard
6042 For the second formula the command
6049 \begin_inset space \textvisiblespace{}
6057 \begin_layout Standard
6058 Here is an overview about all bracket sizes:
6061 \begin_layout Standard
6078 \begin_inset space \textvisiblespace{}
6086 \begin_inset space \textvisiblespace{}
6090 \begin_inset space \textvisiblespace{}
6100 \begin_layout Standard
6102 \begin_inset Formula $\Bigg(\exp\bigg<\Big[\big\{\ln(3x)\big\}^{2}\sin(x)\Big]^{A}\bigg>\Bigg)^{0,5}$
6108 \begin_layout Standard
6115 -commands there is the variant
6122 \begin_inset Index idx
6125 \begin_layout Plain Layout
6133 that adds a bit more space between the bracket and its content, and the
6147 \begin_inset Index idx
6150 \begin_layout Plain Layout
6160 , that don't add additional space.
6165 at the end of the command
6171 is for a left bracket; for a right bracket this will be replaced by an
6177 A left or right bracket can each be an opening or closing bracket.
6180 \begin_layout Standard
6181 In the following table is a comparison of the variants:
6184 \begin_layout Standard
6186 \begin_inset Tabular
6187 <lyxtabular version="3" rows="5" columns="2">
6188 <features booktabs="true" tabularvalignment="middle">
6189 <column alignment="center" valignment="top" width="0pt">
6190 <column alignment="center" valignment="middle">
6192 <cell alignment="center" valignment="top" topline="true" bottomline="true" usebox="none">
6195 \begin_layout Plain Layout
6201 <cell alignment="center" valignment="top" topline="true" bottomline="true" usebox="none">
6204 \begin_layout Plain Layout
6211 <row topspace="2mm">
6212 <cell alignment="center" valignment="top" usebox="none">
6215 \begin_layout Plain Layout
6225 \begin_inset space \textvisiblespace{}
6235 <cell alignment="center" valignment="top" usebox="none">
6238 \begin_layout Plain Layout
6239 \begin_inset Formula $\Bigm(\bigm(\ln(3x)\bigm)^{2}\Bigm)$
6248 <row topspace="2mm">
6249 <cell alignment="center" valignment="top" usebox="none">
6252 \begin_layout Plain Layout
6262 \begin_inset space \textvisiblespace{}
6272 <cell alignment="center" valignment="top" usebox="none">
6275 \begin_layout Plain Layout
6276 \begin_inset Formula $\Big(\big(\ln(3x)\big)^{2}\Big)$
6285 <row topspace="2mm" bottomspace="0.5mm">
6286 <cell alignment="center" valignment="top" usebox="none">
6289 \begin_layout Plain Layout
6299 \begin_inset space \textvisiblespace{}
6309 <cell alignment="center" valignment="top" usebox="none">
6312 \begin_layout Plain Layout
6313 \begin_inset Formula $\Bigl(\bigl(\ln(3x)\bigr)^{2}\Bigr)$
6322 <row topspace="1.5mm" bottomspace="0.5mm">
6323 <cell alignment="center" valignment="top" topline="true" bottomline="true" usebox="none">
6326 \begin_layout Plain Layout
6338 <cell alignment="center" valignment="top" topline="true" bottomline="true" usebox="none">
6341 \begin_layout Plain Layout
6342 \begin_inset Formula $\bigl)\ln(3x)\bigr($
6358 \begin_layout Subsubsection
6359 Automatic Bracket Size
6360 \begin_inset CommandInset label
6362 name "subsec:Automatic-Bracket-Size"
6367 \begin_inset Index idx
6370 \begin_layout Plain Layout
6371 Bracket size ! automatic
6379 \begin_layout Standard
6380 Brackets with variable size can be inserted with the commands
6387 \begin_inset Index idx
6390 \begin_layout Plain Layout
6405 \begin_inset Index idx
6408 \begin_layout Plain Layout
6416 or via the math toolbar button
6419 arg "dialog-show mathdelimiter"
6435 the wanted bracket must be inserted.
6436 The bracket size will then automatically be calculated for the output.
6439 \begin_layout Standard
6441 normal bracket: The command
6448 \begin_inset space \textvisiblespace{}
6452 \begin_inset Formula $\downarrow$
6456 \begin_inset space \textvisiblespace{}
6462 \begin_inset Formula
6472 \begin_layout Standard
6474 multiline bracket: The command
6483 \begin_inset space \textvisiblespace{}
6487 \begin_inset Formula $\downarrow$
6491 \begin_inset space \textvisiblespace{}
6499 \begin_inset Formula
6501 \ln\left(\frac{A}{C}\right)
6509 \begin_layout Standard
6525 \begin_inset space ~
6531 This has the advantage that you can see in \SpecialChar LyX
6532 immediately the real bracket
6533 size and that the matching right bracket will be created too.
6534 \begin_inset Newline newline
6537 The command for the last example would then be:
6548 \begin_inset space \textvisiblespace{}
6552 \begin_inset Formula $\downarrow$
6558 \begin_layout Standard
6559 To omit a left or right bracket, a dot is inserted for the omitted bracket.
6560 For example the command
6567 \begin_inset space \textvisiblespace{}
6571 \begin_inset Formula $\downarrow$
6575 \begin_inset space \textvisiblespace{}
6585 \begin_inset Formula
6587 \left.\frac{A}{B}\right\}
6606 will be converted by \SpecialChar LyX
6607 to brackets in the right size when the document is
6608 reloaded and an omitted bracket will appear as dashed line.
6611 \begin_layout Standard
6612 \begin_inset VSpace bigskip
6615 Because all popular \SpecialChar LaTeX
6616 distributions use e\SpecialChar TeX
6617 , an extension to \SpecialChar LaTeX
6626 \begin_inset Index idx
6629 \begin_layout Plain Layout
6637 is additionally available for all brackets and limits.
6638 With this command the height of the following character is adapted to the
6639 one of the surrounding brackets, what is e.
6640 \begin_inset space \thinspace{}
6644 \begin_inset space \space{}
6647 needed for physical vectors:
6648 \begin_inset Formula
6650 \left\langle \phi\:\middle|\:J=\frac{3}{2}\,,\,M_{J}\right\rangle
6655 For physical vectors there is a special \SpecialChar LaTeX
6656 -package, described in
6657 \begin_inset CommandInset ref
6659 reference "subsec:Physical-Vectors"
6666 \begin_layout Subsection
6668 \begin_inset Index idx
6671 \begin_layout Plain Layout
6672 Brackets ! horizontal
6680 \begin_layout Standard
6682 \begin_inset Tabular
6683 <lyxtabular version="3" rows="4" columns="2">
6684 <features booktabs="true" tabularvalignment="middle">
6685 <column alignment="center" valignment="top" width="0pt">
6686 <column alignment="center" valignment="top" width="0pt">
6688 <cell alignment="center" valignment="top" topline="true" bottomline="true" usebox="none">
6691 \begin_layout Plain Layout
6697 <cell alignment="center" valignment="top" topline="true" bottomline="true" usebox="none">
6700 \begin_layout Plain Layout
6708 <cell alignment="center" valignment="top" usebox="none">
6711 \begin_layout Plain Layout
6715 \begin_inset space \textvisiblespace{}
6719 \begin_inset space \textvisiblespace{}
6723 \begin_inset Index idx
6726 \begin_layout Plain Layout
6739 <cell alignment="center" valignment="top" usebox="none">
6742 \begin_layout Plain Layout
6743 \begin_inset Formula $\overbrace{A+B}^{3}$
6752 <row topspace="2mm">
6753 <cell alignment="center" valignment="top" usebox="none">
6756 \begin_layout Plain Layout
6760 \begin_inset space \textvisiblespace{}
6764 \begin_inset space \textvisiblespace{}
6768 \begin_inset Index idx
6771 \begin_layout Plain Layout
6784 <cell alignment="center" valignment="top" usebox="none">
6787 \begin_layout Plain Layout
6788 \begin_inset Formula $\underbrace{A+B}_{5}$
6798 <cell alignment="center" valignment="top" topline="true" bottomline="true" usebox="none">
6801 \begin_layout Plain Layout
6805 \begin_inset space \textvisiblespace{}
6811 \begin_inset space \textvisiblespace{}
6815 \begin_inset space \textvisiblespace{}
6819 \begin_inset space \textvisiblespace{}
6823 \begin_inset space \textvisiblespace{}
6827 \begin_inset space \textvisiblespace{}
6831 \begin_inset space \textvisiblespace{}
6839 <cell alignment="center" valignment="top" topline="true" bottomline="true" usebox="none">
6842 \begin_layout Plain Layout
6843 \begin_inset Formula $\overbrace{\underbrace{A+B_{w}}_{7}}^{C}$
6859 \begin_layout Standard
6860 In the last example it doesn't matter if
6872 is inserted at first.
6875 \begin_layout Standard
6876 \begin_inset VSpace medskip
6882 \begin_layout Standard
6883 If you set in the document settings under
6886 \begin_inset space ~
6896 \begin_inset Index idx
6899 \begin_layout Plain Layout
6900 Packages ! mathtools
6908 \begin_inset space ~
6913 , you have access to square backets:
6916 \begin_layout Standard
6918 \begin_inset Tabular
6919 <lyxtabular version="3" rows="4" columns="2">
6920 <features booktabs="true" tabularvalignment="middle">
6921 <column alignment="center" valignment="top" width="0pt">
6922 <column alignment="center" valignment="top" width="0pt">
6924 <cell alignment="center" valignment="top" topline="true" bottomline="true" usebox="none">
6927 \begin_layout Plain Layout
6933 <cell alignment="center" valignment="top" topline="true" bottomline="true" usebox="none">
6936 \begin_layout Plain Layout
6944 <cell alignment="center" valignment="top" usebox="none">
6947 \begin_layout Plain Layout
6975 \begin_inset space \textvisiblespace{}
6979 \begin_inset Index idx
6982 \begin_layout Plain Layout
6995 <cell alignment="center" valignment="top" usebox="none">
6998 \begin_layout Plain Layout
6999 \begin_inset Formula $\overbracket{A+B}^{3}$
7008 <row topspace="2mm">
7009 <cell alignment="center" valignment="top" usebox="none">
7012 \begin_layout Plain Layout
7040 \begin_inset space \textvisiblespace{}
7044 \begin_inset Index idx
7047 \begin_layout Plain Layout
7072 <cell alignment="center" valignment="top" usebox="none">
7075 \begin_layout Plain Layout
7076 \begin_inset Formula $\underbracket{A+B}_{5}$
7086 <cell alignment="center" valignment="top" topline="true" bottomline="true" usebox="none">
7089 \begin_layout Plain Layout
7095 \begin_inset space \textvisiblespace{}
7099 \begin_inset space \textvisiblespace{}
7103 \begin_inset space \textvisiblespace{}
7107 \begin_inset space \textvisiblespace{}
7111 \begin_inset space \textvisiblespace{}
7119 <cell alignment="center" valignment="top" topline="true" bottomline="true" usebox="none">
7122 \begin_layout Plain Layout
7123 \begin_inset Formula $\overbracket{\underbracket{A+B_{w}}_{7}}^{C}$
7139 \begin_layout Standard
7152 you can change the thickness of the bracket's stroke by specifying the
7153 desired thickness in square brackets behind the command:
7156 \begin_layout Standard
7158 \begin_inset Tabular
7159 <lyxtabular version="3" rows="3" columns="2">
7160 <features booktabs="true" tabularvalignment="middle">
7161 <column alignment="center" valignment="top" width="0pt">
7162 <column alignment="center" valignment="top" width="0pt">
7164 <cell alignment="center" valignment="top" topline="true" bottomline="true" usebox="none">
7167 \begin_layout Plain Layout
7173 <cell alignment="center" valignment="top" topline="true" bottomline="true" usebox="none">
7176 \begin_layout Plain Layout
7184 <cell alignment="center" valignment="top" usebox="none">
7187 \begin_layout Plain Layout
7217 \begin_inset space \textvisiblespace{}
7225 <cell alignment="center" valignment="top" usebox="none">
7228 \begin_layout Plain Layout
7229 \begin_inset Formula $\overbracket[3pt]{A+B}^{3}$
7238 <row topspace="2mm">
7239 <cell alignment="center" valignment="top" bottomline="true" usebox="none">
7242 \begin_layout Plain Layout
7272 \begin_inset space \textvisiblespace{}
7280 <cell alignment="center" valignment="top" bottomline="true" usebox="none">
7283 \begin_layout Plain Layout
7284 \begin_inset Formula $\underbracket[1pt]{A+B}_{5}$
7300 \begin_layout Standard
7301 \begin_inset VSpace bigskip
7304 When brackets should overlap each other, multiline formulas, as described
7306 \begin_inset CommandInset ref
7308 reference "sec:Multiline-Formulas"
7313 \begin_inset Formula
7315 A & = & \underbrace{gggg+bbqq}_{r}+\:dddd\\
7316 & & \hphantom{gggg+\:}\underbrace{\hphantom{bbqq+dddd}}_{s}
7321 In the first row the formula is inserted together with the first brace.
7322 It is hereby important that the space command
7326 \begin_layout Plain Layout
7327 Space commands are explained in
7328 \begin_inset CommandInset ref
7330 reference "subsec:Predefined-Space"
7345 is inserted before the first
7346 \begin_inset Formula $d$
7349 , because the brace that ends behind the
7350 \begin_inset Formula $q$
7353 prevents that the following
7354 \begin_inset Quotes eld
7358 \begin_inset Quotes erd
7361 is surrounded by space.
7365 \begin_layout Plain Layout
7366 because a bracket is not handled as a character, see
7367 \begin_inset CommandInset ref
7369 reference "subsec:Binary-Operators"
7378 In the second row the second brace is inserted.
7379 As it should begin before the
7380 \begin_inset Formula $b$
7395 \begin_layout Plain Layout
7403 \begin_inset CommandInset ref
7405 reference "subsec:Placeholders"
7414 This space is needed because the
7415 \begin_inset Quotes eld
7419 \begin_inset Quotes erd
7422 is also surrounded by space in the formula.
7423 The brace is placed under the command
7432 \begin_layout Standard
7433 It gets more complicated when brackets overlap each other above and under
7434 the formula, like in the following example:
7438 \begin_layout Plain Layout
7450 \begin_inset Formula
7452 & & \hphantom{gggg+\:}\overbrace{\hphantom{bbqq+dddd}}^{s}\\
7453 A & = & \underbrace{gggg+bbqq}_{r}+\:dddd
7462 \begin_layout Plain Layout
7473 The first formula row is the same as the second row of the previous example,
7474 with the difference that the brace is above.
7475 The second row contains the formula together with the second brace.
7476 To avoid that there is space between the upper brace in the first row and
7477 the formula, the row spacing needs to be reduced.
7478 This is not easily possible due to a bug in \SpecialChar LyX
7483 \begin_layout Plain Layout
7484 \begin_inset CommandInset href
7486 name "LyX-bug #1505"
7487 target "http://www.lyx.org/trac/ticket/1505"
7496 As a solution for the problem, the global formula row separation
7503 \begin_inset Index idx
7506 \begin_layout Plain Layout
7514 must be changed to -6
7515 \begin_inset space \thinspace{}
7518 pt before the formula with the command
7534 is set back after the formula to the standard value of 3
7535 \begin_inset space \thinspace{}
7538 pt using the same command.
7539 More about the row separation in formulas is explained in
7540 \begin_inset CommandInset ref
7542 reference "subsec:Line-Separation"
7549 \begin_layout Section
7551 \begin_inset Index idx
7554 \begin_layout Plain Layout
7563 \begin_layout Standard
7564 Arrows can be inserted via the math toolbar button
7567 arg "math-insert \\leftarrow"
7570 or the commands listed in the following subsections.
7573 \begin_layout Subsection
7575 \begin_inset Index idx
7578 \begin_layout Plain Layout
7587 \begin_layout Standard
7588 \begin_inset space \hfill{}
7592 \begin_inset Tabular
7593 <lyxtabular version="3" rows="8" columns="2">
7594 <features booktabs="true" tabularvalignment="middle">
7595 <column alignment="center" valignment="top" width="0pt">
7596 <column alignment="center" valignment="top" width="0pt">
7598 <cell alignment="center" valignment="top" topline="true" bottomline="true" usebox="none">
7601 \begin_layout Plain Layout
7607 <cell alignment="center" valignment="top" topline="true" bottomline="true" usebox="none">
7610 \begin_layout Plain Layout
7618 <cell alignment="center" valignment="top" usebox="none">
7621 \begin_layout Plain Layout
7629 <cell alignment="center" valignment="top" usebox="none">
7632 \begin_layout Plain Layout
7633 \begin_inset Formula $\gets$
7643 <cell alignment="center" valignment="top" usebox="none">
7646 \begin_layout Plain Layout
7654 <cell alignment="center" valignment="top" usebox="none">
7657 \begin_layout Plain Layout
7658 \begin_inset Formula $\Leftarrow$
7668 <cell alignment="center" valignment="top" usebox="none">
7671 \begin_layout Plain Layout
7679 <cell alignment="center" valignment="top" usebox="none">
7682 \begin_layout Plain Layout
7683 \begin_inset Formula $\longleftarrow$
7693 <cell alignment="center" valignment="top" usebox="none">
7696 \begin_layout Plain Layout
7704 <cell alignment="center" valignment="top" usebox="none">
7707 \begin_layout Plain Layout
7708 \begin_inset Formula $\Longleftarrow$
7718 <cell alignment="center" valignment="top" usebox="none">
7721 \begin_layout Plain Layout
7729 <cell alignment="center" valignment="top" usebox="none">
7732 \begin_layout Plain Layout
7733 \begin_inset Formula $\leftharpoonup$
7743 <cell alignment="center" valignment="top" usebox="none">
7746 \begin_layout Plain Layout
7754 <cell alignment="center" valignment="top" usebox="none">
7757 \begin_layout Plain Layout
7758 \begin_inset Formula $\leftharpoondown$
7768 <cell alignment="center" valignment="top" bottomline="true" usebox="none">
7771 \begin_layout Plain Layout
7779 <cell alignment="center" valignment="top" bottomline="true" usebox="none">
7782 \begin_layout Plain Layout
7783 \begin_inset Formula $\hookleftarrow$
7797 \begin_inset space \hfill{}
7801 \begin_inset Tabular
7802 <lyxtabular version="3" rows="8" columns="2">
7803 <features booktabs="true" tabularvalignment="middle">
7804 <column alignment="center" valignment="top" width="0pt">
7805 <column alignment="center" valignment="top" width="0pt">
7807 <cell alignment="center" valignment="top" topline="true" bottomline="true" usebox="none">
7810 \begin_layout Plain Layout
7816 <cell alignment="center" valignment="top" topline="true" bottomline="true" usebox="none">
7819 \begin_layout Plain Layout
7827 <cell alignment="center" valignment="top" usebox="none">
7830 \begin_layout Plain Layout
7838 <cell alignment="center" valignment="top" usebox="none">
7841 \begin_layout Plain Layout
7842 \begin_inset Formula $\to$
7852 <cell alignment="center" valignment="top" usebox="none">
7855 \begin_layout Plain Layout
7863 <cell alignment="center" valignment="top" usebox="none">
7866 \begin_layout Plain Layout
7867 \begin_inset Formula $\Rightarrow$
7877 <cell alignment="center" valignment="top" usebox="none">
7880 \begin_layout Plain Layout
7888 <cell alignment="center" valignment="top" usebox="none">
7891 \begin_layout Plain Layout
7892 \begin_inset Formula $\longrightarrow$
7902 <cell alignment="center" valignment="top" usebox="none">
7905 \begin_layout Plain Layout
7913 <cell alignment="center" valignment="top" usebox="none">
7916 \begin_layout Plain Layout
7917 \begin_inset Formula $\Longrightarrow$
7927 <cell alignment="center" valignment="top" usebox="none">
7930 \begin_layout Plain Layout
7938 <cell alignment="center" valignment="top" usebox="none">
7941 \begin_layout Plain Layout
7942 \begin_inset Formula $\rightharpoonup$
7952 <cell alignment="center" valignment="top" usebox="none">
7955 \begin_layout Plain Layout
7963 <cell alignment="center" valignment="top" usebox="none">
7966 \begin_layout Plain Layout
7967 \begin_inset Formula $\rightharpoondown$
7977 <cell alignment="center" valignment="top" bottomline="true" usebox="none">
7980 \begin_layout Plain Layout
7988 <cell alignment="center" valignment="top" bottomline="true" usebox="none">
7991 \begin_layout Plain Layout
7992 \begin_inset Formula $\hookrightarrow$
8006 \begin_inset space \hfill{}
8012 \begin_layout Standard
8013 \begin_inset space \hfill{}
8017 \begin_inset Tabular
8018 <lyxtabular version="3" rows="6" columns="2">
8019 <features booktabs="true" tabularvalignment="middle">
8020 <column alignment="center" valignment="top" width="0pt">
8021 <column alignment="center" valignment="top" width="0pt">
8023 <cell alignment="center" valignment="top" topline="true" bottomline="true" usebox="none">
8026 \begin_layout Plain Layout
8032 <cell alignment="center" valignment="top" topline="true" bottomline="true" usebox="none">
8035 \begin_layout Plain Layout
8043 <cell alignment="center" valignment="top" usebox="none">
8046 \begin_layout Plain Layout
8054 <cell alignment="center" valignment="top" usebox="none">
8057 \begin_layout Plain Layout
8058 \begin_inset Formula $\leftrightarrow$
8068 <cell alignment="center" valignment="top" usebox="none">
8071 \begin_layout Plain Layout
8079 <cell alignment="center" valignment="top" usebox="none">
8082 \begin_layout Plain Layout
8083 \begin_inset Formula $\Leftrightarrow$
8093 <cell alignment="center" valignment="top" usebox="none">
8096 \begin_layout Plain Layout
8104 <cell alignment="center" valignment="top" usebox="none">
8107 \begin_layout Plain Layout
8108 \begin_inset Formula $\longleftrightarrow$
8118 <cell alignment="center" valignment="top" usebox="none">
8121 \begin_layout Plain Layout
8129 <cell alignment="center" valignment="top" usebox="none">
8132 \begin_layout Plain Layout
8133 \begin_inset Formula $\Longleftrightarrow$
8143 <cell alignment="center" valignment="top" bottomline="true" usebox="none">
8146 \begin_layout Plain Layout
8154 <cell alignment="center" valignment="top" bottomline="true" usebox="none">
8157 \begin_layout Plain Layout
8158 \begin_inset Formula $\rightleftharpoons$
8172 \begin_inset space \hspace{}
8177 \begin_inset space \hfill{}
8181 \begin_inset Tabular
8182 <lyxtabular version="3" rows="5" columns="2">
8183 <features booktabs="true" tabularvalignment="middle">
8184 <column alignment="center" valignment="top" width="0pt">
8185 <column alignment="center" valignment="top" width="0pt">
8187 <cell alignment="center" valignment="top" topline="true" bottomline="true" usebox="none">
8190 \begin_layout Plain Layout
8196 <cell alignment="center" valignment="top" topline="true" bottomline="true" usebox="none">
8199 \begin_layout Plain Layout
8207 <cell alignment="center" valignment="top" usebox="none">
8210 \begin_layout Plain Layout
8218 <cell alignment="center" valignment="top" usebox="none">
8221 \begin_layout Plain Layout
8222 \begin_inset Formula $\mapsto$
8232 <cell alignment="center" valignment="top" usebox="none">
8235 \begin_layout Plain Layout
8243 <cell alignment="center" valignment="top" usebox="none">
8246 \begin_layout Plain Layout
8247 \begin_inset Formula $\longmapsto$
8257 <cell alignment="center" valignment="top" usebox="none">
8260 \begin_layout Plain Layout
8268 <cell alignment="center" valignment="top" usebox="none">
8271 \begin_layout Plain Layout
8272 \begin_inset Formula $\leadsto$
8282 <cell alignment="center" valignment="top" bottomline="true" usebox="none">
8285 \begin_layout Plain Layout
8293 <cell alignment="center" valignment="top" bottomline="true" usebox="none">
8296 \begin_layout Plain Layout
8297 \begin_inset Formula $\dasharrow$
8311 \begin_inset space \hfill{}
8317 \begin_layout Standard
8318 \begin_inset VSpace medskip
8321 Arrows used as accents like e.
8322 \begin_inset space \thinspace{}
8326 \begin_inset space \space{}
8329 vector arrows are listed in
8330 \begin_inset CommandInset ref
8332 reference "sec:Accents"
8339 \begin_layout Standard
8340 \begin_inset VSpace bigskip
8343 Furthermore there are the labeled arrows
8344 \begin_inset Index idx
8347 \begin_layout Plain Layout
8360 \begin_inset Index idx
8363 \begin_layout Plain Layout
8378 \begin_inset Index idx
8381 \begin_layout Plain Layout
8388 \begin_layout Plain Layout
8403 When inserting one of these commands in a formula, an arrow with two blue
8404 boxes appear where the label can be inserted.
8405 The length of the arrow adapts to the label width.
8408 \begin_layout Standard
8410 \begin_inset Tabular
8411 <lyxtabular version="3" rows="3" columns="2">
8412 <features booktabs="true" tabularvalignment="middle">
8413 <column alignment="center" valignment="top" width="0pt">
8414 <column alignment="center" valignment="top" width="0pt">
8416 <cell alignment="center" valignment="top" topline="true" bottomline="true" usebox="none">
8419 \begin_layout Plain Layout
8425 <cell alignment="center" valignment="top" topline="true" bottomline="true" usebox="none">
8428 \begin_layout Plain Layout
8436 <cell alignment="center" valignment="top" usebox="none">
8439 \begin_layout Plain Layout
8443 \begin_inset space \textvisiblespace{}
8447 \begin_inset Formula $\downarrow$
8451 \begin_inset Formula $\to$
8459 <cell alignment="center" valignment="top" usebox="none">
8462 \begin_layout Plain Layout
8463 \begin_inset Formula $F(a)\xleftarrow[x>0]{x=a}F(x)$
8472 <row topspace="2mm">
8473 <cell alignment="center" valignment="top" bottomline="true" usebox="none">
8476 \begin_layout Plain Layout
8480 \begin_inset space \textvisiblespace{}
8484 \begin_inset Formula $\downarrow$
8488 \begin_inset Formula $\to$
8496 <cell alignment="center" valignment="top" bottomline="true" usebox="none">
8499 \begin_layout Plain Layout
8500 \begin_inset Formula $F(x)\xrightarrow[x>0]{x=a}F(a)$
8516 \begin_layout Standard
8517 \begin_inset VSpace medskip
8523 \begin_layout Standard
8524 If you set in the document settings under
8527 \begin_inset space ~
8537 \begin_inset Index idx
8540 \begin_layout Plain Layout
8541 Packages ! mathtools
8549 \begin_inset space ~
8554 , you have access to the following labeled arrows:
8557 \begin_layout Standard
8558 \begin_inset Newpage newpage
8564 \begin_layout Standard
8566 \begin_inset space \hspace*{\fill}
8570 \begin_inset Tabular
8571 <lyxtabular version="3" rows="7" columns="2">
8572 <features booktabs="true" tabularvalignment="middle">
8573 <column alignment="center" valignment="top" width="0pt">
8574 <column alignment="center" valignment="top" width="0pt">
8576 <cell alignment="center" valignment="top" topline="true" bottomline="true" usebox="none">
8579 \begin_layout Plain Layout
8585 <cell alignment="center" valignment="top" topline="true" bottomline="true" usebox="none">
8588 \begin_layout Plain Layout
8596 <cell alignment="center" valignment="top" usebox="none">
8599 \begin_layout Plain Layout
8619 <cell alignment="center" valignment="top" usebox="none">
8622 \begin_layout Plain Layout
8623 \begin_inset Formula $\xleftrightarrow[x=a]{x>0}$
8632 <row topspace="2mm">
8633 <cell alignment="center" valignment="top" usebox="none">
8636 \begin_layout Plain Layout
8656 <cell alignment="center" valignment="top" usebox="none">
8659 \begin_layout Plain Layout
8660 \begin_inset Formula $\xLeftarrow[x=a]{x>0}$
8669 <row topspace="2mm">
8670 <cell alignment="center" valignment="top" usebox="none">
8673 \begin_layout Plain Layout
8693 <cell alignment="center" valignment="top" usebox="none">
8696 \begin_layout Plain Layout
8697 \begin_inset Formula $\xRightarrow[x=a]{x>0}$
8706 <row topspace="2mm">
8707 <cell alignment="center" valignment="top" usebox="none">
8710 \begin_layout Plain Layout
8730 <cell alignment="center" valignment="top" usebox="none">
8733 \begin_layout Plain Layout
8734 \begin_inset Formula $\xLeftrightarrow[x=a]{x>0}$
8743 <row topspace="2mm">
8744 <cell alignment="center" valignment="top" usebox="none">
8747 \begin_layout Plain Layout
8767 <cell alignment="center" valignment="top" usebox="none">
8770 \begin_layout Plain Layout
8771 \begin_inset Formula $\xhookleftarrow[x=a]{x>0}$
8780 <row topspace="2mm">
8781 <cell alignment="center" valignment="top" bottomline="true" usebox="none">
8784 \begin_layout Plain Layout
8804 <cell alignment="center" valignment="top" bottomline="true" usebox="none">
8807 \begin_layout Plain Layout
8808 \begin_inset Formula $\xhookrightarrow[x=a]{x>0}$
8822 \begin_inset space \hspace*{\fill}
8826 \begin_inset Tabular
8827 <lyxtabular version="3" rows="7" columns="2">
8828 <features booktabs="true" tabularvalignment="middle">
8829 <column alignment="center" valignment="top" width="0pt">
8830 <column alignment="center" valignment="top" width="0pt">
8832 <cell alignment="center" valignment="top" topline="true" bottomline="true" usebox="none">
8835 \begin_layout Plain Layout
8841 <cell alignment="center" valignment="top" topline="true" bottomline="true" usebox="none">
8844 \begin_layout Plain Layout
8852 <cell alignment="center" valignment="top" usebox="none">
8855 \begin_layout Plain Layout
8875 <cell alignment="center" valignment="top" usebox="none">
8878 \begin_layout Plain Layout
8879 \begin_inset Formula $\xleftharpoondown[x=a]{x>0}$
8888 <row topspace="2mm">
8889 <cell alignment="center" valignment="top" usebox="none">
8892 \begin_layout Plain Layout
8912 <cell alignment="center" valignment="top" usebox="none">
8915 \begin_layout Plain Layout
8916 \begin_inset Formula $\xleftharpoonup[x=a]{x>0}$
8925 <row topspace="2mm">
8926 <cell alignment="center" valignment="top" usebox="none">
8929 \begin_layout Plain Layout
8949 <cell alignment="center" valignment="top" usebox="none">
8952 \begin_layout Plain Layout
8953 \begin_inset Formula $\xrightharpoondown[x=a]{x>0}$
8962 <row topspace="2mm">
8963 <cell alignment="center" valignment="top" usebox="none">
8966 \begin_layout Plain Layout
8986 <cell alignment="center" valignment="top" usebox="none">
8989 \begin_layout Plain Layout
8990 \begin_inset Formula $\xrightharpoonup[x=a]{x>0}$
8999 <row topspace="2mm">
9000 <cell alignment="center" valignment="top" usebox="none">
9003 \begin_layout Plain Layout
9023 <cell alignment="center" valignment="top" usebox="none">
9026 \begin_layout Plain Layout
9027 \begin_inset Formula $\xleftrightharpoons[x=a]{x>0}$
9036 <row topspace="2mm">
9037 <cell alignment="center" valignment="top" bottomline="true" usebox="none">
9040 \begin_layout Plain Layout
9060 <cell alignment="center" valignment="top" bottomline="true" usebox="none">
9063 \begin_layout Plain Layout
9064 \begin_inset Formula $\xrightleftharpoons[x=a]{x>0}$
9078 \begin_inset space \hspace*{\fill}
9084 \begin_layout Standard
9085 The command scheme is for all these arrows:
9088 \begin_layout Standard
9090 \begin_inset Tabular
9091 <lyxtabular version="3" rows="2" columns="2">
9092 <features booktabs="true" tabularvalignment="middle">
9093 <column alignment="center" valignment="top" width="0pt">
9094 <column alignment="center" valignment="top" width="0pt">
9096 <cell alignment="center" valignment="top" topline="true" bottomline="true" usebox="none">
9099 \begin_layout Plain Layout
9105 <cell alignment="center" valignment="top" topline="true" bottomline="true" usebox="none">
9108 \begin_layout Plain Layout
9115 <row bottomspace="0.5mm">
9116 <cell alignment="center" valignment="top" bottomline="true" usebox="none">
9119 \begin_layout Plain Layout
9122 xleftrightarrow[x=a]
9125 \begin_inset Formula $\to$
9133 <cell alignment="center" valignment="top" bottomline="true" usebox="none">
9136 \begin_layout Plain Layout
9137 \begin_inset Formula $F(a)\xleftrightarrow[x=a]{x>0}F(x)$
9153 \begin_layout Subsection
9154 Vertical and diagonal Arrows
9155 \begin_inset Index idx
9158 \begin_layout Plain Layout
9165 \begin_inset Index idx
9168 \begin_layout Plain Layout
9177 \begin_layout Standard
9178 \begin_inset space \hfill{}
9182 \begin_inset Tabular
9183 <lyxtabular version="3" rows="7" columns="2">
9184 <features booktabs="true" tabularvalignment="middle">
9185 <column alignment="center" valignment="top" width="0pt">
9186 <column alignment="center" valignment="top" width="0pt">
9188 <cell alignment="center" valignment="top" topline="true" bottomline="true" usebox="none">
9191 \begin_layout Plain Layout
9197 <cell alignment="center" valignment="top" topline="true" bottomline="true" usebox="none">
9200 \begin_layout Plain Layout
9208 <cell alignment="center" valignment="top" usebox="none">
9211 \begin_layout Plain Layout
9219 <cell alignment="center" valignment="top" usebox="none">
9222 \begin_layout Plain Layout
9223 \begin_inset Formula $\uparrow$
9233 <cell alignment="center" valignment="top" usebox="none">
9236 \begin_layout Plain Layout
9244 <cell alignment="center" valignment="top" usebox="none">
9247 \begin_layout Plain Layout
9248 \begin_inset Formula $\Uparrow$
9258 <cell alignment="center" valignment="top" usebox="none">
9261 \begin_layout Plain Layout
9269 <cell alignment="center" valignment="top" usebox="none">
9272 \begin_layout Plain Layout
9273 \begin_inset Formula $\updownarrow$
9283 <cell alignment="center" valignment="top" usebox="none">
9286 \begin_layout Plain Layout
9294 <cell alignment="center" valignment="top" usebox="none">
9297 \begin_layout Plain Layout
9298 \begin_inset Formula $\Updownarrow$
9308 <cell alignment="center" valignment="top" usebox="none">
9311 \begin_layout Plain Layout
9319 <cell alignment="center" valignment="top" usebox="none">
9322 \begin_layout Plain Layout
9323 \begin_inset Formula $\Downarrow$
9333 <cell alignment="center" valignment="top" bottomline="true" usebox="none">
9336 \begin_layout Plain Layout
9344 <cell alignment="center" valignment="top" bottomline="true" usebox="none">
9347 \begin_layout Plain Layout
9348 \begin_inset Formula $\downarrow$
9362 \begin_inset space \hfill{}
9366 \begin_inset Tabular
9367 <lyxtabular version="3" rows="5" columns="2">
9368 <features booktabs="true" tabularvalignment="middle">
9369 <column alignment="center" valignment="top" width="0pt">
9370 <column alignment="center" valignment="top" width="0pt">
9372 <cell alignment="center" valignment="top" topline="true" bottomline="true" usebox="none">
9375 \begin_layout Plain Layout
9381 <cell alignment="center" valignment="top" topline="true" bottomline="true" usebox="none">
9384 \begin_layout Plain Layout
9392 <cell alignment="center" valignment="top" usebox="none">
9395 \begin_layout Plain Layout
9403 <cell alignment="center" valignment="top" usebox="none">
9406 \begin_layout Plain Layout
9407 \begin_inset Formula $\nearrow$
9417 <cell alignment="center" valignment="top" usebox="none">
9420 \begin_layout Plain Layout
9428 <cell alignment="center" valignment="top" usebox="none">
9431 \begin_layout Plain Layout
9432 \begin_inset Formula $\searrow$
9442 <cell alignment="center" valignment="top" usebox="none">
9445 \begin_layout Plain Layout
9453 <cell alignment="center" valignment="top" usebox="none">
9456 \begin_layout Plain Layout
9457 \begin_inset Formula $\swarrow$
9467 <cell alignment="center" valignment="top" bottomline="true" usebox="none">
9470 \begin_layout Plain Layout
9478 <cell alignment="center" valignment="top" bottomline="true" usebox="none">
9481 \begin_layout Plain Layout
9482 \begin_inset Formula $\nwarrow$
9496 \begin_inset space \hfill{}
9502 \begin_layout Standard
9503 \begin_inset VSpace medskip
9506 Vertical arrows can be used also as delimiters together with the commands
9508 \begin_inset CommandInset ref
9510 reference "subsec:Manual-Bracket-Size"
9515 \begin_inset CommandInset ref
9517 reference "subsec:Automatic-Bracket-Size"
9524 \begin_layout Section
9526 \begin_inset CommandInset label
9533 \begin_inset Index idx
9536 \begin_layout Plain Layout
9545 \begin_layout Standard
9546 Accents can be inserted via the math toolbar button
9549 arg "math-insert \\hat"
9552 or the commands listed in the following subsections.
9555 \begin_layout Subsection
9556 Accents for one Character
9560 \begin_layout Plain Layout
9573 \begin_layout Plain Layout
9575 \begin_inset CommandInset ref
9577 reference "subsec:Accents-in-Text"
9590 \begin_layout Plain Layout
9598 \begin_inset Note Note
9601 \begin_layout Plain Layout
9608 is used to avoid that the footnote appears in the PDF-bookmark.
