1 #LyX 2.2 created this file. For more info see http://www.lyx.org/
8 % DO NOT ALTER THIS PREAMBLE!!!
10 % This preamble is designed to ensure that the file prints
11 % out as advertised. If you mess with this preamble,
12 % parts of this document may not print out as expected. If you
13 % have problems LaTeXing this file, please contact
14 % the documentation team
15 % email: lyx-docs@lists.lyx.org
21 % set fonts for nicer pdf view
22 \IfFileExists{lmodern.sty}
23 {\usepackage{lmodern}}{}
25 \fi % end if pdflatex is used
27 % solves the following problem:
28 % If the dection number consits of too many numerals the section heading
29 % will be printed in the TOC without a space between it and the section number.
30 % As solution more space between the number and the heading is inserted:
31 \renewcommand{\l@subsection}{\@dottedtocline{2}{1.5em}{2.8em}}
32 \renewcommand{\l@subsubsection}{\@dottedtocline{3}{4.3em}{3.6em}}
34 % increase link area for cross-references and autoname them,
35 \AtBeginDocument{\renewcommand{\ref}[1]{\mbox{\autoref{#1}}}}
36 \@ifundefined{extrasenglish}{\usepackage[english]{babel}}{}
37 \addto\extrasenglish{%
38 \renewcommand*{\equationautorefname}[1]{}%
39 \renewcommand{\sectionautorefname}{sec.\negthinspace}%
40 \renewcommand{\subsectionautorefname}{sec.\negthinspace}%
41 \renewcommand{\subsubsectionautorefname}{sec.\negthinspace}%
44 % don't load packages twice
45 % see first footnote in sec. 9.3
46 \@ifundefined{textcolor}{\usepackage{color}}{}
48 % the pages of the TOC are numbered roman
49 % and a PDF-bookmark for the TOC is added
51 \let\myTOC\tableofcontents
52 \renewcommand{\tableofcontents}{%
54 \pdfbookmark[1]{\contentsname}{}
57 \pagenumbering{arabic}}
59 % add 0.5 mm vertical space for table rows
60 \@ifundefined{extrarowheight} {\usepackage{array}}{}
61 \setlength{\extrarowheight}{0.5mm}
63 % insert additional vertical space of 1.5 mm between footnotes,
65 \renewcommand{\footnote}[1]{\myFoot{#1\vspace{1.5mm}}}
67 % makes caption labels bold
68 \setkomafont{captionlabel}{\bfseries}
70 % enables calculation of values
73 % for multiple columns used in sec. 24.7
79 % for the Fourier transformation symbol
82 % define a color, used in sec.9.3
83 \definecolor{darkgreen}{cmyk}{0.5, 0, 1, 0.5}
85 % declare operators (see sec. 10.4 and sec. 15.2)
86 \DeclareMathOperator*{\Lozenge}{\blacklozenge}
87 \DeclareMathOperator{\sgn}{sgn}
89 % example definitions for sec. 20.1
90 \newcommand{\gr}{\Longrightarrow}
91 \newcommand{\us}[1]{\underline{#1}}
92 \newcommand{\fb}[3]{\framebox#1#2{$#3$}}
93 \newcommand{\cb}[3][white]{\fcolorbox{#2}{#1}{$#3$}}
94 \newcommand{\fracS}[3][]{\genfrac{}{}{#1}{}{#2}{#3}}
96 % example macro from sec. 19.4
97 %\def\tagform@#1{\maketag@@@{|#1|}}
100 % ------------------------------------
101 % used to check for needed LaTeX packages
104 % check for package undertilde
105 % used for the command \utilde
106 \newboolean{undertilde}
107 \IfFileExists{undertilde.sty}
108 {\usepackage{undertilde}
109 \setboolean{undertilde}{true}}
110 {\setboolean{undertilde}{false}}
112 % check for package eurosym
113 % used for the Euro symbol
115 \IfFileExists{eurosym.sty}
116 {\usepackage[gennarrow]{eurosym}
117 \setboolean{eurosym}{true}}
118 {\setboolean{eurosym}{false}}
120 % check for package braket
121 % used for physical vectors
123 \IfFileExists{braket.sty}
125 \setboolean{braket}{true}}
126 {\setboolean{braket}{false}}
128 % check for package cancel
130 \IfFileExists{cancel.sty}
132 \setboolean{cancel}{true}}
133 {\setboolean{cancel}{false}}
135 % check for package upgreek
137 \IfFileExists{upgreek.sty}
138 {\usepackage{upgreek}
139 \setboolean{upgreek}{true}}
140 {\setboolean{upgreek}{false}}
142 \options bibliography=totoc,index=totoc,BCOR7.5mm,titlepage,captions=tableheading
143 \use_default_options false
144 \maintain_unincluded_children false
146 \language_package default
151 \font_typewriter default
153 \font_default_family default
154 \use_non_tex_fonts false
160 \default_output_format default
162 \bibtex_command default
163 \index_command default
167 \pdf_title "LyX's Math Manual"
168 \pdf_author "LyX Team, Uwe Stöhr"
169 \pdf_subject "LyX-documentation about math"
170 \pdf_keywords "LyX, Mathed"
172 \pdf_bookmarksnumbered true
173 \pdf_bookmarksopen true
174 \pdf_bookmarksopenlevel 1
175 \pdf_breaklinks false
179 \pdf_pdfusetitle false
180 \pdf_quoted_options "linkcolor=black, citecolor=black, urlcolor=blue, filecolor=blue, pdfpagelayout=OneColumn, pdfnewwindow=true, pdfstartview=XYZ, plainpages=false"
183 \use_package amsmath 2
184 \use_package amssymb 2
185 \use_package cancel 0
187 \use_package mathdots 1
188 \use_package mathtools 2
189 \use_package mhchem 1
190 \use_package stackrel 0
191 \use_package stmaryrd 0
192 \use_package undertilde 0
