1 #LyX 2.3 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}{
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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 \use_dash_ligatures false
155 \default_output_format pdf2
157 \bibtex_command default
158 \index_command default
162 \pdf_title "LyX's Math Manual"
163 \pdf_author "LyX Team, Uwe Stöhr"
164 \pdf_subject "LyX-documentation about math"
165 \pdf_keywords "LyX, Mathed"
167 \pdf_bookmarksnumbered true
168 \pdf_bookmarksopen true
169 \pdf_bookmarksopenlevel 1
170 \pdf_breaklinks false
174 \pdf_pdfusetitle false
175 \pdf_quoted_options "linkcolor=black, citecolor=black, urlcolor=blue, filecolor=blue, pdfpagelayout=OneColumn, pdfnewwindow=true, pdfstartview=XYZ, plainpages=false"
178 \use_package amsmath 2
179 \use_package amssymb 2
180 \use_package cancel 0
182 \use_package mathdots 1
183 \use_package mathtools 2
184 \use_package mhchem 1
185 \use_package stackrel 0
186 \use_package stmaryrd 0
187 \use_package undertilde 0
189 \cite_engine_type default
193 \paperorientation portrait
197 \notefontcolor #0000ff
204 \paragraph_separation skip
207 \math_numbering_side default
208 \quotes_style english
212 \paperpagestyle plain
216 \tracking_changes false
217 \output_changes false
220 \html_be_strict false
227 's detailed Math manual
231 by the \SpecialChar LyX
236 \begin_layout Plain Layout
238 If you have comments or error corrections, please send them to the \SpecialChar LyX
243 \begin_inset CommandInset href
245 name "lyx-docs@lists.lyx.org"
246 target "lyx-docs@lists.lyx.org?subject=LyX's Math manual"
258 \begin_inset Note Note
261 \begin_layout Plain Layout
268 \begin_inset Newline newline
272 \begin_inset Newline newline
280 \begin_layout Standard
281 \begin_inset CommandInset toc
282 LatexCommand tableofcontents
289 \begin_layout Standard
290 \begin_inset Note Note
293 \begin_layout Plain Layout
294 To export this document to PDF, PS or DVI the \SpecialChar LaTeX
297 braket, cancel, eurosym, mathdots, mathtools, mhchem, undertilde
304 If they are not installed the document can be exported anyway but the sections
305 where the packages are required will not appear in the output.
310 ; if it is not installed, this file cannot be exported.
313 \begin_layout Plain Layout
314 The latest PDF-version of this document can be found here:
315 \begin_inset Newline newline
320 http://wiki.lyx.org/LyX/Manuals#Math
328 \begin_layout Standard
329 \begin_inset Newpage newpage
335 \begin_layout Section
339 \begin_layout Standard
340 This document explains \SpecialChar LyX
341 's math features and is furthermore a collection
342 of \SpecialChar LaTeX
343 -commands used for mathematical characters and constructs.
344 The explanations are designed for the usage of commands.
345 It is therefore required that you have read the section
356 \begin_layout Standard
357 Most of the characters and many constructs explained in this manual are
358 also accessible via the menu
362 \SpecialChar menuseparator
378 But everybody who has to write lots of formulas will notice that it is
379 much faster to use commands instead of the math toolbar.
380 Therefore this manual is focused on commands but also mentions the correspondin
381 g toolbar buttons when available.
384 \begin_layout Standard
385 If not specially mentioned the commands are only available within formulas.
386 To be able to use all commands explained in this document, the option
390 must be checked in the document settings (menu
392 Document\SpecialChar menuseparator
393 Settings\SpecialChar menuseparator
404 \begin_layout Plain Layout
407 Use AMS math package automatically
413 \begin_layout Plain Layout
422 -math when math constructs are found that are supported by \SpecialChar LyX
431 \begin_layout Standard
432 This document doesn't list all
436 \begin_layout Plain Layout
449 \begin_layout Plain Layout
454 \begin_layout Plain Layout
463 -math commands is in the file
466 \begin_inset CommandInset href
469 target "ftp://ftp.ams.org/pub/tex/doc/amstex/amsguide.pdf"
476 , which is part of every \SpecialChar LaTeX
477 standard installation.
482 for lucidity reasons.
485 \begin_layout Section
489 \begin_layout Standard
490 To create an inline formula
491 \begin_inset Index idx
494 \begin_layout Plain Layout
500 that is embedded into a text line, use one of the shortcuts
506 or the toolbar button
513 \begin_inset Newline newline
516 To create a display style formula
517 \begin_inset Index idx
520 \begin_layout Plain Layout
521 Formula ! display style
526 which will appear bigger, has a different format, and will be in a separate
527 paragraph, use one of these shortcuts:
536 \begin_layout Standard
537 To change a display style formula to an inline formula, set the cursor into
538 the formula and use one of the shortcuts
546 Edit\SpecialChar menuseparator
547 Math\SpecialChar menuseparator
551 The same way is used to change an inline formula to a display style formula.
554 \begin_layout Standard
555 To display parts of an inline formula in the size of a display style formula,
563 \begin_inset Index idx
566 \begin_layout Plain Layout
575 Then a new blue box appears in which the desired formula part is inserted.
578 \begin_layout Standard
579 Only inline formulas are allowed inside tables.
582 \begin_layout Standard
587 can be turned on in the menu
589 View\SpecialChar menuseparator
593 When you click there on
594 \begin_inset Quotes eld
598 \begin_inset Quotes erd
601 the toolbar will be shown permanently at the bottom; this state is visualized
606 menu with a checkmark.
607 When you click in this state again on
608 \begin_inset Quotes eld
612 \begin_inset Quotes erd
623 is only shown when the cursor is within a formula; this state is visualized
624 by the renaming of the menu entry from
625 \begin_inset Quotes eld
629 \begin_inset Quotes erd
633 \begin_inset Quotes eld
641 \begin_inset Quotes erd
647 \begin_layout Standard
650 \begin_inset Index idx
653 \begin_layout Plain Layout
660 is invoked by pressing the toolbar button
668 Insert\SpecialChar menuseparator
680 \begin_layout Standard
681 To change the \SpecialChar LaTeX
683 \begin_inset Index idx
686 \begin_layout Plain Layout
695 Document\SpecialChar menuseparator
696 Settings\SpecialChar menuseparator
706 \begin_layout Standard
707 To edit matrices, case differentiations and multiline formulas subsequently,
710 Edit\SpecialChar menuseparator
715 Edit\SpecialChar menuseparator
717 \begin_inset space \thinspace{}
721 \begin_inset space \thinspace{}
731 When lines and columns are swapped via the menu, the column or line where
732 the cursor is in is exchanged with the column to the right or the line
734 Is the cursor in the last column or row, the exchange is done with the
735 column to the left or the line above.
738 \begin_layout Standard
739 To write text in formulas
743 \begin_layout Plain Layout
744 For multiline formulas the command
751 \begin_inset CommandInset ref
753 reference "subsec:Text-in-multiline"
767 \begin_inset Index idx
770 \begin_layout Plain Layout
777 \begin_inset Index idx
780 \begin_layout Plain Layout
787 This mode is invoked with the shortcut
793 or by the insertion of the command
800 \begin_inset Index idx
803 \begin_layout Plain Layout
812 The text appears black in \SpecialChar LyX
813 and can therefore be distinguished from the
814 other formula parts which appear blue.
815 In the output mathematical text is set upright, in contrary to other formula
819 \begin_layout Subsection*
823 \begin_layout Standard
824 Most of the \SpecialChar LaTeX
825 -commands for math constructs have the following scheme:
828 \begin_layout Standard
844 \begin_layout Standard
845 A command always starts with a backslash
846 \begin_inset Quotes gld
856 \begin_inset Quotes grd
860 To omit optional arguments, also omit the associated brackets.
861 The braces around the required arguments are named in this document as
864 \begin_inset Index idx
867 \begin_layout Plain Layout
875 If you add in a formula a left brace to a command name, \SpecialChar LyX
877 creates a \SpecialChar TeX
879 In all other cases \SpecialChar TeX
880 braces are created in formulas with the command
888 braces appear red in \SpecialChar LyX
889 , in contrary to normal braces which appear blue.
891 mode no command is needed to get \SpecialChar TeX
894 braces don't appear in the output.
897 \begin_layout Standard
898 When commands without arguments, like commands for symbols are entered in
900 mode, a space character must
904 be behind the command to end it.
905 This space doesn't appear in the output.
906 When the space should appear in the output, the space must be followed
907 by a protected space in normal text.
910 \begin_layout Standard
911 A protected space is inserted with
914 arg "command-alternatives space-insert protected ; math-space"
920 \begin_layout Subsection*
921 \begin_inset Newpage newpage
927 \begin_layout Itemize
929 \begin_inset space \textvisiblespace{}
932 denotes a space character to be input.
935 \begin_layout Itemize
937 \begin_inset Formula $\to$
940 denotes the usage of the corresponding arrow key on the keyboard.
945 key can often be used instead of
946 \begin_inset Formula $\to$
950 \begin_inset Formula $\downarrow$
958 \begin_inset Formula $\leftarrow$
962 \begin_inset Formula $\uparrow$
968 \begin_layout Subsection*
972 \begin_layout Standard
974 \begin_inset Float table
980 \begin_layout Plain Layout
982 \begin_inset Caption Standard
984 \begin_layout Plain Layout
985 \begin_inset CommandInset label
987 name "tab:Available-units"
999 \begin_layout Plain Layout
1001 \begin_inset Tabular
1002 <lyxtabular version="3" rows="13" columns="2">
1003 <features booktabs="true" tabularvalignment="middle">
1004 <column alignment="center" valignment="top">
1005 <column alignment="center" valignment="top" width="0pt">
1007 <cell alignment="center" valignment="top" topline="true" bottomline="true" usebox="none">
1010 \begin_layout Plain Layout
1016 <cell alignment="center" valignment="top" topline="true" bottomline="true" usebox="none">
1019 \begin_layout Plain Layout
1027 <cell alignment="center" valignment="top" leftline="true" usebox="none">
1030 \begin_layout Plain Layout
1036 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
1039 \begin_layout Plain Layout
1047 <cell alignment="center" valignment="top" leftline="true" usebox="none">
1050 \begin_layout Plain Layout
1056 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
1059 \begin_layout Plain Layout
1067 <cell alignment="center" valignment="top" leftline="true" usebox="none">
1070 \begin_layout Plain Layout
1076 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
1079 \begin_layout Plain Layout
1081 \begin_inset space \thinspace{}
1085 \begin_inset space \thinspace{}
1095 <cell alignment="center" valignment="top" leftline="true" usebox="none">
1098 \begin_layout Plain Layout
1104 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
1107 \begin_layout Plain Layout
1109 \begin_inset space \thinspace{}
1113 \begin_inset space \thinspace{}
1123 <cell alignment="center" valignment="top" leftline="true" usebox="none">
1126 \begin_layout Plain Layout
1132 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
1135 \begin_layout Plain Layout
1137 \begin_inset space \thinspace{}
1141 \begin_inset space \thinspace{}
1151 <cell alignment="center" valignment="top" leftline="true" usebox="none">
1154 \begin_layout Plain Layout
1160 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
1163 \begin_layout Plain Layout
1165 \begin_inset space \thinspace{}
1169 \begin_inset space \thinspace{}
1179 <cell alignment="center" valignment="top" leftline="true" usebox="none">
1182 \begin_layout Plain Layout
1188 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
1191 \begin_layout Plain Layout
1193 \begin_inset space \thinspace{}
1197 \begin_inset space \thinspace{}
1207 <cell alignment="center" valignment="top" leftline="true" usebox="none">
1210 \begin_layout Plain Layout
1216 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
1219 \begin_layout Plain Layout
1221 \begin_inset space \thinspace{}
1225 \begin_inset Formula $\approx$
1229 \begin_inset space \thinspace{}
1239 <cell alignment="center" valignment="top" leftline="true" usebox="none">
1242 \begin_layout Plain Layout
1248 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
1251 \begin_layout Plain Layout
1253 \begin_inset space \thinspace{}
1257 \begin_inset space \thinspace{}
1267 <cell alignment="center" valignment="top" leftline="true" usebox="none">
1270 \begin_layout Plain Layout
1276 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
1279 \begin_layout Plain Layout
1283 \begin_inset Quotes eld
1289 \begin_inset Quotes erd
1299 <cell alignment="center" valignment="top" leftline="true" usebox="none">
1302 \begin_layout Plain Layout
1308 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
1311 \begin_layout Plain Layout
1313 \begin_inset Quotes eld
1321 \begin_inset Quotes erd
1331 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
1334 \begin_layout Plain Layout
1340 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
1343 \begin_layout Plain Layout
1345 \begin_inset space \thinspace{}
1349 \begin_inset Formula $\nicefrac{1}{18}$
1353 \begin_inset space \thinspace{}
1374 \begin_layout Standard
1375 \begin_inset Newpage newpage
1381 \begin_layout Section
1385 \begin_layout Subsection
1387 \begin_inset Index idx
1390 \begin_layout Plain Layout
1397 \begin_inset Index idx
1400 \begin_layout Plain Layout
1407 \begin_inset Index idx
1410 \begin_layout Plain Layout
1415 \begin_layout Plain Layout
1426 \begin_layout Plain Layout
1439 \begin_inset Index idx
1442 \begin_layout Plain Layout
1447 \begin_layout Plain Layout
1458 \begin_layout Plain Layout
1473 \begin_layout Standard
1474 Indices are created with an underscore
1475 \begin_inset Quotes eld
1479 \begin_inset Quotes erd
1482 or via the math toolbar button
1485 arg "math-subscript"
1488 , exponents with a caret
1489 \begin_inset Quotes eld
1493 \begin_inset Quotes erd
1496 or via the math toolbar button
1499 arg "math-superscript"
1505 \begin_layout Standard
1507 \begin_inset Tabular
1508 <lyxtabular version="3" rows="4" columns="2">
1509 <features booktabs="true" tabularvalignment="middle">
1510 <column alignment="center" valignment="top" width="0pt">
1511 <column alignment="center" valignment="top" width="0pt">
1513 <cell alignment="center" valignment="top" topline="true" bottomline="true" usebox="none">
1516 \begin_layout Plain Layout
1522 <cell alignment="center" valignment="top" topline="true" bottomline="true" usebox="none">
1525 \begin_layout Plain Layout
1533 <cell alignment="center" valignment="top" usebox="none">
1536 \begin_layout Plain Layout
1542 <cell alignment="center" valignment="top" usebox="none">
1545 \begin_layout Plain Layout
1546 \begin_inset Formula $B_{V}$
1555 <row topspace="1.5mm">
1556 <cell alignment="center" valignment="top" usebox="none">
1559 \begin_layout Plain Layout
1565 <cell alignment="center" valignment="top" usebox="none">
1568 \begin_layout Plain Layout
1569 \begin_inset Formula $B^{V}$
1578 <row topspace="1.5mm">
1579 <cell alignment="center" valignment="top" topline="true" bottomline="true" usebox="none">
1582 \begin_layout Plain Layout
1584 \begin_inset space \textvisiblespace{}
1592 <cell alignment="center" valignment="top" topline="true" bottomline="true" usebox="none">
1595 \begin_layout Plain Layout
1596 \begin_inset Formula $B^{A}$
1612 \begin_layout Standard
1613 As the caret is in some languages an accent, vowels will be accentuated
1614 in this case and not set as exponents
1618 \begin_layout Plain Layout
1619 Depending on the used keyboard settings this can also happen for characters
1626 To get exponents in this case, press
1630 after the caret as in the last example.
1633 \begin_layout Subsection
1635 \begin_inset CommandInset label
1637 name "subsec:Fractions"
1642 \begin_inset Index idx
1645 \begin_layout Plain Layout
1654 \begin_layout Standard
1655 Fractions are generated with the command
1662 \begin_inset Index idx
1665 \begin_layout Plain Layout
1673 or via the math toolbar button
1676 arg "math-insert \\frac"
1680 The font size is adjusted automatically, depending on whether the fraction
1681 is in an inline or display style formula.
1682 With the math toolbar button
1685 arg "math-insert \\frac-square"
1688 you can select different fraction types.
1691 \begin_layout Standard
1699 \begin_inset Index idx
1702 \begin_layout Plain Layout
1710 a fraction can be created that always has the size of a display style formula.
1718 \begin_inset Index idx
1721 \begin_layout Plain Layout
1729 the fraction appears always with the size of an inline formula.
1733 \begin_layout Standard
1734 A line with the fraction
1735 \begin_inset Formula $\frac{1}{2}$
1738 that was created with the command
1747 \begin_layout Standard
1748 A line with the fraction
1749 \begin_inset Formula $\dfrac{1}{2}$
1752 that was created with the command
1761 \begin_layout Standard
1763 \begin_inset Tabular
1764 <lyxtabular version="3" rows="4" columns="2">
1765 <features booktabs="true" tabularvalignment="middle">
1766 <column alignment="center" valignment="top" width="0pt">
1767 <column alignment="center" valignment="top" width="0pt">
1769 <cell alignment="center" valignment="top" topline="true" bottomline="true" usebox="none">
1772 \begin_layout Plain Layout
1778 <cell alignment="center" valignment="top" topline="true" bottomline="true" usebox="none">
1781 \begin_layout Plain Layout
1788 <row topspace="1.5mm">
1789 <cell alignment="center" valignment="top" usebox="none">
1792 \begin_layout Plain Layout
1796 \begin_inset space \textvisiblespace{}
1800 \begin_inset Formula $\downarrow$
1808 <cell alignment="center" valignment="top" usebox="none">
1811 \begin_layout Plain Layout
1812 \begin_inset Formula $\frac{A}{B}$
1821 <row topspace="2mm">
1822 <cell alignment="center" valignment="top" usebox="none">
1825 \begin_layout Plain Layout
1829 \begin_inset space \textvisiblespace{}
1833 \begin_inset Formula $\downarrow$
1841 <cell alignment="center" valignment="top" usebox="none">
1844 \begin_layout Plain Layout
1845 \begin_inset Formula $\dfrac{A}{B}$
1854 <row topspace="2mm" bottomspace="1mm">
1855 <cell alignment="center" valignment="top" bottomline="true" usebox="none">
1858 \begin_layout Plain Layout
1862 \begin_inset space \textvisiblespace{}
1868 \begin_inset space \textvisiblespace{}
1872 \begin_inset Formula $\downarrow$
1876 \begin_inset Formula $\downarrow\downarrow$
1884 <cell alignment="center" valignment="top" bottomline="true" usebox="none">
1887 \begin_layout Plain Layout
1888 \begin_inset Formula $\dfrac{e^{\frac{1}{2}}}{3}$
1904 \begin_layout Standard
1905 \begin_inset VSpace bigskip
1909 \begin_inset Newpage newpage
1912 For nested fractions the command
1919 \begin_inset Index idx
1922 \begin_layout Plain Layout
1932 \begin_inset VSpace -3mm
1938 \begin_layout Standard
1939 \begin_inset Formula
1941 \textrm{created with \textbf{\textbackslash frac}} & & \textrm{created with \textbf{\textbackslash cfrac}}\\
1942 \frac{A}{B+\frac{C+\frac{E}{F}}{D}} & & \cfrac{A}{B+\cfrac{C+\cfrac{E}{F}}{D}}
1950 \begin_layout Standard
1951 The command for the example above is:
1954 \begin_layout Standard
1960 \begin_inset space \textvisiblespace{}
1964 \begin_inset Formula $\downarrow$
1970 \begin_inset space \textvisiblespace{}
1976 \begin_inset space \textvisiblespace{}
1980 \begin_inset Formula $\downarrow$
1984 \begin_inset Formula $\downarrow$
1990 \begin_layout Standard
1991 \begin_inset VSpace medskip
1997 \begin_layout Standard
2004 sets the fraction always in the size of a displayed formula, also when
2005 it is part of another fraction.
2008 \begin_layout Standard
2009 It is possible to specify the alignment of the numerator.
2016 is used to left align it, the command
2029 centers the numerator.
2030 These fractions demonstrate the different alignments:
2033 \begin_layout Standard
2036 \begin_inset Formula
2038 \cfrac[l]{A}{B+C}\,,\,\cfrac{A}{B+C}\,,\,\cfrac[r]{A}{B+C}
2046 \begin_layout Standard
2047 \begin_inset Note Greyedout
2050 \begin_layout Plain Layout
2067 are no real \SpecialChar LaTeX
2068 commands but represent the command
2072 cfrac[alignment]{numerator}{denominator}
2075 Therefore you cannot use them in \SpecialChar TeX
2084 \begin_layout Standard
2085 \begin_inset VSpace medskip
2088 It is often advantageous to combine
2101 \begin_inset Formula
2103 \cfrac{A}{B+\cfrac{C+\frac{E}{F}}{D}}
2111 \begin_layout Standard
2112 For inline fractions with a sloped fraction stroke you can use the command
2120 \begin_inset Index idx
2123 \begin_layout Plain Layout
2132 \begin_inset Formula $\nicefrac{5}{31}$
2142 \begin_inset Index idx
2145 \begin_layout Plain Layout
2154 \begin_inset Formula $\unitfrac{5}{31}$
2157 There is furthermore the command
2163 that offers to write a fraction in combination with a number:
2164 \begin_inset Formula $\unitfrac[2]{1}{3}$
2170 \begin_layout Standard
2171 \begin_inset Note Greyedout
2174 \begin_layout Plain Layout
2185 is not a real \SpecialChar LaTeX
2186 command but the command
2187 \begin_inset Newline newline
2194 unitfrac[number]{numerator}{denominator}
2197 Therefore you cannot use it in \SpecialChar TeX
2206 \begin_layout Standard
2207 How to define own fractions where the fraction stroke can be changed, is
2209 \begin_inset CommandInset ref
2211 reference "subsec:Self-defined-Fractions"
2218 \begin_layout Standard
2219 Multiline fractions are explained in
2220 \begin_inset CommandInset ref
2222 reference "subsec:Multiline-Fractions"
2229 \begin_layout Subsection
2231 \begin_inset Index idx
2234 \begin_layout Plain Layout
2243 \begin_layout Standard
2244 Square roots are created with
2251 \begin_inset Index idx
2254 \begin_layout Plain Layout
2262 or the math toolbar button
2265 arg "math-insert \\sqrt"
2268 , all other roots with the command
2275 \begin_inset Index idx
2278 \begin_layout Plain Layout
2286 or with the math toolbar button
2289 arg "math-insert \\root"
2295 \begin_layout Standard
2297 \begin_inset Tabular
2298 <lyxtabular version="3" rows="3" columns="2">
2299 <features booktabs="true" tabularvalignment="middle">
2300 <column alignment="center" valignment="top" width="0pt">
2301 <column alignment="center" valignment="top" width="0pt">
2303 <cell alignment="center" valignment="top" topline="true" bottomline="true" usebox="none">
2306 \begin_layout Plain Layout
2312 <cell alignment="center" valignment="top" topline="true" bottomline="true" usebox="none">
2315 \begin_layout Plain Layout
2322 <row topspace="1mm">
2323 <cell alignment="center" valignment="top" usebox="none">
2326 \begin_layout Plain Layout
2330 \begin_inset space \textvisiblespace{}
2338 <cell alignment="center" valignment="top" usebox="none">
2341 \begin_layout Plain Layout
2342 \begin_inset Formula $\sqrt{A-B}$
2351 <row topspace="1mm">
2352 <cell alignment="center" valignment="top" bottomline="true" usebox="none">
2355 \begin_layout Plain Layout
2359 \begin_inset space \textvisiblespace{}
2363 \begin_inset Formula $\downarrow$
2371 <cell alignment="center" valignment="top" bottomline="true" usebox="none">
2374 \begin_layout Plain Layout
2375 \begin_inset Formula $\sqrt[3]{A-B}$
2391 \begin_layout Standard
2392 A square root can also be created with
2398 when the root index field is left empty.
2401 \begin_layout Standard
2402 With certain indices the distance to the root is too small, like in this
2404 \begin_inset Formula $\sqrt[\beta]{B}$
2408 \begin_inset Newline newline
2412 \begin_inset Formula $\beta$
2416 To avoid this, the commands
2423 \begin_inset Index idx
2426 \begin_layout Plain Layout
2441 \begin_inset Index idx
2444 \begin_layout Plain Layout
2452 are used with the following scheme:
2455 \begin_layout Standard
2469 \begin_layout Standard
2470 Distance is the number of Big Points (unit bp;
2471 \begin_inset Formula $\mathrm{72\,bp=1\,inch}$
2474 ), that the index should be moved to the left or top, resp..
2475 The commands are written to the index.
2476 This way the command
2477 \begin_inset Newline newline
2487 \begin_inset Formula $\to$
2493 \begin_inset Formula $\to$
2499 \begin_inset space \textvisiblespace{}
2503 \begin_inset Formula $\to$
2507 \begin_inset Newline newline
2512 produces a correct typeset formula:
2513 \begin_inset Formula $\sqrt[\leftroot{-1}\uproot{2}\beta]{B}$
2519 \begin_layout Subsection
2520 Binomial Coefficients
2521 \begin_inset Index idx
2524 \begin_layout Plain Layout
2525 Binomial coefficients
2533 \begin_layout Standard
2534 Binomial coefficients are inserted with the command
2541 \begin_inset Index idx
2544 \begin_layout Plain Layout
2552 or with the submenu of the math toolbar button
2555 arg "math-insert \\frac-square"
2571 there are the commands
2578 \begin_inset Index idx
2581 \begin_layout Plain Layout
2596 \begin_inset Index idx
2599 \begin_layout Plain Layout
2608 For other brackets around binomial coeficients there are the commands
2615 \begin_inset Index idx
2618 \begin_layout Plain Layout
2633 \begin_inset Index idx
2636 \begin_layout Plain Layout
2647 \begin_layout Standard
2649 \begin_inset Tabular
2650 <lyxtabular version="3" rows="6" columns="2">
2651 <features booktabs="true" tabularvalignment="middle">
2652 <column alignment="center" valignment="top" width="0pt">
2653 <column alignment="center" valignment="top" width="0pt">
2655 <cell alignment="center" valignment="top" topline="true" bottomline="true" usebox="none">
2658 \begin_layout Plain Layout
2664 <cell alignment="center" valignment="top" topline="true" bottomline="true" usebox="none">
2667 \begin_layout Plain Layout
2674 <row topspace="1mm">
2675 <cell alignment="center" valignment="top" usebox="none">
2678 \begin_layout Plain Layout
2682 \begin_inset space \textvisiblespace{}
2686 \begin_inset Formula $\downarrow$
2694 <cell alignment="center" valignment="top" usebox="none">
2697 \begin_layout Plain Layout
2698 \begin_inset Formula $\binom{A}{B}$
2707 <row topspace="2mm">
2708 <cell alignment="center" valignment="top" usebox="none">
2711 \begin_layout Plain Layout
2715 \begin_inset space \textvisiblespace{}
2719 \begin_inset Formula $\downarrow$
2727 <cell alignment="center" valignment="top" usebox="none">
2730 \begin_layout Plain Layout
2731 \begin_inset Formula $\dbinom{A}{B}$
2740 <row topspace="2mm" bottomspace="0.5mm">
2741 <cell alignment="center" valignment="top" usebox="none">
2744 \begin_layout Plain Layout
2748 \begin_inset space \textvisiblespace{}
2752 \begin_inset Formula $\downarrow$
2760 <cell alignment="center" valignment="top" usebox="none">
2763 \begin_layout Plain Layout
2764 \begin_inset Formula $\tbinom{A}{B}$
2773 <row topspace="1mm">
2774 <cell alignment="center" valignment="top" topline="true" usebox="none">
2777 \begin_layout Plain Layout
2781 \begin_inset space \textvisiblespace{}
2785 \begin_inset Formula $\downarrow$
2793 <cell alignment="center" valignment="top" topline="true" usebox="none">
2796 \begin_layout Plain Layout
2797 \begin_inset Formula ${A \brack B}$
2806 <row topspace="2mm" bottomspace="0.5mm">
2807 <cell alignment="center" valignment="top" bottomline="true" usebox="none">
2810 \begin_layout Plain Layout
2814 \begin_inset space \textvisiblespace{}
2818 \begin_inset Formula $\downarrow$
2826 <cell alignment="center" valignment="top" bottomline="true" usebox="none">
2829 \begin_layout Plain Layout
2830 \begin_inset Formula ${A \brace B}$
2846 \begin_layout Subsection
2847 Case Differentiations
2848 \begin_inset Index idx
2851 \begin_layout Plain Layout
2852 Case differentiations
2860 \begin_layout Standard
2862 \begin_inset Tabular
2863 <lyxtabular version="3" rows="3" columns="2">
2864 <features booktabs="true" tabularvalignment="middle">
2865 <column alignment="center" valignment="top" width="0pt">
2866 <column alignment="center" valignment="top" width="0pt">
2868 <cell alignment="center" valignment="top" topline="true" bottomline="true" usebox="none">
2871 \begin_layout Plain Layout
2877 <cell alignment="center" valignment="top" topline="true" bottomline="true" usebox="none">
2880 \begin_layout Plain Layout
2888 <cell alignment="center" valignment="top" usebox="none">
2891 \begin_layout Plain Layout
2895 \begin_inset space \textvisiblespace{}
2899 \begin_inset Formula $\to$
2903 \begin_inset Index idx
2906 \begin_layout Plain Layout
2919 <cell alignment="center" valignment="top" usebox="none">
2922 \begin_layout Plain Layout
2923 \begin_inset Formula $\begin{cases}
2933 <row topspace="1.5mm">
2934 <cell alignment="center" valignment="top" bottomline="true" usebox="none">
2937 \begin_layout Plain Layout
2941 \begin_inset space \textvisiblespace{}
2947 arg "newline-insert newline"
2955 <cell alignment="center" valignment="top" bottomline="true" usebox="none">
2958 \begin_layout Plain Layout
2959 \begin_inset Formula $\begin{cases}
2960 A & \textrm{for }x>0\\
2961 B & \textrm{for }x=0
2978 \begin_layout Standard
2985 or pressing the math toolbar button
2988 arg "math-insert \\cases"
2991 you can create new lines with the shortcut
2994 arg "newline-insert newline"
2997 or the table toolbar button
3000 arg "tabular-feature append-row"
3006 \begin_layout Standard
3013 is also available via the menu
3015 Insert\SpecialChar menuseparator
3016 Math\SpecialChar menuseparator
3022 \begin_layout Subsection
3024 \begin_inset Index idx
3027 \begin_layout Plain Layout
3036 \begin_layout Standard
3044 \begin_inset Index idx
3047 \begin_layout Plain Layout
3055 every character can be displayed canceled.
3056 The characters are quasi accentuated by a slash.
3059 \begin_layout Standard
3061 \begin_inset Tabular
3062 <lyxtabular version="3" rows="4" columns="2">
3063 <features booktabs="true" tabularvalignment="middle">
3064 <column alignment="center" valignment="top" width="0pt">
3065 <column alignment="center" valignment="top" width="0pt">
3067 <cell alignment="center" valignment="top" topline="true" bottomline="true" usebox="none">
3070 \begin_layout Plain Layout
3076 <cell alignment="center" valignment="top" topline="true" bottomline="true" usebox="none">
3079 \begin_layout Plain Layout
3087 <cell alignment="center" valignment="top" usebox="none">
3090 \begin_layout Plain Layout
3098 <cell alignment="center" valignment="top" usebox="none">
3101 \begin_layout Plain Layout
3102 \begin_inset Formula $\not=$
3112 <cell alignment="center" valignment="top" usebox="none">
3115 \begin_layout Plain Layout
3125 <cell alignment="center" valignment="top" usebox="none">
3128 \begin_layout Plain Layout
3129 \begin_inset Formula $\not\le$
3139 <cell alignment="center" valignment="top" topline="true" bottomline="true" usebox="none">
3142 \begin_layout Plain Layout
3152 <cell alignment="center" valignment="top" topline="true" bottomline="true" usebox="none">
3155 \begin_layout Plain Layout
3156 \begin_inset Formula $\not\parallel$
3172 \begin_layout Standard
3173 The last example shows that not all negations look good.
3174 Therefore there are special commands for some negations (see
3175 \begin_inset CommandInset ref
3177 reference "subsec:Mathematical-Symbols"
3182 \begin_inset CommandInset ref
3184 reference "sec:Relations"
3191 \begin_layout Subsection
3193 \begin_inset CommandInset label
3195 name "subsec:Placeholders"
3200 \begin_inset Index idx
3203 \begin_layout Plain Layout
3210 \begin_inset Index idx
3213 \begin_layout Plain Layout
3214 Chemical characters ! Isotopes
3220 \begin_inset Index idx
3223 \begin_layout Plain Layout
3228 \begin_layout Plain Layout
3239 \begin_layout Plain Layout
3254 \begin_layout Standard
3256 \begin_inset space \thinspace{}
3260 \begin_inset space \space{}
3267 \begin_layout Plain Layout
3268 Typesetting isotopes and chemical symbols is described in
3269 \begin_inset CommandInset ref
3271 reference "subsec:Chemical-Symbols-and"
3280 the following problem occurs:
3283 \begin_layout Standard
3285 \begin_inset Tabular
3286 <lyxtabular version="3" rows="2" columns="2">
3287 <features booktabs="true" tabularvalignment="middle">
3288 <column alignment="center" valignment="top" width="0pt">
3289 <column alignment="center" valignment="top" width="0pt">
3291 <cell alignment="center" valignment="top" usebox="none">
3294 \begin_layout Plain Layout
3295 Indices created with sub- and superscripts:
3300 <cell alignment="center" valignment="top" usebox="none">
3303 \begin_layout Plain Layout
3304 \begin_inset Formula $_{9}^{19}\mathrm{F}$
3313 <row topspace="1.5mm">
3314 <cell alignment="center" valignment="top" usebox="none">
3317 \begin_layout Plain Layout
3323 <cell alignment="center" valignment="top" usebox="none">
3326 \begin_layout Plain Layout
3327 \begin_inset Formula $_{\phantom{1}9}^{19}\mathrm{F}$
3343 \begin_layout Standard
3344 The shorter index is by default placed below or above the first character
3345 of the longer index.
3346 To avoid this there is the command
3353 \begin_inset Index idx
3356 \begin_layout Plain Layout
3364 or the math toolbar button
3365 \begin_inset space \thinspace{}
3372 \begin_layout Plain Layout
3373 can be found in the submenu of the toolbar button
3376 arg "math-insert \\space"
3390 that creates one or more phantom characters.
3397 a small blue box appears that is superposed with two red arrows.
3398 The arrows indicate that the complete width and height of the box content
3399 will be created as placeholder.
3400 Phantom characters are accordingly placeholders with the size of the characters.
3403 \begin_layout Standard
3405 \begin_inset Tabular
3406 <lyxtabular version="3" rows="4" columns="2">
3407 <features booktabs="true" tabularvalignment="middle">
3408 <column alignment="center" valignment="top" width="0pt">
3409 <column alignment="center" valignment="top" width="0pt">
3411 <cell alignment="center" valignment="top" topline="true" bottomline="true" usebox="none">
3414 \begin_layout Plain Layout
3420 <cell alignment="center" valignment="top" topline="true" bottomline="true" usebox="none">
3423 \begin_layout Plain Layout
3430 <row topspace="1.5mm">
3431 <cell alignment="center" valignment="top" usebox="none">
3434 \begin_layout Plain Layout
3436 \begin_inset space \textvisiblespace{}
3442 \begin_inset space \textvisiblespace{}
3446 \begin_inset Formula $\to$
3450 \begin_inset space \textvisiblespace{}
3458 <cell alignment="center" valignment="top" usebox="none">
3461 \begin_layout Plain Layout
3462 \begin_inset Formula $_{\phantom{1}9}^{19}\mathrm{F}$
3471 <row topspace="1.5mm" bottomspace="0.5mm">
3472 <cell alignment="center" valignment="top" usebox="none">
3475 \begin_layout Plain Layout
3477 \begin_inset space \textvisiblespace{}
3483 \begin_inset space \textvisiblespace{}
3487 \begin_inset Formula $\to$
3491 \begin_inset space \textvisiblespace{}
3499 <cell alignment="center" valignment="top" usebox="none">
3502 \begin_layout Plain Layout
3503 \begin_inset Formula $_{\phantom{23}9}^{235}\mathrm{F}$
3512 <row topspace="1.5mm" bottomspace="0.5mm">
3513 <cell alignment="center" valignment="top" topline="true" bottomline="true" usebox="none">
3516 \begin_layout Plain Layout
3520 \begin_inset space \textvisiblespace{}
3526 \begin_inset space \textvisiblespace{}
3530 \begin_inset Formula $\to$
3534 \begin_inset space \textvisiblespace{}
3542 <cell alignment="center" valignment="top" topline="true" bottomline="true" usebox="none">
3545 \begin_layout Plain Layout
3546 \begin_inset Formula $\Lambda_{MMt}^{\phantom{ii}t}$
3562 \begin_layout Standard
3563 Furthermore there are the commands
3570 \begin_inset Index idx
3573 \begin_layout Plain Layout
3594 \begin_inset Index idx
3597 \begin_layout Plain Layout
3618 creates only space for the maximal height of the characters in the box
3619 but not for its width.
3626 creates only space for the width of the box content.
3627 Therefore the boxes of both commands have only one red arrow.
3630 \begin_layout Standard
3631 For example the command
3636 \begin_inset space \textvisiblespace{}
3643 creates space for the height of the integral sign,
3647 \begin_layout Plain Layout
3654 creates an integral sign, see
3655 \begin_inset CommandInset ref
3657 reference "subsec:Big-Operators"
3666 because this is the larger character.
3667 An example application is in
3668 \begin_inset CommandInset ref
3670 reference "subsec:Multiline-Brackets"
3677 \begin_layout Standard
3678 Placeholders can also be used for text when they are inserted via the menu
3681 Insert\SpecialChar menuseparator
3682 Formatting\SpecialChar menuseparator
3688 \begin_layout Standard
3690 \begin_inset Newline newline
3694 \begin_inset Phantom Phantom
3697 \begin_layout Plain Layout
3706 \begin_layout Subsection
3708 \begin_inset Index idx
3711 \begin_layout Plain Layout
3718 \begin_inset Index idx
3721 \begin_layout Plain Layout
3722 Formula ! underlined
3730 \begin_layout Standard
3732 \begin_inset Tabular
3733 <lyxtabular version="3" rows="4" columns="2">
3734 <features booktabs="true" tabularvalignment="middle">
3735 <column alignment="center" valignment="top" width="0pt">
3736 <column alignment="center" valignment="top" width="0pt">
3738 <cell alignment="center" valignment="top" topline="true" bottomline="true" usebox="none">
3741 \begin_layout Plain Layout
3747 <cell alignment="center" valignment="top" topline="true" bottomline="true" usebox="none">
3750 \begin_layout Plain Layout
3757 <row topspace="2mm">
3758 <cell alignment="center" valignment="top" usebox="none">
3761 \begin_layout Plain Layout
3765 \begin_inset space \textvisiblespace{}
3769 \begin_inset Index idx
3772 \begin_layout Plain Layout
3785 <cell alignment="center" valignment="top" usebox="none">
3788 \begin_layout Plain Layout
3789 \begin_inset Formula $\overline{A+B}$
3798 <row bottomspace="1mm">
3799 <cell alignment="center" valignment="top" usebox="none">
3802 \begin_layout Plain Layout
3806 \begin_inset space \textvisiblespace{}
3810 \begin_inset Index idx
3813 \begin_layout Plain Layout
3826 <cell alignment="center" valignment="top" usebox="none">
3829 \begin_layout Plain Layout
3830 \begin_inset Formula $\underline{A+B}$
3839 <row topspace="2mm" bottomspace="1mm">
3840 <cell alignment="center" valignment="top" topline="true" bottomline="true" usebox="none">
3843 \begin_layout Plain Layout
3847 \begin_inset space \textvisiblespace{}
3853 \begin_inset space \textvisiblespace{}
3861 <cell alignment="center" valignment="top" topline="true" bottomline="true" usebox="none">
3864 \begin_layout Plain Layout
3865 \begin_inset Formula $\overline{\underline{A+B}}$
3881 \begin_layout Standard
3882 In the last example it doesn't matter if first
3897 \begin_layout Standard
3898 To double underline use
3907 \begin_layout Standard
3908 It is possible to place up to 6 lines above or below characters.
3911 \begin_layout Standard
3912 \begin_inset VSpace bigskip
3915 Custom lines can be created using the command
3922 \begin_inset Index idx
3925 \begin_layout Plain Layout
3933 which has the following scheme:
3936 \begin_layout Standard
3941 rule[vertical offset]{length}{thickness}
3944 \begin_layout Standard
3945 The optional vertical offset shifts the line upwards (or downwards, when
3946 the value is negative).
3948 \begin_inset CommandInset ref
3950 reference "tab:Available-units"
3954 can be used for the values.
3955 Here are two example lines created with the commands
3956 \begin_inset Newline newline
3963 rule[-2ex]{3cm}{2pt}
3974 \begin_layout Standard
3976 \begin_inset Formula $\rule[-2ex]{3cm}{2pt}\rule{2cm}{1pt}$
3982 \begin_layout Standard
3989 can also be used for text when a line is inserted via the menu
3991 Insert\SpecialChar menuseparator
3992 Formatting\SpecialChar menuseparator
3994 \begin_inset space ~
4002 \begin_layout Standard
4004 \begin_inset CommandInset line
4015 \begin_layout Subsection
4017 \begin_inset CommandInset label
4019 name "subsec:Ellipses"
4024 \begin_inset Index idx
4027 \begin_layout Plain Layout
4036 \begin_layout Standard
4037 There are different types of ellipses available.
4041 \begin_layout Plain Layout
4042 In the math toolbar in the submenu of the button
4045 arg "math-insert \\ldots"
4053 For listings dots at the baseline are used (
4060 \begin_inset Index idx
4063 \begin_layout Plain Layout
4071 ), while for operations dots are needed that are on the same height as the
4079 \begin_inset Index idx
4082 \begin_layout Plain Layout
4091 When using the command
4098 \begin_inset Index idx
4101 \begin_layout Plain Layout
4109 , \SpecialChar LaTeX
4110 decides on the basis of the next character what type is used.
4113 \begin_layout Standard
4115 \begin_inset Tabular
4116 <lyxtabular version="3" rows="9" columns="2">
4117 <features booktabs="true" tabularvalignment="middle">
4118 <column alignment="center" valignment="top" width="0pt">
4119 <column alignment="center" valignment="top" width="0pt">
4121 <cell alignment="center" valignment="top" topline="true" bottomline="true" usebox="none">
4124 \begin_layout Plain Layout
4130 <cell alignment="center" valignment="top" topline="true" bottomline="true" usebox="none">
4133 \begin_layout Plain Layout
4141 <cell alignment="center" valignment="top" usebox="none">
4144 \begin_layout Plain Layout
4146 \begin_inset space \textvisiblespace{}
4152 \begin_inset space \textvisiblespace{}
4160 <cell alignment="center" valignment="top" usebox="none">
4163 \begin_layout Plain Layout
4164 \begin_inset Formula $A_{1},\dots,A_{n}$
4174 <cell alignment="center" valignment="top" usebox="none">
4177 \begin_layout Plain Layout
4179 \begin_inset space \textvisiblespace{}
4185 \begin_inset space \textvisiblespace{}
4193 <cell alignment="center" valignment="top" usebox="none">
4196 \begin_layout Plain Layout
4197 \begin_inset Formula $A_{1}+\dots+A_{n}$
4207 <cell alignment="center" valignment="top" usebox="none">
4210 \begin_layout Plain Layout
4212 \begin_inset space \textvisiblespace{}
4218 \begin_inset space \textvisiblespace{}
4226 <cell alignment="center" valignment="top" usebox="none">
4229 \begin_layout Plain Layout
4230 \begin_inset Formula $A_{1},\ldots,A_{n}$
4240 <cell alignment="center" valignment="top" bottomline="true" usebox="none">
4243 \begin_layout Plain Layout
4245 \begin_inset space \textvisiblespace{}
4251 \begin_inset space \textvisiblespace{}
4259 <cell alignment="center" valignment="top" bottomline="true" usebox="none">
4262 \begin_layout Plain Layout
4263 \begin_inset Formula $A_{1}+\cdots+A_{n}$
4273 <cell alignment="center" valignment="top" usebox="none">
4276 \begin_layout Plain Layout
4284 <cell alignment="center" valignment="top" usebox="none">
4287 \begin_layout Plain Layout
4288 \begin_inset Formula $\vdots$
4298 <cell alignment="center" valignment="top" usebox="none">
4301 \begin_layout Plain Layout
4309 <cell alignment="center" valignment="top" usebox="none">
4312 \begin_layout Plain Layout
4313 \begin_inset Formula $\ddots$
4323 <cell alignment="center" valignment="top" usebox="none">
4326 \begin_layout Plain Layout
4334 <cell alignment="center" valignment="top" usebox="none">
4337 \begin_layout Plain Layout
4338 \begin_inset Formula $\iddots$
4348 <cell alignment="center" valignment="top" topline="true" bottomline="true" usebox="none">
4351 \begin_layout Plain Layout
4353 \begin_inset space \thinspace{}
4356 matrix with the different dots
4361 <cell alignment="center" valignment="top" topline="true" bottomline="true" usebox="none">
4364 \begin_layout Plain Layout
4365 \begin_inset Formula $\begin{array}{ccc}
4366 A_{11} & \cdots & A_{1m}\\
4367 \vdots & \ddots & \vdots\\
4368 A_{n1} & \cdots & A_{nm}
4385 \begin_layout Standard
4386 The ellipses available in menu
4388 Insert\SpecialChar menuseparator
4390 \begin_inset space ~
4404 \begin_layout Standard
4405 \begin_inset VSpace medskip
4414 , one of the options
4416 Use mathdots package (automatically)
4418 must be set in the document settings under
4421 \begin_inset space ~
4427 \begin_inset Newline newline
4432 Use mathdots package
4434 will improve the appearance of all dots in the documents if their font
4435 style or size is not the default.
4438 \begin_layout Standard
4439 \begin_inset VSpace medskip
4442 Specially for matrices there are ellipses that span over several columns.
4443 They are created with the command
4450 \begin_inset Index idx
4453 \begin_layout Plain Layout
4461 , that has the following scheme:
4464 \begin_layout Standard
4469 hdotsfor[distance]{number of columns}
4472 \begin_layout Standard
4473 The number of columns specifies how many columns should be spanned.
4474 Distance is a factor for the distance between the dots.
4477 \begin_layout Standard
4478 In the following matrix the command
4484 was inserted in the first box of the second line, to get an ellipsis with
4485 a dot distance twice as long as with the command
4492 \begin_inset Formula
4494 \left(\begin{array}{cccc}
4503 Note that the matrix fields that should be spanned must be empty, otherwise
4504 you get \SpecialChar LaTeX
4508 \begin_layout Standard
4509 \begin_inset VSpace bigskip
4512 Furthermore you can fill with the command
4519 \begin_inset Index idx
4522 \begin_layout Plain Layout
4530 the rest of a line with dots.