9611 \begin_layout Plain Layout
9619 \begin_inset CommandInset ref
9621 reference "subsec:Formulas-in-Section"
9631 \begin_inset CommandInset label
9633 name "subsec:Accents-for-one"
9638 \begin_inset Index idx
9641 \begin_layout Plain Layout
9642 Accents ! for one character
9650 \begin_layout Standard
9651 \begin_inset space \hfill{}
9655 \begin_inset Tabular
9656 <lyxtabular version="3" rows="8" columns="2">
9657 <features booktabs="true" tabularvalignment="middle">
9658 <column alignment="center" valignment="top" width="0pt">
9659 <column alignment="center" valignment="top" width="0pt">
9661 <cell alignment="center" valignment="top" topline="true" bottomline="true" usebox="none">
9664 \begin_layout Plain Layout
9670 <cell alignment="center" valignment="top" topline="true" bottomline="true" usebox="none">
9673 \begin_layout Plain Layout
9680 <row topspace="1.5mm">
9681 <cell alignment="center" valignment="top" usebox="none">
9684 \begin_layout Plain Layout
9688 \begin_inset space \textvisiblespace{}
9696 <cell alignment="center" valignment="top" usebox="none">
9699 \begin_layout Plain Layout
9700 \begin_inset Formula $\dot{A}$
9709 <row topspace="1.5mm">
9710 <cell alignment="center" valignment="top" usebox="none">
9713 \begin_layout Plain Layout
9717 \begin_inset space \textvisiblespace{}
9725 <cell alignment="center" valignment="top" usebox="none">
9728 \begin_layout Plain Layout
9729 \begin_inset Formula $\ddot{A}$
9738 <row topspace="1.5mm">
9739 <cell alignment="center" valignment="top" usebox="none">
9742 \begin_layout Plain Layout
9746 \begin_inset space \textvisiblespace{}
9754 <cell alignment="center" valignment="top" usebox="none">
9757 \begin_layout Plain Layout
9758 \begin_inset Formula $\dddot{A}$
9767 <row topspace="1.5mm">
9768 <cell alignment="center" valignment="top" usebox="none">
9771 \begin_layout Plain Layout
9775 \begin_inset space \textvisiblespace{}
9783 <cell alignment="center" valignment="top" usebox="none">
9786 \begin_layout Plain Layout
9787 \begin_inset Formula $\ddddot{A}$
9796 <row topspace="1.5mm">
9797 <cell alignment="center" valignment="top" usebox="none">
9800 \begin_layout Plain Layout
9804 \begin_inset space \textvisiblespace{}
9808 \begin_inset Index idx
9811 \begin_layout Plain Layout
9822 <cell alignment="center" valignment="top" usebox="none">
9825 \begin_layout Plain Layout
9826 \begin_inset Formula $\vec{A}$
9835 <row topspace="1.5mm">
9836 <cell alignment="center" valignment="top" usebox="none">
9839 \begin_layout Plain Layout
9843 \begin_inset space \textvisiblespace{}
9851 <cell alignment="center" valignment="top" usebox="none">
9854 \begin_layout Plain Layout
9855 \begin_inset Formula $\bar{A}$
9864 <row topspace="1.5mm">
9865 <cell alignment="center" valignment="top" bottomline="true" usebox="none">
9868 \begin_layout Plain Layout
9872 \begin_inset space \textvisiblespace{}
9880 <cell alignment="center" valignment="top" bottomline="true" usebox="none">
9883 \begin_layout Plain Layout
9884 \begin_inset Formula $\mathring{A}$
9898 \begin_inset space \hfill{}
9902 \begin_inset Tabular
9903 <lyxtabular version="3" rows="7" columns="2">
9904 <features booktabs="true" tabularvalignment="middle">
9905 <column alignment="center" valignment="top" width="0pt">
9906 <column alignment="center" valignment="top" width="0pt">
9908 <cell alignment="center" valignment="top" topline="true" bottomline="true" usebox="none">
9911 \begin_layout Plain Layout
9917 <cell alignment="center" valignment="top" topline="true" bottomline="true" usebox="none">
9920 \begin_layout Plain Layout
9927 <row topspace="1.5mm">
9928 <cell alignment="center" valignment="top" usebox="none">
9931 \begin_layout Plain Layout
9935 \begin_inset space \textvisiblespace{}
9943 <cell alignment="center" valignment="top" usebox="none">
9946 \begin_layout Plain Layout
9947 \begin_inset Formula $\tilde{A}$
9956 <row topspace="1.5mm">
9957 <cell alignment="center" valignment="top" usebox="none">
9960 \begin_layout Plain Layout
9964 \begin_inset space \textvisiblespace{}
9972 <cell alignment="center" valignment="top" usebox="none">
9975 \begin_layout Plain Layout
9976 \begin_inset Formula $\hat{A}$
9985 <row topspace="1.5mm">
9986 <cell alignment="center" valignment="top" usebox="none">
9989 \begin_layout Plain Layout
9993 \begin_inset space \textvisiblespace{}
10001 <cell alignment="center" valignment="top" usebox="none">
10004 \begin_layout Plain Layout
10005 \begin_inset Formula $\check{A}$
10014 <row topspace="1.5mm">
10015 <cell alignment="center" valignment="top" usebox="none">
10018 \begin_layout Plain Layout
10022 \begin_inset space \textvisiblespace{}
10030 <cell alignment="center" valignment="top" usebox="none">
10033 \begin_layout Plain Layout
10034 \begin_inset Formula $\acute{A}$
10043 <row topspace="1.5mm">
10044 <cell alignment="center" valignment="top" usebox="none">
10047 \begin_layout Plain Layout
10051 \begin_inset space \textvisiblespace{}
10059 <cell alignment="center" valignment="top" usebox="none">
10062 \begin_layout Plain Layout
10063 \begin_inset Formula $\grave{A}$
10072 <row topspace="1.5mm">
10073 <cell alignment="center" valignment="top" bottomline="true" usebox="none">
10076 \begin_layout Plain Layout
10080 \begin_inset space \textvisiblespace{}
10088 <cell alignment="center" valignment="top" bottomline="true" usebox="none">
10091 \begin_layout Plain Layout
10092 \begin_inset Formula $\breve{A}$
10106 \begin_inset space \hfill{}
10112 \begin_layout Standard
10113 \begin_inset VSpace bigskip
10119 \begin_layout Standard
10120 You can directly insert accents like é to formulas.
10122 will transform them to the corresponding accent command.
10124 \begin_inset Index idx
10127 \begin_layout Plain Layout
10133 it is better to insert a quotation mark before the vowel.
10134 These two characters are then treated by \SpecialChar LaTeX
10139 character when the formula part with the umlaut is marked as German.
10147 \begin_inset Quotes eld
10151 \begin_inset Quotes erd
10154 umlauts are created as demonstrated in the following example:
10157 \begin_layout Standard
10158 \begin_inset VSpace -2mm
10164 \begin_layout Standard
10166 \begin_inset Tabular
10167 <lyxtabular version="3" rows="3" columns="2">
10168 <features booktabs="true" tabularvalignment="middle">
10169 <column alignment="center" valignment="top" width="0pt">
10170 <column alignment="center" valignment="top">
10172 <cell alignment="center" valignment="top" topline="true" bottomline="true" usebox="none">
10175 \begin_layout Plain Layout
10181 <cell alignment="center" valignment="top" topline="true" bottomline="true" usebox="none">
10184 \begin_layout Plain Layout
10192 <cell alignment="center" valignment="top" usebox="none">
10195 \begin_layout Plain Layout
10196 \begin_inset Quotes grd
10204 <cell alignment="center" valignment="top" usebox="none">
10207 \begin_layout Plain Layout
10208 \begin_inset space \hspace{}
10215 \begin_inset Formula $"i$
10224 <row topspace="1.5mm">
10225 <cell alignment="center" valignment="top" bottomline="true" usebox="none">
10228 \begin_layout Plain Layout
10232 \begin_inset space \textvisiblespace{}
10240 <cell alignment="center" valignment="top" bottomline="true" usebox="none">
10243 \begin_layout Plain Layout
10244 \begin_inset Formula $\ddot{i}$
10260 \begin_layout Standard
10261 Another advantage to
10267 is that umlauts can directly be converted to mathematical text because
10268 the accent commands above are
10274 in mathematical text
10277 To convert an accented character to mathematical text, only the character
10278 under the accent may be converted.
10279 This applies also for all other conversions, e.
10280 \begin_inset space \thinspace{}
10284 \begin_inset space \space{}
10290 \begin_layout Standard
10291 In mathematical text, umlauts and other accented characters can directly
10295 \begin_layout Standard
10296 \begin_inset VSpace bigskip
10302 \begin_layout Standard
10304 also supports a tilde under the character if the \SpecialChar LaTeX
10310 \begin_inset Index idx
10313 \begin_layout Plain Layout
10314 Packages ! undertilde
10319 is installed on your system:
10322 \begin_layout Standard
10326 \begin_layout Plain Layout
10336 \begin_inset Note Note
10339 \begin_layout Plain Layout
10340 The following table will only be displayed when the \SpecialChar LaTeX
10353 \begin_layout Standard
10356 \begin_inset Tabular
10357 <lyxtabular version="3" rows="2" columns="2">
10358 <features booktabs="true" tabularvalignment="middle">
10359 <column alignment="center" valignment="top" width="0pt">
10360 <column alignment="center" valignment="top" width="0pt">
10362 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
10365 \begin_layout Plain Layout
10371 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
10374 \begin_layout Plain Layout
10382 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
10385 \begin_layout Plain Layout
10389 \begin_inset space \textvisiblespace{}
10397 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
10400 \begin_layout Plain Layout
10401 \begin_inset Formula $\utilde{A}$
10417 \begin_layout Standard
10421 \begin_layout Plain Layout
10431 \begin_inset Note Note
10434 \begin_layout Plain Layout
10435 The following will be displayed when the \SpecialChar LaTeX
10448 \begin_layout Standard
10449 You need to install the \SpecialChar LaTeX
10454 to see the rest of this subsection in the output.
10457 \begin_layout Standard
10461 \begin_layout Plain Layout
10473 \begin_layout Standard
10474 \begin_inset Newpage newpage
10480 \begin_layout Subsection
10481 Accents for several Characters
10482 \begin_inset Index idx
10485 \begin_layout Plain Layout
10486 Accents ! for several characters
10494 \begin_layout Standard
10495 \begin_inset space \hfill{}
10499 \begin_inset Tabular
10500 <lyxtabular version="3" rows="5" columns="2">
10501 <features booktabs="true" tabularvalignment="middle">
10502 <column alignment="center" valignment="top" width="0pt">
10503 <column alignment="center" valignment="top" width="0pt">
10505 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
10508 \begin_layout Plain Layout
10514 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
10517 \begin_layout Plain Layout
10524 <row topspace="1.5mm">
10525 <cell alignment="center" valignment="top" usebox="none">
10528 \begin_layout Plain Layout
10532 \begin_inset space \textvisiblespace{}
10540 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
10543 \begin_layout Plain Layout
10544 \begin_inset Formula $\overleftarrow{A=B}$
10553 <row topspace="1.5mm">
10554 <cell alignment="center" valignment="top" usebox="none">
10557 \begin_layout Plain Layout
10561 \begin_inset space \textvisiblespace{}
10569 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
10572 \begin_layout Plain Layout
10573 \begin_inset Formula $\underleftarrow{A=B}$
10582 <row topspace="1.5mm">
10583 <cell alignment="center" valignment="top" usebox="none">
10586 \begin_layout Plain Layout
10590 \begin_inset space \textvisiblespace{}
10598 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
10601 \begin_layout Plain Layout
10602 \begin_inset Formula $\overleftrightarrow{A=B}$
10611 <row topspace="1.5mm" bottomspace="1mm">
10612 <cell alignment="center" valignment="top" bottomline="true" usebox="none">
10615 \begin_layout Plain Layout
10618 underleftrightarrow
10619 \begin_inset space \textvisiblespace{}
10627 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
10630 \begin_layout Plain Layout
10631 \begin_inset Formula $\underleftrightarrow{A=B}$
10645 \begin_inset space \hfill{}
10649 \begin_inset Tabular
10650 <lyxtabular version="3" rows="5" columns="2">
10651 <features booktabs="true" tabularvalignment="middle">
10652 <column alignment="center" valignment="top" width="0pt">
10653 <column alignment="center" valignment="top" width="0pt">
10655 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
10658 \begin_layout Plain Layout
10664 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
10667 \begin_layout Plain Layout
10674 <row topspace="1.5mm">
10675 <cell alignment="center" valignment="top" usebox="none">
10678 \begin_layout Plain Layout
10682 \begin_inset space \textvisiblespace{}
10690 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
10693 \begin_layout Plain Layout
10694 \begin_inset Formula $\overrightarrow{A=B}$
10703 <row topspace="1.5mm">
10704 <cell alignment="center" valignment="top" usebox="none">
10707 \begin_layout Plain Layout
10711 \begin_inset space \textvisiblespace{}
10719 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
10722 \begin_layout Plain Layout
10723 \begin_inset Formula $\underrightarrow{A=B}$
10732 <row topspace="1.5mm">
10733 <cell alignment="center" valignment="top" usebox="none">
10736 \begin_layout Plain Layout
10740 \begin_inset space \textvisiblespace{}
10748 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
10751 \begin_layout Plain Layout
10752 \begin_inset Formula $\widetilde{A=B}$
10761 <row topspace="1.5mm" bottomspace="1mm">
10762 <cell alignment="center" valignment="top" bottomline="true" usebox="none">
10765 \begin_layout Plain Layout
10769 \begin_inset space \textvisiblespace{}
10777 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
10780 \begin_layout Plain Layout
10781 \begin_inset Formula $\widehat{A=B}$
10795 \begin_inset space \hfill{}
10801 \begin_layout Standard
10802 \begin_inset VSpace medskip
10805 With these commands as many characters as you like can be accented.
10818 will only be set in the output with a length of three characters, as shown
10819 in the following example:
10820 \begin_inset Formula
10822 \widetilde{A+B=C-D}
10830 \begin_layout Standard
10838 \begin_inset Index idx
10841 \begin_layout Plain Layout
10856 \begin_inset Index idx
10859 \begin_layout Plain Layout
10867 described in the previous subsection it is also possible to accent several
10874 \begin_inset space \textvisiblespace{}
10878 \begin_inset Formula $\downarrow$
10884 \begin_inset Formula
10886 \underset{***}{A=B}
10894 \begin_layout Section
10896 \begin_inset CommandInset label
10898 name "subsec:Space"
10903 \begin_inset Index idx
10906 \begin_layout Plain Layout
10915 \begin_layout Subsection
10917 \begin_inset CommandInset label
10919 name "subsec:Predefined-Space"
10924 \begin_inset Index idx
10927 \begin_layout Plain Layout
10928 Space ! horizontal ! predefined
10936 \begin_layout Standard
10937 Sometimes it is necessary to insert horizontal space into a formula.
10938 This is done by inserting a protected space (shortcut
10941 arg "command-alternatives space-insert protected ; math-space"
10946 \begin_inset Quotes eld
10952 \begin_inset space \textvisiblespace{}
10958 \begin_inset Quotes erd
10961 appears and by pressing
10965 several times one can select one of eight different space sizes.
10966 The spaces can also be inserted using the math toolbar button
10969 arg "math-insert \\space"
10972 or special commands.
10973 Independent from the inserted command, one can select the size again by
10981 \begin_layout Standard
10984 \begin_inset Tabular
10985 <lyxtabular version="3" rows="6" columns="3">
10986 <features booktabs="true" tabularvalignment="middle">
10987 <column alignment="center" valignment="top">
10988 <column alignment="center" valignment="top" width="15col%">
10989 <column alignment="center" valignment="top">
10991 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
10994 \begin_layout Plain Layout
11000 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
11003 \begin_layout Plain Layout
11013 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
11016 \begin_layout Plain Layout
11024 <cell alignment="center" valignment="top" leftline="true" usebox="none">
11027 \begin_layout Plain Layout
11035 <cell alignment="center" valignment="top" leftline="true" usebox="none">
11038 \begin_layout Plain Layout
11044 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
11047 \begin_layout Plain Layout
11048 \begin_inset Formula $A\,B$
11058 <cell alignment="center" valignment="top" leftline="true" usebox="none">
11061 \begin_layout Plain Layout
11069 <cell alignment="center" valignment="top" leftline="true" usebox="none">
11072 \begin_layout Plain Layout
11078 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
11081 \begin_layout Plain Layout
11082 \begin_inset Formula $A\:B$
11092 <cell alignment="center" valignment="top" leftline="true" usebox="none">
11095 \begin_layout Plain Layout
11103 <cell alignment="center" valignment="top" leftline="true" usebox="none">
11106 \begin_layout Plain Layout
11112 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
11115 \begin_layout Plain Layout
11116 \begin_inset Formula $A\;B$
11126 <cell alignment="center" valignment="top" leftline="true" usebox="none">
11129 \begin_layout Plain Layout
11137 <cell alignment="center" valignment="top" leftline="true" usebox="none">
11140 \begin_layout Plain Layout
11146 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
11149 \begin_layout Plain Layout
11150 \begin_inset Formula $A\quad B$
11160 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
11163 \begin_layout Plain Layout
11171 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
11174 \begin_layout Plain Layout
11180 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
11183 \begin_layout Plain Layout
11184 \begin_inset Formula $A\qquad B$
11198 \begin_inset space \hfill{}
11202 \begin_inset Tabular
11203 <lyxtabular version="3" rows="6" columns="3">
11204 <features booktabs="true" tabularvalignment="middle">
11205 <column alignment="center" valignment="top">
11206 <column alignment="center" valignment="top" width="15col%">
11207 <column alignment="center" valignment="top">
11209 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
11212 \begin_layout Plain Layout
11218 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
11221 \begin_layout Plain Layout
11231 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
11234 \begin_layout Plain Layout
11242 <cell alignment="center" valignment="top" leftline="true" usebox="none">
11245 \begin_layout Plain Layout
11253 <cell alignment="center" valignment="top" leftline="true" usebox="none">
11256 \begin_layout Plain Layout
11262 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
11265 \begin_layout Plain Layout
11266 \begin_inset Formula $A\hfill B$
11276 <cell alignment="center" valignment="top" leftline="true" usebox="none">
11279 \begin_layout Plain Layout
11287 <cell alignment="center" valignment="top" leftline="true" usebox="none">
11290 \begin_layout Plain Layout
11296 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
11299 \begin_layout Plain Layout
11300 \begin_inset Formula $A\hspace*{1em}B$
11310 <cell alignment="center" valignment="top" leftline="true" usebox="none">
11313 \begin_layout Plain Layout
11321 <cell alignment="center" valignment="top" leftline="true" usebox="none">
11324 \begin_layout Plain Layout
11330 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
11333 \begin_layout Plain Layout
11334 \begin_inset Formula $A\hspace{1em}B$
11344 <cell alignment="center" valignment="top" leftline="true" usebox="none">
11347 \begin_layout Plain Layout
11351 \begin_inset space \textvisiblespace{}
11359 <cell alignment="center" valignment="top" leftline="true" usebox="none">
11362 \begin_layout Plain Layout
11368 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
11371 \begin_layout Plain Layout
11372 \begin_inset Formula $A\ B$
11382 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
11385 \begin_layout Plain Layout
11393 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
11396 \begin_layout Plain Layout
11402 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
11405 \begin_layout Plain Layout
11406 \begin_inset Formula $A\!B$
11422 \begin_layout Standard
11424 \begin_inset space ~
11428 \begin_inset space \thinspace{}
11432 \begin_inset space \thinspace{}
11435 7 are variable spaces which are explained in
11436 \begin_inset CommandInset ref
11438 reference "subsec:Variable-Space"
11444 \begin_inset space ~
11447 9 seems to produce no space.
11448 It is displayed red in \SpecialChar LyX
11449 contrary to the other sizes, because it is a negative
11451 There are two more negative spaces:
11454 \begin_layout Standard
11456 \begin_inset Tabular
11457 <lyxtabular version="3" rows="3" columns="3">
11458 <features booktabs="true" tabularvalignment="middle">
11459 <column alignment="center" valignment="middle" width="6.8cm">
11460 <column alignment="center" valignment="top" width="0pt">
11461 <column alignment="center" valignment="top" width="0pt">
11463 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
11466 \begin_layout Plain Layout
11472 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
11475 \begin_layout Plain Layout
11483 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
11486 \begin_layout Plain Layout
11496 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
11499 \begin_layout Plain Layout
11504 keystrokes after inserting the protected space
11509 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
11512 \begin_layout Plain Layout
11518 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
11521 \begin_layout Plain Layout
11529 <cell multicolumn="1" alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
11532 \begin_layout Plain Layout
11538 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
11541 \begin_layout Plain Layout
11542 \begin_inset Formula $A\negmedspace B$
11550 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
11553 \begin_layout Plain Layout
11554 \begin_inset Formula $A\negthickspace B$
11570 \begin_layout Standard
11571 Negative spaces can lead to characters overlapping each other.
11572 Thus they can be used to enforce ligatures, which are e.
11573 \begin_inset space \thinspace{}
11577 \begin_inset space \space{}
11580 useful for summation operators:
11583 \begin_layout Standard
11585 \begin_inset Tabular
11586 <lyxtabular version="3" rows="3" columns="2">
11587 <features booktabs="true" tabularvalignment="middle">
11588 <column alignment="center" valignment="top" width="0pt">
11589 <column alignment="center" valignment="top">
11591 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
11594 \begin_layout Plain Layout
11600 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
11603 \begin_layout Plain Layout
11611 <cell alignment="center" valignment="top" leftline="true" usebox="none">
11614 \begin_layout Plain Layout
11620 \begin_inset space \textvisiblespace{}
11628 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
11631 \begin_layout Plain Layout
11632 \begin_inset Formula $\sum\sum f_{kl}$
11642 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
11645 \begin_layout Plain Layout
11653 \begin_inset space \textvisiblespace{}
11661 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
11664 \begin_layout Plain Layout
11665 \begin_inset Formula $\sum\negmedspace\sum f_{kl}$
11681 \begin_layout Standard
11683 \begin_inset VSpace medskip
11689 \begin_layout Standard
11691 Relations like for example equal signs, are always surrounded by space.
11692 To suppress this, the equal sign is placed into a \SpecialChar TeX
11694 The following example demonstrates this:
11697 \begin_layout Standard
11699 \begin_inset Tabular
11700 <lyxtabular version="3" rows="2" columns="2">
11701 <features tabularvalignment="middle">
11702 <column alignment="center" valignment="top" width="0pt">
11703 <column alignment="center" valignment="top" width="0pt">
11705 <cell alignment="center" valignment="top" usebox="none">
11708 \begin_layout Plain Layout
11714 <cell alignment="center" valignment="top" usebox="none">
11717 \begin_layout Plain Layout
11718 \begin_inset Formula $A=B$
11728 <cell alignment="center" valignment="top" usebox="none">
11731 \begin_layout Plain Layout
11732 equation without space
11737 <cell multicolumn="1" alignment="center" valignment="top" usebox="none">
11740 \begin_layout Plain Layout
11741 \begin_inset Formula $A{=}B$
11757 \begin_layout Standard
11759 The command for the last formula is:
11764 \begin_inset Formula $\to$
11770 \begin_layout Standard
11771 \begin_inset VSpace bigskip
11777 \begin_layout Standard
11778 Spaces are needed for physical units, because the space between the value
11779 and the unit is the smallest one and not a normal space.
11780 For units in text, the smallest space is inserted via the menu
11782 Insert\SpecialChar menuseparator
11783 Formatting\SpecialChar menuseparator
11785 \begin_inset space ~
11793 arg "space-insert thin"
11799 \begin_layout Standard
11800 An example to visualize the difference:
11803 \begin_layout Standard
11804 \begin_inset Tabular
11805 <lyxtabular version="3" rows="2" columns="2">
11806 <features tabularvalignment="middle">
11807 <column alignment="left" valignment="top">
11808 <column alignment="left" valignment="top">
11810 <cell alignment="center" valignment="top" usebox="none">
11813 \begin_layout Plain Layout
11815 \begin_inset Formula $\cdot$
11823 <cell alignment="center" valignment="top" usebox="none">
11826 \begin_layout Plain Layout
11827 space between value and unit
11834 <cell alignment="center" valignment="top" usebox="none">
11837 \begin_layout Plain Layout
11839 \begin_inset space \thinspace{}
11843 \begin_inset Formula $\cdot$
11851 <cell alignment="center" valignment="top" usebox="none">
11854 \begin_layout Plain Layout
11855 smallest space between value and unit
11868 \begin_layout Subsection
11873 \begin_layout Plain Layout
11886 \begin_layout Plain Layout
11887 for vertical space in formulas see
11888 \begin_inset CommandInset ref
11890 reference "subsec:Line-Separation"
11903 \begin_layout Plain Layout
11911 \begin_inset Note Note
11914 \begin_layout Plain Layout
11917 texorpdfstring is used to avoid that the footnote appears in the PDF-bookmark.
11920 \begin_layout Plain Layout
11923 texorpdfstring is in section
11924 \begin_inset CommandInset ref
11926 reference "subsec:Formulas-in-Section"
11936 \begin_inset CommandInset label
11938 name "subsec:Variable-Space"
11943 \begin_inset Index idx
11946 \begin_layout Plain Layout
11947 Space ! horizontal ! variable
11955 \begin_layout Standard
11956 Space with a defined length can be inserted with the command
11963 \begin_inset Index idx
11966 \begin_layout Plain Layout
11976 \begin_inset Quotes eld
11982 \begin_inset space \textvisiblespace{}
11988 \begin_inset Quotes erd
11992 The length can be specified by left-clicking on the
11993 \begin_inset Quotes eld
11999 \begin_inset space \textvisiblespace{}
12005 \begin_inset Quotes erd
12009 The length may also be negative.
12010 When a space would be the first character in a line it would be omitted.
12011 To force its output use the command
12023 or left-click on the
12024 \begin_inset Quotes eld
12030 \begin_inset space \textvisiblespace{}
12036 \begin_inset Quotes erd
12039 and check the option
12044 \begin_inset Newline newline
12047 To insert as much space as is available, the command
12054 \begin_inset Index idx
12057 \begin_layout Plain Layout
12068 \begin_layout Standard
12070 \begin_inset Tabular
12071 <lyxtabular version="3" rows="4" columns="2">
12072 <features booktabs="true" tabularvalignment="middle">
12073 <column alignment="center" valignment="top" width="0pt">
12074 <column alignment="center" valignment="top">
12076 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
12079 \begin_layout Plain Layout
12087 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
12090 \begin_layout Plain Layout
12098 <cell alignment="center" valignment="top" leftline="true" usebox="none">
12101 \begin_layout Plain Layout
12105 \begin_inset space \textvisiblespace{}
12111 \begin_inset space \thinspace{}
12119 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
12122 \begin_layout Plain Layout
12123 \begin_inset Formula $A=B\hspace{3cm}A\not=C$
12133 <cell alignment="center" valignment="top" leftline="true" usebox="none">
12136 \begin_layout Plain Layout
12140 \begin_inset space \textvisiblespace{}
12146 \begin_inset space \thinspace{}
12154 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
12157 \begin_layout Plain Layout
12158 \begin_inset Formula $A\hspace{-1mm}A\not=A$
12168 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
12171 \begin_layout Plain Layout
12175 \begin_inset space \textvisiblespace{}
12183 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
12186 \begin_layout Plain Layout
12187 \begin_inset Formula $A=A\hfill B=B$
12203 \begin_layout Standard
12204 In the last example the available space is given by the longest column entry
12206 In an inline formula the space depends on the length of the line in which
12214 Thus, when the line uses the full width, no space will be created.
12221 only has an effect on displayed formulas when the formula style
12226 (Formula styles are explained in
12227 \begin_inset CommandInset ref
12229 reference "sec:Formula-Styles"
12236 \begin_layout Standard
12243 , there are the commands
12255 that fill the space with a pattern, see
12256 \begin_inset CommandInset ref
12258 reference "subsec:Ellipses"
12265 \begin_layout Standard
12266 For text, variable space can be inserted via the menu
12268 Insert\SpecialChar menuseparator
12269 Formatting\SpecialChar menuseparator
12271 \begin_inset space ~
12279 \begin_layout Standard
12280 This is a line with
12281 \begin_inset space \hspace{}
12286 \begin_inset space \thinspace{}
12292 \begin_layout Standard
12293 This is a line with
12294 \begin_inset space \hfill{}
12300 \begin_layout Subsection
12301 Space besides inline Formulas
12302 \begin_inset Index idx
12305 \begin_layout Plain Layout
12306 Space ! besides inline formulas
12314 \begin_layout Standard
12315 The space that surrounds inline formulas can be adjusted with the length
12323 \begin_inset Index idx
12326 \begin_layout Plain Layout
12335 The value of a length is set with the command
12342 \begin_inset Index idx
12345 \begin_layout Plain Layout
12353 which has the following scheme:
12356 \begin_layout Standard
12361 setlength{length name}{value}
12364 \begin_layout Standard
12372 \begin_inset space \thinspace{}
12378 \begin_layout Standard
12388 \begin_layout Standard
12389 is inserted in \SpecialChar TeX
12392 \begin_inset space \thinspace{}
12395 mm space will now be set around all inline formulas:
12399 \begin_layout Plain Layout
12413 \begin_layout Standard
12414 This is a line with an inline formula
12415 \begin_inset Formula $A=B$
12419 \begin_inset space \thinspace{}
12422 mm surrounding space.
12426 \begin_layout Plain Layout
12440 \begin_layout Standard
12441 To return to the predefined value,
12447 is set to the value 0
12448 \begin_inset space \thinspace{}
12454 \begin_layout Standard
12455 \begin_inset Newpage newpage
12461 \begin_layout Section
12463 \begin_inset Index idx
12466 \begin_layout Plain Layout
12473 \begin_inset Index idx
12476 \begin_layout Plain Layout
12481 \begin_layout Plain Layout
12492 \begin_layout Plain Layout
12507 \begin_layout Standard
12508 Boxes for text are described in chapter
12515 \begin_inset space ~
12523 \begin_layout Subsection
12525 \begin_inset CommandInset label
12527 name "subsec:Boxes-with-Frame"
12532 \begin_inset Index idx
12535 \begin_layout Plain Layout
12544 \begin_layout Standard
12545 It is possible to frame a formula or part of one with the commands
12552 \begin_inset Index idx
12555 \begin_layout Plain Layout
12570 \begin_inset Index idx
12573 \begin_layout Plain Layout
12584 \begin_layout Standard
12585 When one of these commands is inserted in a formula, a blue box appears
12586 within a frame to enter formula parts.
12593 an additional formula has to be created by
12597 within this box, because the box content will otherwise be treated as mathemati
12605 is used, a new formula is automatically created inside the frame.
12608 \begin_layout Standard
12615 is not suitable to frame displayed formulas because the formula will always
12616 be set in the size of the text.
12623 is in contrary not suitable to frame inline formulas, because the formula
12624 will always be set in the size of a displayed formula.
12627 \begin_layout Standard
12641 \begin_inset Index idx
12644 \begin_layout Plain Layout
12652 where additionally the frame width and the alignment can be specified.
12659 is used in the following scheme:
12662 \begin_layout Standard
12667 framebox[frame width][position]{box content}
12670 \begin_layout Standard
12671 The position can either be
12688 right aligns the formula in the box.
12689 When no position is given, the formula will be centered.
12690 \begin_inset Newline newline
12693 If no width is given, also no position can be given.
12694 In this case the frame width is adjusted to the box content like for
12703 \begin_layout Standard
12710 is inserted, a box appears containing three blue boxes.
12711 The first two boxes are surrounded by brackets and denote the two optional
12713 The third box is for formula parts like for
12722 \begin_layout Standard
12724 \begin_inset Tabular
12725 <lyxtabular version="3" rows="5" columns="2">
12726 <features booktabs="true" tabularvalignment="middle">
12727 <column alignment="center" valignment="top" width="0pt">
12728 <column alignment="center" valignment="top">
12730 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
12733 \begin_layout Plain Layout
12739 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
12742 \begin_layout Plain Layout
12749 <row topspace="1.5mm">
12750 <cell alignment="center" valignment="top" usebox="none">
12753 \begin_layout Plain Layout
12757 \begin_inset space \textvisiblespace{}
12767 \begin_inset space \textvisiblespace{}
12775 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
12778 \begin_layout Plain Layout
12779 \begin_inset Formula $\fbox{\ensuremath{\int A=B}}$
12788 <row topspace="1.5mm">
12789 <cell alignment="center" valignment="top" usebox="none">
12792 \begin_layout Plain Layout
12796 \begin_inset space \textvisiblespace{}
12802 \begin_inset space \textvisiblespace{}
12810 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
12813 \begin_layout Plain Layout
12814 \begin_inset Formula $\boxed{\int A=B}$
12823 <row topspace="1.5mm">
12824 <cell alignment="center" valignment="top" usebox="none">
12827 \begin_layout Plain Layout
12831 \begin_inset space \textvisiblespace{}
12839 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
12842 \begin_layout Plain Layout
12843 \begin_inset Formula $A+\fbox{B}$
12852 <row topspace="1.5mm" bottomspace="1mm">
12853 <cell alignment="center" valignment="top" bottomline="true" usebox="none">
12856 \begin_layout Plain Layout
12860 \begin_inset space \textvisiblespace{}
12864 \begin_inset Formula $\to$
12868 \begin_inset Formula $\to$
12878 \begin_inset space \textvisiblespace{}
12882 \begin_inset Formula $\downarrow$
12890 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
12893 \begin_layout Plain Layout
12894 \begin_inset Formula $\framebox[20mm][]{\ensuremath{\frac{A}{B}}}$
12910 \begin_layout Standard
12911 The frame thickness can also be adjusted.
12912 To do this the following commands have to be inserted in \SpecialChar TeX
12917 \begin_layout Standard
12927 \begin_inset Quotes eld
12931 \begin_inset Quotes erd
12945 \begin_inset Quotes eld
12949 \begin_inset Quotes erd
12955 \begin_layout Standard
12956 \begin_inset Quotes eld
12960 \begin_inset Quotes erd
12963 specifies the minimal distance between the frame and the first character
12965 An example for this is the following framed formula:
12969 \begin_layout Plain Layout
12981 \begin_inset Formula
12988 Before this formula the commands
12991 \begin_layout Standard
13013 \begin_layout Standard
13014 were inserted in \SpecialChar TeX
13016 The given values are used for all following boxes.
13019 \begin_layout Standard
13020 To return to the standard frame size, the command
13023 \begin_layout Standard
13048 \begin_layout Plain Layout
13062 \begin_layout Standard
13063 is inserted in \SpecialChar TeX
13064 mode before the next formula.
13067 \begin_layout Subsection
13068 Boxes without Frame
13069 \begin_inset CommandInset label
13071 name "subsec:Boxes-without-Frame"
13076 \begin_inset Index idx
13079 \begin_layout Plain Layout
13080 Boxes ! without frame
13088 \begin_layout Standard
13089 For boxes without a frame there are the following box commands:
13096 \begin_inset Index idx
13099 \begin_layout Plain Layout
13114 \begin_inset Index idx
13117 \begin_layout Plain Layout
13132 \begin_inset Index idx
13135 \begin_layout Plain Layout
13146 \begin_layout Standard
13153 a box can be super- or subscripted.
13154 But in contrary to normal super- and subscripting, the characters in the
13155 box keep their font size.
13162 is used in the following scheme:
13165 \begin_layout Standard
13170 raisebox{height}{box content}
13173 \begin_layout Standard
13174 When the box should contain a formula, an extra formula is needed like for
13185 \begin_inset Note Greyedout
13188 \begin_layout Plain Layout
13199 this extra formula is created by pressing
13203 twice instead of once because \SpecialChar LyX
13204 doesn't yet support
13218 \begin_layout Standard
13220 \begin_inset Tabular
13221 <lyxtabular version="3" rows="4" columns="2">
13222 <features booktabs="true" tabularvalignment="middle">
13223 <column alignment="center" valignment="top" width="0pt">
13224 <column alignment="center" valignment="top">
13226 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
13229 \begin_layout Plain Layout
13235 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
13238 \begin_layout Plain Layout
13246 <cell alignment="center" valignment="top" leftline="true" usebox="none">
13249 \begin_layout Plain Layout
13253 \begin_inset Formula $\to$
13259 \begin_inset Formula $\to$
13267 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
13270 \begin_layout Plain Layout
13271 \begin_inset Formula $H\raisebox{2mm}{al}lo$
13281 <cell alignment="center" valignment="top" leftline="true" usebox="none">
13284 \begin_layout Plain Layout
13288 \begin_inset Formula $\to$
13294 \begin_inset Formula $\to$
13302 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
13305 \begin_layout Plain Layout
13306 \begin_inset Formula $H\raisebox{-2mm}{al}lo$
13316 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
13319 \begin_layout Plain Layout
13323 \begin_inset Formula $\to$
13339 \begin_inset space \textvisiblespace{}
13347 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
13350 \begin_layout Plain Layout
13351 \begin_inset Formula $A=\raisebox{-2mm}{\mbox{\ensuremath{\sqrt{B}}}}$
13367 \begin_layout Standard
13392 , with the difference that there is no frame.
13395 \begin_layout Subsection
13397 \begin_inset CommandInset label
13399 name "subsec:Colored-Boxes"
13404 \begin_inset Index idx
13407 \begin_layout Plain Layout
13416 \begin_layout Standard
13417 To be able to use all commands explained in this section, the \SpecialChar LaTeX
13426 \begin_layout Plain Layout
13427 The \SpecialChar LaTeX
13432 is part of every \SpecialChar LaTeX
13433 standard installation.
13439 \begin_inset Index idx
13442 \begin_layout Plain Layout
13448 has to be loaded in the \SpecialChar LaTeX
13449 -preamble with the line
13453 \begin_layout Plain Layout
13454 When text is colored somewhere in the document with a predefined color,
13456 loads the \SpecialChar LaTeX
13462 Thus it is possible that the package is loaded twice, but this does not
13469 \begin_inset Note Note
13472 \begin_layout Plain Layout
13473 To avoid that the package is loaded twice, a macro was inserted to the \SpecialChar LaTeX
13482 \begin_layout Standard
13490 \begin_layout Standard
13491 \begin_inset VSpace medskip
13494 To color boxes, the command
13501 \begin_inset Index idx
13504 \begin_layout Plain Layout
13512 is used in the following scheme:
13515 \begin_layout Standard
13520 colorbox{color}{box content}
13523 \begin_layout Standard
13524 The box content can also be a box and a
13530 can also be part of another box (see the 2nd and 3rd example).
13531 When the box should contain a formula, an extra formula has to be created,
13532 the same way as for
13542 \begin_layout Plain Layout
13543 This also applies for the command
13557 \begin_layout Standard
13558 One of the following predefined colors can be chosen:
13561 \begin_layout Standard
13595 \begin_layout Standard
13597 \begin_inset Tabular
13598 <lyxtabular version="3" rows="4" columns="2">
13599 <features booktabs="true" tabularvalignment="middle">
13600 <column alignment="center" valignment="top" width="0pt">
13601 <column alignment="center" valignment="top">
13603 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
13606 \begin_layout Plain Layout
13612 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
13615 \begin_layout Plain Layout
13623 <cell alignment="center" valignment="top" leftline="true" usebox="none">
13626 \begin_layout Plain Layout
13630 \begin_inset Formula $\to$
13640 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
13643 \begin_layout Plain Layout
13644 \begin_inset Formula $\colorbox{yellow}{A=B}$
13653 <row topspace="1.5mm">
13654 <cell alignment="center" valignment="top" usebox="none">
13657 \begin_layout Plain Layout
13661 \begin_inset Formula $\to$
13669 \begin_inset space \textvisiblespace{}
13677 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
13680 \begin_layout Plain Layout
13681 \begin_inset Formula $\colorbox{green}{\fbox{A=B}}$
13690 <row topspace="1.5mm" bottomspace="1mm">
13691 <cell alignment="center" valignment="top" bottomline="true" usebox="none">
13694 \begin_layout Plain Layout
13698 \begin_inset space \textvisiblespace{}
13704 \begin_inset Formula $\to$
13720 \begin_inset space \textvisiblespace{}
13728 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
13731 \begin_layout Plain Layout
13732 \begin_inset Formula $\fbox{\colorbox{green}{\mbox{\ensuremath{\int C=D}}}}$
13748 \begin_layout Standard
13755 only colors the box but not the characters in the box.