194 \cite_engine_type default
198 \paperorientation portrait
202 \notefontcolor #0000ff
209 \paragraph_separation skip
211 \quotes_language english
214 \paperpagestyle plain
218 \tracking_changes false
219 \output_changes false
222 \html_be_strict false
229 's detailed Math manual
233 by the \SpecialChar LyX
238 \begin_layout Plain Layout
240 If you have comments or error corrections, please send them to the \SpecialChar LyX
245 \begin_inset CommandInset href
247 name "lyx-docs@lists.lyx.org"
248 target "lyx-docs@lists.lyx.org?subject=LyX's Math manual"
259 \begin_inset Note Note
262 \begin_layout Plain Layout
269 \begin_inset Newline newline
273 \begin_inset Newline newline
281 \begin_layout Standard
282 \begin_inset CommandInset toc
283 LatexCommand tableofcontents
290 \begin_layout Standard
291 \begin_inset Note Note
294 \begin_layout Plain Layout
295 To export this document to PDF, PS or DVI the \SpecialChar LaTeX
298 braket, cancel, eurosym, mathdots, mathtools, mhchem, undertilde
305 If they are not installed the document can be exported anyway but the sections
306 where the packages are required will not appear in the output.
311 ; if it is not installed, this file cannot be exported.
314 \begin_layout Plain Layout
315 The latest PDF-version of this document can be found here:
316 \begin_inset Newline newline
321 http://wiki.lyx.org/LyX/DocumentationDevelopment#Math
329 \begin_layout Standard
330 \begin_inset Newpage newpage
336 \begin_layout Section
340 \begin_layout Standard
341 This document explains \SpecialChar LyX
342 's math features and is furthermore a collection
343 of \SpecialChar LaTeX
344 -commands used for mathematical characters and constructs.
345 The explanations are designed for the usage of commands.
346 It is therefore required that you have read the section
357 \begin_layout Standard
358 Most of the characters and many constructs explained in this manual are
359 also accessible via the menu
363 \SpecialChar menuseparator
379 But everybody who has to write lots of formulas will notice that it is
380 much faster to use commands instead of the math toolbar.
381 Therefore this manual is focused on commands but also mentions the correspondin
382 g toolbar buttons when available.
385 \begin_layout Standard
386 If not specially mentioned the commands are only available within formulas.
387 To be able to use all commands explained in this document, the option
391 must be checked in the document settings (menu
393 Document\SpecialChar menuseparator
394 Settings\SpecialChar menuseparator
405 \begin_layout Plain Layout
408 Use AMS math package automatically
414 \begin_layout Plain Layout
423 -math when math constructs are found that are supported by \SpecialChar LyX
432 \begin_layout Standard
433 This document doesn't list all
437 \begin_layout Plain Layout
450 \begin_layout Plain Layout
455 \begin_layout Plain Layout
464 -math commands is in the file
467 \begin_inset CommandInset href
470 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"
1503 \begin_inset Separator parbreak
1509 \begin_layout Standard
1511 \begin_inset Tabular
1512 <lyxtabular version="3" rows="4" columns="2">
1513 <features booktabs="true" tabularvalignment="middle">
1514 <column alignment="center" valignment="top" width="0pt">
1515 <column alignment="center" valignment="top" width="0pt">
1517 <cell alignment="center" valignment="top" topline="true" bottomline="true" usebox="none">
1520 \begin_layout Plain Layout
1526 <cell alignment="center" valignment="top" topline="true" bottomline="true" usebox="none">
1529 \begin_layout Plain Layout
1537 <cell alignment="center" valignment="top" usebox="none">
1540 \begin_layout Plain Layout
1546 <cell alignment="center" valignment="top" usebox="none">
1549 \begin_layout Plain Layout
1550 \begin_inset Formula $B_{V}$
1559 <row topspace="1.5mm">
1560 <cell alignment="center" valignment="top" usebox="none">
1563 \begin_layout Plain Layout
1569 <cell alignment="center" valignment="top" usebox="none">
1572 \begin_layout Plain Layout
1573 \begin_inset Formula $B^{V}$
1582 <row topspace="1.5mm">
1583 <cell alignment="center" valignment="top" topline="true" bottomline="true" usebox="none">
1586 \begin_layout Plain Layout
1588 \begin_inset space \textvisiblespace{}
1596 <cell alignment="center" valignment="top" topline="true" bottomline="true" usebox="none">
1599 \begin_layout Plain Layout
1600 \begin_inset Formula $B^{A}$
1616 \begin_layout Standard
1617 As the caret is in some languages an accent, vowels will be accentuated
1618 in this case and not set as exponents
1622 \begin_layout Plain Layout
1623 Depending on the used keyboard settings this can also happen for characters
1630 To get exponents in this case, press
1634 after the caret as in the last example.