4531 The effect of these commands is the same as with
4538 \begin_inset CommandInset ref
4540 reference "subsec:Variable-Space"
4547 \begin_layout Standard
4548 For example the command
4553 \begin_inset space \textvisiblespace{}
4561 \begin_layout Standard
4562 \begin_inset Formula $A\dotfill B$
4568 \begin_layout Standard
4575 there is for a line the command
4582 \begin_inset Index idx
4585 \begin_layout Plain Layout
4596 \begin_layout Standard
4597 \begin_inset Formula $A\hrulefill B$
4603 \begin_layout Standard
4604 To use the commands for text, they have to be inserted in \SpecialChar TeX
4608 \begin_layout Section
4610 \begin_inset CommandInset label
4617 \begin_inset Index idx
4620 \begin_layout Plain Layout
4629 \begin_layout Standard
4630 Matrices can be inserted via the math toolbar button
4633 arg "dialog-show mathmatrix"
4638 Insert\SpecialChar menuseparator
4639 Math\SpecialChar menuseparator
4643 In the matrix dialog you can specify the number of columns and rows, the
4644 alignment and the decoration.
4645 The vertical alignment is only of importance for matrices in inline formulas:
4648 \begin_layout Standard
4649 The first matrix is top
4650 \begin_inset Formula $\begin{array}[t]{cccc}
4658 \begin_inset Formula $\begin{array}{cccc}
4665 and the third bottom
4666 \begin_inset Formula $\begin{array}[b]{cccc}
4676 \begin_layout Standard
4677 The horizontal alignment specifies how the column entries should be aligned.
4678 It is set by entering a letter for every column.
4683 denotes left aligned,
4692 To create for example a 4
4697 \begin_inset space ~
4700 matrix where the first column is left aligned, the second and third are
4701 centered and the last one is right aligned, one enters for the horizontal
4707 Normally in a matrix all columns are centered, therefore the default for
4715 \begin_layout Standard
4716 Horizontal alignment:
4719 \begin_layout Standard
4725 \begin_inset Formula $\begin{array}{lll}
4737 \begin_inset Formula $\begin{array}{ccc}
4749 \begin_inset Formula $\begin{array}{rrr}
4759 \begin_layout Standard
4760 To add or delete rows and columns subsequently, the math toolbar buttons
4764 arg "tabular-feature append-row"
4770 arg "tabular-feature delete-row"
4774 \begin_inset space \thinspace{}
4779 Edit\SpecialChar menuseparator
4783 New rows can also be created with
4786 arg "newline-insert newline"
4792 \begin_layout Standard
4793 \begin_inset VSpace bigskip
4800 adds parentheses in the selected style around the matrix.
4801 Alternatively, parentheses can can either be created with the commands
4809 \begin_inset Index idx
4812 \begin_layout Plain Layout
4827 \begin_inset Index idx
4830 \begin_layout Plain Layout
4841 \begin_inset space ~
4847 \begin_inset CommandInset ref
4849 reference "subsec:Automatic-Bracket-Size"
4853 , or by using the following commands:
4854 \begin_inset VSpace medskip
4860 \begin_layout Standard
4861 \begin_inset space \hfill{}
4865 \begin_inset Tabular
4866 <lyxtabular version="3" rows="4" columns="2">
4867 <features booktabs="true" tabularvalignment="middle">
4868 <column alignment="center" valignment="top" width="0pt">
4869 <column alignment="center" valignment="top">
4871 <cell alignment="center" valignment="top" topline="true" bottomline="true" usebox="none">
4874 \begin_layout Plain Layout
4880 <cell alignment="center" valignment="top" topline="true" bottomline="true" usebox="none">
4883 \begin_layout Plain Layout
4890 <row topspace="1.5mm">
4891 <cell alignment="center" valignment="top" usebox="none">
4894 \begin_layout Plain Layout
4898 \begin_inset space \textvisiblespace{}
4906 \begin_inset space \thinspace{}
4914 <cell alignment="center" valignment="top" usebox="none">
4917 \begin_layout Plain Layout
4918 \begin_inset Formula $\begin{bmatrix}\begin{array}{cc}
4919 0 & \textrm{-}\mathrm{i}\\
4921 \end{array}\end{bmatrix}$
4930 <row topspace="1.5mm" bottomspace="0.5mm">
4931 <cell alignment="center" valignment="top" usebox="none">
4934 \begin_layout Plain Layout
4938 \begin_inset space \textvisiblespace{}
4946 \begin_inset space \thinspace{}
4954 <cell alignment="center" valignment="top" usebox="none">
4957 \begin_layout Plain Layout
4958 \begin_inset Formula $\begin{Bmatrix}\begin{array}{cc}
4959 0 & \textrm{-}\mathrm{i}\\
4961 \end{array}\end{Bmatrix}$
4971 <cell alignment="center" valignment="top" bottomline="true" usebox="none">
4974 \begin_layout Plain Layout
4978 \begin_inset space \textvisiblespace{}
4986 \begin_inset space \thinspace{}
4994 <cell alignment="center" valignment="top" bottomline="true" usebox="none">
4997 \begin_layout Plain Layout
4998 \begin_inset Formula $\begin{pmatrix}\begin{array}{cc}
4999 0 & \textrm{-}\mathrm{i}\\
5001 \end{array}\end{pmatrix}$
5015 \begin_inset space \hfill{}
5019 \begin_inset Tabular
5020 <lyxtabular version="3" rows="4" columns="2">
5021 <features booktabs="true" tabularvalignment="middle">
5022 <column alignment="center" valignment="top" width="0pt">
5023 <column alignment="center" valignment="top">
5025 <cell alignment="center" valignment="top" topline="true" bottomline="true" usebox="none">
5028 \begin_layout Plain Layout
5034 <cell alignment="center" valignment="top" topline="true" bottomline="true" usebox="none">
5037 \begin_layout Plain Layout
5044 <row topspace="1.5mm">
5045 <cell alignment="center" valignment="top" usebox="none">
5048 \begin_layout Plain Layout
5052 \begin_inset space \textvisiblespace{}
5060 \begin_inset space \thinspace{}
5068 <cell alignment="center" valignment="top" usebox="none">
5071 \begin_layout Plain Layout
5072 \begin_inset Formula $\begin{vmatrix}\begin{array}{cc}
5073 0 & \textrm{-}\mathrm{i}\\
5075 \end{array}\end{vmatrix}$
5084 <row topspace="1.5mm" bottomspace="0.5mm">
5085 <cell alignment="center" valignment="top" usebox="none">
5088 \begin_layout Plain Layout
5092 \begin_inset space \textvisiblespace{}
5100 \begin_inset space \thinspace{}
5108 <cell alignment="center" valignment="top" usebox="none">
5111 \begin_layout Plain Layout
5112 \begin_inset Formula $\begin{Vmatrix}\begin{array}{cc}
5113 0 & \textrm{-}\mathrm{i}\\
5115 \end{array}\end{Vmatrix}$
5125 <cell alignment="center" valignment="top" bottomline="true" usebox="none">
5128 \begin_layout Plain Layout
5132 \begin_inset space \textvisiblespace{}
5140 \begin_inset space \thinspace{}
5148 <cell alignment="center" valignment="top" bottomline="true" usebox="none">
5151 \begin_layout Plain Layout
5152 \begin_inset Formula $\begin{matrix}\begin{array}{cc}
5153 0 & \textrm{-}\mathrm{i}\\
5155 \end{array}\end{matrix}$
5169 \begin_inset space \hfill{}
5175 \begin_layout Standard
5176 \begin_inset VSpace medskip
5180 \begin_inset space \thinspace{}
5184 \begin_inset space \space{}
5193 is inserted, a blue box appears between two vertical lines where the matrix
5195 \begin_inset Newline newline
5198 Note that decorated matrices ignore the vertical alignment.
5201 \begin_layout Standard
5202 \begin_inset VSpace bigskip
5205 As all multiline formulas are matrices, the length
5212 \begin_inset Index idx
5215 \begin_layout Plain Layout
5223 that is described in
5224 \begin_inset CommandInset ref
5226 reference "subsec:Column-Separation"
5230 can also be used to change the column separation of matrices.
5233 \begin_layout Standard
5234 To change the row separation, the command
5241 \begin_inset Index idx
5244 \begin_layout Plain Layout
5253 It is used as follows:
5256 \begin_layout Standard
5263 arraystretch}{stretch factor}
5264 \begin_inset Index idx
5267 \begin_layout Plain Layout
5278 \begin_layout Standard
5285 assigns the stretch factor to the predefined command
5293 \begin_inset space \thinspace{}
5297 \begin_inset space \space{}
5300 the row separation, use the factor 2.
5301 This is then used for all following matrices.
5302 To go back to the original separation, assign the factor 1 to
5311 \begin_layout Standard
5312 To set matrices into a text line, the command
5319 \begin_inset Index idx
5322 \begin_layout Plain Layout
5331 When it is inserted a blue box with two dashed lines appears.
5332 In this box the matrix is inserted.
5335 \begin_layout Standard
5337 \begin_inset Formula $\left(\begin{smallmatrix}A & B\\
5339 \end{smallmatrix}\right)$
5345 \begin_layout Section
5346 Brackets and Delimiters
5347 \begin_inset Index idx
5350 \begin_layout Plain Layout
5357 \begin_inset Index idx
5360 \begin_layout Plain Layout
5369 \begin_layout Subsection
5370 Vertical Brackets and Delimiters
5371 \begin_inset Index idx
5374 \begin_layout Plain Layout
5383 \begin_layout Standard
5384 \begin_inset space \hfill{}
5388 \begin_inset Tabular
5389 <lyxtabular version="3" rows="9" columns="2">
5390 <features booktabs="true" tabularvalignment="middle">
5391 <column alignment="center" valignment="top" width="0pt">
5392 <column alignment="center" valignment="top" width="0pt">
5394 <cell alignment="center" valignment="top" topline="true" bottomline="true" usebox="none">
5397 \begin_layout Plain Layout
5403 <cell alignment="center" valignment="top" topline="true" bottomline="true" usebox="none">
5406 \begin_layout Plain Layout
5414 <cell alignment="center" valignment="top" usebox="none">
5417 \begin_layout Plain Layout
5423 <cell alignment="center" valignment="top" usebox="none">
5426 \begin_layout Plain Layout
5427 \begin_inset Formula $($
5437 <cell alignment="center" valignment="top" usebox="none">
5440 \begin_layout Plain Layout
5446 <cell alignment="center" valignment="top" usebox="none">
5449 \begin_layout Plain Layout
5450 \begin_inset Formula $\{$
5460 <cell alignment="center" valignment="top" usebox="none">
5463 \begin_layout Plain Layout
5469 <cell alignment="center" valignment="top" usebox="none">
5472 \begin_layout Plain Layout
5473 \begin_inset Formula $[$
5483 <cell alignment="center" valignment="top" usebox="none">
5486 \begin_layout Plain Layout
5494 <cell alignment="center" valignment="top" usebox="none">
5497 \begin_layout Plain Layout
5498 \begin_inset Formula $\langle$
5508 <cell alignment="center" valignment="top" usebox="none">
5511 \begin_layout Plain Layout
5519 <cell alignment="center" valignment="top" usebox="none">
5522 \begin_layout Plain Layout
5523 \begin_inset Formula $\lceil$
5533 <cell alignment="center" valignment="top" usebox="none">
5536 \begin_layout Plain Layout
5544 <cell alignment="center" valignment="top" usebox="none">
5547 \begin_layout Plain Layout
5548 \begin_inset Formula $\lfloor$
5558 <cell alignment="center" valignment="top" usebox="none">
5561 \begin_layout Plain Layout
5567 <cell alignment="center" valignment="top" usebox="none">
5570 \begin_layout Plain Layout
5571 \begin_inset Formula $/$
5581 <cell alignment="center" valignment="top" bottomline="true" usebox="none">
5584 \begin_layout Plain Layout
5590 <cell alignment="center" valignment="top" bottomline="true" usebox="none">
5593 \begin_layout Plain Layout
5594 \begin_inset Formula $|$
5608 \begin_inset space \hfill{}
5612 \begin_inset Tabular
5613 <lyxtabular version="3" rows="9" columns="2">
5614 <features booktabs="true" tabularvalignment="middle">
5615 <column alignment="center" valignment="top" width="0pt">
5616 <column alignment="center" valignment="top" width="0pt">
5618 <cell alignment="center" valignment="top" topline="true" bottomline="true" usebox="none">
5621 \begin_layout Plain Layout
5627 <cell alignment="center" valignment="top" topline="true" bottomline="true" usebox="none">
5630 \begin_layout Plain Layout
5638 <cell alignment="center" valignment="top" usebox="none">
5641 \begin_layout Plain Layout
5647 <cell alignment="center" valignment="top" usebox="none">
5650 \begin_layout Plain Layout
5651 \begin_inset Formula $)$
5661 <cell alignment="center" valignment="top" usebox="none">
5664 \begin_layout Plain Layout
5670 <cell alignment="center" valignment="top" usebox="none">
5673 \begin_layout Plain Layout
5674 \begin_inset Formula $\}$
5684 <cell alignment="center" valignment="top" usebox="none">
5687 \begin_layout Plain Layout
5693 <cell alignment="center" valignment="top" usebox="none">
5696 \begin_layout Plain Layout
5697 \begin_inset Formula $]$
5707 <cell alignment="center" valignment="top" usebox="none">
5710 \begin_layout Plain Layout
5718 <cell alignment="center" valignment="top" usebox="none">
5721 \begin_layout Plain Layout
5722 \begin_inset Formula $\rangle$
5732 <cell alignment="center" valignment="top" usebox="none">
5735 \begin_layout Plain Layout
5743 <cell alignment="center" valignment="top" usebox="none">
5746 \begin_layout Plain Layout
5747 \begin_inset Formula $\rceil$
5757 <cell alignment="center" valignment="top" usebox="none">
5760 \begin_layout Plain Layout
5768 <cell alignment="center" valignment="top" usebox="none">
5771 \begin_layout Plain Layout
5772 \begin_inset Formula $\rfloor$
5782 <cell alignment="center" valignment="top" usebox="none">
5785 \begin_layout Plain Layout
5795 <cell alignment="center" valignment="top" usebox="none">
5798 \begin_layout Plain Layout
5799 \begin_inset Formula $\backslash$
5809 <cell alignment="center" valignment="top" bottomline="true" usebox="none">
5812 \begin_layout Plain Layout
5820 <cell alignment="center" valignment="top" bottomline="true" usebox="none">
5823 \begin_layout Plain Layout
5824 \begin_inset Formula $\|$
5838 \begin_inset space \hfill{}
5844 \begin_layout Standard
5847 \begin_inset Note Greyedout
5850 \begin_layout Plain Layout
5863 \begin_inset Index idx
5866 \begin_layout Plain Layout
5874 must be used for the backslash, because the command
5882 produces a line break there.
5890 \begin_layout Standard
5891 For all characters listed above the size can be adjusted with the commands
5892 described in the following two subsections.
5893 When using these commands, the characters < and > can directly be used
5894 instead of the commands
5909 \begin_layout Subsubsection
5911 \begin_inset CommandInset label
5913 name "subsec:Manual-Bracket-Size"
5918 \begin_inset Index idx
5921 \begin_layout Plain Layout
5922 Bracket size ! manual
5930 \begin_layout Standard
5931 The bracket size can be specified manually by the \SpecialChar LaTeX
5939 \begin_inset Index idx
5942 \begin_layout Plain Layout
5975 denotes the smallest and
5981 the largest bracket size.
5984 \begin_layout Standard
5985 These commands are used to emphasize levels of brackets:
5988 \begin_layout Standard
5990 \begin_inset Tabular
5991 <lyxtabular version="3" rows="2" columns="2">
5992 <features booktabs="true" tabularvalignment="middle">
5993 <column alignment="center" valignment="top" width="0pt">
5994 <column alignment="center" valignment="top" width="0pt">
5996 <cell alignment="center" valignment="top" usebox="none">
5999 \begin_layout Plain Layout
6000 all brackets in the same size:
6005 <cell alignment="center" valignment="top" usebox="none">
6008 \begin_layout Plain Layout
6009 \begin_inset Formula $((A+B)(A-B))^{C}$
6018 <row topspace="2mm">
6019 <cell alignment="center" valignment="top" usebox="none">
6022 \begin_layout Plain Layout
6028 <cell alignment="center" valignment="top" usebox="none">
6031 \begin_layout Plain Layout
6032 \begin_inset Formula $\Big((A+B)(A-B)\Big)^{C}$
6048 \begin_layout Standard
6049 For the second formula the command
6056 \begin_inset space \textvisiblespace{}
6064 \begin_layout Standard
6065 Here is an overview about all bracket sizes:
6068 \begin_layout Standard
6085 \begin_inset space \textvisiblespace{}
6093 \begin_inset space \textvisiblespace{}
6097 \begin_inset space \textvisiblespace{}
6107 \begin_layout Standard
6109 \begin_inset Formula $\Bigg(\exp\bigg<\Big[\big\{\ln(3x)\big\}^{2}\sin(x)\Big]^{A}\bigg>\Bigg)^{0,5}$
6115 \begin_layout Standard
6122 -commands there is the variant
6129 \begin_inset Index idx
6132 \begin_layout Plain Layout
6140 that adds a bit more space between the bracket and its content, and the
6154 \begin_inset Index idx
6157 \begin_layout Plain Layout
6167 , that don't add additional space.
6172 at the end of the command
6178 is for a left bracket; for a right bracket this will be replaced by an
6184 A left or right bracket can each be an opening or closing bracket.
6187 \begin_layout Standard
6188 In the following table is a comparison of the variants:
6191 \begin_layout Standard
6193 \begin_inset Tabular
6194 <lyxtabular version="3" rows="5" columns="2">
6195 <features booktabs="true" tabularvalignment="middle">
6196 <column alignment="center" valignment="top" width="0pt">
6197 <column alignment="center" valignment="middle">
6199 <cell alignment="center" valignment="top" topline="true" bottomline="true" usebox="none">
6202 \begin_layout Plain Layout
6208 <cell alignment="center" valignment="top" topline="true" bottomline="true" usebox="none">
6211 \begin_layout Plain Layout
6218 <row topspace="2mm">
6219 <cell alignment="center" valignment="top" usebox="none">
6222 \begin_layout Plain Layout
6232 \begin_inset space \textvisiblespace{}
6242 <cell alignment="center" valignment="top" usebox="none">
6245 \begin_layout Plain Layout
6246 \begin_inset Formula $\Bigm(\bigm(\ln(3x)\bigm)^{2}\Bigm)$
6255 <row topspace="2mm">
6256 <cell alignment="center" valignment="top" usebox="none">
6259 \begin_layout Plain Layout
6269 \begin_inset space \textvisiblespace{}
6279 <cell alignment="center" valignment="top" usebox="none">
6282 \begin_layout Plain Layout
6283 \begin_inset Formula $\Big(\big(\ln(3x)\big)^{2}\Big)$
6292 <row topspace="2mm" bottomspace="0.5mm">
6293 <cell alignment="center" valignment="top" usebox="none">
6296 \begin_layout Plain Layout
6306 \begin_inset space \textvisiblespace{}
6316 <cell alignment="center" valignment="top" usebox="none">
6319 \begin_layout Plain Layout
6320 \begin_inset Formula $\Bigl(\bigl(\ln(3x)\bigr)^{2}\Bigr)$
6329 <row topspace="1.5mm" bottomspace="0.5mm">
6330 <cell alignment="center" valignment="top" topline="true" bottomline="true" usebox="none">
6333 \begin_layout Plain Layout
6345 <cell alignment="center" valignment="top" topline="true" bottomline="true" usebox="none">
6348 \begin_layout Plain Layout
6349 \begin_inset Formula $\bigl)\ln(3x)\bigr($
6365 \begin_layout Subsubsection
6366 Automatic Bracket Size
6367 \begin_inset CommandInset label
6369 name "subsec:Automatic-Bracket-Size"
6374 \begin_inset Index idx
6377 \begin_layout Plain Layout
6378 Bracket size ! automatic
6386 \begin_layout Standard
6387 Brackets with variable size can be inserted with the commands
6394 \begin_inset Index idx
6397 \begin_layout Plain Layout
6412 \begin_inset Index idx
6415 \begin_layout Plain Layout
6423 or via the math toolbar button
6426 arg "dialog-show mathdelimiter"
6442 the wanted bracket must be inserted.
6443 The bracket size will then automatically be calculated for the output.
6446 \begin_layout Standard
6448 normal bracket: The command
6455 \begin_inset space \textvisiblespace{}
6459 \begin_inset Formula $\downarrow$
6463 \begin_inset space \textvisiblespace{}
6469 \begin_inset Formula
6479 \begin_layout Standard
6481 multiline bracket: The command
6490 \begin_inset space \textvisiblespace{}
6494 \begin_inset Formula $\downarrow$
6498 \begin_inset space \textvisiblespace{}
6506 \begin_inset Formula
6508 \ln\left(\frac{A}{C}\right)
6516 \begin_layout Standard
6532 \begin_inset space ~
6538 This has the advantage that you can see in \SpecialChar LyX
6539 immediately the real bracket
6540 size and that the matching right bracket will be created too.
6541 \begin_inset Newline newline
6544 The command for the last example would then be:
6555 \begin_inset space \textvisiblespace{}
6559 \begin_inset Formula $\downarrow$
6565 \begin_layout Standard
6566 To omit a left or right bracket, a dot is inserted for the omitted bracket.
6567 For example the command
6574 \begin_inset space \textvisiblespace{}
6578 \begin_inset Formula $\downarrow$
6582 \begin_inset space \textvisiblespace{}
6592 \begin_inset Formula
6594 \left.\frac{A}{B}\right\}
6613 will be converted by \SpecialChar LyX
6614 to brackets in the right size when the document is
6615 reloaded and an omitted bracket will appear as dashed line.
6618 \begin_layout Standard
6619 \begin_inset VSpace bigskip
6622 Because all popular \SpecialChar LaTeX
6623 distributions use e\SpecialChar TeX
6624 , an extension to \SpecialChar LaTeX
6633 \begin_inset Index idx
6636 \begin_layout Plain Layout
6644 is additionally available for all brackets and limits.
6645 With this command the height of the following character is adapted to the
6646 one of the surrounding brackets, what is e.
6647 \begin_inset space \thinspace{}
6651 \begin_inset space \space{}
6654 needed for physical vectors:
6655 \begin_inset Formula
6657 \left\langle \phi\:\middle|\:J=\frac{3}{2}\,,\,M_{J}\right\rangle
6662 For physical vectors there is a special \SpecialChar LaTeX
6663 -package, described in
6664 \begin_inset CommandInset ref
6666 reference "subsec:Physical-Vectors"
6673 \begin_layout Subsection
6675 \begin_inset Index idx
6678 \begin_layout Plain Layout
6679 Brackets ! horizontal
6687 \begin_layout Standard
6689 \begin_inset Tabular
6690 <lyxtabular version="3" rows="4" columns="2">
6691 <features booktabs="true" tabularvalignment="middle">
6692 <column alignment="center" valignment="top" width="0pt">
6693 <column alignment="center" valignment="top" width="0pt">
6695 <cell alignment="center" valignment="top" topline="true" bottomline="true" usebox="none">
6698 \begin_layout Plain Layout
6704 <cell alignment="center" valignment="top" topline="true" bottomline="true" usebox="none">
6707 \begin_layout Plain Layout
6715 <cell alignment="center" valignment="top" usebox="none">
6718 \begin_layout Plain Layout
6722 \begin_inset space \textvisiblespace{}
6726 \begin_inset space \textvisiblespace{}
6730 \begin_inset Index idx
6733 \begin_layout Plain Layout
6746 <cell alignment="center" valignment="top" usebox="none">
6749 \begin_layout Plain Layout
6750 \begin_inset Formula $\overbrace{A+B}^{3}$
6759 <row topspace="2mm">
6760 <cell alignment="center" valignment="top" usebox="none">
6763 \begin_layout Plain Layout
6767 \begin_inset space \textvisiblespace{}
6771 \begin_inset space \textvisiblespace{}
6775 \begin_inset Index idx
6778 \begin_layout Plain Layout
6791 <cell alignment="center" valignment="top" usebox="none">
6794 \begin_layout Plain Layout
6795 \begin_inset Formula $\underbrace{A+B}_{5}$
6805 <cell alignment="center" valignment="top" topline="true" bottomline="true" usebox="none">
6808 \begin_layout Plain Layout
6812 \begin_inset space \textvisiblespace{}
6818 \begin_inset space \textvisiblespace{}
6822 \begin_inset space \textvisiblespace{}
6826 \begin_inset space \textvisiblespace{}
6830 \begin_inset space \textvisiblespace{}
6834 \begin_inset space \textvisiblespace{}
6838 \begin_inset space \textvisiblespace{}
6846 <cell alignment="center" valignment="top" topline="true" bottomline="true" usebox="none">
6849 \begin_layout Plain Layout
6850 \begin_inset Formula $\overbrace{\underbrace{A+B_{w}}_{7}}^{C}$
6866 \begin_layout Standard
6867 In the last example it doesn't matter if
6879 is inserted at first.
6882 \begin_layout Standard
6883 \begin_inset VSpace medskip
6889 \begin_layout Standard
6890 If you set in the document settings under
6893 \begin_inset space ~
6903 \begin_inset Index idx
6906 \begin_layout Plain Layout
6907 Packages ! mathtools
6915 \begin_inset space ~
6920 , you have access to square backets:
6923 \begin_layout Standard
6925 \begin_inset Tabular
6926 <lyxtabular version="3" rows="4" columns="2">
6927 <features booktabs="true" tabularvalignment="middle">
6928 <column alignment="center" valignment="top" width="0pt">
6929 <column alignment="center" valignment="top" width="0pt">
6931 <cell alignment="center" valignment="top" topline="true" bottomline="true" usebox="none">
6934 \begin_layout Plain Layout
6940 <cell alignment="center" valignment="top" topline="true" bottomline="true" usebox="none">
6943 \begin_layout Plain Layout
6951 <cell alignment="center" valignment="top" usebox="none">
6954 \begin_layout Plain Layout
6982 \begin_inset space \textvisiblespace{}
6986 \begin_inset Index idx
6989 \begin_layout Plain Layout
7002 <cell alignment="center" valignment="top" usebox="none">
7005 \begin_layout Plain Layout
7006 \begin_inset Formula $\overbracket{A+B}^{3}$
7015 <row topspace="2mm">
7016 <cell alignment="center" valignment="top" usebox="none">
7019 \begin_layout Plain Layout
7047 \begin_inset space \textvisiblespace{}
7051 \begin_inset Index idx
7054 \begin_layout Plain Layout
7079 <cell alignment="center" valignment="top" usebox="none">
7082 \begin_layout Plain Layout
7083 \begin_inset Formula $\underbracket{A+B}_{5}$
7093 <cell alignment="center" valignment="top" topline="true" bottomline="true" usebox="none">
7096 \begin_layout Plain Layout
7102 \begin_inset space \textvisiblespace{}
7106 \begin_inset space \textvisiblespace{}
7110 \begin_inset space \textvisiblespace{}
7114 \begin_inset space \textvisiblespace{}
7118 \begin_inset space \textvisiblespace{}
7126 <cell alignment="center" valignment="top" topline="true" bottomline="true" usebox="none">
7129 \begin_layout Plain Layout
7130 \begin_inset Formula $\overbracket{\underbracket{A+B_{w}}_{7}}^{C}$
7146 \begin_layout Standard
7159 you can change the thickness of the bracket's stroke by specifying the
7160 desired thickness in square brackets behind the command:
7163 \begin_layout Standard
7165 \begin_inset Tabular
7166 <lyxtabular version="3" rows="3" columns="2">
7167 <features booktabs="true" tabularvalignment="middle">
7168 <column alignment="center" valignment="top" width="0pt">
7169 <column alignment="center" valignment="top" width="0pt">
7171 <cell alignment="center" valignment="top" topline="true" bottomline="true" usebox="none">
7174 \begin_layout Plain Layout
7180 <cell alignment="center" valignment="top" topline="true" bottomline="true" usebox="none">
7183 \begin_layout Plain Layout
7191 <cell alignment="center" valignment="top" usebox="none">
7194 \begin_layout Plain Layout
7224 \begin_inset space \textvisiblespace{}
7232 <cell alignment="center" valignment="top" usebox="none">
7235 \begin_layout Plain Layout
7236 \begin_inset Formula $\overbracket[3pt]{A+B}^{3}$
7245 <row topspace="2mm">
7246 <cell alignment="center" valignment="top" bottomline="true" usebox="none">
7249 \begin_layout Plain Layout
7279 \begin_inset space \textvisiblespace{}
7287 <cell alignment="center" valignment="top" bottomline="true" usebox="none">
7290 \begin_layout Plain Layout
7291 \begin_inset Formula $\underbracket[1pt]{A+B}_{5}$
7307 \begin_layout Standard
7308 \begin_inset VSpace bigskip
7311 When brackets should overlap each other, multiline formulas, as described
7313 \begin_inset CommandInset ref
7315 reference "sec:Multiline-Formulas"
7320 \begin_inset Formula
7322 A & = & \underbrace{gggg+bbqq}_{r}+\:dddd\\
7323 & & \hphantom{gggg+\:}\underbrace{\hphantom{bbqq+dddd}}_{s}
7328 In the first row the formula is inserted together with the first brace.
7329 It is hereby important that the space command
7333 \begin_layout Plain Layout
7334 Space commands are explained in
7335 \begin_inset CommandInset ref
7337 reference "subsec:Predefined-Space"
7352 is inserted before the first
7353 \begin_inset Formula $d$
7356 , because the brace that ends behind the
7357 \begin_inset Formula $q$
7360 prevents that the following
7361 \begin_inset Quotes eld
7365 \begin_inset Quotes erd
7368 is surrounded by space.
7372 \begin_layout Plain Layout
7373 because a bracket is not handled as a character, see
7374 \begin_inset CommandInset ref
7376 reference "subsec:Binary-Operators"
7385 In the second row the second brace is inserted.
7386 As it should begin before the
7387 \begin_inset Formula $b$
7402 \begin_layout Plain Layout
7410 \begin_inset CommandInset ref
7412 reference "subsec:Placeholders"
7421 This space is needed because the
7422 \begin_inset Quotes eld
7426 \begin_inset Quotes erd
7429 is also surrounded by space in the formula.
7430 The brace is placed under the command
7439 \begin_layout Standard
7440 It gets more complicated when brackets overlap each other above and under
7441 the formula, like in the following example:
7445 \begin_layout Plain Layout
7457 \begin_inset Formula
7459 & & \hphantom{gggg+\:}\overbrace{\hphantom{bbqq+dddd}}^{s}\\
7460 A & = & \underbrace{gggg+bbqq}_{r}+\:dddd
7469 \begin_layout Plain Layout
7480 The first formula row is the same as the second row of the previous example,
7481 with the difference that the brace is above.
7482 The second row contains the formula together with the second brace.
7483 To avoid that there is space between the upper brace in the first row and
7484 the formula, the row spacing needs to be reduced.
7485 This is not easily possible due to a bug in \SpecialChar LyX
7490 \begin_layout Plain Layout
7491 \begin_inset CommandInset href
7493 name "LyX-bug #1505"
7494 target "http://www.lyx.org/trac/ticket/1505"
7504 As a solution for the problem, the global formula row separation
7511 \begin_inset Index idx
7514 \begin_layout Plain Layout
7522 must be changed to -6
7523 \begin_inset space \thinspace{}
7526 pt before the formula with the command
7542 is set back after the formula to the standard value of 3
7543 \begin_inset space \thinspace{}
7546 pt using the same command.
7547 More about the row separation in formulas is explained in
7548 \begin_inset CommandInset ref
7550 reference "subsec:Line-Separation"
7557 \begin_layout Section
7559 \begin_inset Index idx
7562 \begin_layout Plain Layout
7571 \begin_layout Standard
7572 Arrows can be inserted via the math toolbar button
7575 arg "math-insert \\leftarrow"
7578 or the commands listed in the following subsections.
7581 \begin_layout Subsection
7583 \begin_inset Index idx
7586 \begin_layout Plain Layout
7595 \begin_layout Standard
7596 \begin_inset space \hfill{}
7600 \begin_inset Tabular
7601 <lyxtabular version="3" rows="8" columns="2">
7602 <features booktabs="true" tabularvalignment="middle">
7603 <column alignment="center" valignment="top" width="0pt">
7604 <column alignment="center" valignment="top" width="0pt">
7606 <cell alignment="center" valignment="top" topline="true" bottomline="true" usebox="none">
7609 \begin_layout Plain Layout
7615 <cell alignment="center" valignment="top" topline="true" bottomline="true" usebox="none">
7618 \begin_layout Plain Layout
7626 <cell alignment="center" valignment="top" usebox="none">
7629 \begin_layout Plain Layout
7637 <cell alignment="center" valignment="top" usebox="none">
7640 \begin_layout Plain Layout
7641 \begin_inset Formula $\gets$
7651 <cell alignment="center" valignment="top" usebox="none">
7654 \begin_layout Plain Layout
7662 <cell alignment="center" valignment="top" usebox="none">
7665 \begin_layout Plain Layout
7666 \begin_inset Formula $\Leftarrow$
7676 <cell alignment="center" valignment="top" usebox="none">
7679 \begin_layout Plain Layout
7687 <cell alignment="center" valignment="top" usebox="none">
7690 \begin_layout Plain Layout
7691 \begin_inset Formula $\longleftarrow$
7701 <cell alignment="center" valignment="top" usebox="none">
7704 \begin_layout Plain Layout
7712 <cell alignment="center" valignment="top" usebox="none">
7715 \begin_layout Plain Layout
7716 \begin_inset Formula $\Longleftarrow$
7726 <cell alignment="center" valignment="top" usebox="none">
7729 \begin_layout Plain Layout
7737 <cell alignment="center" valignment="top" usebox="none">
7740 \begin_layout Plain Layout
7741 \begin_inset Formula $\leftharpoonup$
7751 <cell alignment="center" valignment="top" usebox="none">
7754 \begin_layout Plain Layout
7762 <cell alignment="center" valignment="top" usebox="none">
7765 \begin_layout Plain Layout
7766 \begin_inset Formula $\leftharpoondown$
7776 <cell alignment="center" valignment="top" bottomline="true" usebox="none">
7779 \begin_layout Plain Layout
7787 <cell alignment="center" valignment="top" bottomline="true" usebox="none">
7790 \begin_layout Plain Layout
7791 \begin_inset Formula $\hookleftarrow$
7805 \begin_inset space \hfill{}
7809 \begin_inset Tabular
7810 <lyxtabular version="3" rows="8" columns="2">
7811 <features booktabs="true" tabularvalignment="middle">
7812 <column alignment="center" valignment="top" width="0pt">
7813 <column alignment="center" valignment="top" width="0pt">
7815 <cell alignment="center" valignment="top" topline="true" bottomline="true" usebox="none">
7818 \begin_layout Plain Layout
7824 <cell alignment="center" valignment="top" topline="true" bottomline="true" usebox="none">
7827 \begin_layout Plain Layout
7835 <cell alignment="center" valignment="top" usebox="none">
7838 \begin_layout Plain Layout
7846 <cell alignment="center" valignment="top" usebox="none">
7849 \begin_layout Plain Layout
7850 \begin_inset Formula $\to$
7860 <cell alignment="center" valignment="top" usebox="none">
7863 \begin_layout Plain Layout
7871 <cell alignment="center" valignment="top" usebox="none">
7874 \begin_layout Plain Layout
7875 \begin_inset Formula $\Rightarrow$
7885 <cell alignment="center" valignment="top" usebox="none">
7888 \begin_layout Plain Layout
7896 <cell alignment="center" valignment="top" usebox="none">
7899 \begin_layout Plain Layout
7900 \begin_inset Formula $\longrightarrow$
7910 <cell alignment="center" valignment="top" usebox="none">
7913 \begin_layout Plain Layout
7921 <cell alignment="center" valignment="top" usebox="none">
7924 \begin_layout Plain Layout
7925 \begin_inset Formula $\Longrightarrow$
7935 <cell alignment="center" valignment="top" usebox="none">
7938 \begin_layout Plain Layout
7946 <cell alignment="center" valignment="top" usebox="none">
7949 \begin_layout Plain Layout
7950 \begin_inset Formula $\rightharpoonup$
7960 <cell alignment="center" valignment="top" usebox="none">
7963 \begin_layout Plain Layout
7971 <cell alignment="center" valignment="top" usebox="none">
7974 \begin_layout Plain Layout
7975 \begin_inset Formula $\rightharpoondown$
7985 <cell alignment="center" valignment="top" bottomline="true" usebox="none">
7988 \begin_layout Plain Layout
7996 <cell alignment="center" valignment="top" bottomline="true" usebox="none">
7999 \begin_layout Plain Layout
8000 \begin_inset Formula $\hookrightarrow$
8014 \begin_inset space \hfill{}
8020 \begin_layout Standard
8021 \begin_inset space \hfill{}
8025 \begin_inset Tabular
8026 <lyxtabular version="3" rows="6" columns="2">
8027 <features booktabs="true" tabularvalignment="middle">
8028 <column alignment="center" valignment="top" width="0pt">
8029 <column alignment="center" valignment="top" width="0pt">
8031 <cell alignment="center" valignment="top" topline="true" bottomline="true" usebox="none">
8034 \begin_layout Plain Layout
8040 <cell alignment="center" valignment="top" topline="true" bottomline="true" usebox="none">
8043 \begin_layout Plain Layout
8051 <cell alignment="center" valignment="top" usebox="none">
8054 \begin_layout Plain Layout
8062 <cell alignment="center" valignment="top" usebox="none">
8065 \begin_layout Plain Layout
8066 \begin_inset Formula $\leftrightarrow$
8076 <cell alignment="center" valignment="top" usebox="none">
8079 \begin_layout Plain Layout
8087 <cell alignment="center" valignment="top" usebox="none">
8090 \begin_layout Plain Layout
8091 \begin_inset Formula $\Leftrightarrow$
8101 <cell alignment="center" valignment="top" usebox="none">
8104 \begin_layout Plain Layout
8112 <cell alignment="center" valignment="top" usebox="none">
8115 \begin_layout Plain Layout
8116 \begin_inset Formula $\longleftrightarrow$
8126 <cell alignment="center" valignment="top" usebox="none">
8129 \begin_layout Plain Layout
8137 <cell alignment="center" valignment="top" usebox="none">
8140 \begin_layout Plain Layout
8141 \begin_inset Formula $\Longleftrightarrow$
8151 <cell alignment="center" valignment="top" bottomline="true" usebox="none">
8154 \begin_layout Plain Layout
8162 <cell alignment="center" valignment="top" bottomline="true" usebox="none">
8165 \begin_layout Plain Layout
8166 \begin_inset Formula $\rightleftharpoons$
8180 \begin_inset space \hspace{}
8185 \begin_inset space \hfill{}
8189 \begin_inset Tabular
8190 <lyxtabular version="3" rows="5" columns="2">
8191 <features booktabs="true" tabularvalignment="middle">
8192 <column alignment="center" valignment="top" width="0pt">
8193 <column alignment="center" valignment="top" width="0pt">
8195 <cell alignment="center" valignment="top" topline="true" bottomline="true" usebox="none">
8198 \begin_layout Plain Layout
8204 <cell alignment="center" valignment="top" topline="true" bottomline="true" usebox="none">
8207 \begin_layout Plain Layout
8215 <cell alignment="center" valignment="top" usebox="none">
8218 \begin_layout Plain Layout
8226 <cell alignment="center" valignment="top" usebox="none">
8229 \begin_layout Plain Layout
8230 \begin_inset Formula $\mapsto$
8240 <cell alignment="center" valignment="top" usebox="none">
8243 \begin_layout Plain Layout
8251 <cell alignment="center" valignment="top" usebox="none">
8254 \begin_layout Plain Layout
8255 \begin_inset Formula $\longmapsto$
8265 <cell alignment="center" valignment="top" usebox="none">
8268 \begin_layout Plain Layout
8276 <cell alignment="center" valignment="top" usebox="none">
8279 \begin_layout Plain Layout
8280 \begin_inset Formula $\leadsto$
8290 <cell alignment="center" valignment="top" bottomline="true" usebox="none">
8293 \begin_layout Plain Layout
8301 <cell alignment="center" valignment="top" bottomline="true" usebox="none">
8304 \begin_layout Plain Layout
8305 \begin_inset Formula $\dasharrow$
8319 \begin_inset space \hfill{}
8325 \begin_layout Standard
8326 \begin_inset VSpace medskip
8329 Arrows used as accents like e.
8330 \begin_inset space \thinspace{}
8334 \begin_inset space \space{}
8337 vector arrows are listed in
8338 \begin_inset CommandInset ref
8340 reference "sec:Accents"
8347 \begin_layout Standard
8348 \begin_inset VSpace bigskip
8351 Furthermore there are the labeled arrows
8352 \begin_inset Index idx
8355 \begin_layout Plain Layout
8368 \begin_inset Index idx
8371 \begin_layout Plain Layout
8386 \begin_inset Index idx
8389 \begin_layout Plain Layout
8396 \begin_layout Plain Layout
8411 When inserting one of these commands in a formula, an arrow with two blue
8412 boxes appear where the label can be inserted.