13756 To color all characters, the whole formula is highlighted and the desired
13757 color is chosen in the
13760 \begin_inset space ~
13766 The dialog can be called with the toolbar button
13769 arg "dialog-show character"
13774 Edit\SpecialChar menuseparator
13776 \begin_inset space ~
13779 Style\SpecialChar menuseparator
13783 The formula number then has the same color as the formula.
13784 When the formula number should get another color than the formula characters,
13785 the color must be changed within the formula.
13788 \begin_layout Standard
13792 \begin_layout Standard
13795 \begin_inset Formula
13797 \int A=B\label{eq:red}
13805 \begin_inset Formula
13807 \textcolor{red}{\int A=B}\label{eq:redgreen}
13815 \begin_layout Standard
13817 \begin_inset CommandInset ref
13823 is completely colored red.
13824 \begin_inset Newline newline
13828 \begin_inset CommandInset ref
13830 reference "eq:redgreen"
13834 was first completely colored green to set the color for the formula number.
13835 Subsequently the formula characters were colored red.
13838 \begin_layout Standard
13839 \begin_inset VSpace bigskip
13842 To color the frame different than the rest of the box, the command
13849 \begin_inset Index idx
13852 \begin_layout Plain Layout
13860 is used in the following scheme:
13863 \begin_layout Standard
13868 fcolorbox{frame color}{color}{box content}
13871 \begin_layout Standard
13878 is an extension of the command
13885 The frame width is set, like for
13908 \begin_layout Plain Layout
13920 \begin_inset Formula
13922 \fcolorbox{cyan}{magenta}{A=B}
13931 \begin_layout Plain Layout
13945 \begin_layout Standard
13946 This formula was created with the command
13947 \begin_inset Newline newline
13955 \begin_inset Formula $\to$
13961 \begin_inset Formula $\to$
13971 \begin_layout Standard
13972 \begin_inset VSpace bigskip
13975 To use other colors than the predefined ones, they have to be defined first.
13978 \begin_layout Standard
13979 One can for example define the color
13980 \begin_inset Quotes eld
13988 \begin_inset Quotes erd
13991 with the \SpecialChar LaTeX
13995 \begin_layout Standard
14000 definecolor{darkgreen}{cmyk}{0.5,
14015 \begin_inset Index idx
14018 \begin_layout Plain Layout
14029 \begin_layout Standard
14034 is the color space that denotes the colors
14051 The four comma separated numbers are the portion factor for the corresponding
14052 colors of the color space.
14053 The factors can be in the range of 0
14054 \begin_inset space \thinspace{}
14058 \begin_inset space \thinspace{}
14066 also the color space
14070 can be used for definitions.
14087 , so that there are in this case three portion factors for the corresponding
14089 Furthermore there is the color space
14093 with one portion factor for the gray value.
14096 \begin_layout Standard
14097 As example a framed box with the new defined color
14101 where the characters have been colored
14106 \begin_inset Formula
14108 \colorbox{darkgreen}{\color{yellow}\boxed{\int A\,\mathrm{d}x=\frac{\sqrt[5]{B}}{\ln\left(\frac{1}{3}\right)}}}
14116 \begin_layout Standard
14117 Self-defined colors can also be used for text with the help of the command
14125 \begin_inset Index idx
14128 \begin_layout Plain Layout
14137 \begin_layout Standard
14141 \begin_layout Plain Layout
14145 textcolor{darkgreen}{
14151 \begin_inset Quotes eld
14155 \begin_inset Quotes erd
14162 \begin_layout Plain Layout
14172 \begin_layout Standard
14180 \begin_inset Index idx
14183 \begin_layout Plain Layout
14191 is used in the scheme
14195 textcolor{color}{characters to color}
14200 \begin_layout Subsection
14202 \begin_inset CommandInset label
14204 name "subsec:Paragraph-Boxes"
14209 \begin_inset Index idx
14212 \begin_layout Plain Layout
14213 Boxes ! as paragraph
14221 \begin_layout Standard
14222 A box that can contain several lines and paragraphs, a so-called paragraph
14223 box (parbox), can be created with the menu
14225 Insert\SpecialChar menuseparator
14228 or the toolbar button
14237 \begin_layout Standard
14238 The following example shows a framed parbox in a line:
14241 \begin_layout Standard
14242 \begin_inset VSpace medskip
14246 \begin_inset Box Boxed
14256 height_special "totalheight"
14261 backgroundcolor "none"
14264 \begin_layout Plain Layout
14265 This is a paragraph box.
14267 \begin_inset space \thinspace{}
14270 cm long and can also contain formulas:
14271 \begin_inset Formula $\int A\,\mathrm{d}s=C$
14282 \begin_layout Standard
14283 \begin_inset VSpace medskip
14289 \begin_layout Standard
14290 Such a box is created by right-clicking on the gray box inset.
14291 A dialog pops up showing the box properties.
14305 \begin_inset space \thinspace{}
14310 Vertical Box Alignment
14315 \begin_layout Standard
14316 \begin_inset VSpace medskip
14319 In \SpecialChar LaTeX
14320 a parbox is created with the command
14327 \begin_inset Index idx
14330 \begin_layout Plain Layout
14338 which has the following scheme:
14341 \begin_layout Standard
14346 parbox[position]{width}{box content}
14349 \begin_layout Standard
14364 \begin_inset Quotes eld
14368 \begin_inset Quotes erd
14371 means that the box is aligned within the surrounding text with its last
14378 \begin_inset Quotes eld
14382 \begin_inset Quotes erd
14385 this is done with the first line.
14386 When no position is given, the box will be vertically centered, see section
14394 \begin_inset space ~
14399 manual for examples.
14402 \begin_layout Standard
14403 \begin_inset VSpace bigskip
14406 To frame formulas completely, including the formula number, the formula
14407 must be set into a parbox.
14408 To do this, the command
14422 is inserted in \SpecialChar TeX
14423 mode before the formula.
14431 \begin_inset Index idx
14434 \begin_layout Plain Layout
14442 is hereby the line width set for the document.
14443 Because the frame is outside the parbox, 2
14444 \begin_inset space \thinspace{}
14447 times the frame separation and the frame thickness must be subtracted from
14449 To be able to multiply and subtract in arguments, the \SpecialChar LaTeX
14458 \begin_layout Plain Layout
14463 is part of every \SpecialChar LaTeX
14464 standard installation.
14470 \begin_inset Index idx
14473 \begin_layout Plain Layout
14479 must be loaded in the \SpecialChar LaTeX
14480 -preamble with the line
14483 \begin_layout Standard
14491 \begin_layout Standard
14492 Behind the formula both boxes are closed by entering
14496 in \SpecialChar TeX
14498 Here is an example:
14502 \begin_layout Plain Layout
14516 \begin_layout Standard
14520 \begin_layout Plain Layout
14538 \begin_inset Formula
14540 \int A\,\mathrm{d}x=\frac{\sqrt[5]{B}}{\ln\left(\frac{1}{3}\right)}
14549 \begin_layout Plain Layout
14560 \begin_layout Plain Layout
14574 \begin_layout Standard
14575 \begin_inset VSpace medskip
14578 As a parbox is used as the argument of
14584 , there is in this case no difference between
14599 \begin_layout Standard
14600 \begin_inset VSpace bigskip
14603 Paragraph boxes are very useful to comment formulas directly.
14610 is used in combination with the command
14624 \begin_inset CommandInset ref
14626 reference "subsec:User-defined-Numbering"
14633 \begin_layout Standard
14634 An example of a formula commented with
14643 \begin_layout Standard
14647 \begin_layout Plain Layout
14660 This is a description.
14661 It is distinctly separated from the formula and multiline.
14665 \begin_layout Plain Layout
14677 \begin_layout Standard
14678 Such a formula must be inserted completely in \SpecialChar TeX
14679 mode because \SpecialChar LyX
14681 support the command
14688 The formula is created with the following command sequence:
14691 \begin_layout Standard
14704 is inserted in \SpecialChar TeX
14709 \begin_layout Plain Layout
14710 When the formula style
14722 can also be replaced by
14729 (formula styles see
14730 \begin_inset CommandInset ref
14732 reference "sec:Formula-Styles"
14741 Then the description follows as normal text and finally
14747 is inserted in \SpecialChar TeX
14761 hereby create a displayed formula.
14764 \begin_layout Standard
14771 can be seen in this example that was
14772 \begin_inset Quotes eld
14776 \begin_inset Quotes erd
14779 using the mathematical textmode:
14780 \begin_inset Formula
14782 5x-7b=3b\textrm{This is a description. It is not separated from the formula ...}
14790 \begin_layout Section
14792 \begin_inset Index idx
14795 \begin_layout Plain Layout
14804 \begin_layout Subsection
14806 \begin_inset CommandInset label
14808 name "subsec:Big-Operators"
14813 \begin_inset Index idx
14816 \begin_layout Plain Layout
14823 \begin_inset Index idx
14826 \begin_layout Plain Layout
14833 \begin_inset Index idx
14836 \begin_layout Plain Layout
14845 \begin_layout Standard
14846 To be able to use all integral operators listed here, the option
14848 Use esint package automatically
14850 must be set in the document settings under
14853 \begin_inset space ~
14861 \begin_layout Standard
14862 \begin_inset space \hfill{}
14866 \begin_inset Tabular
14867 <lyxtabular version="3" rows="11" columns="2">
14868 <features booktabs="true" tabularvalignment="middle">
14869 <column alignment="center" valignment="top" width="0pt">
14870 <column alignment="center" valignment="top" width="0pt">
14872 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
14875 \begin_layout Plain Layout
14881 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
14884 \begin_layout Plain Layout
14892 <cell alignment="center" valignment="top" leftline="true" usebox="none">
14895 \begin_layout Plain Layout
14899 \begin_inset Index idx
14902 \begin_layout Plain Layout
14915 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
14918 \begin_layout Plain Layout
14919 \begin_inset Formula $\int$
14929 <cell alignment="center" valignment="top" leftline="true" usebox="none">
14932 \begin_layout Plain Layout
14940 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
14943 \begin_layout Plain Layout
14944 \begin_inset Formula $\oint$
14954 <cell alignment="center" valignment="top" leftline="true" usebox="none">
14957 \begin_layout Plain Layout
14965 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
14968 \begin_layout Plain Layout
14969 \begin_inset Formula $\ointctrclockwise$
14979 <cell alignment="center" valignment="top" leftline="true" usebox="none">
14982 \begin_layout Plain Layout
14990 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
14993 \begin_layout Plain Layout
14994 \begin_inset Formula $\ointclockwise$
15004 <cell alignment="center" valignment="top" leftline="true" usebox="none">
15007 \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 $\sqint$
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
15045 \begin_inset Formula $\fint$
15055 <cell alignment="center" valignment="top" leftline="true" usebox="none">
15058 \begin_layout Plain Layout
15066 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
15069 \begin_layout Plain Layout
15071 \begin_inset Formula $\landupint$
15081 <cell alignment="center" valignment="top" leftline="true" usebox="none">
15084 \begin_layout Plain Layout
15092 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
15095 \begin_layout Plain Layout
15097 \begin_inset Formula $\landdownint$
15107 <cell alignment="center" valignment="top" leftline="true" usebox="none">
15110 \begin_layout Plain Layout
15118 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
15121 \begin_layout Plain Layout
15122 \begin_inset Formula $\bigcap$
15132 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
15135 \begin_layout Plain Layout
15143 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
15146 \begin_layout Plain Layout
15147 \begin_inset Formula $\bigcup$
15161 \begin_inset space \hfill{}
15165 \begin_inset Tabular
15166 <lyxtabular version="3" rows="11" columns="2">
15167 <features booktabs="true" tabularvalignment="middle">
15168 <column alignment="center" valignment="top" width="0pt">
15169 <column alignment="center" valignment="top" width="0pt">
15171 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
15174 \begin_layout Plain Layout
15180 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
15183 \begin_layout Plain Layout
15191 <cell alignment="center" valignment="top" leftline="true" usebox="none">
15194 \begin_layout Plain Layout
15198 \begin_inset Index idx
15201 \begin_layout Plain Layout
15214 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
15217 \begin_layout Plain Layout
15218 \begin_inset Formula $\sum$
15228 <cell alignment="center" valignment="top" leftline="true" usebox="none">
15231 \begin_layout Plain Layout
15235 \begin_inset Index idx
15238 \begin_layout Plain Layout
15245 \begin_layout Plain Layout
15264 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
15267 \begin_layout Plain Layout
15268 \begin_inset Formula $\prod$
15278 <cell alignment="center" valignment="top" leftline="true" usebox="none">
15281 \begin_layout Plain Layout
15289 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
15292 \begin_layout Plain Layout
15293 \begin_inset Formula $\coprod$
15303 <cell alignment="center" valignment="top" leftline="true" usebox="none">
15306 \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 $\bigodot$
15328 <cell alignment="center" valignment="top" leftline="true" usebox="none">
15331 \begin_layout Plain Layout
15339 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
15342 \begin_layout Plain Layout
15343 \begin_inset Formula $\bigotimes$
15353 <cell alignment="center" valignment="top" leftline="true" usebox="none">
15356 \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 $\bigoplus$
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 $\bigwedge$
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 $\bigvee$
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 $\bigsqcup$
15453 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
15456 \begin_layout Plain Layout
15464 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
15467 \begin_layout Plain Layout
15468 \begin_inset Formula $\biguplus$
15482 \begin_inset space \hfill{}
15488 \begin_layout Standard
15489 All big operators can also be inserted via the math toolbar button
15492 arg "math-insert \\intop"
15498 \begin_layout Standard
15499 The operators are called big because they are bigger than the sometimes
15500 equal looking binary operators.
15501 All big operators can have limits as described in the next subsection.
15504 \begin_layout Standard
15505 For all integral operators there is a second version available, ending in
15523 These operators are different from
15530 \begin_inset space \space{}
15533 in the style the operator limits are displayed, see
15534 \begin_inset CommandInset ref
15536 reference "subsec:Operator-Limits"
15544 \begin_layout Subsubsection*
15545 Advice for Integrals
15548 \begin_layout Standard
15553 in an integral is an operator, that therefore has to be set upright.
15554 This is done by highlighting the
15558 and using the keyboard shortcut
15568 \begin_layout Plain Layout
15574 \begin_inset CommandInset ref
15576 reference "subsec:Font-Styles"
15586 Finally the smallest space is inserted before the
15590 , as this is usual for operators.
15594 \begin_layout Standard
15596 \begin_inset Formula $\int A(x)dx$
15600 \begin_inset Newline newline
15604 \begin_inset Phantom HPhantom
15607 \begin_layout Plain Layout
15614 \begin_inset Formula $\int A(x)\,\mathrm{d}x$
15620 \begin_layout Standard
15621 For multiple integrals there are the following commands:
15622 \begin_inset VSpace medskip
15628 \begin_layout Standard
15629 \begin_inset space \hfill{}
15633 \begin_inset Tabular
15634 <lyxtabular version="3" rows="4" columns="2">
15635 <features booktabs="true" tabularvalignment="middle">
15636 <column alignment="center" valignment="top" width="0pt">
15637 <column alignment="center" valignment="top" width="0pt">
15639 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
15642 \begin_layout Plain Layout
15648 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
15651 \begin_layout Plain Layout
15658 <row bottomspace="1mm">
15659 <cell alignment="center" valignment="top" usebox="none">
15662 \begin_layout Plain Layout
15670 <cell alignment="center" valignment="top" usebox="none">
15673 \begin_layout Plain Layout
15674 \begin_inset Formula $\iint$
15683 <row bottomspace="1mm">
15684 <cell alignment="center" valignment="top" usebox="none">
15687 \begin_layout Plain Layout
15695 <cell alignment="center" valignment="top" usebox="none">
15698 \begin_layout Plain Layout
15699 \begin_inset Formula $\oiint$
15708 <row bottomspace="1mm">
15709 <cell alignment="center" valignment="top" bottomline="true" usebox="none">
15712 \begin_layout Plain Layout
15720 <cell alignment="center" valignment="top" bottomline="true" usebox="none">
15723 \begin_layout Plain Layout
15724 \begin_inset Formula $\sqiint$
15738 \begin_inset space \hfill{}
15742 \begin_inset Tabular
15743 <lyxtabular version="3" rows="4" columns="2">
15744 <features booktabs="true" tabularvalignment="middle">
15745 <column alignment="center" valignment="top" width="0pt">
15746 <column alignment="center" valignment="top" width="0pt">
15748 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
15751 \begin_layout Plain Layout
15757 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
15760 \begin_layout Plain Layout
15767 <row bottomspace="1mm">
15768 <cell alignment="center" valignment="top" usebox="none">
15771 \begin_layout Plain Layout
15779 <cell alignment="center" valignment="top" usebox="none">
15782 \begin_layout Plain Layout
15783 \begin_inset Formula $\iiint$
15792 <row bottomspace="1mm">
15793 <cell alignment="center" valignment="top" usebox="none">
15796 \begin_layout Plain Layout
15804 <cell alignment="center" valignment="top" usebox="none">
15807 \begin_layout Plain Layout
15808 \begin_inset Formula $\iiiint$
15817 <row bottomspace="1mm">
15818 <cell alignment="center" valignment="top" bottomline="true" usebox="none">
15821 \begin_layout Plain Layout
15829 <cell alignment="center" valignment="top" bottomline="true" usebox="none">
15832 \begin_layout Plain Layout
15833 \begin_inset Formula $\dotsint$
15847 \begin_inset space \hfill{}
15853 \begin_layout Subsection
15855 \begin_inset CommandInset label
15857 name "subsec:Operator-Limits"
15862 \begin_inset Index idx
15865 \begin_layout Plain Layout
15874 \begin_layout Standard
15875 Limits are created by super- and subscripts:
15878 \begin_layout Standard
15880 \begin_inset Tabular
15881 <lyxtabular version="3" rows="2" columns="2">
15882 <features booktabs="true" tabularvalignment="middle">
15883 <column alignment="center" valignment="top" width="0pt">
15884 <column alignment="center" valignment="top" width="0pt">
15886 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
15889 \begin_layout Plain Layout
15895 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
15898 \begin_layout Plain Layout
15906 <cell alignment="center" valignment="top" bottomline="true" usebox="none">
15909 \begin_layout Plain Layout
15915 \begin_inset space \textvisiblespace{}
15919 \begin_inset Formula $\to$
15923 \begin_inset Formula $\to$
15931 <cell alignment="center" valignment="top" bottomline="true" usebox="none">
15934 \begin_layout Plain Layout
15935 \begin_inset Formula $\prod_{0}^{\infty}A(x)$
15951 \begin_layout Standard
15952 Limits of inline formulas are set right beside the operator.
15953 Limits in displayed formulas are set above or below the operator, except
15954 for integral limits.
15957 \begin_layout Standard
15958 To force that the limits are set beside the operator, the cursor is set
15959 directly behind the operator and the limits type is changed with the menu
15962 Edit\SpecialChar menuseparator
15963 Math\SpecialChar menuseparator
15982 \begin_layout Standard
15983 The default limits type is this:
15984 \begin_inset Formula
15986 \sum_{x=0}^{\infty}\frac{1}{x^{2}}
15991 This is how it looks when the limits type was changed to
15998 \begin_inset Formula
16000 \sum\nolimits _{x=0}^{\infty}\frac{1}{x^{2}}
16005 For integrals, except those ending with
16021 etc., the limits are by default set beside the operator.
16022 But for multiple integrals the limits are often set below the operator.
16023 In the following example the limits type was therefore set to
16027 and so set below the integrals:
16028 \begin_inset Formula
16030 \iiint\limits _{V}X\,\mathrm{d}V=U\label{eq:VolInt}
16038 \begin_layout Standard
16039 \begin_inset VSpace medskip
16042 To specify conditions for limits, the commands
16049 \begin_inset Index idx
16052 \begin_layout Plain Layout
16067 \begin_inset Index idx
16070 \begin_layout Plain Layout
16079 To create for example this expression
16080 \begin_inset Formula
16082 \sum_{\begin{subarray}{c}
16086 \end{subarray}}^{n}k^{-2}\label{eq:substack}
16094 \begin_layout Standard
16095 the following has to be done:
16096 \begin_inset Newline newline
16108 \begin_inset space \textvisiblespace{}
16114 One is now in a blue box under the summation operator and insert there
16120 \begin_inset space \textvisiblespace{}
16126 The blue box is now within a purple box and now several lines can be written
16128 A new line is created by inserting a line break (
16131 arg "newline-insert newline"
16136 \begin_inset Newline newline
16141 0<k<1000 Ctrl+Return
16142 \begin_inset Newline newline
16147 is typed in, a new box appears below for the new line.
16150 \begin_layout Standard
16151 The alignment of the lines can be changed to left aligned with the
16161 Edit\SpecialChar menuseparator
16165 To get right alignment,
16170 \begin_inset space \textvisiblespace{}
16175 is inserted at the beginning of the line.
16178 \begin_layout Standard
16191 with the difference that the lines are always centered.
16194 \begin_layout Standard
16195 \begin_inset VSpace bigskip
16199 \begin_inset CommandInset ref
16201 reference "eq:substack"
16205 there can be too much space beside an operator, because the characters
16206 following the operator are set beside the limits.
16207 To avoid this the command
16214 \begin_inset Index idx
16217 \begin_layout Plain Layout
16226 To activate it, set in the document settings under
16229 \begin_inset space ~
16239 \begin_inset Index idx
16242 \begin_layout Plain Layout
16243 Packages ! mathtools
16251 \begin_inset space ~
16263 sets the space besides the operator to 0
16264 \begin_inset space \thinspace{}
16268 \begin_inset Newline newline
16272 \begin_inset CommandInset ref
16274 reference "eq:substack"
16278 , one uses the command
16281 \begin_layout Standard
16289 \begin_layout Standard
16290 and inserts the operator with its limits into the braces.
16291 Behind the brace one continues the formula:
16292 \begin_inset Formula
16294 \smashoperator{\sum_{\begin{subarray}{c}
16298 \end{subarray}}^{n}}k^{-2}
16306 \begin_layout Standard
16307 It is possible to set the space of only one side of the operator to 0
16308 \begin_inset space \thinspace{}
16312 To do this write either
16331 stands for the left and
16335 for the right side of the operator.
16336 Here is an example of the possible
16345 \begin_layout Standard
16346 \begin_inset Formula
16348 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}
16356 \begin_layout Standard
16357 \begin_inset VSpace bigskip
16363 \begin_layout Standard
16364 When several consecutive operators have limits the typesetting of the limits
16365 looks often imperfect in the output, see this example:
16366 \begin_inset Formula
16368 \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}
16373 To improve the typesetting set in the document settings under
16376 \begin_inset space ~
16386 \begin_inset Index idx
16389 \begin_layout Plain Layout
16390 Packages ! mathtools
16398 \begin_inset space ~
16404 Then insert into your formula the command
16411 \begin_inset Index idx
16414 \begin_layout Plain Layout
16422 directly before the first operator.
16423 The example will then look like this:
16424 \begin_inset Formula
16426 \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}
16434 \begin_layout Standard
16435 \begin_inset VSpace bigskip
16438 How to use one limit for several operators is described in
16439 \begin_inset CommandInset ref
16441 reference "subsec:Self-defined-Operators"
16448 \begin_layout Subsection
16449 Decoration for Operators
16450 \begin_inset Index idx
16453 \begin_layout Plain Layout
16454 Operators ! Decoration
16462 \begin_layout Standard
16470 \begin_inset Index idx
16473 \begin_layout Plain Layout
16488 \begin_inset Index idx
16491 \begin_layout Plain Layout
16499 characters can be placed above or below an operator, respectively.
16507 \begin_inset Index idx
16510 \begin_layout Plain Layout
16518 characters can be set before and behind a big operator.
16521 \begin_layout Standard
16523 \begin_inset space ~
16535 \begin_layout Itemize
16542 is used to set characters at the corners of the operator
16545 \begin_layout Itemize
16552 is used to set characters before and/or behind the operator (this variant
16553 represents \SpecialChar LaTeX
16563 \begin_layout Itemize
16570 is used to set characters at the left corners and/or behind the operator
16573 \begin_layout Itemize
16580 is used to set characters at the right corners and/or before the operator
16583 \begin_layout Standard
16584 For example the command
16589 \begin_inset space \textvisiblespace{}
16595 \begin_inset space \textvisiblespace{}
16599 \begin_inset Formula $\to$
16603 \begin_inset Formula $\to$
16607 \begin_inset space \textvisiblespace{}
16617 \begin_inset Formula
16619 \sideset{}{'}\sum_{k=1}^{n}
16627 \begin_layout Standard
16628 \begin_inset Note Greyedout
16631 \begin_layout Plain Layout
16638 can only be used to decorate big operators, binary operators are not allowed.
16646 \begin_layout Standard
16659 can also be used to decorate symbols and characters.
16660 For example, the command
16665 \begin_inset space \textvisiblespace{}
16671 \begin_inset space \textvisiblespace{}
16677 \begin_inset Formula $\uparrow$
16685 \begin_inset Formula
16687 \overset{a}{\maltese}
16695 \begin_layout Subsection
16697 \begin_inset CommandInset label
16699 name "subsec:Binary-Operators"
16704 \begin_inset Index idx
16707 \begin_layout Plain Layout
16716 \begin_layout Standard
16717 Binary operators are surrounded by space when there is a character before
16719 \begin_inset VSpace medskip
16725 \begin_layout Standard
16726 \begin_inset Tabular
16727 <lyxtabular version="3" rows="13" columns="2">
16728 <features booktabs="true" tabularvalignment="middle">
16729 <column alignment="center" valignment="top" width="0pt">
16730 <column alignment="center" valignment="top" width="0pt">
16732 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
16735 \begin_layout Plain Layout
16737 \begin_inset Note Note
16740 \begin_layout Plain Layout
16747 is only used as spacer.
16757 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
16760 \begin_layout Plain Layout
16768 <cell alignment="center" valignment="top" leftline="true" usebox="none">
16771 \begin_layout Plain Layout
16777 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
16780 \begin_layout Plain Layout
16781 \begin_inset Formula $+$
16791 <cell alignment="center" valignment="top" leftline="true" usebox="none">
16794 \begin_layout Plain Layout
16800 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
16803 \begin_layout Plain Layout
16804 \begin_inset Formula $-$
16814 <cell alignment="center" valignment="top" leftline="true" usebox="none">
16817 \begin_layout Plain Layout
16825 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
16828 \begin_layout Plain Layout
16829 \begin_inset Formula $\pm$
16839 <cell alignment="center" valignment="top" leftline="true" usebox="none">
16842 \begin_layout Plain Layout
16850 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
16853 \begin_layout Plain Layout
16854 \begin_inset Formula $\mp$
16864 <cell alignment="center" valignment="top" leftline="true" usebox="none">
16867 \begin_layout Plain Layout
16875 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
16878 \begin_layout Plain Layout
16879 \begin_inset Formula $\cdot$
16889 <cell alignment="center" valignment="top" leftline="true" usebox="none">
16892 \begin_layout Plain Layout
16900 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
16903 \begin_layout Plain Layout
16904 \begin_inset Formula $\times$
16914 <cell alignment="center" valignment="top" leftline="true" usebox="none">
16917 \begin_layout Plain Layout
16925 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
16928 \begin_layout Plain Layout
16929 \begin_inset Formula $\div$
16939 <cell alignment="center" valignment="top" leftline="true" usebox="none">
16942 \begin_layout Plain Layout
16946 \begin_layout Plain Layout
16959 \begin_layout Plain Layout
16971 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
16974 \begin_layout Plain Layout
16975 \begin_inset Formula $*$
16985 <cell alignment="center" valignment="top" leftline="true" usebox="none">
16988 \begin_layout Plain Layout
16996 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
16999 \begin_layout Plain Layout
17000 \begin_inset Formula $\star$
17010 <cell alignment="center" valignment="top" leftline="true" usebox="none">
17013 \begin_layout Plain Layout
17021 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
17024 \begin_layout Plain Layout
17025 \begin_inset Formula $\circ$
17035 <cell alignment="center" valignment="top" leftline="true" usebox="none">
17038 \begin_layout Plain Layout
17046 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
17049 \begin_layout Plain Layout
17050 \begin_inset Formula $\diamond$
17060 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
17063 \begin_layout Plain Layout
17071 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
17074 \begin_layout Plain Layout
17075 \begin_inset Formula $\bullet$
17089 \begin_inset space \hfill{}
17093 \begin_inset Tabular
17094 <lyxtabular version="3" rows="13" columns="2">
17095 <features booktabs="true" tabularvalignment="middle">
17096 <column alignment="center" valignment="top" width="0pt">
17097 <column alignment="center" valignment="top" width="0pt">
17099 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
17102 \begin_layout Plain Layout
17108 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
17111 \begin_layout Plain Layout
17119 <cell alignment="center" valignment="top" leftline="true" usebox="none">
17122 \begin_layout Plain Layout
17130 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
17133 \begin_layout Plain Layout
17134 \begin_inset Formula $\nabla$
17144 <cell alignment="center" valignment="top" leftline="true" usebox="none">
17147 \begin_layout Plain Layout
17155 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
17158 \begin_layout Plain Layout
17159 \begin_inset Formula $\bigtriangledown$
17169 <cell alignment="center" valignment="top" leftline="true" usebox="none">
17172 \begin_layout Plain Layout
17180 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
17183 \begin_layout Plain Layout
17184 \begin_inset Formula $\bigtriangleup$
17194 <cell alignment="center" valignment="top" leftline="true" usebox="none">
17197 \begin_layout Plain Layout
17205 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
17208 \begin_layout Plain Layout
17209 \begin_inset Formula $\Box$
17219 <cell alignment="center" valignment="top" leftline="true" usebox="none">
17222 \begin_layout Plain Layout
17230 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
17233 \begin_layout Plain Layout
17234 \begin_inset Formula $\cap$
17244 <cell alignment="center" valignment="top" leftline="true" usebox="none">
17247 \begin_layout Plain Layout
17255 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
17258 \begin_layout Plain Layout
17259 \begin_inset Formula $\cup$
17269 <cell alignment="center" valignment="top" leftline="true" usebox="none">
17272 \begin_layout Plain Layout
17280 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
17283 \begin_layout Plain Layout
17284 \begin_inset Formula $\dagger$
17294 <cell alignment="center" valignment="top" leftline="true" usebox="none">
17297 \begin_layout Plain Layout
17305 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
17308 \begin_layout Plain Layout
17309 \begin_inset Formula $\ddagger$
17319 <cell alignment="center" valignment="top" leftline="true" usebox="none">
17322 \begin_layout Plain Layout
17330 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
17333 \begin_layout Plain Layout
17334 \begin_inset Formula $\wr$
17344 <cell alignment="center" valignment="top" leftline="true" usebox="none">
17347 \begin_layout Plain Layout
17355 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
17358 \begin_layout Plain Layout
17359 \begin_inset Formula $\bigcirc$
17369 <cell alignment="center" valignment="top" leftline="true" usebox="none">
17372 \begin_layout Plain Layout
17380 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
17383 \begin_layout Plain Layout
17384 \begin_inset Formula $\wedge$
17394 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
17397 \begin_layout Plain Layout
17405 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
17408 \begin_layout Plain Layout
17409 \begin_inset Formula $\vee$
17423 \begin_inset space \hfill{}
17427 \begin_inset Tabular
17428 <lyxtabular version="3" rows="13" columns="2">
17429 <features booktabs="true" tabularvalignment="middle">
17430 <column alignment="center" valignment="top" width="0pt">
17431 <column alignment="center" valignment="top" width="0pt">
17433 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
17436 \begin_layout Plain Layout
17442 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
17445 \begin_layout Plain Layout
17453 <cell alignment="center" valignment="top" leftline="true" usebox="none">
17456 \begin_layout Plain Layout
17464 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
17467 \begin_layout Plain Layout
17468 \begin_inset Formula $\oplus$
17478 <cell alignment="center" valignment="top" leftline="true" usebox="none">
17481 \begin_layout Plain Layout
17489 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
17492 \begin_layout Plain Layout
17493 \begin_inset Formula $\ominus$
17503 <cell alignment="center" valignment="top" leftline="true" usebox="none">
17506 \begin_layout Plain Layout
17514 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
17517 \begin_layout Plain Layout
17518 \begin_inset Formula $\otimes$
17528 <cell alignment="center" valignment="top" leftline="true" usebox="none">
17531 \begin_layout Plain Layout
17539 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
17542 \begin_layout Plain Layout
17543 \begin_inset Formula $\oslash$
17553 <cell alignment="center" valignment="top" leftline="true" usebox="none">
17556 \begin_layout Plain Layout
17564 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
17567 \begin_layout Plain Layout
17568 \begin_inset Formula $\odot$
17578 <cell alignment="center" valignment="top" leftline="true" usebox="none">
17581 \begin_layout Plain Layout
17589 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
17592 \begin_layout Plain Layout
17593 \begin_inset Formula $\amalg$
17603 <cell alignment="center" valignment="top" leftline="true" usebox="none">
17606 \begin_layout Plain Layout
17614 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
17617 \begin_layout Plain Layout
17618 \begin_inset Formula $\uplus$
17628 <cell alignment="center" valignment="top" leftline="true" usebox="none">
17631 \begin_layout Plain Layout
17639 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
17642 \begin_layout Plain Layout
17643 \begin_inset Formula $\setminus$
17653 <cell alignment="center" valignment="top" leftline="true" usebox="none">
17656 \begin_layout Plain Layout
17664 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
17667 \begin_layout Plain Layout
17668 \begin_inset Formula $\sqcap$
17678 <cell alignment="center" valignment="top" leftline="true" usebox="none">
17681 \begin_layout Plain Layout
17689 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
17692 \begin_layout Plain Layout
17693 \begin_inset Formula $\sqcup$
17703 <cell alignment="center" valignment="top" leftline="true" usebox="none">
17706 \begin_layout Plain Layout
17714 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
17717 \begin_layout Plain Layout
17718 \begin_inset Formula $\triangleleft$
17728 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
17731 \begin_layout Plain Layout
17739 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
17742 \begin_layout Plain Layout
17743 \begin_inset Formula $\triangleright$
17759 \begin_layout Standard
17760 All binary operators can also be inserted via the math toolbar button
17763 arg "math-insert \\pm"
17769 \begin_layout Standard
17770 To typeset the Laplace operator also
17787 \begin_inset Formula $\nabla^{2}$
17790 ) can be used instead of
17799 \begin_layout Standard
17806 Insert\SpecialChar menuseparator
17818 \begin_layout Subsection
17819 Self-defined Operators
17820 \begin_inset CommandInset label
17822 name "subsec:Self-defined-Operators"
17827 \begin_inset Index idx
17830 \begin_layout Plain Layout
17831 Operators ! self-defined
17839 \begin_layout Standard
17840 With the help of the command
17844 DeclareMathOperator
17847 \begin_inset Index idx
17850 \begin_layout Plain Layout
17855 DeclareMathOperator
17860 custom operators can be defined in the \SpecialChar LaTeX
17862 Its command scheme is:
17865 \begin_layout Standard
17870 DeclareMathOperator{new command}{display}
17873 \begin_layout Standard
17874 Display can be characters or symbols that define how the operator looks
17876 To define a big operator a * is set behind the command.
17877 All self-defined big operators can have limits as described in
17878 \begin_inset CommandInset ref
17880 reference "subsec:Operator-Limits"
17887 \begin_layout Standard
17888 For example the \SpecialChar LaTeX
17892 \begin_layout Standard
17897 DeclareMathOperator*{
17904 \begin_layout Standard
17905 defines the command
17911 , that inserts a big operator consisting of the lozenge symbol from
17912 \begin_inset CommandInset ref
17914 reference "subsec:Miscellaneous-Symbols"
17919 \begin_inset Formula
17921 \Lozenge_{n=1}^{\infty}
17926 The command for this formula is:
17937 \begin_inset Formula $\to$
17943 \begin_layout Standard
17944 \begin_inset VSpace bigskip
17947 When self-defined operators are not used several times in the document,
17948 they can also be defined with the commands
17955 \begin_inset Index idx
17958 \begin_layout Plain Layout
17973 \begin_inset Index idx
17976 \begin_layout Plain Layout
17984 , which have the following scheme:
17987 \begin_layout Standard
18001 \begin_layout Standard
18008 defines big operators,
18017 \begin_layout Standard
18025 \begin_inset space \thinspace{}
18029 \begin_inset space \space{}
18032 be used to use one limit for several operators:
18035 \begin_layout Standard
18036 \begin_inset Formula
18038 \mathop{\sum\negmedspace\sum}_{i,j=1}^{N}
18046 \begin_layout Standard
18047 The command for the formula above is:
18048 \begin_inset Newline newline
18064 \begin_inset space \textvisiblespace{}
18070 \begin_inset Formula $\to$
18076 \begin_inset space \textvisiblespace{}
18084 \begin_layout Section
18086 \begin_inset Index idx
18089 \begin_layout Plain Layout
18098 \begin_layout Subsection
18100 \begin_inset CommandInset label
18102 name "subsec:Font-Styles"
18107 \begin_inset Index idx
18110 \begin_layout Plain Layout
18119 \begin_layout Standard
18120 Latin letters in formulas can be set in one of the following font styles:
18123 \begin_layout Standard
18125 \begin_inset Tabular
18126 <lyxtabular version="3" rows="6" columns="3">
18127 <features booktabs="true" tabularvalignment="middle">
18128 <column alignment="center" valignment="top" width="0pt">
18129 <column alignment="center" valignment="top">
18130 <column alignment="center" valignment="top">
18132 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
18135 \begin_layout Plain Layout
18141 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
18144 \begin_layout Plain Layout
18150 <cell alignment="center" valignment="top" topline="true" bottomline="true" usebox="none">
18153 \begin_layout Plain Layout
18161 <cell alignment="center" valignment="top" leftline="true" usebox="none">
18164 \begin_layout Plain Layout
18170 \begin_inset space \textvisiblespace{}
18180 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
18183 \begin_layout Plain Layout
18184 \begin_inset Formula $\mathbb{ABC}$
18192 <cell alignment="center" valignment="top" usebox="none">
18195 \begin_layout Plain Layout
18203 <cell alignment="center" valignment="top" leftline="true" usebox="none">
18206 \begin_layout Plain Layout
18212 \begin_inset space \textvisiblespace{}
18222 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
18225 \begin_layout Plain Layout
18226 \begin_inset Formula $\mathbf{AbC}$
18234 <cell alignment="center" valignment="top" usebox="none">
18237 \begin_layout Plain Layout
18250 <cell alignment="center" valignment="top" leftline="true" usebox="none">
18253 \begin_layout Plain Layout
18259 \begin_inset space \textvisiblespace{}
18269 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
18272 \begin_layout Plain Layout
18273 \begin_inset Formula $\boldsymbol{AbC}$
18281 <cell alignment="center" valignment="top" usebox="none">
18284 \begin_layout Plain Layout
18287 arg "font-boldsymbol"
18297 <cell alignment="center" valignment="top" leftline="true" usebox="none">
18300 \begin_layout Plain Layout
18306 \begin_inset space \textvisiblespace{}
18316 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
18319 \begin_layout Plain Layout
18320 \begin_inset Formula $\mathcal{ABC}$
18328 <cell alignment="center" valignment="top" usebox="none">
18331 \begin_layout Plain Layout
18339 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
18342 \begin_layout Plain Layout
18348 \begin_inset space \textvisiblespace{}
18358 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
18361 \begin_layout Plain Layout
18362 \begin_inset Formula $\mathfrak{AbC}$
18370 <cell alignment="center" valignment="top" bottomline="true" usebox="none">
18373 \begin_layout Plain Layout
18387 \begin_layout Standard
18389 \begin_inset Tabular
18390 <lyxtabular version="3" rows="6" columns="3">
18391 <features booktabs="true" tabularvalignment="middle">
18392 <column alignment="center" valignment="top" width="0pt">
18393 <column alignment="center" valignment="top">
18394 <column alignment="center" valignment="top">
18396 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
18399 \begin_layout Plain Layout
18405 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
18408 \begin_layout Plain Layout
18414 <cell alignment="center" valignment="top" topline="true" bottomline="true" usebox="none">
18417 \begin_layout Plain Layout
18425 <cell alignment="center" valignment="top" leftline="true" usebox="none">
18428 \begin_layout Plain Layout
18434 \begin_inset space \textvisiblespace{}
18444 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
18447 \begin_layout Plain Layout
18448 \begin_inset Formula $\mathit{AbC}$
18456 <cell alignment="center" valignment="top" usebox="none">
18459 \begin_layout Plain Layout
18467 <cell alignment="center" valignment="top" leftline="true" usebox="none">
18470 \begin_layout Plain Layout
18476 \begin_inset space \textvisiblespace{}
18486 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
18489 \begin_layout Plain Layout
18490 \begin_inset Formula $\mathrm{AbC}$
18498 <cell alignment="center" valignment="top" usebox="none">
18501 \begin_layout Plain Layout
18514 <cell alignment="center" valignment="top" leftline="true" usebox="none">
18517 \begin_layout Plain Layout
18523 \begin_inset space \textvisiblespace{}
18533 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
18536 \begin_layout Plain Layout
18537 \begin_inset Formula $\mathsf{AbC}$
18545 <cell alignment="center" valignment="top" usebox="none">
18548 \begin_layout Plain Layout
18561 <cell alignment="center" valignment="top" leftline="true" usebox="none">
18564 \begin_layout Plain Layout
18570 \begin_inset space \textvisiblespace{}
18580 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
18583 \begin_layout Plain Layout
18584 \begin_inset Formula $\mathtt{AbC}$
18592 <cell alignment="center" valignment="top" usebox="none">
18595 \begin_layout Plain Layout
18598 arg "font-typewriter"
18608 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
18611 \begin_layout Plain Layout
18617 \begin_inset space \textvisiblespace{}
18627 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
18630 \begin_layout Plain Layout
18631 \begin_inset Formula $\mathscr{ABC}$
18639 <cell alignment="center" valignment="top" bottomline="true" usebox="none">
18642 \begin_layout Plain Layout
18656 \begin_layout Standard
18657 \begin_inset Note Greyedout
18660 \begin_layout Plain Layout
18683 can only be used for big letters.