1637 \begin_layout Subsection
1639 \begin_inset CommandInset label
1641 name "subsec:Fractions"
1646 \begin_inset Index idx
1649 \begin_layout Plain Layout
1658 \begin_layout Standard
1659 Fractions are generated with the command
1666 \begin_inset Index idx
1669 \begin_layout Plain Layout
1677 or via the math toolbar button
1680 arg "math-insert \\frac"
1684 The font size is adjusted automatically, depending on whether the fraction
1685 is in an inline or display style formula.
1686 With the math toolbar button
1689 arg "math-insert \\frac-square"
1692 you can select different fraction types.
1695 \begin_layout Standard
1703 \begin_inset Index idx
1706 \begin_layout Plain Layout
1714 a fraction can be created that always has the size of a display style formula.
1722 \begin_inset Index idx
1725 \begin_layout Plain Layout
1733 the fraction appears always with the size of an inline formula.
1737 \begin_layout Standard
1738 A line with the fraction
1739 \begin_inset Formula $\frac{1}{2}$
1742 that was created with the command
1751 \begin_layout Standard
1752 A line with the fraction
1753 \begin_inset Formula $\dfrac{1}{2}$
1756 that was created with the command
1763 \begin_inset Separator parbreak
1769 \begin_layout Standard
1771 \begin_inset Tabular
1772 <lyxtabular version="3" rows="4" columns="2">
1773 <features booktabs="true" tabularvalignment="middle">
1774 <column alignment="center" valignment="top" width="0pt">
1775 <column alignment="center" valignment="top" width="0pt">
1777 <cell alignment="center" valignment="top" topline="true" bottomline="true" usebox="none">
1780 \begin_layout Plain Layout
1786 <cell alignment="center" valignment="top" topline="true" bottomline="true" usebox="none">
1789 \begin_layout Plain Layout
1796 <row topspace="1.5mm">
1797 <cell alignment="center" valignment="top" usebox="none">
1800 \begin_layout Plain Layout
1804 \begin_inset space \textvisiblespace{}
1808 \begin_inset Formula $\downarrow$
1816 <cell alignment="center" valignment="top" usebox="none">
1819 \begin_layout Plain Layout
1820 \begin_inset Formula $\frac{A}{B}$
1829 <row topspace="2mm">
1830 <cell alignment="center" valignment="top" usebox="none">
1833 \begin_layout Plain Layout
1837 \begin_inset space \textvisiblespace{}
1841 \begin_inset Formula $\downarrow$
1849 <cell alignment="center" valignment="top" usebox="none">
1852 \begin_layout Plain Layout
1853 \begin_inset Formula $\dfrac{A}{B}$
1862 <row topspace="2mm" bottomspace="1mm">
1863 <cell alignment="center" valignment="top" bottomline="true" usebox="none">
1866 \begin_layout Plain Layout
1870 \begin_inset space \textvisiblespace{}
1876 \begin_inset space \textvisiblespace{}
1880 \begin_inset Formula $\downarrow$
1884 \begin_inset Formula $\downarrow\downarrow$
1892 <cell alignment="center" valignment="top" bottomline="true" usebox="none">
1895 \begin_layout Plain Layout
1896 \begin_inset Formula $\dfrac{e^{\frac{1}{2}}}{3}$
1912 \begin_layout Standard
1913 \begin_inset VSpace bigskip
1917 \begin_inset Newpage newpage
1920 For nested fractions the command
1927 \begin_inset Index idx
1930 \begin_layout Plain Layout
1940 \begin_inset VSpace -3mm
1946 \begin_layout Standard
1947 \begin_inset Formula
1949 \textrm{created with \textbf{\textbackslash frac}} & & \textrm{created with \textbf{\textbackslash cfrac}}\\
1950 \frac{A}{B+\frac{C+\frac{E}{F}}{D}} & & \cfrac{A}{B+\cfrac{C+\cfrac{E}{F}}{D}}
1958 \begin_layout Standard
1959 The command for the example above is:
1962 \begin_layout Standard
1968 \begin_inset space \textvisiblespace{}
1972 \begin_inset Formula $\downarrow$
1978 \begin_inset space \textvisiblespace{}
1984 \begin_inset space \textvisiblespace{}
1988 \begin_inset Formula $\downarrow$
1992 \begin_inset Formula $\downarrow$
1998 \begin_layout Standard
1999 \begin_inset VSpace medskip
2005 \begin_layout Standard
2012 sets the fraction always in the size of a displayed formula, also when
2013 it is part of another fraction.