8413 The length of the arrow adapts to the label width.
8416 \begin_layout Standard
8418 \begin_inset Tabular
8419 <lyxtabular version="3" rows="3" columns="2">
8420 <features booktabs="true" tabularvalignment="middle">
8421 <column alignment="center" valignment="top" width="0pt">
8422 <column alignment="center" valignment="top" width="0pt">
8424 <cell alignment="center" valignment="top" topline="true" bottomline="true" usebox="none">
8427 \begin_layout Plain Layout
8433 <cell alignment="center" valignment="top" topline="true" bottomline="true" usebox="none">
8436 \begin_layout Plain Layout
8444 <cell alignment="center" valignment="top" usebox="none">
8447 \begin_layout Plain Layout
8451 \begin_inset space \textvisiblespace{}
8455 \begin_inset Formula $\downarrow$
8459 \begin_inset Formula $\to$
8467 <cell alignment="center" valignment="top" usebox="none">
8470 \begin_layout Plain Layout
8471 \begin_inset Formula $F(a)\xleftarrow[x>0]{x=a}F(x)$
8480 <row topspace="2mm">
8481 <cell alignment="center" valignment="top" bottomline="true" usebox="none">
8484 \begin_layout Plain Layout
8488 \begin_inset space \textvisiblespace{}
8492 \begin_inset Formula $\downarrow$
8496 \begin_inset Formula $\to$
8504 <cell alignment="center" valignment="top" bottomline="true" usebox="none">
8507 \begin_layout Plain Layout
8508 \begin_inset Formula $F(x)\xrightarrow[x>0]{x=a}F(a)$
8524 \begin_layout Standard
8525 \begin_inset VSpace medskip
8531 \begin_layout Standard
8532 If you set in the document settings under
8535 \begin_inset space ~
8545 \begin_inset Index idx
8548 \begin_layout Plain Layout
8549 Packages ! mathtools
8557 \begin_inset space ~
8562 , you have access to the following labeled arrows:
8565 \begin_layout Standard
8566 \begin_inset Newpage newpage
8572 \begin_layout Standard
8574 \begin_inset space \hspace*{\fill}
8578 \begin_inset Tabular
8579 <lyxtabular version="3" rows="7" columns="2">
8580 <features booktabs="true" tabularvalignment="middle">
8581 <column alignment="center" valignment="top" width="0pt">
8582 <column alignment="center" valignment="top" width="0pt">
8584 <cell alignment="center" valignment="top" topline="true" bottomline="true" usebox="none">
8587 \begin_layout Plain Layout
8593 <cell alignment="center" valignment="top" topline="true" bottomline="true" usebox="none">
8596 \begin_layout Plain Layout
8604 <cell alignment="center" valignment="top" usebox="none">
8607 \begin_layout Plain Layout
8627 <cell alignment="center" valignment="top" usebox="none">
8630 \begin_layout Plain Layout
8631 \begin_inset Formula $\xleftrightarrow[x=a]{x>0}$
8640 <row topspace="2mm">
8641 <cell alignment="center" valignment="top" usebox="none">
8644 \begin_layout Plain Layout
8664 <cell alignment="center" valignment="top" usebox="none">
8667 \begin_layout Plain Layout
8668 \begin_inset Formula $\xLeftarrow[x=a]{x>0}$
8677 <row topspace="2mm">
8678 <cell alignment="center" valignment="top" usebox="none">
8681 \begin_layout Plain Layout
8701 <cell alignment="center" valignment="top" usebox="none">
8704 \begin_layout Plain Layout
8705 \begin_inset Formula $\xRightarrow[x=a]{x>0}$
8714 <row topspace="2mm">
8715 <cell alignment="center" valignment="top" usebox="none">
8718 \begin_layout Plain Layout
8738 <cell alignment="center" valignment="top" usebox="none">
8741 \begin_layout Plain Layout
8742 \begin_inset Formula $\xLeftrightarrow[x=a]{x>0}$
8751 <row topspace="2mm">
8752 <cell alignment="center" valignment="top" usebox="none">
8755 \begin_layout Plain Layout
8775 <cell alignment="center" valignment="top" usebox="none">
8778 \begin_layout Plain Layout
8779 \begin_inset Formula $\xhookleftarrow[x=a]{x>0}$
8788 <row topspace="2mm">
8789 <cell alignment="center" valignment="top" bottomline="true" usebox="none">
8792 \begin_layout Plain Layout
8812 <cell alignment="center" valignment="top" bottomline="true" usebox="none">
8815 \begin_layout Plain Layout
8816 \begin_inset Formula $\xhookrightarrow[x=a]{x>0}$
8830 \begin_inset space \hspace*{\fill}
8834 \begin_inset Tabular
8835 <lyxtabular version="3" rows="7" columns="2">
8836 <features booktabs="true" tabularvalignment="middle">
8837 <column alignment="center" valignment="top" width="0pt">
8838 <column alignment="center" valignment="top" width="0pt">
8840 <cell alignment="center" valignment="top" topline="true" bottomline="true" usebox="none">
8843 \begin_layout Plain Layout
8849 <cell alignment="center" valignment="top" topline="true" bottomline="true" usebox="none">
8852 \begin_layout Plain Layout
8860 <cell alignment="center" valignment="top" usebox="none">
8863 \begin_layout Plain Layout
8883 <cell alignment="center" valignment="top" usebox="none">
8886 \begin_layout Plain Layout
8887 \begin_inset Formula $\xleftharpoondown[x=a]{x>0}$
8896 <row topspace="2mm">
8897 <cell alignment="center" valignment="top" usebox="none">
8900 \begin_layout Plain Layout
8920 <cell alignment="center" valignment="top" usebox="none">
8923 \begin_layout Plain Layout
8924 \begin_inset Formula $\xleftharpoonup[x=a]{x>0}$
8933 <row topspace="2mm">
8934 <cell alignment="center" valignment="top" usebox="none">
8937 \begin_layout Plain Layout
8957 <cell alignment="center" valignment="top" usebox="none">
8960 \begin_layout Plain Layout
8961 \begin_inset Formula $\xrightharpoondown[x=a]{x>0}$
8970 <row topspace="2mm">
8971 <cell alignment="center" valignment="top" usebox="none">
8974 \begin_layout Plain Layout
8994 <cell alignment="center" valignment="top" usebox="none">
8997 \begin_layout Plain Layout
8998 \begin_inset Formula $\xrightharpoonup[x=a]{x>0}$
9007 <row topspace="2mm">
9008 <cell alignment="center" valignment="top" usebox="none">
9011 \begin_layout Plain Layout
9031 <cell alignment="center" valignment="top" usebox="none">
9034 \begin_layout Plain Layout
9035 \begin_inset Formula $\xleftrightharpoons[x=a]{x>0}$
9044 <row topspace="2mm">
9045 <cell alignment="center" valignment="top" bottomline="true" usebox="none">
9048 \begin_layout Plain Layout
9068 <cell alignment="center" valignment="top" bottomline="true" usebox="none">
9071 \begin_layout Plain Layout
9072 \begin_inset Formula $\xrightleftharpoons[x=a]{x>0}$
9086 \begin_inset space \hspace*{\fill}
9092 \begin_layout Standard
9093 The command scheme is for all these arrows:
9096 \begin_layout Standard
9098 \begin_inset Tabular
9099 <lyxtabular version="3" rows="2" columns="2">
9100 <features booktabs="true" tabularvalignment="middle">
9101 <column alignment="center" valignment="top" width="0pt">
9102 <column alignment="center" valignment="top" width="0pt">
9104 <cell alignment="center" valignment="top" topline="true" bottomline="true" usebox="none">
9107 \begin_layout Plain Layout
9113 <cell alignment="center" valignment="top" topline="true" bottomline="true" usebox="none">
9116 \begin_layout Plain Layout
9123 <row bottomspace="0.5mm">
9124 <cell alignment="center" valignment="top" bottomline="true" usebox="none">
9127 \begin_layout Plain Layout
9130 xleftrightarrow[x=a]
9133 \begin_inset Formula $\to$
9141 <cell alignment="center" valignment="top" bottomline="true" usebox="none">
9144 \begin_layout Plain Layout
9145 \begin_inset Formula $F(a)\xleftrightarrow[x=a]{x>0}F(x)$
9161 \begin_layout Subsection
9162 Vertical and diagonal Arrows
9163 \begin_inset Index idx
9166 \begin_layout Plain Layout
9173 \begin_inset Index idx
9176 \begin_layout Plain Layout
9185 \begin_layout Standard
9186 \begin_inset space \hfill{}
9190 \begin_inset Tabular
9191 <lyxtabular version="3" rows="7" columns="2">
9192 <features booktabs="true" tabularvalignment="middle">
9193 <column alignment="center" valignment="top" width="0pt">
9194 <column alignment="center" valignment="top" width="0pt">
9196 <cell alignment="center" valignment="top" topline="true" bottomline="true" usebox="none">
9199 \begin_layout Plain Layout
9205 <cell alignment="center" valignment="top" topline="true" bottomline="true" usebox="none">
9208 \begin_layout Plain Layout
9216 <cell alignment="center" valignment="top" usebox="none">
9219 \begin_layout Plain Layout
9227 <cell alignment="center" valignment="top" usebox="none">
9230 \begin_layout Plain Layout
9231 \begin_inset Formula $\uparrow$
9241 <cell alignment="center" valignment="top" usebox="none">
9244 \begin_layout Plain Layout
9252 <cell alignment="center" valignment="top" usebox="none">
9255 \begin_layout Plain Layout
9256 \begin_inset Formula $\Uparrow$
9266 <cell alignment="center" valignment="top" usebox="none">
9269 \begin_layout Plain Layout
9277 <cell alignment="center" valignment="top" usebox="none">
9280 \begin_layout Plain Layout
9281 \begin_inset Formula $\updownarrow$
9291 <cell alignment="center" valignment="top" usebox="none">
9294 \begin_layout Plain Layout
9302 <cell alignment="center" valignment="top" usebox="none">
9305 \begin_layout Plain Layout
9306 \begin_inset Formula $\Updownarrow$
9316 <cell alignment="center" valignment="top" usebox="none">
9319 \begin_layout Plain Layout
9327 <cell alignment="center" valignment="top" usebox="none">
9330 \begin_layout Plain Layout
9331 \begin_inset Formula $\Downarrow$
9341 <cell alignment="center" valignment="top" bottomline="true" usebox="none">
9344 \begin_layout Plain Layout
9352 <cell alignment="center" valignment="top" bottomline="true" usebox="none">
9355 \begin_layout Plain Layout
9356 \begin_inset Formula $\downarrow$
9370 \begin_inset space \hfill{}
9374 \begin_inset Tabular
9375 <lyxtabular version="3" rows="5" columns="2">
9376 <features booktabs="true" tabularvalignment="middle">
9377 <column alignment="center" valignment="top" width="0pt">
9378 <column alignment="center" valignment="top" width="0pt">
9380 <cell alignment="center" valignment="top" topline="true" bottomline="true" usebox="none">
9383 \begin_layout Plain Layout
9389 <cell alignment="center" valignment="top" topline="true" bottomline="true" usebox="none">
9392 \begin_layout Plain Layout
9400 <cell alignment="center" valignment="top" usebox="none">
9403 \begin_layout Plain Layout
9411 <cell alignment="center" valignment="top" usebox="none">
9414 \begin_layout Plain Layout
9415 \begin_inset Formula $\nearrow$
9425 <cell alignment="center" valignment="top" usebox="none">
9428 \begin_layout Plain Layout
9436 <cell alignment="center" valignment="top" usebox="none">
9439 \begin_layout Plain Layout
9440 \begin_inset Formula $\searrow$
9450 <cell alignment="center" valignment="top" usebox="none">
9453 \begin_layout Plain Layout
9461 <cell alignment="center" valignment="top" usebox="none">
9464 \begin_layout Plain Layout
9465 \begin_inset Formula $\swarrow$
9475 <cell alignment="center" valignment="top" bottomline="true" usebox="none">
9478 \begin_layout Plain Layout
9486 <cell alignment="center" valignment="top" bottomline="true" usebox="none">
9489 \begin_layout Plain Layout
9490 \begin_inset Formula $\nwarrow$
9504 \begin_inset space \hfill{}
9510 \begin_layout Standard
9511 \begin_inset VSpace medskip
9514 Vertical arrows can be used also as delimiters together with the commands
9516 \begin_inset CommandInset ref
9518 reference "subsec:Manual-Bracket-Size"
9523 \begin_inset CommandInset ref
9525 reference "subsec:Automatic-Bracket-Size"
9532 \begin_layout Section
9534 \begin_inset CommandInset label
9541 \begin_inset Index idx
9544 \begin_layout Plain Layout
9553 \begin_layout Standard
9554 Accents can be inserted via the math toolbar button
9557 arg "math-insert \\hat"
9560 or the commands listed in the following subsections.
9563 \begin_layout Subsection
9564 Accents for one Character
9568 \begin_layout Plain Layout
9581 \begin_layout Plain Layout
9583 \begin_inset CommandInset ref
9585 reference "subsec:Accents-in-Text"
9598 \begin_layout Plain Layout
9606 \begin_inset Note Note
9609 \begin_layout Plain Layout
9616 is used to avoid that the footnote appears in the PDF-bookmark.
9619 \begin_layout Plain Layout
9627 \begin_inset CommandInset ref
9629 reference "subsec:Formulas-in-Section"
9639 \begin_inset CommandInset label
9641 name "subsec:Accents-for-one"
9646 \begin_inset Index idx
9649 \begin_layout Plain Layout
9650 Accents ! for one character
9658 \begin_layout Standard
9659 \begin_inset space \hfill{}
9663 \begin_inset Tabular
9664 <lyxtabular version="3" rows="8" columns="2">
9665 <features booktabs="true" tabularvalignment="middle">
9666 <column alignment="center" valignment="top" width="0pt">
9667 <column alignment="center" valignment="top" width="0pt">
9669 <cell alignment="center" valignment="top" topline="true" bottomline="true" usebox="none">
9672 \begin_layout Plain Layout
9678 <cell alignment="center" valignment="top" topline="true" bottomline="true" usebox="none">
9681 \begin_layout Plain Layout
9688 <row topspace="1.5mm">
9689 <cell alignment="center" valignment="top" usebox="none">
9692 \begin_layout Plain Layout
9696 \begin_inset space \textvisiblespace{}
9704 <cell alignment="center" valignment="top" usebox="none">
9707 \begin_layout Plain Layout
9708 \begin_inset Formula $\dot{A}$
9717 <row topspace="1.5mm">
9718 <cell alignment="center" valignment="top" usebox="none">
9721 \begin_layout Plain Layout
9725 \begin_inset space \textvisiblespace{}
9733 <cell alignment="center" valignment="top" usebox="none">
9736 \begin_layout Plain Layout
9737 \begin_inset Formula $\ddot{A}$
9746 <row topspace="1.5mm">
9747 <cell alignment="center" valignment="top" usebox="none">
9750 \begin_layout Plain Layout
9754 \begin_inset space \textvisiblespace{}
9762 <cell alignment="center" valignment="top" usebox="none">
9765 \begin_layout Plain Layout
9766 \begin_inset Formula $\dddot{A}$
9775 <row topspace="1.5mm">
9776 <cell alignment="center" valignment="top" usebox="none">
9779 \begin_layout Plain Layout
9783 \begin_inset space \textvisiblespace{}
9791 <cell alignment="center" valignment="top" usebox="none">
9794 \begin_layout Plain Layout
9795 \begin_inset Formula $\ddddot{A}$
9804 <row topspace="1.5mm">
9805 <cell alignment="center" valignment="top" usebox="none">
9808 \begin_layout Plain Layout
9812 \begin_inset space \textvisiblespace{}
9816 \begin_inset Index idx
9819 \begin_layout Plain Layout
9830 <cell alignment="center" valignment="top" usebox="none">
9833 \begin_layout Plain Layout
9834 \begin_inset Formula $\vec{A}$
9843 <row topspace="1.5mm">
9844 <cell alignment="center" valignment="top" usebox="none">
9847 \begin_layout Plain Layout
9851 \begin_inset space \textvisiblespace{}
9859 <cell alignment="center" valignment="top" usebox="none">
9862 \begin_layout Plain Layout
9863 \begin_inset Formula $\bar{A}$
9872 <row topspace="1.5mm">
9873 <cell alignment="center" valignment="top" bottomline="true" usebox="none">
9876 \begin_layout Plain Layout
9880 \begin_inset space \textvisiblespace{}
9888 <cell alignment="center" valignment="top" bottomline="true" usebox="none">
9891 \begin_layout Plain Layout
9892 \begin_inset Formula $\mathring{A}$
9906 \begin_inset space \hfill{}
9910 \begin_inset Tabular
9911 <lyxtabular version="3" rows="7" columns="2">
9912 <features booktabs="true" tabularvalignment="middle">
9913 <column alignment="center" valignment="top" width="0pt">
9914 <column alignment="center" valignment="top" width="0pt">
9916 <cell alignment="center" valignment="top" topline="true" bottomline="true" usebox="none">
9919 \begin_layout Plain Layout
9925 <cell alignment="center" valignment="top" topline="true" bottomline="true" usebox="none">
9928 \begin_layout Plain Layout
9935 <row topspace="1.5mm">
9936 <cell alignment="center" valignment="top" usebox="none">
9939 \begin_layout Plain Layout
9943 \begin_inset space \textvisiblespace{}
9951 <cell alignment="center" valignment="top" usebox="none">
9954 \begin_layout Plain Layout
9955 \begin_inset Formula $\tilde{A}$
9964 <row topspace="1.5mm">
9965 <cell alignment="center" valignment="top" usebox="none">
9968 \begin_layout Plain Layout
9972 \begin_inset space \textvisiblespace{}
9980 <cell alignment="center" valignment="top" usebox="none">
9983 \begin_layout Plain Layout
9984 \begin_inset Formula $\hat{A}$
9993 <row topspace="1.5mm">
9994 <cell alignment="center" valignment="top" usebox="none">
9997 \begin_layout Plain Layout
10001 \begin_inset space \textvisiblespace{}
10009 <cell alignment="center" valignment="top" usebox="none">
10012 \begin_layout Plain Layout
10013 \begin_inset Formula $\check{A}$
10022 <row topspace="1.5mm">
10023 <cell alignment="center" valignment="top" usebox="none">
10026 \begin_layout Plain Layout
10030 \begin_inset space \textvisiblespace{}
10038 <cell alignment="center" valignment="top" usebox="none">
10041 \begin_layout Plain Layout
10042 \begin_inset Formula $\acute{A}$
10051 <row topspace="1.5mm">
10052 <cell alignment="center" valignment="top" usebox="none">
10055 \begin_layout Plain Layout
10059 \begin_inset space \textvisiblespace{}
10067 <cell alignment="center" valignment="top" usebox="none">
10070 \begin_layout Plain Layout
10071 \begin_inset Formula $\grave{A}$
10080 <row topspace="1.5mm">
10081 <cell alignment="center" valignment="top" bottomline="true" usebox="none">
10084 \begin_layout Plain Layout
10088 \begin_inset space \textvisiblespace{}
10096 <cell alignment="center" valignment="top" bottomline="true" usebox="none">
10099 \begin_layout Plain Layout
10100 \begin_inset Formula $\breve{A}$
10114 \begin_inset space \hfill{}
10120 \begin_layout Standard
10121 \begin_inset VSpace bigskip
10127 \begin_layout Standard
10128 You can directly insert accents like é to formulas.
10130 will transform them to the corresponding accent command.
10132 \begin_inset Index idx
10135 \begin_layout Plain Layout
10141 it is better to insert a quotation mark before the vowel.
10142 These two characters are then treated by \SpecialChar LaTeX
10147 character when the formula part with the umlaut is marked as German.
10155 \begin_inset Quotes eld
10159 \begin_inset Quotes erd
10162 umlauts are created as demonstrated in the following example:
10165 \begin_layout Standard
10166 \begin_inset VSpace -2mm
10172 \begin_layout Standard
10174 \begin_inset Tabular
10175 <lyxtabular version="3" rows="3" columns="2">
10176 <features booktabs="true" tabularvalignment="middle">
10177 <column alignment="center" valignment="top" width="0pt">
10178 <column alignment="center" valignment="top">
10180 <cell alignment="center" valignment="top" topline="true" bottomline="true" usebox="none">
10183 \begin_layout Plain Layout
10189 <cell alignment="center" valignment="top" topline="true" bottomline="true" usebox="none">
10192 \begin_layout Plain Layout
10200 <cell alignment="center" valignment="top" usebox="none">
10203 \begin_layout Plain Layout
10204 \begin_inset Quotes grd
10212 <cell alignment="center" valignment="top" usebox="none">
10215 \begin_layout Plain Layout
10216 \begin_inset space \hspace{}
10223 \begin_inset Formula $"i$
10232 <row topspace="1.5mm">
10233 <cell alignment="center" valignment="top" bottomline="true" usebox="none">
10236 \begin_layout Plain Layout
10240 \begin_inset space \textvisiblespace{}
10248 <cell alignment="center" valignment="top" bottomline="true" usebox="none">
10251 \begin_layout Plain Layout
10252 \begin_inset Formula $\ddot{i}$
10268 \begin_layout Standard
10269 Another advantage to
10275 is that umlauts can directly be converted to mathematical text because
10276 the accent commands above are
10282 in mathematical text
10285 To convert an accented character to mathematical text, only the character
10286 under the accent may be converted.
10287 This applies also for all other conversions, e.
10288 \begin_inset space \thinspace{}
10292 \begin_inset space \space{}
10298 \begin_layout Standard
10299 In mathematical text, umlauts and other accented characters can directly
10303 \begin_layout Standard
10304 \begin_inset VSpace bigskip
10310 \begin_layout Standard
10312 also supports a tilde under the character if the \SpecialChar LaTeX
10318 \begin_inset Index idx
10321 \begin_layout Plain Layout
10322 Packages ! undertilde
10327 is installed on your system:
10330 \begin_layout Standard
10334 \begin_layout Plain Layout
10344 \begin_inset Note Note
10347 \begin_layout Plain Layout
10348 The following table will only be displayed when the \SpecialChar LaTeX
10361 \begin_layout Standard
10364 \begin_inset Tabular
10365 <lyxtabular version="3" rows="2" columns="2">
10366 <features booktabs="true" tabularvalignment="middle">
10367 <column alignment="center" valignment="top" width="0pt">
10368 <column alignment="center" valignment="top" width="0pt">
10370 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
10373 \begin_layout Plain Layout
10379 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
10382 \begin_layout Plain Layout
10390 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
10393 \begin_layout Plain Layout
10397 \begin_inset space \textvisiblespace{}
10405 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
10408 \begin_layout Plain Layout
10409 \begin_inset Formula $\utilde{A}$
10425 \begin_layout Standard
10429 \begin_layout Plain Layout
10439 \begin_inset Note Note
10442 \begin_layout Plain Layout
10443 The following will be displayed when the \SpecialChar LaTeX
10456 \begin_layout Standard
10457 You need to install the \SpecialChar LaTeX
10462 to see the rest of this subsection in the output.
10465 \begin_layout Standard
10469 \begin_layout Plain Layout
10481 \begin_layout Standard
10482 \begin_inset Newpage newpage
10488 \begin_layout Subsection
10489 Accents for several Characters
10490 \begin_inset Index idx
10493 \begin_layout Plain Layout
10494 Accents ! for several characters
10502 \begin_layout Standard
10503 \begin_inset space \hfill{}
10507 \begin_inset Tabular
10508 <lyxtabular version="3" rows="5" columns="2">
10509 <features booktabs="true" tabularvalignment="middle">
10510 <column alignment="center" valignment="top" width="0pt">
10511 <column alignment="center" valignment="top" width="0pt">
10513 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
10516 \begin_layout Plain Layout
10522 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
10525 \begin_layout Plain Layout
10532 <row topspace="1.5mm">
10533 <cell alignment="center" valignment="top" usebox="none">
10536 \begin_layout Plain Layout
10540 \begin_inset space \textvisiblespace{}
10548 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
10551 \begin_layout Plain Layout
10552 \begin_inset Formula $\overleftarrow{A=B}$
10561 <row topspace="1.5mm">
10562 <cell alignment="center" valignment="top" usebox="none">
10565 \begin_layout Plain Layout
10569 \begin_inset space \textvisiblespace{}
10577 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
10580 \begin_layout Plain Layout
10581 \begin_inset Formula $\underleftarrow{A=B}$
10590 <row topspace="1.5mm">
10591 <cell alignment="center" valignment="top" usebox="none">
10594 \begin_layout Plain Layout
10598 \begin_inset space \textvisiblespace{}
10606 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
10609 \begin_layout Plain Layout
10610 \begin_inset Formula $\overleftrightarrow{A=B}$
10619 <row topspace="1.5mm" bottomspace="1mm">
10620 <cell alignment="center" valignment="top" bottomline="true" usebox="none">
10623 \begin_layout Plain Layout
10626 underleftrightarrow
10627 \begin_inset space \textvisiblespace{}
10635 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
10638 \begin_layout Plain Layout
10639 \begin_inset Formula $\underleftrightarrow{A=B}$
10653 \begin_inset space \hfill{}
10657 \begin_inset Tabular
10658 <lyxtabular version="3" rows="5" columns="2">
10659 <features booktabs="true" tabularvalignment="middle">
10660 <column alignment="center" valignment="top" width="0pt">
10661 <column alignment="center" valignment="top" width="0pt">
10663 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
10666 \begin_layout Plain Layout
10672 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
10675 \begin_layout Plain Layout
10682 <row topspace="1.5mm">
10683 <cell alignment="center" valignment="top" usebox="none">
10686 \begin_layout Plain Layout
10690 \begin_inset space \textvisiblespace{}
10698 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
10701 \begin_layout Plain Layout
10702 \begin_inset Formula $\overrightarrow{A=B}$
10711 <row topspace="1.5mm">
10712 <cell alignment="center" valignment="top" usebox="none">
10715 \begin_layout Plain Layout
10719 \begin_inset space \textvisiblespace{}
10727 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
10730 \begin_layout Plain Layout
10731 \begin_inset Formula $\underrightarrow{A=B}$
10740 <row topspace="1.5mm">
10741 <cell alignment="center" valignment="top" usebox="none">
10744 \begin_layout Plain Layout
10748 \begin_inset space \textvisiblespace{}
10756 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
10759 \begin_layout Plain Layout
10760 \begin_inset Formula $\widetilde{A=B}$
10769 <row topspace="1.5mm" bottomspace="1mm">
10770 <cell alignment="center" valignment="top" bottomline="true" usebox="none">
10773 \begin_layout Plain Layout
10777 \begin_inset space \textvisiblespace{}
10785 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
10788 \begin_layout Plain Layout
10789 \begin_inset Formula $\widehat{A=B}$
10803 \begin_inset space \hfill{}
10809 \begin_layout Standard
10810 \begin_inset VSpace medskip
10813 With these commands as many characters as you like can be accented.
10826 will only be set in the output with a length of three characters, as shown
10827 in the following example:
10828 \begin_inset Formula
10830 \widetilde{A+B=C-D}
10838 \begin_layout Standard
10846 \begin_inset Index idx
10849 \begin_layout Plain Layout
10864 \begin_inset Index idx
10867 \begin_layout Plain Layout
10875 described in the previous subsection it is also possible to accent several
10882 \begin_inset space \textvisiblespace{}
10886 \begin_inset Formula $\downarrow$
10892 \begin_inset Formula
10894 \underset{***}{A=B}
10902 \begin_layout Section
10904 \begin_inset CommandInset label
10906 name "subsec:Space"
10911 \begin_inset Index idx
10914 \begin_layout Plain Layout
10923 \begin_layout Subsection
10925 \begin_inset CommandInset label
10927 name "subsec:Predefined-Space"
10932 \begin_inset Index idx
10935 \begin_layout Plain Layout
10936 Space ! horizontal ! predefined
10944 \begin_layout Standard
10945 Sometimes it is necessary to insert horizontal space into a formula.
10946 This is done by inserting a protected space (shortcut
10949 arg "command-alternatives space-insert protected ; math-space"
10954 \begin_inset Quotes eld
10960 \begin_inset space \textvisiblespace{}
10966 \begin_inset Quotes erd
10969 appears and by pressing
10973 several times one can select one of eight different space sizes.
10974 The spaces can also be inserted using the math toolbar button
10977 arg "math-insert \\space"
10980 or special commands.
10981 Independent from the inserted command, one can select the size again by
10989 \begin_layout Standard
10992 \begin_inset Tabular
10993 <lyxtabular version="3" rows="6" columns="3">
10994 <features booktabs="true" tabularvalignment="middle">
10995 <column alignment="center" valignment="top">
10996 <column alignment="center" valignment="top" width="15col%">
10997 <column alignment="center" valignment="top">
10999 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
11002 \begin_layout Plain Layout
11008 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
11011 \begin_layout Plain Layout
11021 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
11024 \begin_layout Plain Layout
11032 <cell alignment="center" valignment="top" leftline="true" usebox="none">
11035 \begin_layout Plain Layout
11043 <cell alignment="center" valignment="top" leftline="true" usebox="none">
11046 \begin_layout Plain Layout
11052 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
11055 \begin_layout Plain Layout
11056 \begin_inset Formula $A\,B$
11066 <cell alignment="center" valignment="top" leftline="true" usebox="none">
11069 \begin_layout Plain Layout
11077 <cell alignment="center" valignment="top" leftline="true" usebox="none">
11080 \begin_layout Plain Layout
11086 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
11089 \begin_layout Plain Layout
11090 \begin_inset Formula $A\:B$
11100 <cell alignment="center" valignment="top" leftline="true" usebox="none">
11103 \begin_layout Plain Layout
11111 <cell alignment="center" valignment="top" leftline="true" usebox="none">
11114 \begin_layout Plain Layout
11120 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
11123 \begin_layout Plain Layout
11124 \begin_inset Formula $A\;B$
11134 <cell alignment="center" valignment="top" leftline="true" usebox="none">
11137 \begin_layout Plain Layout
11145 <cell alignment="center" valignment="top" leftline="true" usebox="none">
11148 \begin_layout Plain Layout
11154 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
11157 \begin_layout Plain Layout
11158 \begin_inset Formula $A\quad B$
11168 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
11171 \begin_layout Plain Layout
11179 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
11182 \begin_layout Plain Layout
11188 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
11191 \begin_layout Plain Layout
11192 \begin_inset Formula $A\qquad B$
11206 \begin_inset space \hfill{}
11210 \begin_inset Tabular
11211 <lyxtabular version="3" rows="6" columns="3">
11212 <features booktabs="true" tabularvalignment="middle">
11213 <column alignment="center" valignment="top">
11214 <column alignment="center" valignment="top" width="15col%">
11215 <column alignment="center" valignment="top">
11217 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
11220 \begin_layout Plain Layout
11226 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
11229 \begin_layout Plain Layout
11239 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
11242 \begin_layout Plain Layout
11250 <cell alignment="center" valignment="top" leftline="true" usebox="none">
11253 \begin_layout Plain Layout
11261 <cell alignment="center" valignment="top" leftline="true" usebox="none">
11264 \begin_layout Plain Layout
11270 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
11273 \begin_layout Plain Layout
11274 \begin_inset Formula $A\hfill B$
11284 <cell alignment="center" valignment="top" leftline="true" usebox="none">
11287 \begin_layout Plain Layout
11295 <cell alignment="center" valignment="top" leftline="true" usebox="none">
11298 \begin_layout Plain Layout
11304 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
11307 \begin_layout Plain Layout
11308 \begin_inset Formula $A\hspace*{1em}B$
11318 <cell alignment="center" valignment="top" leftline="true" usebox="none">
11321 \begin_layout Plain Layout
11329 <cell alignment="center" valignment="top" leftline="true" usebox="none">
11332 \begin_layout Plain Layout
11338 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
11341 \begin_layout Plain Layout
11342 \begin_inset Formula $A\hspace{1em}B$
11352 <cell alignment="center" valignment="top" leftline="true" usebox="none">
11355 \begin_layout Plain Layout
11359 \begin_inset space \textvisiblespace{}
11367 <cell alignment="center" valignment="top" leftline="true" usebox="none">
11370 \begin_layout Plain Layout
11376 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
11379 \begin_layout Plain Layout
11380 \begin_inset Formula $A\ B$
11390 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
11393 \begin_layout Plain Layout
11401 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
11404 \begin_layout Plain Layout
11410 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
11413 \begin_layout Plain Layout
11414 \begin_inset Formula $A\!B$
11430 \begin_layout Standard
11432 \begin_inset space ~
11436 \begin_inset space \thinspace{}
11440 \begin_inset space \thinspace{}
11443 7 are variable spaces which are explained in
11444 \begin_inset CommandInset ref
11446 reference "subsec:Variable-Space"
11452 \begin_inset space ~
11455 9 seems to produce no space.
11456 It is displayed red in \SpecialChar LyX
11457 contrary to the other sizes, because it is a negative
11459 There are two more negative spaces:
11462 \begin_layout Standard
11464 \begin_inset Tabular
11465 <lyxtabular version="3" rows="3" columns="3">
11466 <features booktabs="true" tabularvalignment="middle">
11467 <column alignment="center" valignment="middle" width="6.8cm">
11468 <column alignment="center" valignment="top" width="0pt">
11469 <column alignment="center" valignment="top" width="0pt">
11471 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
11474 \begin_layout Plain Layout
11480 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
11483 \begin_layout Plain Layout
11491 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
11494 \begin_layout Plain Layout
11504 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
11507 \begin_layout Plain Layout
11512 keystrokes after inserting the protected space
11517 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
11520 \begin_layout Plain Layout
11526 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
11529 \begin_layout Plain Layout
11537 <cell multicolumn="1" alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
11540 \begin_layout Plain Layout
11546 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
11549 \begin_layout Plain Layout
11550 \begin_inset Formula $A\negmedspace B$
11558 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
11561 \begin_layout Plain Layout
11562 \begin_inset Formula $A\negthickspace B$
11578 \begin_layout Standard
11579 Negative spaces can lead to characters overlapping each other.
11580 Thus they can be used to enforce ligatures, which are e.
11581 \begin_inset space \thinspace{}
11585 \begin_inset space \space{}
11588 useful for summation operators:
11591 \begin_layout Standard
11593 \begin_inset Tabular
11594 <lyxtabular version="3" rows="3" columns="2">
11595 <features booktabs="true" tabularvalignment="middle">
11596 <column alignment="center" valignment="top" width="0pt">
11597 <column alignment="center" valignment="top">
11599 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
11602 \begin_layout Plain Layout
11608 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
11611 \begin_layout Plain Layout
11619 <cell alignment="center" valignment="top" leftline="true" usebox="none">
11622 \begin_layout Plain Layout
11628 \begin_inset space \textvisiblespace{}
11636 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
11639 \begin_layout Plain Layout
11640 \begin_inset Formula $\sum\sum f_{kl}$
11650 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
11653 \begin_layout Plain Layout
11661 \begin_inset space \textvisiblespace{}
11669 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
11672 \begin_layout Plain Layout
11673 \begin_inset Formula $\sum\negmedspace\sum f_{kl}$
11689 \begin_layout Standard
11691 \begin_inset VSpace medskip
11697 \begin_layout Standard
11699 Relations like for example equal signs, are always surrounded by space.
11700 To suppress this, the equal sign is placed into a \SpecialChar TeX
11702 The following example demonstrates this:
11705 \begin_layout Standard
11707 \begin_inset Tabular
11708 <lyxtabular version="3" rows="2" columns="2">
11709 <features tabularvalignment="middle">
11710 <column alignment="center" valignment="top" width="0pt">
11711 <column alignment="center" valignment="top" width="0pt">
11713 <cell alignment="center" valignment="top" usebox="none">
11716 \begin_layout Plain Layout
11722 <cell alignment="center" valignment="top" usebox="none">
11725 \begin_layout Plain Layout
11726 \begin_inset Formula $A=B$
11736 <cell alignment="center" valignment="top" usebox="none">
11739 \begin_layout Plain Layout
11740 equation without space
11745 <cell multicolumn="1" alignment="center" valignment="top" usebox="none">
11748 \begin_layout Plain Layout
11749 \begin_inset Formula $A{=}B$
11765 \begin_layout Standard
11767 The command for the last formula is:
11772 \begin_inset Formula $\to$
11778 \begin_layout Standard
11779 \begin_inset VSpace bigskip
11785 \begin_layout Standard
11786 Spaces are needed for physical units, because the space between the value
11787 and the unit is the smallest one and not a normal space.
11788 For units in text, the smallest space is inserted via the menu
11790 Insert\SpecialChar menuseparator
11791 Formatting\SpecialChar menuseparator
11793 \begin_inset space ~
11801 arg "space-insert thin"
11807 \begin_layout Standard
11808 An example to visualize the difference:
11811 \begin_layout Standard
11812 \begin_inset Tabular
11813 <lyxtabular version="3" rows="2" columns="2">
11814 <features tabularvalignment="middle">
11815 <column alignment="left" valignment="top">
11816 <column alignment="left" valignment="top">
11818 <cell alignment="center" valignment="top" usebox="none">
11821 \begin_layout Plain Layout
11823 \begin_inset Formula $\cdot$
11831 <cell alignment="center" valignment="top" usebox="none">
11834 \begin_layout Plain Layout
11835 space between value and unit
11842 <cell alignment="center" valignment="top" usebox="none">
11845 \begin_layout Plain Layout
11847 \begin_inset space \thinspace{}
11851 \begin_inset Formula $\cdot$
11859 <cell alignment="center" valignment="top" usebox="none">
11862 \begin_layout Plain Layout
11863 smallest space between value and unit
11876 \begin_layout Subsection
11881 \begin_layout Plain Layout
11894 \begin_layout Plain Layout
11895 for vertical space in formulas see
11896 \begin_inset CommandInset ref
11898 reference "subsec:Line-Separation"
11911 \begin_layout Plain Layout
11919 \begin_inset Note Note
11922 \begin_layout Plain Layout
11925 texorpdfstring is used to avoid that the footnote appears in the PDF-bookmark.
11928 \begin_layout Plain Layout
11931 texorpdfstring is in section
11932 \begin_inset CommandInset ref
11934 reference "subsec:Formulas-in-Section"
11944 \begin_inset CommandInset label
11946 name "subsec:Variable-Space"
11951 \begin_inset Index idx
11954 \begin_layout Plain Layout
11955 Space ! horizontal ! variable
11963 \begin_layout Standard
11964 Space with a defined length can be inserted with the command
11971 \begin_inset Index idx
11974 \begin_layout Plain Layout
11984 \begin_inset Quotes eld
11990 \begin_inset space \textvisiblespace{}
11996 \begin_inset Quotes erd
12000 The length can be specified by left-clicking on the
12001 \begin_inset Quotes eld
12007 \begin_inset space \textvisiblespace{}
12013 \begin_inset Quotes erd
12017 The length may also be negative.
12018 When a space would be the first character in a line it would be omitted.
12019 To force its output use the command
12031 or left-click on the
12032 \begin_inset Quotes eld
12038 \begin_inset space \textvisiblespace{}
12044 \begin_inset Quotes erd
12047 and check the option
12052 \begin_inset Newline newline
12055 To insert as much space as is available, the command
12062 \begin_inset Index idx
12065 \begin_layout Plain Layout
12076 \begin_layout Standard
12078 \begin_inset Tabular
12079 <lyxtabular version="3" rows="4" columns="2">
12080 <features booktabs="true" tabularvalignment="middle">
12081 <column alignment="center" valignment="top" width="0pt">
12082 <column alignment="center" valignment="top">
12084 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
12087 \begin_layout Plain Layout
12095 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
12098 \begin_layout Plain Layout
12106 <cell alignment="center" valignment="top" leftline="true" usebox="none">
12109 \begin_layout Plain Layout
12113 \begin_inset space \textvisiblespace{}
12119 \begin_inset space \thinspace{}
12127 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
12130 \begin_layout Plain Layout
12131 \begin_inset Formula $A=B\hspace{3cm}A\not=C$
12141 <cell alignment="center" valignment="top" leftline="true" usebox="none">
12144 \begin_layout Plain Layout
12148 \begin_inset space \textvisiblespace{}
12154 \begin_inset space \thinspace{}
12162 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
12165 \begin_layout Plain Layout
12166 \begin_inset Formula $A\hspace{-1mm}A\not=A$
12176 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
12179 \begin_layout Plain Layout
12183 \begin_inset space \textvisiblespace{}
12191 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
12194 \begin_layout Plain Layout
12195 \begin_inset Formula $A=A\hfill B=B$
12211 \begin_layout Standard
12212 In the last example the available space is given by the longest column entry
12214 In an inline formula the space depends on the length of the line in which
12222 Thus, when the line uses the full width, no space will be created.
12229 only has an effect on displayed formulas when the formula style
12234 (Formula styles are explained in
12235 \begin_inset CommandInset ref
12237 reference "sec:Formula-Styles"
12244 \begin_layout Standard
12251 , there are the commands
12263 that fill the space with a pattern, see
12264 \begin_inset CommandInset ref
12266 reference "subsec:Ellipses"
12273 \begin_layout Standard
12274 For text, variable space can be inserted via the menu
12276 Insert\SpecialChar menuseparator
12277 Formatting\SpecialChar menuseparator
12279 \begin_inset space ~
12287 \begin_layout Standard
12288 This is a line with
12289 \begin_inset space \hspace{}
12294 \begin_inset space \thinspace{}
12300 \begin_layout Standard
12301 This is a line with
12302 \begin_inset space \hfill{}
12308 \begin_layout Subsection
12309 Space besides inline Formulas
12310 \begin_inset Index idx
12313 \begin_layout Plain Layout
12314 Space ! besides inline formulas
12322 \begin_layout Standard
12323 The space that surrounds inline formulas can be adjusted with the length
12331 \begin_inset Index idx
12334 \begin_layout Plain Layout
12343 The value of a length is set with the command
12350 \begin_inset Index idx
12353 \begin_layout Plain Layout
12361 which has the following scheme:
12364 \begin_layout Standard
12369 setlength{length name}{value}
12372 \begin_layout Standard
12380 \begin_inset space \thinspace{}
12386 \begin_layout Standard
12396 \begin_layout Standard
12397 is inserted in \SpecialChar TeX
12400 \begin_inset space \thinspace{}
12403 mm space will now be set around all inline formulas:
12407 \begin_layout Plain Layout
12421 \begin_layout Standard
12422 This is a line with an inline formula
12423 \begin_inset Formula $A=B$
12427 \begin_inset space \thinspace{}
12430 mm surrounding space.
12434 \begin_layout Plain Layout
12448 \begin_layout Standard
12449 To return to the predefined value,
12455 is set to the value 0
12456 \begin_inset space \thinspace{}
12462 \begin_layout Standard
12463 \begin_inset Newpage newpage
12469 \begin_layout Section
12471 \begin_inset Index idx
12474 \begin_layout Plain Layout
12481 \begin_inset Index idx
12484 \begin_layout Plain Layout
12489 \begin_layout Plain Layout
12500 \begin_layout Plain Layout
12515 \begin_layout Standard
12516 Boxes for text are described in chapter
12523 \begin_inset space ~
12531 \begin_layout Subsection
12533 \begin_inset CommandInset label
12535 name "subsec:Boxes-with-Frame"
12540 \begin_inset Index idx
12543 \begin_layout Plain Layout
12552 \begin_layout Standard
12553 It is possible to frame a formula or part of one with the commands
12560 \begin_inset Index idx
12563 \begin_layout Plain Layout
12578 \begin_inset Index idx
12581 \begin_layout Plain Layout
12592 \begin_layout Standard
12593 When one of these commands is inserted in a formula, a blue box appears
12594 within a frame to enter formula parts.
12601 an additional formula has to be created by
12605 within this box, because the box content will otherwise be treated as mathemati
12613 is used, a new formula is automatically created inside the frame.
12616 \begin_layout Standard
12623 is not suitable to frame displayed formulas because the formula will always
12624 be set in the size of the text.
12631 is in contrary not suitable to frame inline formulas, because the formula
12632 will always be set in the size of a displayed formula.
12635 \begin_layout Standard
12649 \begin_inset Index idx
12652 \begin_layout Plain Layout
12660 where additionally the frame width and the alignment can be specified.
12667 is used in the following scheme:
12670 \begin_layout Standard
12675 framebox[frame width][position]{box content}
12678 \begin_layout Standard
12679 The position can either be
12696 right aligns the formula in the box.
12697 When no position is given, the formula will be centered.
12698 \begin_inset Newline newline
12701 If no width is given, also no position can be given.
12702 In this case the frame width is adjusted to the box content like for
12711 \begin_layout Standard
12718 is inserted, a box appears containing three blue boxes.
12719 The first two boxes are surrounded by brackets and denote the two optional
12721 The third box is for formula parts like for
12730 \begin_layout Standard
12732 \begin_inset Tabular
12733 <lyxtabular version="3" rows="5" columns="2">
12734 <features booktabs="true" tabularvalignment="middle">
12735 <column alignment="center" valignment="top" width="0pt">
12736 <column alignment="center" valignment="top">
12738 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
12741 \begin_layout Plain Layout
12747 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
12750 \begin_layout Plain Layout
12757 <row topspace="1.5mm">
12758 <cell alignment="center" valignment="top" usebox="none">
12761 \begin_layout Plain Layout
12765 \begin_inset space \textvisiblespace{}
12775 \begin_inset space \textvisiblespace{}
12783 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
12786 \begin_layout Plain Layout
12787 \begin_inset Formula $\fbox{\ensuremath{\int A=B}}$
12796 <row topspace="1.5mm">
12797 <cell alignment="center" valignment="top" usebox="none">
12800 \begin_layout Plain Layout
12804 \begin_inset space \textvisiblespace{}
12810 \begin_inset space \textvisiblespace{}
12818 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
12821 \begin_layout Plain Layout
12822 \begin_inset Formula $\boxed{\int A=B}$
12831 <row topspace="1.5mm">
12832 <cell alignment="center" valignment="top" usebox="none">
12835 \begin_layout Plain Layout
12839 \begin_inset space \textvisiblespace{}
12847 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
12850 \begin_layout Plain Layout
12851 \begin_inset Formula $A+\fbox{B}$
12860 <row topspace="1.5mm" bottomspace="1mm">
12861 <cell alignment="center" valignment="top" bottomline="true" usebox="none">
12864 \begin_layout Plain Layout
12868 \begin_inset space \textvisiblespace{}
12872 \begin_inset Formula $\to$
12876 \begin_inset Formula $\to$
12886 \begin_inset space \textvisiblespace{}
12890 \begin_inset Formula $\downarrow$
12898 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
12901 \begin_layout Plain Layout
12902 \begin_inset Formula $\framebox[20mm][]{\ensuremath{\frac{A}{B}}}$
12918 \begin_layout Standard
12919 The frame thickness can also be adjusted.
12920 To do this the following commands have to be inserted in \SpecialChar TeX
12925 \begin_layout Standard
12935 \begin_inset Quotes eld
12939 \begin_inset Quotes erd
12953 \begin_inset Quotes eld
12957 \begin_inset Quotes erd
12963 \begin_layout Standard
12964 \begin_inset Quotes eld
12968 \begin_inset Quotes erd
12971 specifies the minimal distance between the frame and the first character
12973 An example for this is the following framed formula:
12977 \begin_layout Plain Layout
12989 \begin_inset Formula
12996 Before this formula the commands
12999 \begin_layout Standard
13021 \begin_layout Standard
13022 were inserted in \SpecialChar TeX
13024 The given values are used for all following boxes.
13027 \begin_layout Standard
13028 To return to the standard frame size, the command
13031 \begin_layout Standard
13056 \begin_layout Plain Layout
13070 \begin_layout Standard
13071 is inserted in \SpecialChar TeX
13072 mode before the next formula.
13075 \begin_layout Subsection
13076 Boxes without Frame
13077 \begin_inset CommandInset label
13079 name "subsec:Boxes-without-Frame"
13084 \begin_inset Index idx
13087 \begin_layout Plain Layout
13088 Boxes ! without frame
13096 \begin_layout Standard
13097 For boxes without a frame there are the following box commands:
13104 \begin_inset Index idx
13107 \begin_layout Plain Layout
13122 \begin_inset Index idx
13125 \begin_layout Plain Layout
13140 \begin_inset Index idx
13143 \begin_layout Plain Layout
13154 \begin_layout Standard
13161 a box can be super- or subscripted.
13162 But in contrary to normal super- and subscripting, the characters in the
13163 box keep their font size.
13170 is used in the following scheme:
13173 \begin_layout Standard
13178 raisebox{height}{box content}
13181 \begin_layout Standard
13182 When the box should contain a formula, an extra formula is needed like for
13193 \begin_inset Note Greyedout
13196 \begin_layout Plain Layout
13207 this extra formula is created by pressing
13211 twice instead of once because \SpecialChar LyX
13212 doesn't yet support
13226 \begin_layout Standard
13228 \begin_inset Tabular
13229 <lyxtabular version="3" rows="4" columns="2">
13230 <features booktabs="true" tabularvalignment="middle">
13231 <column alignment="center" valignment="top" width="0pt">
13232 <column alignment="center" valignment="top">
13234 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
13237 \begin_layout Plain Layout
13243 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
13246 \begin_layout Plain Layout
13254 <cell alignment="center" valignment="top" leftline="true" usebox="none">
13257 \begin_layout Plain Layout
13261 \begin_inset Formula $\to$
13267 \begin_inset Formula $\to$
13275 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
13278 \begin_layout Plain Layout
13279 \begin_inset Formula $H\raisebox{2mm}{al}lo$
13289 <cell alignment="center" valignment="top" leftline="true" usebox="none">
13292 \begin_layout Plain Layout
13296 \begin_inset Formula $\to$
13302 \begin_inset Formula $\to$
13310 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
13313 \begin_layout Plain Layout
13314 \begin_inset Formula $H\raisebox{-2mm}{al}lo$
13324 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
13327 \begin_layout Plain Layout
13331 \begin_inset Formula $\to$
13347 \begin_inset space \textvisiblespace{}
13355 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
13358 \begin_layout Plain Layout
13359 \begin_inset Formula $A=\raisebox{-2mm}{\mbox{\ensuremath{\sqrt{B}}}}$
13375 \begin_layout Standard
13400 , with the difference that there is no frame.
13403 \begin_layout Subsection
13405 \begin_inset CommandInset label
13407 name "subsec:Colored-Boxes"
13412 \begin_inset Index idx
13415 \begin_layout Plain Layout
13424 \begin_layout Standard
13425 To be able to use all commands explained in this section, the \SpecialChar LaTeX
13434 \begin_layout Plain Layout
13435 The \SpecialChar LaTeX
13440 is part of every \SpecialChar LaTeX
13441 standard installation.
13447 \begin_inset Index idx
13450 \begin_layout Plain Layout
13456 has to be loaded in the \SpecialChar LaTeX
13457 -preamble with the line
13461 \begin_layout Plain Layout
13462 When text is colored somewhere in the document with a predefined color,
13464 loads the \SpecialChar LaTeX
13470 Thus it is possible that the package is loaded twice, but this does not
13477 \begin_inset Note Note
13480 \begin_layout Plain Layout
13481 To avoid that the package is loaded twice, a macro was inserted to the \SpecialChar LaTeX
13490 \begin_layout Standard
13498 \begin_layout Standard
13499 \begin_inset VSpace medskip
13502 To color boxes, the command
13509 \begin_inset Index idx
13512 \begin_layout Plain Layout
13520 is used in the following scheme:
13523 \begin_layout Standard
13528 colorbox{color}{box content}
13531 \begin_layout Standard
13532 The box content can also be a box and a
13538 can also be part of another box (see the 2nd and 3rd example).
13539 When the box should contain a formula, an extra formula has to be created,
13540 the same way as for
13550 \begin_layout Plain Layout
13551 This also applies for the command
13565 \begin_layout Standard
13566 One of the following predefined colors can be chosen:
13569 \begin_layout Standard
13603 \begin_layout Standard
13605 \begin_inset Tabular
13606 <lyxtabular version="3" rows="4" columns="2">
13607 <features booktabs="true" tabularvalignment="middle">
13608 <column alignment="center" valignment="top" width="0pt">
13609 <column alignment="center" valignment="top">
13611 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
13614 \begin_layout Plain Layout
13620 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
13623 \begin_layout Plain Layout
13631 <cell alignment="center" valignment="top" leftline="true" usebox="none">
13634 \begin_layout Plain Layout
13638 \begin_inset Formula $\to$
13648 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
13651 \begin_layout Plain Layout
13652 \begin_inset Formula $\colorbox{yellow}{A=B}$
13661 <row topspace="1.5mm">
13662 <cell alignment="center" valignment="top" usebox="none">
13665 \begin_layout Plain Layout
13669 \begin_inset Formula $\to$
13677 \begin_inset space \textvisiblespace{}
13685 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
13688 \begin_layout Plain Layout
13689 \begin_inset Formula $\colorbox{green}{\fbox{A=B}}$
13698 <row topspace="1.5mm" bottomspace="1mm">
13699 <cell alignment="center" valignment="top" bottomline="true" usebox="none">
13702 \begin_layout Plain Layout
13706 \begin_inset space \textvisiblespace{}
13712 \begin_inset Formula $\to$
13728 \begin_inset space \textvisiblespace{}
13736 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
13739 \begin_layout Plain Layout
13740 \begin_inset Formula $\fbox{\colorbox{green}{\mbox{\ensuremath{\int C=D}}}}$
13756 \begin_layout Standard
13763 only colors the box but not the characters in the box.