18691 \begin_layout Standard
18692 Predefined is the style
18701 \begin_layout Standard
18702 The style commands work also for letters in mathematical constructs:
18703 \begin_inset Formula
18705 \mathfrak{A=\frac{b}{C}}
18713 \begin_layout Standard
18714 Characters in mathematical text don't appear in a math font style but in
18715 the text font style
18722 That their style can't be set correctly via the text style dialog is a
18723 bug in \SpecialChar LyX
18728 \begin_layout Plain Layout
18729 \begin_inset CommandInset href
18731 name "LyX-bug #4629"
18732 target "http://www.lyx.org/trac/ticket/4629"
18744 \begin_layout Standard
18745 Instead of the style commands the dialog
18747 Edit\SpecialChar menuseparator
18748 Math\SpecialChar menuseparator
18751 or the toolbar button
18754 arg "math-insert \\font"
18760 \begin_layout Subsection
18762 \begin_inset CommandInset label
18764 name "subsec:Bold-Formulas"
18769 \begin_inset Index idx
18772 \begin_layout Plain Layout
18781 \begin_layout Standard
18782 To make a complete formula bold, the command
18788 from the previous subsection cannot be used, because it doesn't work for
18789 small Greek letters.
18790 Furthermore it prints Latin letters always upright, like in the following
18794 \begin_layout Standard
18795 \begin_inset Formula
18797 \mathbf{\int_{n}^{2}f(\theta)=\Gamma}\qquad\textrm{equation with \textbackslash mathbf}
18805 \begin_layout Standard
18806 To display the formula correctly, the command
18813 \begin_inset Formula
18815 \boldsymbol{\int_{n}^{2}f(\theta)=\Gamma\qquad\textrm{equation with \textbackslash boldsymbol}}
18820 It is also possible to set the formula in a
18822 boldmath environment
18825 This environment is created by inserting the command
18832 \begin_inset Index idx
18835 \begin_layout Plain Layout
18843 in \SpecialChar TeX
18845 To end the environment, the command
18852 \begin_inset Index idx
18855 \begin_layout Plain Layout
18863 is inserted in \SpecialChar TeX
18868 \begin_layout Plain Layout
18878 \begin_inset Formula
18880 \int_{n}^{2}f(\theta)=\Gamma\qquad\textrm{equation in a boldmath environment}
18889 \begin_layout Plain Layout
18901 \begin_layout Subsection
18903 \begin_inset Index idx
18906 \begin_layout Plain Layout
18915 \begin_layout Standard
18916 Formulas can be colored like normal text: Highlight a formula or a formula
18922 Here is a formula in magenta:
18923 \begin_inset Formula
18925 {\color{magenta}\int A\,\mathrm{d}x=\frac{\sqrt[5]{B}}{\ln\left(\frac{1}{3}\right)}}
18933 \begin_layout Standard
18934 You can also define your own colors as described in
18935 \begin_inset CommandInset ref
18937 reference "subsec:Colored-Boxes"
18942 They can be used with the \SpecialChar TeX
18950 \begin_inset Index idx
18953 \begin_layout Plain Layout
18964 \begin_layout Standard
18969 textcolor{color}{characters or formula}
18972 \begin_layout Standard
18973 The following example was colored completely dark green and partly red:
18976 \begin_layout Standard
18980 \begin_layout Plain Layout
18984 textcolor{darkgreen}{
18990 \begin_inset Formula
18992 \int A\,\mathrm{d}x=\frac{{\color{red}\sqrt[5]{B}}}{\ln\left(\frac{1}{3}\right)}
19001 \begin_layout Plain Layout
19011 \begin_layout Standard
19012 Due to a bug in \SpecialChar LyX
19013 only complete formulas can be colored with self-defined
19018 \begin_layout Plain Layout
19019 \begin_inset CommandInset href
19021 name "LyX-bug #5269"
19022 target "http://www.lyx.org/trac/ticket/5269"
19034 \begin_layout Subsection
19036 \begin_inset CommandInset label
19038 name "subsec:Font-Sizes"
19043 \begin_inset Index idx
19046 \begin_layout Plain Layout
19055 \begin_layout Standard
19056 For characters in formulas there are, analog to characters in text, the
19057 following size commands:
19060 \begin_layout Standard
19104 \begin_inset Newline newline
19126 \begin_layout Standard
19127 The size produced by the commands depends on the document font size, which
19128 corresponds to the command
19135 The other commands produce smaller or larger sizes than
19142 The font size can however not exceed a certain value.
19143 Is for example the document font size 12
19144 \begin_inset space \thinspace{}
19153 switches to the same size as
19163 \begin_layout Standard
19164 A size command is inserted in \SpecialChar TeX
19165 mode before the formula and sets the size
19166 for all following formula and text characters.
19167 To switch back to the initial size, the command
19173 is inserted behind the formula in \SpecialChar TeX
19177 \begin_layout Standard
19178 Within a formula the size can be changed using the following size commands
19179 or the toolbar button
19182 arg "math-insert \\style"
19188 \begin_layout Standard
19191 \begin_inset Tabular
19192 <lyxtabular version="3" rows="5" columns="2">
19193 <features booktabs="true" tabularvalignment="middle">
19194 <column alignment="center" valignment="top" width="0pt">
19195 <column alignment="center" valignment="top">
19197 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
19200 \begin_layout Plain Layout
19206 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
19209 \begin_layout Plain Layout
19217 <cell alignment="center" valignment="top" leftline="true" usebox="none">
19220 \begin_layout Plain Layout
19224 \begin_inset Index idx
19227 \begin_layout Plain Layout
19240 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
19243 \begin_layout Plain Layout
19244 \begin_inset Formula ${\displaystyle E_{\mathrm{pot_{1}}}=\frac{K}{l+\frac{m}{n_{2}}}}$
19253 <row topspace="1mm">
19254 <cell alignment="center" valignment="top" usebox="none">
19257 \begin_layout Plain Layout
19265 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
19268 \begin_layout Plain Layout
19269 \begin_inset Formula ${\textstyle E_{\mathrm{pot_{1}}}=\frac{K}{l+\frac{m}{n_{2}}}}$
19279 <cell alignment="center" valignment="top" leftline="true" usebox="none">
19282 \begin_layout Plain Layout
19290 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
19293 \begin_layout Plain Layout
19294 \begin_inset Formula ${\scriptstyle E_{\mathrm{pot_{1}}}=\frac{K}{l+\frac{m}{n_{2}}}}$
19304 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
19307 \begin_layout Plain Layout
19315 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
19318 \begin_layout Plain Layout
19319 \begin_inset Formula ${\scriptscriptstyle E_{\mathrm{pot_{1}}}=\frac{K}{l+\frac{m}{n_{2}}}}$
19335 \begin_layout Standard
19336 After entering these commands, a blue box appears in which the formula parts
19340 \begin_layout Standard
19341 There is a further method to change the font size, that though only works
19342 for symbols or letters in mathematical text.
19343 To use it, one of the above text size commands is inserted in mathematical
19345 All following characters until the end of the mathematical text or until
19346 another size command will have the selected size.
19348 \begin_inset VSpace -2mm
19354 \begin_layout Standard
19358 \begin_layout Plain Layout
19368 \begin_inset Formula
19370 A=\frac{B}{c}\cdot\maltese
19376 \begin_inset Formula
19378 \maltese A\textrm{\Large\maltese\textit{A}}\textrm{\tiny\maltese\textit{A}}
19387 \begin_layout Plain Layout
19399 \begin_layout Standard
19400 \begin_inset VSpace medskip
19403 Before both formulas the command
19410 The command for the second formula is:
19411 \begin_inset Newline newline
19419 \begin_inset space \textvisiblespace{}
19425 \begin_inset space \textvisiblespace{}
19431 \begin_inset space \textvisiblespace{}
19437 \begin_inset space \textvisiblespace{}
19441 \begin_inset Formula $\to$
19445 \begin_inset Formula $\to$
19449 \begin_inset Newline newline
19453 \begin_inset space \hspace*{}
19464 \begin_inset space \textvisiblespace{}
19470 \begin_inset space \textvisiblespace{}
19476 \begin_inset space \textvisiblespace{}
19482 \begin_layout Standard
19483 If a symbol cannot be displayed in different sizes, it will always be displayed
19484 in the default size.
19487 \begin_layout Section
19489 \begin_inset Index idx
19492 \begin_layout Plain Layout
19501 \begin_layout Standard
19502 Greek letters can also be inserted via the toolbar button
19505 arg "math-insert \\alpha"
19509 All international typesetting norms purport that Greek letters in math
19510 have to be typeset italic/slanted.
19511 In some languages, like French or Russian, they are nevertheless sometimes
19515 \begin_layout Subsection
19517 \begin_inset Index idx
19520 \begin_layout Plain Layout
19521 Greek letters ! small
19529 \begin_layout Standard
19530 \begin_inset space \hfill{}
19534 \begin_inset Tabular
19535 <lyxtabular version="3" rows="11" columns="2">
19536 <features booktabs="true" tabularvalignment="middle">
19537 <column alignment="center" valignment="top" width="0pt">
19538 <column alignment="center" valignment="top" width="0pt">
19540 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
19543 \begin_layout Plain Layout
19549 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
19552 \begin_layout Plain Layout
19560 <cell alignment="center" valignment="top" leftline="true" usebox="none">
19563 \begin_layout Plain Layout
19571 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
19574 \begin_layout Plain Layout
19575 \begin_inset Formula $\alpha$
19585 <cell alignment="center" valignment="top" leftline="true" usebox="none">
19588 \begin_layout Plain Layout
19596 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
19599 \begin_layout Plain Layout
19600 \begin_inset Formula $\beta$
19610 <cell alignment="center" valignment="top" leftline="true" usebox="none">
19613 \begin_layout Plain Layout
19621 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
19624 \begin_layout Plain Layout
19625 \begin_inset Formula $\gamma$
19635 <cell alignment="center" valignment="top" leftline="true" usebox="none">
19638 \begin_layout Plain Layout
19646 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
19649 \begin_layout Plain Layout
19650 \begin_inset Formula $\delta$
19660 <cell alignment="center" valignment="top" leftline="true" usebox="none">
19663 \begin_layout Plain Layout
19671 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
19674 \begin_layout Plain Layout
19675 \begin_inset Formula $\epsilon$
19685 <cell alignment="center" valignment="top" leftline="true" usebox="none">
19688 \begin_layout Plain Layout
19696 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
19699 \begin_layout Plain Layout
19700 \begin_inset Formula $\varepsilon$
19710 <cell alignment="center" valignment="top" leftline="true" usebox="none">
19713 \begin_layout Plain Layout
19721 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
19724 \begin_layout Plain Layout
19725 \begin_inset Formula $\zeta$
19735 <cell alignment="center" valignment="top" leftline="true" usebox="none">
19738 \begin_layout Plain Layout
19746 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
19749 \begin_layout Plain Layout
19750 \begin_inset Formula $\eta$
19760 <cell alignment="center" valignment="top" leftline="true" usebox="none">
19763 \begin_layout Plain Layout
19771 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
19774 \begin_layout Plain Layout
19775 \begin_inset Formula $\theta$
19785 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
19788 \begin_layout Plain Layout
19796 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
19799 \begin_layout Plain Layout
19800 \begin_inset Formula $\vartheta$
19814 \begin_inset space \hfill{}
19818 \begin_inset Tabular
19819 <lyxtabular version="3" rows="12" columns="2">
19820 <features booktabs="true" tabularvalignment="middle">
19821 <column alignment="center" valignment="top" width="0pt">
19822 <column alignment="center" valignment="top" width="0pt">
19824 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
19827 \begin_layout Plain Layout
19833 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
19836 \begin_layout Plain Layout
19844 <cell alignment="center" valignment="top" leftline="true" usebox="none">
19847 \begin_layout Plain Layout
19855 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
19858 \begin_layout Plain Layout
19859 \begin_inset Formula $\iota$
19869 <cell alignment="center" valignment="top" leftline="true" usebox="none">
19872 \begin_layout Plain Layout
19880 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
19883 \begin_layout Plain Layout
19884 \begin_inset Formula $\kappa$
19894 <cell alignment="center" valignment="top" leftline="true" usebox="none">
19897 \begin_layout Plain Layout
19905 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
19908 \begin_layout Plain Layout
19909 \begin_inset Formula $\varkappa$
19919 <cell alignment="center" valignment="top" leftline="true" usebox="none">
19922 \begin_layout Plain Layout
19930 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
19933 \begin_layout Plain Layout
19934 \begin_inset Formula $\lambda$
19944 <cell alignment="center" valignment="top" leftline="true" usebox="none">
19947 \begin_layout Plain Layout
19955 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
19958 \begin_layout Plain Layout
19959 \begin_inset Formula $\mu$
19969 <cell alignment="center" valignment="top" leftline="true" usebox="none">
19972 \begin_layout Plain Layout
19980 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
19983 \begin_layout Plain Layout
19984 \begin_inset Formula $\nu$
19994 <cell alignment="center" valignment="top" leftline="true" usebox="none">
19997 \begin_layout Plain Layout
20005 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
20008 \begin_layout Plain Layout
20009 \begin_inset Formula $\xi$
20019 <cell alignment="center" valignment="top" leftline="true" usebox="none">
20022 \begin_layout Plain Layout
20028 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
20031 \begin_layout Plain Layout
20032 \begin_inset Formula $o$
20042 <cell alignment="center" valignment="top" leftline="true" usebox="none">
20045 \begin_layout Plain Layout
20053 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
20056 \begin_layout Plain Layout
20057 \begin_inset Formula $\pi$
20067 <cell alignment="center" valignment="top" leftline="true" usebox="none">
20070 \begin_layout Plain Layout
20078 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
20081 \begin_layout Plain Layout
20082 \begin_inset Formula $\varpi$
20092 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
20095 \begin_layout Plain Layout
20103 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
20106 \begin_layout Plain Layout
20107 \begin_inset Formula $\rho$
20121 \begin_inset space \hfill{}
20125 \begin_inset Tabular
20126 <lyxtabular version="3" rows="11" columns="2">
20127 <features booktabs="true" tabularvalignment="middle">
20128 <column alignment="center" valignment="top" width="0pt">
20129 <column alignment="center" valignment="top" width="0pt">
20131 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
20134 \begin_layout Plain Layout
20140 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
20143 \begin_layout Plain Layout
20151 <cell alignment="center" valignment="top" leftline="true" usebox="none">
20154 \begin_layout Plain Layout
20162 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
20165 \begin_layout Plain Layout
20166 \begin_inset Formula $\varrho$
20176 <cell alignment="center" valignment="top" leftline="true" usebox="none">
20179 \begin_layout Plain Layout
20187 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
20190 \begin_layout Plain Layout
20191 \begin_inset Formula $\sigma$
20201 <cell alignment="center" valignment="top" leftline="true" usebox="none">
20204 \begin_layout Plain Layout
20212 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
20215 \begin_layout Plain Layout
20216 \begin_inset Formula $\varsigma$
20226 <cell alignment="center" valignment="top" leftline="true" usebox="none">
20229 \begin_layout Plain Layout
20237 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
20240 \begin_layout Plain Layout
20241 \begin_inset Formula $\tau$
20251 <cell alignment="center" valignment="top" leftline="true" usebox="none">
20254 \begin_layout Plain Layout
20262 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
20265 \begin_layout Plain Layout
20266 \begin_inset Formula $\upsilon$
20276 <cell alignment="center" valignment="top" leftline="true" usebox="none">
20279 \begin_layout Plain Layout
20287 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
20290 \begin_layout Plain Layout
20291 \begin_inset Formula $\phi$
20301 <cell alignment="center" valignment="top" leftline="true" usebox="none">
20304 \begin_layout Plain Layout
20312 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
20315 \begin_layout Plain Layout
20316 \begin_inset Formula $\varphi$
20326 <cell alignment="center" valignment="top" leftline="true" usebox="none">
20329 \begin_layout Plain Layout
20337 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
20340 \begin_layout Plain Layout
20341 \begin_inset Formula $\chi$
20351 <cell alignment="center" valignment="top" leftline="true" usebox="none">
20354 \begin_layout Plain Layout
20362 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
20365 \begin_layout Plain Layout
20366 \begin_inset Formula $\psi$
20376 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
20379 \begin_layout Plain Layout
20387 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
20390 \begin_layout Plain Layout
20391 \begin_inset Formula $\omega$
20405 \begin_inset space \hfill{}
20411 \begin_layout Standard
20412 \begin_inset VSpace medskip
20418 \begin_layout Standard
20419 How to create special upright Greek letters is explained in
20420 \begin_inset CommandInset ref
20422 reference "subsec:Upright-small-Greek"
20429 \begin_layout Subsection
20431 \begin_inset Index idx
20434 \begin_layout Plain Layout
20435 Greek letters ! big
20443 \begin_layout Standard
20444 \begin_inset space \hfill{}
20448 \begin_inset Tabular
20449 <lyxtabular version="3" rows="7" columns="2">
20450 <features booktabs="true" tabularvalignment="middle">
20451 <column alignment="center" valignment="top" width="0pt">
20452 <column alignment="center" valignment="top" width="0pt">
20454 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
20457 \begin_layout Plain Layout
20463 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
20466 \begin_layout Plain Layout
20474 <cell alignment="center" valignment="top" leftline="true" usebox="none">
20477 \begin_layout Plain Layout
20485 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
20488 \begin_layout Plain Layout
20489 \begin_inset Formula $\Gamma$
20499 <cell alignment="center" valignment="top" leftline="true" usebox="none">
20502 \begin_layout Plain Layout
20510 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
20513 \begin_layout Plain Layout
20514 \begin_inset Formula $\Delta$
20524 <cell alignment="center" valignment="top" leftline="true" usebox="none">
20527 \begin_layout Plain Layout
20535 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
20538 \begin_layout Plain Layout
20539 \begin_inset Formula $\Theta$
20549 <cell alignment="center" valignment="top" leftline="true" usebox="none">
20552 \begin_layout Plain Layout
20560 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
20563 \begin_layout Plain Layout
20564 \begin_inset Formula $\Lambda$
20574 <cell alignment="center" valignment="top" leftline="true" usebox="none">
20577 \begin_layout Plain Layout
20585 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
20588 \begin_layout Plain Layout
20589 \begin_inset Formula $\Xi$
20599 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
20602 \begin_layout Plain Layout
20610 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
20613 \begin_layout Plain Layout
20614 \begin_inset Formula $\Pi$
20628 \begin_inset space \hfill{}
20632 \begin_inset Tabular
20633 <lyxtabular version="3" rows="6" columns="2">
20634 <features booktabs="true" tabularvalignment="middle">
20635 <column alignment="center" valignment="top" width="0pt">
20636 <column alignment="center" valignment="top" width="0pt">
20638 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
20641 \begin_layout Plain Layout
20647 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
20650 \begin_layout Plain Layout
20658 <cell alignment="center" valignment="top" leftline="true" usebox="none">
20661 \begin_layout Plain Layout
20669 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
20672 \begin_layout Plain Layout
20673 \begin_inset Formula $\Sigma$
20683 <cell alignment="center" valignment="top" leftline="true" usebox="none">
20686 \begin_layout Plain Layout
20694 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
20697 \begin_layout Plain Layout
20698 \begin_inset Formula $\Upsilon$
20708 <cell alignment="center" valignment="top" leftline="true" usebox="none">
20711 \begin_layout Plain Layout
20719 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
20722 \begin_layout Plain Layout
20723 \begin_inset Formula $\Phi$
20733 <cell alignment="center" valignment="top" leftline="true" usebox="none">
20736 \begin_layout Plain Layout
20744 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
20747 \begin_layout Plain Layout
20748 \begin_inset Formula $\Psi$
20758 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
20761 \begin_layout Plain Layout
20769 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
20772 \begin_layout Plain Layout
20773 \begin_inset Formula $\Omega$
20787 \begin_inset space \hfill{}
20793 \begin_layout Standard
20794 \begin_inset VSpace medskip
20797 That the big Greek letters appear upright is caused by a design bug when
20800 To get correct italic big letters, begin every command with
20805 For example the command
20812 \begin_inset Formula $\varGamma$
20816 Another way is to load the package
20824 \begin_layout Plain Layout
20829 is part of the \SpecialChar LaTeX
20835 \begin_inset Index idx
20838 \begin_layout Plain Layout
20843 \begin_layout Plain Layout
20863 \begin_inset Index idx
20866 \begin_layout Plain Layout
20872 with the \SpecialChar LaTeX
20876 \begin_layout Standard
20881 usepackage{fixmath}
20884 \begin_layout Standard
20885 Then all big Greek letters in a document will automatically be typeset italic.
20888 \begin_layout Subsection
20890 \begin_inset Index idx
20893 \begin_layout Plain Layout
20894 Greek letters ! bold
20902 \begin_layout Standard
20903 Greek letters cannot be set with different font styles like Latin letters.
20904 They can only be made bold with the command
20911 \begin_inset Index idx
20914 \begin_layout Plain Layout
20925 \begin_layout Standard
20927 \begin_inset Tabular
20928 <lyxtabular version="3" rows="3" columns="2">
20929 <features booktabs="true" tabularvalignment="middle">
20930 <column alignment="center" valignment="top" width="0pt">
20931 <column alignment="center" valignment="top">
20933 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
20936 \begin_layout Plain Layout
20942 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
20945 \begin_layout Plain Layout
20953 <cell alignment="center" valignment="top" leftline="true" usebox="none">
20956 \begin_layout Plain Layout
20968 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
20971 \begin_layout Plain Layout
20972 \begin_inset Formula $\Upsilon\boldsymbol{\Upsilon}$
20982 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
20985 \begin_layout Plain Layout
20997 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
21000 \begin_layout Plain Layout
21001 \begin_inset Formula $\theta\boldsymbol{\theta}$
21017 \begin_layout Section
21022 \begin_layout Plain Layout
21035 \begin_layout Plain Layout
21036 A list with all symbols of most of the \SpecialChar LaTeX
21037 -packages can be found in
21038 \begin_inset CommandInset citation
21053 \begin_layout Plain Layout
21061 \begin_inset Note Note
21064 \begin_layout Plain Layout
21067 texorpdfstring is used to avoid that the footnote appears in the PDF-bookmark.
21070 \begin_layout Plain Layout
21073 texorpdfstring is in section
21074 \begin_inset CommandInset ref
21076 reference "subsec:Formulas-in-Section"
21086 \begin_inset Index idx
21089 \begin_layout Plain Layout
21098 \begin_layout Standard
21099 Many of the symbols listed in this section can also be inserted via the
21103 arg "math-insert \\nabla"
21109 arg "math-insert \\digamma"
21115 \begin_layout Subsection
21116 Mathematical Symbols
21117 \begin_inset CommandInset label
21119 name "subsec:Mathematical-Symbols"
21124 \begin_inset Index idx
21127 \begin_layout Plain Layout
21128 Symbols ! mathematical
21136 \begin_layout Standard
21137 \begin_inset Tabular
21138 <lyxtabular version="3" rows="10" columns="2">
21139 <features booktabs="true" tabularvalignment="middle">
21140 <column alignment="center" valignment="top" width="0pt">
21141 <column alignment="center" valignment="top" width="0pt">
21143 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
21146 \begin_layout Plain Layout
21152 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
21155 \begin_layout Plain Layout
21163 <cell alignment="center" valignment="top" leftline="true" usebox="none">
21166 \begin_layout Plain Layout
21174 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
21177 \begin_layout Plain Layout
21178 \begin_inset Formula $\neg$
21188 <cell alignment="center" valignment="top" leftline="true" usebox="none">
21191 \begin_layout Plain Layout
21199 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
21202 \begin_layout Plain Layout
21203 \begin_inset Formula $\Im$
21213 <cell alignment="center" valignment="top" leftline="true" usebox="none">
21216 \begin_layout Plain Layout
21224 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
21227 \begin_layout Plain Layout
21228 \begin_inset Formula $\Re$
21238 <cell alignment="center" valignment="top" leftline="true" usebox="none">
21241 \begin_layout Plain Layout
21249 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
21252 \begin_layout Plain Layout
21253 \begin_inset Formula $\aleph$
21263 <cell alignment="center" valignment="top" leftline="true" usebox="none">
21266 \begin_layout Plain Layout
21274 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
21277 \begin_layout Plain Layout
21278 \begin_inset Formula $\partial$
21288 <cell alignment="center" valignment="top" leftline="true" usebox="none">
21291 \begin_layout Plain Layout
21299 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
21302 \begin_layout Plain Layout
21303 \begin_inset Formula $\infty$
21313 <cell alignment="center" valignment="top" leftline="true" usebox="none">
21316 \begin_layout Plain Layout
21324 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
21327 \begin_layout Plain Layout
21328 \begin_inset Formula $\wp$
21338 <cell alignment="center" valignment="top" leftline="true" usebox="none">
21341 \begin_layout Plain Layout
21349 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
21352 \begin_layout Plain Layout
21353 \begin_inset Formula $\imath$
21363 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
21366 \begin_layout Plain Layout
21374 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
21377 \begin_layout Plain Layout
21378 \begin_inset Formula $\jmath$
21392 \begin_inset space \hfill{}
21396 \begin_inset Tabular
21397 <lyxtabular version="3" rows="10" columns="2">
21398 <features booktabs="true" tabularvalignment="middle">
21399 <column alignment="center" valignment="top" width="0pt">
21400 <column alignment="center" valignment="top" width="0pt">
21402 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
21405 \begin_layout Plain Layout
21411 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
21414 \begin_layout Plain Layout
21416 \begin_inset Note Note
21419 \begin_layout Plain Layout
21426 is only used as spacer.
21438 <cell alignment="center" valignment="top" leftline="true" usebox="none">
21441 \begin_layout Plain Layout
21449 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
21452 \begin_layout Plain Layout
21453 \begin_inset Formula $\forall$
21463 <cell alignment="center" valignment="top" leftline="true" usebox="none">
21466 \begin_layout Plain Layout
21474 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
21477 \begin_layout Plain Layout
21478 \begin_inset Formula $\exists$
21488 <cell alignment="center" valignment="top" leftline="true" usebox="none">
21491 \begin_layout Plain Layout
21499 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
21502 \begin_layout Plain Layout
21503 \begin_inset Formula $\nexists$
21513 <cell alignment="center" valignment="top" leftline="true" usebox="none">
21516 \begin_layout Plain Layout
21524 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
21527 \begin_layout Plain Layout
21528 \begin_inset Formula $\emptyset$
21538 <cell alignment="center" valignment="top" leftline="true" usebox="none">
21541 \begin_layout Plain Layout
21549 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
21552 \begin_layout Plain Layout
21553 \begin_inset Formula $\varnothing$
21563 <cell alignment="center" valignment="top" leftline="true" usebox="none">
21566 \begin_layout Plain Layout
21574 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
21577 \begin_layout Plain Layout
21578 \begin_inset Formula $\dag$
21588 <cell alignment="center" valignment="top" leftline="true" usebox="none">
21591 \begin_layout Plain Layout
21599 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
21602 \begin_layout Plain Layout
21603 \begin_inset Formula $\ddag$
21613 <cell alignment="center" valignment="top" leftline="true" usebox="none">
21616 \begin_layout Plain Layout
21624 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
21627 \begin_layout Plain Layout
21631 \begin_layout Plain Layout
21641 \begin_inset Formula $\complement$
21648 \begin_layout Plain Layout
21662 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
21665 \begin_layout Plain Layout
21673 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
21676 \begin_layout Plain Layout
21677 \begin_inset Formula $\Bbbk$
21691 \begin_inset space \hfill{}
21695 \begin_inset Tabular
21696 <lyxtabular version="3" rows="10" columns="2">
21697 <features booktabs="true" tabularvalignment="middle">
21698 <column alignment="center" valignment="top" width="0pt">
21699 <column alignment="center" valignment="top" width="0pt">
21701 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
21704 \begin_layout Plain Layout
21710 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
21713 \begin_layout Plain Layout
21721 <cell alignment="center" valignment="top" leftline="true" usebox="none">
21724 \begin_layout Plain Layout
21732 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
21735 \begin_layout Plain Layout
21736 \begin_inset Formula $\prime$
21746 <cell alignment="center" valignment="top" leftline="true" usebox="none">
21749 \begin_layout Plain Layout
21757 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
21760 \begin_layout Plain Layout
21761 \begin_inset Formula $\backprime$
21771 <cell alignment="center" valignment="top" leftline="true" usebox="none">
21774 \begin_layout Plain Layout
21782 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
21785 \begin_layout Plain Layout
21786 \begin_inset Formula $\mho$
21796 <cell alignment="center" valignment="top" leftline="true" usebox="none">
21799 \begin_layout Plain Layout
21807 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
21810 \begin_layout Plain Layout
21811 \begin_inset Formula $\triangle$
21821 <cell alignment="center" valignment="top" leftline="true" usebox="none">
21824 \begin_layout Plain Layout
21832 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
21835 \begin_layout Plain Layout
21836 \begin_inset Formula $\angle$
21846 <cell alignment="center" valignment="top" leftline="true" usebox="none">
21849 \begin_layout Plain Layout
21857 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
21860 \begin_layout Plain Layout
21861 \begin_inset Formula $\measuredangle$
21871 <cell alignment="center" valignment="top" leftline="true" usebox="none">
21874 \begin_layout Plain Layout
21882 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
21885 \begin_layout Plain Layout
21886 \begin_inset Formula $\sphericalangle$
21896 <cell alignment="center" valignment="top" leftline="true" usebox="none">
21899 \begin_layout Plain Layout
21907 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
21910 \begin_layout Plain Layout
21911 \begin_inset Formula $\top$
21921 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
21924 \begin_layout Plain Layout
21932 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
21935 \begin_layout Plain Layout
21936 \begin_inset Formula $\bot$
21952 \begin_layout Subsection
21953 Miscellaneous Symbols
21954 \begin_inset CommandInset label
21956 name "subsec:Miscellaneous-Symbols"
21961 \begin_inset Index idx
21964 \begin_layout Plain Layout
21965 Symbols ! miscellaneous
21973 \begin_layout Standard
21976 \begin_inset Tabular
21977 <lyxtabular version="3" rows="10" columns="2">
21978 <features booktabs="true" tabularvalignment="middle">
21979 <column alignment="center" valignment="top" width="0pt">
21980 <column alignment="center" valignment="top" width="0pt">
21982 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
21985 \begin_layout Plain Layout
21991 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
21994 \begin_layout Plain Layout
22002 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
22005 \begin_layout Plain Layout
22013 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
22016 \begin_layout Plain Layout
22017 \begin_inset Formula $\flat$
22027 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
22030 \begin_layout Plain Layout
22038 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
22041 \begin_layout Plain Layout
22042 \begin_inset Formula $\natural$
22052 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
22055 \begin_layout Plain Layout
22063 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
22066 \begin_layout Plain Layout
22067 \begin_inset Formula $\sharp$
22077 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
22080 \begin_layout Plain Layout
22088 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
22091 \begin_layout Plain Layout
22092 \begin_inset Formula $\surd$
22102 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
22105 \begin_layout Plain Layout
22113 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
22116 \begin_layout Plain Layout
22117 \begin_inset Formula $\checkmark$
22127 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
22130 \begin_layout Plain Layout
22138 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
22141 \begin_layout Plain Layout
22142 \begin_inset Formula $\yen$
22152 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
22155 \begin_layout Plain Layout
22163 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
22166 \begin_layout Plain Layout
22167 \begin_inset Formula $\pounds$
22177 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
22180 \begin_layout Plain Layout
22186 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
22189 \begin_layout Plain Layout
22190 \begin_inset Formula $\$$
22200 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
22203 \begin_layout Plain Layout
22209 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
22212 \begin_layout Plain Layout
22213 \begin_inset Formula $§$
22227 \begin_inset space \hfill{}
22231 \begin_inset Tabular
22232 <lyxtabular version="3" rows="10" columns="2">
22233 <features booktabs="true" tabularvalignment="middle">
22234 <column alignment="center" valignment="top" width="0pt">
22235 <column alignment="center" valignment="top">
22237 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
22240 \begin_layout Plain Layout
22246 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
22249 \begin_layout Plain Layout
22257 <cell alignment="center" valignment="top" leftline="true" usebox="none">
22260 \begin_layout Plain Layout
22268 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
22271 \begin_layout Plain Layout
22272 \begin_inset Formula $\hbar$
22282 <cell alignment="center" valignment="top" leftline="true" usebox="none">
22285 \begin_layout Plain Layout
22293 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
22296 \begin_layout Plain Layout
22297 \begin_inset Formula $\hslash$
22307 <cell alignment="center" valignment="top" leftline="true" usebox="none">
22310 \begin_layout Plain Layout
22318 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
22321 \begin_layout Plain Layout
22322 \begin_inset Formula $\clubsuit$
22332 <cell alignment="center" valignment="top" leftline="true" usebox="none">
22335 \begin_layout Plain Layout
22343 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
22346 \begin_layout Plain Layout
22347 \begin_inset Formula $\spadesuit$
22357 <cell alignment="center" valignment="top" leftline="true" usebox="none">
22360 \begin_layout Plain Layout
22368 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
22371 \begin_layout Plain Layout
22372 \begin_inset Formula $\bigstar$
22382 <cell alignment="center" valignment="top" leftline="true" usebox="none">
22385 \begin_layout Plain Layout
22393 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
22396 \begin_layout Plain Layout
22397 \begin_inset Formula $\blacklozenge$
22407 <cell alignment="center" valignment="top" leftline="true" usebox="none">
22410 \begin_layout Plain Layout
22418 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
22421 \begin_layout Plain Layout
22422 \begin_inset Formula $\blacktriangle$
22432 <cell alignment="center" valignment="top" leftline="true" usebox="none">
22435 \begin_layout Plain Layout
22443 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
22446 \begin_layout Plain Layout
22447 \begin_inset Formula $\blacktriangledown$
22457 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
22460 \begin_layout Plain Layout
22468 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
22471 \begin_layout Plain Layout
22472 \begin_inset Formula $\bullet$
22486 \begin_inset space \hfill{}
22490 \begin_inset Tabular
22491 <lyxtabular version="3" rows="10" columns="2">
22492 <features booktabs="true" tabularvalignment="middle">
22493 <column alignment="center" valignment="top" width="0pt">
22494 <column alignment="center" valignment="top" width="0pt">
22496 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
22499 \begin_layout Plain Layout
22505 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
22508 \begin_layout Plain Layout
22516 <cell alignment="center" valignment="top" leftline="true" usebox="none">
22519 \begin_layout Plain Layout
22527 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
22530 \begin_layout Plain Layout
22531 \begin_inset Formula $\diamondsuit$
22541 <cell alignment="center" valignment="top" rightline="true" usebox="none">
22544 \begin_layout Plain Layout
22552 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
22555 \begin_layout Plain Layout
22556 \begin_inset Formula $\Diamond$
22566 <cell alignment="center" valignment="top" leftline="true" usebox="none">
22569 \begin_layout Plain Layout
22577 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
22580 \begin_layout Plain Layout
22581 \begin_inset Formula $\heartsuit$
22591 <cell alignment="center" valignment="top" leftline="true" usebox="none">
22594 \begin_layout Plain Layout
22602 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
22605 \begin_layout Plain Layout
22606 \begin_inset Formula $\P$
22616 <cell alignment="center" valignment="top" leftline="true" usebox="none">
22619 \begin_layout Plain Layout
22627 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
22630 \begin_layout Plain Layout
22631 \begin_inset Formula $\copyright$
22641 <cell alignment="center" valignment="top" leftline="true" usebox="none">
22644 \begin_layout Plain Layout
22652 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
22655 \begin_layout Plain Layout
22656 \begin_inset Formula $\circledR$
22666 <cell alignment="center" valignment="top" leftline="true" usebox="none">
22669 \begin_layout Plain Layout
22677 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
22680 \begin_layout Plain Layout
22681 \begin_inset Formula $\maltese$
22691 <cell alignment="center" valignment="top" leftline="true" usebox="none">
22694 \begin_layout Plain Layout
22702 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
22705 \begin_layout Plain Layout
22706 \begin_inset Formula $\diagup$
22716 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
22719 \begin_layout Plain Layout
22727 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
22730 \begin_layout Plain Layout
22731 \begin_inset Formula $\diagdown$
22747 \begin_layout Standard
22748 \begin_inset VSpace medskip
22754 \begin_layout Standard
22755 Some symbols can be displayed in different sizes, see
22756 \begin_inset CommandInset ref
22758 reference "subsec:Font-Sizes"
22765 \begin_layout Subsection
22767 \begin_inset Index idx
22770 \begin_layout Plain Layout
22771 Symbols ! Euro-symbol
22777 \begin_inset Index idx
22780 \begin_layout Plain Layout
22787 \begin_layout Plain Layout
22804 \begin_layout Standard
22805 To use the Euro symbol in formulas, the \SpecialChar LaTeX
22811 \begin_inset Index idx
22814 \begin_layout Plain Layout
22820 must be installed and loaded with the \SpecialChar LaTeX
22824 \begin_layout Standard
22829 usepackage[gennarrow]{eurosym}
22832 \begin_layout Standard
22833 The Euro symbol can now be inserted with the command
22840 \begin_inset Index idx
22843 \begin_layout Plain Layout
22854 \begin_layout Standard
22855 The Euro symbol can directly be inserted with the € key in mathematical
22856 text, without having
22871 can also be inserted in \SpecialChar TeX
22873 The official currency symbol can then be inserted with the command
22880 \begin_inset Index idx
22883 \begin_layout Plain Layout
22891 , that is only available in \SpecialChar TeX
22895 \begin_layout Standard
22899 \begin_layout Plain Layout
22909 \begin_inset Note Note
22912 \begin_layout Plain Layout
22913 The following table will only be displayed when the \SpecialChar LaTeX
22926 \begin_layout Standard
22927 An overview about the different Euro symbols:
22930 \begin_layout Standard
22932 \begin_inset Tabular
22933 <lyxtabular version="3" rows="4" columns="3">
22934 <features booktabs="true" tabularvalignment="middle">
22935 <column alignment="center" valignment="top" width="0pt">
22936 <column alignment="center" valignment="top" width="0pt">
22937 <column alignment="center" valignment="top" width="0pt">
22939 <cell alignment="center" valignment="top" bottomline="true" usebox="none">
22942 \begin_layout Plain Layout
22946 \begin_layout Plain Layout
22950 cmidrule[0.08em]{2-3}
22960 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
22963 \begin_layout Plain Layout
22969 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
22972 \begin_layout Plain Layout
22980 <cell alignment="center" valignment="top" leftline="true" usebox="none">
22983 \begin_layout Plain Layout
22989 <cell alignment="center" valignment="top" leftline="true" usebox="none">
22992 \begin_layout Plain Layout
23000 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
23003 \begin_layout Plain Layout
23004 \begin_inset Formula $\euro$
23014 <cell alignment="center" valignment="top" leftline="true" usebox="none">
23017 \begin_layout Plain Layout
23023 <cell alignment="center" valignment="top" leftline="true" usebox="none">
23026 \begin_layout Plain Layout
23032 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
23035 \begin_layout Plain Layout
23036 \begin_inset Formula $\mbox{€}$
23046 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
23049 \begin_layout Plain Layout
23056 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
23059 \begin_layout Plain Layout
23067 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
23070 \begin_layout Plain Layout
23074 \begin_layout Plain Layout
23094 \begin_inset Note Note
23097 \begin_layout Plain Layout
23104 is used here only for table borders.