2016 \begin_layout Standard
2017 It is possible to specify the alignment of the numerator.
2024 is used to left align it, the command
2037 centers the numerator.
2038 These fractions demonstrate the different alignments:
2041 \begin_layout Standard
2044 \begin_inset Formula
2046 \cfrac[l]{A}{B+C}\,,\,\cfrac{A}{B+C}\,,\,\cfrac[r]{A}{B+C}
2054 \begin_layout Standard
2055 \begin_inset Note Greyedout
2058 \begin_layout Plain Layout
2075 are no real \SpecialChar LaTeX
2076 commands but represent the command
2080 cfrac[alignment]{numerator}{denominator}
2083 Therefore you cannot use them in \SpecialChar TeX
2092 \begin_layout Standard
2093 \begin_inset VSpace medskip
2096 It is often advantageous to combine
2109 \begin_inset Formula
2111 \cfrac{A}{B+\cfrac{C+\frac{E}{F}}{D}}
2119 \begin_layout Standard
2120 For inline fractions with a sloped fraction stroke you can use the command
2128 \begin_inset Index idx
2131 \begin_layout Plain Layout
2140 \begin_inset Formula $\nicefrac{5}{31}$
2150 \begin_inset Index idx
2153 \begin_layout Plain Layout
2162 \begin_inset Formula $\unitfrac{5}{31}$
2165 There is furthermore the command
2171 that offers to write a fraction in combination with a number:
2172 \begin_inset Formula $\unitfrac[2]{1}{3}$
2178 \begin_layout Standard
2179 \begin_inset Note Greyedout
2182 \begin_layout Plain Layout
2193 is not a real \SpecialChar LaTeX
2194 command but the command
2195 \begin_inset Newline newline
2202 unitfrac[number]{numerator}{denominator}
2205 Therefore you cannot use it in \SpecialChar TeX
2214 \begin_layout Standard
2215 How to define own fractions where the fraction stroke can be changed, is
2217 \begin_inset CommandInset ref
2219 reference "subsec:Self-defined-Fractions"
2226 \begin_layout Standard
2227 Multiline fractions are explained in
2228 \begin_inset CommandInset ref
2230 reference "subsec:Multiline-Fractions"
2237 \begin_layout Subsection
2239 \begin_inset Index idx
2242 \begin_layout Plain Layout
2251 \begin_layout Standard
2252 Square roots are created with
2259 \begin_inset Index idx
2262 \begin_layout Plain Layout
2270 or the math toolbar button
2273 arg "math-insert \\sqrt"
2276 , all other roots with the command
2283 \begin_inset Index idx
2286 \begin_layout Plain Layout
2294 or with the math toolbar button
2297 arg "math-insert \\root"
2301 \begin_inset Separator parbreak
2307 \begin_layout Standard
2309 \begin_inset Tabular
2310 <lyxtabular version="3" rows="3" columns="2">
2311 <features booktabs="true" tabularvalignment="middle">
2312 <column alignment="center" valignment="top" width="0pt">
2313 <column alignment="center" valignment="top" width="0pt">
2315 <cell alignment="center" valignment="top" topline="true" bottomline="true" usebox="none">
2318 \begin_layout Plain Layout
2324 <cell alignment="center" valignment="top" topline="true" bottomline="true" usebox="none">
2327 \begin_layout Plain Layout
2334 <row topspace="1mm">
2335 <cell alignment="center" valignment="top" usebox="none">
2338 \begin_layout Plain Layout
2342 \begin_inset space \textvisiblespace{}
2350 <cell alignment="center" valignment="top" usebox="none">
2353 \begin_layout Plain Layout
2354 \begin_inset Formula $\sqrt{A-B}$
2363 <row topspace="1mm">
2364 <cell alignment="center" valignment="top" bottomline="true" usebox="none">
2367 \begin_layout Plain Layout
2371 \begin_inset space \textvisiblespace{}
2375 \begin_inset Formula $\downarrow$
2383 <cell alignment="center" valignment="top" bottomline="true" usebox="none">
2386 \begin_layout Plain Layout
2387 \begin_inset Formula $\sqrt[3]{A-B}$
2403 \begin_layout Standard
2404 A square root can also be created with
2410 when the root index field is left empty.