13764 To color all characters, the whole formula is highlighted and the desired
13765 color is chosen in the
13768 \begin_inset space ~
13774 The dialog can be called with the toolbar button
13777 arg "dialog-show character"
13782 Edit\SpecialChar menuseparator
13784 \begin_inset space ~
13787 Style\SpecialChar menuseparator
13791 The formula number then has the same color as the formula.
13792 When the formula number should get another color than the formula characters,
13793 the color must be changed within the formula.
13796 \begin_layout Standard
13800 \begin_layout Standard
13803 \begin_inset Formula
13805 \int A=B\label{eq:red}
13813 \begin_inset Formula
13815 \textcolor{red}{\int A=B}\label{eq:redgreen}
13823 \begin_layout Standard
13825 \begin_inset CommandInset ref
13831 is completely colored red.
13832 \begin_inset Newline newline
13836 \begin_inset CommandInset ref
13838 reference "eq:redgreen"
13842 was first completely colored green to set the color for the formula number.
13843 Subsequently the formula characters were colored red.
13846 \begin_layout Standard
13847 \begin_inset VSpace bigskip
13850 To color the frame different than the rest of the box, the command
13857 \begin_inset Index idx
13860 \begin_layout Plain Layout
13868 is used in the following scheme:
13871 \begin_layout Standard
13876 fcolorbox{frame color}{color}{box content}
13879 \begin_layout Standard
13886 is an extension of the command
13893 The frame width is set, like for
13916 \begin_layout Plain Layout
13928 \begin_inset Formula
13930 \fcolorbox{cyan}{magenta}{A=B}
13939 \begin_layout Plain Layout
13953 \begin_layout Standard
13954 This formula was created with the command
13955 \begin_inset Newline newline
13963 \begin_inset Formula $\to$
13969 \begin_inset Formula $\to$
13979 \begin_layout Standard
13980 \begin_inset VSpace bigskip
13983 To use other colors than the predefined ones, they have to be defined first.
13986 \begin_layout Standard
13987 One can for example define the color
13988 \begin_inset Quotes eld
13996 \begin_inset Quotes erd
13999 with the \SpecialChar LaTeX
14003 \begin_layout Standard
14008 definecolor{darkgreen}{cmyk}{0.5,
14023 \begin_inset Index idx
14026 \begin_layout Plain Layout
14037 \begin_layout Standard
14042 is the color space that denotes the colors
14059 The four comma separated numbers are the portion factor for the corresponding
14060 colors of the color space.
14061 The factors can be in the range of 0
14062 \begin_inset space \thinspace{}
14066 \begin_inset space \thinspace{}
14074 also the color space
14078 can be used for definitions.
14095 , so that there are in this case three portion factors for the corresponding
14097 Furthermore there is the color space
14101 with one portion factor for the gray value.
14104 \begin_layout Standard
14105 As example a framed box with the new defined color
14109 where the characters have been colored
14114 \begin_inset Formula
14116 \colorbox{darkgreen}{\color{yellow}\boxed{\int A\,\mathrm{d}x=\frac{\sqrt[5]{B}}{\ln\left(\frac{1}{3}\right)}}}
14124 \begin_layout Standard
14125 Self-defined colors can also be used for text with the help of the command
14133 \begin_inset Index idx
14136 \begin_layout Plain Layout
14145 \begin_layout Standard
14149 \begin_layout Plain Layout
14153 textcolor{darkgreen}{
14159 \begin_inset Quotes eld
14163 \begin_inset Quotes erd
14170 \begin_layout Plain Layout
14180 \begin_layout Standard
14188 \begin_inset Index idx
14191 \begin_layout Plain Layout
14199 is used in the scheme
14203 textcolor{color}{characters to color}
14208 \begin_layout Subsection
14210 \begin_inset CommandInset label
14212 name "subsec:Paragraph-Boxes"
14217 \begin_inset Index idx
14220 \begin_layout Plain Layout
14221 Boxes ! as paragraph
14229 \begin_layout Standard
14230 A box that can contain several lines and paragraphs, a so-called paragraph
14231 box (parbox), can be created with the menu
14233 Insert\SpecialChar menuseparator
14236 or the toolbar button
14245 \begin_layout Standard
14246 The following example shows a framed parbox in a line:
14249 \begin_layout Standard
14250 \begin_inset VSpace medskip
14254 \begin_inset Box Boxed
14264 height_special "totalheight"
14269 backgroundcolor "none"
14272 \begin_layout Plain Layout
14273 This is a paragraph box.
14275 \begin_inset space \thinspace{}
14278 cm long and can also contain formulas:
14279 \begin_inset Formula $\int A\,\mathrm{d}s=C$
14290 \begin_layout Standard
14291 \begin_inset VSpace medskip
14297 \begin_layout Standard
14298 Such a box is created by right-clicking on the gray box inset.
14299 A dialog pops up showing the box properties.
14313 \begin_inset space \thinspace{}
14318 Vertical Box Alignment
14323 \begin_layout Standard
14324 \begin_inset VSpace medskip
14327 In \SpecialChar LaTeX
14328 a parbox is created with the command
14335 \begin_inset Index idx
14338 \begin_layout Plain Layout
14346 which has the following scheme:
14349 \begin_layout Standard
14354 parbox[position]{width}{box content}
14357 \begin_layout Standard
14372 \begin_inset Quotes eld
14376 \begin_inset Quotes erd
14379 means that the box is aligned within the surrounding text with its last
14386 \begin_inset Quotes eld
14390 \begin_inset Quotes erd
14393 this is done with the first line.
14394 When no position is given, the box will be vertically centered, see section
14402 \begin_inset space ~
14407 manual for examples.
14410 \begin_layout Standard
14411 \begin_inset VSpace bigskip
14414 To frame formulas completely, including the formula number, the formula
14415 must be set into a parbox.
14416 To do this, the command
14430 is inserted in \SpecialChar TeX
14431 mode before the formula.
14439 \begin_inset Index idx
14442 \begin_layout Plain Layout
14450 is hereby the line width set for the document.
14451 Because the frame is outside the parbox, 2
14452 \begin_inset space \thinspace{}
14455 times the frame separation and the frame thickness must be subtracted from
14457 To be able to multiply and subtract in arguments, the \SpecialChar LaTeX
14466 \begin_layout Plain Layout
14471 is part of every \SpecialChar LaTeX
14472 standard installation.
14478 \begin_inset Index idx
14481 \begin_layout Plain Layout
14487 must be loaded in the \SpecialChar LaTeX
14488 -preamble with the line
14491 \begin_layout Standard
14499 \begin_layout Standard
14500 Behind the formula both boxes are closed by entering
14504 in \SpecialChar TeX
14506 Here is an example:
14510 \begin_layout Plain Layout
14524 \begin_layout Standard
14528 \begin_layout Plain Layout
14546 \begin_inset Formula
14548 \int A\,\mathrm{d}x=\frac{\sqrt[5]{B}}{\ln\left(\frac{1}{3}\right)}
14557 \begin_layout Plain Layout
14568 \begin_layout Plain Layout
14582 \begin_layout Standard
14583 \begin_inset VSpace medskip
14586 As a parbox is used as the argument of
14592 , there is in this case no difference between
14607 \begin_layout Standard
14608 \begin_inset VSpace bigskip
14611 Paragraph boxes are very useful to comment formulas directly.
14618 is used in combination with the command
14632 \begin_inset CommandInset ref
14634 reference "subsec:User-defined-Numbering"
14641 \begin_layout Standard
14642 An example of a formula commented with
14651 \begin_layout Standard
14655 \begin_layout Plain Layout
14668 This is a description.
14669 It is distinctly separated from the formula and multiline.
14673 \begin_layout Plain Layout
14685 \begin_layout Standard
14686 Such a formula must be inserted completely in \SpecialChar TeX
14687 mode because \SpecialChar LyX
14689 support the command
14696 The formula is created with the following command sequence:
14699 \begin_layout Standard
14712 is inserted in \SpecialChar TeX
14717 \begin_layout Plain Layout
14718 When the formula style
14730 can also be replaced by
14737 (formula styles see
14738 \begin_inset CommandInset ref
14740 reference "sec:Formula-Styles"
14749 Then the description follows as normal text and finally
14755 is inserted in \SpecialChar TeX
14769 hereby create a displayed formula.
14772 \begin_layout Standard
14779 can be seen in this example that was
14780 \begin_inset Quotes eld
14784 \begin_inset Quotes erd
14787 using the mathematical textmode:
14788 \begin_inset Formula
14790 5x-7b=3b\textrm{This is a description. It is not separated from the formula ...}
14798 \begin_layout Section
14800 \begin_inset Index idx
14803 \begin_layout Plain Layout
14812 \begin_layout Subsection
14814 \begin_inset CommandInset label
14816 name "subsec:Big-Operators"
14821 \begin_inset Index idx
14824 \begin_layout Plain Layout
14831 \begin_inset Index idx
14834 \begin_layout Plain Layout
14841 \begin_inset Index idx
14844 \begin_layout Plain Layout
14853 \begin_layout Standard
14854 To be able to use all integral operators listed here, the option
14856 Use esint package automatically
14858 must be set in the document settings under
14861 \begin_inset space ~
14869 \begin_layout Standard
14870 \begin_inset space \hfill{}
14874 \begin_inset Tabular
14875 <lyxtabular version="3" rows="11" columns="2">
14876 <features booktabs="true" tabularvalignment="middle">
14877 <column alignment="center" valignment="top" width="0pt">
14878 <column alignment="center" valignment="top" width="0pt">
14880 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
14883 \begin_layout Plain Layout
14889 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
14892 \begin_layout Plain Layout
14900 <cell alignment="center" valignment="top" leftline="true" usebox="none">
14903 \begin_layout Plain Layout
14907 \begin_inset Index idx
14910 \begin_layout Plain Layout
14923 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
14926 \begin_layout Plain Layout
14927 \begin_inset Formula $\int$
14937 <cell alignment="center" valignment="top" leftline="true" usebox="none">
14940 \begin_layout Plain Layout
14948 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
14951 \begin_layout Plain Layout
14952 \begin_inset Formula $\oint$
14962 <cell alignment="center" valignment="top" leftline="true" usebox="none">
14965 \begin_layout Plain Layout
14973 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
14976 \begin_layout Plain Layout
14977 \begin_inset Formula $\ointctrclockwise$
14987 <cell alignment="center" valignment="top" leftline="true" usebox="none">
14990 \begin_layout Plain Layout
14998 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
15001 \begin_layout Plain Layout
15002 \begin_inset Formula $\ointclockwise$
15012 <cell alignment="center" valignment="top" leftline="true" usebox="none">
15015 \begin_layout Plain Layout
15023 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
15026 \begin_layout Plain Layout
15027 \begin_inset Formula $\sqint$
15037 <cell alignment="center" valignment="top" leftline="true" usebox="none">
15040 \begin_layout Plain Layout
15048 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
15051 \begin_layout Plain Layout
15053 \begin_inset Formula $\fint$
15063 <cell alignment="center" valignment="top" leftline="true" usebox="none">
15066 \begin_layout Plain Layout
15074 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
15077 \begin_layout Plain Layout
15079 \begin_inset Formula $\landupint$
15089 <cell alignment="center" valignment="top" leftline="true" usebox="none">
15092 \begin_layout Plain Layout
15100 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
15103 \begin_layout Plain Layout
15105 \begin_inset Formula $\landdownint$
15115 <cell alignment="center" valignment="top" leftline="true" usebox="none">
15118 \begin_layout Plain Layout
15126 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
15129 \begin_layout Plain Layout
15130 \begin_inset Formula $\bigcap$
15140 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
15143 \begin_layout Plain Layout
15151 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
15154 \begin_layout Plain Layout
15155 \begin_inset Formula $\bigcup$
15169 \begin_inset space \hfill{}
15173 \begin_inset Tabular
15174 <lyxtabular version="3" rows="11" columns="2">
15175 <features booktabs="true" tabularvalignment="middle">
15176 <column alignment="center" valignment="top" width="0pt">
15177 <column alignment="center" valignment="top" width="0pt">
15179 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
15182 \begin_layout Plain Layout
15188 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
15191 \begin_layout Plain Layout
15199 <cell alignment="center" valignment="top" leftline="true" usebox="none">
15202 \begin_layout Plain Layout
15206 \begin_inset Index idx
15209 \begin_layout Plain Layout
15222 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
15225 \begin_layout Plain Layout
15226 \begin_inset Formula $\sum$
15236 <cell alignment="center" valignment="top" leftline="true" usebox="none">
15239 \begin_layout Plain Layout
15243 \begin_inset Index idx
15246 \begin_layout Plain Layout
15253 \begin_layout Plain Layout
15272 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
15275 \begin_layout Plain Layout
15276 \begin_inset Formula $\prod$
15286 <cell alignment="center" valignment="top" leftline="true" usebox="none">
15289 \begin_layout Plain Layout
15297 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
15300 \begin_layout Plain Layout
15301 \begin_inset Formula $\coprod$
15311 <cell alignment="center" valignment="top" leftline="true" usebox="none">
15314 \begin_layout Plain Layout
15322 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
15325 \begin_layout Plain Layout
15326 \begin_inset Formula $\bigodot$
15336 <cell alignment="center" valignment="top" leftline="true" usebox="none">
15339 \begin_layout Plain Layout
15347 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
15350 \begin_layout Plain Layout
15351 \begin_inset Formula $\bigotimes$
15361 <cell alignment="center" valignment="top" leftline="true" usebox="none">
15364 \begin_layout Plain Layout
15372 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
15375 \begin_layout Plain Layout
15376 \begin_inset Formula $\bigoplus$
15386 <cell alignment="center" valignment="top" leftline="true" usebox="none">
15389 \begin_layout Plain Layout
15397 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
15400 \begin_layout Plain Layout
15401 \begin_inset Formula $\bigwedge$
15411 <cell alignment="center" valignment="top" leftline="true" usebox="none">
15414 \begin_layout Plain Layout
15422 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
15425 \begin_layout Plain Layout
15426 \begin_inset Formula $\bigvee$
15436 <cell alignment="center" valignment="top" leftline="true" usebox="none">
15439 \begin_layout Plain Layout
15447 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
15450 \begin_layout Plain Layout
15451 \begin_inset Formula $\bigsqcup$
15461 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
15464 \begin_layout Plain Layout
15472 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
15475 \begin_layout Plain Layout
15476 \begin_inset Formula $\biguplus$
15490 \begin_inset space \hfill{}
15496 \begin_layout Standard
15497 All big operators can also be inserted via the math toolbar button
15500 arg "math-insert \\intop"
15506 \begin_layout Standard
15507 The operators are called big because they are bigger than the sometimes
15508 equal looking binary operators.
15509 All big operators can have limits as described in the next subsection.
15512 \begin_layout Standard
15513 For all integral operators there is a second version available, ending in
15531 These operators are different from
15538 \begin_inset space \space{}
15541 in the style the operator limits are displayed, see
15542 \begin_inset CommandInset ref
15544 reference "subsec:Operator-Limits"
15552 \begin_layout Subsubsection*
15553 Advice for Integrals
15556 \begin_layout Standard
15561 in an integral is an operator, that therefore has to be set upright.
15562 This is done by highlighting the
15566 and using the keyboard shortcut
15576 \begin_layout Plain Layout
15582 \begin_inset CommandInset ref
15584 reference "subsec:Font-Styles"
15594 Finally the smallest space is inserted before the
15598 , as this is usual for operators.
15602 \begin_layout Standard
15604 \begin_inset Formula $\int A(x)dx$
15608 \begin_inset Newline newline
15612 \begin_inset Phantom HPhantom
15615 \begin_layout Plain Layout
15622 \begin_inset Formula $\int A(x)\,\mathrm{d}x$
15628 \begin_layout Standard
15629 For multiple integrals there are the following commands:
15630 \begin_inset VSpace medskip
15636 \begin_layout Standard
15637 \begin_inset space \hfill{}
15641 \begin_inset Tabular
15642 <lyxtabular version="3" rows="4" columns="2">
15643 <features booktabs="true" tabularvalignment="middle">
15644 <column alignment="center" valignment="top" width="0pt">
15645 <column alignment="center" valignment="top" width="0pt">
15647 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
15650 \begin_layout Plain Layout
15656 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
15659 \begin_layout Plain Layout
15666 <row bottomspace="1mm">
15667 <cell alignment="center" valignment="top" usebox="none">
15670 \begin_layout Plain Layout
15678 <cell alignment="center" valignment="top" usebox="none">
15681 \begin_layout Plain Layout
15682 \begin_inset Formula $\iint$
15691 <row bottomspace="1mm">
15692 <cell alignment="center" valignment="top" usebox="none">
15695 \begin_layout Plain Layout
15703 <cell alignment="center" valignment="top" usebox="none">
15706 \begin_layout Plain Layout
15707 \begin_inset Formula $\oiint$
15716 <row bottomspace="1mm">
15717 <cell alignment="center" valignment="top" bottomline="true" usebox="none">
15720 \begin_layout Plain Layout
15728 <cell alignment="center" valignment="top" bottomline="true" usebox="none">
15731 \begin_layout Plain Layout
15732 \begin_inset Formula $\sqiint$
15746 \begin_inset space \hfill{}
15750 \begin_inset Tabular
15751 <lyxtabular version="3" rows="4" columns="2">
15752 <features booktabs="true" tabularvalignment="middle">
15753 <column alignment="center" valignment="top" width="0pt">
15754 <column alignment="center" valignment="top" width="0pt">
15756 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
15759 \begin_layout Plain Layout
15765 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
15768 \begin_layout Plain Layout
15775 <row bottomspace="1mm">
15776 <cell alignment="center" valignment="top" usebox="none">
15779 \begin_layout Plain Layout
15787 <cell alignment="center" valignment="top" usebox="none">
15790 \begin_layout Plain Layout
15791 \begin_inset Formula $\iiint$
15800 <row bottomspace="1mm">
15801 <cell alignment="center" valignment="top" usebox="none">
15804 \begin_layout Plain Layout
15812 <cell alignment="center" valignment="top" usebox="none">
15815 \begin_layout Plain Layout
15816 \begin_inset Formula $\iiiint$
15825 <row bottomspace="1mm">
15826 <cell alignment="center" valignment="top" bottomline="true" usebox="none">
15829 \begin_layout Plain Layout
15837 <cell alignment="center" valignment="top" bottomline="true" usebox="none">
15840 \begin_layout Plain Layout
15841 \begin_inset Formula $\dotsint$
15855 \begin_inset space \hfill{}
15861 \begin_layout Subsection
15863 \begin_inset CommandInset label
15865 name "subsec:Operator-Limits"
15870 \begin_inset Index idx
15873 \begin_layout Plain Layout
15882 \begin_layout Standard
15883 Limits are created by super- and subscripts:
15886 \begin_layout Standard
15888 \begin_inset Tabular
15889 <lyxtabular version="3" rows="2" columns="2">
15890 <features booktabs="true" tabularvalignment="middle">
15891 <column alignment="center" valignment="top" width="0pt">
15892 <column alignment="center" valignment="top" width="0pt">
15894 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
15897 \begin_layout Plain Layout
15903 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
15906 \begin_layout Plain Layout
15914 <cell alignment="center" valignment="top" bottomline="true" usebox="none">
15917 \begin_layout Plain Layout
15923 \begin_inset space \textvisiblespace{}
15927 \begin_inset Formula $\to$
15931 \begin_inset Formula $\to$
15939 <cell alignment="center" valignment="top" bottomline="true" usebox="none">
15942 \begin_layout Plain Layout
15943 \begin_inset Formula $\prod_{0}^{\infty}A(x)$
15959 \begin_layout Standard
15960 Limits of inline formulas are set right beside the operator.
15961 Limits in displayed formulas are set above or below the operator, except
15962 for integral limits.
15965 \begin_layout Standard
15966 To force that the limits are set beside the operator, the cursor is set
15967 directly behind the operator and the limits type is changed with the menu
15970 Edit\SpecialChar menuseparator
15971 Math\SpecialChar menuseparator
15990 \begin_layout Standard
15991 The default limits type is this:
15992 \begin_inset Formula
15994 \sum_{x=0}^{\infty}\frac{1}{x^{2}}
15999 This is how it looks when the limits type was changed to
16006 \begin_inset Formula
16008 \sum\nolimits _{x=0}^{\infty}\frac{1}{x^{2}}
16013 For integrals, except those ending with
16029 etc., the limits are by default set beside the operator.
16030 But for multiple integrals the limits are often set below the operator.
16031 In the following example the limits type was therefore set to
16035 and so set below the integrals:
16036 \begin_inset Formula
16038 \iiint\limits _{V}X\,\mathrm{d}V=U\label{eq:VolInt}
16046 \begin_layout Standard
16047 \begin_inset VSpace medskip
16050 To specify conditions for limits, the commands
16057 \begin_inset Index idx
16060 \begin_layout Plain Layout
16075 \begin_inset Index idx
16078 \begin_layout Plain Layout
16087 To create for example this expression
16088 \begin_inset Formula
16090 \sum_{\begin{subarray}{c}
16094 \end{subarray}}^{n}k^{-2}\label{eq:substack}
16102 \begin_layout Standard
16103 the following has to be done:
16104 \begin_inset Newline newline
16116 \begin_inset space \textvisiblespace{}
16122 One is now in a blue box under the summation operator and insert there
16128 \begin_inset space \textvisiblespace{}
16134 The blue box is now within a purple box and now several lines can be written
16136 A new line is created by inserting a line break (
16139 arg "newline-insert newline"
16144 \begin_inset Newline newline
16149 0<k<1000 Ctrl+Return
16150 \begin_inset Newline newline
16155 is typed in, a new box appears below for the new line.
16158 \begin_layout Standard
16159 The alignment of the lines can be changed to left aligned with the
16169 Edit\SpecialChar menuseparator
16173 To get right alignment,
16178 \begin_inset space \textvisiblespace{}
16183 is inserted at the beginning of the line.
16186 \begin_layout Standard
16199 with the difference that the lines are always centered.
16202 \begin_layout Standard
16203 \begin_inset VSpace bigskip
16207 \begin_inset CommandInset ref
16209 reference "eq:substack"
16213 there can be too much space beside an operator, because the characters
16214 following the operator are set beside the limits.
16215 To avoid this the command
16222 \begin_inset Index idx
16225 \begin_layout Plain Layout
16234 To activate it, set in the document settings under
16237 \begin_inset space ~
16247 \begin_inset Index idx
16250 \begin_layout Plain Layout
16251 Packages ! mathtools
16259 \begin_inset space ~
16271 sets the space besides the operator to 0
16272 \begin_inset space \thinspace{}
16276 \begin_inset Newline newline
16280 \begin_inset CommandInset ref
16282 reference "eq:substack"
16286 , one uses the command
16289 \begin_layout Standard
16297 \begin_layout Standard
16298 and inserts the operator with its limits into the braces.
16299 Behind the brace one continues the formula:
16300 \begin_inset Formula
16302 \smashoperator{\sum_{\begin{subarray}{c}
16306 \end{subarray}}^{n}}k^{-2}
16314 \begin_layout Standard
16315 It is possible to set the space of only one side of the operator to 0
16316 \begin_inset space \thinspace{}
16320 To do this write either
16339 stands for the left and
16343 for the right side of the operator.
16344 Here is an example of the possible
16353 \begin_layout Standard
16354 \begin_inset Formula
16356 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}
16364 \begin_layout Standard
16365 \begin_inset VSpace bigskip
16371 \begin_layout Standard
16372 When several consecutive operators have limits the typesetting of the limits
16373 looks often imperfect in the output, see this example:
16374 \begin_inset Formula
16376 \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}
16381 To improve the typesetting set in the document settings under
16384 \begin_inset space ~
16394 \begin_inset Index idx
16397 \begin_layout Plain Layout
16398 Packages ! mathtools
16406 \begin_inset space ~
16412 Then insert into your formula the command
16419 \begin_inset Index idx
16422 \begin_layout Plain Layout
16430 directly before the first operator.
16431 The example will then look like this:
16432 \begin_inset Formula
16434 \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}
16442 \begin_layout Standard
16443 \begin_inset VSpace bigskip
16446 How to use one limit for several operators is described in
16447 \begin_inset CommandInset ref
16449 reference "subsec:Self-defined-Operators"
16456 \begin_layout Subsection
16457 Decoration for Operators
16458 \begin_inset Index idx
16461 \begin_layout Plain Layout
16462 Operators ! Decoration
16470 \begin_layout Standard
16478 \begin_inset Index idx
16481 \begin_layout Plain Layout
16496 \begin_inset Index idx
16499 \begin_layout Plain Layout
16507 characters can be placed above or below an operator, respectively.
16515 \begin_inset Index idx
16518 \begin_layout Plain Layout
16526 characters can be set before and behind a big operator.
16529 \begin_layout Standard
16531 \begin_inset space ~
16543 \begin_layout Itemize
16550 is used to set characters at the corners of the operator
16553 \begin_layout Itemize
16560 is used to set characters before and/or behind the operator (this variant
16561 represents \SpecialChar LaTeX
16571 \begin_layout Itemize
16578 is used to set characters at the left corners and/or behind the operator
16581 \begin_layout Itemize
16588 is used to set characters at the right corners and/or before the operator
16591 \begin_layout Standard
16592 For example the command
16597 \begin_inset space \textvisiblespace{}
16603 \begin_inset space \textvisiblespace{}
16607 \begin_inset Formula $\to$
16611 \begin_inset Formula $\to$
16615 \begin_inset space \textvisiblespace{}
16625 \begin_inset Formula
16627 \sideset{}{'}\sum_{k=1}^{n}
16635 \begin_layout Standard
16636 \begin_inset Note Greyedout
16639 \begin_layout Plain Layout
16646 can only be used to decorate big operators, binary operators are not allowed.
16654 \begin_layout Standard
16667 can also be used to decorate symbols and characters.
16668 For example, the command
16673 \begin_inset space \textvisiblespace{}
16679 \begin_inset space \textvisiblespace{}
16685 \begin_inset Formula $\uparrow$
16693 \begin_inset Formula
16695 \overset{a}{\maltese}
16703 \begin_layout Subsection
16705 \begin_inset CommandInset label
16707 name "subsec:Binary-Operators"
16712 \begin_inset Index idx
16715 \begin_layout Plain Layout
16724 \begin_layout Standard
16725 Binary operators are surrounded by space when there is a character before
16727 \begin_inset VSpace medskip
16733 \begin_layout Standard
16734 \begin_inset Tabular
16735 <lyxtabular version="3" rows="13" columns="2">
16736 <features booktabs="true" tabularvalignment="middle">
16737 <column alignment="center" valignment="top" width="0pt">
16738 <column alignment="center" valignment="top" width="0pt">
16740 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
16743 \begin_layout Plain Layout
16745 \begin_inset Note Note
16748 \begin_layout Plain Layout
16755 is only used as spacer.
16765 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
16768 \begin_layout Plain Layout
16776 <cell alignment="center" valignment="top" leftline="true" usebox="none">
16779 \begin_layout Plain Layout
16785 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
16788 \begin_layout Plain Layout
16789 \begin_inset Formula $+$
16799 <cell alignment="center" valignment="top" leftline="true" usebox="none">
16802 \begin_layout Plain Layout
16808 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
16811 \begin_layout Plain Layout
16812 \begin_inset Formula $-$
16822 <cell alignment="center" valignment="top" leftline="true" usebox="none">
16825 \begin_layout Plain Layout
16833 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
16836 \begin_layout Plain Layout
16837 \begin_inset Formula $\pm$
16847 <cell alignment="center" valignment="top" leftline="true" usebox="none">
16850 \begin_layout Plain Layout
16858 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
16861 \begin_layout Plain Layout
16862 \begin_inset Formula $\mp$
16872 <cell alignment="center" valignment="top" leftline="true" usebox="none">
16875 \begin_layout Plain Layout
16883 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
16886 \begin_layout Plain Layout
16887 \begin_inset Formula $\cdot$
16897 <cell alignment="center" valignment="top" leftline="true" usebox="none">
16900 \begin_layout Plain Layout
16908 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
16911 \begin_layout Plain Layout
16912 \begin_inset Formula $\times$
16922 <cell alignment="center" valignment="top" leftline="true" usebox="none">
16925 \begin_layout Plain Layout
16933 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
16936 \begin_layout Plain Layout
16937 \begin_inset Formula $\div$
16947 <cell alignment="center" valignment="top" leftline="true" usebox="none">
16950 \begin_layout Plain Layout
16954 \begin_layout Plain Layout
16967 \begin_layout Plain Layout
16979 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
16982 \begin_layout Plain Layout
16983 \begin_inset Formula $*$
16993 <cell alignment="center" valignment="top" leftline="true" usebox="none">
16996 \begin_layout Plain Layout
17004 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
17007 \begin_layout Plain Layout
17008 \begin_inset Formula $\star$
17018 <cell alignment="center" valignment="top" leftline="true" usebox="none">
17021 \begin_layout Plain Layout
17029 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
17032 \begin_layout Plain Layout
17033 \begin_inset Formula $\circ$
17043 <cell alignment="center" valignment="top" leftline="true" usebox="none">
17046 \begin_layout Plain Layout
17054 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
17057 \begin_layout Plain Layout
17058 \begin_inset Formula $\diamond$
17068 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
17071 \begin_layout Plain Layout
17079 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
17082 \begin_layout Plain Layout
17083 \begin_inset Formula $\bullet$
17097 \begin_inset space \hfill{}
17101 \begin_inset Tabular
17102 <lyxtabular version="3" rows="13" columns="2">
17103 <features booktabs="true" tabularvalignment="middle">
17104 <column alignment="center" valignment="top" width="0pt">
17105 <column alignment="center" valignment="top" width="0pt">
17107 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
17110 \begin_layout Plain Layout
17116 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
17119 \begin_layout Plain Layout
17127 <cell alignment="center" valignment="top" leftline="true" usebox="none">
17130 \begin_layout Plain Layout
17138 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
17141 \begin_layout Plain Layout
17142 \begin_inset Formula $\nabla$
17152 <cell alignment="center" valignment="top" leftline="true" usebox="none">
17155 \begin_layout Plain Layout
17163 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
17166 \begin_layout Plain Layout
17167 \begin_inset Formula $\bigtriangledown$
17177 <cell alignment="center" valignment="top" leftline="true" usebox="none">
17180 \begin_layout Plain Layout
17188 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
17191 \begin_layout Plain Layout
17192 \begin_inset Formula $\bigtriangleup$
17202 <cell alignment="center" valignment="top" leftline="true" usebox="none">
17205 \begin_layout Plain Layout
17213 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
17216 \begin_layout Plain Layout
17217 \begin_inset Formula $\Box$
17227 <cell alignment="center" valignment="top" leftline="true" usebox="none">
17230 \begin_layout Plain Layout
17238 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
17241 \begin_layout Plain Layout
17242 \begin_inset Formula $\cap$
17252 <cell alignment="center" valignment="top" leftline="true" usebox="none">
17255 \begin_layout Plain Layout
17263 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
17266 \begin_layout Plain Layout
17267 \begin_inset Formula $\cup$
17277 <cell alignment="center" valignment="top" leftline="true" usebox="none">
17280 \begin_layout Plain Layout
17288 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
17291 \begin_layout Plain Layout
17292 \begin_inset Formula $\dagger$
17302 <cell alignment="center" valignment="top" leftline="true" usebox="none">
17305 \begin_layout Plain Layout
17313 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
17316 \begin_layout Plain Layout
17317 \begin_inset Formula $\ddagger$
17327 <cell alignment="center" valignment="top" leftline="true" usebox="none">
17330 \begin_layout Plain Layout
17338 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
17341 \begin_layout Plain Layout
17342 \begin_inset Formula $\wr$
17352 <cell alignment="center" valignment="top" leftline="true" usebox="none">
17355 \begin_layout Plain Layout
17363 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
17366 \begin_layout Plain Layout
17367 \begin_inset Formula $\bigcirc$
17377 <cell alignment="center" valignment="top" leftline="true" usebox="none">
17380 \begin_layout Plain Layout
17388 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
17391 \begin_layout Plain Layout
17392 \begin_inset Formula $\wedge$
17402 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
17405 \begin_layout Plain Layout
17413 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
17416 \begin_layout Plain Layout
17417 \begin_inset Formula $\vee$
17431 \begin_inset space \hfill{}
17435 \begin_inset Tabular
17436 <lyxtabular version="3" rows="13" columns="2">
17437 <features booktabs="true" tabularvalignment="middle">
17438 <column alignment="center" valignment="top" width="0pt">
17439 <column alignment="center" valignment="top" width="0pt">
17441 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
17444 \begin_layout Plain Layout
17450 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
17453 \begin_layout Plain Layout
17461 <cell alignment="center" valignment="top" leftline="true" usebox="none">
17464 \begin_layout Plain Layout
17472 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
17475 \begin_layout Plain Layout
17476 \begin_inset Formula $\oplus$
17486 <cell alignment="center" valignment="top" leftline="true" usebox="none">
17489 \begin_layout Plain Layout
17497 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
17500 \begin_layout Plain Layout
17501 \begin_inset Formula $\ominus$
17511 <cell alignment="center" valignment="top" leftline="true" usebox="none">
17514 \begin_layout Plain Layout
17522 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
17525 \begin_layout Plain Layout
17526 \begin_inset Formula $\otimes$
17536 <cell alignment="center" valignment="top" leftline="true" usebox="none">
17539 \begin_layout Plain Layout
17547 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
17550 \begin_layout Plain Layout
17551 \begin_inset Formula $\oslash$
17561 <cell alignment="center" valignment="top" leftline="true" usebox="none">
17564 \begin_layout Plain Layout
17572 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
17575 \begin_layout Plain Layout
17576 \begin_inset Formula $\odot$
17586 <cell alignment="center" valignment="top" leftline="true" usebox="none">
17589 \begin_layout Plain Layout
17597 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
17600 \begin_layout Plain Layout
17601 \begin_inset Formula $\amalg$
17611 <cell alignment="center" valignment="top" leftline="true" usebox="none">
17614 \begin_layout Plain Layout
17622 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
17625 \begin_layout Plain Layout
17626 \begin_inset Formula $\uplus$
17636 <cell alignment="center" valignment="top" leftline="true" usebox="none">
17639 \begin_layout Plain Layout
17647 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
17650 \begin_layout Plain Layout
17651 \begin_inset Formula $\setminus$
17661 <cell alignment="center" valignment="top" leftline="true" usebox="none">
17664 \begin_layout Plain Layout
17672 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
17675 \begin_layout Plain Layout
17676 \begin_inset Formula $\sqcap$
17686 <cell alignment="center" valignment="top" leftline="true" usebox="none">
17689 \begin_layout Plain Layout
17697 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
17700 \begin_layout Plain Layout
17701 \begin_inset Formula $\sqcup$
17711 <cell alignment="center" valignment="top" leftline="true" usebox="none">
17714 \begin_layout Plain Layout
17722 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
17725 \begin_layout Plain Layout
17726 \begin_inset Formula $\triangleleft$
17736 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
17739 \begin_layout Plain Layout
17747 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
17750 \begin_layout Plain Layout
17751 \begin_inset Formula $\triangleright$
17767 \begin_layout Standard
17768 All binary operators can also be inserted via the math toolbar button
17771 arg "math-insert \\pm"
17777 \begin_layout Standard
17778 To typeset the Laplace operator also
17795 \begin_inset Formula $\nabla^{2}$
17798 ) can be used instead of
17807 \begin_layout Standard
17814 Insert\SpecialChar menuseparator
17826 \begin_layout Subsection
17827 Self-defined Operators
17828 \begin_inset CommandInset label
17830 name "subsec:Self-defined-Operators"
17835 \begin_inset Index idx
17838 \begin_layout Plain Layout
17839 Operators ! self-defined
17847 \begin_layout Standard
17848 With the help of the command
17852 DeclareMathOperator
17855 \begin_inset Index idx
17858 \begin_layout Plain Layout
17863 DeclareMathOperator
17868 custom operators can be defined in the \SpecialChar LaTeX
17870 Its command scheme is:
17873 \begin_layout Standard
17878 DeclareMathOperator{new command}{display}
17881 \begin_layout Standard
17882 Display can be characters or symbols that define how the operator looks
17884 To define a big operator a * is set behind the command.
17885 All self-defined big operators can have limits as described in
17886 \begin_inset CommandInset ref
17888 reference "subsec:Operator-Limits"
17895 \begin_layout Standard
17896 For example the \SpecialChar LaTeX
17900 \begin_layout Standard
17905 DeclareMathOperator*{
17912 \begin_layout Standard
17913 defines the command
17919 , that inserts a big operator consisting of the lozenge symbol from
17920 \begin_inset CommandInset ref
17922 reference "subsec:Miscellaneous-Symbols"
17927 \begin_inset Formula
17929 \Lozenge_{n=1}^{\infty}
17934 The command for this formula is:
17945 \begin_inset Formula $\to$
17951 \begin_layout Standard
17952 \begin_inset VSpace bigskip
17955 When self-defined operators are not used several times in the document,
17956 they can also be defined with the commands
17963 \begin_inset Index idx
17966 \begin_layout Plain Layout
17981 \begin_inset Index idx
17984 \begin_layout Plain Layout
17992 , which have the following scheme:
17995 \begin_layout Standard
18009 \begin_layout Standard
18016 defines big operators,
18025 \begin_layout Standard
18033 \begin_inset space \thinspace{}
18037 \begin_inset space \space{}
18040 be used to use one limit for several operators:
18043 \begin_layout Standard
18044 \begin_inset Formula
18046 \mathop{\sum\negmedspace\sum}_{i,j=1}^{N}
18054 \begin_layout Standard
18055 The command for the formula above is:
18056 \begin_inset Newline newline
18072 \begin_inset space \textvisiblespace{}
18078 \begin_inset Formula $\to$
18084 \begin_inset space \textvisiblespace{}
18092 \begin_layout Section
18094 \begin_inset Index idx
18097 \begin_layout Plain Layout
18106 \begin_layout Subsection
18108 \begin_inset CommandInset label
18110 name "subsec:Font-Styles"
18115 \begin_inset Index idx
18118 \begin_layout Plain Layout
18127 \begin_layout Standard
18128 Latin letters in formulas can be set in one of the following font styles:
18131 \begin_layout Standard
18133 \begin_inset Tabular
18134 <lyxtabular version="3" rows="6" columns="3">
18135 <features booktabs="true" tabularvalignment="middle">
18136 <column alignment="center" valignment="top" width="0pt">
18137 <column alignment="center" valignment="top">
18138 <column alignment="center" valignment="top">
18140 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
18143 \begin_layout Plain Layout
18149 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
18152 \begin_layout Plain Layout
18158 <cell alignment="center" valignment="top" topline="true" bottomline="true" usebox="none">
18161 \begin_layout Plain Layout
18169 <cell alignment="center" valignment="top" leftline="true" usebox="none">
18172 \begin_layout Plain Layout
18178 \begin_inset space \textvisiblespace{}
18188 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
18191 \begin_layout Plain Layout
18192 \begin_inset Formula $\mathbb{ABC}$
18200 <cell alignment="center" valignment="top" usebox="none">
18203 \begin_layout Plain Layout
18211 <cell alignment="center" valignment="top" leftline="true" usebox="none">
18214 \begin_layout Plain Layout
18220 \begin_inset space \textvisiblespace{}
18230 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
18233 \begin_layout Plain Layout
18234 \begin_inset Formula $\mathbf{AbC}$
18242 <cell alignment="center" valignment="top" usebox="none">
18245 \begin_layout Plain Layout
18258 <cell alignment="center" valignment="top" leftline="true" usebox="none">
18261 \begin_layout Plain Layout
18267 \begin_inset space \textvisiblespace{}
18277 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
18280 \begin_layout Plain Layout
18281 \begin_inset Formula $\boldsymbol{AbC}$
18289 <cell alignment="center" valignment="top" usebox="none">
18292 \begin_layout Plain Layout
18295 arg "font-boldsymbol"
18305 <cell alignment="center" valignment="top" leftline="true" usebox="none">
18308 \begin_layout Plain Layout
18314 \begin_inset space \textvisiblespace{}
18324 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
18327 \begin_layout Plain Layout
18328 \begin_inset Formula $\mathcal{ABC}$
18336 <cell alignment="center" valignment="top" usebox="none">
18339 \begin_layout Plain Layout
18347 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
18350 \begin_layout Plain Layout
18356 \begin_inset space \textvisiblespace{}
18366 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
18369 \begin_layout Plain Layout
18370 \begin_inset Formula $\mathfrak{AbC}$
18378 <cell alignment="center" valignment="top" bottomline="true" usebox="none">
18381 \begin_layout Plain Layout
18395 \begin_layout Standard
18397 \begin_inset Tabular
18398 <lyxtabular version="3" rows="6" columns="3">
18399 <features booktabs="true" tabularvalignment="middle">
18400 <column alignment="center" valignment="top" width="0pt">
18401 <column alignment="center" valignment="top">
18402 <column alignment="center" valignment="top">
18404 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
18407 \begin_layout Plain Layout
18413 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
18416 \begin_layout Plain Layout
18422 <cell alignment="center" valignment="top" topline="true" bottomline="true" usebox="none">
18425 \begin_layout Plain Layout
18433 <cell alignment="center" valignment="top" leftline="true" usebox="none">
18436 \begin_layout Plain Layout
18442 \begin_inset space \textvisiblespace{}
18452 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
18455 \begin_layout Plain Layout
18456 \begin_inset Formula $\mathit{AbC}$
18464 <cell alignment="center" valignment="top" usebox="none">
18467 \begin_layout Plain Layout
18475 <cell alignment="center" valignment="top" leftline="true" usebox="none">
18478 \begin_layout Plain Layout
18484 \begin_inset space \textvisiblespace{}
18494 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
18497 \begin_layout Plain Layout
18498 \begin_inset Formula $\mathrm{AbC}$
18506 <cell alignment="center" valignment="top" usebox="none">
18509 \begin_layout Plain Layout
18522 <cell alignment="center" valignment="top" leftline="true" usebox="none">
18525 \begin_layout Plain Layout
18531 \begin_inset space \textvisiblespace{}
18541 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
18544 \begin_layout Plain Layout
18545 \begin_inset Formula $\mathsf{AbC}$
18553 <cell alignment="center" valignment="top" usebox="none">
18556 \begin_layout Plain Layout
18569 <cell alignment="center" valignment="top" leftline="true" usebox="none">
18572 \begin_layout Plain Layout
18578 \begin_inset space \textvisiblespace{}
18588 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
18591 \begin_layout Plain Layout
18592 \begin_inset Formula $\mathtt{AbC}$
18600 <cell alignment="center" valignment="top" usebox="none">
18603 \begin_layout Plain Layout
18606 arg "font-typewriter"
18616 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
18619 \begin_layout Plain Layout
18625 \begin_inset space \textvisiblespace{}
18635 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
18638 \begin_layout Plain Layout
18639 \begin_inset Formula $\mathscr{ABC}$
18647 <cell alignment="center" valignment="top" bottomline="true" usebox="none">
18650 \begin_layout Plain Layout
18664 \begin_layout Standard
18665 \begin_inset Note Greyedout
18668 \begin_layout Plain Layout
18691 can only be used for big letters.
18699 \begin_layout Standard
18700 Predefined is the style
18709 \begin_layout Standard
18710 The style commands work also for letters in mathematical constructs:
18711 \begin_inset Formula
18713 \mathfrak{A=\frac{b}{C}}
18721 \begin_layout Standard
18722 Characters in mathematical text don't appear in a math font style but in
18723 the text font style
18730 That their style can't be set correctly via the text style dialog is a
18731 bug in \SpecialChar LyX
18736 \begin_layout Plain Layout
18737 \begin_inset CommandInset href
18739 name "LyX-bug #4629"
18740 target "http://www.lyx.org/trac/ticket/4629"
18753 \begin_layout Standard
18754 Instead of the style commands the dialog
18756 Edit\SpecialChar menuseparator
18757 Math\SpecialChar menuseparator
18760 or the toolbar button
18763 arg "math-insert \\font"
18769 \begin_layout Subsection
18771 \begin_inset CommandInset label
18773 name "subsec:Bold-Formulas"
18778 \begin_inset Index idx
18781 \begin_layout Plain Layout
18790 \begin_layout Standard
18791 To make a complete formula bold, the command
18797 from the previous subsection cannot be used, because it doesn't work for
18798 small Greek letters.
18799 Furthermore it prints Latin letters always upright, like in the following
18803 \begin_layout Standard
18804 \begin_inset Formula
18806 \mathbf{\int_{n}^{2}f(\theta)=\Gamma}\qquad\textrm{equation with \textbackslash mathbf}
18814 \begin_layout Standard
18815 To display the formula correctly, the command
18822 \begin_inset Formula
18824 \boldsymbol{\int_{n}^{2}f(\theta)=\Gamma\qquad\textrm{equation with \textbackslash boldsymbol}}
18829 It is also possible to set the formula in a
18831 boldmath environment
18834 This environment is created by inserting the command
18841 \begin_inset Index idx
18844 \begin_layout Plain Layout
18852 in \SpecialChar TeX
18854 To end the environment, the command
18861 \begin_inset Index idx
18864 \begin_layout Plain Layout
18872 is inserted in \SpecialChar TeX
18877 \begin_layout Plain Layout
18887 \begin_inset Formula
18889 \int_{n}^{2}f(\theta)=\Gamma\qquad\textrm{equation in a boldmath environment}
18898 \begin_layout Plain Layout
18910 \begin_layout Subsection
18912 \begin_inset Index idx
18915 \begin_layout Plain Layout
18924 \begin_layout Standard
18925 Formulas can be colored like normal text: Highlight a formula or a formula
18931 Here is a formula in magenta:
18932 \begin_inset Formula
18934 {\color{magenta}\int A\,\mathrm{d}x=\frac{\sqrt[5]{B}}{\ln\left(\frac{1}{3}\right)}}
18942 \begin_layout Standard
18943 You can also define your own colors as described in
18944 \begin_inset CommandInset ref
18946 reference "subsec:Colored-Boxes"
18951 They can be used with the \SpecialChar TeX
18959 \begin_inset Index idx
18962 \begin_layout Plain Layout
18973 \begin_layout Standard
18978 textcolor{color}{characters or formula}
18981 \begin_layout Standard
18982 The following example was colored completely dark green and partly red:
18985 \begin_layout Standard
18989 \begin_layout Plain Layout
18993 textcolor{darkgreen}{
18999 \begin_inset Formula
19001 \int A\,\mathrm{d}x=\frac{{\color{red}\sqrt[5]{B}}}{\ln\left(\frac{1}{3}\right)}
19010 \begin_layout Plain Layout
19020 \begin_layout Standard
19021 Due to a bug in \SpecialChar LyX
19022 only complete formulas can be colored with self-defined
19027 \begin_layout Plain Layout
19028 \begin_inset CommandInset href
19030 name "LyX-bug #5269"
19031 target "http://www.lyx.org/trac/ticket/5269"
19044 \begin_layout Subsection
19046 \begin_inset CommandInset label
19048 name "subsec:Font-Sizes"
19053 \begin_inset Index idx
19056 \begin_layout Plain Layout
19065 \begin_layout Standard
19066 For characters in formulas there are, analog to characters in text, the
19067 following size commands:
19070 \begin_layout Standard
19114 \begin_inset Newline newline
19136 \begin_layout Standard
19137 The size produced by the commands depends on the document font size, which
19138 corresponds to the command
19145 The other commands produce smaller or larger sizes than
19152 The font size can however not exceed a certain value.
19153 Is for example the document font size 12
19154 \begin_inset space \thinspace{}
19163 switches to the same size as
19173 \begin_layout Standard
19174 A size command is inserted in \SpecialChar TeX
19175 mode before the formula and sets the size
19176 for all following formula and text characters.