23114 manual for details.
23122 \begin_layout Standard
23126 \begin_layout Plain Layout
23136 \begin_inset Note Note
23139 \begin_layout Plain Layout
23140 The following will be displayed when the \SpecialChar LaTeX
23153 \begin_layout Standard
23154 You need to install the \SpecialChar LaTeX
23159 to see the rest of this subsection in the output.
23162 \begin_layout Standard
23166 \begin_layout Plain Layout
23178 \begin_layout Section
23180 \begin_inset CommandInset label
23182 name "sec:Relations"
23187 \begin_inset Index idx
23190 \begin_layout Plain Layout
23197 \begin_inset Index idx
23200 \begin_layout Plain Layout
23205 \begin_layout Plain Layout
23216 \begin_layout Plain Layout
23231 \begin_layout Standard
23232 All following relations can also be inserted via the toolbar button
23235 arg "math-insert \\leq"
23241 \begin_layout Standard
23242 \begin_inset Tabular
23243 <lyxtabular version="3" rows="17" columns="2">
23244 <features booktabs="true" tabularvalignment="middle">
23245 <column alignment="center" valignment="top" width="0pt">
23246 <column alignment="center" valignment="top" width="0pt">
23248 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
23251 \begin_layout Plain Layout
23257 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
23260 \begin_layout Plain Layout
23268 <cell alignment="center" valignment="top" leftline="true" usebox="none">
23271 \begin_layout Plain Layout
23277 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
23280 \begin_layout Plain Layout
23281 \begin_inset Formula $<$
23291 <cell alignment="center" valignment="top" leftline="true" usebox="none">
23294 \begin_layout Plain Layout
23302 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
23305 \begin_layout Plain Layout
23306 \begin_inset Formula $\le$
23316 <cell alignment="center" valignment="top" leftline="true" usebox="none">
23319 \begin_layout Plain Layout
23327 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
23330 \begin_layout Plain Layout
23331 \begin_inset Formula $\ll$
23341 <cell alignment="center" valignment="top" leftline="true" usebox="none">
23344 \begin_layout Plain Layout
23352 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
23355 \begin_layout Plain Layout
23356 \begin_inset Formula $\prec$
23366 <cell alignment="center" valignment="top" leftline="true" usebox="none">
23369 \begin_layout Plain Layout
23377 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
23380 \begin_layout Plain Layout
23381 \begin_inset Formula $\preceq$
23391 <cell alignment="center" valignment="top" leftline="true" usebox="none">
23394 \begin_layout Plain Layout
23402 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
23405 \begin_layout Plain Layout
23406 \begin_inset Formula $\subset$
23416 <cell alignment="center" valignment="top" leftline="true" usebox="none">
23419 \begin_layout Plain Layout
23427 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
23430 \begin_layout Plain Layout
23431 \begin_inset Formula $\subseteq$
23441 <cell alignment="center" valignment="top" leftline="true" usebox="none">
23444 \begin_layout Plain Layout
23452 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
23455 \begin_layout Plain Layout
23456 \begin_inset Formula $\sqsubseteq$
23466 <cell alignment="center" valignment="top" leftline="true" usebox="none">
23469 \begin_layout Plain Layout
23477 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
23480 \begin_layout Plain Layout
23481 \begin_inset Formula $\in$
23491 <cell alignment="center" valignment="top" leftline="true" usebox="none">
23494 \begin_layout Plain Layout
23502 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
23505 \begin_layout Plain Layout
23506 \begin_inset Formula $\vdash$
23516 <cell alignment="center" valignment="top" leftline="true" usebox="none">
23519 \begin_layout Plain Layout
23527 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
23530 \begin_layout Plain Layout
23531 \begin_inset Formula $\smile$
23541 <cell alignment="center" valignment="top" leftline="true" usebox="none">
23544 \begin_layout Plain Layout
23552 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
23555 \begin_layout Plain Layout
23556 \begin_inset Formula $\lhd$
23566 <cell alignment="center" valignment="top" leftline="true" usebox="none">
23569 \begin_layout Plain Layout
23577 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
23580 \begin_layout Plain Layout
23581 \begin_inset Formula $\unlhd$
23591 <cell alignment="center" valignment="top" leftline="true" usebox="none">
23594 \begin_layout Plain Layout
23602 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
23605 \begin_layout Plain Layout
23606 \begin_inset Formula $\gtrless$
23616 <cell alignment="center" valignment="top" leftline="true" usebox="none">
23619 \begin_layout Plain Layout
23627 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
23630 \begin_layout Plain Layout
23631 \begin_inset Formula $\mid$
23641 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
23644 \begin_layout Plain Layout
23652 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
23655 \begin_layout Plain Layout
23656 \begin_inset Formula $\nmid$
23670 \begin_inset space \hfill{}
23674 \begin_inset Tabular
23675 <lyxtabular version="3" rows="17" columns="2">
23676 <features booktabs="true" tabularvalignment="middle">
23677 <column alignment="center" valignment="top" width="0pt">
23678 <column alignment="center" valignment="top" width="0pt">
23680 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
23683 \begin_layout Plain Layout
23689 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
23692 \begin_layout Plain Layout
23700 <cell alignment="center" valignment="top" leftline="true" usebox="none">
23703 \begin_layout Plain Layout
23709 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
23712 \begin_layout Plain Layout
23713 \begin_inset Formula $=$
23723 <cell alignment="center" valignment="top" leftline="true" usebox="none">
23726 \begin_layout Plain Layout
23734 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
23737 \begin_layout Plain Layout
23738 \begin_inset Formula $\not=$
23748 <cell alignment="center" valignment="top" leftline="true" usebox="none">
23751 \begin_layout Plain Layout
23759 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
23762 \begin_layout Plain Layout
23763 \begin_inset Formula $\equiv$
23773 <cell alignment="center" valignment="top" leftline="true" usebox="none">
23776 \begin_layout Plain Layout
23784 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
23787 \begin_layout Plain Layout
23788 \begin_inset Formula $\sim$
23798 <cell alignment="center" valignment="top" leftline="true" usebox="none">
23801 \begin_layout Plain Layout
23809 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
23812 \begin_layout Plain Layout
23813 \begin_inset Formula $\simeq$
23823 <cell alignment="center" valignment="top" leftline="true" usebox="none">
23826 \begin_layout Plain Layout
23834 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
23837 \begin_layout Plain Layout
23838 \begin_inset Formula $\approx$
23848 <cell alignment="center" valignment="top" leftline="true" usebox="none">
23851 \begin_layout Plain Layout
23859 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
23862 \begin_layout Plain Layout
23863 \begin_inset Formula $\cong$
23873 <cell alignment="center" valignment="top" leftline="true" usebox="none">
23876 \begin_layout Plain Layout
23884 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
23887 \begin_layout Plain Layout
23888 \begin_inset Formula $\bowtie$
23898 <cell alignment="center" valignment="top" leftline="true" usebox="none">
23901 \begin_layout Plain Layout
23909 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
23912 \begin_layout Plain Layout
23913 \begin_inset Formula $\notin$
23923 <cell alignment="center" valignment="top" leftline="true" usebox="none">
23926 \begin_layout Plain Layout
23934 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
23937 \begin_layout Plain Layout
23938 \begin_inset Formula $\perp$
23948 <cell alignment="center" valignment="top" leftline="true" usebox="none">
23951 \begin_layout Plain Layout
23959 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
23962 \begin_layout Plain Layout
23963 \begin_inset Formula $\propto$
23973 <cell alignment="center" valignment="top" leftline="true" usebox="none">
23976 \begin_layout Plain Layout
23984 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
23987 \begin_layout Plain Layout
23988 \begin_inset Formula $\asymp$
23998 <cell alignment="center" valignment="top" leftline="true" usebox="none">
24001 \begin_layout Plain Layout
24009 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
24012 \begin_layout Plain Layout
24013 \begin_inset Formula $\doteq$
24023 <cell alignment="center" valignment="top" leftline="true" usebox="none">
24026 \begin_layout Plain Layout
24034 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
24037 \begin_layout Plain Layout
24038 \begin_inset Formula $\circeq$
24048 <cell alignment="center" valignment="top" leftline="true" usebox="none">
24051 \begin_layout Plain Layout
24059 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
24062 \begin_layout Plain Layout
24063 \begin_inset Formula $\models$
24073 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
24076 \begin_layout Plain Layout
24084 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
24087 \begin_layout Plain Layout
24088 \begin_inset Formula $\widehat{=}$
24102 \begin_inset space \hfill{}
24106 \begin_inset Tabular
24107 <lyxtabular version="3" rows="17" columns="2">
24108 <features booktabs="true" tabularvalignment="middle">
24109 <column alignment="center" valignment="top" width="0pt">
24110 <column alignment="center" valignment="top" width="0pt">
24112 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
24115 \begin_layout Plain Layout
24121 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
24124 \begin_layout Plain Layout
24132 <cell alignment="center" valignment="top" leftline="true" usebox="none">
24135 \begin_layout Plain Layout
24141 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
24144 \begin_layout Plain Layout
24145 \begin_inset Formula $>$
24155 <cell alignment="center" valignment="top" leftline="true" usebox="none">
24158 \begin_layout Plain Layout
24166 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
24169 \begin_layout Plain Layout
24170 \begin_inset Formula $\ge$
24180 <cell alignment="center" valignment="top" leftline="true" usebox="none">
24183 \begin_layout Plain Layout
24191 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
24194 \begin_layout Plain Layout
24195 \begin_inset Formula $\gg$
24205 <cell alignment="center" valignment="top" leftline="true" usebox="none">
24208 \begin_layout Plain Layout
24216 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
24219 \begin_layout Plain Layout
24220 \begin_inset Formula $\succ$
24230 <cell alignment="center" valignment="top" leftline="true" usebox="none">
24233 \begin_layout Plain Layout
24241 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
24244 \begin_layout Plain Layout
24245 \begin_inset Formula $\succeq$
24255 <cell alignment="center" valignment="top" leftline="true" usebox="none">
24258 \begin_layout Plain Layout
24266 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
24269 \begin_layout Plain Layout
24270 \begin_inset Formula $\supset$
24280 <cell alignment="center" valignment="top" leftline="true" usebox="none">
24283 \begin_layout Plain Layout
24291 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
24294 \begin_layout Plain Layout
24295 \begin_inset Formula $\supseteq$
24305 <cell alignment="center" valignment="top" leftline="true" usebox="none">
24308 \begin_layout Plain Layout
24316 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
24319 \begin_layout Plain Layout
24320 \begin_inset Formula $\sqsupseteq$
24330 <cell alignment="center" valignment="top" leftline="true" usebox="none">
24333 \begin_layout Plain Layout
24341 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
24344 \begin_layout Plain Layout
24345 \begin_inset Formula $\ni$
24355 <cell alignment="center" valignment="top" leftline="true" usebox="none">
24358 \begin_layout Plain Layout
24366 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
24369 \begin_layout Plain Layout
24370 \begin_inset Formula $\dashv$
24380 <cell alignment="center" valignment="top" leftline="true" usebox="none">
24383 \begin_layout Plain Layout
24391 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
24394 \begin_layout Plain Layout
24395 \begin_inset Formula $\frown$
24405 <cell alignment="center" valignment="top" leftline="true" usebox="none">
24408 \begin_layout Plain Layout
24416 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
24419 \begin_layout Plain Layout
24420 \begin_inset Formula $\rhd$
24430 <cell alignment="center" valignment="top" leftline="true" usebox="none">
24433 \begin_layout Plain Layout
24441 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
24444 \begin_layout Plain Layout
24445 \begin_inset Formula $\unrhd$
24455 <cell alignment="center" valignment="top" leftline="true" usebox="none">
24458 \begin_layout Plain Layout
24466 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
24469 \begin_layout Plain Layout
24470 \begin_inset Formula $\lessgtr$
24480 <cell alignment="center" valignment="top" leftline="true" usebox="none">
24483 \begin_layout Plain Layout
24491 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
24494 \begin_layout Plain Layout
24495 \begin_inset Formula $\parallel$
24505 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
24508 \begin_layout Plain Layout
24516 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
24519 \begin_layout Plain Layout
24520 \begin_inset Formula $\nparallel$
24536 \begin_layout Standard
24537 \begin_inset VSpace medskip
24552 are bigger than the equal looking operators
24567 \begin_layout Standard
24569 supports also many special relations.
24570 Use the toolbar button
24573 arg "math-insert \\leqq"
24576 to see a list of these relations.
24579 \begin_layout Standard
24580 Relations are, in contrary to symbols, always surrounded by space.
24583 \begin_layout Standard
24584 Relations with labels can be created with the command
24591 \begin_inset Index idx
24594 \begin_layout Plain Layout
24605 \begin_layout Standard
24607 \begin_inset Tabular
24608 <lyxtabular version="3" rows="2" columns="2">
24609 <features booktabs="true" tabularvalignment="middle">
24610 <column alignment="center" valignment="top" width="0pt">
24611 <column alignment="center" valignment="top">
24613 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
24616 \begin_layout Plain Layout
24622 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
24625 \begin_layout Plain Layout
24632 <row topspace="1.5mm">
24633 <cell alignment="center" valignment="top" bottomline="true" usebox="none">
24636 \begin_layout Plain Layout
24640 \begin_inset space \textvisiblespace{}
24648 \begin_inset space \textvisiblespace{}
24652 \begin_inset Formula $\downarrow$
24658 \begin_inset space \textvisiblespace{}
24662 \begin_inset space \textvisiblespace{}
24670 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
24673 \begin_layout Plain Layout
24674 \begin_inset Formula $A(r)\stackrel{r\to\infty}{\approx}B$
24690 \begin_layout Section
24694 \begin_layout Subsection
24695 Predefined Functions
24696 \begin_inset CommandInset label
24698 name "subsec:Predefined-Functions"
24703 \begin_inset Index idx
24706 \begin_layout Plain Layout
24707 Functions ! predefined
24715 \begin_layout Standard
24716 In general, variables are set
24720 in mathematical expressions, but not function names, because
24721 \begin_inset Formula $sin$
24724 could be misunderstood as
24725 \begin_inset Formula $s\cdot i\cdot n$
24729 Therefore there are predefined functions which are additionally a bit separated
24731 They are inserted as commands starting with a backslash before their name.
24734 \begin_layout Standard
24736 \begin_inset Tabular
24737 <lyxtabular version="3" rows="2" columns="2">
24738 <features booktabs="true" tabularvalignment="middle">
24739 <column alignment="center" valignment="top" width="0pt">
24740 <column alignment="center" valignment="top" width="0pt">
24742 <cell alignment="center" valignment="top" topline="true" bottomline="true" usebox="none">
24745 \begin_layout Plain Layout
24751 <cell alignment="center" valignment="top" topline="true" bottomline="true" rightline="true" usebox="none">
24754 \begin_layout Plain Layout
24762 <cell alignment="center" valignment="top" bottomline="true" usebox="none">
24765 \begin_layout Plain Layout
24771 <cell alignment="center" valignment="top" bottomline="true" rightline="true" usebox="none">
24774 \begin_layout Plain Layout
24775 \begin_inset Formula $Asin(x)+B$
24789 \begin_inset space \quad{}
24793 \begin_inset Tabular
24794 <lyxtabular version="3" rows="2" columns="2">
24795 <features booktabs="true" tabularvalignment="middle">
24796 <column alignment="center" valignment="top" width="0pt">
24797 <column alignment="center" valignment="top" width="0pt">
24799 <cell alignment="center" valignment="top" topline="true" bottomline="true" usebox="none">
24802 \begin_layout Plain Layout
24808 <cell alignment="center" valignment="top" topline="true" bottomline="true" usebox="none">
24811 \begin_layout Plain Layout
24819 <cell alignment="center" valignment="top" bottomline="true" usebox="none">
24822 \begin_layout Plain Layout
24830 <cell alignment="center" valignment="top" bottomline="true" usebox="none">
24833 \begin_layout Plain Layout
24834 \begin_inset Formula $A\sin(x)+B$
24850 \begin_layout Standard
24851 The following functions are predefined:
24854 \begin_layout Standard
24855 \begin_inset VSpace -2mm
24861 \begin_layout Standard
24863 \begin_inset Tabular
24864 <lyxtabular version="3" rows="9" columns="4">
24865 <features booktabs="true" tabularvalignment="middle">
24866 <column alignment="center" valignment="top" width="0pt">
24867 <column alignment="center" valignment="top" width="0pt">
24868 <column alignment="center" valignment="top" width="0pt">
24869 <column alignment="center" valignment="top" width="0pt">
24871 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
24874 \begin_layout Plain Layout
24880 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
24883 \begin_layout Plain Layout
24889 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
24892 \begin_layout Plain Layout
24898 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
24901 \begin_layout Plain Layout
24909 <cell alignment="center" valignment="top" leftline="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" rightline="true" usebox="none">
24945 \begin_layout Plain Layout
24955 <cell alignment="center" valignment="top" leftline="true" usebox="none">
24958 \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" rightline="true" usebox="none">
24991 \begin_layout Plain Layout
25001 <cell alignment="center" valignment="top" leftline="true" usebox="none">
25004 \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" rightline="true" usebox="none">
25037 \begin_layout Plain Layout
25047 <cell alignment="center" valignment="top" leftline="true" usebox="none">
25050 \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" rightline="true" usebox="none">
25083 \begin_layout Plain Layout
25093 <cell alignment="center" valignment="top" leftline="true" usebox="none">
25096 \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" rightline="true" usebox="none">
25129 \begin_layout Plain Layout
25139 <cell alignment="center" valignment="top" leftline="true" usebox="none">
25142 \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" rightline="true" usebox="none">
25175 \begin_layout Plain Layout
25185 <cell alignment="center" valignment="top" leftline="true" usebox="none">
25188 \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" rightline="true" usebox="none">
25221 \begin_layout Plain Layout
25231 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
25234 \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" rightline="true" usebox="none">
25267 \begin_layout Plain Layout
25283 \begin_layout Standard
25284 They can also be inserted with the math toolbar button
25287 arg "math-insert \\functions"
25293 \begin_layout Subsection
25294 Self-defined Functions
25295 \begin_inset Index idx
25298 \begin_layout Plain Layout
25299 Functions ! self-defined
25307 \begin_layout Standard
25308 To use a function that is not predefined, like for example the sign function
25309 sgn(x), there are two possibilities:
25312 \begin_layout Itemize
25313 Define the function by inserting the following line to the \SpecialChar LaTeX
25318 \begin_layout Plain Layout
25323 DeclareMathOperator
25326 \begin_inset CommandInset ref
25328 reference "subsec:Self-defined-Operators"
25338 \begin_inset Newline newline
25342 \begin_inset VSpace -3mm
25346 \begin_inset Newline newline
25353 DeclareMathOperator{
25358 \begin_inset Index idx
25361 \begin_layout Plain Layout
25366 DeclareMathOperator
25372 \begin_inset Newline newline
25376 \begin_inset VSpace -2mm
25380 \begin_inset Newline newline
25383 Now the new defined function can be called with the command
25392 \begin_layout Itemize
25393 Write the formula as usual, mark the formula name, in our example the letters
25398 , and change it to mathematical text.
25399 Finally, a space is inserted between prefactor and function.
25402 \begin_layout Standard
25403 The result is the same with both methods as with a predefined function
25407 \begin_layout Plain Layout
25408 In \SpecialChar LyX
25409 self-defined functions are displayed red, predefined ones black.
25417 \begin_layout Standard
25419 \begin_inset Tabular
25420 <lyxtabular version="3" rows="3" columns="2">
25421 <features booktabs="true" tabularvalignment="middle">
25422 <column alignment="center" valignment="top" width="0pt">
25423 <column alignment="center" valignment="top" width="0pt">
25425 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
25428 \begin_layout Plain Layout
25434 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
25437 \begin_layout Plain Layout
25445 <cell alignment="center" valignment="top" leftline="true" usebox="none">
25448 \begin_layout Plain Layout
25456 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
25459 \begin_layout Plain Layout
25460 \begin_inset Formula $A\sgn(x)+B$
25470 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
25473 \begin_layout Plain Layout
25477 \begin_inset Formula $\underbrace{\textrm{sgn}}_{\textrm{Alt+M}\,\textrm{M}}$
25485 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
25488 \begin_layout Plain Layout
25489 \begin_inset Formula $A\,\textrm{sgn}(x)+B$
25505 \begin_layout Standard
25506 The first method is more suitable when the self-defined function should
25507 be used several times.
25510 \begin_layout Subsection
25512 \begin_inset Index idx
25515 \begin_layout Plain Layout
25524 \begin_layout Standard
25525 For limits, in addition to the commands
25532 \begin_inset Index idx
25535 \begin_layout Plain Layout
25555 the following functions are defined:
25558 \begin_layout Standard
25560 \begin_inset Tabular
25561 <lyxtabular version="3" rows="5" columns="2">
25562 <features booktabs="true" tabularvalignment="middle">
25563 <column alignment="center" valignment="top" width="0pt">
25564 <column alignment="center" valignment="top" width="0pt">
25566 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
25569 \begin_layout Plain Layout
25575 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
25578 \begin_layout Plain Layout
25586 <cell alignment="center" valignment="top" leftline="true" usebox="none">
25589 \begin_layout Plain Layout
25597 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
25600 \begin_layout Plain Layout
25601 \begin_inset Formula $\varliminf$
25610 <row topspace="1.5mm">
25611 <cell alignment="center" valignment="top" usebox="none">
25614 \begin_layout Plain Layout
25622 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
25625 \begin_layout Plain Layout
25626 \begin_inset Formula $\varlimsup$
25635 <row topspace="1.5mm">
25636 <cell alignment="center" valignment="top" usebox="none">
25639 \begin_layout Plain Layout
25647 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
25650 \begin_layout Plain Layout
25651 \begin_inset Formula $\varprojlim$
25660 <row topspace="1.5mm" bottomspace="1mm">
25661 <cell alignment="center" valignment="top" bottomline="true" usebox="none">
25664 \begin_layout Plain Layout
25672 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
25675 \begin_layout Plain Layout
25676 \begin_inset Formula $\varinjlim$
25692 \begin_layout Standard
25693 \begin_inset VSpace medskip
25696 The limit is created by inserting a subscript.
25697 It is set right beside the function in an inline formula:
25700 \begin_layout Standard
25702 \begin_inset Tabular
25703 <lyxtabular version="3" rows="2" columns="2">
25704 <features booktabs="true" tabularvalignment="middle">
25705 <column alignment="center" valignment="top" width="0pt">
25706 <column alignment="center" valignment="top" width="0pt">
25708 <cell alignment="center" valignment="top" bottomline="true" usebox="none">
25711 \begin_layout Plain Layout
25717 <cell alignment="center" valignment="top" bottomline="true" usebox="none">
25720 \begin_layout Plain Layout
25728 <cell alignment="center" valignment="top" usebox="none">
25731 \begin_layout Plain Layout
25737 \begin_inset space \textvisiblespace{}
25741 \begin_inset space \textvisiblespace{}
25749 <cell alignment="center" valignment="top" usebox="none">
25752 \begin_layout Plain Layout
25753 \begin_inset Formula $\lim_{x\to A}x=B$
25769 \begin_layout Standard
25770 In a displayed formula the limit is set below the formula, as usual:
25771 \begin_inset Formula
25781 \begin_layout Standard
25782 \begin_inset VSpace medskip
25788 \begin_layout Standard
25789 How to adjust the typesetting of the limits see
25790 \begin_inset CommandInset ref
25792 reference "subsec:Operator-Limits"
25799 \begin_layout Subsection
25801 \begin_inset Index idx
25804 \begin_layout Plain Layout
25805 Functions ! modulo-
25813 \begin_layout Standard
25814 The modulo-function is special, because it exists in four variants.
25815 The variants in a displayed formula are:
25816 \begin_inset Formula
25818 \underline{\textrm{Command}\raisebox{-0.9mm}{}} & & \underline{\textrm{Result}}\\
25819 \mathrm{a\backslash mod\textrm{␣}b} & & a\mod b\\
25820 \mathrm{a\backslash pmod\textrm{␣}b} & & a\pmod b\\
25821 \mathrm{a\backslash bmod\textrm{␣}b} & & a\bmod b\\
25822 \mathrm{a\backslash pod\textrm{␣}b} & & a\pod b
25830 \begin_layout Standard
25831 In an inline formula less space is set before the function names for all
25833 By default the modulo-functions take only the first following character
25835 To use more than one character, one has to put them into \SpecialChar TeX
25837 \begin_inset Formula
25839 \underline{\textrm{Command}\raisebox{-0.9mm}{}} & & \underline{\textrm{Result}}\\
25840 \mathrm{a\backslash pod\textrm{␣}bcd} & & a\pod bcd\\
25841 \mathrm{a\backslash pod\backslash\{bc\to d} & & a\pod{bc}d
25849 \begin_layout Section
25851 \begin_inset Index idx
25854 \begin_layout Plain Layout
25863 \begin_layout Standard
25864 The characters ^ and _ would normally create a superscript and subscript,
25866 To get these characters you have to insert them with a leading
25871 \begin_layout Standard
25874 \begin_inset Tabular
25875 <lyxtabular version="3" rows="3" columns="2">
25876 <features booktabs="true" tabularvalignment="middle">
25877 <column alignment="left" valignment="top" width="0pt">
25878 <column alignment="block" valignment="top">
25880 <cell alignment="left" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
25883 \begin_layout Plain Layout
25889 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
25892 \begin_layout Plain Layout
25900 <cell alignment="left" valignment="top" leftline="true" usebox="none">
25903 \begin_layout Plain Layout
25907 \begin_inset space \textvisiblespace{}
25915 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
25918 \begin_layout Plain Layout
25919 \begin_inset Formula $\mathcircumflex$
25929 <cell alignment="left" valignment="top" bottomline="true" leftline="true" usebox="none">
25932 \begin_layout Plain Layout
25940 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
25943 \begin_layout Plain Layout
25944 \begin_inset Formula $\_$
25960 \begin_layout Subsection
25961 Special Characters in Mathematical Text
25964 \begin_layout Standard
25965 The following commands can only be used in mathematical text or in \SpecialChar TeX
25969 \begin_layout Standard
25970 \begin_inset space \hfill{}
25974 \begin_inset Tabular
25975 <lyxtabular version="3" rows="8" columns="2">
25976 <features booktabs="true" tabularvalignment="middle">
25977 <column alignment="left" valignment="top" width="0pt">
25978 <column alignment="block" valignment="top">
25980 <cell alignment="left" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
25983 \begin_layout Plain Layout
25989 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
25992 \begin_layout Plain Layout
26000 <cell alignment="left" valignment="top" leftline="true" usebox="none">
26003 \begin_layout Plain Layout
26011 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
26014 \begin_layout Plain Layout
26015 \begin_inset Formula $\textrm{œ}$
26025 <cell alignment="left" valignment="top" leftline="true" usebox="none">
26028 \begin_layout Plain Layout
26036 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
26039 \begin_layout Plain Layout
26040 \begin_inset Formula $\textrm{Œ}$
26050 <cell alignment="left" valignment="top" leftline="true" usebox="none">
26053 \begin_layout Plain Layout
26061 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
26064 \begin_layout Plain Layout
26065 \begin_inset Formula $\textrm{æ}$
26075 <cell alignment="left" valignment="top" leftline="true" usebox="none">
26078 \begin_layout Plain Layout
26086 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
26089 \begin_layout Plain Layout
26090 \begin_inset Formula $\textrm{Æ}$
26100 <cell alignment="left" valignment="top" leftline="true" usebox="none">
26103 \begin_layout Plain Layout
26111 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
26114 \begin_layout Plain Layout
26115 \begin_inset Formula $\textrm{å}$
26125 <cell alignment="left" valignment="top" leftline="true" usebox="none">
26128 \begin_layout Plain Layout
26132 \begin_inset Index idx
26135 \begin_layout Plain Layout
26142 \begin_layout Plain Layout
26163 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
26166 \begin_layout Plain Layout
26167 \begin_inset Formula $\textrm{Å}$
26177 <cell alignment="left" valignment="top" bottomline="true" leftline="true" usebox="none">
26180 \begin_layout Plain Layout
26188 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
26191 \begin_layout Plain Layout
26192 \begin_inset Formula $\textrm{ı}$
26206 \begin_inset space \hfill{}
26210 \begin_inset Tabular
26211 <lyxtabular version="3" rows="8" columns="2">
26212 <features booktabs="true" tabularvalignment="middle">
26213 <column alignment="left" valignment="top" width="0pt">
26214 <column alignment="center" valignment="top">
26216 <cell alignment="left" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
26219 \begin_layout Plain Layout
26221 \begin_inset Note Note
26224 \begin_layout Plain Layout
26226 \begin_inset space \thinspace{}
26229 mm is used for separation, because otherwise the output will be ¡ and ¿
26240 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
26243 \begin_layout Plain Layout
26251 <cell alignment="left" valignment="top" leftline="true" usebox="none">
26254 \begin_layout Plain Layout
26262 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
26265 \begin_layout Plain Layout
26266 \begin_inset Formula $\textrm{ø}$
26276 <cell alignment="left" valignment="top" leftline="true" usebox="none">
26279 \begin_layout Plain Layout
26287 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
26290 \begin_layout Plain Layout
26291 \begin_inset Formula $\textrm{Ø}$
26301 <cell alignment="left" valignment="top" leftline="true" usebox="none">
26304 \begin_layout Plain Layout
26312 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
26315 \begin_layout Plain Layout
26316 \begin_inset Formula $\textrm{ł}$
26326 <cell alignment="left" valignment="top" leftline="true" usebox="none">
26329 \begin_layout Plain Layout
26337 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
26340 \begin_layout Plain Layout
26341 \begin_inset Formula $\textrm{Ł}$
26351 <cell alignment="left" valignment="top" leftline="true" usebox="none">
26354 \begin_layout Plain Layout
26356 \begin_inset space \hspace{}
26361 \begin_inset space \textvisiblespace{}
26369 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
26372 \begin_layout Plain Layout
26373 \begin_inset Formula $\textrm{!`}$
26383 <cell alignment="left" valignment="top" leftline="true" usebox="none">
26386 \begin_layout Plain Layout
26388 \begin_inset space \hspace{}
26393 \begin_inset space \textvisiblespace{}
26401 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
26404 \begin_layout Plain Layout
26405 \begin_inset Formula $\textrm{?`}$
26415 <cell alignment="left" valignment="top" bottomline="true" leftline="true" usebox="none">
26418 \begin_layout Plain Layout
26426 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
26429 \begin_layout Plain Layout
26430 \begin_inset Formula $\textrm{ȷ}$
26444 \begin_inset space \hfill{}
26450 \begin_layout Standard
26452 \begin_inset Formula $\textrm{\textrm{Å}}$
26456 \begin_inset Formula $\textrm{\textrm{Ø}}$
26459 can also be inserted via the math toolbar button
26462 arg "math-insert \\digamma"
26468 \begin_layout Standard
26469 An exception are the commands
26472 \begin_inset space \hspace{}
26481 \begin_inset space \hspace{}
26487 , because they can be inserted in \SpecialChar LyX
26491 \begin_layout Subsection
26493 \begin_inset CommandInset label
26495 name "subsec:Accents-in-Text"
26500 \begin_inset Index idx
26503 \begin_layout Plain Layout
26512 \begin_layout Standard
26513 With the following commands all letters can be accented.
26514 The commands must be inserted in \SpecialChar TeX
26518 \begin_layout Standard
26519 \begin_inset space \hfill{}
26523 \begin_inset Tabular
26524 <lyxtabular version="3" rows="8" columns="2">
26525 <features booktabs="true" tabularvalignment="middle">
26526 <column alignment="left" valignment="top" width="0pt">
26527 <column alignment="block" valignment="top">
26529 <cell alignment="left" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
26532 \begin_layout Plain Layout
26538 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
26541 \begin_layout Plain Layout
26549 <cell alignment="left" valignment="top" leftline="true" usebox="none">
26552 \begin_layout Plain Layout
26556 \begin_inset Quotes grd
26564 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
26567 \begin_layout Plain Layout
26571 \begin_layout Plain Layout
26587 <cell alignment="left" valignment="top" leftline="true" usebox="none">
26590 \begin_layout Plain Layout
26598 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
26601 \begin_layout Plain Layout
26605 \begin_layout Plain Layout
26621 <cell alignment="left" valignment="top" leftline="true" usebox="none">
26624 \begin_layout Plain Layout
26628 \begin_inset space \textvisiblespace{}
26636 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
26639 \begin_layout Plain Layout
26643 \begin_layout Plain Layout
26659 <cell alignment="left" valignment="top" leftline="true" usebox="none">
26662 \begin_layout Plain Layout
26670 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
26673 \begin_layout Plain Layout
26677 \begin_layout Plain Layout
26693 <cell alignment="left" valignment="top" leftline="true" usebox="none">
26696 \begin_layout Plain Layout
26700 \begin_inset space \textvisiblespace{}
26708 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
26711 \begin_layout Plain Layout
26715 \begin_layout Plain Layout
26731 <cell alignment="left" valignment="top" leftline="true" usebox="none">
26734 \begin_layout Plain Layout
26738 \begin_inset space \textvisiblespace{}
26746 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
26749 \begin_layout Plain Layout
26753 \begin_layout Plain Layout
26769 <cell alignment="left" valignment="top" bottomline="true" leftline="true" usebox="none">
26772 \begin_layout Plain Layout
26776 \begin_inset space \textvisiblespace{}
26784 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
26787 \begin_layout Plain Layout
26791 \begin_layout Plain Layout
26811 \begin_inset space \hfill{}
26815 \begin_inset Tabular
26816 <lyxtabular version="3" rows="8" columns="2">
26817 <features booktabs="true" tabularvalignment="middle">
26818 <column alignment="left" valignment="top" width="0pt">
26819 <column alignment="center" valignment="top">
26821 <cell alignment="left" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
26824 \begin_layout Plain Layout
26830 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
26833 \begin_layout Plain Layout
26841 <cell alignment="left" valignment="top" leftline="true" usebox="none">
26844 \begin_layout Plain Layout
26848 \begin_inset space \textvisiblespace{}
26856 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
26859 \begin_layout Plain Layout
26863 \begin_layout Plain Layout
26879 <cell alignment="left" valignment="top" leftline="true" usebox="none">
26882 \begin_layout Plain Layout
26890 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
26893 \begin_layout Plain Layout
26897 \begin_layout Plain Layout
26913 <cell alignment="left" valignment="top" leftline="true" usebox="none">
26916 \begin_layout Plain Layout
26920 \begin_inset Index idx
26923 \begin_layout Plain Layout
26934 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
26937 \begin_layout Plain Layout
26941 \begin_layout Plain Layout
26957 <cell alignment="left" valignment="top" leftline="true" usebox="none">
26960 \begin_layout Plain Layout
26968 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
26971 \begin_layout Plain Layout
26975 \begin_layout Plain Layout
26991 <cell alignment="left" valignment="top" leftline="true" usebox="none">
26994 \begin_layout Plain Layout
26998 \begin_inset space \textvisiblespace{}
27006 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
27009 \begin_layout Plain Layout
27013 \begin_layout Plain Layout
27029 <cell alignment="left" valignment="top" leftline="true" usebox="none">
27032 \begin_layout Plain Layout
27036 \begin_inset space \textvisiblespace{}
27044 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
27047 \begin_layout Plain Layout
27051 \begin_layout Plain Layout
27067 <cell alignment="left" valignment="top" leftline="true" usebox="none">
27070 \begin_layout Plain Layout
27074 \begin_inset space \textvisiblespace{}
27082 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
27085 \begin_layout Plain Layout
27089 \begin_layout Plain Layout
27109 \begin_inset space \hfill{}
27115 \begin_layout Standard
27116 \begin_inset VSpace medskip
27125 also two different characters can be accented.