2413 \begin_layout Standard
2414 With certain indices the distance to the root is too small, like in this
2416 \begin_inset Formula $\sqrt[\beta]{B}$
2420 \begin_inset Newline newline
2424 \begin_inset Formula $\beta$
2428 To avoid this, the commands
2435 \begin_inset Index idx
2438 \begin_layout Plain Layout
2453 \begin_inset Index idx
2456 \begin_layout Plain Layout
2464 are used with the following scheme:
2467 \begin_layout Standard
2481 \begin_layout Standard
2482 Distance is the number of Big Points (unit bp;
2483 \begin_inset Formula $\mathrm{72\,bp=1\,inch}$
2486 ), that the index should be moved to the left or top, resp..
2487 The commands are written to the index.
2488 This way the command
2489 \begin_inset Newline newline
2499 \begin_inset Formula $\to$
2505 \begin_inset Formula $\to$
2511 \begin_inset space \textvisiblespace{}
2515 \begin_inset Formula $\to$
2519 \begin_inset Newline newline
2524 produces a correct typeset formula:
2525 \begin_inset Formula $\sqrt[\leftroot{-1}\uproot{2}\beta]{B}$
2531 \begin_layout Subsection
2532 Binomial Coefficients
2533 \begin_inset Index idx
2536 \begin_layout Plain Layout
2537 Binomial coefficients
2545 \begin_layout Standard
2546 Binomial coefficients are inserted with the command
2553 \begin_inset Index idx
2556 \begin_layout Plain Layout
2564 or with the submenu of the math toolbar button
2567 arg "math-insert \\frac-square"
2583 there are the commands
2590 \begin_inset Index idx
2593 \begin_layout Plain Layout
2608 \begin_inset Index idx
2611 \begin_layout Plain Layout
2620 For other brackets around binomial coeficients there are the commands
2627 \begin_inset Index idx
2630 \begin_layout Plain Layout
2645 \begin_inset Index idx
2648 \begin_layout Plain Layout
2657 \begin_inset Separator parbreak
2663 \begin_layout Standard
2665 \begin_inset Tabular
2666 <lyxtabular version="3" rows="6" columns="2">
2667 <features booktabs="true" tabularvalignment="middle">
2668 <column alignment="center" valignment="top" width="0pt">
2669 <column alignment="center" valignment="top" width="0pt">
2671 <cell alignment="center" valignment="top" topline="true" bottomline="true" usebox="none">
2674 \begin_layout Plain Layout
2680 <cell alignment="center" valignment="top" topline="true" bottomline="true" usebox="none">
2683 \begin_layout Plain Layout
2690 <row topspace="1mm">
2691 <cell alignment="center" valignment="top" usebox="none">
2694 \begin_layout Plain Layout
2698 \begin_inset space \textvisiblespace{}
2702 \begin_inset Formula $\downarrow$
2710 <cell alignment="center" valignment="top" usebox="none">
2713 \begin_layout Plain Layout
2714 \begin_inset Formula $\binom{A}{B}$
2723 <row topspace="2mm">
2724 <cell alignment="center" valignment="top" usebox="none">
2727 \begin_layout Plain Layout
2731 \begin_inset space \textvisiblespace{}
2735 \begin_inset Formula $\downarrow$
2743 <cell alignment="center" valignment="top" usebox="none">
2746 \begin_layout Plain Layout
2747 \begin_inset Formula $\dbinom{A}{B}$
2756 <row topspace="2mm" bottomspace="0.5mm">
2757 <cell alignment="center" valignment="top" usebox="none">
2760 \begin_layout Plain Layout
2764 \begin_inset space \textvisiblespace{}
2768 \begin_inset Formula $\downarrow$
2776 <cell alignment="center" valignment="top" usebox="none">
2779 \begin_layout Plain Layout
2780 \begin_inset Formula $\tbinom{A}{B}$
2789 <row topspace="1mm">
2790 <cell alignment="center" valignment="top" topline="true" usebox="none">
2793 \begin_layout Plain Layout
2797 \begin_inset space \textvisiblespace{}
2801 \begin_inset Formula $\downarrow$
2809 <cell alignment="center" valignment="top" topline="true" usebox="none">
2812 \begin_layout Plain Layout
2813 \begin_inset Formula ${A \brack B}$
2822 <row topspace="2mm" bottomspace="0.5mm">