19177 To switch back to the initial size, the command
19183 is inserted behind the formula in \SpecialChar TeX
19187 \begin_layout Standard
19188 Within a formula the size can be changed using the following size commands
19189 or the toolbar button
19192 arg "math-insert \\style"
19198 \begin_layout Standard
19201 \begin_inset Tabular
19202 <lyxtabular version="3" rows="5" columns="2">
19203 <features booktabs="true" tabularvalignment="middle">
19204 <column alignment="center" valignment="top" width="0pt">
19205 <column alignment="center" valignment="top">
19207 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
19210 \begin_layout Plain Layout
19216 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
19219 \begin_layout Plain Layout
19227 <cell alignment="center" valignment="top" leftline="true" usebox="none">
19230 \begin_layout Plain Layout
19234 \begin_inset Index idx
19237 \begin_layout Plain Layout
19250 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
19253 \begin_layout Plain Layout
19254 \begin_inset Formula ${\displaystyle E_{\mathrm{pot_{1}}}=\frac{K}{l+\frac{m}{n_{2}}}}$
19263 <row topspace="1mm">
19264 <cell alignment="center" valignment="top" usebox="none">
19267 \begin_layout Plain Layout
19275 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
19278 \begin_layout Plain Layout
19279 \begin_inset Formula ${\textstyle E_{\mathrm{pot_{1}}}=\frac{K}{l+\frac{m}{n_{2}}}}$
19289 <cell alignment="center" valignment="top" leftline="true" usebox="none">
19292 \begin_layout Plain Layout
19300 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
19303 \begin_layout Plain Layout
19304 \begin_inset Formula ${\scriptstyle E_{\mathrm{pot_{1}}}=\frac{K}{l+\frac{m}{n_{2}}}}$
19314 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
19317 \begin_layout Plain Layout
19325 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
19328 \begin_layout Plain Layout
19329 \begin_inset Formula ${\scriptscriptstyle E_{\mathrm{pot_{1}}}=\frac{K}{l+\frac{m}{n_{2}}}}$
19345 \begin_layout Standard
19346 After entering these commands, a blue box appears in which the formula parts
19350 \begin_layout Standard
19351 There is a further method to change the font size, that though only works
19352 for symbols or letters in mathematical text.
19353 To use it, one of the above text size commands is inserted in mathematical
19355 All following characters until the end of the mathematical text or until
19356 another size command will have the selected size.
19358 \begin_inset VSpace -2mm
19364 \begin_layout Standard
19368 \begin_layout Plain Layout
19378 \begin_inset Formula
19380 A=\frac{B}{c}\cdot\maltese
19386 \begin_inset Formula
19388 \maltese A\textrm{\Large\maltese\textit{A}}\textrm{\tiny\maltese\textit{A}}
19397 \begin_layout Plain Layout
19409 \begin_layout Standard
19410 \begin_inset VSpace medskip
19413 Before both formulas the command
19420 The command for the second formula is:
19421 \begin_inset Newline newline
19429 \begin_inset space \textvisiblespace{}
19435 \begin_inset space \textvisiblespace{}
19441 \begin_inset space \textvisiblespace{}
19447 \begin_inset space \textvisiblespace{}
19451 \begin_inset Formula $\to$
19455 \begin_inset Formula $\to$
19459 \begin_inset Newline newline
19463 \begin_inset space \hspace*{}
19474 \begin_inset space \textvisiblespace{}
19480 \begin_inset space \textvisiblespace{}
19486 \begin_inset space \textvisiblespace{}
19492 \begin_layout Standard
19493 If a symbol cannot be displayed in different sizes, it will always be displayed
19494 in the default size.
19497 \begin_layout Section
19499 \begin_inset Index idx
19502 \begin_layout Plain Layout
19511 \begin_layout Standard
19512 Greek letters can also be inserted via the toolbar button
19515 arg "math-insert \\alpha"
19519 All international typesetting norms purport that Greek letters in math
19520 have to be typeset italic/slanted.
19521 In some languages, like French or Russian, they are nevertheless sometimes
19525 \begin_layout Subsection
19527 \begin_inset Index idx
19530 \begin_layout Plain Layout
19531 Greek letters ! small
19539 \begin_layout Standard
19540 \begin_inset space \hfill{}
19544 \begin_inset Tabular
19545 <lyxtabular version="3" rows="11" columns="2">
19546 <features booktabs="true" tabularvalignment="middle">
19547 <column alignment="center" valignment="top" width="0pt">
19548 <column alignment="center" valignment="top" width="0pt">
19550 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
19553 \begin_layout Plain Layout
19559 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
19562 \begin_layout Plain Layout
19570 <cell alignment="center" valignment="top" leftline="true" usebox="none">
19573 \begin_layout Plain Layout
19581 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
19584 \begin_layout Plain Layout
19585 \begin_inset Formula $\alpha$
19595 <cell alignment="center" valignment="top" leftline="true" usebox="none">
19598 \begin_layout Plain Layout
19606 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
19609 \begin_layout Plain Layout
19610 \begin_inset Formula $\beta$
19620 <cell alignment="center" valignment="top" leftline="true" usebox="none">
19623 \begin_layout Plain Layout
19631 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
19634 \begin_layout Plain Layout
19635 \begin_inset Formula $\gamma$
19645 <cell alignment="center" valignment="top" leftline="true" usebox="none">
19648 \begin_layout Plain Layout
19656 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
19659 \begin_layout Plain Layout
19660 \begin_inset Formula $\delta$
19670 <cell alignment="center" valignment="top" leftline="true" usebox="none">
19673 \begin_layout Plain Layout
19681 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
19684 \begin_layout Plain Layout
19685 \begin_inset Formula $\epsilon$
19695 <cell alignment="center" valignment="top" leftline="true" usebox="none">
19698 \begin_layout Plain Layout
19706 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
19709 \begin_layout Plain Layout
19710 \begin_inset Formula $\varepsilon$
19720 <cell alignment="center" valignment="top" leftline="true" usebox="none">
19723 \begin_layout Plain Layout
19731 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
19734 \begin_layout Plain Layout
19735 \begin_inset Formula $\zeta$
19745 <cell alignment="center" valignment="top" leftline="true" usebox="none">
19748 \begin_layout Plain Layout
19756 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
19759 \begin_layout Plain Layout
19760 \begin_inset Formula $\eta$
19770 <cell alignment="center" valignment="top" leftline="true" usebox="none">
19773 \begin_layout Plain Layout
19781 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
19784 \begin_layout Plain Layout
19785 \begin_inset Formula $\theta$
19795 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
19798 \begin_layout Plain Layout
19806 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
19809 \begin_layout Plain Layout
19810 \begin_inset Formula $\vartheta$
19824 \begin_inset space \hfill{}
19828 \begin_inset Tabular
19829 <lyxtabular version="3" rows="12" columns="2">
19830 <features booktabs="true" tabularvalignment="middle">
19831 <column alignment="center" valignment="top" width="0pt">
19832 <column alignment="center" valignment="top" width="0pt">
19834 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
19837 \begin_layout Plain Layout
19843 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
19846 \begin_layout Plain Layout
19854 <cell alignment="center" valignment="top" leftline="true" usebox="none">
19857 \begin_layout Plain Layout
19865 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
19868 \begin_layout Plain Layout
19869 \begin_inset Formula $\iota$
19879 <cell alignment="center" valignment="top" leftline="true" usebox="none">
19882 \begin_layout Plain Layout
19890 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
19893 \begin_layout Plain Layout
19894 \begin_inset Formula $\kappa$
19904 <cell alignment="center" valignment="top" leftline="true" usebox="none">
19907 \begin_layout Plain Layout
19915 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
19918 \begin_layout Plain Layout
19919 \begin_inset Formula $\varkappa$
19929 <cell alignment="center" valignment="top" leftline="true" usebox="none">
19932 \begin_layout Plain Layout
19940 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
19943 \begin_layout Plain Layout
19944 \begin_inset Formula $\lambda$
19954 <cell alignment="center" valignment="top" leftline="true" usebox="none">
19957 \begin_layout Plain Layout
19965 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
19968 \begin_layout Plain Layout
19969 \begin_inset Formula $\mu$
19979 <cell alignment="center" valignment="top" leftline="true" usebox="none">
19982 \begin_layout Plain Layout
19990 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
19993 \begin_layout Plain Layout
19994 \begin_inset Formula $\nu$
20004 <cell alignment="center" valignment="top" leftline="true" usebox="none">
20007 \begin_layout Plain Layout
20015 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
20018 \begin_layout Plain Layout
20019 \begin_inset Formula $\xi$
20029 <cell alignment="center" valignment="top" leftline="true" usebox="none">
20032 \begin_layout Plain Layout
20038 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
20041 \begin_layout Plain Layout
20042 \begin_inset Formula $o$
20052 <cell alignment="center" valignment="top" leftline="true" usebox="none">
20055 \begin_layout Plain Layout
20063 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
20066 \begin_layout Plain Layout
20067 \begin_inset Formula $\pi$
20077 <cell alignment="center" valignment="top" leftline="true" usebox="none">
20080 \begin_layout Plain Layout
20088 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
20091 \begin_layout Plain Layout
20092 \begin_inset Formula $\varpi$
20102 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
20105 \begin_layout Plain Layout
20113 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
20116 \begin_layout Plain Layout
20117 \begin_inset Formula $\rho$
20131 \begin_inset space \hfill{}
20135 \begin_inset Tabular
20136 <lyxtabular version="3" rows="11" columns="2">
20137 <features booktabs="true" tabularvalignment="middle">
20138 <column alignment="center" valignment="top" width="0pt">
20139 <column alignment="center" valignment="top" width="0pt">
20141 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
20144 \begin_layout Plain Layout
20150 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
20153 \begin_layout Plain Layout
20161 <cell alignment="center" valignment="top" leftline="true" usebox="none">
20164 \begin_layout Plain Layout
20172 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
20175 \begin_layout Plain Layout
20176 \begin_inset Formula $\varrho$
20186 <cell alignment="center" valignment="top" leftline="true" usebox="none">
20189 \begin_layout Plain Layout
20197 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
20200 \begin_layout Plain Layout
20201 \begin_inset Formula $\sigma$
20211 <cell alignment="center" valignment="top" leftline="true" usebox="none">
20214 \begin_layout Plain Layout
20222 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
20225 \begin_layout Plain Layout
20226 \begin_inset Formula $\varsigma$
20236 <cell alignment="center" valignment="top" leftline="true" usebox="none">
20239 \begin_layout Plain Layout
20247 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
20250 \begin_layout Plain Layout
20251 \begin_inset Formula $\tau$
20261 <cell alignment="center" valignment="top" leftline="true" usebox="none">
20264 \begin_layout Plain Layout
20272 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
20275 \begin_layout Plain Layout
20276 \begin_inset Formula $\upsilon$
20286 <cell alignment="center" valignment="top" leftline="true" usebox="none">
20289 \begin_layout Plain Layout
20297 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
20300 \begin_layout Plain Layout
20301 \begin_inset Formula $\phi$
20311 <cell alignment="center" valignment="top" leftline="true" usebox="none">
20314 \begin_layout Plain Layout
20322 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
20325 \begin_layout Plain Layout
20326 \begin_inset Formula $\varphi$
20336 <cell alignment="center" valignment="top" leftline="true" usebox="none">
20339 \begin_layout Plain Layout
20347 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
20350 \begin_layout Plain Layout
20351 \begin_inset Formula $\chi$
20361 <cell alignment="center" valignment="top" leftline="true" usebox="none">
20364 \begin_layout Plain Layout
20372 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
20375 \begin_layout Plain Layout
20376 \begin_inset Formula $\psi$
20386 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
20389 \begin_layout Plain Layout
20397 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
20400 \begin_layout Plain Layout
20401 \begin_inset Formula $\omega$
20415 \begin_inset space \hfill{}
20421 \begin_layout Standard
20422 \begin_inset VSpace medskip
20428 \begin_layout Standard
20429 How to create special upright Greek letters is explained in
20430 \begin_inset CommandInset ref
20432 reference "subsec:Upright-small-Greek"
20439 \begin_layout Subsection
20441 \begin_inset Index idx
20444 \begin_layout Plain Layout
20445 Greek letters ! big
20453 \begin_layout Standard
20454 \begin_inset space \hfill{}
20458 \begin_inset Tabular
20459 <lyxtabular version="3" rows="7" columns="2">
20460 <features booktabs="true" tabularvalignment="middle">
20461 <column alignment="center" valignment="top" width="0pt">
20462 <column alignment="center" valignment="top" width="0pt">
20464 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
20467 \begin_layout Plain Layout
20473 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
20476 \begin_layout Plain Layout
20484 <cell alignment="center" valignment="top" leftline="true" usebox="none">
20487 \begin_layout Plain Layout
20495 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
20498 \begin_layout Plain Layout
20499 \begin_inset Formula $\Gamma$
20509 <cell alignment="center" valignment="top" leftline="true" usebox="none">
20512 \begin_layout Plain Layout
20520 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
20523 \begin_layout Plain Layout
20524 \begin_inset Formula $\Delta$
20534 <cell alignment="center" valignment="top" leftline="true" usebox="none">
20537 \begin_layout Plain Layout
20545 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
20548 \begin_layout Plain Layout
20549 \begin_inset Formula $\Theta$
20559 <cell alignment="center" valignment="top" leftline="true" usebox="none">
20562 \begin_layout Plain Layout
20570 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
20573 \begin_layout Plain Layout
20574 \begin_inset Formula $\Lambda$
20584 <cell alignment="center" valignment="top" leftline="true" usebox="none">
20587 \begin_layout Plain Layout
20595 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
20598 \begin_layout Plain Layout
20599 \begin_inset Formula $\Xi$
20609 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
20612 \begin_layout Plain Layout
20620 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
20623 \begin_layout Plain Layout
20624 \begin_inset Formula $\Pi$
20638 \begin_inset space \hfill{}
20642 \begin_inset Tabular
20643 <lyxtabular version="3" rows="6" columns="2">
20644 <features booktabs="true" tabularvalignment="middle">
20645 <column alignment="center" valignment="top" width="0pt">
20646 <column alignment="center" valignment="top" width="0pt">
20648 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
20651 \begin_layout Plain Layout
20657 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
20660 \begin_layout Plain Layout
20668 <cell alignment="center" valignment="top" leftline="true" usebox="none">
20671 \begin_layout Plain Layout
20679 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
20682 \begin_layout Plain Layout
20683 \begin_inset Formula $\Sigma$
20693 <cell alignment="center" valignment="top" leftline="true" usebox="none">
20696 \begin_layout Plain Layout
20704 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
20707 \begin_layout Plain Layout
20708 \begin_inset Formula $\Upsilon$
20718 <cell alignment="center" valignment="top" leftline="true" usebox="none">
20721 \begin_layout Plain Layout
20729 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
20732 \begin_layout Plain Layout
20733 \begin_inset Formula $\Phi$
20743 <cell alignment="center" valignment="top" leftline="true" usebox="none">
20746 \begin_layout Plain Layout
20754 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
20757 \begin_layout Plain Layout
20758 \begin_inset Formula $\Psi$
20768 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
20771 \begin_layout Plain Layout
20779 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
20782 \begin_layout Plain Layout
20783 \begin_inset Formula $\Omega$
20797 \begin_inset space \hfill{}
20803 \begin_layout Standard
20804 \begin_inset VSpace medskip
20807 That the big Greek letters appear upright is caused by a design bug when
20810 To get correct italic big letters, begin every command with
20815 For example the command
20822 \begin_inset Formula $\varGamma$
20826 Another way is to load the package
20834 \begin_layout Plain Layout
20839 is part of the \SpecialChar LaTeX
20845 \begin_inset Index idx
20848 \begin_layout Plain Layout
20853 \begin_layout Plain Layout
20873 \begin_inset Index idx
20876 \begin_layout Plain Layout
20882 with the \SpecialChar LaTeX
20886 \begin_layout Standard
20891 usepackage{fixmath}
20894 \begin_layout Standard
20895 Then all big Greek letters in a document will automatically be typeset italic.
20898 \begin_layout Subsection
20900 \begin_inset Index idx
20903 \begin_layout Plain Layout
20904 Greek letters ! bold
20912 \begin_layout Standard
20913 Greek letters cannot be set with different font styles like Latin letters.
20914 They can only be made bold with the command
20921 \begin_inset Index idx
20924 \begin_layout Plain Layout
20935 \begin_layout Standard
20937 \begin_inset Tabular
20938 <lyxtabular version="3" rows="3" columns="2">
20939 <features booktabs="true" tabularvalignment="middle">
20940 <column alignment="center" valignment="top" width="0pt">
20941 <column alignment="center" valignment="top">
20943 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
20946 \begin_layout Plain Layout
20952 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
20955 \begin_layout Plain Layout
20963 <cell alignment="center" valignment="top" leftline="true" usebox="none">
20966 \begin_layout Plain Layout
20978 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
20981 \begin_layout Plain Layout
20982 \begin_inset Formula $\Upsilon\boldsymbol{\Upsilon}$
20992 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
20995 \begin_layout Plain Layout
21007 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
21010 \begin_layout Plain Layout
21011 \begin_inset Formula $\theta\boldsymbol{\theta}$
21027 \begin_layout Section
21032 \begin_layout Plain Layout
21045 \begin_layout Plain Layout
21046 A list with all symbols of most of the \SpecialChar LaTeX
21047 -packages can be found in
21048 \begin_inset CommandInset citation
21064 \begin_layout Plain Layout
21072 \begin_inset Note Note
21075 \begin_layout Plain Layout
21078 texorpdfstring is used to avoid that the footnote appears in the PDF-bookmark.
21081 \begin_layout Plain Layout
21084 texorpdfstring is in section
21085 \begin_inset CommandInset ref
21087 reference "subsec:Formulas-in-Section"
21097 \begin_inset Index idx
21100 \begin_layout Plain Layout
21109 \begin_layout Standard
21110 Many of the symbols listed in this section can also be inserted via the
21114 arg "math-insert \\nabla"
21120 arg "math-insert \\digamma"
21126 \begin_layout Subsection
21127 Mathematical Symbols
21128 \begin_inset CommandInset label
21130 name "subsec:Mathematical-Symbols"
21135 \begin_inset Index idx
21138 \begin_layout Plain Layout
21139 Symbols ! mathematical
21147 \begin_layout Standard
21148 \begin_inset Tabular
21149 <lyxtabular version="3" rows="10" columns="2">
21150 <features booktabs="true" tabularvalignment="middle">
21151 <column alignment="center" valignment="top" width="0pt">
21152 <column alignment="center" valignment="top" width="0pt">
21154 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
21157 \begin_layout Plain Layout
21163 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
21166 \begin_layout Plain Layout
21174 <cell alignment="center" valignment="top" leftline="true" usebox="none">
21177 \begin_layout Plain Layout
21185 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
21188 \begin_layout Plain Layout
21189 \begin_inset Formula $\neg$
21199 <cell alignment="center" valignment="top" leftline="true" usebox="none">
21202 \begin_layout Plain Layout
21210 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
21213 \begin_layout Plain Layout
21214 \begin_inset Formula $\Im$
21224 <cell alignment="center" valignment="top" leftline="true" usebox="none">
21227 \begin_layout Plain Layout
21235 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
21238 \begin_layout Plain Layout
21239 \begin_inset Formula $\Re$
21249 <cell alignment="center" valignment="top" leftline="true" usebox="none">
21252 \begin_layout Plain Layout
21260 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
21263 \begin_layout Plain Layout
21264 \begin_inset Formula $\aleph$
21274 <cell alignment="center" valignment="top" leftline="true" usebox="none">
21277 \begin_layout Plain Layout
21285 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
21288 \begin_layout Plain Layout
21289 \begin_inset Formula $\partial$
21299 <cell alignment="center" valignment="top" leftline="true" usebox="none">
21302 \begin_layout Plain Layout
21310 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
21313 \begin_layout Plain Layout
21314 \begin_inset Formula $\infty$
21324 <cell alignment="center" valignment="top" leftline="true" usebox="none">
21327 \begin_layout Plain Layout
21335 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
21338 \begin_layout Plain Layout
21339 \begin_inset Formula $\wp$
21349 <cell alignment="center" valignment="top" leftline="true" usebox="none">
21352 \begin_layout Plain Layout
21360 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
21363 \begin_layout Plain Layout
21364 \begin_inset Formula $\imath$
21374 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
21377 \begin_layout Plain Layout
21385 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
21388 \begin_layout Plain Layout
21389 \begin_inset Formula $\jmath$
21403 \begin_inset space \hfill{}
21407 \begin_inset Tabular
21408 <lyxtabular version="3" rows="10" columns="2">
21409 <features booktabs="true" tabularvalignment="middle">
21410 <column alignment="center" valignment="top" width="0pt">
21411 <column alignment="center" valignment="top" width="0pt">
21413 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
21416 \begin_layout Plain Layout
21422 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
21425 \begin_layout Plain Layout
21427 \begin_inset Note Note
21430 \begin_layout Plain Layout
21437 is only used as spacer.
21449 <cell alignment="center" valignment="top" leftline="true" usebox="none">
21452 \begin_layout Plain Layout
21460 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
21463 \begin_layout Plain Layout
21464 \begin_inset Formula $\forall$
21474 <cell alignment="center" valignment="top" leftline="true" usebox="none">
21477 \begin_layout Plain Layout
21485 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
21488 \begin_layout Plain Layout
21489 \begin_inset Formula $\exists$
21499 <cell alignment="center" valignment="top" leftline="true" usebox="none">
21502 \begin_layout Plain Layout
21510 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
21513 \begin_layout Plain Layout
21514 \begin_inset Formula $\nexists$
21524 <cell alignment="center" valignment="top" leftline="true" usebox="none">
21527 \begin_layout Plain Layout
21535 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
21538 \begin_layout Plain Layout
21539 \begin_inset Formula $\emptyset$
21549 <cell alignment="center" valignment="top" leftline="true" usebox="none">
21552 \begin_layout Plain Layout
21560 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
21563 \begin_layout Plain Layout
21564 \begin_inset Formula $\varnothing$
21574 <cell alignment="center" valignment="top" leftline="true" usebox="none">
21577 \begin_layout Plain Layout
21585 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
21588 \begin_layout Plain Layout
21589 \begin_inset Formula $\dag$
21599 <cell alignment="center" valignment="top" leftline="true" usebox="none">
21602 \begin_layout Plain Layout
21610 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
21613 \begin_layout Plain Layout
21614 \begin_inset Formula $\ddag$
21624 <cell alignment="center" valignment="top" leftline="true" usebox="none">
21627 \begin_layout Plain Layout
21635 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
21638 \begin_layout Plain Layout
21642 \begin_layout Plain Layout
21652 \begin_inset Formula $\complement$
21659 \begin_layout Plain Layout
21673 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
21676 \begin_layout Plain Layout
21684 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
21687 \begin_layout Plain Layout
21688 \begin_inset Formula $\Bbbk$
21702 \begin_inset space \hfill{}
21706 \begin_inset Tabular
21707 <lyxtabular version="3" rows="10" columns="2">
21708 <features booktabs="true" tabularvalignment="middle">
21709 <column alignment="center" valignment="top" width="0pt">
21710 <column alignment="center" valignment="top" width="0pt">
21712 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
21715 \begin_layout Plain Layout
21721 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
21724 \begin_layout Plain Layout
21732 <cell alignment="center" valignment="top" leftline="true" usebox="none">
21735 \begin_layout Plain Layout
21743 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
21746 \begin_layout Plain Layout
21747 \begin_inset Formula $\prime$
21757 <cell alignment="center" valignment="top" leftline="true" usebox="none">
21760 \begin_layout Plain Layout
21768 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
21771 \begin_layout Plain Layout
21772 \begin_inset Formula $\backprime$
21782 <cell alignment="center" valignment="top" leftline="true" usebox="none">
21785 \begin_layout Plain Layout
21793 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
21796 \begin_layout Plain Layout
21797 \begin_inset Formula $\mho$
21807 <cell alignment="center" valignment="top" leftline="true" usebox="none">
21810 \begin_layout Plain Layout
21818 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
21821 \begin_layout Plain Layout
21822 \begin_inset Formula $\triangle$
21832 <cell alignment="center" valignment="top" leftline="true" usebox="none">
21835 \begin_layout Plain Layout
21843 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
21846 \begin_layout Plain Layout
21847 \begin_inset Formula $\angle$
21857 <cell alignment="center" valignment="top" leftline="true" usebox="none">
21860 \begin_layout Plain Layout
21868 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
21871 \begin_layout Plain Layout
21872 \begin_inset Formula $\measuredangle$
21882 <cell alignment="center" valignment="top" leftline="true" usebox="none">
21885 \begin_layout Plain Layout
21893 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
21896 \begin_layout Plain Layout
21897 \begin_inset Formula $\sphericalangle$
21907 <cell alignment="center" valignment="top" leftline="true" usebox="none">
21910 \begin_layout Plain Layout
21918 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
21921 \begin_layout Plain Layout
21922 \begin_inset Formula $\top$
21932 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
21935 \begin_layout Plain Layout
21943 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
21946 \begin_layout Plain Layout
21947 \begin_inset Formula $\bot$
21963 \begin_layout Subsection
21964 Miscellaneous Symbols
21965 \begin_inset CommandInset label
21967 name "subsec:Miscellaneous-Symbols"
21972 \begin_inset Index idx
21975 \begin_layout Plain Layout
21976 Symbols ! miscellaneous
21984 \begin_layout Standard
21987 \begin_inset Tabular
21988 <lyxtabular version="3" rows="10" columns="2">
21989 <features booktabs="true" tabularvalignment="middle">
21990 <column alignment="center" valignment="top" width="0pt">
21991 <column alignment="center" valignment="top" width="0pt">
21993 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
21996 \begin_layout Plain Layout
22002 <cell alignment="center" valignment="top" topline="true" bottomline="true" 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
22024 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
22027 \begin_layout Plain Layout
22028 \begin_inset Formula $\flat$
22038 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
22041 \begin_layout Plain Layout
22049 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
22052 \begin_layout Plain Layout
22053 \begin_inset Formula $\natural$
22063 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
22066 \begin_layout Plain Layout
22074 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
22077 \begin_layout Plain Layout
22078 \begin_inset Formula $\sharp$
22088 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
22091 \begin_layout Plain Layout
22099 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
22102 \begin_layout Plain Layout
22103 \begin_inset Formula $\surd$
22113 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
22116 \begin_layout Plain Layout
22124 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
22127 \begin_layout Plain Layout
22128 \begin_inset Formula $\checkmark$
22138 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
22141 \begin_layout Plain Layout
22149 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
22152 \begin_layout Plain Layout
22153 \begin_inset Formula $\yen$
22163 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
22166 \begin_layout Plain Layout
22174 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
22177 \begin_layout Plain Layout
22178 \begin_inset Formula $\pounds$
22188 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
22191 \begin_layout Plain Layout
22197 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
22200 \begin_layout Plain Layout
22201 \begin_inset Formula $\$$
22211 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
22214 \begin_layout Plain Layout
22220 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
22223 \begin_layout Plain Layout
22224 \begin_inset Formula $§$
22238 \begin_inset space \hfill{}
22242 \begin_inset Tabular
22243 <lyxtabular version="3" rows="10" columns="2">
22244 <features booktabs="true" tabularvalignment="middle">
22245 <column alignment="center" valignment="top" width="0pt">
22246 <column alignment="center" valignment="top">
22248 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
22251 \begin_layout Plain Layout
22257 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
22260 \begin_layout Plain Layout
22268 <cell alignment="center" valignment="top" leftline="true" usebox="none">
22271 \begin_layout Plain Layout
22279 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
22282 \begin_layout Plain Layout
22283 \begin_inset Formula $\hbar$
22293 <cell alignment="center" valignment="top" leftline="true" usebox="none">
22296 \begin_layout Plain Layout
22304 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
22307 \begin_layout Plain Layout
22308 \begin_inset Formula $\hslash$
22318 <cell alignment="center" valignment="top" leftline="true" usebox="none">
22321 \begin_layout Plain Layout
22329 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
22332 \begin_layout Plain Layout
22333 \begin_inset Formula $\clubsuit$
22343 <cell alignment="center" valignment="top" leftline="true" usebox="none">
22346 \begin_layout Plain Layout
22354 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
22357 \begin_layout Plain Layout
22358 \begin_inset Formula $\spadesuit$
22368 <cell alignment="center" valignment="top" leftline="true" usebox="none">
22371 \begin_layout Plain Layout
22379 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
22382 \begin_layout Plain Layout
22383 \begin_inset Formula $\bigstar$
22393 <cell alignment="center" valignment="top" leftline="true" usebox="none">
22396 \begin_layout Plain Layout
22404 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
22407 \begin_layout Plain Layout
22408 \begin_inset Formula $\blacklozenge$
22418 <cell alignment="center" valignment="top" leftline="true" usebox="none">
22421 \begin_layout Plain Layout
22429 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
22432 \begin_layout Plain Layout
22433 \begin_inset Formula $\blacktriangle$
22443 <cell alignment="center" valignment="top" leftline="true" usebox="none">
22446 \begin_layout Plain Layout
22454 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
22457 \begin_layout Plain Layout
22458 \begin_inset Formula $\blacktriangledown$
22468 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
22471 \begin_layout Plain Layout
22479 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
22482 \begin_layout Plain Layout
22483 \begin_inset Formula $\bullet$
22497 \begin_inset space \hfill{}
22501 \begin_inset Tabular
22502 <lyxtabular version="3" rows="10" columns="2">
22503 <features booktabs="true" tabularvalignment="middle">
22504 <column alignment="center" valignment="top" width="0pt">
22505 <column alignment="center" valignment="top" width="0pt">
22507 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
22510 \begin_layout Plain Layout
22516 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
22519 \begin_layout Plain Layout
22527 <cell alignment="center" valignment="top" leftline="true" usebox="none">
22530 \begin_layout Plain Layout
22538 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
22541 \begin_layout Plain Layout
22542 \begin_inset Formula $\diamondsuit$
22552 <cell alignment="center" valignment="top" rightline="true" usebox="none">
22555 \begin_layout Plain Layout
22563 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
22566 \begin_layout Plain Layout
22567 \begin_inset Formula $\Diamond$
22577 <cell alignment="center" valignment="top" leftline="true" usebox="none">
22580 \begin_layout Plain Layout
22588 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
22591 \begin_layout Plain Layout
22592 \begin_inset Formula $\heartsuit$
22602 <cell alignment="center" valignment="top" leftline="true" usebox="none">
22605 \begin_layout Plain Layout
22613 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
22616 \begin_layout Plain Layout
22617 \begin_inset Formula $\P$
22627 <cell alignment="center" valignment="top" leftline="true" usebox="none">
22630 \begin_layout Plain Layout
22638 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
22641 \begin_layout Plain Layout
22642 \begin_inset Formula $\copyright$
22652 <cell alignment="center" valignment="top" leftline="true" usebox="none">
22655 \begin_layout Plain Layout
22663 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
22666 \begin_layout Plain Layout
22667 \begin_inset Formula $\circledR$
22677 <cell alignment="center" valignment="top" leftline="true" usebox="none">
22680 \begin_layout Plain Layout
22688 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
22691 \begin_layout Plain Layout
22692 \begin_inset Formula $\maltese$
22702 <cell alignment="center" valignment="top" leftline="true" usebox="none">
22705 \begin_layout Plain Layout
22713 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
22716 \begin_layout Plain Layout
22717 \begin_inset Formula $\diagup$
22727 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
22730 \begin_layout Plain Layout
22738 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
22741 \begin_layout Plain Layout
22742 \begin_inset Formula $\diagdown$
22758 \begin_layout Standard
22759 \begin_inset VSpace medskip
22765 \begin_layout Standard
22766 Some symbols can be displayed in different sizes, see
22767 \begin_inset CommandInset ref
22769 reference "subsec:Font-Sizes"
22776 \begin_layout Subsection
22778 \begin_inset Index idx
22781 \begin_layout Plain Layout
22782 Symbols ! Euro-symbol
22788 \begin_inset Index idx
22791 \begin_layout Plain Layout
22798 \begin_layout Plain Layout
22815 \begin_layout Standard
22816 To use the Euro symbol in formulas, the \SpecialChar LaTeX
22822 \begin_inset Index idx
22825 \begin_layout Plain Layout
22831 must be installed and loaded with the \SpecialChar LaTeX
22835 \begin_layout Standard
22840 usepackage[gennarrow]{eurosym}
22843 \begin_layout Standard
22844 The Euro symbol can now be inserted with the command
22851 \begin_inset Index idx
22854 \begin_layout Plain Layout
22865 \begin_layout Standard
22866 The Euro symbol can directly be inserted with the € key in mathematical
22867 text, without having
22882 can also be inserted in \SpecialChar TeX
22884 The official currency symbol can then be inserted with the command
22891 \begin_inset Index idx
22894 \begin_layout Plain Layout
22902 , that is only available in \SpecialChar TeX
22906 \begin_layout Standard
22910 \begin_layout Plain Layout
22920 \begin_inset Note Note
22923 \begin_layout Plain Layout
22924 The following table will only be displayed when the \SpecialChar LaTeX
22937 \begin_layout Standard
22938 An overview about the different Euro symbols:
22941 \begin_layout Standard
22943 \begin_inset Tabular
22944 <lyxtabular version="3" rows="4" columns="3">
22945 <features booktabs="true" tabularvalignment="middle">
22946 <column alignment="center" valignment="top" width="0pt">
22947 <column alignment="center" valignment="top" width="0pt">
22948 <column alignment="center" valignment="top" width="0pt">
22950 <cell alignment="center" valignment="top" bottomline="true" usebox="none">
22953 \begin_layout Plain Layout
22957 \begin_layout Plain Layout
22961 cmidrule[0.08em]{2-3}
22971 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
22974 \begin_layout Plain Layout
22980 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
22983 \begin_layout Plain Layout
22991 <cell alignment="center" valignment="top" leftline="true" usebox="none">
22994 \begin_layout Plain Layout
23000 <cell alignment="center" valignment="top" leftline="true" usebox="none">
23003 \begin_layout Plain Layout
23011 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
23014 \begin_layout Plain Layout
23015 \begin_inset Formula $\euro$
23025 <cell alignment="center" valignment="top" leftline="true" usebox="none">
23028 \begin_layout Plain Layout
23034 <cell alignment="center" valignment="top" leftline="true" usebox="none">
23037 \begin_layout Plain Layout
23043 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
23046 \begin_layout Plain Layout
23047 \begin_inset Formula $\mbox{€}$
23057 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
23060 \begin_layout Plain Layout
23067 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
23070 \begin_layout Plain Layout
23078 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
23081 \begin_layout Plain Layout
23085 \begin_layout Plain Layout
23105 \begin_inset Note Note
23108 \begin_layout Plain Layout
23115 is used here only for table borders.
23125 manual for details.
23133 \begin_layout Standard
23137 \begin_layout Plain Layout
23147 \begin_inset Note Note
23150 \begin_layout Plain Layout
23151 The following will be displayed when the \SpecialChar LaTeX
23164 \begin_layout Standard
23165 You need to install the \SpecialChar LaTeX
23170 to see the rest of this subsection in the output.
23173 \begin_layout Standard
23177 \begin_layout Plain Layout
23189 \begin_layout Section
23191 \begin_inset CommandInset label
23193 name "sec:Relations"
23198 \begin_inset Index idx
23201 \begin_layout Plain Layout
23208 \begin_inset Index idx
23211 \begin_layout Plain Layout
23216 \begin_layout Plain Layout
23227 \begin_layout Plain Layout
23242 \begin_layout Standard
23243 All following relations can also be inserted via the toolbar button
23246 arg "math-insert \\leq"
23252 \begin_layout Standard
23253 \begin_inset Tabular
23254 <lyxtabular version="3" rows="17" columns="2">
23255 <features booktabs="true" tabularvalignment="middle">
23256 <column alignment="center" valignment="top" width="0pt">
23257 <column alignment="center" valignment="top" width="0pt">
23259 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
23262 \begin_layout Plain Layout
23268 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
23271 \begin_layout Plain Layout
23279 <cell alignment="center" valignment="top" leftline="true" usebox="none">
23282 \begin_layout Plain Layout
23288 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
23291 \begin_layout Plain Layout
23292 \begin_inset Formula $<$
23302 <cell alignment="center" valignment="top" leftline="true" usebox="none">
23305 \begin_layout Plain Layout
23313 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
23316 \begin_layout Plain Layout
23317 \begin_inset Formula $\le$
23327 <cell alignment="center" valignment="top" leftline="true" usebox="none">
23330 \begin_layout Plain Layout
23338 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
23341 \begin_layout Plain Layout
23342 \begin_inset Formula $\ll$
23352 <cell alignment="center" valignment="top" leftline="true" usebox="none">
23355 \begin_layout Plain Layout
23363 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
23366 \begin_layout Plain Layout
23367 \begin_inset Formula $\prec$
23377 <cell alignment="center" valignment="top" leftline="true" usebox="none">
23380 \begin_layout Plain Layout
23388 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
23391 \begin_layout Plain Layout
23392 \begin_inset Formula $\preceq$
23402 <cell alignment="center" valignment="top" leftline="true" usebox="none">
23405 \begin_layout Plain Layout
23413 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
23416 \begin_layout Plain Layout
23417 \begin_inset Formula $\subset$
23427 <cell alignment="center" valignment="top" leftline="true" usebox="none">
23430 \begin_layout Plain Layout
23438 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
23441 \begin_layout Plain Layout
23442 \begin_inset Formula $\subseteq$
23452 <cell alignment="center" valignment="top" leftline="true" usebox="none">
23455 \begin_layout Plain Layout
23463 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
23466 \begin_layout Plain Layout
23467 \begin_inset Formula $\sqsubseteq$
23477 <cell alignment="center" valignment="top" leftline="true" usebox="none">
23480 \begin_layout Plain Layout
23488 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
23491 \begin_layout Plain Layout
23492 \begin_inset Formula $\in$
23502 <cell alignment="center" valignment="top" leftline="true" usebox="none">
23505 \begin_layout Plain Layout
23513 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
23516 \begin_layout Plain Layout
23517 \begin_inset Formula $\vdash$
23527 <cell alignment="center" valignment="top" leftline="true" usebox="none">
23530 \begin_layout Plain Layout
23538 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
23541 \begin_layout Plain Layout
23542 \begin_inset Formula $\smile$
23552 <cell alignment="center" valignment="top" leftline="true" usebox="none">
23555 \begin_layout Plain Layout
23563 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
23566 \begin_layout Plain Layout
23567 \begin_inset Formula $\lhd$
23577 <cell alignment="center" valignment="top" leftline="true" usebox="none">
23580 \begin_layout Plain Layout
23588 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
23591 \begin_layout Plain Layout
23592 \begin_inset Formula $\unlhd$
23602 <cell alignment="center" valignment="top" leftline="true" usebox="none">
23605 \begin_layout Plain Layout
23613 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
23616 \begin_layout Plain Layout
23617 \begin_inset Formula $\gtrless$
23627 <cell alignment="center" valignment="top" leftline="true" usebox="none">
23630 \begin_layout Plain Layout
23638 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
23641 \begin_layout Plain Layout
23642 \begin_inset Formula $\mid$
23652 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
23655 \begin_layout Plain Layout
23663 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
23666 \begin_layout Plain Layout
23667 \begin_inset Formula $\nmid$
23681 \begin_inset space \hfill{}
23685 \begin_inset Tabular
23686 <lyxtabular version="3" rows="17" columns="2">
23687 <features booktabs="true" tabularvalignment="middle">
23688 <column alignment="center" valignment="top" width="0pt">
23689 <column alignment="center" valignment="top" width="0pt">
23691 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
23694 \begin_layout Plain Layout
23700 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
23703 \begin_layout Plain Layout
23711 <cell alignment="center" valignment="top" leftline="true" usebox="none">
23714 \begin_layout Plain Layout
23720 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
23723 \begin_layout Plain Layout
23724 \begin_inset Formula $=$
23734 <cell alignment="center" valignment="top" leftline="true" usebox="none">
23737 \begin_layout Plain Layout
23745 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
23748 \begin_layout Plain Layout
23749 \begin_inset Formula $\not=$
23759 <cell alignment="center" valignment="top" leftline="true" usebox="none">
23762 \begin_layout Plain Layout
23770 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
23773 \begin_layout Plain Layout
23774 \begin_inset Formula $\equiv$
23784 <cell alignment="center" valignment="top" leftline="true" usebox="none">
23787 \begin_layout Plain Layout
23795 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
23798 \begin_layout Plain Layout
23799 \begin_inset Formula $\sim$
23809 <cell alignment="center" valignment="top" leftline="true" usebox="none">
23812 \begin_layout Plain Layout
23820 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
23823 \begin_layout Plain Layout
23824 \begin_inset Formula $\simeq$
23834 <cell alignment="center" valignment="top" leftline="true" usebox="none">
23837 \begin_layout Plain Layout
23845 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
23848 \begin_layout Plain Layout
23849 \begin_inset Formula $\approx$
23859 <cell alignment="center" valignment="top" leftline="true" usebox="none">
23862 \begin_layout Plain Layout
23870 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
23873 \begin_layout Plain Layout
23874 \begin_inset Formula $\cong$
23884 <cell alignment="center" valignment="top" leftline="true" usebox="none">
23887 \begin_layout Plain Layout
23895 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
23898 \begin_layout Plain Layout
23899 \begin_inset Formula $\bowtie$
23909 <cell alignment="center" valignment="top" leftline="true" usebox="none">
23912 \begin_layout Plain Layout
23920 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
23923 \begin_layout Plain Layout
23924 \begin_inset Formula $\notin$
23934 <cell alignment="center" valignment="top" leftline="true" usebox="none">
23937 \begin_layout Plain Layout
23945 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
23948 \begin_layout Plain Layout
23949 \begin_inset Formula $\perp$
23959 <cell alignment="center" valignment="top" leftline="true" usebox="none">
23962 \begin_layout Plain Layout
23970 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
23973 \begin_layout Plain Layout
23974 \begin_inset Formula $\propto$
23984 <cell alignment="center" valignment="top" leftline="true" usebox="none">
23987 \begin_layout Plain Layout
23995 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
23998 \begin_layout Plain Layout
23999 \begin_inset Formula $\asymp$
24009 <cell alignment="center" valignment="top" leftline="true" usebox="none">
24012 \begin_layout Plain Layout
24020 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
24023 \begin_layout Plain Layout
24024 \begin_inset Formula $\doteq$
24034 <cell alignment="center" valignment="top" leftline="true" usebox="none">
24037 \begin_layout Plain Layout
24045 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
24048 \begin_layout Plain Layout
24049 \begin_inset Formula $\circeq$
24059 <cell alignment="center" valignment="top" leftline="true" usebox="none">
24062 \begin_layout Plain Layout
24070 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
24073 \begin_layout Plain Layout
24074 \begin_inset Formula $\models$
24084 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
24087 \begin_layout Plain Layout
24095 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
24098 \begin_layout Plain Layout
24099 \begin_inset Formula $\widehat{=}$
24113 \begin_inset space \hfill{}
24117 \begin_inset Tabular
24118 <lyxtabular version="3" rows="17" columns="2">
24119 <features booktabs="true" tabularvalignment="middle">
24120 <column alignment="center" valignment="top" width="0pt">
24121 <column alignment="center" valignment="top" width="0pt">
24123 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
24126 \begin_layout Plain Layout
24132 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
24135 \begin_layout Plain Layout
24143 <cell alignment="center" valignment="top" leftline="true" usebox="none">
24146 \begin_layout Plain Layout
24152 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
24155 \begin_layout Plain Layout
24156 \begin_inset Formula $>$
24166 <cell alignment="center" valignment="top" leftline="true" usebox="none">
24169 \begin_layout Plain Layout
24177 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
24180 \begin_layout Plain Layout
24181 \begin_inset Formula $\ge$
24191 <cell alignment="center" valignment="top" leftline="true" usebox="none">
24194 \begin_layout Plain Layout
24202 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
24205 \begin_layout Plain Layout
24206 \begin_inset Formula $\gg$
24216 <cell alignment="center" valignment="top" leftline="true" usebox="none">
24219 \begin_layout Plain Layout
24227 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
24230 \begin_layout Plain Layout
24231 \begin_inset Formula $\succ$
24241 <cell alignment="center" valignment="top" leftline="true" usebox="none">
24244 \begin_layout Plain Layout
24252 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
24255 \begin_layout Plain Layout
24256 \begin_inset Formula $\succeq$
24266 <cell alignment="center" valignment="top" leftline="true" usebox="none">
24269 \begin_layout Plain Layout
24277 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
24280 \begin_layout Plain Layout
24281 \begin_inset Formula $\supset$
24291 <cell alignment="center" valignment="top" leftline="true" usebox="none">
24294 \begin_layout Plain Layout
24302 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
24305 \begin_layout Plain Layout
24306 \begin_inset Formula $\supseteq$
24316 <cell alignment="center" valignment="top" leftline="true" usebox="none">
24319 \begin_layout Plain Layout
24327 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
24330 \begin_layout Plain Layout
24331 \begin_inset Formula $\sqsupseteq$
24341 <cell alignment="center" valignment="top" leftline="true" usebox="none">
24344 \begin_layout Plain Layout
24352 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
24355 \begin_layout Plain Layout
24356 \begin_inset Formula $\ni$
24366 <cell alignment="center" valignment="top" leftline="true" usebox="none">
24369 \begin_layout Plain Layout
24377 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
24380 \begin_layout Plain Layout
24381 \begin_inset Formula $\dashv$
24391 <cell alignment="center" valignment="top" leftline="true" usebox="none">
24394 \begin_layout Plain Layout
24402 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
24405 \begin_layout Plain Layout
24406 \begin_inset Formula $\frown$
24416 <cell alignment="center" valignment="top" leftline="true" usebox="none">
24419 \begin_layout Plain Layout
24427 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
24430 \begin_layout Plain Layout
24431 \begin_inset Formula $\rhd$
24441 <cell alignment="center" valignment="top" leftline="true" usebox="none">
24444 \begin_layout Plain Layout
24452 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
24455 \begin_layout Plain Layout
24456 \begin_inset Formula $\unrhd$
24466 <cell alignment="center" valignment="top" leftline="true" usebox="none">
24469 \begin_layout Plain Layout
24477 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
24480 \begin_layout Plain Layout
24481 \begin_inset Formula $\lessgtr$
24491 <cell alignment="center" valignment="top" leftline="true" usebox="none">
24494 \begin_layout Plain Layout
24502 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
24505 \begin_layout Plain Layout
24506 \begin_inset Formula $\parallel$
24516 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
24519 \begin_layout Plain Layout
24527 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
24530 \begin_layout Plain Layout
24531 \begin_inset Formula $\nparallel$
24547 \begin_layout Standard
24548 \begin_inset VSpace medskip
24563 are bigger than the equal looking operators
24578 \begin_layout Standard
24580 supports also many special relations.