27131 \begin_inset space \textvisiblespace{}
27140 \begin_layout Plain Layout
27152 \begin_layout Standard
27165 can in combination with vowels directly be inserted with the keyboard without
27166 using \SpecialChar TeX
27168 The same applies for the tilde
27172 \begin_layout Plain Layout
27173 This only applies for keyboards where the tilde is defined as accent.
27182 in combination with
27197 \begin_layout Standard
27240 and accents that are inserted directly with the keyboard are also available
27241 in mathematical text.
27242 For the other accents there are special math commands to be used in formulas,
27244 \begin_inset CommandInset ref
27246 reference "subsec:Accents-for-one"
27253 \begin_layout Standard
27254 \begin_inset VSpace bigskip
27257 Furthermore, with the command
27264 \begin_inset Index idx
27267 \begin_layout Plain Layout
27275 all numbers and letters can be set into a circle, quasi accented with a
27276 circle, similar to the copyright symbol.
27279 \begin_layout Standard
27281 \begin_inset Tabular
27282 <lyxtabular version="3" rows="3" columns="2">
27283 <features booktabs="true" tabularvalignment="middle">
27284 <column alignment="center" valignment="top" width="0pt">
27285 <column alignment="center" valignment="top">
27287 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
27290 \begin_layout Plain Layout
27296 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
27299 \begin_layout Plain Layout
27307 <cell alignment="center" valignment="top" leftline="true" usebox="none">
27310 \begin_layout Plain Layout
27318 <cell multicolumn="1" alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
27321 \begin_layout Plain Layout
27325 \begin_layout Plain Layout
27340 <row topspace="1mm">
27341 <cell alignment="center" valignment="top" bottomline="true" usebox="none">
27344 \begin_layout Plain Layout
27355 raisebox{-1.5pt}{W}}
27360 <cell multicolumn="1" alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
27363 \begin_layout Plain Layout
27367 \begin_layout Plain Layout
27397 \begin_layout Standard
27398 One has to take care that the character fits in the circle.
27409 \begin_layout Plain Layout
27411 \begin_inset CommandInset ref
27413 reference "subsec:Font-Sizes"
27422 specifies thereby the size of the circle.
27433 \begin_layout Plain Layout
27435 \begin_inset CommandInset ref
27437 reference "subsec:Boxes-without-Frame"
27446 the character can be centered.
27449 \begin_layout Subsection
27451 \begin_inset Index idx
27454 \begin_layout Plain Layout
27463 \begin_layout Standard
27464 Old-style figures (also known as old-style numerals) are created with the
27472 \begin_inset Index idx
27475 \begin_layout Plain Layout
27484 The command can be used in formulas and in \SpecialChar TeX
27486 The command scheme is:
27489 \begin_layout Standard
27494 oldstylenums{number}
27497 \begin_layout Standard
27502 oldstylenums{0123456789
27505 \begin_inset Formula $\oldstylenums{0123456789}$
27511 \begin_layout Section
27513 \begin_inset CommandInset label
27515 name "sec:Formula-Styles"
27520 \begin_inset Index idx
27523 \begin_layout Plain Layout
27532 \begin_layout Itemize
27533 There are two different alignment styles:
27537 \begin_layout Description
27538 Centered is the predefined standard
27541 \begin_layout Description
27542 Indented for this the option
27546 must be inserted in the menu
27548 Document\SpecialChar menuseparator
27554 \begin_inset space ~
27560 \begin_layout Standard
27565 is used, the indentation can be adjusted with the length
27572 \begin_inset Index idx
27575 \begin_layout Plain Layout
27584 Should the distance be 15
27585 \begin_inset space \thinspace{}
27588 mm, the following command line is inserted in the \SpecialChar LaTeX
27592 \begin_layout Standard
27602 \begin_layout Standard
27603 When no length is specified, a predefined value will be used.
27604 The value depends on the used document class.
27608 \begin_layout Itemize
27609 And two different numbering styles:
27613 \begin_layout Description
27614 Right is the predefined standard
27617 \begin_layout Description
27618 Left for this the option
27622 must be inserted in the menu
27624 Document\SpecialChar menuseparator
27630 \begin_inset space ~
27637 \begin_layout Standard
27646 can also be used together.
27647 In this case both options are inserted, separated by a comma.
27650 \begin_layout Standard
27651 The chosen styles are used for all displayed formulas of the document.
27652 When both, centered and indented formulas should be created in a document,
27658 The indented formulas are then set in a flalign environment, see
27659 \begin_inset CommandInset ref
27661 reference "subsec:Flalign-Environment"
27668 \begin_layout Section
27670 \begin_inset CommandInset label
27672 name "sec:Multiline-Formulas"
27677 \begin_inset Index idx
27680 \begin_layout Plain Layout
27681 Formula ! multiline
27689 \begin_layout Subsection
27693 \begin_layout Standard
27694 In \SpecialChar LyX
27695 multiline formulas are created by pressing
27698 arg "newline-insert newline"
27702 This creates either an
27706 that is described in
27707 \begin_inset CommandInset ref
27709 reference "subsec:Standard-align-Environment"
27713 or, when automatically loading the package
27717 is disabled in the document settings, an
27719 eqnarray environment
27721 that is described in
27722 \begin_inset CommandInset ref
27724 reference "subsec:Eqnarray-Environment"
27729 The align environment is recommended because it provides in any case a
27730 typographically correct output.
27733 \begin_layout Standard
27734 There are other multiline formula environments that can be created via the
27737 Insert\SpecialChar menuseparator
27741 These environments are described in the following sections.
27744 \begin_layout Standard
27745 In all multiline formula environments a new line is created by pressing
27749 arg "newline-insert newline"
27753 To add or delete lines, the math toolbar buttons
27756 arg "tabular-feature append-row"
27762 arg "tabular-feature delete-row"
27765 , respectively, or the menu
27767 Edit\SpecialChar menuseparator
27773 \begin_layout Subsubsection
27775 \begin_inset CommandInset label
27777 name "subsec:Line-Separation"
27782 \begin_inset Index idx
27785 \begin_layout Plain Layout
27786 Formula ! multiline ! Line separation
27794 \begin_layout Standard
27795 There is sometimes not enough space in multiline formulas between the lines:
27796 \begin_inset Formula
27798 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}\\
27799 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
27807 \begin_layout Standard
27808 In \SpecialChar LaTeX
27809 additional line space is specified as optional argument of the new line
27811 This is not yet possible in \SpecialChar LyX
27816 \begin_layout Plain Layout
27818 \begin_inset CommandInset href
27820 name "LyX-bug #1505"
27821 target "http://www.lyx.org/trac/ticket/1505"
27830 , therefore the whole formula must be inserted in \SpecialChar TeX
27832 To add in our example space, the command
27840 is inserted at the end of the first line.
27845 \begin_layout Plain Layout
27852 \begin_layout Plain Layout
27854 B^{2}(B^{2}-2r_{g}^{2}+2x_{0}^{2}-2r_{k}^{2})+4x_{0}^{2}x^{2}+4x_{0}xD &
27857 textrm{-}4x^{2}B^{2}+4x_{0}xB^{2}
27864 \begin_layout Plain Layout
27868 left(B^{2}+x_{0}^{2}
27876 left(B^{2}-2r_{g}^{2}+2x_{0}^{2}-2r_{k}^{2}
27881 \begin_layout Plain Layout
27893 \begin_layout Standard
27894 \begin_inset VSpace bigskip
27897 To set the line separation for all lines in a formula, the length
27904 \begin_inset Index idx
27907 \begin_layout Plain Layout
27917 \begin_inset Formula $\mbox{line separation}=\mathrm{6\,pt+\backslash jot}$
27928 \begin_inset space \thinspace{}
27933 \begin_inset space \thinspace{}
27936 mm additional line separation as in the previous example, the command
27939 \begin_layout Standard
27949 \begin_layout Standard
27950 is inserted in \SpecialChar TeX
27951 mode before the formula.
27952 This requires that the \SpecialChar LaTeX
27961 \begin_layout Plain Layout
27966 is part of every \SpecialChar LaTeX
27967 standard installation.
27973 \begin_inset Index idx
27976 \begin_layout Plain Layout
27982 was loaded in \SpecialChar LaTeX
27983 -preamble with the line
27986 \begin_layout Standard
27994 \begin_layout Standard
27999 \begin_layout Plain Layout
28011 \begin_inset Formula
28013 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}\\
28014 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
28022 \begin_layout Standard
28026 \begin_layout Plain Layout
28037 To get back to the predefined distance,
28043 is set to the value 3
28044 \begin_inset space \thinspace{}
28050 \begin_layout Subsubsection
28052 \begin_inset CommandInset label
28054 name "subsec:Column-Separation"
28059 \begin_inset Index idx
28062 \begin_layout Plain Layout
28063 Formula ! multiline ! Column separation
28071 \begin_layout Standard
28072 Multiline formulas form a matrix.
28073 A formula in the eqnarray environment is for example a matrix with three
28075 By changing the column separation in this environment, the space beside
28076 the relation sign can be changed.
28079 \begin_layout Standard
28080 The column separation is specified with the length
28087 \begin_inset Index idx
28090 \begin_layout Plain Layout
28099 \begin_inset Newline newline
28102 column separation = 2
28103 \begin_inset space \thinspace{}
28113 \begin_inset Newline newline
28119 \begin_layout Standard
28129 \begin_layout Standard
28130 inserted in \SpecialChar TeX
28131 mode, sets for all following formulas a column separation of
28133 \begin_inset space \thinspace{}
28137 To get back to the predefined distance,
28144 \begin_inset space \thinspace{}
28150 \begin_layout Standard
28152 \begin_inset space \thinspace{}
28155 cm column separation:
28159 \begin_layout Plain Layout
28171 \begin_inset Formula
28179 A formula with the predefined column separation for matrices of 10
28180 \begin_inset space \thinspace{}
28187 \begin_layout Plain Layout
28199 \begin_inset Formula
28210 \begin_layout Standard
28211 \begin_inset Newpage newpage
28217 \begin_layout Subsubsection
28219 \begin_inset Index idx
28222 \begin_layout Plain Layout
28231 \begin_layout Standard
28232 Long formulas can be typeset using these methods:
28235 \begin_layout Itemize
28236 When one side of the equation is much shorter than the line width, this
28237 one is chosen for the left side and the right side is typeset over two
28239 \begin_inset Formula
28241 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 \\
28242 & & -\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}
28247 The minus sign at the beginning of the second line does normally not appear
28248 as an operator because it is the first character of the line.
28249 Thus it would not be surrounded by space and could not be distinguished
28250 from the fraction bar.
28252 \begin_inset space \thinspace{}
28255 pt space was inserted behind the minus sign with the command
28265 \begin_layout Plain Layout
28273 \begin_inset CommandInset ref
28275 reference "subsec:Variable-Space"
28285 \begin_inset Index idx
28288 \begin_layout Plain Layout
28299 \begin_layout Itemize
28300 When both sides of the equation are too long, the command
28307 \begin_inset Index idx
28310 \begin_layout Plain Layout
28319 It is inserted in the first column of the first line and causes all further
28320 insertions to overwrite the following columns:
28321 \begin_inset Formula
28323 \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 \\
28324 & & -\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 \\
28325 & & =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}
28330 After the insertion of
28336 , the cursor is in a purple box that is a bit shifted to the left from the
28338 In this the formula is inserted.
28339 \begin_inset Newline newline
28342 The content of the further lines is inserted to the second or another formula
28344 The greater the column number where it was inserted, the larger the indentation.
28345 \begin_inset VSpace medskip
28349 \begin_inset Newline newline
28353 \begin_inset Note Greyedout
28356 \begin_layout Plain Layout
28357 Note the following when using
28366 \begin_layout Itemize
28367 The formula doesn't use the full page width.
28369 \begin_inset space \thinspace{}
28373 \begin_inset space \space{}
28377 \begin_inset Formula $-B^{2}$
28380 is added to the first line in the above example, it would have been outside
28382 To better use the width, negative space can be inserted at the beginning
28386 \begin_layout Itemize
28387 Due to a bug in \SpecialChar LyX
28388 the cursor cannot be set with the mouse into the first
28393 \begin_layout Plain Layout
28394 \begin_inset CommandInset href
28396 name "LyX-bug #1429"
28397 target "http://www.lyx.org/trac/ticket/1429"
28406 One can only set the cursor at the beginning of the line and move it with
28415 \begin_layout Itemize
28416 Other methods to set long formulas are offered by the environments described
28418 \begin_inset CommandInset ref
28420 reference "subsec:Multline-Environment"
28425 \begin_inset CommandInset ref
28427 reference "subsec:Multiline-Formula-Parts"
28434 \begin_layout Subsubsection
28435 Multiline Fractions
28436 \begin_inset CommandInset label
28438 name "subsec:Multiline-Fractions"
28443 \begin_inset Index idx
28446 \begin_layout Plain Layout
28447 Fractions ! multiline
28455 \begin_layout Standard
28456 There are cases where the denominator and/or the numerator of a fraction
28457 is so long that the fraction does not fit into one line.
28458 It is then necessary to add a line break within the fraction.
28459 This can be done using the command
28466 \begin_inset Index idx
28469 \begin_layout Plain Layout
28478 To activate it, set in the document settings under
28481 \begin_inset space ~
28491 \begin_inset Index idx
28494 \begin_layout Plain Layout
28495 Packages ! mathtools
28503 \begin_inset space ~
28518 \begin_layout Standard
28523 splitfrac{first line}{second line}
28526 \begin_layout Standard
28527 and is used as denominator and/or numerator:
28530 \begin_layout Standard
28531 \begin_inset Formula
28533 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}
28538 The command for the first numerator above is:
28541 \begin_layout Standard
28546 splitfrac{xy+xy+xy+xy+xy
28547 \begin_inset space \textvisiblespace{}
28555 \begin_layout Subsubsection
28557 \begin_inset CommandInset label
28559 name "subsec:Multiline-Brackets"
28564 \begin_inset Index idx
28567 \begin_layout Plain Layout
28568 Brackets ! for multiline expressions
28576 \begin_layout Standard
28577 For brackets spanning multiple lines the following problem occurs:
28578 \begin_inset Formula
28580 A & = & \sin(x)\left[\prod_{R=1}^{\infty}\frac{1}{R}+\cdots\right.\\
28581 & & \left.\cdots+B-D\right]
28589 \begin_layout Standard
28590 The closing bracket is smaller than the opening bracket because brackets
28591 with variable size may not span multiple lines.
28594 \begin_layout Standard
28595 To set the bracket size for the second line correctly, the first line is
28603 \begin_inset Index idx
28606 \begin_layout Plain Layout
28614 and the second line with
28622 \begin_layout Plain Layout
28636 \begin_inset CommandInset ref
28638 reference "subsec:Automatic-Bracket-Size"
28650 \begin_inset Index idx
28653 \begin_layout Plain Layout
28676 \begin_inset space \textvisiblespace{}
28686 \begin_inset space \textvisiblespace{}
28696 \begin_inset space \textvisiblespace{}
28702 \begin_inset Formula $\downarrow$
28708 \begin_inset Index idx
28711 \begin_layout Plain Layout
28719 is inserted, because the multiplication operator with its limits is the
28720 largest symbol in the first line and this should be the size for the bracket
28721 in the second line.
28724 \begin_layout Standard
28725 The result is this:
28726 \begin_inset Formula
28728 A & = & \sin(x)\left[\prod_{R=1}^{\infty}\frac{1}{R}+\cdots\right.\\
28729 & & \left.\vphantom{\prod_{R=1}^{\infty}}\cdots+B-D\right]
28737 \begin_layout Subsection
28741 \begin_layout Standard
28742 Align environments can be used for every kind of multiline formulas.
28743 They are especially useful to set several formulas side by side.
28746 \begin_layout Standard
28747 Align environments consist of columns.
28748 The odd columns are right aligned, the even ones left aligned.
28749 Every line in an Align environment can be numbered.
28752 \begin_layout Standard
28753 Align environments are created via the menu
28755 Insert\SpecialChar menuseparator
28761 Edit\SpecialChar menuseparator
28762 Math\SpecialChar menuseparator
28763 Change Formula Type
28765 already existing formulas can be converted to Align environments.
28768 \begin_layout Standard
28769 To add or delete columns, the math toolbar buttons
28772 arg "tabular-feature append-column"
28778 arg "tabular-feature delete-column"
28781 , respectively, or the menu
28783 Edit\SpecialChar menuseparator
28789 \begin_layout Subsubsection
28790 Standard align Environment
28791 \begin_inset CommandInset label
28793 name "subsec:Standard-align-Environment"
28798 \begin_inset Index idx
28801 \begin_layout Plain Layout
28802 Formula ! multiline ! align environment
28810 \begin_layout Standard
28811 This Align environment is created by pressing
28814 arg "newline-insert newline"
28817 in a formula or by the menu
28819 Insert\SpecialChar menuseparator
28820 Math\SpecialChar menuseparator
28821 AMS align Environment
28826 \begin_layout Standard
28827 An example for two formulas set side by side, that are created with a four
28828 column align environment:
28829 \begin_inset Formula
28831 A & =\sin(B) & C & =D\\
28832 C & \ne A & B & \ne D
28837 As it can be seen, the formulas in this environment are placed so as if
28846 \begin_layout Plain Layout
28854 \begin_inset CommandInset ref
28856 reference "subsec:Variable-Space"
28867 before the first and after every even column.
28868 When the formula style
28874 \begin_layout Plain Layout
28876 \begin_inset CommandInset ref
28878 reference "sec:Formula-Styles"
28889 is used, the formula is set without the
28895 before the first column.
28898 \begin_layout Subsubsection
28899 Alignat Environment
28900 \begin_inset Index idx
28903 \begin_layout Plain Layout
28904 Formula ! multiline ! alignat environment
28912 \begin_layout Standard
28913 The alignat environment has no predefined column separation.
28914 It can be inserted manually with the spaces that are described
28915 \begin_inset CommandInset ref
28917 reference "subsec:Space"
28924 \begin_layout Standard
28925 The above example in the alignat environment where 1
28926 \begin_inset space \thinspace{}
28929 cm space was inserted at the beginning of the second formula:
28930 \begin_inset Formula
28931 \begin{alignat*}{2}
28932 A & =\sin(B) & \hspace{1cm}C & =D\\
28933 C & \ne A & B & \ne D
28938 Because the column separation can be set separately for every column, this
28939 environment is especially suitable to set three and more formulas side
28943 \begin_layout Subsubsection
28944 Flalign Environment
28945 \begin_inset CommandInset label
28947 name "subsec:Flalign-Environment"
28952 \begin_inset Index idx
28955 \begin_layout Plain Layout
28956 Formula ! multiline ! flalign environment
28964 \begin_layout Standard
28965 In this environment the first two columns are always set as much as possible
28966 to the left and the last two ones to the right.
28968 \begin_inset Formula
28970 A & =1 & B & =2 & C & =3\\
28971 X & =\textrm{-}1 & Y & =\textrm{-}2 & Z & =4
28979 \begin_layout Standard
28980 By creating a flalign environment with an odd number of columns where an
28981 empty \SpecialChar TeX
28982 brace is inserted to the last column, several formulas in a document
28983 can be set to the left, although the formula style
28988 As example the indented formula
28989 \begin_inset CommandInset ref
28991 reference "eq:VolInt"
28996 \begin_inset Formula
28998 \hspace{30pt}\iiint\limits _{V}X\,\mathrm{d}V & =U & {}
29003 The first two columns contain the formula.
29004 To indent it as with the formula style
29009 \begin_inset space \thinspace{}
29012 pt space was inserted at the beginning of the first column.
29015 \begin_layout Subsection
29016 Eqnarray Environment
29017 \begin_inset CommandInset label
29019 name "subsec:Eqnarray-Environment"
29024 \begin_inset Index idx
29027 \begin_layout Plain Layout
29028 Formula ! multiline ! eqnarray environment
29036 \begin_layout Standard
29037 When this environment has been created, three blue boxes appear.
29038 The content of the first box is right aligned, the content of the last
29040 The content of the middle box appears centered and a bit smaller, because
29041 it is designed to insert there only relation characters.
29042 \begin_inset Formula
29044 \frac{ABC}{D} & \frac{ABC}{D} & \frac{ABC}{D}\\
29054 \begin_layout Subsection
29056 \begin_inset Index idx
29059 \begin_layout Plain Layout
29060 Formula ! multiline ! gather environment
29068 \begin_layout Standard
29069 This environment consists of only one centered column.
29070 Every line can be numbered.
29071 \begin_inset Formula
29082 \begin_layout Subsection
29083 Multline Environment
29084 \begin_inset CommandInset label
29086 name "subsec:Multline-Environment"
29091 \begin_inset Index idx
29094 \begin_layout Plain Layout
29095 Formula ! multiline ! multline environment
29103 \begin_layout Standard
29104 The multline environment consists, like the gather environment, of only
29106 But the first line is left aligned, the last one right aligned.
29107 All other lines are centered.
29108 Therefore this environment is suitable for long formulas.
29110 \begin_inset CommandInset ref
29112 reference "eq:lefteqn"
29116 in the multline environment:
29117 \begin_inset Formula
29119 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}\\
29120 -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}\\
29121 =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}}
29129 \begin_layout Standard
29130 In the output only the last (first) line of a multline environment appears
29131 numbered when the document numbering is right (left).
29135 \begin_layout Plain Layout
29136 numbering styles see
29137 \begin_inset CommandInset ref
29139 reference "sec:Formula-Styles"
29151 \begin_layout Standard
29159 \begin_inset Index idx
29162 \begin_layout Plain Layout
29177 \begin_inset Index idx
29180 \begin_layout Plain Layout
29188 a centered line can be right or left aligned, respectively.
29189 The commands are used as follows:
29192 \begin_layout Standard
29197 shoveright{line content}
29203 shoveleft{line content}
29206 \begin_layout Standard
29207 \begin_inset VSpace medskip
29217 \begin_inset Index idx
29220 \begin_layout Plain Layout
29228 specifies the distance of the first line from the left page margin.
29229 Predefined is the length 0
29230 \begin_inset space \thinspace{}
29236 \begin_layout Standard
29237 As example the above formula where the command
29240 \begin_layout Standard
29250 \begin_layout Standard
29251 was inserted in \SpecialChar TeX
29256 \begin_layout Plain Layout
29268 \begin_inset Formula
29270 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}\\
29271 \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}}\\
29272 =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}}
29281 \begin_layout Plain Layout
29292 The second line was left aligned using
29301 \begin_layout Subsection
29302 Multiline Formula Parts
29303 \begin_inset CommandInset label
29305 name "subsec:Multiline-Formula-Parts"
29310 \begin_inset Index idx
29313 \begin_layout Plain Layout
29314 Formula ! multiline ! formula parts
29322 \begin_layout Standard
29323 To display only parts of a formula with multiple lines, one of the following
29324 environments is used:
29341 They can be inserted via the menu
29343 Insert\SpecialChar menuseparator
29346 or by using the commands described in this section.
29349 \begin_layout Standard
29350 The first three have the same properties as the corresponding multiline
29351 formula environments, but it is possible to set further formula parts beside
29354 \begin_inset Formula
29356 \left.\begin{aligned}\Delta x\Delta p & \ge\frac{\hbar}{2}\\
29357 \Delta E\Delta t & \ge\frac{\hbar}{2}
29359 \right\} \textrm{Uncertainty relations}
29367 \begin_layout Standard
29368 To get this formula, a displayed formula is created where the command
29375 \begin_inset Index idx
29378 \begin_layout Plain Layout
29387 A purple box appears around the blue formula box where now columns and
29388 lines can be added.
29389 Outside the multiline environment other formula parts can be set, like
29393 \begin_layout Standard
29394 The aligned environment is also suitable for long formulas whose lines are
29395 horizontally aligned.
29396 Using aligned in a displayed formula has the advantage that the formula
29397 number is vertically centered behind the lines.
29399 \begin_inset CommandInset ref
29401 reference "eq:shortlong"
29405 in the aligned environment:
29406 \begin_inset Formula
29408 \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}|}\\
29409 & -\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}|}
29418 \begin_layout Standard
29419 To use the environments
29438 \begin_inset Index idx
29441 \begin_layout Plain Layout
29456 \begin_inset Index idx
29459 \begin_layout Plain Layout
29474 \begin_inset Index idx
29477 \begin_layout Plain Layout
29485 are inserted, respectively.
29486 The split environment has the same properties as the aligned environment
29487 but it can only have two columns.
29490 \begin_layout Subsection
29491 Text in multiline Formulas
29492 \begin_inset CommandInset label
29494 name "subsec:Text-in-multiline"
29499 \begin_inset Index idx
29502 \begin_layout Plain Layout
29509 \begin_inset Index idx
29512 \begin_layout Plain Layout
29513 Formula ! multiline ! text
29521 \begin_layout Standard
29522 In the Align environments, and the multline and gather environment, text
29523 can be inserted that will appear in a separate line and doesn't affect
29524 the column alignment.
29525 To do this, the command
29532 \begin_inset Index idx
29535 \begin_layout Plain Layout
29543 is used in the following scheme:
29546 \begin_layout Standard
29554 \begin_layout Standard
29555 The text should not be longer than a line because it cannot be hyphenated.
29556 As \SpecialChar LyX
29557 doesn't yet support
29563 directly, the text is written as mathematical text.
29570 must hereby be at the beginning of a line and appears in the output above
29572 An example where the text was inserted at the beginning of the second line:
29573 \begin_inset Formula
29575 I & =a\sqrt{2}\int_{0}^{2\pi}\sqrt{1+\cos(\phi)}\;\mathrm{d}\phi\\
29576 \intertext{\text{integrand is symmetric to \ensuremath{\phi=\pi}, therefore}} & =2a\sqrt{2}\int_{0}^{\pi}\sqrt{1+\cos(\phi)}\;\mathrm{d}\phi
29584 \begin_layout Standard
29591 always creates some vertical space between the text and the formula lines.
29592 To avoid this space, set in the document settings under
29595 \begin_inset space ~
29605 \begin_inset Index idx
29608 \begin_layout Plain Layout
29609 Packages ! mathtools
29617 \begin_inset space ~
29623 Then you can use the command
29630 \begin_inset Index idx
29633 \begin_layout Plain Layout
29650 \begin_layout Standard
29651 \begin_inset Formula
29653 I & =a\sqrt{2}\int_{0}^{2\pi}\sqrt{1+\cos(\phi)}\;\mathrm{d}\phi\\
29654 \shortintertext{\text{integrand is symmetric to \ensuremath{\phi=\pi}, therefore}} & =2a\sqrt{2}\int_{0}^{\pi}\sqrt{1+\cos(\phi)}\;\mathrm{d}\phi
29662 \begin_layout Section
29664 \begin_inset Index idx
29667 \begin_layout Plain Layout
29674 \begin_inset Index idx
29677 \begin_layout Plain Layout
29678 Formula ! numbering|see
29682 \begin_layout Plain Layout
29693 \begin_layout Plain Layout
29708 \begin_layout Subsection
29712 \begin_layout Standard
29713 Numbered formulas can be created with the menu
29715 Insert\SpecialChar menuseparator
29716 Math\SpecialChar menuseparator
29718 \begin_inset space ~
29726 \begin_inset space ~
29732 Existing formulas can be numbered with the menu
29734 Edit\SpecialChar menuseparator
29735 Math\SpecialChar menuseparator
29737 \begin_inset space ~
29745 arg "math-number-toggle"
29749 The formula number is displayed in \SpecialChar LyX
29750 behind the formula as a number sign
29752 The number sign is replaced in the output by the formula number.
29755 \begin_layout Standard
29756 When numbering is turned on in multiline formulas, all lines will be numbered.
29757 But the numbering can be controlled with the menu
29759 Edit\SpecialChar menuseparator
29760 Math\SpecialChar menuseparator
29762 \begin_inset space ~
29766 \begin_inset space ~
29770 \begin_inset space ~
29778 arg "math-number-line-toggle"
29784 \begin_layout Standard
29785 Except for inline formulas, all formulas can be numbered with two different
29787 \begin_inset CommandInset ref
29789 reference "sec:Formula-Styles"
29796 \begin_layout Subsection
29798 \begin_inset Index idx
29801 \begin_layout Plain Layout
29802 Cross-references ! to formulas
29810 \begin_layout Standard
29811 All labeled formulas can be cross-referenced.
29812 A label is added by the menu
29814 Insert\SpecialChar menuseparator
29817 or the toolbar button
29824 The cursor must hereby be inside a displayed formula.
29825 Alternatively you can right-click on the formula and choose
29830 A dialog pops up displaying the prefix
29835 The label is inserted there behind the prefix.
29836 The predefined prefix means
29837 \begin_inset Quotes eld
29841 \begin_inset Quotes erd
29844 and makes it easier to find labels in large documents because it marks
29845 it as formula label to divide it from e.
29846 \begin_inset space \thinspace{}
29850 \begin_inset space \space{}
29854 To change a label, the menu
29856 Insert\SpecialChar menuseparator
29859 is used again or you right-click on a formula and then on
29866 \begin_layout Standard
29867 The name of the label is displayed in \SpecialChar LyX
29868 within two parentheses behind formula.
29869 A formula with a label is always numbered.
29872 \begin_layout Standard
29873 Cross-references are inserted via the menu
29875 Insert\SpecialChar menuseparator
29878 or with the toolbar button
29881 arg "dialog-show-new-inset ref"
29885 A formula cross-reference appears in the output as formula number.
29886 When in the cross-reference dialog window the format
29890 is chosen, the cross-reference appears in the output as formula number
29892 \begin_inset Newline newline
29895 By right-clicking on a cross-reference in \SpecialChar LyX
29896 , one jumps to the formula that
29900 \begin_layout Standard
29901 Here are as examples cross-references to formulas of the following subsections:
29902 \begin_inset Note Note
29905 \begin_layout Plain Layout
29906 Note the different cross-reference types.
29914 \begin_layout Standard
29916 \begin_inset CommandInset ref
29923 \begin_inset CommandInset ref
29931 \begin_inset CommandInset ref
29937 ) big Latin letters are used for the numbering in contrary to (
29938 \begin_inset CommandInset ref
29947 \begin_layout Standard
29948 \begin_inset VSpace medskip
29951 When the argument of
29959 \begin_layout Plain Layout
29967 \begin_inset CommandInset ref
29969 reference "subsec:User-defined-Numbering"
29980 contains a box like in
29981 \begin_inset CommandInset ref
29983 reference "subsec:Paragraph-Boxes"
29987 , the formula cannot be referenced.
29990 \begin_layout Subsection
29992 \begin_inset Index idx
29995 \begin_layout Plain Layout
29996 Formula numbering ! subnumbering
30004 \begin_layout Standard
30005 With the help of the commands
30009 begin{subequations}
30017 formulas can be subnumbered.
30018 Both commands are inserted in \SpecialChar TeX
30022 \begin_layout Standard
30024 \begin_inset Formula
30035 \begin_layout Plain Layout
30039 begin{subequations}
30045 \begin_inset VSpace -5mm
30049 \begin_inset Formula
30057 \begin_inset Formula
30067 \begin_layout Standard
30071 \begin_layout Plain Layout
30083 \begin_layout Standard
30084 To create the example, the following is done:
30087 \begin_layout Enumerate
30088 first formula is inserted
30091 \begin_layout Enumerate
30096 begin{subequations}
30097 \begin_inset Newline newline
30102 is inserted after the first formula
30105 \begin_layout Enumerate
30106 second formula is inserted
30109 \begin_layout Enumerate
30110 third formula is inserted
30113 \begin_layout Enumerate
30120 is inserted after the third formula
30123 \begin_layout Standard
30124 Every formula between the commands
30136 will be subnumbered with a, b, c, \SpecialChar ldots
30138 For multiline formulas every line will be subnumbered.
30141 \begin_layout Standard
30142 Referencing subequations work like for normal equations:
30143 \begin_inset CommandInset ref
30150 \begin_inset CommandInset ref
30157 If you want to reference the subequations collectively, insert a label
30162 begin{subequations}
30166 \begin_inset CommandInset ref
30168 reference "eq:Here-is-an"
30175 \begin_layout Standard
30176 By inserting commands in \SpecialChar TeX
30177 mode, a space is created between the first two
30180 \begin_inset space \thinspace{}
30183 mm vertical space is inserted after the command
30187 begin{subequations}
30190 When the formula style
30196 \begin_layout Plain Layout
30198 \begin_inset CommandInset ref
30200 reference "sec:Formula-Styles"
30212 \begin_inset space \thinspace{}
30215 mm space is inserted instead.
30218 \begin_layout Standard
30219 To get another subnumber instead of small Latin letters, insert this command
30224 begin{subequations}
30229 \begin_layout Standard
30238 theparentequation -
30243 \begin_layout Standard
30250 creates hereby the parent number and
30256 adds a small Roman number as subnumber.
30257 For more information about the customization of the numbering, see
30258 \begin_inset CommandInset ref
30260 reference "subsec:Numbering-with-Roman"
30267 \begin_layout Standard
30268 Here is an example for a multiline formula where the numbering is customized
30269 and turned off for the second line:
30273 \begin_layout Plain Layout
30277 begin{subequations}
30283 \begin_inset CommandInset label
30285 name "eq:Here-is-an"
30293 \begin_layout Plain Layout
30301 theparentequation -
30309 \begin_inset Formula
30311 A & = & (B-Z)^{2}=(B-Z)(B-Z)\\
30312 & = & B^{2}-ZB-BZ+Z^{2}\nonumber \\
30313 & = & B^{2}-2BZ+Z^{2}
30322 \begin_layout Plain Layout
30334 \begin_layout Subsection
30335 User-defined Numbering
30336 \begin_inset CommandInset label
30338 name "subsec:User-defined-Numbering"
30343 \begin_inset Index idx
30346 \begin_layout Plain Layout
30347 Formula numbering ! user-defined
30355 \begin_layout Standard
30356 \begin_inset Index idx
30359 \begin_layout Plain Layout
30360 Formula numbering ! self-defined delimiters
30365 With the standard numbering parentheses are set around the formula number.
30366 To replace the parentheses for example by vertical bars, the following
30367 line is added to the \SpecialChar LaTeX
30371 \begin_layout Standard
30383 \begin_inset Note Note
30386 \begin_layout Plain Layout
30387 This macro is already declared in the \SpecialChar LaTeX
30388 -preamble for testing.
30389 To activate it, remove the percent sign at the beginning.
30397 \begin_layout Standard
30398 To use other characters, the vertical bars besides the
30402 are replaced by one ore more characters.
30403 To get only the formula number the vertical bars are omitted.
30406 \begin_layout Standard
30407 \begin_inset VSpace bigskip
30410 When there should be an expression of your choice instead of the consecutive
30411 formula number in parentheses behind the formula, the command
30418 \begin_inset Index idx
30421 \begin_layout Plain Layout
30430 \begin_inset Formula
30432 A+B=C\tag{something}\label{eq:tag}
30437 In this example the command
30442 \begin_inset space \textvisiblespace{}
30447 was inserted in the formula.
30450 \begin_layout Standard
30456 \begin_inset space \textvisiblespace{}
30461 is inserted instead, the star prevents the parentheses around the expression:
30462 \begin_inset Formula
30464 A+B=C\tag*{something}
30472 \begin_layout Standard
30473 \begin_inset VSpace bigskip
30476 To restart the formula numbering with new document parts or sections, the
30477 following command is used:
30480 \begin_layout Standard
30485 @addtoreset{equation}{part}
30488 \begin_inset Index idx
30491 \begin_layout Plain Layout
30496 \begin_layout Plain Layout
30507 \begin_layout Plain Layout
30520 \begin_layout Plain Layout
30531 \begin_layout Plain Layout
30544 \begin_inset Newline newline
30548 \begin_inset Newline newline
30555 @addtoreset{equation}{section}
30558 \begin_layout Standard
30559 To be able to use these commands in \SpecialChar TeX
30561 \begin_inset Quotes eld
30565 \begin_inset Quotes erd
30568 character has to be made
30569 \begin_inset Quotes eld
30573 \begin_inset Quotes erd
30576 for \SpecialChar LaTeX
30591 So the command sequence in \SpecialChar TeX
30595 \begin_layout Standard
30601 \begin_inset Newline newline
30606 @addtoreset{equation}{section}
30607 \begin_inset Newline newline
30615 \begin_layout Standard
30616 In the \SpecialChar LaTeX
30629 can be omitted as they are automatically internally inserted by \SpecialChar LyX
30633 \begin_layout Standard
30648 \begin_layout Plain Layout
30653 is part of the \SpecialChar LaTeX
30659 \begin_inset Index idx
30662 \begin_layout Plain Layout
30663 Packages ! carlisle
30668 that is part of every \SpecialChar LaTeX
30669 standard installation.