2823 <cell alignment="center" valignment="top" bottomline="true" usebox="none">
2826 \begin_layout Plain Layout
2830 \begin_inset space \textvisiblespace{}
2834 \begin_inset Formula $\downarrow$
2842 <cell alignment="center" valignment="top" bottomline="true" usebox="none">
2845 \begin_layout Plain Layout
2846 \begin_inset Formula ${A \brace B}$
2862 \begin_layout Subsection
2863 Case Differentiations
2864 \begin_inset Index idx
2867 \begin_layout Plain Layout
2868 Case differentiations
2876 \begin_layout Standard
2878 \begin_inset Tabular
2879 <lyxtabular version="3" rows="3" columns="2">
2880 <features booktabs="true" tabularvalignment="middle">
2881 <column alignment="center" valignment="top" width="0pt">
2882 <column alignment="center" valignment="top" width="0pt">
2884 <cell alignment="center" valignment="top" topline="true" bottomline="true" usebox="none">
2887 \begin_layout Plain Layout
2893 <cell alignment="center" valignment="top" topline="true" bottomline="true" usebox="none">
2896 \begin_layout Plain Layout
2904 <cell alignment="center" valignment="top" usebox="none">
2907 \begin_layout Plain Layout
2911 \begin_inset space \textvisiblespace{}
2915 \begin_inset Formula $\to$
2919 \begin_inset Index idx
2922 \begin_layout Plain Layout
2935 <cell alignment="center" valignment="top" usebox="none">
2938 \begin_layout Plain Layout
2939 \begin_inset Formula $\begin{cases}
2949 <row topspace="1.5mm">
2950 <cell alignment="center" valignment="top" bottomline="true" usebox="none">
2953 \begin_layout Plain Layout
2957 \begin_inset space \textvisiblespace{}
2963 arg "newline-insert newline"
2971 <cell alignment="center" valignment="top" bottomline="true" usebox="none">
2974 \begin_layout Plain Layout
2975 \begin_inset Formula $\begin{cases}
2976 A & \textrm{for }x>0\\
2977 B & \textrm{for }x=0
2994 \begin_layout Standard
3001 or pressing the math toolbar button
3004 arg "math-insert \\cases"
3007 you can create new lines with the shortcut
3010 arg "newline-insert newline"
3013 or the table toolbar button
3016 arg "inset-modify tabular append-row"
3022 \begin_layout Standard
3029 is also available via the menu
3031 Insert\SpecialChar menuseparator
3032 Math\SpecialChar menuseparator
3038 \begin_layout Subsection
3040 \begin_inset Index idx
3043 \begin_layout Plain Layout
3052 \begin_layout Standard
3060 \begin_inset Index idx
3063 \begin_layout Plain Layout
3071 every character can be displayed canceled.
3072 The characters are quasi accentuated by a slash.
3073 \begin_inset Separator parbreak
3079 \begin_layout Standard
3081 \begin_inset Tabular
3082 <lyxtabular version="3" rows="4" columns="2">
3083 <features booktabs="true" tabularvalignment="middle">
3084 <column alignment="center" valignment="top" width="0pt">
3085 <column alignment="center" valignment="top" width="0pt">
3087 <cell alignment="center" valignment="top" topline="true" bottomline="true" usebox="none">
3090 \begin_layout Plain Layout
3096 <cell alignment="center" valignment="top" topline="true" bottomline="true" usebox="none">
3099 \begin_layout Plain Layout
3107 <cell alignment="center" valignment="top" usebox="none">
3110 \begin_layout Plain Layout
3118 <cell alignment="center" valignment="top" usebox="none">
3121 \begin_layout Plain Layout
3122 \begin_inset Formula $\not=$
3132 <cell alignment="center" valignment="top" usebox="none">
3135 \begin_layout Plain Layout
3145 <cell alignment="center" valignment="top" usebox="none">
3148 \begin_layout Plain Layout
3149 \begin_inset Formula $\not\le$
3159 <cell alignment="center" valignment="top" topline="true" bottomline="true" usebox="none">
3162 \begin_layout Plain Layout
3172 <cell alignment="center" valignment="top" topline="true" bottomline="true" usebox="none">