24581 Use the toolbar button
24584 arg "math-insert \\leqq"
24587 to see a list of these relations.
24590 \begin_layout Standard
24591 Relations are, in contrary to symbols, always surrounded by space.
24594 \begin_layout Standard
24595 Relations with labels can be created with the command
24602 \begin_inset Index idx
24605 \begin_layout Plain Layout
24616 \begin_layout Standard
24618 \begin_inset Tabular
24619 <lyxtabular version="3" rows="2" columns="2">
24620 <features booktabs="true" tabularvalignment="middle">
24621 <column alignment="center" valignment="top" width="0pt">
24622 <column alignment="center" valignment="top">
24624 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
24627 \begin_layout Plain Layout
24633 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
24636 \begin_layout Plain Layout
24643 <row topspace="1.5mm">
24644 <cell alignment="center" valignment="top" bottomline="true" usebox="none">
24647 \begin_layout Plain Layout
24651 \begin_inset space \textvisiblespace{}
24659 \begin_inset space \textvisiblespace{}
24663 \begin_inset Formula $\downarrow$
24669 \begin_inset space \textvisiblespace{}
24673 \begin_inset space \textvisiblespace{}
24681 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
24684 \begin_layout Plain Layout
24685 \begin_inset Formula $A(r)\stackrel{r\to\infty}{\approx}B$
24701 \begin_layout Section
24705 \begin_layout Subsection
24706 Predefined Functions
24707 \begin_inset CommandInset label
24709 name "subsec:Predefined-Functions"
24714 \begin_inset Index idx
24717 \begin_layout Plain Layout
24718 Functions ! predefined
24726 \begin_layout Standard
24727 In general, variables are set
24731 in mathematical expressions, but not function names, because
24732 \begin_inset Formula $sin$
24735 could be misunderstood as
24736 \begin_inset Formula $s\cdot i\cdot n$
24740 Therefore there are predefined functions which are additionally a bit separated
24742 They are inserted as commands starting with a backslash before their name.
24745 \begin_layout Standard
24747 \begin_inset Tabular
24748 <lyxtabular version="3" rows="2" columns="2">
24749 <features booktabs="true" tabularvalignment="middle">
24750 <column alignment="center" valignment="top" width="0pt">
24751 <column alignment="center" valignment="top" width="0pt">
24753 <cell alignment="center" valignment="top" topline="true" bottomline="true" usebox="none">
24756 \begin_layout Plain Layout
24762 <cell alignment="center" valignment="top" topline="true" bottomline="true" rightline="true" usebox="none">
24765 \begin_layout Plain Layout
24773 <cell alignment="center" valignment="top" bottomline="true" usebox="none">
24776 \begin_layout Plain Layout
24782 <cell alignment="center" valignment="top" bottomline="true" rightline="true" usebox="none">
24785 \begin_layout Plain Layout
24786 \begin_inset Formula $Asin(x)+B$
24800 \begin_inset space \quad{}
24804 \begin_inset Tabular
24805 <lyxtabular version="3" rows="2" columns="2">
24806 <features booktabs="true" tabularvalignment="middle">
24807 <column alignment="center" valignment="top" width="0pt">
24808 <column alignment="center" valignment="top" width="0pt">
24810 <cell alignment="center" valignment="top" topline="true" bottomline="true" usebox="none">
24813 \begin_layout Plain Layout
24819 <cell alignment="center" valignment="top" topline="true" bottomline="true" usebox="none">
24822 \begin_layout Plain Layout
24830 <cell alignment="center" valignment="top" bottomline="true" usebox="none">
24833 \begin_layout Plain Layout
24841 <cell alignment="center" valignment="top" bottomline="true" usebox="none">
24844 \begin_layout Plain Layout
24845 \begin_inset Formula $A\sin(x)+B$
24861 \begin_layout Standard
24862 The following functions are predefined:
24865 \begin_layout Standard
24866 \begin_inset VSpace -2mm
24872 \begin_layout Standard
24874 \begin_inset Tabular
24875 <lyxtabular version="3" rows="9" columns="4">
24876 <features booktabs="true" tabularvalignment="middle">
24877 <column alignment="center" valignment="top" width="0pt">
24878 <column alignment="center" valignment="top" width="0pt">
24879 <column alignment="center" valignment="top" width="0pt">
24880 <column alignment="center" valignment="top" width="0pt">
24882 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
24885 \begin_layout Plain Layout
24891 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
24894 \begin_layout Plain Layout
24900 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
24903 \begin_layout Plain Layout
24909 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
24912 \begin_layout Plain Layout
24920 <cell alignment="center" valignment="top" leftline="true" usebox="none">
24923 \begin_layout Plain Layout
24931 <cell alignment="center" valignment="top" leftline="true" usebox="none">
24934 \begin_layout Plain Layout
24942 <cell alignment="center" valignment="top" leftline="true" usebox="none">
24945 \begin_layout Plain Layout
24953 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
24956 \begin_layout Plain Layout
24966 <cell alignment="center" valignment="top" leftline="true" usebox="none">
24969 \begin_layout Plain Layout
24977 <cell alignment="center" valignment="top" leftline="true" usebox="none">
24980 \begin_layout Plain Layout
24988 <cell alignment="center" valignment="top" leftline="true" usebox="none">
24991 \begin_layout Plain Layout
24999 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
25002 \begin_layout Plain Layout
25012 <cell alignment="center" valignment="top" leftline="true" usebox="none">
25015 \begin_layout Plain Layout
25023 <cell alignment="center" valignment="top" leftline="true" usebox="none">
25026 \begin_layout Plain Layout
25034 <cell alignment="center" valignment="top" leftline="true" usebox="none">
25037 \begin_layout Plain Layout
25045 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
25048 \begin_layout Plain Layout
25058 <cell alignment="center" valignment="top" leftline="true" usebox="none">
25061 \begin_layout Plain Layout
25069 <cell alignment="center" valignment="top" leftline="true" usebox="none">
25072 \begin_layout Plain Layout
25080 <cell alignment="center" valignment="top" leftline="true" usebox="none">
25083 \begin_layout Plain Layout
25091 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
25094 \begin_layout Plain Layout
25104 <cell alignment="center" valignment="top" leftline="true" usebox="none">
25107 \begin_layout Plain Layout
25115 <cell alignment="center" valignment="top" leftline="true" usebox="none">
25118 \begin_layout Plain Layout
25126 <cell alignment="center" valignment="top" leftline="true" usebox="none">
25129 \begin_layout Plain Layout
25137 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
25140 \begin_layout Plain Layout
25150 <cell alignment="center" valignment="top" leftline="true" usebox="none">
25153 \begin_layout Plain Layout
25161 <cell alignment="center" valignment="top" leftline="true" usebox="none">
25164 \begin_layout Plain Layout
25172 <cell alignment="center" valignment="top" leftline="true" usebox="none">
25175 \begin_layout Plain Layout
25183 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
25186 \begin_layout Plain Layout
25196 <cell alignment="center" valignment="top" leftline="true" usebox="none">
25199 \begin_layout Plain Layout
25207 <cell alignment="center" valignment="top" leftline="true" usebox="none">
25210 \begin_layout Plain Layout
25218 <cell alignment="center" valignment="top" leftline="true" usebox="none">
25221 \begin_layout Plain Layout
25229 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
25232 \begin_layout Plain Layout
25242 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
25245 \begin_layout Plain Layout
25253 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
25256 \begin_layout Plain Layout
25264 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
25267 \begin_layout Plain Layout
25275 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
25278 \begin_layout Plain Layout
25294 \begin_layout Standard
25295 They can also be inserted with the math toolbar button
25298 arg "math-insert \\functions"
25304 \begin_layout Subsection
25305 Self-defined Functions
25306 \begin_inset Index idx
25309 \begin_layout Plain Layout
25310 Functions ! self-defined
25318 \begin_layout Standard
25319 To use a function that is not predefined, like for example the sign function
25320 sgn(x), there are two possibilities:
25323 \begin_layout Itemize
25324 Define the function by inserting the following line to the \SpecialChar LaTeX
25329 \begin_layout Plain Layout
25334 DeclareMathOperator
25337 \begin_inset CommandInset ref
25339 reference "subsec:Self-defined-Operators"
25349 \begin_inset Newline newline
25353 \begin_inset VSpace -3mm
25357 \begin_inset Newline newline
25364 DeclareMathOperator{
25369 \begin_inset Index idx
25372 \begin_layout Plain Layout
25377 DeclareMathOperator
25383 \begin_inset Newline newline
25387 \begin_inset VSpace -2mm
25391 \begin_inset Newline newline
25394 Now the new defined function can be called with the command
25403 \begin_layout Itemize
25404 Write the formula as usual, mark the formula name, in our example the letters
25409 , and change it to mathematical text.
25410 Finally, a space is inserted between prefactor and function.
25413 \begin_layout Standard
25414 The result is the same with both methods as with a predefined function
25418 \begin_layout Plain Layout
25419 In \SpecialChar LyX
25420 self-defined functions are displayed red, predefined ones black.
25428 \begin_layout Standard
25430 \begin_inset Tabular
25431 <lyxtabular version="3" rows="3" columns="2">
25432 <features booktabs="true" tabularvalignment="middle">
25433 <column alignment="center" valignment="top" width="0pt">
25434 <column alignment="center" valignment="top" width="0pt">
25436 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
25439 \begin_layout Plain Layout
25445 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
25448 \begin_layout Plain Layout
25456 <cell alignment="center" valignment="top" leftline="true" usebox="none">
25459 \begin_layout Plain Layout
25467 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
25470 \begin_layout Plain Layout
25471 \begin_inset Formula $A\sgn(x)+B$
25481 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
25484 \begin_layout Plain Layout
25488 \begin_inset Formula $\underbrace{\textrm{sgn}}_{\textrm{Alt+M}\,\textrm{M}}$
25496 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
25499 \begin_layout Plain Layout
25500 \begin_inset Formula $A\,\textrm{sgn}(x)+B$
25516 \begin_layout Standard
25517 The first method is more suitable when the self-defined function should
25518 be used several times.
25521 \begin_layout Subsection
25523 \begin_inset Index idx
25526 \begin_layout Plain Layout
25535 \begin_layout Standard
25536 For limits, in addition to the commands
25543 \begin_inset Index idx
25546 \begin_layout Plain Layout
25566 the following functions are defined:
25569 \begin_layout Standard
25571 \begin_inset Tabular
25572 <lyxtabular version="3" rows="5" columns="2">
25573 <features booktabs="true" tabularvalignment="middle">
25574 <column alignment="center" valignment="top" width="0pt">
25575 <column alignment="center" valignment="top" width="0pt">
25577 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
25580 \begin_layout Plain Layout
25586 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
25589 \begin_layout Plain Layout
25597 <cell alignment="center" valignment="top" leftline="true" usebox="none">
25600 \begin_layout Plain Layout
25608 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
25611 \begin_layout Plain Layout
25612 \begin_inset Formula $\varliminf$
25621 <row topspace="1.5mm">
25622 <cell alignment="center" valignment="top" usebox="none">
25625 \begin_layout Plain Layout
25633 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
25636 \begin_layout Plain Layout
25637 \begin_inset Formula $\varlimsup$
25646 <row topspace="1.5mm">
25647 <cell alignment="center" valignment="top" usebox="none">
25650 \begin_layout Plain Layout
25658 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
25661 \begin_layout Plain Layout
25662 \begin_inset Formula $\varprojlim$
25671 <row topspace="1.5mm" bottomspace="1mm">
25672 <cell alignment="center" valignment="top" bottomline="true" usebox="none">
25675 \begin_layout Plain Layout
25683 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
25686 \begin_layout Plain Layout
25687 \begin_inset Formula $\varinjlim$
25703 \begin_layout Standard
25704 \begin_inset VSpace medskip
25707 The limit is created by inserting a subscript.
25708 It is set right beside the function in an inline formula:
25711 \begin_layout Standard
25713 \begin_inset Tabular
25714 <lyxtabular version="3" rows="2" columns="2">
25715 <features booktabs="true" tabularvalignment="middle">
25716 <column alignment="center" valignment="top" width="0pt">
25717 <column alignment="center" valignment="top" width="0pt">
25719 <cell alignment="center" valignment="top" bottomline="true" usebox="none">
25722 \begin_layout Plain Layout
25728 <cell alignment="center" valignment="top" bottomline="true" usebox="none">
25731 \begin_layout Plain Layout
25739 <cell alignment="center" valignment="top" usebox="none">
25742 \begin_layout Plain Layout
25748 \begin_inset space \textvisiblespace{}
25752 \begin_inset space \textvisiblespace{}
25760 <cell alignment="center" valignment="top" usebox="none">
25763 \begin_layout Plain Layout
25764 \begin_inset Formula $\lim_{x\to A}x=B$
25780 \begin_layout Standard
25781 In a displayed formula the limit is set below the formula, as usual:
25782 \begin_inset Formula
25792 \begin_layout Standard
25793 \begin_inset VSpace medskip
25799 \begin_layout Standard
25800 How to adjust the typesetting of the limits see
25801 \begin_inset CommandInset ref
25803 reference "subsec:Operator-Limits"
25810 \begin_layout Subsection
25812 \begin_inset Index idx
25815 \begin_layout Plain Layout
25816 Functions ! modulo-
25824 \begin_layout Standard
25825 The modulo-function is special, because it exists in four variants.
25826 The variants in a displayed formula are:
25827 \begin_inset Formula
25829 \underline{\textrm{Command}\raisebox{-0.9mm}{}} & & \underline{\textrm{Result}}\\
25830 \mathrm{a\backslash mod\textrm{␣}b} & & a\mod b\\
25831 \mathrm{a\backslash pmod\textrm{␣}b} & & a\pmod b\\
25832 \mathrm{a\backslash bmod\textrm{␣}b} & & a\bmod b\\
25833 \mathrm{a\backslash pod\textrm{␣}b} & & a\pod b
25841 \begin_layout Standard
25842 In an inline formula less space is set before the function names for all
25844 By default the modulo-functions take only the first following character
25846 To use more than one character, one has to put them into \SpecialChar TeX
25848 \begin_inset Formula
25850 \underline{\textrm{Command}\raisebox{-0.9mm}{}} & & \underline{\textrm{Result}}\\
25851 \mathrm{a\backslash pod\textrm{␣}bcd} & & a\pod bcd\\
25852 \mathrm{a\backslash pod\backslash\{bc\to d} & & a\pod{bc}d
25860 \begin_layout Section
25862 \begin_inset Index idx
25865 \begin_layout Plain Layout
25874 \begin_layout Standard
25875 The characters ^ and _ would normally create a superscript and subscript,
25877 To get these characters you have to insert them with a leading
25882 \begin_layout Standard
25885 \begin_inset Tabular
25886 <lyxtabular version="3" rows="3" columns="2">
25887 <features booktabs="true" tabularvalignment="middle">
25888 <column alignment="left" valignment="top" width="0pt">
25889 <column alignment="block" valignment="top">
25891 <cell alignment="left" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
25894 \begin_layout Plain Layout
25900 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
25903 \begin_layout Plain Layout
25911 <cell alignment="left" valignment="top" leftline="true" usebox="none">
25914 \begin_layout Plain Layout
25918 \begin_inset space \textvisiblespace{}
25926 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
25929 \begin_layout Plain Layout
25930 \begin_inset Formula $\mathcircumflex$
25940 <cell alignment="left" valignment="top" bottomline="true" leftline="true" usebox="none">
25943 \begin_layout Plain Layout
25951 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
25954 \begin_layout Plain Layout
25955 \begin_inset Formula $\_$
25971 \begin_layout Subsection
25972 Special Characters in Mathematical Text
25975 \begin_layout Standard
25976 The following commands can only be used in mathematical text or in \SpecialChar TeX
25980 \begin_layout Standard
25981 \begin_inset space \hfill{}
25985 \begin_inset Tabular
25986 <lyxtabular version="3" rows="8" columns="2">
25987 <features booktabs="true" tabularvalignment="middle">
25988 <column alignment="left" valignment="top" width="0pt">
25989 <column alignment="block" valignment="top">
25991 <cell alignment="left" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
25994 \begin_layout Plain Layout
26000 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
26003 \begin_layout Plain Layout
26011 <cell alignment="left" valignment="top" leftline="true" usebox="none">
26014 \begin_layout Plain Layout
26022 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
26025 \begin_layout Plain Layout
26026 \begin_inset Formula $\textrm{œ}$
26036 <cell alignment="left" valignment="top" leftline="true" usebox="none">
26039 \begin_layout Plain Layout
26047 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
26050 \begin_layout Plain Layout
26051 \begin_inset Formula $\textrm{Œ}$
26061 <cell alignment="left" valignment="top" leftline="true" usebox="none">
26064 \begin_layout Plain Layout
26072 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
26075 \begin_layout Plain Layout
26076 \begin_inset Formula $\textrm{æ}$
26086 <cell alignment="left" valignment="top" leftline="true" usebox="none">
26089 \begin_layout Plain Layout
26097 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
26100 \begin_layout Plain Layout
26101 \begin_inset Formula $\textrm{Æ}$
26111 <cell alignment="left" valignment="top" leftline="true" usebox="none">
26114 \begin_layout Plain Layout
26122 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
26125 \begin_layout Plain Layout
26126 \begin_inset Formula $\textrm{å}$
26136 <cell alignment="left" valignment="top" leftline="true" usebox="none">
26139 \begin_layout Plain Layout
26143 \begin_inset Index idx
26146 \begin_layout Plain Layout
26153 \begin_layout Plain Layout
26174 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
26177 \begin_layout Plain Layout
26178 \begin_inset Formula $\textrm{Å}$
26188 <cell alignment="left" valignment="top" bottomline="true" leftline="true" usebox="none">
26191 \begin_layout Plain Layout
26199 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
26202 \begin_layout Plain Layout
26203 \begin_inset Formula $\textrm{ı}$
26217 \begin_inset space \hfill{}
26221 \begin_inset Tabular
26222 <lyxtabular version="3" rows="8" columns="2">
26223 <features booktabs="true" tabularvalignment="middle">
26224 <column alignment="left" valignment="top" width="0pt">
26225 <column alignment="center" valignment="top">
26227 <cell alignment="left" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
26230 \begin_layout Plain Layout
26232 \begin_inset Note Note
26235 \begin_layout Plain Layout
26237 \begin_inset space \thinspace{}
26240 mm is used for separation, because otherwise the output will be ¡ and ¿
26251 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
26254 \begin_layout Plain Layout
26262 <cell alignment="left" valignment="top" leftline="true" usebox="none">
26265 \begin_layout Plain Layout
26273 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
26276 \begin_layout Plain Layout
26277 \begin_inset Formula $\textrm{ø}$
26287 <cell alignment="left" valignment="top" leftline="true" usebox="none">
26290 \begin_layout Plain Layout
26298 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
26301 \begin_layout Plain Layout
26302 \begin_inset Formula $\textrm{Ø}$
26312 <cell alignment="left" valignment="top" leftline="true" usebox="none">
26315 \begin_layout Plain Layout
26323 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
26326 \begin_layout Plain Layout
26327 \begin_inset Formula $\textrm{ł}$
26337 <cell alignment="left" valignment="top" leftline="true" usebox="none">
26340 \begin_layout Plain Layout
26348 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
26351 \begin_layout Plain Layout
26352 \begin_inset Formula $\textrm{Ł}$
26362 <cell alignment="left" valignment="top" leftline="true" usebox="none">
26365 \begin_layout Plain Layout
26367 \begin_inset space \hspace{}
26372 \begin_inset space \textvisiblespace{}
26380 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
26383 \begin_layout Plain Layout
26384 \begin_inset Formula $\textrm{!`}$
26394 <cell alignment="left" valignment="top" leftline="true" usebox="none">
26397 \begin_layout Plain Layout
26399 \begin_inset space \hspace{}
26404 \begin_inset space \textvisiblespace{}
26412 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
26415 \begin_layout Plain Layout
26416 \begin_inset Formula $\textrm{?`}$
26426 <cell alignment="left" valignment="top" bottomline="true" leftline="true" usebox="none">
26429 \begin_layout Plain Layout
26437 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
26440 \begin_layout Plain Layout
26441 \begin_inset Formula $\textrm{ȷ}$
26455 \begin_inset space \hfill{}
26461 \begin_layout Standard
26463 \begin_inset Formula $\textrm{\textrm{Å}}$
26467 \begin_inset Formula $\textrm{\textrm{Ø}}$
26470 can also be inserted via the math toolbar button
26473 arg "math-insert \\digamma"
26479 \begin_layout Standard
26480 An exception are the commands
26483 \begin_inset space \hspace{}
26492 \begin_inset space \hspace{}
26498 , because they can be inserted in \SpecialChar LyX
26502 \begin_layout Subsection
26504 \begin_inset CommandInset label
26506 name "subsec:Accents-in-Text"
26511 \begin_inset Index idx
26514 \begin_layout Plain Layout
26523 \begin_layout Standard
26524 With the following commands all letters can be accented.
26525 The commands must be inserted in \SpecialChar TeX
26529 \begin_layout Standard
26530 \begin_inset space \hfill{}
26534 \begin_inset Tabular
26535 <lyxtabular version="3" rows="8" columns="2">
26536 <features booktabs="true" tabularvalignment="middle">
26537 <column alignment="left" valignment="top" width="0pt">
26538 <column alignment="block" valignment="top">
26540 <cell alignment="left" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
26543 \begin_layout Plain Layout
26549 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
26552 \begin_layout Plain Layout
26560 <cell alignment="left" valignment="top" leftline="true" usebox="none">
26563 \begin_layout Plain Layout
26567 \begin_inset Quotes grd
26575 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
26578 \begin_layout Plain Layout
26582 \begin_layout Plain Layout
26598 <cell alignment="left" valignment="top" leftline="true" usebox="none">
26601 \begin_layout Plain Layout
26609 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
26612 \begin_layout Plain Layout
26616 \begin_layout Plain Layout
26632 <cell alignment="left" valignment="top" leftline="true" usebox="none">
26635 \begin_layout Plain Layout
26639 \begin_inset space \textvisiblespace{}
26647 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
26650 \begin_layout Plain Layout
26654 \begin_layout Plain Layout
26670 <cell alignment="left" valignment="top" leftline="true" usebox="none">
26673 \begin_layout Plain Layout
26681 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
26684 \begin_layout Plain Layout
26688 \begin_layout Plain Layout
26704 <cell alignment="left" valignment="top" leftline="true" usebox="none">
26707 \begin_layout Plain Layout
26711 \begin_inset space \textvisiblespace{}
26719 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
26722 \begin_layout Plain Layout
26726 \begin_layout Plain Layout
26742 <cell alignment="left" valignment="top" leftline="true" usebox="none">
26745 \begin_layout Plain Layout
26749 \begin_inset space \textvisiblespace{}
26757 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
26760 \begin_layout Plain Layout
26764 \begin_layout Plain Layout
26780 <cell alignment="left" valignment="top" bottomline="true" leftline="true" usebox="none">
26783 \begin_layout Plain Layout
26787 \begin_inset space \textvisiblespace{}
26795 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
26798 \begin_layout Plain Layout
26802 \begin_layout Plain Layout
26822 \begin_inset space \hfill{}
26826 \begin_inset Tabular
26827 <lyxtabular version="3" rows="8" columns="2">
26828 <features booktabs="true" tabularvalignment="middle">
26829 <column alignment="left" valignment="top" width="0pt">
26830 <column alignment="center" valignment="top">
26832 <cell alignment="left" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
26835 \begin_layout Plain Layout
26841 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
26844 \begin_layout Plain Layout
26852 <cell alignment="left" valignment="top" leftline="true" usebox="none">
26855 \begin_layout Plain Layout
26859 \begin_inset space \textvisiblespace{}
26867 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
26870 \begin_layout Plain Layout
26874 \begin_layout Plain Layout
26890 <cell alignment="left" valignment="top" leftline="true" usebox="none">
26893 \begin_layout Plain Layout
26901 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
26904 \begin_layout Plain Layout
26908 \begin_layout Plain Layout
26924 <cell alignment="left" valignment="top" leftline="true" usebox="none">
26927 \begin_layout Plain Layout
26931 \begin_inset Index idx
26934 \begin_layout Plain Layout
26945 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
26948 \begin_layout Plain Layout
26952 \begin_layout Plain Layout
26968 <cell alignment="left" valignment="top" leftline="true" usebox="none">
26971 \begin_layout Plain Layout
26979 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
26982 \begin_layout Plain Layout
26986 \begin_layout Plain Layout
27002 <cell alignment="left" valignment="top" leftline="true" usebox="none">
27005 \begin_layout Plain Layout
27009 \begin_inset space \textvisiblespace{}
27017 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
27020 \begin_layout Plain Layout
27024 \begin_layout Plain Layout
27040 <cell alignment="left" valignment="top" leftline="true" usebox="none">
27043 \begin_layout Plain Layout
27047 \begin_inset space \textvisiblespace{}
27055 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
27058 \begin_layout Plain Layout
27062 \begin_layout Plain Layout
27078 <cell alignment="left" valignment="top" leftline="true" usebox="none">
27081 \begin_layout Plain Layout
27085 \begin_inset space \textvisiblespace{}
27093 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
27096 \begin_layout Plain Layout
27100 \begin_layout Plain Layout
27120 \begin_inset space \hfill{}
27126 \begin_layout Standard
27127 \begin_inset VSpace medskip
27136 also two different characters can be accented.
27142 \begin_inset space \textvisiblespace{}
27151 \begin_layout Plain Layout
27163 \begin_layout Standard
27176 can in combination with vowels directly be inserted with the keyboard without
27177 using \SpecialChar TeX
27179 The same applies for the tilde
27183 \begin_layout Plain Layout
27184 This only applies for keyboards where the tilde is defined as accent.
27193 in combination with
27208 \begin_layout Standard
27251 and accents that are inserted directly with the keyboard are also available
27252 in mathematical text.
27253 For the other accents there are special math commands to be used in formulas,
27255 \begin_inset CommandInset ref
27257 reference "subsec:Accents-for-one"
27264 \begin_layout Standard
27265 \begin_inset VSpace bigskip
27268 Furthermore, with the command
27275 \begin_inset Index idx
27278 \begin_layout Plain Layout
27286 all numbers and letters can be set into a circle, quasi accented with a
27287 circle, similar to the copyright symbol.
27290 \begin_layout Standard
27292 \begin_inset Tabular
27293 <lyxtabular version="3" rows="3" columns="2">
27294 <features booktabs="true" tabularvalignment="middle">
27295 <column alignment="center" valignment="top" width="0pt">
27296 <column alignment="center" valignment="top">
27298 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
27301 \begin_layout Plain Layout
27307 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
27310 \begin_layout Plain Layout
27318 <cell alignment="center" valignment="top" leftline="true" usebox="none">
27321 \begin_layout Plain Layout
27329 <cell multicolumn="1" alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
27332 \begin_layout Plain Layout
27336 \begin_layout Plain Layout
27351 <row topspace="1mm">
27352 <cell alignment="center" valignment="top" bottomline="true" usebox="none">
27355 \begin_layout Plain Layout
27366 raisebox{-1.5pt}{W}}
27371 <cell multicolumn="1" alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
27374 \begin_layout Plain Layout
27378 \begin_layout Plain Layout
27408 \begin_layout Standard
27409 One has to take care that the character fits in the circle.
27420 \begin_layout Plain Layout
27422 \begin_inset CommandInset ref
27424 reference "subsec:Font-Sizes"
27433 specifies thereby the size of the circle.
27444 \begin_layout Plain Layout
27446 \begin_inset CommandInset ref
27448 reference "subsec:Boxes-without-Frame"
27457 the character can be centered.
27460 \begin_layout Subsection
27462 \begin_inset Index idx
27465 \begin_layout Plain Layout
27474 \begin_layout Standard
27475 Old-style figures (also known as old-style numerals) are created with the
27483 \begin_inset Index idx
27486 \begin_layout Plain Layout
27495 The command can be used in formulas and in \SpecialChar TeX
27497 The command scheme is:
27500 \begin_layout Standard
27505 oldstylenums{number}
27508 \begin_layout Standard
27513 oldstylenums{0123456789
27516 \begin_inset Formula $\oldstylenums{0123456789}$
27522 \begin_layout Section
27524 \begin_inset CommandInset label
27526 name "sec:Formula-Styles"
27531 \begin_inset Index idx
27534 \begin_layout Plain Layout
27543 \begin_layout Itemize
27544 There are two different alignment styles:
27548 \begin_layout Description
27549 Centered is the predefined standard.
27552 \begin_layout Description
27553 Indented this can be set using the menu
27555 Document\SpecialChar menuseparator
27561 \begin_inset space ~
27567 \begin_layout Standard
27572 is used, the indentation can be adjusted.
27573 The default value depends on the used document class.
27577 \begin_layout Itemize
27578 And two different numbering styles that can be set in the menu
27580 Document\SpecialChar menuseparator
27586 \begin_inset space ~
27595 \begin_layout Description
27596 Right is in most cases the default.
27599 \begin_layout Description
27604 \begin_layout Standard
27605 The chosen styles are used for all displayed formulas of the document.
27606 When both, centered and indented formulas should be created in a document,
27612 The indented formulas are then set in a flalign environment, see
27613 \begin_inset CommandInset ref
27615 reference "subsec:Flalign-Environment"
27622 \begin_layout Section
27624 \begin_inset CommandInset label
27626 name "sec:Multiline-Formulas"
27631 \begin_inset Index idx
27634 \begin_layout Plain Layout
27635 Formula ! multiline
27643 \begin_layout Subsection
27647 \begin_layout Standard
27648 In \SpecialChar LyX
27649 multiline formulas are created by pressing
27652 arg "newline-insert newline"
27656 This creates either an
27660 that is described in
27661 \begin_inset CommandInset ref
27663 reference "subsec:Standard-align-Environment"
27667 or, when automatically loading the package
27671 is disabled in the document settings, an
27673 eqnarray environment
27675 that is described in
27676 \begin_inset CommandInset ref
27678 reference "subsec:Eqnarray-Environment"
27683 The align environment is recommended because it provides in any case a
27684 typographically correct output.
27687 \begin_layout Standard
27688 There are other multiline formula environments that can be created via the
27691 Insert\SpecialChar menuseparator
27695 These environments are described in the following sections.
27698 \begin_layout Standard
27699 In all multiline formula environments a new line is created by pressing
27703 arg "newline-insert newline"
27707 To add or delete lines, the math toolbar buttons
27710 arg "tabular-feature append-row"
27716 arg "tabular-feature delete-row"
27719 , respectively, or the menu
27721 Edit\SpecialChar menuseparator
27727 \begin_layout Subsubsection
27729 \begin_inset CommandInset label
27731 name "subsec:Line-Separation"
27736 \begin_inset Index idx
27739 \begin_layout Plain Layout
27740 Formula ! multiline ! Line separation
27748 \begin_layout Standard
27749 There is sometimes not enough space in multiline formulas between the lines:
27750 \begin_inset Formula
27752 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}\\
27753 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
27761 \begin_layout Standard
27762 In \SpecialChar LaTeX
27763 additional line space is specified as optional argument of the new line
27765 This is not yet possible in \SpecialChar LyX
27770 \begin_layout Plain Layout
27772 \begin_inset CommandInset href
27774 name "LyX-bug #1505"
27775 target "http://www.lyx.org/trac/ticket/1505"
27785 , therefore the whole formula must be inserted in \SpecialChar TeX
27787 To add in our example space, the command
27795 is inserted at the end of the first line.
27800 \begin_layout Plain Layout
27807 \begin_layout Plain Layout
27809 B^{2}(B^{2}-2r_{g}^{2}+2x_{0}^{2}-2r_{k}^{2})+4x_{0}^{2}x^{2}+4x_{0}xD &
27812 textrm{-}4x^{2}B^{2}+4x_{0}xB^{2}
27819 \begin_layout Plain Layout
27823 left(B^{2}+x_{0}^{2}
27831 left(B^{2}-2r_{g}^{2}+2x_{0}^{2}-2r_{k}^{2}
27836 \begin_layout Plain Layout
27848 \begin_layout Standard
27849 \begin_inset VSpace bigskip
27852 To set the line separation for all lines in a formula, the length
27859 \begin_inset Index idx
27862 \begin_layout Plain Layout
27872 \begin_inset Formula $\mbox{line separation}=\mathrm{6\,pt+\backslash jot}$
27883 \begin_inset space \thinspace{}
27888 \begin_inset space \thinspace{}
27891 mm additional line separation as in the previous example, the command
27894 \begin_layout Standard
27904 \begin_layout Standard
27905 is inserted in \SpecialChar TeX
27906 mode before the formula.
27907 This requires that the \SpecialChar LaTeX
27916 \begin_layout Plain Layout
27921 is part of every \SpecialChar LaTeX
27922 standard installation.
27928 \begin_inset Index idx
27931 \begin_layout Plain Layout
27937 was loaded in \SpecialChar LaTeX
27938 -preamble with the line
27941 \begin_layout Standard
27949 \begin_layout Standard
27954 \begin_layout Plain Layout
27966 \begin_inset Formula
27968 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}\\
27969 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
27977 \begin_layout Standard
27981 \begin_layout Plain Layout
27992 To get back to the predefined distance,
27998 is set to the value 3
27999 \begin_inset space \thinspace{}
28005 \begin_layout Subsubsection
28007 \begin_inset CommandInset label
28009 name "subsec:Column-Separation"
28014 \begin_inset Index idx
28017 \begin_layout Plain Layout
28018 Formula ! multiline ! Column separation
28026 \begin_layout Standard
28027 Multiline formulas form a matrix.
28028 A formula in the eqnarray environment is for example a matrix with three
28030 By changing the column separation in this environment, the space beside
28031 the relation sign can be changed.
28034 \begin_layout Standard
28035 The column separation is specified with the length
28042 \begin_inset Index idx
28045 \begin_layout Plain Layout
28054 \begin_inset Newline newline
28057 column separation = 2
28058 \begin_inset space \thinspace{}
28068 \begin_inset Newline newline
28074 \begin_layout Standard
28084 \begin_layout Standard
28085 inserted in \SpecialChar TeX
28086 mode, sets for all following formulas a column separation of
28088 \begin_inset space \thinspace{}
28092 To get back to the predefined distance,
28099 \begin_inset space \thinspace{}
28105 \begin_layout Standard
28107 \begin_inset space \thinspace{}
28110 cm column separation:
28114 \begin_layout Plain Layout
28126 \begin_inset Formula
28134 A formula with the predefined column separation for matrices of 10
28135 \begin_inset space \thinspace{}
28142 \begin_layout Plain Layout
28154 \begin_inset Formula
28165 \begin_layout Standard
28166 \begin_inset Newpage newpage
28172 \begin_layout Subsubsection
28174 \begin_inset Index idx
28177 \begin_layout Plain Layout
28186 \begin_layout Standard
28187 Long formulas can be typeset using these methods:
28190 \begin_layout Itemize
28191 When one side of the equation is much shorter than the line width, this
28192 one is chosen for the left side and the right side is typeset over two
28194 \begin_inset Formula
28196 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 \\
28197 & & -\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}
28202 The minus sign at the beginning of the second line does normally not appear
28203 as an operator because it is the first character of the line.
28204 Thus it would not be surrounded by space and could not be distinguished
28205 from the fraction bar.
28207 \begin_inset space \thinspace{}
28210 pt space was inserted behind the minus sign with the command
28220 \begin_layout Plain Layout
28228 \begin_inset CommandInset ref
28230 reference "subsec:Variable-Space"
28240 \begin_inset Index idx
28243 \begin_layout Plain Layout
28254 \begin_layout Itemize
28255 When both sides of the equation are too long, the command
28262 \begin_inset Index idx
28265 \begin_layout Plain Layout
28274 It is inserted in the first column of the first line and causes all further
28275 insertions to overwrite the following columns:
28276 \begin_inset Formula
28278 \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 \\
28279 & & -\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 \\
28280 & & =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}
28285 After the insertion of
28291 , the cursor is in a purple box that is a bit shifted to the left from the
28293 In this the formula is inserted.
28294 \begin_inset Newline newline
28297 The content of the further lines is inserted to the second or another formula
28299 The greater the column number where it was inserted, the larger the indentation.
28300 \begin_inset VSpace medskip
28304 \begin_inset Newline newline
28308 \begin_inset Note Greyedout
28311 \begin_layout Plain Layout
28312 Note the following when using
28321 \begin_layout Itemize
28322 The formula doesn't use the full page width.
28324 \begin_inset space \thinspace{}
28328 \begin_inset space \space{}
28332 \begin_inset Formula $-B^{2}$
28335 is added to the first line in the above example, it would have been outside
28337 To better use the width, negative space can be inserted at the beginning
28341 \begin_layout Itemize
28342 Due to a bug in \SpecialChar LyX
28343 the cursor cannot be set with the mouse into the first
28348 \begin_layout Plain Layout
28349 \begin_inset CommandInset href
28351 name "LyX-bug #1429"
28352 target "http://www.lyx.org/trac/ticket/1429"
28362 One can only set the cursor at the beginning of the line and move it with
28371 \begin_layout Itemize
28372 Other methods to set long formulas are offered by the environments described
28374 \begin_inset CommandInset ref
28376 reference "subsec:Multline-Environment"
28381 \begin_inset CommandInset ref
28383 reference "subsec:Multiline-Formula-Parts"
28390 \begin_layout Subsubsection
28391 Multiline Fractions
28392 \begin_inset CommandInset label
28394 name "subsec:Multiline-Fractions"
28399 \begin_inset Index idx
28402 \begin_layout Plain Layout
28403 Fractions ! multiline
28411 \begin_layout Standard
28412 There are cases where the denominator and/or the numerator of a fraction
28413 is so long that the fraction does not fit into one line.
28414 It is then necessary to add a line break within the fraction.
28415 This can be done using the command
28422 \begin_inset Index idx
28425 \begin_layout Plain Layout
28434 To activate it, set in the document settings under
28437 \begin_inset space ~
28447 \begin_inset Index idx
28450 \begin_layout Plain Layout
28451 Packages ! mathtools
28459 \begin_inset space ~
28474 \begin_layout Standard
28479 splitfrac{first line}{second line}
28482 \begin_layout Standard
28483 and is used as denominator and/or numerator:
28486 \begin_layout Standard
28487 \begin_inset Formula
28489 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}
28494 The command for the first numerator above is:
28497 \begin_layout Standard
28502 splitfrac{xy+xy+xy+xy+xy
28503 \begin_inset space \textvisiblespace{}
28511 \begin_layout Subsubsection
28513 \begin_inset CommandInset label
28515 name "subsec:Multiline-Brackets"
28520 \begin_inset Index idx
28523 \begin_layout Plain Layout
28524 Brackets ! for multiline expressions
28532 \begin_layout Standard
28533 For brackets spanning multiple lines the following problem occurs:
28534 \begin_inset Formula
28536 A & = & \sin(x)\left[\prod_{R=1}^{\infty}\frac{1}{R}+\cdots\right.\\
28537 & & \left.\cdots+B-D\right]
28545 \begin_layout Standard
28546 The closing bracket is smaller than the opening bracket because brackets
28547 with variable size may not span multiple lines.
28550 \begin_layout Standard
28551 To set the bracket size for the second line correctly, the first line is
28559 \begin_inset Index idx
28562 \begin_layout Plain Layout
28570 and the second line with
28578 \begin_layout Plain Layout
28592 \begin_inset CommandInset ref
28594 reference "subsec:Automatic-Bracket-Size"
28606 \begin_inset Index idx
28609 \begin_layout Plain Layout
28632 \begin_inset space \textvisiblespace{}
28642 \begin_inset space \textvisiblespace{}
28652 \begin_inset space \textvisiblespace{}
28658 \begin_inset Formula $\downarrow$
28664 \begin_inset Index idx
28667 \begin_layout Plain Layout
28675 is inserted, because the multiplication operator with its limits is the
28676 largest symbol in the first line and this should be the size for the bracket
28677 in the second line.
28680 \begin_layout Standard
28681 The result is this:
28682 \begin_inset Formula
28684 A & = & \sin(x)\left[\prod_{R=1}^{\infty}\frac{1}{R}+\cdots\right.\\
28685 & & \left.\vphantom{\prod_{R=1}^{\infty}}\cdots+B-D\right]
28693 \begin_layout Subsection
28697 \begin_layout Standard
28698 Align environments can be used for every kind of multiline formulas.
28699 They are especially useful to set several formulas side by side.
28702 \begin_layout Standard
28703 Align environments consist of columns.
28704 The odd columns are right aligned, the even ones left aligned.
28705 Every line in an Align environment can be numbered.
28708 \begin_layout Standard
28709 Align environments are created via the menu
28711 Insert\SpecialChar menuseparator
28717 Edit\SpecialChar menuseparator
28718 Math\SpecialChar menuseparator
28719 Change Formula Type
28721 already existing formulas can be converted to Align environments.
28724 \begin_layout Standard
28725 To add or delete columns, the math toolbar buttons
28728 arg "tabular-feature append-column"
28734 arg "tabular-feature delete-column"
28737 , respectively, or the menu
28739 Edit\SpecialChar menuseparator
28745 \begin_layout Subsubsection
28746 Standard align Environment
28747 \begin_inset CommandInset label
28749 name "subsec:Standard-align-Environment"
28754 \begin_inset Index idx
28757 \begin_layout Plain Layout
28758 Formula ! multiline ! align environment
28766 \begin_layout Standard
28767 This Align environment is created by pressing
28770 arg "newline-insert newline"
28773 in a formula or by the menu
28775 Insert\SpecialChar menuseparator
28776 Math\SpecialChar menuseparator
28777 AMS align Environment
28782 \begin_layout Standard
28783 An example for two formulas set side by side, that are created with a four
28784 column align environment:
28785 \begin_inset Formula
28787 A & =\sin(B) & C & =D\\
28788 C & \ne A & B & \ne D
28793 As it can be seen, the formulas in this environment are placed so as if
28802 \begin_layout Plain Layout
28810 \begin_inset CommandInset ref
28812 reference "subsec:Variable-Space"
28823 before the first and after every even column.
28824 When the formula style
28830 \begin_layout Plain Layout
28832 \begin_inset CommandInset ref
28834 reference "sec:Formula-Styles"
28845 is used, the formula is set without the
28851 before the first column.
28854 \begin_layout Subsubsection
28855 Alignat Environment
28856 \begin_inset Index idx
28859 \begin_layout Plain Layout
28860 Formula ! multiline ! alignat environment
28868 \begin_layout Standard
28869 The alignat environment has no predefined column separation.
28870 It can be inserted manually with the spaces that are described
28871 \begin_inset CommandInset ref
28873 reference "subsec:Space"
28880 \begin_layout Standard
28881 The above example in the alignat environment where 1
28882 \begin_inset space \thinspace{}
28885 cm space was inserted at the beginning of the second formula:
28886 \begin_inset Formula
28887 \begin{alignat*}{2}
28888 A & =\sin(B) & \hspace{1cm}C & =D\\
28889 C & \ne A & B & \ne D
28894 Because the column separation can be set separately for every column, this
28895 environment is especially suitable to set three and more formulas side
28899 \begin_layout Subsubsection
28900 Flalign Environment
28901 \begin_inset CommandInset label
28903 name "subsec:Flalign-Environment"
28908 \begin_inset Index idx
28911 \begin_layout Plain Layout
28912 Formula ! multiline ! flalign environment
28920 \begin_layout Standard
28921 In this environment the first two columns are always set as much as possible
28922 to the left and the last two ones to the right.
28924 \begin_inset Formula
28926 A & =1 & B & =2 & C & =3\\
28927 X & =\textrm{-}1 & Y & =\textrm{-}2 & Z & =4
28935 \begin_layout Standard
28936 By creating a flalign environment with an odd number of columns where an
28937 empty \SpecialChar TeX
28938 brace is inserted to the last column, several formulas in a document
28939 can be set to the left, although the formula style
28944 As example the indented formula
28945 \begin_inset CommandInset ref
28947 reference "eq:VolInt"
28952 \begin_inset Formula
28954 \hspace{30pt}\iiint\limits _{V}X\,\mathrm{d}V & =U & {}
28959 The first two columns contain the formula.
28960 To indent it as with the formula style
28965 \begin_inset space \thinspace{}
28968 pt space was inserted at the beginning of the first column.
28971 \begin_layout Subsection
28972 Eqnarray Environment
28973 \begin_inset CommandInset label
28975 name "subsec:Eqnarray-Environment"
28980 \begin_inset Index idx
28983 \begin_layout Plain Layout
28984 Formula ! multiline ! eqnarray environment
28992 \begin_layout Standard
28993 When this environment has been created, three blue boxes appear.
28994 The content of the first box is right aligned, the content of the last
28996 The content of the middle box appears centered and a bit smaller, because
28997 it is designed to insert there only relation characters.
28998 \begin_inset Formula
29000 \frac{ABC}{D} & \frac{ABC}{D} & \frac{ABC}{D}\\
29010 \begin_layout Subsection
29012 \begin_inset Index idx
29015 \begin_layout Plain Layout
29016 Formula ! multiline ! gather environment
29024 \begin_layout Standard
29025 This environment consists of only one centered column.
29026 Every line can be numbered.
29027 \begin_inset Formula
29038 \begin_layout Subsection
29039 Multline Environment
29040 \begin_inset CommandInset label
29042 name "subsec:Multline-Environment"
29047 \begin_inset Index idx
29050 \begin_layout Plain Layout
29051 Formula ! multiline ! multline environment
29059 \begin_layout Standard
29060 The multline environment consists, like the gather environment, of only
29062 But the first line is left aligned, the last one right aligned.
29063 All other lines are centered.
29064 Therefore this environment is suitable for long formulas.
29066 \begin_inset CommandInset ref
29068 reference "eq:lefteqn"
29072 in the multline environment:
29073 \begin_inset Formula
29075 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}\\
29076 -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}\\
29077 =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}}
29085 \begin_layout Standard
29086 In the output only the last (first) line of a multline environment appears
29087 numbered when the document numbering is right (left).