30675 \begin_inset Index idx
30678 \begin_layout Plain Layout
30679 Packages ! remreset
30684 has to be loaded in the \SpecialChar LaTeX
30685 -preamble with the line
30688 \begin_layout Standard
30693 usepackage{remreset}
30696 \begin_layout Standard
30704 \begin_inset Index idx
30707 \begin_layout Plain Layout
30712 \begin_layout Plain Layout
30723 \begin_layout Plain Layout
30736 \begin_layout Plain Layout
30747 \begin_layout Plain Layout
30759 can be used with the same scheme as
30768 \begin_layout Standard
30769 \begin_inset VSpace bigskip
30772 Sometimes formulas should be numbered in the following form:
30775 \begin_layout Standard
30778 (section number.formula number)
30781 \begin_layout Standard
30782 The formula number should start with every section with
30783 \begin_inset Quotes eld
30787 \begin_inset Quotes erd
30793 \begin_layout Standard
30794 For this case there is the command
30801 \begin_inset Index idx
30804 \begin_layout Plain Layout
30812 , which is used with the following scheme:
30815 \begin_layout Standard
30820 numberwithin{counter}{sectioning}
30823 \begin_layout Standard
30824 Counter denotes what kind of numbering is affected, sectioning denotes what
30825 number is before the dot.
30828 \begin_layout Standard
30829 Thus in our case the following \SpecialChar LaTeX
30830 preamble or \SpecialChar TeX
30834 \begin_layout Standard
30839 numberwithin{equation}{section}
30842 \begin_layout Standard
30843 This is the result:
30847 \begin_layout Plain Layout
30851 numberwithin{equation}{section}
30857 \begin_inset Formula
30867 \begin_layout Standard
30869 \begin_inset space \thinspace{}
30873 \begin_inset space \space{}
30876 tables so that the number of the part is the sectioning,
30877 \begin_inset Newline newline
30884 numberwithin{table}{part}
30889 \begin_layout Standard
30890 To go back to the standard numbering or to prevent this kind of numbering
30891 when it is defined by the document class, the following command is inserted
30892 as \SpecialChar TeX
30893 code or to the \SpecialChar LaTeX
30897 \begin_layout Standard
30907 \begin_inset Index idx
30910 \begin_layout Plain Layout
30924 \begin_layout Plain Layout
30940 \begin_inset Newline newline
30948 \begin_inset Newline newline
30960 \begin_layout Standard
30967 uses internally the command
30973 , described above, that also needs to be reverted.
30977 \begin_layout Plain Layout
30984 \begin_layout Plain Layout
30988 @removefromreset{equation}{section}
30991 \begin_layout Plain Layout
31003 \begin_layout Standard
31004 \begin_inset Newpage newpage
31010 \begin_layout Subsection
31011 Numbering with Roman Numbers and Letters
31012 \begin_inset CommandInset label
31014 name "subsec:Numbering-with-Roman"
31019 \begin_inset Index idx
31022 \begin_layout Plain Layout
31023 Formula numbering ! with letters
31029 \begin_inset Index idx
31032 \begin_layout Plain Layout
31033 Formula numbering ! with Roman numbers
31041 \begin_layout Standard
31042 Formulas can also be numbered with Roman numbers and Latin letters.
31043 To number for example with small Roman numbers, the command
31046 \begin_layout Standard
31058 \begin_layout Standard
31059 is inserted before the formula in \SpecialChar TeX
31068 \begin_inset Index idx
31071 \begin_layout Plain Layout
31079 redefines the predefined command
31095 \begin_layout Plain Layout
31102 has the same scheme like the command
31108 that is described in
31109 \begin_inset CommandInset ref
31111 reference "subsec:The-Command-newcommand"
31124 is the formula counter.
31131 is used as prefix for a counter, the value of the counter is output as
31133 When a formula is numbered, \SpecialChar LaTeX
31134 sets internally the command
31140 behind the formula.
31146 \begin_inset Index idx
31149 \begin_layout Plain Layout
31159 outputs the counter as small Roman number.
31162 \begin_layout Standard
31163 All formulas behind the command
31173 are now numbered Roman.
31174 To switch to numbering with big Roman numbers, the command is inserted
31188 \begin_inset Index idx
31191 \begin_layout Plain Layout
31203 \begin_inset Quotes eld
31207 \begin_inset Quotes erd
31210 with small Latin letters there is the command
31217 \begin_inset Index idx
31220 \begin_layout Plain Layout
31228 , for big ones there is the command
31235 \begin_inset Index idx
31238 \begin_layout Plain Layout
31251 \begin_layout Standard
31252 \begin_inset Note Greyedout
31255 \begin_layout Plain Layout
31262 \begin_inset space ~
31265 formulas can be numbered with Latin letters in one document.
31273 \begin_layout Standard
31277 \begin_layout Plain Layout
31293 \begin_layout Standard
31294 \begin_inset Formula
31296 A=\textrm{small roman}
31305 \begin_layout Plain Layout
31319 \begin_inset Formula
31321 B=\textrm{big Roman}\label{eq:Rom}
31330 \begin_layout Plain Layout
31344 \begin_inset Formula
31346 C=\textrm{small Latin}
31355 \begin_layout Plain Layout
31369 \begin_inset Formula
31371 D=\textrm{big Latin}\label{eq:Lat}
31379 \begin_layout Standard
31380 To switch back to the default numbering, insert the command:
31383 \begin_layout Standard
31393 \begin_inset Index idx
31396 \begin_layout Plain Layout
31407 \begin_layout Standard
31411 \begin_layout Plain Layout
31425 \begin_inset Formula
31435 \begin_layout Standard
31436 \begin_inset VSpace medskip
31439 As you see, formulas are numbered serially independent from the numbering
31441 When then numbering should start with
31442 \begin_inset Quotes eld
31446 \begin_inset Quotes erd
31449 when the style is changed, new equation counters have to be defined.
31450 A description about this can be found in the file
31451 \begin_inset CommandInset href
31453 name "Formula-numbering.lyx"
31454 target "run:Formula-numbering.lyx"
31461 \begin_layout Section
31462 Chemical Symbols and Equations
31463 \begin_inset CommandInset label
31465 name "subsec:Chemical-Symbols-and"
31470 \begin_inset Index idx
31473 \begin_layout Plain Layout
31474 Chemical characters ! Symbols
31480 \begin_inset Index idx
31483 \begin_layout Plain Layout
31490 \begin_inset Index idx
31493 \begin_layout Plain Layout
31502 \begin_layout Standard
31503 An example text from chemistry:
31506 \begin_layout Quote
31508 \begin_inset Formula $\mathrm{SO_{4}^{2-}}$
31511 -ion reacts with two
31512 \begin_inset Formula $\mathrm{Na^{+}}$
31515 -ions to sodium sulfate
31516 \begin_inset Formula $\left(\mathrm{Na_{2}SO_{4}}\right)$
31520 The chemical equation for this is:
31521 \begin_inset Formula
31523 \mathrm{2\,Na^{+}+SO_{4}^{2-}\longrightarrow Na_{2}SO_{4}}\label{eq:chem-reaction}
31531 \begin_layout Standard
31532 This chemical equation can directly be created as formula.
31533 To avoid that the symbols appear italic, everything is highlighted and
31534 changed by the shortcut
31540 to the upright font style.
31544 \begin_layout Plain Layout
31550 \begin_inset CommandInset ref
31552 reference "subsec:Font-Styles"
31564 \begin_layout Standard
31565 A more convenient way to typeset chemical formulas is to use the command
31573 \begin_inset Index idx
31576 \begin_layout Plain Layout
31584 that is available when the \SpecialChar LaTeX
31590 \begin_inset Index idx
31593 \begin_layout Plain Layout
31606 to a formula a new blue box appears where chemical formulas can be inserted
31607 in an intuitive way.
31610 \begin_layout Standard
31612 \begin_inset Tabular
31613 <lyxtabular version="3" rows="10" columns="2">
31614 <features booktabs="true" tabularvalignment="middle">
31615 <column alignment="center" valignment="top" width="0pt">
31616 <column alignment="center" valignment="top">
31618 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
31621 \begin_layout Plain Layout
31627 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
31630 \begin_layout Plain Layout
31638 <cell alignment="center" valignment="top" leftline="true" usebox="none">
31641 \begin_layout Plain Layout
31645 \begin_inset space \textvisiblespace{}
31653 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
31656 \begin_layout Plain Layout
31657 \begin_inset Formula $\ce{H2CO3}$
31666 <row topspace="1.5mm">
31667 <cell alignment="center" valignment="top" usebox="none">
31670 \begin_layout Plain Layout
31674 \begin_inset space \textvisiblespace{}
31682 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
31685 \begin_layout Plain Layout
31686 \begin_inset Formula $\ce{SO4^{2-}}$
31695 <row topspace="1.5mm">
31696 <cell alignment="center" valignment="top" usebox="none">
31699 \begin_layout Plain Layout
31703 \begin_inset space \textvisiblespace{}
31711 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
31714 \begin_layout Plain Layout
31715 \begin_inset Formula $\ce{(NH4)2S}$
31724 <row topspace="1.5mm">
31725 <cell alignment="center" valignment="top" usebox="none">
31728 \begin_layout Plain Layout
31732 \begin_inset space \textvisiblespace{}
31740 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
31743 \begin_layout Plain Layout
31744 \begin_inset Formula $\ce{KCr(SO4)2.12H2O}$
31753 <row topspace="1.5mm">
31754 <cell alignment="center" valignment="top" usebox="none">
31757 \begin_layout Plain Layout
31761 \begin_inset space \textvisiblespace{}
31767 \begin_inset space \textvisiblespace{}
31773 \begin_inset space \textvisiblespace{}
31781 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
31784 \begin_layout Plain Layout
31785 \begin_inset Formula $\ce{A-B\dbond C\tbond D}$
31794 <row topspace="1.5mm">
31795 <cell alignment="center" valignment="top" usebox="none">
31798 \begin_layout Plain Layout
31802 \begin_inset space \textvisiblespace{}
31806 \begin_inset Formula $\downarrow$
31810 \begin_inset Formula $\to$
31818 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
31821 \begin_layout Plain Layout
31822 \begin_inset Formula $\ce{_{90}^{227}Th+}$
31832 <cell alignment="center" valignment="top" leftline="true" usebox="none">
31835 \begin_layout Plain Layout
31839 \begin_inset space \textvisiblespace{}
31845 \begin_inset space \textvisiblespace{}
31851 \begin_inset space \textvisiblespace{}
31859 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
31862 \begin_layout Plain Layout
31863 \begin_inset Formula $\ce{\ensuremath{\mu\hyphen}Cl}$
31873 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
31876 \begin_layout Plain Layout
31880 \begin_inset space \textvisiblespace{}
31884 \begin_inset space \textvisiblespace{}
31888 \begin_inset space \textvisiblespace{}
31892 \begin_inset space \textvisiblespace{}
31896 \begin_inset space \textvisiblespace{}
31904 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
31907 \begin_layout Plain Layout
31908 \begin_inset Formula $\ce{CO2 + C <=> 2CO}$
31917 <row topspace="1.5mm">
31918 <cell alignment="center" valignment="top" bottomline="true" usebox="none">
31921 \begin_layout Plain Layout
31925 \begin_inset space \textvisiblespace{}
31929 \begin_inset space \textvisiblespace{}
31933 \begin_inset space \textvisiblespace{}
31937 \begin_inset space \textvisiblespace{}
31945 \begin_inset space \textvisiblespace{}
31953 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
31956 \begin_layout Plain Layout
31957 \begin_inset Formula $\ce{CO2 + C ->[\alpha][\beta] 2CO}$
31973 \begin_layout Standard
31974 \begin_inset Note Greyedout
31977 \begin_layout Plain Layout
31983 It is not possible in \SpecialChar LyX
31984 to use the character ^ to get an up-arrow as described
31990 One instead uses a negative thin space followed by the command
31997 \begin_inset Formula $\ce{Fe + 2H+ -> Fe^{2+} + H2\negthinspace\uparrow}$
32008 \begin_layout Standard
32015 the command for equation
32016 \begin_inset space ~
32020 \begin_inset CommandInset ref
32022 reference "eq:chem-reaction"
32027 \begin_inset Newline newline
32035 \begin_inset space \textvisiblespace{}
32039 \begin_inset space \textvisiblespace{}
32043 \begin_inset space \textvisiblespace{}
32047 \begin_inset space \textvisiblespace{}
32051 \begin_inset space \textvisiblespace{}
32055 \begin_inset space \textvisiblespace{}
32061 \begin_layout Standard
32062 To create multiline chemical equations first a multiline formula is created
32064 \begin_inset CommandInset ref
32066 reference "sec:Multiline-Formulas"
32071 Afterwards the command
32077 is used in every small blue box of the formula.
32079 \begin_inset CommandInset ref
32081 reference "eq:TEOS-reaction-1"
32086 \begin_inset CommandInset ref
32088 reference "eq:TEOS-reaction-2"
32092 are an example of a multi-stage chemical reaction where every equation
32093 has its own number.
32094 \begin_inset Formula
32096 \ce{TEOS + 4O} & \ce{->} & \ce{Si(OH)4 + 4C2H4O}\label{eq:TEOS-reaction-1}\\
32097 \ce{Si(OH)4} & \ce{->} & \ce{SiO2 + 2H2O}\label{eq:TEOS-reaction-2}
32105 \begin_layout Standard
32116 package provides the command
32123 \begin_inset Index idx
32126 \begin_layout Plain Layout
32134 that has to be used for special cases.
32135 For more information about
32141 and more examples have a look at the documentation of
32146 \begin_inset CommandInset citation
32155 \begin_layout Section
32159 \begin_layout Standard
32161 supports two types of commutative diagrams:
32169 that are explained in the following.
32172 \begin_layout Subsection
32174 \begin_inset Index idx
32177 \begin_layout Plain Layout
32186 \begin_layout Standard
32187 Diagrams of this type visualize relations by vertical and horizontal lines
32189 \begin_inset Formula
32191 \begin{CD}A@>>>B@>>>C\\
32202 \begin_layout Standard
32203 To get them, the command
32208 \begin_inset Index idx
32211 \begin_layout Plain Layout
32221 is inserted to a formula.
32222 A blue box appears with two dashed lines where further commands can be
32227 arg "newline-insert newline"
32230 a new line is created.
32231 Horizontal relations are inserted in odd, vertical in even formula lines.
32234 \begin_layout Standard
32235 To create the relations there are the following commands:
32238 \begin_layout Itemize
32243 creates a left arrow,
32254 \begin_layout Itemize
32259 creates an up arrow,
32267 a vertical equal sign
32270 \begin_layout Itemize
32276 is a placeholder for non-existent relations
32279 \begin_layout Standard
32280 All arrows can be labeled as follows:
32283 \begin_layout Itemize
32284 If text inserted between the first and second < or >, resp., it is placed
32286 When it is inserted between the second and third one, it appears under
32290 \begin_layout Itemize
32291 When text for vertical arrows is inserted between the first and second A
32292 or V, resp., it is placed left beside the arrow.
32293 When it is inserted between the second and third one, it appears right
32295 If the text contains an A or V, these letters must be set into a \SpecialChar TeX
32299 \begin_layout Standard
32300 As example a diagram with all possible relations:
32303 \begin_layout Standard
32304 \begin_inset Formula
32306 \begin{CD}A@>j>>B@>>k>C@=F\\
32317 \begin_layout Standard
32318 The command for this is:
32319 \begin_inset Newline newline
32327 \begin_inset space \textvisiblespace{}
32330 A@>j>>B@>>k>C@=F Ctrl+Return
32331 \begin_inset Newline newline
32335 \begin_inset Phantom HPhantom
32338 \begin_layout Plain Layout
32344 \begin_inset space \textvisiblespace{}
32357 \begin_inset Formula $\to$
32363 \begin_inset Newline newline
32367 \begin_inset Phantom HPhantom
32370 \begin_layout Plain Layout
32376 \begin_inset space \textvisiblespace{}
32387 \begin_layout Subsection
32389 \begin_inset Index idx
32392 \begin_layout Plain Layout
32393 Diagrams ! xymatrix
32401 \begin_layout Standard
32402 To be able to use xymatrices, the \SpecialChar LaTeX
32408 A xymatrix is created by inserting the command
32415 Then you are able to add new matrix columns and rows like for normal matrices,
32417 \begin_inset CommandInset ref
32419 reference "sec:Matrices"
32426 \begin_layout Standard
32427 In contrary to amscd diagrams, xymatrices supports diagonal and curved arrows,
32429 All possibilities to create commutative diagrams and decorations are explained
32434 that you find in the menu
32436 Help\SpecialChar menuseparator
32438 \begin_inset space ~
32446 \begin_layout Subsection
32452 \begin_inset Index idx
32455 \begin_layout Plain Layout
32464 \begin_layout Standard
32469 -diagrams, the \SpecialChar LaTeX
32479 -diagram is created by inserting the command
32486 Then you are able to add new matrix columns and rows like for normal matrices,
32488 \begin_inset CommandInset ref
32490 reference "sec:Matrices"
32497 \begin_layout Standard
32498 Examples how to create
32502 diagrams in \SpecialChar LyX
32505 Feynman-diagram manual
32507 that you find in the menu
32509 Help\SpecialChar menuseparator
32511 \begin_inset space ~
32519 \begin_layout Standard
32520 \begin_inset Newpage newpage
32526 \begin_layout Section
32527 User-defined Commands
32528 \begin_inset Index idx
32531 \begin_layout Plain Layout
32532 User-defined commands
32540 \begin_layout Standard
32541 \begin_inset Note Greyedout
32544 \begin_layout Plain Layout
32549 The names of user-defined commands and macros may only consist of Latin
32558 \begin_layout Subsection
32562 \begin_inset CommandInset label
32564 name "subsec:The-Command-newcommand"
32569 \begin_inset Index idx
32572 \begin_layout Plain Layout
32573 User-defined commands !
32581 \begin_inset Index idx
32584 \begin_layout Plain Layout
32595 \begin_layout Standard
32596 Many \SpecialChar LaTeX
32597 -commands are too long to be used frequently.
32598 But it is possible to define with the command
32604 new shorter commands.
32607 \begin_layout Standard
32608 The command scheme of
32617 \begin_layout Standard
32622 newcommand{new command name}[number of arguments][optional
32627 \begin_inset Newline newline
32631 \begin_inset Phantom HPhantom
32634 \begin_layout Plain Layout
32644 {command definition}
32647 \begin_layout Standard
32648 \begin_inset Note Greyedout
32651 \begin_layout Plain Layout
32656 Assure that the name of the new command is not already used in your document
32657 or by \SpecialChar LaTeX
32658 -packages that you use.
32659 When you for example define the command
32671 , you get an error message because
32677 is already defined as command for
32678 \begin_inset Quotes eld
32682 \begin_inset Formula $\le$
32686 \begin_inset Quotes erd
32697 \begin_layout Standard
32698 The number of arguments is an integer in the range 0
32699 \begin_inset space \thinspace{}
32703 \begin_inset space \thinspace{}
32706 9 and specifies how many arguments the new command should have.
32707 With the optional value a value for an optional argument can be predefined.
32708 When this is done, the
32716 rgument of the new command is automatically an optional one.
32719 \begin_layout Standard
32720 Here are some examples:
32723 \begin_layout Itemize
32724 To define the command
32736 , the \SpecialChar LaTeX
32738 \begin_inset VSpace medskip
32742 \begin_inset Newline newline
32756 \begin_layout Itemize
32757 To define the command
32769 , the argument (that should be underlined) must be taken into account.
32770 For this the preamble line is:
32771 \begin_inset VSpace medskip
32775 \begin_inset Newline newline
32789 \begin_inset VSpace medskip
32793 \begin_inset Newline newline
32800 acts as argument placeholder, the
32804 behind it denotes that it is the placeholder for the first argument.
32807 \begin_layout Itemize
32815 \begin_inset space \thinspace{}
32819 \begin_inset space \space{}
32829 \begin_inset VSpace medskip
32833 \begin_inset Newline newline
32844 framebox#1#2{$#3$}}
32847 \begin_inset VSpace medskip
32851 \begin_inset Newline newline
32854 The two Dollar signs creates the extra formula needed for
32861 \begin_inset CommandInset ref
32863 reference "subsec:Boxes-with-Frame"
32870 \begin_layout Itemize
32871 To create a new command for
32877 where the color for the box need not be specified, the argument for the
32878 color is defined optional:
32879 \begin_inset VSpace medskip
32883 \begin_inset Newline newline
32894 fcolorbox{#2}{#1}{$#3$}}
32897 \begin_inset VSpace medskip
32901 \begin_inset Newline newline
32904 When the color is not specified when using
32910 , the predefined color
32917 \begin_layout Standard
32918 A test of the new defined commands:
32921 \begin_layout Standard
32923 \begin_inset Tabular
32924 <lyxtabular version="3" rows="6" columns="2">
32925 <features booktabs="true" tabularvalignment="middle">
32926 <column alignment="center" valignment="top" width="0pt">
32927 <column alignment="center" valignment="top">
32929 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
32932 \begin_layout Plain Layout
32938 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
32941 \begin_layout Plain Layout
32949 <cell alignment="center" valignment="top" leftline="true" usebox="none">
32952 \begin_layout Plain Layout
32956 \begin_inset space \textvisiblespace{}
32964 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
32967 \begin_layout Plain Layout
32968 \begin_inset Formula $A\gr B$
32978 <cell alignment="center" valignment="top" leftline="true" usebox="none">
32981 \begin_layout Plain Layout
32989 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
32992 \begin_layout Plain Layout
32993 \begin_inset Formula $\us{ABcd}$
33002 <row topspace="1mm">
33003 <cell alignment="center" valignment="top" usebox="none">
33006 \begin_layout Plain Layout
33010 \begin_inset Formula $\to$
33016 \begin_inset Formula $\to$
33024 \begin_inset space \textvisiblespace{}
33032 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
33035 \begin_layout Plain Layout
33036 \begin_inset Formula $\fb{[2cm]}{}{\int A=B}$
33045 <row topspace="1.5mm">
33046 <cell alignment="center" valignment="top" usebox="none">
33049 \begin_layout Plain Layout
33053 \begin_inset Formula $\to$
33061 \begin_inset space \textvisiblespace{}
33069 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
33072 \begin_layout Plain Layout
33073 \begin_inset Formula $\cb{red}{\int A=B}$
33082 <row topspace="1.5mm" bottomspace="1mm">
33083 <cell alignment="center" valignment="top" bottomline="true" usebox="none">
33086 \begin_layout Plain Layout
33092 \begin_inset Formula $\to$
33100 \begin_inset space \textvisiblespace{}
33108 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
33111 \begin_layout Plain Layout
33112 \begin_inset Formula $\cb[green]{red}{\int A=B}$
33128 \begin_layout Subsection
33130 \begin_inset Index idx
33133 \begin_layout Plain Layout
33134 User-defined commands! Math macros
33140 \begin_inset Index idx
33143 \begin_layout Plain Layout
33152 \begin_layout Standard
33153 User-defined commands are especially convenient for complex expressions.
33154 When you are for example dealing with a document that has quadratic equations,
33155 the same solution type occurs several times.
33156 The general form of a quadratic equation is
33157 \begin_inset Formula
33159 0=\lambda^{2}+p\lambda+q
33164 The general form of the solution is
33165 \begin_inset Formula
33167 \lambda_{1,2}=-\frac{p}{2}\pm\sqrt{\frac{p²}{4}-q}
33175 \begin_layout Standard
33176 To define a command for the solution formula where only the three parameters
33178 \begin_inset Formula $\lambda$
33182 \begin_inset Formula $p$
33186 \begin_inset Formula $q$
33189 need to be specified and the index of
33190 \begin_inset Formula $\lambda$
33193 can be given optionally, the \SpecialChar LaTeX
33195 \begin_inset Newline newline
33211 \begin_inset Newline newline
33215 \begin_inset Phantom HPhantom
33218 \begin_layout Plain Layout
33232 frac{#3^{2}}{4}-#4}}
33235 \begin_layout Standard
33236 To create with this the solution formula, the command
33237 \begin_inset Newline newline
33247 \begin_inset Formula $\to$
33253 \begin_inset Formula $\to$
33260 is inserted to a formula
33265 \begin_layout Standard
33266 The definition of the new command is unintuitive because one has to know
33267 the schemes of all used \SpecialChar LaTeX
33269 \begin_inset space \thinspace{}
33273 \begin_inset space \space{}
33276 that a fraction is inserted in \SpecialChar LaTeX
33281 frac{numerator}{denominator}
33284 Furthermore one can easily forget a brace in the definition and cannot
33285 see in \SpecialChar LyX
33286 what the new command is doing.
33287 To avoid these problems \SpecialChar LyX
33288 offers the possibility to use math macros instead
33298 \begin_layout Standard
33299 A math macro is created by using the menu
33301 Insert\SpecialChar menuseparator
33302 Math\SpecialChar menuseparator
33305 or the toolbar button
33308 arg "math-macro newmacroname_newcommand"
33312 The math macro toolbar appears together with the following box where the
33314 \begin_inset Newline newline
33318 \begin_inset space \hspace*{\fill}
33322 \begin_inset Graphics
33323 filename clipart/macrobox.png
33329 \begin_inset space \hspace*{\fill}
33333 \begin_inset Newline newline
33337 \begin_inset FormulaMacro
33338 \newcommand{\qG}[4][1,\,2]{#2_{#1}=-\frac{#3}{2}\pm\sqrt{\frac{#3^{2}}{4}-#4}}
33343 newmacroname is the default name of the macro that should be changed to
33344 something sensible.
33345 The wanted formula is inserted in the first blue box.
33346 An argument placeholder is inserted with the command
33353 \begin_inset space \thinspace{}
33357 \begin_inset space \space{}
33366 or by using the macro toolbar button
33369 arg "math-macro-add-param"
33373 Argument placeholders are displayed red.
33375 \begin_inset space ~
33378 arguments are possible.
33379 Optional arguments are created with the toolbar button
33382 arg "math-macro-add-optional-param"
33386 The first non-optional argument can be transformed to an optional one with
33390 arg "math-macro-make-optional"
33394 In the second blue box the appearance of the macro in \SpecialChar LyX
33396 Normally you want to see it as it is defined, so the box is kept empty.
33397 But when you have created a macro that needs lot of space on the screen,
33398 you can insert in the box for example
33399 \begin_inset Newline newline
33429 \begin_inset Newline newline
33434 For the macro only the arguments with the macro name in front of them will
33435 then be displayed in \SpecialChar LyX
33436 , leading to a better overview.
33437 The formula appears in the output as defined in the first box.
33438 \begin_inset Newline newline
33441 The appearance of macros in formulas can furthermore be changed for single
33442 macros by setting the cursor in the macro and using the menu
33444 View\SpecialChar menuseparator
33446 \begin_inset space ~
33450 \begin_inset space ~
33458 \begin_layout Standard
33459 To use a macro, the macro name is inserted as command to a formula, in our
33467 Our macro looks in \SpecialChar LyX
33469 \begin_inset Newline newline
33473 \begin_inset space \hspace*{\fill}
33477 \begin_inset Graphics
33478 filename clipart/macrouse.png
33484 \begin_inset space \hspace*{\fill}
33488 \begin_inset Newline newline
33491 Here is our macro example with the arguments
33492 \begin_inset Formula $x$
33496 \begin_inset Formula $\ln(x)$
33500 \begin_inset Formula $B$
33506 \begin_layout Standard
33507 \begin_inset Formula
33517 \begin_layout Standard
33521 Tools\SpecialChar menuseparator
33522 Preferences\SpecialChar menuseparator
33523 Editing\SpecialChar menuseparator
33526 different styles to edit macros.
33527 To find the style that suits you the most, choose a style and set the cursor
33528 in a macro formula to see the difference.
33531 \begin_layout Standard
33532 A math macro is transformed internally to a
33538 command when exporting the document.
33545 command is not placed in the \SpecialChar LaTeX
33546 -preamble, therefore macros can only be used
33547 in formulas that are in the document below the macro definition box.
33550 \begin_layout Standard
33551 Math macros can also be directly created from a
33558 When writing for example the command
33561 \begin_inset Newline newline
33570 xleftarrow[#2]{#1}}
33571 \begin_inset Newline newline
33576 in \SpecialChar LyX
33577 as normal text, highlighting it completely and using then the shortcut
33582 , the command will be transformed to a math macro.
33583 Using this method you need to be careful that the
33589 command is typed correctly, otherwise you get a faulty macro leading to
33594 \begin_layout Standard
33595 Math macros currently have the problem that further formulas in macro definition
33596 s are handled wrongly.
33597 Therefore the example
33604 \begin_inset CommandInset ref
33606 reference "subsec:The-Command-newcommand"
33610 cannot be created as macro.
33613 \begin_layout Standard
33614 When the cursor is in a macro definition box, you will see the macro toolbar
33615 in \SpecialChar LyX
33619 \begin_layout Standard
33620 \begin_inset VSpace defskip
33626 \begin_layout Standard
33627 \begin_inset Graphics
33628 filename clipart/MacroToolbar.png
33633 \begin_inset Index idx
33636 \begin_layout Plain Layout
33645 \begin_layout Standard
33646 \begin_inset VSpace defskip
33652 \begin_layout Standard
33653 The macro toolbar contains from left to right the following buttons:
33656 \begin_layout Standard
33657 \begin_inset VSpace defskip
33663 \begin_layout Standard
33664 \begin_inset Tabular
33665 <lyxtabular version="3" rows="9" columns="2">
33666 <features islongtable="true" longtabularalignment="center">
33667 <column alignment="left" valignment="top">
33668 <column alignment="left" valignment="top" width="85col%">
33669 <row interlinespace="2.5mm">
33670 <cell alignment="center" valignment="top" usebox="none">
33673 \begin_layout Plain Layout
33676 arg "math-macro-remove-param"
33684 <cell alignment="center" valignment="top" usebox="none">
33687 \begin_layout Plain Layout
33690 Edit\SpecialChar menuseparator
33691 Math\SpecialChar menuseparator
33693 \begin_inset space ~
33696 Definition\SpecialChar menuseparator
33697 Remove Last Argument
33703 <row interlinespace="2.5mm">
33704 <cell alignment="center" valignment="top" usebox="none">
33707 \begin_layout Plain Layout
33710 arg "math-macro-add-param"
33718 <cell alignment="center" valignment="top" usebox="none">
33721 \begin_layout Plain Layout
33724 Edit\SpecialChar menuseparator
33725 Math\SpecialChar menuseparator
33727 \begin_inset space ~
33730 Definition\SpecialChar menuseparator
33737 <row interlinespace="2.5mm">
33738 <cell alignment="center" valignment="top" usebox="none">
33741 \begin_layout Plain Layout
33744 arg "math-macro-make-optional"
33752 <cell alignment="center" valignment="top" usebox="none">
33755 \begin_layout Plain Layout
33758 Edit\SpecialChar menuseparator
33759 Math\SpecialChar menuseparator
33761 \begin_inset space ~
33764 Definition\SpecialChar menuseparator
33765 Transform First Non-Optional to
33766 \begin_inset Newline newline
33770 \begin_inset Phantom HPhantom
33773 \begin_layout Plain Layout
33776 Edit\SpecialChar menuseparator
33777 Math\SpecialChar menuseparator
33779 \begin_inset space ~
33782 Definition\SpecialChar menuseparator
33794 <row interlinespace="2.5mm">
33795 <cell alignment="center" valignment="top" usebox="none">
33798 \begin_layout Plain Layout
33801 arg "math-macro-make-nonoptional"
33809 <cell alignment="center" valignment="top" usebox="none">
33812 \begin_layout Plain Layout
33815 Edit\SpecialChar menuseparator
33816 Math\SpecialChar menuseparator
33818 \begin_inset space ~
33821 Definition\SpecialChar menuseparator
33822 Transform Last Optional to
33823 \begin_inset Newline newline
33827 \begin_inset Phantom HPhantom
33830 \begin_layout Plain Layout
33833 Edit\SpecialChar menuseparator
33834 Math\SpecialChar menuseparator
33836 \begin_inset space ~
33839 Definition\SpecialChar menuseparator
33845 Non-Optional Argument
33851 <row interlinespace="2.5mm">
33852 <cell alignment="center" valignment="top" usebox="none">
33855 \begin_layout Plain Layout
33858 arg "math-macro-remove-optional-param"
33866 <cell alignment="center" valignment="top" usebox="none">
33869 \begin_layout Plain Layout
33872 Edit\SpecialChar menuseparator
33873 Math\SpecialChar menuseparator
33875 \begin_inset space ~
33878 Definition\SpecialChar menuseparator
33879 Remove Optional Argument
33885 <row interlinespace="2.5mm">
33886 <cell alignment="center" valignment="top" usebox="none">
33889 \begin_layout Plain Layout
33892 arg "math-macro-add-optional-param"
33900 <cell alignment="center" valignment="top" usebox="none">
33903 \begin_layout Plain Layout
33906 Edit\SpecialChar menuseparator
33907 Math\SpecialChar menuseparator
33909 \begin_inset space ~
33912 Definition\SpecialChar menuseparator
33913 Insert Optional Argument
33919 <row interlinespace="2.5mm">
33920 <cell alignment="center" valignment="top" usebox="none">
33923 \begin_layout Plain Layout
33926 arg "math-macro-remove-greedy-param"
33934 <cell alignment="center" valignment="top" usebox="none">
33937 \begin_layout Plain Layout
33940 Edit\SpecialChar menuseparator
33941 Math\SpecialChar menuseparator
33943 \begin_inset space ~
33946 Definition\SpecialChar menuseparator
33947 Remove Last Argument
33948 \begin_inset Newline newline
33952 \begin_inset Phantom HPhantom
33955 \begin_layout Plain Layout
33958 Edit\SpecialChar menuseparator
33959 Math\SpecialChar menuseparator
33961 \begin_inset space ~
33964 Definition\SpecialChar menuseparator
33970 Spitting Out To The Right
33976 <row interlinespace="2.5mm">
33977 <cell alignment="center" valignment="top" usebox="none">
33980 \begin_layout Plain Layout
33983 arg "math-macro-append-greedy-param"
33991 <cell alignment="center" valignment="top" usebox="none">
33994 \begin_layout Plain Layout
33997 Edit\SpecialChar menuseparator
33998 Math\SpecialChar menuseparator
34000 \begin_inset space ~
34003 Definition\SpecialChar menuseparator
34005 \begin_inset Newline newline
34009 \begin_inset Phantom HPhantom
34012 \begin_layout Plain Layout
34015 Edit\SpecialChar menuseparator
34016 Math\SpecialChar menuseparator
34018 \begin_inset space ~
34021 Definition\SpecialChar menuseparator
34027 Eating From The Right
34033 <row interlinespace="2.5mm">
34034 <cell alignment="center" valignment="top" usebox="none">
34037 \begin_layout Plain Layout
34040 arg "math-macro-add-greedy-optional-param"
34048 <cell alignment="center" valignment="top" usebox="none">
34051 \begin_layout Plain Layout
34054 Edit\SpecialChar menuseparator
34055 Math\SpecialChar menuseparator
34057 \begin_inset space ~
34060 Definition\SpecialChar menuseparator
34061 Append Optional Argument
34062 \begin_inset Newline newline
34066 \begin_inset Phantom HPhantom
34069 \begin_layout Plain Layout
34072 Edit\SpecialChar menuseparator
34073 Math\SpecialChar menuseparator
34075 \begin_inset space ~
34078 Definition\SpecialChar menuseparator
34084 Eating From The Right
34097 \begin_layout Section
34098 Computer Algebra Systems
34101 \begin_layout Standard
34103 offers the exchange between mathematical expressions written in \SpecialChar LyX
34105 editor and external applications or user defined scripts.
34106 Currently supported applications are
34123 Note that the set of supported mathematical constructs is limited only
34124 to very simple cases.
34127 \begin_layout Subsection
34131 \begin_layout Standard
34132 Write some expression in a formula, go to the
34134 Edit\SpecialChar menuseparator
34135 Math\SpecialChar menuseparator
34136 Use Computer Algebra System
34138 menu and choose the application you have installed on the computer.
34139 After that the result of computation should show on the right side of the
34140 expression together with the
34141 \begin_inset Quotes eld
34145 \begin_inset Quotes erd
34151 \begin_layout Standard
34152 Here are few simple examples (with results from
34156 ) to show what kind of computations can be performed:
34159 \begin_layout Itemize
34160 \begin_inset Formula $\frac{37}{3}*2-\sum_{i=1}^{3}i^{i}=-\frac{22}{3}$
34166 \begin_layout Itemize
34167 \begin_inset Formula $\frac{37.0}{3}=12.33333333333333$
34173 \begin_layout Itemize
34174 \begin_inset Formula $\int_{1}^{2}\sin(x)dx=\cos1-\cos2$
34180 \begin_layout Itemize
34181 \begin_inset Formula $\int\left(\frac{1}{1+x^{3}}\right)dx=-\frac{\log\left(x^{2}-x+1\right)}{6}+\frac{\arctan\left(\frac{2\,x-1}{\sqrt{3}}\right)}{\sqrt{3}}+\frac{\log\left(x+1\right)}{3}$
34185 \begin_inset Newline newline
34189 \begin_inset Note Greyedout
34192 \begin_layout Plain Layout
34197 One needs to use proper delimiter insets
34198 \begin_inset Formula $\left(\right)$
34201 instead of simple '(' ')' characters.
34209 \begin_layout Itemize
34210 \begin_inset Formula $\det\left[\begin{array}{ccc}
34214 \end{array}\right]=-56$
34220 \begin_layout Itemize
34221 \begin_inset Formula $\lim_{x\rightarrow0}\left(\frac{\sin(x)}{x}\right)=1$
34227 \begin_layout Itemize
34228 \begin_inset Formula $powerseries\left(-\log\left(5-x\right),x,1\right)=\sum_{{\mathit{i}_{2}}=0}^{\infty}{\frac{4^{-{\mathit{i}_{2}}-1}\,\left(x-1\right)^{{\mathit{i}_{2}}+1}}{{\mathit{i}_{2}}+1}}-\log4$
34234 \begin_layout Itemize
34235 \begin_inset Formula $solve\left(x_{1}+y_{1}^{3}=y_{1}+x_{1}^{2},x_{1}\right)=\left[x_{1}=-\frac{\sqrt{4\,y_{1}^{3}-4\,y_{1}+1}-1}{2},x_{1}=\frac{\sqrt{4\,y_{1}^{3}-4\,y_{1}+1}+1}{2}\right]$
34241 \begin_layout Subsection
34245 \begin_layout Standard
34246 Currently there is no keyboard shortcut for calling the algebra applications.
34247 One can easily bind a shortcut to the
34261 \begin_inset space \thinspace{}
34265 \begin_inset space \space{}
34272 key inside the math editor.
34277 one would use this shortcut definition command:
34280 \begin_layout Standard
34283 command-alternatives paragraph-break;math-extern maxima
34286 \begin_layout Section
34288 \begin_inset Index idx
34291 \begin_layout Plain Layout
34300 \begin_layout Subsection
34302 \begin_inset Index idx
34305 \begin_layout Plain Layout
34314 \begin_layout Standard
34315 Negative numbers often look ugly in formulas because the minus sign before
34316 the number is set with the same length as the minus operator sign.