3175 \begin_layout Plain Layout
3176 \begin_inset Formula $\not\parallel$
3192 \begin_layout Standard
3193 The last example shows that not all negations look good.
3194 Therefore there are special commands for some negations (see
3195 \begin_inset CommandInset ref
3197 reference "subsec:Mathematical-Symbols"
3202 \begin_inset CommandInset ref
3204 reference "sec:Relations"
3211 \begin_layout Subsection
3213 \begin_inset CommandInset label
3215 name "subsec:Placeholders"
3220 \begin_inset Index idx
3223 \begin_layout Plain Layout
3230 \begin_inset Index idx
3233 \begin_layout Plain Layout
3234 Chemical characters ! Isotopes
3240 \begin_inset Index idx
3243 \begin_layout Plain Layout
3248 \begin_layout Plain Layout
3259 \begin_layout Plain Layout
3274 \begin_layout Standard
3276 \begin_inset space \thinspace{}
3280 \begin_inset space \space{}
3287 \begin_layout Plain Layout
3288 Typesetting isotopes and chemical symbols is described in
3289 \begin_inset CommandInset ref
3291 reference "subsec:Chemical-Symbols-and"
3300 the following problem occurs:
3301 \begin_inset Separator parbreak
3307 \begin_layout Standard
3309 \begin_inset Tabular
3310 <lyxtabular version="3" rows="2" columns="2">
3311 <features booktabs="true" tabularvalignment="middle">
3312 <column alignment="center" valignment="top" width="0pt">
3313 <column alignment="center" valignment="top" width="0pt">
3315 <cell alignment="center" valignment="top" usebox="none">
3318 \begin_layout Plain Layout
3319 Indices created with sub- and superscripts:
3324 <cell alignment="center" valignment="top" usebox="none">
3327 \begin_layout Plain Layout
3328 \begin_inset Formula $_{9}^{19}\mathrm{F}$
3337 <row topspace="1.5mm">
3338 <cell alignment="center" valignment="top" usebox="none">
3341 \begin_layout Plain Layout
3347 <cell alignment="center" valignment="top" usebox="none">
3350 \begin_layout Plain Layout
3351 \begin_inset Formula $_{\phantom{1}9}^{19}\mathrm{F}$
3367 \begin_layout Standard
3368 The shorter index is by default placed below or above the first character
3369 of the longer index.
3370 To avoid this there is the command
3377 \begin_inset Index idx
3380 \begin_layout Plain Layout
3388 or the math toolbar button
3389 \begin_inset space \thinspace{}
3396 \begin_layout Plain Layout
3397 can be found in the submenu of the toolbar button
3400 arg "math-insert \\space"
3409 \begin_inset Graphics
3410 filename ../../../../LyX 2.2/Resources/images/math/phantom.png
3415 that creates one or more phantom characters.
3422 a small blue box appears that is superposed with two red arrows.
3423 The arrows indicate that the complete width and height of the box content
3424 will be created as placeholder.
3425 Phantom characters are accordingly placeholders with the size of the characters.
3426 \begin_inset Separator parbreak
3432 \begin_layout Standard
3434 \begin_inset Tabular
3435 <lyxtabular version="3" rows="4" columns="2">
3436 <features booktabs="true" tabularvalignment="middle">
3437 <column alignment="center" valignment="top" width="0pt">
3438 <column alignment="center" valignment="top" width="0pt">
3440 <cell alignment="center" valignment="top" topline="true" bottomline="true" usebox="none">
3443 \begin_layout Plain Layout
3449 <cell alignment="center" valignment="top" topline="true" bottomline="true" usebox="none">
3452 \begin_layout Plain Layout
3459 <row topspace="1.5mm">
3460 <cell alignment="center" valignment="top" usebox="none">
3463 \begin_layout Plain Layout
3465 \begin_inset space \textvisiblespace{}
3471 \begin_inset space \textvisiblespace{}
3475 \begin_inset Formula $\to$
3479 \begin_inset space \textvisiblespace{}
3487 <cell alignment="center" valignment="top" usebox="none">
3490 \begin_layout Plain Layout
3491 \begin_inset Formula $_{\phantom{1}9}^{19}\mathrm{F}$
3500 <row topspace="1.5mm" bottomspace="0.5mm">
3501 <cell alignment="center" valignment="top" usebox="none">
3504 \begin_layout Plain Layout
3506 \begin_inset space \textvisiblespace{}
3512 \begin_inset space \textvisiblespace{}
3516 \begin_inset Formula $\to$
3520 \begin_inset space \textvisiblespace{}
3528 <cell alignment="center" valignment="top" usebox="none">
3531 \begin_layout Plain Layout
3532 \begin_inset Formula $_{\phantom{23}9}^{235}\mathrm{F}$
3541 <row topspace="1.5mm" bottomspace="0.5mm">
3542 <cell alignment="center" valignment="top" topline="true" bottomline="true" usebox="none">
3545 \begin_layout Plain Layout
3549 \begin_inset space \textvisiblespace{}
3555 \begin_inset space \textvisiblespace{}
3559 \begin_inset Formula $\to$
3563 \begin_inset space \textvisiblespace{}
3571 <cell alignment="center" valignment="top" topline="true" bottomline="true" usebox="none">
3574 \begin_layout Plain Layout
3575 \begin_inset Formula $\Lambda_{MMt}^{\phantom{ii}t}$
3591 \begin_layout Standard
3592 Furthermore there are the commands
3599 \begin_inset Index idx
3602 \begin_layout Plain Layout
3611 \begin_inset space ~
3615 \begin_inset Graphics
3616 filename ../../../../LyX 2.2/Resources/images/math/vphantom.png
3628 \begin_inset Index idx
3631 \begin_layout Plain Layout
3640 \begin_inset space ~
3644 \begin_inset Graphics
3645 filename ../../../../LyX 2.2/Resources/images/math/hphantom.png
3657 creates only space for the maximal height of the characters in the box
3658 but not for its width.