29091 \begin_layout Plain Layout
29092 numbering styles see
29093 \begin_inset CommandInset ref
29095 reference "sec:Formula-Styles"
29107 \begin_layout Standard
29115 \begin_inset Index idx
29118 \begin_layout Plain Layout
29133 \begin_inset Index idx
29136 \begin_layout Plain Layout
29144 a centered line can be right or left aligned, respectively.
29145 The commands are used as follows:
29148 \begin_layout Standard
29153 shoveright{line content}
29159 shoveleft{line content}
29162 \begin_layout Standard
29163 \begin_inset VSpace medskip
29173 \begin_inset Index idx
29176 \begin_layout Plain Layout
29184 specifies the distance of the first line from the left page margin.
29185 Predefined is the length 0
29186 \begin_inset space \thinspace{}
29192 \begin_layout Standard
29193 As example the above formula where the command
29196 \begin_layout Standard
29206 \begin_layout Standard
29207 was inserted in \SpecialChar TeX
29212 \begin_layout Plain Layout
29224 \begin_inset Formula
29226 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}\\
29227 \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}}\\
29228 =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}}
29237 \begin_layout Plain Layout
29248 The second line was left aligned using
29257 \begin_layout Subsection
29258 Multiline Formula Parts
29259 \begin_inset CommandInset label
29261 name "subsec:Multiline-Formula-Parts"
29266 \begin_inset Index idx
29269 \begin_layout Plain Layout
29270 Formula ! multiline ! formula parts
29278 \begin_layout Standard
29279 To display only parts of a formula with multiple lines, one of the following
29280 environments is used:
29297 They can be inserted via the menu
29299 Insert\SpecialChar menuseparator
29302 or by using the commands described in this section.
29305 \begin_layout Standard
29306 The first three have the same properties as the corresponding multiline
29307 formula environments, but it is possible to set further formula parts beside
29310 \begin_inset Formula
29312 \left.\begin{aligned}\Delta x\Delta p & \ge\frac{\hbar}{2}\\
29313 \Delta E\Delta t & \ge\frac{\hbar}{2}
29315 \right\} \textrm{Uncertainty relations}
29323 \begin_layout Standard
29324 To get this formula, a displayed formula is created where the command
29331 \begin_inset Index idx
29334 \begin_layout Plain Layout
29343 A purple box appears around the blue formula box where now columns and
29344 lines can be added.
29345 Outside the multiline environment other formula parts can be set, like
29349 \begin_layout Standard
29350 The aligned environment is also suitable for long formulas whose lines are
29351 horizontally aligned.
29352 Using aligned in a displayed formula has the advantage that the formula
29353 number is vertically centered behind the lines.
29355 \begin_inset CommandInset ref
29357 reference "eq:shortlong"
29361 in the aligned environment:
29362 \begin_inset Formula
29364 \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}|}\\
29365 & -\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}|}
29374 \begin_layout Standard
29375 To use the environments
29394 \begin_inset Index idx
29397 \begin_layout Plain Layout
29412 \begin_inset Index idx
29415 \begin_layout Plain Layout
29430 \begin_inset Index idx
29433 \begin_layout Plain Layout
29441 are inserted, respectively.
29442 The split environment has the same properties as the aligned environment
29443 but it can only have two columns.
29446 \begin_layout Subsection
29447 Text in multiline Formulas
29448 \begin_inset CommandInset label
29450 name "subsec:Text-in-multiline"
29455 \begin_inset Index idx
29458 \begin_layout Plain Layout
29465 \begin_inset Index idx
29468 \begin_layout Plain Layout
29469 Formula ! multiline ! text
29477 \begin_layout Standard
29478 In the Align environments, and the multline and gather environment, text
29479 can be inserted that will appear in a separate line and doesn't affect
29480 the column alignment.
29481 To do this, the command
29488 \begin_inset Index idx
29491 \begin_layout Plain Layout
29499 is used in the following scheme:
29502 \begin_layout Standard
29510 \begin_layout Standard
29511 The text should not be longer than a line because it cannot be hyphenated.
29512 As \SpecialChar LyX
29513 doesn't yet support
29519 directly, the text is written as mathematical text.
29526 must hereby be at the beginning of a line and appears in the output above
29528 An example where the text was inserted at the beginning of the second line:
29529 \begin_inset Formula
29531 I & =a\sqrt{2}\int_{0}^{2\pi}\sqrt{1+\cos(\phi)}\;\mathrm{d}\phi\\
29532 \intertext{\text{integrand is symmetric to \ensuremath{\phi=\pi}, therefore}} & =2a\sqrt{2}\int_{0}^{\pi}\sqrt{1+\cos(\phi)}\;\mathrm{d}\phi
29540 \begin_layout Standard
29547 always creates some vertical space between the text and the formula lines.
29548 To avoid this space, set in the document settings under
29551 \begin_inset space ~
29561 \begin_inset Index idx
29564 \begin_layout Plain Layout
29565 Packages ! mathtools
29573 \begin_inset space ~
29579 Then you can use the command
29586 \begin_inset Index idx
29589 \begin_layout Plain Layout
29606 \begin_layout Standard
29607 \begin_inset Formula
29609 I & =a\sqrt{2}\int_{0}^{2\pi}\sqrt{1+\cos(\phi)}\;\mathrm{d}\phi\\
29610 \shortintertext{\text{integrand is symmetric to \ensuremath{\phi=\pi}, therefore}} & =2a\sqrt{2}\int_{0}^{\pi}\sqrt{1+\cos(\phi)}\;\mathrm{d}\phi
29618 \begin_layout Section
29620 \begin_inset Index idx
29623 \begin_layout Plain Layout
29630 \begin_inset Index idx
29633 \begin_layout Plain Layout
29634 Formula ! numbering|see
29638 \begin_layout Plain Layout
29649 \begin_layout Plain Layout
29664 \begin_layout Subsection
29668 \begin_layout Standard
29669 Numbered formulas can be created with the menu
29671 Insert\SpecialChar menuseparator
29672 Math\SpecialChar menuseparator
29674 \begin_inset space ~
29682 \begin_inset space ~
29688 Existing formulas can be numbered with the menu
29690 Edit\SpecialChar menuseparator
29691 Math\SpecialChar menuseparator
29693 \begin_inset space ~
29701 arg "math-number-toggle"
29705 The formula number is displayed in \SpecialChar LyX
29706 behind the formula as a number sign
29708 The number sign is replaced in the output by the formula number.
29711 \begin_layout Standard
29712 When numbering is turned on in multiline formulas, all lines will be numbered.
29713 But the numbering can be controlled with the menu
29715 Edit\SpecialChar menuseparator
29716 Math\SpecialChar menuseparator
29718 \begin_inset space ~
29722 \begin_inset space ~
29726 \begin_inset space ~
29734 arg "math-number-line-toggle"
29740 \begin_layout Standard
29741 Except for inline formulas, all formulas can be numbered with two different
29743 \begin_inset CommandInset ref
29745 reference "sec:Formula-Styles"
29752 \begin_layout Subsection
29754 \begin_inset Index idx
29757 \begin_layout Plain Layout
29758 Cross-references ! to formulas
29766 \begin_layout Standard
29767 All labeled formulas can be cross-referenced.
29768 A label is added by the menu
29770 Insert\SpecialChar menuseparator
29773 or the toolbar button
29780 The cursor must hereby be inside a displayed formula.
29781 Alternatively you can right-click on the formula and choose
29786 A dialog pops up displaying the prefix
29791 The label is inserted there behind the prefix.
29792 The predefined prefix means
29793 \begin_inset Quotes eld
29797 \begin_inset Quotes erd
29800 and makes it easier to find labels in large documents because it marks
29801 it as formula label to divide it from e.
29802 \begin_inset space \thinspace{}
29806 \begin_inset space \space{}
29810 To change a label, the menu
29812 Insert\SpecialChar menuseparator
29815 is used again or you right-click on a formula and then on
29822 \begin_layout Standard
29823 The name of the label is displayed in \SpecialChar LyX
29824 within two parentheses behind formula.
29825 A formula with a label is always numbered.
29828 \begin_layout Standard
29829 Cross-references are inserted via the menu
29831 Insert\SpecialChar menuseparator
29834 or with the toolbar button
29837 arg "dialog-show-new-inset ref"
29841 A formula cross-reference appears in the output as formula number.
29842 When in the cross-reference dialog window the format
29846 is chosen, the cross-reference appears in the output as formula number
29848 \begin_inset Newline newline
29851 By right-clicking on a cross-reference in \SpecialChar LyX
29852 , one jumps to the formula that
29856 \begin_layout Standard
29857 Here are as examples cross-references to formulas of the following subsections:
29858 \begin_inset Note Note
29861 \begin_layout Plain Layout
29862 Note the different cross-reference types.
29870 \begin_layout Standard
29872 \begin_inset CommandInset ref
29879 \begin_inset CommandInset ref
29887 \begin_inset CommandInset ref
29893 ) big Latin letters are used for the numbering in contrary to (
29894 \begin_inset CommandInset ref
29903 \begin_layout Standard
29904 \begin_inset VSpace medskip
29907 When the argument of
29915 \begin_layout Plain Layout
29923 \begin_inset CommandInset ref
29925 reference "subsec:User-defined-Numbering"
29936 contains a box like in
29937 \begin_inset CommandInset ref
29939 reference "subsec:Paragraph-Boxes"
29943 , the formula cannot be referenced.
29946 \begin_layout Subsection
29948 \begin_inset Index idx
29951 \begin_layout Plain Layout
29952 Formula numbering ! subnumbering
29960 \begin_layout Standard
29961 With the help of the commands
29965 begin{subequations}
29973 formulas can be subnumbered.
29974 Both commands are inserted in \SpecialChar TeX
29978 \begin_layout Standard
29980 \begin_inset Formula
29991 \begin_layout Plain Layout
29995 begin{subequations}
30001 \begin_inset VSpace -5mm
30005 \begin_inset Formula
30013 \begin_inset Formula
30023 \begin_layout Standard
30027 \begin_layout Plain Layout
30039 \begin_layout Standard
30040 To create the example, the following is done:
30043 \begin_layout Enumerate
30044 first formula is inserted
30047 \begin_layout Enumerate
30052 begin{subequations}
30053 \begin_inset Newline newline
30058 is inserted after the first formula
30061 \begin_layout Enumerate
30062 second formula is inserted
30065 \begin_layout Enumerate
30066 third formula is inserted
30069 \begin_layout Enumerate
30076 is inserted after the third formula
30079 \begin_layout Standard
30080 Every formula between the commands
30092 will be subnumbered with a, b, c, \SpecialChar ldots
30094 For multiline formulas every line will be subnumbered.
30097 \begin_layout Standard
30098 Referencing subequations work like for normal equations:
30099 \begin_inset CommandInset ref
30106 \begin_inset CommandInset ref
30113 If you want to reference the subequations collectively, insert a label
30118 begin{subequations}
30122 \begin_inset CommandInset ref
30124 reference "eq:Here-is-an"
30131 \begin_layout Standard
30132 By inserting commands in \SpecialChar TeX
30133 mode, a space is created between the first two
30136 \begin_inset space \thinspace{}
30139 mm vertical space is inserted after the command
30143 begin{subequations}
30146 When the formula style
30152 \begin_layout Plain Layout
30154 \begin_inset CommandInset ref
30156 reference "sec:Formula-Styles"
30168 \begin_inset space \thinspace{}
30171 mm space is inserted instead.
30174 \begin_layout Standard
30175 To get another subnumber instead of small Latin letters, insert this command
30180 begin{subequations}
30185 \begin_layout Standard
30194 theparentequation -
30199 \begin_layout Standard
30206 creates hereby the parent number and
30212 adds a small Roman number as subnumber.
30213 For more information about the customization of the numbering, see
30214 \begin_inset CommandInset ref
30216 reference "subsec:Numbering-with-Roman"
30223 \begin_layout Standard
30224 Here is an example for a multiline formula where the numbering is customized
30225 and turned off for the second line:
30229 \begin_layout Plain Layout
30233 begin{subequations}
30239 \begin_inset CommandInset label
30241 name "eq:Here-is-an"
30249 \begin_layout Plain Layout
30257 theparentequation -
30265 \begin_inset Formula
30267 A & = & (B-Z)^{2}=(B-Z)(B-Z)\\
30268 & = & B^{2}-ZB-BZ+Z^{2}\nonumber \\
30269 & = & B^{2}-2BZ+Z^{2}
30278 \begin_layout Plain Layout
30290 \begin_layout Subsection
30291 User-defined Numbering
30292 \begin_inset CommandInset label
30294 name "subsec:User-defined-Numbering"
30299 \begin_inset Index idx
30302 \begin_layout Plain Layout
30303 Formula numbering ! user-defined
30311 \begin_layout Standard
30312 \begin_inset Index idx
30315 \begin_layout Plain Layout
30316 Formula numbering ! self-defined delimiters
30321 With the standard numbering parentheses are set around the formula number.
30322 To replace the parentheses for example by vertical bars, the following
30323 line is added to the \SpecialChar LaTeX
30327 \begin_layout Standard
30339 \begin_inset Note Note
30342 \begin_layout Plain Layout
30343 This macro is already declared in the \SpecialChar LaTeX
30344 -preamble for testing.
30345 To activate it, remove the percent sign at the beginning.
30353 \begin_layout Standard
30354 To use other characters, the vertical bars besides the
30358 are replaced by one ore more characters.
30359 To get only the formula number the vertical bars are omitted.
30362 \begin_layout Standard
30363 \begin_inset VSpace bigskip
30366 When there should be an expression of your choice instead of the consecutive
30367 formula number in parentheses behind the formula, the command
30374 \begin_inset Index idx
30377 \begin_layout Plain Layout
30386 \begin_inset Formula
30388 A+B=C\tag{something}\label{eq:tag}
30393 In this example the command
30398 \begin_inset space \textvisiblespace{}
30403 was inserted in the formula.
30406 \begin_layout Standard
30412 \begin_inset space \textvisiblespace{}
30417 is inserted instead, the star prevents the parentheses around the expression:
30418 \begin_inset Formula
30420 A+B=C\tag*{something}
30428 \begin_layout Standard
30429 \begin_inset VSpace bigskip
30432 To restart the formula numbering with new document parts or sections, the
30433 following command is used:
30436 \begin_layout Standard
30441 @addtoreset{equation}{part}
30444 \begin_inset Index idx
30447 \begin_layout Plain Layout
30452 \begin_layout Plain Layout
30463 \begin_layout Plain Layout
30476 \begin_layout Plain Layout
30487 \begin_layout Plain Layout
30500 \begin_inset Newline newline
30504 \begin_inset Newline newline
30511 @addtoreset{equation}{section}
30514 \begin_layout Standard
30515 To be able to use these commands in \SpecialChar TeX
30517 \begin_inset Quotes eld
30521 \begin_inset Quotes erd
30524 character has to be made
30525 \begin_inset Quotes eld
30529 \begin_inset Quotes erd
30532 for \SpecialChar LaTeX
30547 So the command sequence in \SpecialChar TeX
30551 \begin_layout Standard
30557 \begin_inset Newline newline
30562 @addtoreset{equation}{section}
30563 \begin_inset Newline newline
30571 \begin_layout Standard
30572 In the \SpecialChar LaTeX
30585 can be omitted as they are automatically internally inserted by \SpecialChar LyX
30589 \begin_layout Standard
30604 \begin_layout Plain Layout
30609 is part of the \SpecialChar LaTeX
30615 \begin_inset Index idx
30618 \begin_layout Plain Layout
30619 Packages ! carlisle
30624 that is part of every \SpecialChar LaTeX
30625 standard installation.
30631 \begin_inset Index idx
30634 \begin_layout Plain Layout
30635 Packages ! remreset
30640 has to be loaded in the \SpecialChar LaTeX
30641 -preamble with the line
30644 \begin_layout Standard
30649 usepackage{remreset}
30652 \begin_layout Standard
30660 \begin_inset Index idx
30663 \begin_layout Plain Layout
30668 \begin_layout Plain Layout
30679 \begin_layout Plain Layout
30692 \begin_layout Plain Layout
30703 \begin_layout Plain Layout
30715 can be used with the same scheme as
30724 \begin_layout Standard
30725 \begin_inset VSpace bigskip
30728 Sometimes formulas should be numbered in the following form:
30731 \begin_layout Standard
30734 (section number.formula number)
30737 \begin_layout Standard
30738 The formula number should start with every section with
30739 \begin_inset Quotes eld
30743 \begin_inset Quotes erd
30749 \begin_layout Standard
30750 For this case there is the command
30757 \begin_inset Index idx
30760 \begin_layout Plain Layout
30768 , which is used with the following scheme:
30771 \begin_layout Standard
30776 numberwithin{counter}{sectioning}
30779 \begin_layout Standard
30780 Counter denotes what kind of numbering is affected, sectioning denotes what
30781 number is before the dot.
30784 \begin_layout Standard
30785 Thus in our case the following \SpecialChar LaTeX
30786 preamble or \SpecialChar TeX
30790 \begin_layout Standard
30795 numberwithin{equation}{section}
30798 \begin_layout Standard
30799 This is the result:
30803 \begin_layout Plain Layout
30807 numberwithin{equation}{section}
30813 \begin_inset Formula
30823 \begin_layout Standard
30825 \begin_inset space \thinspace{}
30829 \begin_inset space \space{}
30832 tables so that the number of the part is the sectioning,
30833 \begin_inset Newline newline
30840 numberwithin{table}{part}
30845 \begin_layout Standard
30846 To go back to the standard numbering or to prevent this kind of numbering
30847 when it is defined by the document class, the following command is inserted
30848 as \SpecialChar TeX
30849 code or to the \SpecialChar LaTeX
30853 \begin_layout Standard
30863 \begin_inset Index idx
30866 \begin_layout Plain Layout
30880 \begin_layout Plain Layout
30896 \begin_inset Newline newline
30904 \begin_inset Newline newline
30916 \begin_layout Standard
30923 uses internally the command
30929 , described above, that also needs to be reverted.
30933 \begin_layout Plain Layout
30940 \begin_layout Plain Layout
30944 @removefromreset{equation}{section}
30947 \begin_layout Plain Layout
30959 \begin_layout Standard
30960 \begin_inset Newpage newpage
30966 \begin_layout Subsection
30967 Numbering with Roman Numbers and Letters
30968 \begin_inset CommandInset label
30970 name "subsec:Numbering-with-Roman"
30975 \begin_inset Index idx
30978 \begin_layout Plain Layout
30979 Formula numbering ! with letters
30985 \begin_inset Index idx
30988 \begin_layout Plain Layout
30989 Formula numbering ! with Roman numbers
30997 \begin_layout Standard
30998 Formulas can also be numbered with Roman numbers and Latin letters.
30999 To number for example with small Roman numbers, the command
31002 \begin_layout Standard
31014 \begin_layout Standard
31015 is inserted before the formula in \SpecialChar TeX
31024 \begin_inset Index idx
31027 \begin_layout Plain Layout
31035 redefines the predefined command
31051 \begin_layout Plain Layout
31058 has the same scheme like the command
31064 that is described in
31065 \begin_inset CommandInset ref
31067 reference "subsec:The-Command-newcommand"
31080 is the formula counter.
31087 is used as prefix for a counter, the value of the counter is output as
31089 When a formula is numbered, \SpecialChar LaTeX
31090 sets internally the command
31096 behind the formula.
31102 \begin_inset Index idx
31105 \begin_layout Plain Layout
31115 outputs the counter as small Roman number.
31118 \begin_layout Standard
31119 All formulas behind the command
31129 are now numbered Roman.
31130 To switch to numbering with big Roman numbers, the command is inserted
31144 \begin_inset Index idx
31147 \begin_layout Plain Layout
31159 \begin_inset Quotes eld
31163 \begin_inset Quotes erd
31166 with small Latin letters there is the command
31173 \begin_inset Index idx
31176 \begin_layout Plain Layout
31184 , for big ones there is the command
31191 \begin_inset Index idx
31194 \begin_layout Plain Layout
31207 \begin_layout Standard
31208 \begin_inset Note Greyedout
31211 \begin_layout Plain Layout
31218 \begin_inset space ~
31221 formulas can be numbered with Latin letters in one document.
31229 \begin_layout Standard
31233 \begin_layout Plain Layout
31249 \begin_layout Standard
31250 \begin_inset Formula
31252 A=\textrm{small roman}
31261 \begin_layout Plain Layout
31275 \begin_inset Formula
31277 B=\textrm{big Roman}\label{eq:Rom}
31286 \begin_layout Plain Layout
31300 \begin_inset Formula
31302 C=\textrm{small Latin}
31311 \begin_layout Plain Layout
31325 \begin_inset Formula
31327 D=\textrm{big Latin}\label{eq:Lat}
31335 \begin_layout Standard
31336 To switch back to the default numbering, insert the command:
31339 \begin_layout Standard
31349 \begin_inset Index idx
31352 \begin_layout Plain Layout
31363 \begin_layout Standard
31367 \begin_layout Plain Layout
31381 \begin_inset Formula
31391 \begin_layout Standard
31392 \begin_inset VSpace medskip
31395 As you see, formulas are numbered serially independent from the numbering
31397 When then numbering should start with
31398 \begin_inset Quotes eld
31402 \begin_inset Quotes erd
31405 when the style is changed, new equation counters have to be defined.
31406 A description about this can be found in the file
31407 \begin_inset CommandInset href
31409 name "Formula-numbering.lyx"
31410 target "run:Formula-numbering.lyx"
31418 \begin_layout Section
31419 Chemical Symbols and Equations
31420 \begin_inset CommandInset label
31422 name "subsec:Chemical-Symbols-and"
31427 \begin_inset Index idx
31430 \begin_layout Plain Layout
31431 Chemical characters ! Symbols
31437 \begin_inset Index idx
31440 \begin_layout Plain Layout
31447 \begin_inset Index idx
31450 \begin_layout Plain Layout
31459 \begin_layout Standard
31460 An example text from chemistry:
31463 \begin_layout Quote
31465 \begin_inset Formula $\mathrm{SO_{4}^{2-}}$
31468 -ion reacts with two
31469 \begin_inset Formula $\mathrm{Na^{+}}$
31472 -ions to sodium sulfate
31473 \begin_inset Formula $\left(\mathrm{Na_{2}SO_{4}}\right)$
31477 The chemical equation for this is:
31478 \begin_inset Formula
31480 \mathrm{2\,Na^{+}+SO_{4}^{2-}\longrightarrow Na_{2}SO_{4}}\label{eq:chem-reaction}
31488 \begin_layout Standard
31489 This chemical equation can directly be created as formula.
31490 To avoid that the symbols appear italic, everything is highlighted and
31491 changed by the shortcut
31497 to the upright font style.
31501 \begin_layout Plain Layout
31507 \begin_inset CommandInset ref
31509 reference "subsec:Font-Styles"
31521 \begin_layout Standard
31522 A more convenient way to typeset chemical formulas is to use the command
31530 \begin_inset Index idx
31533 \begin_layout Plain Layout
31541 that is available when the \SpecialChar LaTeX
31547 \begin_inset Index idx
31550 \begin_layout Plain Layout
31563 to a formula a new blue box appears where chemical formulas can be inserted
31564 in an intuitive way.
31567 \begin_layout Standard
31569 \begin_inset Tabular
31570 <lyxtabular version="3" rows="10" columns="2">
31571 <features booktabs="true" tabularvalignment="middle">
31572 <column alignment="center" valignment="top" width="0pt">
31573 <column alignment="center" valignment="top">
31575 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
31578 \begin_layout Plain Layout
31584 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
31587 \begin_layout Plain Layout
31595 <cell alignment="center" valignment="top" leftline="true" usebox="none">
31598 \begin_layout Plain Layout
31602 \begin_inset space \textvisiblespace{}
31610 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
31613 \begin_layout Plain Layout
31614 \begin_inset Formula $\ce{H2CO3}$
31623 <row topspace="1.5mm">
31624 <cell alignment="center" valignment="top" usebox="none">
31627 \begin_layout Plain Layout
31631 \begin_inset space \textvisiblespace{}
31639 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
31642 \begin_layout Plain Layout
31643 \begin_inset Formula $\ce{SO4^{2-}}$
31652 <row topspace="1.5mm">
31653 <cell alignment="center" valignment="top" usebox="none">
31656 \begin_layout Plain Layout
31660 \begin_inset space \textvisiblespace{}
31668 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
31671 \begin_layout Plain Layout
31672 \begin_inset Formula $\ce{(NH4)2S}$
31681 <row topspace="1.5mm">
31682 <cell alignment="center" valignment="top" usebox="none">
31685 \begin_layout Plain Layout
31689 \begin_inset space \textvisiblespace{}
31697 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
31700 \begin_layout Plain Layout
31701 \begin_inset Formula $\ce{KCr(SO4)2.12H2O}$
31710 <row topspace="1.5mm">
31711 <cell alignment="center" valignment="top" usebox="none">
31714 \begin_layout Plain Layout
31718 \begin_inset space \textvisiblespace{}
31724 \begin_inset space \textvisiblespace{}
31730 \begin_inset space \textvisiblespace{}
31738 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
31741 \begin_layout Plain Layout
31742 \begin_inset Formula $\ce{A-B\dbond C\tbond D}$
31751 <row topspace="1.5mm">
31752 <cell alignment="center" valignment="top" usebox="none">
31755 \begin_layout Plain Layout
31759 \begin_inset space \textvisiblespace{}
31763 \begin_inset Formula $\downarrow$
31767 \begin_inset Formula $\to$
31775 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
31778 \begin_layout Plain Layout
31779 \begin_inset Formula $\ce{_{90}^{227}Th+}$
31789 <cell alignment="center" valignment="top" leftline="true" usebox="none">
31792 \begin_layout Plain Layout
31796 \begin_inset space \textvisiblespace{}
31802 \begin_inset space \textvisiblespace{}
31808 \begin_inset space \textvisiblespace{}
31816 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
31819 \begin_layout Plain Layout
31820 \begin_inset Formula $\ce{\ensuremath{\mu\hyphen}Cl}$
31830 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
31833 \begin_layout Plain Layout
31837 \begin_inset space \textvisiblespace{}
31841 \begin_inset space \textvisiblespace{}
31845 \begin_inset space \textvisiblespace{}
31849 \begin_inset space \textvisiblespace{}
31853 \begin_inset space \textvisiblespace{}
31861 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
31864 \begin_layout Plain Layout
31865 \begin_inset Formula $\ce{CO2 + C <=> 2CO}$
31874 <row topspace="1.5mm">
31875 <cell alignment="center" valignment="top" bottomline="true" usebox="none">
31878 \begin_layout Plain Layout
31882 \begin_inset space \textvisiblespace{}
31886 \begin_inset space \textvisiblespace{}
31890 \begin_inset space \textvisiblespace{}
31894 \begin_inset space \textvisiblespace{}
31902 \begin_inset space \textvisiblespace{}
31910 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
31913 \begin_layout Plain Layout
31914 \begin_inset Formula $\ce{CO2 + C ->[\alpha][\beta] 2CO}$
31930 \begin_layout Standard
31931 \begin_inset Note Greyedout
31934 \begin_layout Plain Layout
31940 It is not possible in \SpecialChar LyX
31941 to use the character ^ to get an up-arrow as described
31947 One instead uses a negative thin space followed by the command
31954 \begin_inset Formula $\ce{Fe + 2H+ -> Fe^{2+} + H2\negthinspace\uparrow}$
31965 \begin_layout Standard
31972 the command for equation
31973 \begin_inset space ~
31977 \begin_inset CommandInset ref
31979 reference "eq:chem-reaction"
31984 \begin_inset Newline newline
31992 \begin_inset space \textvisiblespace{}
31996 \begin_inset space \textvisiblespace{}
32000 \begin_inset space \textvisiblespace{}
32004 \begin_inset space \textvisiblespace{}
32008 \begin_inset space \textvisiblespace{}
32012 \begin_inset space \textvisiblespace{}
32018 \begin_layout Standard
32019 To create multiline chemical equations first a multiline formula is created
32021 \begin_inset CommandInset ref
32023 reference "sec:Multiline-Formulas"
32028 Afterwards the command
32034 is used in every small blue box of the formula.
32036 \begin_inset CommandInset ref
32038 reference "eq:TEOS-reaction-1"
32043 \begin_inset CommandInset ref
32045 reference "eq:TEOS-reaction-2"
32049 are an example of a multi-stage chemical reaction where every equation
32050 has its own number.
32051 \begin_inset Formula
32053 \ce{TEOS + 4O} & \ce{->} & \ce{Si(OH)4 + 4C2H4O}\label{eq:TEOS-reaction-1}\\
32054 \ce{Si(OH)4} & \ce{->} & \ce{SiO2 + 2H2O}\label{eq:TEOS-reaction-2}
32062 \begin_layout Standard
32073 package provides the command
32080 \begin_inset Index idx
32083 \begin_layout Plain Layout
32091 that has to be used for special cases.
32092 For more information about
32098 and more examples have a look at the documentation of
32103 \begin_inset CommandInset citation
32113 \begin_layout Section
32117 \begin_layout Standard
32119 supports two types of commutative diagrams:
32127 that are explained in the following.
32130 \begin_layout Subsection
32132 \begin_inset Index idx
32135 \begin_layout Plain Layout
32144 \begin_layout Standard
32145 Diagrams of this type visualize relations by vertical and horizontal lines
32147 \begin_inset Formula
32149 \begin{CD}A@>>>B@>>>C\\
32160 \begin_layout Standard
32161 To get them, the command
32166 \begin_inset Index idx
32169 \begin_layout Plain Layout
32179 is inserted to a formula.
32180 A blue box appears with two dashed lines where further commands can be
32185 arg "newline-insert newline"
32188 a new line is created.
32189 Horizontal relations are inserted in odd, vertical in even formula lines.
32192 \begin_layout Standard
32193 To create the relations there are the following commands:
32196 \begin_layout Itemize
32201 creates a left arrow,
32212 \begin_layout Itemize
32217 creates an up arrow,
32225 a vertical equal sign
32228 \begin_layout Itemize
32234 is a placeholder for non-existent relations
32237 \begin_layout Standard
32238 All arrows can be labeled as follows:
32241 \begin_layout Itemize
32242 If text inserted between the first and second < or >, resp., it is placed
32244 When it is inserted between the second and third one, it appears under
32248 \begin_layout Itemize
32249 When text for vertical arrows is inserted between the first and second A
32250 or V, resp., it is placed left beside the arrow.
32251 When it is inserted between the second and third one, it appears right
32253 If the text contains an A or V, these letters must be set into a \SpecialChar TeX
32257 \begin_layout Standard
32258 As example a diagram with all possible relations:
32261 \begin_layout Standard
32262 \begin_inset Formula
32264 \begin{CD}A@>j>>B@>>k>C@=F\\
32275 \begin_layout Standard
32276 The command for this is:
32277 \begin_inset Newline newline
32285 \begin_inset space \textvisiblespace{}
32288 A@>j>>B@>>k>C@=F Ctrl+Return
32289 \begin_inset Newline newline
32293 \begin_inset Phantom HPhantom
32296 \begin_layout Plain Layout
32302 \begin_inset space \textvisiblespace{}
32315 \begin_inset Formula $\to$
32321 \begin_inset Newline newline
32325 \begin_inset Phantom HPhantom
32328 \begin_layout Plain Layout
32334 \begin_inset space \textvisiblespace{}
32345 \begin_layout Subsection
32347 \begin_inset Index idx
32350 \begin_layout Plain Layout
32351 Diagrams ! xymatrix
32359 \begin_layout Standard
32360 To be able to use xymatrices, the \SpecialChar LaTeX
32366 A xymatrix is created by inserting the command
32373 Then you are able to add new matrix columns and rows like for normal matrices,
32375 \begin_inset CommandInset ref
32377 reference "sec:Matrices"
32384 \begin_layout Standard
32385 In contrary to amscd diagrams, xymatrices supports diagonal and curved arrows,
32387 All possibilities to create commutative diagrams and decorations are explained
32392 that you find in the menu
32394 Help\SpecialChar menuseparator
32396 \begin_inset space ~
32404 \begin_layout Subsection
32410 \begin_inset Index idx
32413 \begin_layout Plain Layout
32422 \begin_layout Standard
32427 -diagrams, the \SpecialChar LaTeX
32437 -diagram is created by inserting the command
32444 Then you are able to add new matrix columns and rows like for normal matrices,
32446 \begin_inset CommandInset ref
32448 reference "sec:Matrices"
32455 \begin_layout Standard
32456 Examples how to create
32460 diagrams in \SpecialChar LyX
32463 Feynman-diagram manual
32465 that you find in the menu
32467 Help\SpecialChar menuseparator
32469 \begin_inset space ~
32477 \begin_layout Standard
32478 \begin_inset Newpage newpage
32484 \begin_layout Section
32485 User-defined Commands
32486 \begin_inset Index idx
32489 \begin_layout Plain Layout
32490 User-defined commands
32498 \begin_layout Standard
32499 \begin_inset Note Greyedout
32502 \begin_layout Plain Layout
32507 The names of user-defined commands and macros may only consist of Latin
32516 \begin_layout Subsection
32520 \begin_inset CommandInset label
32522 name "subsec:The-Command-newcommand"
32527 \begin_inset Index idx
32530 \begin_layout Plain Layout
32531 User-defined commands !
32539 \begin_inset Index idx
32542 \begin_layout Plain Layout
32553 \begin_layout Standard
32554 Many \SpecialChar LaTeX
32555 -commands are too long to be used frequently.
32556 But it is possible to define with the command
32562 new shorter commands.
32565 \begin_layout Standard
32566 The command scheme of
32575 \begin_layout Standard
32580 newcommand{new command name}[number of arguments][optional
32585 \begin_inset Newline newline
32589 \begin_inset Phantom HPhantom
32592 \begin_layout Plain Layout
32602 {command definition}
32605 \begin_layout Standard
32606 \begin_inset Note Greyedout
32609 \begin_layout Plain Layout
32614 Assure that the name of the new command is not already used in your document
32615 or by \SpecialChar LaTeX
32616 -packages that you use.
32617 When you for example define the command
32629 , you get an error message because
32635 is already defined as command for
32636 \begin_inset Quotes eld
32640 \begin_inset Formula $\le$
32644 \begin_inset Quotes erd
32655 \begin_layout Standard
32656 The number of arguments is an integer in the range 0
32657 \begin_inset space \thinspace{}
32661 \begin_inset space \thinspace{}
32664 9 and specifies how many arguments the new command should have.
32665 With the optional value a value for an optional argument can be predefined.
32666 When this is done, the
32674 rgument of the new command is automatically an optional one.
32677 \begin_layout Standard
32678 Here are some examples:
32681 \begin_layout Itemize
32682 To define the command
32694 , the \SpecialChar LaTeX
32696 \begin_inset VSpace medskip
32700 \begin_inset Newline newline
32714 \begin_layout Itemize
32715 To define the command
32727 , the argument (that should be underlined) must be taken into account.
32728 For this the preamble line is:
32729 \begin_inset VSpace medskip
32733 \begin_inset Newline newline
32747 \begin_inset VSpace medskip
32751 \begin_inset Newline newline
32758 acts as argument placeholder, the
32762 behind it denotes that it is the placeholder for the first argument.
32765 \begin_layout Itemize
32773 \begin_inset space \thinspace{}
32777 \begin_inset space \space{}
32787 \begin_inset VSpace medskip
32791 \begin_inset Newline newline
32802 framebox#1#2{$#3$}}
32805 \begin_inset VSpace medskip
32809 \begin_inset Newline newline
32812 The two Dollar signs creates the extra formula needed for
32819 \begin_inset CommandInset ref
32821 reference "subsec:Boxes-with-Frame"
32828 \begin_layout Itemize
32829 To create a new command for
32835 where the color for the box need not be specified, the argument for the
32836 color is defined optional:
32837 \begin_inset VSpace medskip
32841 \begin_inset Newline newline
32852 fcolorbox{#2}{#1}{$#3$}}
32855 \begin_inset VSpace medskip
32859 \begin_inset Newline newline
32862 When the color is not specified when using
32868 , the predefined color
32875 \begin_layout Standard
32876 A test of the new defined commands:
32879 \begin_layout Standard
32881 \begin_inset Tabular
32882 <lyxtabular version="3" rows="6" columns="2">
32883 <features booktabs="true" tabularvalignment="middle">
32884 <column alignment="center" valignment="top" width="0pt">
32885 <column alignment="center" valignment="top">
32887 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
32890 \begin_layout Plain Layout
32896 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
32899 \begin_layout Plain Layout
32907 <cell alignment="center" valignment="top" leftline="true" usebox="none">
32910 \begin_layout Plain Layout
32914 \begin_inset space \textvisiblespace{}
32922 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
32925 \begin_layout Plain Layout
32926 \begin_inset Formula $A\gr B$
32936 <cell alignment="center" valignment="top" leftline="true" usebox="none">
32939 \begin_layout Plain Layout
32947 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
32950 \begin_layout Plain Layout
32951 \begin_inset Formula $\us{ABcd}$
32960 <row topspace="1mm">
32961 <cell alignment="center" valignment="top" usebox="none">
32964 \begin_layout Plain Layout
32968 \begin_inset Formula $\to$
32974 \begin_inset Formula $\to$
32982 \begin_inset space \textvisiblespace{}
32990 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
32993 \begin_layout Plain Layout
32994 \begin_inset Formula $\fb{[2cm]}{}{\int A=B}$
33003 <row topspace="1.5mm">
33004 <cell alignment="center" valignment="top" usebox="none">
33007 \begin_layout Plain Layout
33011 \begin_inset Formula $\to$
33019 \begin_inset space \textvisiblespace{}
33027 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
33030 \begin_layout Plain Layout
33031 \begin_inset Formula $\cb{red}{\int A=B}$
33040 <row topspace="1.5mm" bottomspace="1mm">
33041 <cell alignment="center" valignment="top" bottomline="true" usebox="none">
33044 \begin_layout Plain Layout
33050 \begin_inset Formula $\to$
33058 \begin_inset space \textvisiblespace{}
33066 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
33069 \begin_layout Plain Layout
33070 \begin_inset Formula $\cb[green]{red}{\int A=B}$
33086 \begin_layout Subsection
33088 \begin_inset Index idx
33091 \begin_layout Plain Layout
33092 User-defined commands! Math macros
33098 \begin_inset Index idx
33101 \begin_layout Plain Layout
33110 \begin_layout Standard
33111 User-defined commands are especially convenient for complex expressions.
33112 When you are for example dealing with a document that has quadratic equations,
33113 the same solution type occurs several times.
33114 The general form of a quadratic equation is
33115 \begin_inset Formula
33117 0=\lambda^{2}+p\lambda+q
33122 The general form of the solution is
33123 \begin_inset Formula
33125 \lambda_{1,2}=-\frac{p}{2}\pm\sqrt{\frac{p²}{4}-q}
33133 \begin_layout Standard
33134 To define a command for the solution formula where only the three parameters
33136 \begin_inset Formula $\lambda$
33140 \begin_inset Formula $p$
33144 \begin_inset Formula $q$
33147 need to be specified and the index of
33148 \begin_inset Formula $\lambda$
33151 can be given optionally, the \SpecialChar LaTeX
33153 \begin_inset Newline newline
33169 \begin_inset Newline newline
33173 \begin_inset Phantom HPhantom
33176 \begin_layout Plain Layout
33190 frac{#3^{2}}{4}-#4}}
33193 \begin_layout Standard
33194 To create with this the solution formula, the command
33195 \begin_inset Newline newline
33205 \begin_inset Formula $\to$
33211 \begin_inset Formula $\to$
33218 is inserted to a formula
33223 \begin_layout Standard
33224 The definition of the new command is unintuitive because one has to know
33225 the schemes of all used \SpecialChar LaTeX
33227 \begin_inset space \thinspace{}
33231 \begin_inset space \space{}
33234 that a fraction is inserted in \SpecialChar LaTeX
33239 frac{numerator}{denominator}
33242 Furthermore one can easily forget a brace in the definition and cannot
33243 see in \SpecialChar LyX
33244 what the new command is doing.
33245 To avoid these problems \SpecialChar LyX
33246 offers the possibility to use math macros instead
33256 \begin_layout Standard
33257 A math macro is created by using the menu
33259 Insert\SpecialChar menuseparator
33260 Math\SpecialChar menuseparator
33263 or the toolbar button
33266 arg "math-macro newmacroname_newcommand"
33270 The math macro toolbar appears together with the following box where the
33272 \begin_inset Newline newline
33276 \begin_inset space \hspace*{\fill}
33280 \begin_inset Graphics
33281 filename clipart/macrobox.png
33287 \begin_inset space \hspace*{\fill}
33291 \begin_inset Newline newline
33295 \begin_inset FormulaMacro
33296 \newcommand{\qG}[4][1,\,2]{#2_{#1}=-\frac{#3}{2}\pm\sqrt{\frac{#3^{2}}{4}-#4}}
33301 newmacroname is the default name of the macro that should be changed to
33302 something sensible.
33303 The wanted formula is inserted in the first blue box.
33304 An argument placeholder is inserted with the command
33311 \begin_inset space \thinspace{}
33315 \begin_inset space \space{}
33324 or by using the macro toolbar button
33327 arg "math-macro-add-param"
33331 Argument placeholders are displayed red.
33333 \begin_inset space ~
33336 arguments are possible.
33337 Optional arguments are created with the toolbar button
33340 arg "math-macro-add-optional-param"
33344 The first non-optional argument can be transformed to an optional one with
33348 arg "math-macro-make-optional"
33352 In the second blue box the appearance of the macro in \SpecialChar LyX
33354 Normally you want to see it as it is defined, so the box is kept empty.
33355 But when you have created a macro that needs lot of space on the screen,
33356 you can insert in the box for example
33357 \begin_inset Newline newline
33387 \begin_inset Newline newline
33392 For the macro only the arguments with the macro name in front of them will
33393 then be displayed in \SpecialChar LyX
33394 , leading to a better overview.
33395 The formula appears in the output as defined in the first box.
33396 \begin_inset Newline newline
33399 The appearance of macros in formulas can furthermore be changed for single
33400 macros by setting the cursor in the macro and using the menu
33402 View\SpecialChar menuseparator
33404 \begin_inset space ~
33408 \begin_inset space ~
33416 \begin_layout Standard
33417 To use a macro, the macro name is inserted as command to a formula, in our
33425 Our macro looks in \SpecialChar LyX
33427 \begin_inset Newline newline
33431 \begin_inset space \hspace*{\fill}
33435 \begin_inset Graphics
33436 filename clipart/macrouse.png
33442 \begin_inset space \hspace*{\fill}
33446 \begin_inset Newline newline
33449 Here is our macro example with the arguments
33450 \begin_inset Formula $x$
33454 \begin_inset Formula $\ln(x)$
33458 \begin_inset Formula $B$
33464 \begin_layout Standard
33465 \begin_inset Formula
33475 \begin_layout Standard
33479 Tools\SpecialChar menuseparator
33480 Preferences\SpecialChar menuseparator
33481 Editing\SpecialChar menuseparator
33484 different styles to edit macros.
33485 To find the style that suits you the most, choose a style and set the cursor
33486 in a macro formula to see the difference.
33489 \begin_layout Standard
33490 A math macro is transformed internally to a
33496 command when exporting the document.
33503 command is not placed in the \SpecialChar LaTeX
33504 -preamble, therefore macros can only be used
33505 in formulas that are in the document below the macro definition box.
33508 \begin_layout Standard
33509 Math macros can also be directly created from a
33516 When writing for example the command
33519 \begin_inset Newline newline
33528 xleftarrow[#2]{#1}}
33529 \begin_inset Newline newline
33534 in \SpecialChar LyX
33535 as normal text, highlighting it completely and using then the shortcut
33540 , the command will be transformed to a math macro.
33541 Using this method you need to be careful that the
33547 command is typed correctly, otherwise you get a faulty macro leading to
33552 \begin_layout Standard
33553 Math macros currently have the problem that further formulas in macro definition
33554 s are handled wrongly.
33555 Therefore the example
33562 \begin_inset CommandInset ref
33564 reference "subsec:The-Command-newcommand"
33568 cannot be created as macro.