34317 When writing the negative number in normal text, the minus sign appears
34321 \begin_layout Standard
34322 Thus, the problem disappears when converting the minus sign to mathematical
34326 \begin_layout Standard
34327 An example to visualize the problem:
34330 \begin_layout Standard
34332 \begin_inset Tabular
34333 <lyxtabular version="3" rows="3" columns="2">
34334 <features booktabs="true" tabularvalignment="middle">
34335 <column alignment="right" valignment="top" width="0pt">
34336 <column alignment="left" valignment="top">
34338 <cell alignment="right" valignment="top" topline="true" leftline="true" usebox="none">
34341 \begin_layout Plain Layout
34347 <cell alignment="center" valignment="top" topline="true" rightline="true" usebox="none">
34350 \begin_layout Plain Layout
34358 <cell alignment="right" valignment="top" leftline="true" usebox="none">
34361 \begin_layout Plain Layout
34367 <cell alignment="center" valignment="top" rightline="true" usebox="none">
34370 \begin_layout Plain Layout
34371 \begin_inset Formula $x=-2$
34381 <cell alignment="right" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
34384 \begin_layout Plain Layout
34390 <cell alignment="center" valignment="top" topline="true" bottomline="true" rightline="true" usebox="none">
34393 \begin_layout Plain Layout
34394 \begin_inset Formula $x=\textrm{-}2$
34410 \begin_layout Subsection
34411 Comma as decimal Separator
34412 \begin_inset Index idx
34415 \begin_layout Plain Layout
34424 \begin_layout Standard
34425 In \SpecialChar LaTeX
34426 a comma inside a formula is used, according to the English convention,
34427 as number group separator.
34428 So there will be space added behind all commas in formulas.
34431 \begin_layout Standard
34432 To avoid this, the comma is highlighted and changed to mathematical text
34442 \begin_layout Standard
34443 To use all formula commas in the document as decimal separator, the file
34452 \begin_layout Plain Layout
34457 is part of the \SpecialChar LaTeX
34463 \begin_inset Index idx
34466 \begin_layout Plain Layout
34471 \begin_layout Plain Layout
34491 \begin_inset Index idx
34494 \begin_layout Plain Layout
34500 is loaded with the \SpecialChar LaTeX
34504 \begin_layout Standard
34512 \begin_layout Subsection
34514 \begin_inset CommandInset label
34516 name "subsec:Physical-Vectors"
34521 \begin_inset Index idx
34524 \begin_layout Plain Layout
34533 \begin_layout Standard
34534 Predefined vectors are offered by the \SpecialChar LaTeX
34540 \begin_inset Index idx
34543 \begin_layout Plain Layout
34549 that is loaded with the \SpecialChar LaTeX
34553 \begin_layout Standard
34561 \begin_layout Standard
34565 \begin_layout Plain Layout
34575 \begin_inset Note Note
34578 \begin_layout Plain Layout
34579 The following table will only be displayed when the \SpecialChar LaTeX
34592 \begin_layout Standard
34593 The following commands are defined:
34596 \begin_layout Standard
34598 \begin_inset Tabular
34599 <lyxtabular version="3" rows="4" columns="2">
34600 <features booktabs="true" tabularvalignment="middle">
34601 <column alignment="center" valignment="top" width="0pt">
34602 <column alignment="center" valignment="top">
34604 <cell alignment="center" valignment="top" topline="true" bottomline="true" usebox="none">
34607 \begin_layout Plain Layout
34613 <cell alignment="center" valignment="top" topline="true" bottomline="true" usebox="none">
34616 \begin_layout Plain Layout
34624 <cell alignment="center" valignment="top" usebox="none">
34627 \begin_layout Plain Layout
34637 <cell alignment="center" valignment="top" usebox="none">
34640 \begin_layout Plain Layout
34641 \begin_inset Formula $\Bra{\psi}$
34651 <cell alignment="center" valignment="top" usebox="none">
34654 \begin_layout Plain Layout
34664 <cell alignment="center" valignment="top" usebox="none">
34667 \begin_layout Plain Layout
34668 \begin_inset Formula $\Ket{\psi}$
34678 <cell alignment="center" valignment="top" bottomline="true" usebox="none">
34681 \begin_layout Plain Layout
34693 <cell alignment="center" valignment="top" bottomline="true" usebox="none">
34696 \begin_layout Plain Layout
34697 \begin_inset Formula $\Braket{\psi|\phi}$
34713 \begin_layout Standard
34720 assures that all vertical bars are set in the size of the surrounding brackets:
34721 \begin_inset Formula
34723 \Braket{\phi|J=\frac{3}{2}\,,\,M_{J}}
34732 \begin_layout Plain Layout
34742 \begin_inset Note Note
34745 \begin_layout Plain Layout
34746 The following will be displayed when the \SpecialChar LaTeX
34759 \begin_layout Standard
34760 You need to install the \SpecialChar LaTeX
34765 to see the rest of this subsection in the output.
34768 \begin_layout Standard
34772 \begin_layout Plain Layout
34784 \begin_layout Standard
34791 can also be achieved using the command
34797 , that is described in
34798 \begin_inset CommandInset ref
34800 reference "subsec:Automatic-Bracket-Size"
34807 \begin_layout Subsection
34808 Self-defined Fractions
34809 \begin_inset CommandInset label
34811 name "subsec:Self-defined-Fractions"
34816 \begin_inset Index idx
34819 \begin_layout Plain Layout
34820 Fractions ! self-defined
34828 \begin_layout Standard
34829 To define custom commands for fractions, the command
34836 \begin_inset Index idx
34839 \begin_layout Plain Layout
34846 \begin_layout Plain Layout
34860 is used in the following scheme:
34863 \begin_layout Standard
34876 bracket}{fraction bar thickness}{style}
34877 \begin_inset Newline newline
34881 \begin_inset Phantom HPhantom
34884 \begin_layout Plain Layout
34894 {numerator}{denominator}
34897 \begin_layout Standard
34898 The style is a number in the range of 0
34899 \begin_inset space \thinspace{}
34903 \begin_inset space \thinspace{}
34909 \begin_layout Standard
34911 \begin_inset Tabular
34912 <lyxtabular version="3" rows="5" columns="2">
34913 <features booktabs="true" tabularvalignment="middle">
34914 <column alignment="center" valignment="top" width="0pt">
34915 <column alignment="center" valignment="top">
34917 <cell alignment="center" valignment="top" topline="true" bottomline="true" usebox="none">
34920 \begin_layout Plain Layout
34926 <cell alignment="center" valignment="top" topline="true" bottomline="true" usebox="none">
34929 \begin_layout Plain Layout
34937 <cell alignment="center" valignment="top" usebox="none">
34940 \begin_layout Plain Layout
34946 <cell alignment="center" valignment="top" usebox="none">
34949 \begin_layout Plain Layout
34950 display style formula
34957 <cell alignment="center" valignment="top" usebox="none">
34960 \begin_layout Plain Layout
34966 <cell alignment="center" valignment="top" usebox="none">
34969 \begin_layout Plain Layout
34977 <cell alignment="center" valignment="top" usebox="none">
34980 \begin_layout Plain Layout
34986 <cell alignment="center" valignment="top" usebox="none">
34989 \begin_layout Plain Layout
34997 <cell alignment="center" valignment="top" bottomline="true" usebox="none">
35000 \begin_layout Plain Layout
35006 <cell alignment="center" valignment="top" bottomline="true" usebox="none">
35009 \begin_layout Plain Layout
35023 \begin_layout Standard
35024 When no style is given, the size is adjusted to the surrounding environment
35025 like for the command
35034 \begin_layout Standard
35035 When no fraction bar thickness is given, the predefined value of 0.4
35036 \begin_inset space \thinspace{}
35042 \begin_layout Standard
35043 \begin_inset VSpace medskip
35046 For example, the commands
35059 \begin_inset CommandInset ref
35061 reference "subsec:Fractions"
35065 are defined with the commands
35068 \begin_layout Standard
35077 genfrac{}{}{}{0}{#1}{#2}}
35080 \begin_layout Standard
35084 \begin_layout Standard
35093 genfrac{(}{)}{0pt}{1}{#1}{#2}}
35096 \begin_layout Standard
35097 \begin_inset VSpace medskip
35100 To define a fraction where the fraction bar thickness can be given as optional
35101 argument, the following line is inserted to the \SpecialChar LaTeX
35105 \begin_layout Standard
35114 genfrac{}{}{#1}{}{#2}{#3}}
35117 \begin_layout Standard
35119 \begin_inset Formula
35121 \text{Command} & & \mathrm{\backslash fracS[1mm]\backslash\{A\to\backslash\{B} & & \mathrm{\backslash fracS[5mm]\backslash\{A\to\backslash\{B}\\
35122 \text{Result} & & \fracS[1mm]{A}{B} & & \fracS[5mm]{A}{B}
35127 As one can see, the distance of the numerator and the denominator to the
35128 fraction bar is round about three times the bar thickness.
35131 \begin_layout Standard
35132 \begin_inset Newpage newpage
35138 \begin_layout Subsection
35140 \begin_inset Index idx
35143 \begin_layout Plain Layout
35152 \begin_layout Standard
35153 There are four ways to cancel formulas or parts of formulas:
35156 \begin_layout Standard
35160 \begin_layout Plain Layout
35170 \begin_inset Note Note
35173 \begin_layout Plain Layout
35174 The following table will only be displayed when the \SpecialChar LaTeX
35187 \begin_layout Standard
35189 \begin_inset Tabular
35190 <lyxtabular version="3" rows="5" columns="2">
35191 <features booktabs="true" tabularvalignment="middle">
35192 <column alignment="center" valignment="top" width="0pt">
35193 <column alignment="center" valignment="top">
35195 <cell alignment="center" valignment="top" topline="true" bottomline="true" usebox="none">
35198 \begin_layout Plain Layout
35204 <cell alignment="center" valignment="top" topline="true" bottomline="true" usebox="none">
35207 \begin_layout Plain Layout
35215 <cell alignment="center" valignment="top" usebox="none">
35218 \begin_layout Plain Layout
35222 \begin_inset space \textvisiblespace{}
35228 \begin_inset space \textvisiblespace{}
35236 <cell alignment="center" valignment="top" usebox="none">
35239 \begin_layout Plain Layout
35240 \begin_inset Formula $\cancel{\int A=B}$
35249 <row topspace="1.5mm">
35250 <cell alignment="center" valignment="top" usebox="none">
35253 \begin_layout Plain Layout
35257 \begin_inset space \textvisiblespace{}
35263 \begin_inset space \textvisiblespace{}
35271 <cell alignment="center" valignment="top" usebox="none">
35274 \begin_layout Plain Layout
35275 \begin_inset Formula $\bcancel{\int A=B}$
35284 <row topspace="1.5mm">
35285 <cell alignment="center" valignment="top" usebox="none">
35288 \begin_layout Plain Layout
35292 \begin_inset space \textvisiblespace{}
35298 \begin_inset space \textvisiblespace{}
35306 <cell alignment="center" valignment="top" usebox="none">
35309 \begin_layout Plain Layout
35310 \begin_inset Formula $\xcancel{\int A=B}$
35320 <cell alignment="center" valignment="top" topline="true" bottomline="true" usebox="none">
35323 \begin_layout Plain Layout
35327 \begin_inset space \textvisiblespace{}
35333 \begin_inset space \textvisiblespace{}
35337 \begin_inset Formula $\to$
35345 <cell alignment="center" valignment="top" topline="true" bottomline="true" usebox="none">
35348 \begin_layout Plain Layout
35349 \begin_inset Formula $\cancelto{1}{\int A=B}\hspace{3mm}$
35365 \begin_layout Standard
35372 is especially suitable to visualize the reduction of fractions within formulas:
35373 \begin_inset Formula
35375 \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}}}
35383 \begin_layout Standard
35384 To change the size of
35391 \begin_inset Quotes eld
35395 \begin_inset Quotes erd
35398 value one can add the \SpecialChar LaTeX
35402 \begin_layout Standard
35407 PassOptionsToPackage{option}{cancel}
35410 \begin_layout Standard
35419 which leads to the same size as for the canceled value, or
35423 which makes is it a bit smaller than normal.
35426 \begin_layout Standard
35427 To color the cancellation bar one adds this command as \SpecialChar TeX
35431 \begin_layout Standard
35443 \begin_layout Standard
35448 can be replaced by a color of your choice.
35451 \begin_layout Standard
35455 \begin_layout Plain Layout
35471 \begin_layout Standard
35472 \begin_inset Formula
35474 \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}}}
35482 \begin_layout Standard
35486 \begin_layout Plain Layout
35500 \begin_inset Note Note
35503 \begin_layout Plain Layout
35512 \begin_layout Standard
35513 For further customizations, see the documentation of the package
35518 \begin_inset CommandInset citation
35525 \begin_inset Index idx
35528 \begin_layout Plain Layout
35537 \begin_layout Standard
35541 \begin_layout Plain Layout
35551 \begin_inset Note Note
35554 \begin_layout Plain Layout
35555 The following will be displayed when the \SpecialChar LaTeX
35568 \begin_layout Standard
35569 You need to install the \SpecialChar LaTeX
35574 to see the rest of this subsection in the output.
35577 \begin_layout Standard
35581 \begin_layout Plain Layout
35593 \begin_layout Subsection
35594 Formulas in Section Headings
35595 \begin_inset CommandInset label
35597 name "subsec:Formulas-in-Section"
35602 \begin_inset Index idx
35605 \begin_layout Plain Layout
35606 Formula ! in section headings
35614 \begin_layout Standard
35615 When formulas are used in section headings, the following has to be taken
35619 \begin_layout Standard
35620 \begin_inset Note Greyedout
35623 \begin_layout Plain Layout
35629 \begin_inset Index idx
35632 \begin_layout Plain Layout
35633 Packages ! hyperref
35638 support is enabled in the document settings dialog under
35641 \begin_inset space ~
35646 , PDF-bookmarks are created for every section heading in the table of contents.
35647 If a section heading contains formulas, they are incorrectly displayed
35648 in the bookmark text, because formulas in bookmarks infringe the PDF convention
35657 \begin_layout Standard
35658 Both problems can be solved by inserting at the end of the section heading
35659 a short title with the menu
35661 Insert\SpecialChar menuseparator
35663 \begin_inset space ~
35669 Short titles are used as alternative for multiline section headings to
35670 keep the table of contents clearly arranged.
35671 Only the short title appears in the table of contents and therefore also
35672 in the PDF-bookmark.
35675 \begin_layout Standard
35676 When formulas should be used in the table of contents but
35680 is used, one can use the following command in \SpecialChar TeX
35684 \begin_layout Standard
35689 texorpdfstring{part}{alternative}
35690 \begin_inset Index idx
35693 \begin_layout Plain Layout
35704 \begin_layout Standard
35705 Part is the part of the heading that shouldn't appear in the PDF-bookmark.
35706 This can be characters, formulas, footnotes, but also cross-references.
35707 The alternative is used instead of the part for the bookmark.
35710 \begin_layout Standard
35711 Here are two example headings:
35712 \begin_inset VSpace -3mm
35719 \begin_layout Plain Layout
35731 \begin_layout Subsubsection
35732 Heading without formula in table of contents
35733 \begin_inset Formula $\sqrt{-1}=\mathrm{i}$
35737 \begin_inset Argument 1
35740 \begin_layout Plain Layout
35741 Heading without formula in table of contents
35749 \begin_layout Subsubsection
35750 Heading with formula in table of contents
35754 \begin_layout Plain Layout
35764 \begin_inset Formula $\sqrt{-1}=\mathrm{i}$
35771 \begin_layout Plain Layout
35781 \begin_layout Standard
35785 \begin_layout Plain Layout
35794 In the first heading a short title was used, in the second one
35803 \begin_layout Standard
35804 To get the same formatting as for the other headings, the complete heading
35813 \begin_layout Plain Layout
35815 \begin_inset CommandInset ref
35817 reference "subsec:Bold-Formulas"
35829 \begin_layout Subsection
35830 Formulas in multi-column Text
35831 \begin_inset Index idx
35834 \begin_layout Plain Layout
35835 Formula ! in multi-column text
35843 \begin_layout Standard
35844 Formulas in multi-column text are often too wide to fit into a column and
35845 thus need to be set over the whole page width.
35846 This is done by using the \SpecialChar LaTeX
35855 \begin_layout Plain Layout
35860 is part of every \SpecialChar LaTeX
35861 standard installation.
35867 \begin_inset Index idx
35870 \begin_layout Plain Layout
35871 Packages ! multicol
35876 , that is loaded with the \SpecialChar LaTeX
35880 \begin_layout Standard
35885 usepackage{multicol}
35888 \begin_layout Standard
35889 \begin_inset Note Greyedout
35892 \begin_layout Plain Layout
35893 Note that in this case the setting
35896 \begin_inset space ~
35903 Document\SpecialChar menuseparator
35909 \begin_inset space ~
35929 \begin_layout Standard
35930 Before the multi-column text the command
35933 \begin_layout Standard
35938 begin{multicols}{column number}
35941 \begin_layout Standard
35942 is written in \SpecialChar TeX
35944 The column number is a number in the range of 2
35945 \begin_inset space \thinspace{}
35949 \begin_inset space \thinspace{}
35953 Before the formula the multi-column text is ended by inserting the command
35956 \begin_layout Standard
35964 \begin_layout Standard
35965 in \SpecialChar TeX
35969 \begin_layout Standard
35970 Due to the command some space is automatically added before the formula.
35972 \begin_inset space \thinspace{}
35975 mm vertical space is inserted before the formula.
35976 When the formula style
35982 \begin_layout Plain Layout
35984 \begin_inset CommandInset ref
35986 reference "sec:Formula-Styles"
35998 \begin_inset space \thinspace{}
36001 mm space is inserted instead.
36004 \begin_layout Standard
36005 As example a multi-column text with a displayed formula:
36008 \begin_layout Standard
36014 \begin_layout Plain Layout
36018 begin{multicols}{2}
36023 Das Spektrum wird fouriertransformiert.
36024 Die Fouriertransformation wird verwendet, um die überlagerten Signale (Netzwerk
36025 , Lösungsmittel) zu trennen.
36026 Nachdem wir die Phasenverschiebung bestimmen konnten, interessiert uns
36027 nun das Aussehen des Ausgangssignals.
36028 Im Experiment haben wir es mit sehr vielen Teilchen zu tun, so dass man
36029 über alle Phasen integrieren muss.
36031 \begin_inset Formula $S$
36034 unser normiertes Ausgangssignal und
36035 \begin_inset Formula $P$
36038 die Phasenverteilungsfunktion, so ergibt sich die Beziehung
36042 \begin_layout Plain Layout
36052 \begin_inset VSpace -6mm
36056 \begin_inset Formula
36058 S(t)=S_{0}(t)\int_{-\infty}^{\infty}P(\phi,t)\mathrm{e}^{\mathrm{i}\phi}\,\mathrm{d}\phi
36067 \begin_layout Plain Layout
36071 begin{multicols}{2}
36077 \begin_inset Formula $S_{0}$
36080 das Signal ohne Gradient ist und die Normierungsbedingung
36081 \begin_inset Formula $\int_{-\infty}^{\infty}P(\phi,t)\,\mathrm{d}\phi=1$
36085 Nun dürfen wir aber nicht den Relaxationsprozess außer Acht lassen.
36087 \begin_inset Formula $\nicefrac{\pi}{2}$
36091 \begin_inset space \thinspace{}
36094 -rf-Puls beginnt sich die Magnetisierung zu entfokussieren, wodurch sich
36095 das Signal zusätzlich abschwächt.
36096 Diese Abschwächung verläuft exponentiell in Abhängigkeit der so genannten
36098 \begin_inset Formula $T_{2}$
36104 \begin_layout Standard
36110 \begin_layout Plain Layout
36122 \begin_layout Subsection
36123 Formulas with Description of Variables
36124 \begin_inset Index idx
36127 \begin_layout Plain Layout
36128 Formula ! with description of variables
36136 \begin_layout Standard
36137 To describe variables within a formula, like in formula
36138 \begin_inset CommandInset ref
36140 reference "eq:within"
36149 \begin_inset Formula $n$
36153 \begin_inset space ~
36156 matrix is used with left aligned columns for the
36157 \begin_inset Formula $n$
36164 \begin_layout Plain Layout
36166 \begin_inset CommandInset ref
36168 reference "sec:Matrices"
36177 To set the description in a smaller size, before the matrix e.
36178 \begin_inset space \thinspace{}
36182 \begin_inset space \space{}
36195 \begin_layout Plain Layout
36197 \begin_inset CommandInset ref
36199 reference "subsec:Font-Sizes"
36211 \begin_layout Standard
36212 When the formula style
36218 \begin_layout Plain Layout
36220 \begin_inset CommandInset ref
36222 reference "sec:Formula-Styles"
36243 \begin_layout Plain Layout
36250 only works in formulas with the style
36255 \begin_inset CommandInset ref
36257 reference "subsec:Variable-Space"
36266 is inserted before and after the matrix to have the same separation of
36267 the matrix from the equation and the side margin.
36270 \begin_layout Standard
36271 When the formula style
36275 is used, the method described in
36276 \begin_inset CommandInset ref
36278 reference "subsec:Flalign-Environment"
36282 is used to indent formulas.
36284 \begin_inset CommandInset ref
36286 reference "eq:within"
36290 consists of five columns where in the first two columns contain the equation,
36291 the third the matrix and the last one an empty \SpecialChar TeX
36293 \begin_inset Formula
36295 \hspace{30pt}F_{A} & =\rho·V·g & \footnotesize\begin{array}{ll}
36296 \rho & \textrm{density}\\
36297 V & \textrm{volume}\\
36298 g & \textrm{gravitational acceleration}
36299 \end{array} & & {}\label{eq:within}
36307 \begin_layout Subsection
36308 Upright small Greek Letters
36309 \begin_inset CommandInset label
36311 name "subsec:Upright-small-Greek"
36316 \begin_inset Index idx
36319 \begin_layout Plain Layout
36320 Greek letters ! upright
36328 \begin_layout Standard
36329 Most of the math fonts only provide italic small Greek letters.
36330 But for symbols of elementary particles like pions and neutrinos, upright
36331 Greek letters are needed.
36340 \begin_layout Plain Layout
36345 is part of the \SpecialChar LaTeX
36351 \begin_inset Index idx
36354 \begin_layout Plain Layout
36359 \begin_layout Plain Layout
36379 \begin_inset Index idx
36382 \begin_layout Plain Layout
36388 that is loaded with the \SpecialChar LaTeX
36392 \begin_layout Standard
36397 usepackage{upgreek}
36400 \begin_layout Standard
36406 \begin_layout Plain Layout
36416 \begin_inset Note Note
36419 \begin_layout Plain Layout
36420 The following table will only be displayed when the \SpecialChar LaTeX
36430 They are created when the command for a small Greek letter is started with
36436 For example the command
36443 \begin_inset Formula $\uptau$
36449 \begin_layout Standard
36450 With these commands reactions of elementary particles can be typeset:
36451 \begin_inset Formula
36453 \uppi^{+}\to\upmu^{+}+\upnu_{\upmu}
36461 \begin_layout Standard
36462 The upright letters are more bold and wider than the italic ones.
36463 They should therefore not be used for units like
36464 \begin_inset Quotes eld
36468 \begin_inset Quotes erd
36474 \begin_layout Standard
36478 \begin_layout Plain Layout
36488 \begin_inset Note Note
36491 \begin_layout Plain Layout
36492 The following will be displayed when the \SpecialChar LaTeX
36505 \begin_layout Standard
36506 You need to install the \SpecialChar LaTeX
36511 to see the rest of this subsection in the output.
36514 \begin_layout Standard
36518 \begin_layout Plain Layout
36530 \begin_layout Subsection
36531 Text Characters in Formulas
36532 \begin_inset Index idx
36535 \begin_layout Plain Layout
36544 \begin_layout Standard
36545 In some cases you might want to insert text characters directly into formulas.
36546 When for example the centered dot · is often used in formulas like
36547 \begin_inset Formula $\nu=5·10^{5}\,\mathrm{Hz}$
36550 , one would have to insert the command
36560 \begin_layout Plain Layout
36562 \begin_inset CommandInset ref
36564 reference "subsec:Binary-Operators"
36573 all the time, because this character is defined in all encodings as text
36575 But the encoding can be changed by this \SpecialChar LaTeX
36579 \begin_layout Standard
36584 Declare Inputtext{183}{
36594 f\SpecialChar ligaturebreak
36598 \begin_layout Standard
36599 The character encoding (menu
36601 Document\SpecialChar menuseparator
36602 Settings\SpecialChar menuseparator
36605 ) specifies what character appears when a keyboard key is pressed.
36606 When the key for the character '·' is pressed, internally the command
36613 But this command is not available in a formula so that you would get \SpecialChar LaTeX
36615 With the changed encoding the right command is chosen automatically, depending
36616 on if the character was inserted into a formula or not.
36619 \begin_layout Standard
36620 The encoding of several characters is saved in definition files.
36621 For example the encoding
36625 is defined in the file
36629 which is in the installation folder of \SpecialChar LaTeX
36631 Encodings should only be changed via the \SpecialChar LaTeX
36632 -preamble and not in the definition
36634 Otherwise documents could not be edited by other \SpecialChar LyX
36635 users working on other
36639 \begin_layout Standard
36640 \begin_inset VSpace medskip
36643 Besides the centered dot, in this document the degree sign ° is defined
36644 with the following \SpecialChar LaTeX
36645 -preamble line so that it can be directly inserted into
36649 \begin_layout Standard
36654 DeclareInputtext{176}{
36664 f\SpecialChar ligaturebreak
36668 \begin_layout Subsection
36670 -comments in formulas
36671 \begin_inset Index idx
36674 \begin_layout Plain Layout
36684 \begin_layout Standard
36685 In text you can insert a comment that will only be visible in the \SpecialChar LaTeX
36687 code of your file with the menu
36689 Insert\SpecialChar menuseparator
36690 Note\SpecialChar menuseparator
36694 This is not possible in a formula but you can insert \SpecialChar LaTeX
36699 \begin_layout Standard
36707 \begin_layout Standard
36708 This creates a box in which you can write your comment.
36709 Due to a bug in \SpecialChar LyX
36714 \begin_layout Plain Layout
36715 \begin_inset CommandInset href
36717 name "LyX-bug #9002"
36718 target "http://www.lyx.org/trac/ticket/9002"
36727 you cannot write normal text inside the comment, even when you use mathematical
36728 text, you will see its \SpecialChar LaTeX
36729 -commands in the \SpecialChar LaTeX
36731 \begin_inset Newline newline
36734 This a formula with a \SpecialChar LaTeX
36736 \begin_inset Formula
36738 A=B%\text{This is the comment}
36746 \begin_layout Standard
36747 \begin_inset Newpage newpage
36753 \begin_layout Section
36756 \begin_inset Index idx
36759 \begin_layout Plain Layout
36768 \begin_layout Standard
36769 This section is a summary of the most important typographic rules, listed
36774 \begin_layout Plain Layout
36775 This collection was partly taken from the German semi-official dictionary
36777 \begin_inset Quotes eld
36781 \begin_inset Quotes erd
36785 \begin_inset CommandInset citation
36791 that lists some of the ISO rules.
36792 More rules are listed in
36793 \begin_inset CommandInset citation
36807 \begin_layout Itemize
36816 \begin_layout Plain Layout
36817 done with font styles, see
36818 \begin_inset CommandInset ref
36820 reference "subsec:Font-Styles"
36829 , no matter if they appear in italic text: 30
36830 \begin_inset space \thinspace{}
36834 \begin_inset Newline newline
36837 Between the value and the unit is the smallest space, see
36838 \begin_inset CommandInset ref
36840 reference "subsec:Predefined-Space"
36845 \begin_inset Newline newline
36848 This convention is automatically fulfilled when the command
36855 When it is entered to a formula, two boxes appear.
36856 In the first one the value is inserted, in the second one the unit, and
36858 \begin_inset Formula $\unit[30]{km/h}$
36862 \begin_inset space \thinspace{}
36872 is not a real \SpecialChar LaTeX
36873 command but the command
36879 , therefore you cannot use it in \SpecialChar TeX
36883 \begin_layout Itemize
36884 Percent and perthousand signs are set like physical units:
36885 \begin_inset Newline newline
36889 \begin_inset space \thinspace{}
36895 \begin_layout Itemize
36896 The degree sign follows directly on the value: 15°, but not when it is used
36898 \begin_inset space \thinspace{}
36904 \begin_layout Itemize
36905 In numbers with more than four digits the smallest space is inserted before
36906 every third digit to group them:
36916 \begin_inset space \thinspace{}
36920 \begin_inset space \thinspace{}
36926 \begin_layout Itemize
36927 For dimensions like 120×90×40
36928 \begin_inset space \thinspace{}
36931 cm the multiplication sign
36932 \begin_inset Quotes eld
36936 \begin_inset Quotes erd
36940 It is available either via the command
36948 Insert\SpecialChar menuseparator
36949 Special Character\SpecialChar menuseparator
36955 \begin_layout Itemize
36956 Functions with names consisting of several letters are set upright to avoid
36958 \begin_inset CommandInset ref
36960 reference "subsec:Predefined-Functions"
36967 \begin_layout Itemize
36968 Indices consisting of several letters, are set upright:
36969 \begin_inset Formula $E_{\mathrm{kin}}$
36973 \begin_inset Newline newline
36976 Components of matrices are set italic:
36977 \begin_inset Formula $\hat{H}_{kl}$
36983 \begin_layout Itemize
36984 The differentiation/integration operator 'd', the Euler's number 'e' and
36985 the imaginary unit 'i' should be set upright, to avoid mixing them up with
36989 \begin_layout Itemize
36990 The character that denotes a
36994 transformation is inserted either by the command
36999 \begin_inset space \textvisiblespace{}
37006 Insert\SpecialChar menuseparator
37007 Special Character\SpecialChar menuseparator
37008 Symbols\SpecialChar menuseparator
37010 \begin_inset space ~
37016 \begin_inset Formula $\mathscr{F}$
37022 \begin_layout Standard
37023 \begin_inset Newpage newpage
37029 \begin_layout Section
37031 \begin_inset Index idx
37034 \begin_layout Plain Layout
37043 \begin_layout Standard
37044 Some characters and symbols can be created with several commands.
37045 Here is a list of the synonym commands:
37048 \begin_layout Standard
37049 \begin_inset VSpace bigskip
37053 \begin_inset space \hfill{}
37057 \begin_inset Tabular
37058 <lyxtabular version="3" rows="12" columns="2">
37059 <features booktabs="true" tabularvalignment="middle">
37060 <column alignment="center" valignment="top" width="0pt">
37061 <column alignment="center" valignment="top" width="0pt">
37063 <cell alignment="center" valignment="top" topline="true" bottomline="true" usebox="none">
37066 \begin_layout Plain Layout
37072 <cell alignment="center" valignment="top" topline="true" bottomline="true" usebox="none">
37075 \begin_layout Plain Layout
37083 <cell alignment="center" valignment="top" usebox="none">
37086 \begin_layout Plain Layout
37094 <cell alignment="center" valignment="top" usebox="none">
37097 \begin_layout Plain Layout
37105 <cell alignment="center" valignment="top" usebox="none">
37108 \begin_layout Plain Layout
37116 <cell alignment="center" valignment="top" usebox="none">
37119 \begin_layout Plain Layout
37129 <cell alignment="center" valignment="top" usebox="none">
37132 \begin_layout Plain Layout
37140 <cell alignment="center" valignment="top" usebox="none">
37143 \begin_layout Plain Layout
37153 <cell alignment="center" valignment="top" usebox="none">
37156 \begin_layout Plain Layout
37164 <cell alignment="center" valignment="top" usebox="none">
37167 \begin_layout Plain Layout
37175 <cell alignment="center" valignment="top" usebox="none">
37178 \begin_layout Plain Layout
37186 <cell alignment="center" valignment="top" usebox="none">
37189 \begin_layout Plain Layout
37197 <cell alignment="center" valignment="top" usebox="none">
37200 \begin_layout Plain Layout
37208 <cell alignment="center" valignment="top" usebox="none">
37211 \begin_layout Plain Layout
37221 <cell alignment="center" valignment="top" usebox="none">
37224 \begin_layout Plain Layout
37232 <cell alignment="center" valignment="top" usebox="none">
37235 \begin_layout Plain Layout
37245 <cell alignment="center" valignment="top" usebox="none">
37248 \begin_layout Plain Layout
37256 <cell alignment="center" valignment="top" usebox="none">
37259 \begin_layout Plain Layout
37269 <cell alignment="center" valignment="top" usebox="none">
37272 \begin_layout Plain Layout
37280 <cell alignment="center" valignment="top" usebox="none">
37283 \begin_layout Plain Layout
37293 <cell alignment="center" valignment="top" usebox="none">
37296 \begin_layout Plain Layout
37304 <cell alignment="center" valignment="top" usebox="none">
37307 \begin_layout Plain Layout
37315 <cell alignment="center" valignment="top" bottomline="true" usebox="none">
37318 \begin_layout Plain Layout
37326 <cell alignment="center" valignment="top" bottomline="true" usebox="none">
37329 \begin_layout Plain Layout
37341 \begin_inset space \hfill{}
37345 \begin_inset Tabular
37346 <lyxtabular version="3" rows="12" columns="2">
37347 <features booktabs="true" tabularvalignment="middle">
37348 <column alignment="center" valignment="top" width="0pt">
37349 <column alignment="center" valignment="top" width="0pt">
37351 <cell alignment="center" valignment="top" topline="true" bottomline="true" usebox="none">
37354 \begin_layout Plain Layout
37360 <cell alignment="center" valignment="top" topline="true" bottomline="true" usebox="none">
37363 \begin_layout Plain Layout
37371 <cell alignment="center" valignment="top" usebox="none">
37374 \begin_layout Plain Layout
37382 <cell alignment="center" valignment="top" usebox="none">
37385 \begin_layout Plain Layout
37397 <cell alignment="center" valignment="top" usebox="none">
37400 \begin_layout Plain Layout
37408 <cell alignment="center" valignment="top" usebox="none">
37411 \begin_layout Plain Layout
37421 <cell alignment="center" valignment="top" usebox="none">
37424 \begin_layout Plain Layout
37432 <cell alignment="center" valignment="top" usebox="none">
37435 \begin_layout Plain Layout
37445 <cell alignment="center" valignment="top" usebox="none">
37448 \begin_layout Plain Layout
37456 <cell alignment="center" valignment="top" usebox="none">
37459 \begin_layout Plain Layout
37467 <cell alignment="center" valignment="top" usebox="none">
37470 \begin_layout Plain Layout
37478 <cell alignment="center" valignment="top" usebox="none">
37481 \begin_layout Plain Layout
37489 <cell alignment="center" valignment="top" usebox="none">
37492 \begin_layout Plain Layout
37500 <cell alignment="center" valignment="top" usebox="none">
37503 \begin_layout Plain Layout
37513 <cell alignment="center" valignment="top" usebox="none">
37516 \begin_layout Plain Layout
37524 <cell alignment="center" valignment="top" usebox="none">
37527 \begin_layout Plain Layout
37537 <cell alignment="center" valignment="top" usebox="none">
37540 \begin_layout Plain Layout
37548 <cell alignment="center" valignment="top" usebox="none">
37551 \begin_layout Plain Layout
37561 <cell alignment="center" valignment="top" usebox="none">
37564 \begin_layout Plain Layout
37572 <cell alignment="center" valignment="top" usebox="none">
37575 \begin_layout Plain Layout
37585 <cell alignment="center" valignment="top" usebox="none">
37588 \begin_layout Plain Layout
37596 <cell alignment="center" valignment="top" usebox="none">
37599 \begin_layout Plain Layout
37609 <cell alignment="center" valignment="top" bottomline="true" usebox="none">
37612 \begin_layout Plain Layout
37620 <cell alignment="center" valignment="top" bottomline="true" usebox="none">
37623 \begin_layout Plain Layout
37637 \begin_inset space \hfill{}
37643 \begin_layout Standard
37644 \begin_inset Newpage newpage
37650 \begin_layout Bibliography
37651 \begin_inset CommandInset bibitem
37652 LatexCommand bibitem
37664 The \SpecialChar LaTeX
37668 Addison Wesley, 2004
37671 \begin_layout Bibliography
37672 \begin_inset CommandInset bibitem
37673 LatexCommand bibitem
37679 \begin_inset CommandInset href
37682 target "ftp://ftp.dante.de/tex-archive/info/math/voss/mathmode/Mathmode.pdf"
37686 of \SpecialChar LaTeX
37690 \begin_layout Bibliography
37691 \begin_inset CommandInset bibitem
37692 LatexCommand bibitem
37698 \begin_inset CommandInset href
37701 target "http://mirrors.ctan.org/macros/latex/required/amslatex/math/amsldoc.pdf"
37709 \begin_layout Plain Layout
37718 -\SpecialChar LaTeX
37722 \begin_layout Bibliography
37723 \begin_inset CommandInset bibitem
37724 LatexCommand bibitem
37730 \begin_inset CommandInset href
37733 target "ftp://ftp.dante.de/tex-archive/info/symbols/comprehensive/symbols-a4.pdf"
37737 of all symbols available with \SpecialChar LaTeX
37741 \begin_layout Bibliography
37742 \begin_inset CommandInset bibitem
37743 LatexCommand bibitem
37749 \begin_inset CommandInset href
37751 name "Documentation"
37752 target "http://mirrors.ctan.org/macros/latex/contrib/cancel/cancel.pdf"
37756 of the \SpecialChar LaTeX
37762 \begin_inset Index idx
37765 \begin_layout Plain Layout
37774 \begin_layout Bibliography
37775 \begin_inset CommandInset bibitem
37776 LatexCommand bibitem
37782 \begin_inset CommandInset href
37784 name "Documentation"
37785 target "http://www.tug.org/applications/hyperref/ftp/doc/manual.pdf"
37789 of the \SpecialChar LaTeX
37795 \begin_inset Index idx
37798 \begin_layout Plain Layout
37799 Packages ! hyperref
37807 \begin_layout Bibliography
37808 \begin_inset CommandInset bibitem
37809 LatexCommand bibitem
37815 \begin_inset CommandInset href
37817 name "Documentation"
37818 target "http://www.ctan.org/tex-archive/macros/latex/contrib/mhchem/mhchem.pdf"
37822 of the \SpecialChar LaTeX
37828 \begin_inset Index idx
37831 \begin_layout Plain Layout
37840 \begin_layout Bibliography
37841 \begin_inset CommandInset bibitem
37842 LatexCommand bibitem
37853 Auflage, Duden 2001
37856 \begin_layout Bibliography
37857 \begin_inset CommandInset bibitem
37858 LatexCommand bibitem
37864 \begin_inset CommandInset href
37867 target "http://physics.nist.gov/Pubs/SP811/sec11.html"
37871 for reviewing manuscripts
37874 \begin_layout Standard
37875 \begin_inset CommandInset index_print
37876 LatexCommand printindex