33571 \begin_layout Standard
33572 When the cursor is in a macro definition box, you will see the macro toolbar
33573 in \SpecialChar LyX
33577 \begin_layout Standard
33578 \begin_inset VSpace defskip
33584 \begin_layout Standard
33585 \begin_inset Graphics
33586 filename clipart/MacroToolbar.png
33591 \begin_inset Index idx
33594 \begin_layout Plain Layout
33603 \begin_layout Standard
33604 \begin_inset VSpace defskip
33610 \begin_layout Standard
33611 The macro toolbar contains from left to right the following buttons:
33614 \begin_layout Standard
33615 \begin_inset VSpace defskip
33621 \begin_layout Standard
33622 \begin_inset Tabular
33623 <lyxtabular version="3" rows="9" columns="2">
33624 <features islongtable="true" longtabularalignment="center">
33625 <column alignment="left" valignment="top">
33626 <column alignment="left" valignment="top" width="85col%">
33627 <row interlinespace="2.5mm">
33628 <cell alignment="center" valignment="top" usebox="none">
33631 \begin_layout Plain Layout
33634 arg "math-macro-remove-param"
33642 <cell alignment="center" valignment="top" usebox="none">
33645 \begin_layout Plain Layout
33648 Edit\SpecialChar menuseparator
33649 Math\SpecialChar menuseparator
33651 \begin_inset space ~
33654 Definition\SpecialChar menuseparator
33655 Remove Last Argument
33661 <row interlinespace="2.5mm">
33662 <cell alignment="center" valignment="top" usebox="none">
33665 \begin_layout Plain Layout
33668 arg "math-macro-add-param"
33676 <cell alignment="center" valignment="top" usebox="none">
33679 \begin_layout Plain Layout
33682 Edit\SpecialChar menuseparator
33683 Math\SpecialChar menuseparator
33685 \begin_inset space ~
33688 Definition\SpecialChar menuseparator
33695 <row interlinespace="2.5mm">
33696 <cell alignment="center" valignment="top" usebox="none">
33699 \begin_layout Plain Layout
33702 arg "math-macro-make-optional"
33710 <cell alignment="center" valignment="top" usebox="none">
33713 \begin_layout Plain Layout
33716 Edit\SpecialChar menuseparator
33717 Math\SpecialChar menuseparator
33719 \begin_inset space ~
33722 Definition\SpecialChar menuseparator
33723 Transform First Non-Optional to
33724 \begin_inset Newline newline
33728 \begin_inset Phantom HPhantom
33731 \begin_layout Plain Layout
33734 Edit\SpecialChar menuseparator
33735 Math\SpecialChar menuseparator
33737 \begin_inset space ~
33740 Definition\SpecialChar menuseparator
33752 <row interlinespace="2.5mm">
33753 <cell alignment="center" valignment="top" usebox="none">
33756 \begin_layout Plain Layout
33759 arg "math-macro-make-nonoptional"
33767 <cell alignment="center" valignment="top" usebox="none">
33770 \begin_layout Plain Layout
33773 Edit\SpecialChar menuseparator
33774 Math\SpecialChar menuseparator
33776 \begin_inset space ~
33779 Definition\SpecialChar menuseparator
33780 Transform Last Optional to
33781 \begin_inset Newline newline
33785 \begin_inset Phantom HPhantom
33788 \begin_layout Plain Layout
33791 Edit\SpecialChar menuseparator
33792 Math\SpecialChar menuseparator
33794 \begin_inset space ~
33797 Definition\SpecialChar menuseparator
33803 Non-Optional Argument
33809 <row interlinespace="2.5mm">
33810 <cell alignment="center" valignment="top" usebox="none">
33813 \begin_layout Plain Layout
33816 arg "math-macro-remove-optional-param"
33824 <cell alignment="center" valignment="top" usebox="none">
33827 \begin_layout Plain Layout
33830 Edit\SpecialChar menuseparator
33831 Math\SpecialChar menuseparator
33833 \begin_inset space ~
33836 Definition\SpecialChar menuseparator
33837 Remove Optional Argument
33843 <row interlinespace="2.5mm">
33844 <cell alignment="center" valignment="top" usebox="none">
33847 \begin_layout Plain Layout
33850 arg "math-macro-add-optional-param"
33858 <cell alignment="center" valignment="top" usebox="none">
33861 \begin_layout Plain Layout
33864 Edit\SpecialChar menuseparator
33865 Math\SpecialChar menuseparator
33867 \begin_inset space ~
33870 Definition\SpecialChar menuseparator
33871 Insert Optional Argument
33877 <row interlinespace="2.5mm">
33878 <cell alignment="center" valignment="top" usebox="none">
33881 \begin_layout Plain Layout
33884 arg "math-macro-remove-greedy-param"
33892 <cell alignment="center" valignment="top" usebox="none">
33895 \begin_layout Plain Layout
33898 Edit\SpecialChar menuseparator
33899 Math\SpecialChar menuseparator
33901 \begin_inset space ~
33904 Definition\SpecialChar menuseparator
33905 Remove Last Argument
33906 \begin_inset Newline newline
33910 \begin_inset Phantom HPhantom
33913 \begin_layout Plain Layout
33916 Edit\SpecialChar menuseparator
33917 Math\SpecialChar menuseparator
33919 \begin_inset space ~
33922 Definition\SpecialChar menuseparator
33928 Spitting Out To The Right
33934 <row interlinespace="2.5mm">
33935 <cell alignment="center" valignment="top" usebox="none">
33938 \begin_layout Plain Layout
33941 arg "math-macro-append-greedy-param"
33949 <cell alignment="center" valignment="top" usebox="none">
33952 \begin_layout Plain Layout
33955 Edit\SpecialChar menuseparator
33956 Math\SpecialChar menuseparator
33958 \begin_inset space ~
33961 Definition\SpecialChar menuseparator
33963 \begin_inset Newline newline
33967 \begin_inset Phantom HPhantom
33970 \begin_layout Plain Layout
33973 Edit\SpecialChar menuseparator
33974 Math\SpecialChar menuseparator
33976 \begin_inset space ~
33979 Definition\SpecialChar menuseparator
33985 Eating From The Right
33991 <row interlinespace="2.5mm">
33992 <cell alignment="center" valignment="top" usebox="none">
33995 \begin_layout Plain Layout
33998 arg "math-macro-add-greedy-optional-param"
34006 <cell alignment="center" valignment="top" usebox="none">
34009 \begin_layout Plain Layout
34012 Edit\SpecialChar menuseparator
34013 Math\SpecialChar menuseparator
34015 \begin_inset space ~
34018 Definition\SpecialChar menuseparator
34019 Append Optional Argument
34020 \begin_inset Newline newline
34024 \begin_inset Phantom HPhantom
34027 \begin_layout Plain Layout
34030 Edit\SpecialChar menuseparator
34031 Math\SpecialChar menuseparator
34033 \begin_inset space ~
34036 Definition\SpecialChar menuseparator
34042 Eating From The Right
34055 \begin_layout Section
34056 Computer Algebra Systems
34059 \begin_layout Standard
34061 offers the exchange between mathematical expressions written in \SpecialChar LyX
34063 editor and external applications or user defined scripts.
34064 Currently supported applications are
34081 Note that the set of supported mathematical constructs is limited only
34082 to very simple cases.
34085 \begin_layout Subsection
34089 \begin_layout Standard
34090 Write some expression in a formula, go to the
34092 Edit\SpecialChar menuseparator
34093 Math\SpecialChar menuseparator
34094 Use Computer Algebra System
34096 menu and choose the application you have installed on the computer.
34097 After that the result of computation should show on the right side of the
34098 expression together with the
34099 \begin_inset Quotes eld
34103 \begin_inset Quotes erd
34109 \begin_layout Standard
34110 Here are few simple examples (with results from
34114 ) to show what kind of computations can be performed:
34117 \begin_layout Itemize
34118 \begin_inset Formula $\frac{37}{3}*2-\sum_{i=1}^{3}i^{i}=-\frac{22}{3}$
34124 \begin_layout Itemize
34125 \begin_inset Formula $\frac{37.0}{3}=12.33333333333333$
34131 \begin_layout Itemize
34132 \begin_inset Formula $\int_{1}^{2}\sin(x)dx=\cos1-\cos2$
34138 \begin_layout Itemize
34139 \begin_inset Formula $\int\left(\frac{1}{1+x^{3}}\right)dx=-\frac{\log\left(x^{2}-x+1\right)}{6}+\frac{\arctan\left(\frac{2\,x-1}{\sqrt{3}}\right)}{\sqrt{3}}+\frac{\log\left(x+1\right)}{3}$
34143 \begin_inset Newline newline
34147 \begin_inset Note Greyedout
34150 \begin_layout Plain Layout
34155 One needs to use proper delimiter insets
34156 \begin_inset Formula $\left(\right)$
34159 instead of simple '(' ')' characters.
34167 \begin_layout Itemize
34168 \begin_inset Formula $\det\left[\begin{array}{ccc}
34172 \end{array}\right]=-56$
34178 \begin_layout Itemize
34179 \begin_inset Formula $\lim_{x\rightarrow0}\left(\frac{\sin(x)}{x}\right)=1$
34185 \begin_layout Itemize
34186 \begin_inset Formula $powerseries\left(-\log\left(5-x\right),x,1\right)=\sum_{{\mathit{i}_{2}}=0}^{\infty}{\frac{4^{-{\mathit{i}_{2}}-1}\,\left(x-1\right)^{{\mathit{i}_{2}}+1}}{{\mathit{i}_{2}}+1}}-\log4$
34192 \begin_layout Itemize
34193 \begin_inset Formula $solve\left(x_{1}+y_{1}^{3}=y_{1}+x_{1}^{2},x_{1}\right)=\left[x_{1}=-\frac{\sqrt{4\,y_{1}^{3}-4\,y_{1}+1}-1}{2},x_{1}=\frac{\sqrt{4\,y_{1}^{3}-4\,y_{1}+1}+1}{2}\right]$
34199 \begin_layout Subsection
34203 \begin_layout Standard
34204 Currently there is no keyboard shortcut for calling the algebra applications.
34205 One can easily bind a shortcut to the
34219 \begin_inset space \thinspace{}
34223 \begin_inset space \space{}
34230 key inside the math editor.
34235 one would use this shortcut definition command:
34238 \begin_layout Standard
34241 command-alternatives paragraph-break;math-extern maxima
34244 \begin_layout Section
34246 \begin_inset Index idx
34249 \begin_layout Plain Layout
34258 \begin_layout Subsection
34260 \begin_inset Index idx
34263 \begin_layout Plain Layout
34272 \begin_layout Standard
34273 Negative numbers often look ugly in formulas because the minus sign before
34274 the number is set with the same length as the minus operator sign.
34275 When writing the negative number in normal text, the minus sign appears
34279 \begin_layout Standard
34280 Thus, the problem disappears when converting the minus sign to mathematical
34284 \begin_layout Standard
34285 An example to visualize the problem:
34288 \begin_layout Standard
34290 \begin_inset Tabular
34291 <lyxtabular version="3" rows="3" columns="2">
34292 <features booktabs="true" tabularvalignment="middle">
34293 <column alignment="right" valignment="top" width="0pt">
34294 <column alignment="left" valignment="top">
34296 <cell alignment="right" valignment="top" topline="true" leftline="true" usebox="none">
34299 \begin_layout Plain Layout
34305 <cell alignment="center" valignment="top" topline="true" rightline="true" usebox="none">
34308 \begin_layout Plain Layout
34316 <cell alignment="right" valignment="top" leftline="true" usebox="none">
34319 \begin_layout Plain Layout
34325 <cell alignment="center" valignment="top" rightline="true" usebox="none">
34328 \begin_layout Plain Layout
34329 \begin_inset Formula $x=-2$
34339 <cell alignment="right" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
34342 \begin_layout Plain Layout
34348 <cell alignment="center" valignment="top" topline="true" bottomline="true" rightline="true" usebox="none">
34351 \begin_layout Plain Layout
34352 \begin_inset Formula $x=\textrm{-}2$
34368 \begin_layout Subsection
34369 Comma as decimal Separator
34370 \begin_inset Index idx
34373 \begin_layout Plain Layout
34382 \begin_layout Standard
34383 In \SpecialChar LaTeX
34384 a comma inside a formula is used, according to the English convention,
34385 as number group separator.
34386 So there will be space added behind all commas in formulas.
34389 \begin_layout Standard
34390 To avoid this, the comma is highlighted and changed to mathematical text
34400 \begin_layout Standard
34401 To use all formula commas in the document as decimal separator, the file
34410 \begin_layout Plain Layout
34415 is part of the \SpecialChar LaTeX
34421 \begin_inset Index idx
34424 \begin_layout Plain Layout
34429 \begin_layout Plain Layout
34449 \begin_inset Index idx
34452 \begin_layout Plain Layout
34458 is loaded with the \SpecialChar LaTeX
34462 \begin_layout Standard
34470 \begin_layout Subsection
34472 \begin_inset CommandInset label
34474 name "subsec:Physical-Vectors"
34479 \begin_inset Index idx
34482 \begin_layout Plain Layout
34491 \begin_layout Standard
34492 Predefined vectors are offered by the \SpecialChar LaTeX
34498 \begin_inset Index idx
34501 \begin_layout Plain Layout
34507 that is loaded with the \SpecialChar LaTeX
34511 \begin_layout Standard
34519 \begin_layout Standard
34523 \begin_layout Plain Layout
34533 \begin_inset Note Note
34536 \begin_layout Plain Layout
34537 The following table will only be displayed when the \SpecialChar LaTeX
34550 \begin_layout Standard
34551 The following commands are defined:
34554 \begin_layout Standard
34556 \begin_inset Tabular
34557 <lyxtabular version="3" rows="4" columns="2">
34558 <features booktabs="true" tabularvalignment="middle">
34559 <column alignment="center" valignment="top" width="0pt">
34560 <column alignment="center" valignment="top">
34562 <cell alignment="center" valignment="top" topline="true" bottomline="true" usebox="none">
34565 \begin_layout Plain Layout
34571 <cell alignment="center" valignment="top" topline="true" bottomline="true" usebox="none">
34574 \begin_layout Plain Layout
34582 <cell alignment="center" valignment="top" usebox="none">
34585 \begin_layout Plain Layout
34595 <cell alignment="center" valignment="top" usebox="none">
34598 \begin_layout Plain Layout
34599 \begin_inset Formula $\Bra{\psi}$
34609 <cell alignment="center" valignment="top" usebox="none">
34612 \begin_layout Plain Layout
34622 <cell alignment="center" valignment="top" usebox="none">
34625 \begin_layout Plain Layout
34626 \begin_inset Formula $\Ket{\psi}$
34636 <cell alignment="center" valignment="top" bottomline="true" usebox="none">
34639 \begin_layout Plain Layout
34651 <cell alignment="center" valignment="top" bottomline="true" usebox="none">
34654 \begin_layout Plain Layout
34655 \begin_inset Formula $\Braket{\psi|\phi}$
34671 \begin_layout Standard
34678 assures that all vertical bars are set in the size of the surrounding brackets:
34679 \begin_inset Formula
34681 \Braket{\phi|J=\frac{3}{2}\,,\,M_{J}}
34690 \begin_layout Plain Layout
34700 \begin_inset Note Note
34703 \begin_layout Plain Layout
34704 The following will be displayed when the \SpecialChar LaTeX
34717 \begin_layout Standard
34718 You need to install the \SpecialChar LaTeX
34723 to see the rest of this subsection in the output.
34726 \begin_layout Standard
34730 \begin_layout Plain Layout
34742 \begin_layout Standard
34749 can also be achieved using the command
34755 , that is described in
34756 \begin_inset CommandInset ref
34758 reference "subsec:Automatic-Bracket-Size"
34765 \begin_layout Subsection
34766 Self-defined Fractions
34767 \begin_inset CommandInset label
34769 name "subsec:Self-defined-Fractions"
34774 \begin_inset Index idx
34777 \begin_layout Plain Layout
34778 Fractions ! self-defined
34786 \begin_layout Standard
34787 To define custom commands for fractions, the command
34794 \begin_inset Index idx
34797 \begin_layout Plain Layout
34804 \begin_layout Plain Layout
34818 is used in the following scheme:
34821 \begin_layout Standard
34834 bracket}{fraction bar thickness}{style}
34835 \begin_inset Newline newline
34839 \begin_inset Phantom HPhantom
34842 \begin_layout Plain Layout
34852 {numerator}{denominator}
34855 \begin_layout Standard
34856 The style is a number in the range of 0
34857 \begin_inset space \thinspace{}
34861 \begin_inset space \thinspace{}
34867 \begin_layout Standard
34869 \begin_inset Tabular
34870 <lyxtabular version="3" rows="5" columns="2">
34871 <features booktabs="true" tabularvalignment="middle">
34872 <column alignment="center" valignment="top" width="0pt">
34873 <column alignment="center" valignment="top">
34875 <cell alignment="center" valignment="top" topline="true" bottomline="true" usebox="none">
34878 \begin_layout Plain Layout
34884 <cell alignment="center" valignment="top" topline="true" bottomline="true" usebox="none">
34887 \begin_layout Plain Layout
34895 <cell alignment="center" valignment="top" usebox="none">
34898 \begin_layout Plain Layout
34904 <cell alignment="center" valignment="top" usebox="none">
34907 \begin_layout Plain Layout
34908 display style formula
34915 <cell alignment="center" valignment="top" usebox="none">
34918 \begin_layout Plain Layout
34924 <cell alignment="center" valignment="top" usebox="none">
34927 \begin_layout Plain Layout
34935 <cell alignment="center" valignment="top" usebox="none">
34938 \begin_layout Plain Layout
34944 <cell alignment="center" valignment="top" usebox="none">
34947 \begin_layout Plain Layout
34955 <cell alignment="center" valignment="top" bottomline="true" usebox="none">
34958 \begin_layout Plain Layout
34964 <cell alignment="center" valignment="top" bottomline="true" usebox="none">
34967 \begin_layout Plain Layout
34981 \begin_layout Standard
34982 When no style is given, the size is adjusted to the surrounding environment
34983 like for the command
34992 \begin_layout Standard
34993 When no fraction bar thickness is given, the predefined value of 0.4
34994 \begin_inset space \thinspace{}
35000 \begin_layout Standard
35001 \begin_inset VSpace medskip
35004 For example, the commands
35017 \begin_inset CommandInset ref
35019 reference "subsec:Fractions"
35023 are defined with the commands
35026 \begin_layout Standard
35035 genfrac{}{}{}{0}{#1}{#2}}
35038 \begin_layout Standard
35042 \begin_layout Standard
35051 genfrac{(}{)}{0pt}{1}{#1}{#2}}
35054 \begin_layout Standard
35055 \begin_inset VSpace medskip
35058 To define a fraction where the fraction bar thickness can be given as optional
35059 argument, the following line is inserted to the \SpecialChar LaTeX
35063 \begin_layout Standard
35072 genfrac{}{}{#1}{}{#2}{#3}}
35075 \begin_layout Standard
35077 \begin_inset Formula
35079 \text{Command} & & \mathrm{\backslash fracS[1mm]\backslash\{A\to\backslash\{B} & & \mathrm{\backslash fracS[5mm]\backslash\{A\to\backslash\{B}\\
35080 \text{Result} & & \fracS[1mm]{A}{B} & & \fracS[5mm]{A}{B}
35085 As one can see, the distance of the numerator and the denominator to the
35086 fraction bar is round about three times the bar thickness.
35089 \begin_layout Standard
35090 \begin_inset Newpage newpage
35096 \begin_layout Subsection
35098 \begin_inset Index idx
35101 \begin_layout Plain Layout
35110 \begin_layout Standard
35111 There are four ways to cancel formulas or parts of formulas:
35114 \begin_layout Standard
35118 \begin_layout Plain Layout
35128 \begin_inset Note Note
35131 \begin_layout Plain Layout
35132 The following table will only be displayed when the \SpecialChar LaTeX
35145 \begin_layout Standard
35147 \begin_inset Tabular
35148 <lyxtabular version="3" rows="5" columns="2">
35149 <features booktabs="true" tabularvalignment="middle">
35150 <column alignment="center" valignment="top" width="0pt">
35151 <column alignment="center" valignment="top">
35153 <cell alignment="center" valignment="top" topline="true" bottomline="true" usebox="none">
35156 \begin_layout Plain Layout
35162 <cell alignment="center" valignment="top" topline="true" bottomline="true" usebox="none">
35165 \begin_layout Plain Layout
35173 <cell alignment="center" valignment="top" usebox="none">
35176 \begin_layout Plain Layout
35180 \begin_inset space \textvisiblespace{}
35186 \begin_inset space \textvisiblespace{}
35194 <cell alignment="center" valignment="top" usebox="none">
35197 \begin_layout Plain Layout
35198 \begin_inset Formula $\cancel{\int A=B}$
35207 <row topspace="1.5mm">
35208 <cell alignment="center" valignment="top" usebox="none">
35211 \begin_layout Plain Layout
35215 \begin_inset space \textvisiblespace{}
35221 \begin_inset space \textvisiblespace{}
35229 <cell alignment="center" valignment="top" usebox="none">
35232 \begin_layout Plain Layout
35233 \begin_inset Formula $\bcancel{\int A=B}$
35242 <row topspace="1.5mm">
35243 <cell alignment="center" valignment="top" usebox="none">
35246 \begin_layout Plain Layout
35250 \begin_inset space \textvisiblespace{}
35256 \begin_inset space \textvisiblespace{}
35264 <cell alignment="center" valignment="top" usebox="none">
35267 \begin_layout Plain Layout
35268 \begin_inset Formula $\xcancel{\int A=B}$
35278 <cell alignment="center" valignment="top" topline="true" bottomline="true" usebox="none">
35281 \begin_layout Plain Layout
35285 \begin_inset space \textvisiblespace{}
35291 \begin_inset space \textvisiblespace{}
35295 \begin_inset Formula $\to$
35303 <cell alignment="center" valignment="top" topline="true" bottomline="true" usebox="none">
35306 \begin_layout Plain Layout
35307 \begin_inset Formula $\cancelto{1}{\int A=B}\hspace{3mm}$
35323 \begin_layout Standard
35330 is especially suitable to visualize the reduction of fractions within formulas:
35331 \begin_inset Formula
35333 \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}}}
35341 \begin_layout Standard
35342 To change the size of
35349 \begin_inset Quotes eld
35353 \begin_inset Quotes erd
35356 value one can add the \SpecialChar LaTeX
35360 \begin_layout Standard
35365 PassOptionsToPackage{option}{cancel}
35368 \begin_layout Standard
35377 which leads to the same size as for the canceled value, or
35381 which makes is it a bit smaller than normal.
35384 \begin_layout Standard
35385 To color the cancellation bar one adds this command as \SpecialChar TeX
35389 \begin_layout Standard
35401 \begin_layout Standard
35406 can be replaced by a color of your choice.
35409 \begin_layout Standard
35413 \begin_layout Plain Layout
35429 \begin_layout Standard
35430 \begin_inset Formula
35432 \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}}}
35440 \begin_layout Standard
35444 \begin_layout Plain Layout
35458 \begin_inset Note Note
35461 \begin_layout Plain Layout
35470 \begin_layout Standard
35471 For further customizations, see the documentation of the package
35476 \begin_inset CommandInset citation
35484 \begin_inset Index idx
35487 \begin_layout Plain Layout
35496 \begin_layout Standard
35500 \begin_layout Plain Layout
35510 \begin_inset Note Note
35513 \begin_layout Plain Layout
35514 The following will be displayed when the \SpecialChar LaTeX
35527 \begin_layout Standard
35528 You need to install the \SpecialChar LaTeX
35533 to see the rest of this subsection in the output.
35536 \begin_layout Standard
35540 \begin_layout Plain Layout
35552 \begin_layout Subsection
35553 Formulas in Section Headings
35554 \begin_inset CommandInset label
35556 name "subsec:Formulas-in-Section"
35561 \begin_inset Index idx
35564 \begin_layout Plain Layout
35565 Formula ! in section headings
35573 \begin_layout Standard
35574 When formulas are used in section headings, the following has to be taken
35578 \begin_layout Standard
35579 \begin_inset Note Greyedout
35582 \begin_layout Plain Layout
35588 \begin_inset Index idx
35591 \begin_layout Plain Layout
35592 Packages ! hyperref
35597 support is enabled in the document settings dialog under
35600 \begin_inset space ~
35605 , PDF-bookmarks are created for every section heading in the table of contents.
35606 If a section heading contains formulas, they are incorrectly displayed
35607 in the bookmark text, because formulas in bookmarks infringe the PDF convention
35616 \begin_layout Standard
35617 Both problems can be solved by inserting at the end of the section heading
35618 a short title with the menu
35620 Insert\SpecialChar menuseparator
35622 \begin_inset space ~
35628 Short titles are used as alternative for multiline section headings to
35629 keep the table of contents clearly arranged.
35630 Only the short title appears in the table of contents and therefore also
35631 in the PDF-bookmark.
35634 \begin_layout Standard
35635 When formulas should be used in the table of contents but
35639 is used, one can use the following command in \SpecialChar TeX
35643 \begin_layout Standard
35648 texorpdfstring{part}{alternative}
35649 \begin_inset Index idx
35652 \begin_layout Plain Layout
35663 \begin_layout Standard
35664 Part is the part of the heading that shouldn't appear in the PDF-bookmark.
35665 This can be characters, formulas, footnotes, but also cross-references.
35666 The alternative is used instead of the part for the bookmark.
35669 \begin_layout Standard
35670 Here are two example headings:
35671 \begin_inset VSpace -3mm
35678 \begin_layout Plain Layout
35690 \begin_layout Subsubsection
35691 Heading without formula in table of contents
35692 \begin_inset Formula $\sqrt{-1}=\mathrm{i}$
35696 \begin_inset Argument 1
35699 \begin_layout Plain Layout
35700 Heading without formula in table of contents
35708 \begin_layout Subsubsection
35709 Heading with formula in table of contents
35713 \begin_layout Plain Layout
35723 \begin_inset Formula $\sqrt{-1}=\mathrm{i}$
35730 \begin_layout Plain Layout
35740 \begin_layout Standard
35744 \begin_layout Plain Layout
35753 In the first heading a short title was used, in the second one
35762 \begin_layout Standard
35763 To get the same formatting as for the other headings, the complete heading
35772 \begin_layout Plain Layout
35774 \begin_inset CommandInset ref
35776 reference "subsec:Bold-Formulas"
35788 \begin_layout Subsection
35789 Formulas in multi-column Text
35790 \begin_inset Index idx
35793 \begin_layout Plain Layout
35794 Formula ! in multi-column text
35802 \begin_layout Standard
35803 Formulas in multi-column text are often too wide to fit into a column and
35804 thus need to be set over the whole page width.
35805 This is done by using the \SpecialChar LaTeX
35814 \begin_layout Plain Layout
35819 is part of every \SpecialChar LaTeX
35820 standard installation.
35826 \begin_inset Index idx
35829 \begin_layout Plain Layout
35830 Packages ! multicol
35835 , that is loaded with the \SpecialChar LaTeX
35839 \begin_layout Standard
35844 usepackage{multicol}
35847 \begin_layout Standard
35848 \begin_inset Note Greyedout
35851 \begin_layout Plain Layout
35852 Note that in this case the setting
35855 \begin_inset space ~
35862 Document\SpecialChar menuseparator
35868 \begin_inset space ~
35888 \begin_layout Standard
35889 Before the multi-column text the command
35892 \begin_layout Standard
35897 begin{multicols}{column number}
35900 \begin_layout Standard
35901 is written in \SpecialChar TeX
35903 The column number is a number in the range of 2
35904 \begin_inset space \thinspace{}
35908 \begin_inset space \thinspace{}
35912 Before the formula the multi-column text is ended by inserting the command
35915 \begin_layout Standard
35923 \begin_layout Standard
35924 in \SpecialChar TeX
35928 \begin_layout Standard
35929 Due to the command some space is automatically added before the formula.
35931 \begin_inset space \thinspace{}
35934 mm vertical space is inserted before the formula.
35935 When the formula style
35941 \begin_layout Plain Layout
35943 \begin_inset CommandInset ref
35945 reference "sec:Formula-Styles"
35957 \begin_inset space \thinspace{}
35960 mm space is inserted instead.
35963 \begin_layout Standard
35964 As example a multi-column text with a displayed formula:
35967 \begin_layout Standard
35973 \begin_layout Plain Layout
35977 begin{multicols}{2}
35982 Das Spektrum wird fouriertransformiert.
35983 Die Fouriertransformation wird verwendet, um die überlagerten Signale (Netzwerk
35984 , Lösungsmittel) zu trennen.
35985 Nachdem wir die Phasenverschiebung bestimmen konnten, interessiert uns
35986 nun das Aussehen des Ausgangssignals.
35987 Im Experiment haben wir es mit sehr vielen Teilchen zu tun, so dass man
35988 über alle Phasen integrieren muss.
35990 \begin_inset Formula $S$
35993 unser normiertes Ausgangssignal und
35994 \begin_inset Formula $P$
35997 die Phasenverteilungsfunktion, so ergibt sich die Beziehung
36001 \begin_layout Plain Layout
36011 \begin_inset VSpace -6mm
36015 \begin_inset Formula
36017 S(t)=S_{0}(t)\int_{-\infty}^{\infty}P(\phi,t)\mathrm{e}^{\mathrm{i}\phi}\,\mathrm{d}\phi
36026 \begin_layout Plain Layout
36030 begin{multicols}{2}
36036 \begin_inset Formula $S_{0}$
36039 das Signal ohne Gradient ist und die Normierungsbedingung
36040 \begin_inset Formula $\int_{-\infty}^{\infty}P(\phi,t)\,\mathrm{d}\phi=1$
36044 Nun dürfen wir aber nicht den Relaxationsprozess außer Acht lassen.
36046 \begin_inset Formula $\nicefrac{\pi}{2}$
36050 \begin_inset space \thinspace{}
36053 -rf-Puls beginnt sich die Magnetisierung zu entfokussieren, wodurch sich
36054 das Signal zusätzlich abschwächt.
36055 Diese Abschwächung verläuft exponentiell in Abhängigkeit der so genannten
36057 \begin_inset Formula $T_{2}$
36063 \begin_layout Standard
36069 \begin_layout Plain Layout
36081 \begin_layout Subsection
36082 Formulas with Description of Variables
36083 \begin_inset Index idx
36086 \begin_layout Plain Layout
36087 Formula ! with description of variables
36095 \begin_layout Standard
36096 To describe variables within a formula, like in formula
36097 \begin_inset CommandInset ref
36099 reference "eq:within"
36108 \begin_inset Formula $n$
36112 \begin_inset space ~
36115 matrix is used with left aligned columns for the
36116 \begin_inset Formula $n$
36123 \begin_layout Plain Layout
36125 \begin_inset CommandInset ref
36127 reference "sec:Matrices"
36136 To set the description in a smaller size, before the matrix e.
36137 \begin_inset space \thinspace{}
36141 \begin_inset space \space{}
36154 \begin_layout Plain Layout
36156 \begin_inset CommandInset ref
36158 reference "subsec:Font-Sizes"
36170 \begin_layout Standard
36171 When the formula style
36177 \begin_layout Plain Layout
36179 \begin_inset CommandInset ref
36181 reference "sec:Formula-Styles"
36202 \begin_layout Plain Layout
36209 only works in formulas with the style
36214 \begin_inset CommandInset ref
36216 reference "subsec:Variable-Space"
36225 is inserted before and after the matrix to have the same separation of
36226 the matrix from the equation and the side margin.
36229 \begin_layout Standard
36230 When the formula style
36234 is used, the method described in
36235 \begin_inset CommandInset ref
36237 reference "subsec:Flalign-Environment"
36241 is used to indent formulas.
36243 \begin_inset CommandInset ref
36245 reference "eq:within"
36249 consists of five columns where in the first two columns contain the equation,
36250 the third the matrix and the last one an empty \SpecialChar TeX
36252 \begin_inset Formula
36254 \hspace{30pt}F_{A} & =\rho·V·g & \footnotesize\begin{array}{ll}
36255 \rho & \textrm{density}\\
36256 V & \textrm{volume}\\
36257 g & \textrm{gravitational acceleration}
36258 \end{array} & & {}\label{eq:within}
36266 \begin_layout Subsection
36267 Upright small Greek Letters
36268 \begin_inset CommandInset label
36270 name "subsec:Upright-small-Greek"
36275 \begin_inset Index idx
36278 \begin_layout Plain Layout
36279 Greek letters ! upright
36287 \begin_layout Standard
36288 Most of the math fonts only provide italic small Greek letters.
36289 But for symbols of elementary particles like pions and neutrinos, upright
36290 Greek letters are needed.
36299 \begin_layout Plain Layout
36304 is part of the \SpecialChar LaTeX
36310 \begin_inset Index idx
36313 \begin_layout Plain Layout
36318 \begin_layout Plain Layout
36338 \begin_inset Index idx
36341 \begin_layout Plain Layout
36347 that is loaded with the \SpecialChar LaTeX
36351 \begin_layout Standard
36356 usepackage{upgreek}
36359 \begin_layout Standard
36365 \begin_layout Plain Layout
36375 \begin_inset Note Note
36378 \begin_layout Plain Layout
36379 The following table will only be displayed when the \SpecialChar LaTeX
36389 They are created when the command for a small Greek letter is started with
36395 For example the command
36402 \begin_inset Formula $\uptau$
36408 \begin_layout Standard
36409 With these commands reactions of elementary particles can be typeset:
36410 \begin_inset Formula
36412 \uppi^{+}\to\upmu^{+}+\upnu_{\upmu}
36420 \begin_layout Standard
36421 The upright letters are more bold and wider than the italic ones.
36422 They should therefore not be used for units like
36423 \begin_inset Quotes eld
36427 \begin_inset Quotes erd
36433 \begin_layout Standard
36437 \begin_layout Plain Layout
36447 \begin_inset Note Note
36450 \begin_layout Plain Layout
36451 The following will be displayed when the \SpecialChar LaTeX
36464 \begin_layout Standard
36465 You need to install the \SpecialChar LaTeX
36470 to see the rest of this subsection in the output.
36473 \begin_layout Standard
36477 \begin_layout Plain Layout
36489 \begin_layout Subsection
36490 Text Characters in Formulas
36491 \begin_inset Index idx
36494 \begin_layout Plain Layout
36503 \begin_layout Standard
36504 In some cases you might want to insert text characters directly into formulas.
36505 When for example the centered dot · is often used in formulas like
36506 \begin_inset Formula $\nu=5·10^{5}\,\mathrm{Hz}$
36509 , one would have to insert the command
36519 \begin_layout Plain Layout
36521 \begin_inset CommandInset ref
36523 reference "subsec:Binary-Operators"
36532 all the time, because this character is defined in all encodings as text
36534 But the encoding can be changed by this \SpecialChar LaTeX
36538 \begin_layout Standard
36543 Declare Inputtext{183}{
36553 f\SpecialChar ligaturebreak
36557 \begin_layout Standard
36558 The character encoding (menu
36560 Document\SpecialChar menuseparator
36561 Settings\SpecialChar menuseparator
36564 ) specifies what character appears when a keyboard key is pressed.
36565 When the key for the character '·' is pressed, internally the command
36572 But this command is not available in a formula so that you would get \SpecialChar LaTeX
36574 With the changed encoding the right command is chosen automatically, depending
36575 on if the character was inserted into a formula or not.
36578 \begin_layout Standard
36579 The encoding of several characters is saved in definition files.
36580 For example the encoding
36584 is defined in the file
36588 which is in the installation folder of \SpecialChar LaTeX
36590 Encodings should only be changed via the \SpecialChar LaTeX
36591 -preamble and not in the definition
36593 Otherwise documents could not be edited by other \SpecialChar LyX
36594 users working on other
36598 \begin_layout Standard
36599 \begin_inset VSpace medskip
36602 Besides the centered dot, in this document the degree sign ° is defined
36603 with the following \SpecialChar LaTeX
36604 -preamble line so that it can be directly inserted into
36608 \begin_layout Standard
36613 DeclareInputtext{176}{
36623 f\SpecialChar ligaturebreak
36627 \begin_layout Subsection
36629 -comments in formulas
36630 \begin_inset Index idx
36633 \begin_layout Plain Layout
36643 \begin_layout Standard
36644 In text you can insert a comment that will only be visible in the \SpecialChar LaTeX
36646 code of your file with the menu
36648 Insert\SpecialChar menuseparator
36649 Note\SpecialChar menuseparator
36653 This is not possible in a formula but you can insert \SpecialChar LaTeX
36658 \begin_layout Standard
36666 \begin_layout Standard
36667 This creates a box in which you can write your comment.
36668 Due to a bug in \SpecialChar LyX
36673 \begin_layout Plain Layout
36674 \begin_inset CommandInset href
36676 name "LyX-bug #9002"
36677 target "http://www.lyx.org/trac/ticket/9002"
36687 you cannot write normal text inside the comment, even when you use mathematical
36688 text, you will see its \SpecialChar LaTeX
36689 -commands in the \SpecialChar LaTeX
36691 \begin_inset Newline newline
36694 This a formula with a \SpecialChar LaTeX
36696 \begin_inset Formula
36698 A=B%\text{This is the comment}
36706 \begin_layout Standard
36707 \begin_inset Newpage newpage
36713 \begin_layout Section
36716 \begin_inset Index idx
36719 \begin_layout Plain Layout
36728 \begin_layout Standard
36729 This section is a summary of the most important typographic rules, listed
36734 \begin_layout Plain Layout
36735 This collection was partly taken from the German semi-official dictionary
36737 \begin_inset Quotes eld
36741 \begin_inset Quotes erd
36745 \begin_inset CommandInset citation
36752 that lists some of the ISO rules.
36753 More rules are listed in
36754 \begin_inset CommandInset citation
36769 \begin_layout Itemize
36778 \begin_layout Plain Layout
36779 done with font styles, see
36780 \begin_inset CommandInset ref
36782 reference "subsec:Font-Styles"
36791 , no matter if they appear in italic text: 30
36792 \begin_inset space \thinspace{}
36796 \begin_inset Newline newline
36799 Between the value and the unit is the smallest space, see
36800 \begin_inset CommandInset ref
36802 reference "subsec:Predefined-Space"
36807 \begin_inset Newline newline
36810 This convention is automatically fulfilled when the command
36817 When it is entered to a formula, two boxes appear.
36818 In the first one the value is inserted, in the second one the unit, and
36820 \begin_inset Formula $\unit[30]{km/h}$
36824 \begin_inset space \thinspace{}
36834 is not a real \SpecialChar LaTeX
36835 command but the command
36841 , therefore you cannot use it in \SpecialChar TeX
36845 \begin_layout Itemize
36846 Percent and perthousand signs are set like physical units:
36847 \begin_inset Newline newline
36851 \begin_inset space \thinspace{}
36857 \begin_layout Itemize
36858 The degree sign follows directly on the value: 15°, but not when it is used
36860 \begin_inset space \thinspace{}
36866 \begin_layout Itemize
36867 In numbers with more than four digits the smallest space is inserted before
36868 every third digit to group them:
36878 \begin_inset space \thinspace{}
36882 \begin_inset space \thinspace{}
36888 \begin_layout Itemize
36889 For dimensions like 120×90×40
36890 \begin_inset space \thinspace{}
36893 cm the multiplication sign
36894 \begin_inset Quotes eld
36898 \begin_inset Quotes erd
36902 It is available either via the command
36910 Insert\SpecialChar menuseparator
36911 Special Character\SpecialChar menuseparator
36917 \begin_layout Itemize
36918 Functions with names consisting of several letters are set upright to avoid
36920 \begin_inset CommandInset ref
36922 reference "subsec:Predefined-Functions"
36929 \begin_layout Itemize
36930 Indices consisting of several letters, are set upright:
36931 \begin_inset Formula $E_{\mathrm{kin}}$
36935 \begin_inset Newline newline
36938 Components of matrices are set italic:
36939 \begin_inset Formula $\hat{H}_{kl}$
36945 \begin_layout Itemize
36946 The differentiation/integration operator 'd', the Euler's number 'e' and
36947 the imaginary unit 'i' should be set upright, to avoid mixing them up with
36951 \begin_layout Itemize
36952 The character that denotes a
36956 transformation is inserted either by the command
36961 \begin_inset space \textvisiblespace{}
36968 Insert\SpecialChar menuseparator
36969 Special Character\SpecialChar menuseparator
36970 Symbols\SpecialChar menuseparator
36972 \begin_inset space ~
36978 \begin_inset Formula $\mathscr{F}$
36984 \begin_layout Standard
36985 \begin_inset Newpage newpage
36991 \begin_layout Section
36993 \begin_inset Index idx
36996 \begin_layout Plain Layout
37005 \begin_layout Standard
37006 Some characters and symbols can be created with several commands.
37007 Here is a list of the synonym commands:
37010 \begin_layout Standard
37011 \begin_inset VSpace bigskip
37015 \begin_inset space \hfill{}
37019 \begin_inset Tabular
37020 <lyxtabular version="3" rows="12" columns="2">
37021 <features booktabs="true" tabularvalignment="middle">
37022 <column alignment="center" valignment="top" width="0pt">
37023 <column alignment="center" valignment="top" width="0pt">
37025 <cell alignment="center" valignment="top" topline="true" bottomline="true" usebox="none">
37028 \begin_layout Plain Layout
37034 <cell alignment="center" valignment="top" topline="true" bottomline="true" usebox="none">
37037 \begin_layout Plain Layout
37045 <cell alignment="center" valignment="top" usebox="none">
37048 \begin_layout Plain Layout
37056 <cell alignment="center" valignment="top" usebox="none">
37059 \begin_layout Plain Layout
37067 <cell alignment="center" valignment="top" usebox="none">
37070 \begin_layout Plain Layout
37078 <cell alignment="center" valignment="top" usebox="none">
37081 \begin_layout Plain Layout
37091 <cell alignment="center" valignment="top" usebox="none">
37094 \begin_layout Plain Layout
37102 <cell alignment="center" valignment="top" usebox="none">
37105 \begin_layout Plain Layout
37115 <cell alignment="center" valignment="top" usebox="none">
37118 \begin_layout Plain Layout
37126 <cell alignment="center" valignment="top" usebox="none">
37129 \begin_layout Plain Layout
37137 <cell alignment="center" valignment="top" usebox="none">
37140 \begin_layout Plain Layout
37148 <cell alignment="center" valignment="top" usebox="none">
37151 \begin_layout Plain Layout
37159 <cell alignment="center" valignment="top" usebox="none">
37162 \begin_layout Plain Layout
37170 <cell alignment="center" valignment="top" usebox="none">
37173 \begin_layout Plain Layout
37183 <cell alignment="center" valignment="top" usebox="none">
37186 \begin_layout Plain Layout
37194 <cell alignment="center" valignment="top" usebox="none">
37197 \begin_layout Plain Layout
37207 <cell alignment="center" valignment="top" usebox="none">
37210 \begin_layout Plain Layout
37218 <cell alignment="center" valignment="top" usebox="none">
37221 \begin_layout Plain Layout
37231 <cell alignment="center" valignment="top" usebox="none">
37234 \begin_layout Plain Layout
37242 <cell alignment="center" valignment="top" usebox="none">
37245 \begin_layout Plain Layout
37255 <cell alignment="center" valignment="top" usebox="none">
37258 \begin_layout Plain Layout
37266 <cell alignment="center" valignment="top" usebox="none">
37269 \begin_layout Plain Layout
37277 <cell alignment="center" valignment="top" bottomline="true" usebox="none">
37280 \begin_layout Plain Layout
37288 <cell alignment="center" valignment="top" bottomline="true" usebox="none">
37291 \begin_layout Plain Layout
37303 \begin_inset space \hfill{}
37307 \begin_inset Tabular
37308 <lyxtabular version="3" rows="12" columns="2">
37309 <features booktabs="true" tabularvalignment="middle">
37310 <column alignment="center" valignment="top" width="0pt">
37311 <column alignment="center" valignment="top" width="0pt">
37313 <cell alignment="center" valignment="top" topline="true" bottomline="true" usebox="none">
37316 \begin_layout Plain Layout
37322 <cell alignment="center" valignment="top" topline="true" bottomline="true" usebox="none">
37325 \begin_layout Plain Layout
37333 <cell alignment="center" valignment="top" usebox="none">
37336 \begin_layout Plain Layout
37344 <cell alignment="center" valignment="top" usebox="none">
37347 \begin_layout Plain Layout
37359 <cell alignment="center" valignment="top" usebox="none">
37362 \begin_layout Plain Layout
37370 <cell alignment="center" valignment="top" usebox="none">
37373 \begin_layout Plain Layout
37383 <cell alignment="center" valignment="top" usebox="none">
37386 \begin_layout Plain Layout
37394 <cell alignment="center" valignment="top" usebox="none">
37397 \begin_layout Plain Layout
37407 <cell alignment="center" valignment="top" usebox="none">
37410 \begin_layout Plain Layout
37418 <cell alignment="center" valignment="top" usebox="none">
37421 \begin_layout Plain Layout
37429 <cell alignment="center" valignment="top" usebox="none">
37432 \begin_layout Plain Layout
37440 <cell alignment="center" valignment="top" usebox="none">
37443 \begin_layout Plain Layout
37451 <cell alignment="center" valignment="top" usebox="none">
37454 \begin_layout Plain Layout
37462 <cell alignment="center" valignment="top" usebox="none">
37465 \begin_layout Plain Layout
37475 <cell alignment="center" valignment="top" usebox="none">
37478 \begin_layout Plain Layout
37486 <cell alignment="center" valignment="top" usebox="none">
37489 \begin_layout Plain Layout
37499 <cell alignment="center" valignment="top" usebox="none">
37502 \begin_layout Plain Layout
37510 <cell alignment="center" valignment="top" usebox="none">
37513 \begin_layout Plain Layout
37523 <cell alignment="center" valignment="top" usebox="none">
37526 \begin_layout Plain Layout
37534 <cell alignment="center" valignment="top" usebox="none">
37537 \begin_layout Plain Layout
37547 <cell alignment="center" valignment="top" usebox="none">
37550 \begin_layout Plain Layout
37558 <cell alignment="center" valignment="top" usebox="none">
37561 \begin_layout Plain Layout
37571 <cell alignment="center" valignment="top" bottomline="true" usebox="none">
37574 \begin_layout Plain Layout
37582 <cell alignment="center" valignment="top" bottomline="true" usebox="none">
37585 \begin_layout Plain Layout
37599 \begin_inset space \hfill{}
37605 \begin_layout Standard
37606 \begin_inset Newpage newpage
37612 \begin_layout Bibliography
37613 \begin_inset CommandInset bibitem
37614 LatexCommand bibitem
37627 The \SpecialChar LaTeX
37631 Addison Wesley, 2004
37634 \begin_layout Bibliography
37635 \begin_inset CommandInset bibitem
37636 LatexCommand bibitem
37643 \begin_inset CommandInset href
37646 target "https://www.tug.org/~hvoss/PDF/mathmode.pdf"
37651 of \SpecialChar LaTeX
37655 \begin_layout Bibliography
37656 \begin_inset CommandInset bibitem
37657 LatexCommand bibitem
37664 \begin_inset CommandInset href
37667 target "http://mirrors.ctan.org/macros/latex/required/amslatex/math/amsldoc.pdf"
37676 \begin_layout Plain Layout
37685 -\SpecialChar LaTeX
37689 \begin_layout Bibliography
37690 \begin_inset CommandInset bibitem
37691 LatexCommand bibitem
37698 \begin_inset CommandInset href
37701 target "ftp://ftp.dante.de/tex-archive/info/symbols/comprehensive/symbols-a4.pdf"
37706 of all symbols available with \SpecialChar LaTeX
37710 \begin_layout Bibliography
37711 \begin_inset CommandInset bibitem
37712 LatexCommand bibitem
37719 \begin_inset CommandInset href
37721 name "Documentation"
37722 target "http://mirrors.ctan.org/macros/latex/contrib/cancel/cancel.pdf"
37727 of the \SpecialChar LaTeX
37733 \begin_inset Index idx
37736 \begin_layout Plain Layout
37745 \begin_layout Bibliography
37746 \begin_inset CommandInset bibitem
37747 LatexCommand bibitem
37754 \begin_inset CommandInset href
37756 name "Documentation"
37757 target "http://www.tug.org/applications/hyperref/ftp/doc/manual.pdf"
37762 of the \SpecialChar LaTeX
37768 \begin_inset Index idx
37771 \begin_layout Plain Layout
37772 Packages ! hyperref
37780 \begin_layout Bibliography
37781 \begin_inset CommandInset bibitem
37782 LatexCommand bibitem
37789 \begin_inset CommandInset href
37791 name "Documentation"
37792 target "http://www.ctan.org/tex-archive/macros/latex/contrib/mhchem/mhchem.pdf"
37797 of the \SpecialChar LaTeX
37803 \begin_inset Index idx
37806 \begin_layout Plain Layout
37815 \begin_layout Bibliography
37816 \begin_inset CommandInset bibitem
37817 LatexCommand bibitem
37829 Auflage, Duden 2001
37832 \begin_layout Bibliography
37833 \begin_inset CommandInset bibitem
37834 LatexCommand bibitem
37841 \begin_inset CommandInset href
37844 target "http://physics.nist.gov/Pubs/SP811/sec11.html"
37849 for reviewing manuscripts
37852 \begin_layout Standard
37853 \begin_inset CommandInset index_print
37854 LatexCommand printindex