3665 creates only space for the width of the box content.
3666 Therefore the boxes of both commands have only one red arrow.
3669 \begin_layout Standard
3670 For example the command
3675 \begin_inset space \textvisiblespace{}
3682 creates space for the height of the integral sign,
3686 \begin_layout Plain Layout
3693 creates an integral sign, see
3694 \begin_inset CommandInset ref
3696 reference "subsec:Big-Operators"
3705 because this is the larger character.
3706 An example application is in
3707 \begin_inset CommandInset ref
3709 reference "subsec:Multiline-Brackets"
3716 \begin_layout Standard
3717 Placeholders can also be used for text when they are inserted via the menu
3720 Insert\SpecialChar menuseparator
3721 Formatting\SpecialChar menuseparator
3727 \begin_layout Standard
3729 \begin_inset Newline newline
3733 \begin_inset Phantom Phantom
3736 \begin_layout Plain Layout
3745 \begin_layout Subsection
3747 \begin_inset Index idx
3750 \begin_layout Plain Layout
3757 \begin_inset Index idx
3760 \begin_layout Plain Layout
3761 Formula ! underlined
3769 \begin_layout Standard
3771 \begin_inset Tabular
3772 <lyxtabular version="3" rows="4" columns="2">
3773 <features booktabs="true" tabularvalignment="middle">
3774 <column alignment="center" valignment="top" width="0pt">
3775 <column alignment="center" valignment="top" width="0pt">
3777 <cell alignment="center" valignment="top" topline="true" bottomline="true" usebox="none">
3780 \begin_layout Plain Layout
3786 <cell alignment="center" valignment="top" topline="true" bottomline="true" usebox="none">
3789 \begin_layout Plain Layout
3796 <row topspace="2mm">
3797 <cell alignment="center" valignment="top" usebox="none">
3800 \begin_layout Plain Layout
3804 \begin_inset space \textvisiblespace{}
3808 \begin_inset Index idx
3811 \begin_layout Plain Layout
3824 <cell alignment="center" valignment="top" usebox="none">
3827 \begin_layout Plain Layout
3828 \begin_inset Formula $\overline{A+B}$
3837 <row bottomspace="1mm">
3838 <cell alignment="center" valignment="top" usebox="none">
3841 \begin_layout Plain Layout
3845 \begin_inset space \textvisiblespace{}
3849 \begin_inset Index idx
3852 \begin_layout Plain Layout
3865 <cell alignment="center" valignment="top" usebox="none">
3868 \begin_layout Plain Layout
3869 \begin_inset Formula $\underline{A+B}$
3878 <row topspace="2mm" bottomspace="1mm">
3879 <cell alignment="center" valignment="top" topline="true" bottomline="true" usebox="none">
3882 \begin_layout Plain Layout
3886 \begin_inset space \textvisiblespace{}
3892 \begin_inset space \textvisiblespace{}
3900 <cell alignment="center" valignment="top" topline="true" bottomline="true" usebox="none">
3903 \begin_layout Plain Layout
3904 \begin_inset Formula $\overline{\underline{A+B}}$
3920 \begin_layout Standard
3921 In the last example it doesn't matter if first
3936 \begin_layout Standard
3937 To double underline use
3946 \begin_layout Standard
3947 It is possible to place up to 6 lines above or below characters.
3950 \begin_layout Standard
3951 \begin_inset VSpace bigskip
3954 Custom lines can be created using the command
3961 \begin_inset Index idx
3964 \begin_layout Plain Layout
3972 which has the following scheme:
3975 \begin_layout Standard
3980 rule[vertical offset]{length}{thickness}
3983 \begin_layout Standard
3984 The optional vertical offset shifts the line upwards (or downwards, when
3985 the value is negative).
3987 \begin_inset CommandInset ref
3989 reference "tab:Available-units"
3993 can be used for the values.
3994 Here are two example lines created with the commands
3995 \begin_inset Newline newline
4002 rule[-2ex]{3cm}{2pt}
4013 \begin_layout Standard
4015 \begin_inset Formula $\rule[-2ex]{3cm}{2pt}\rule{2cm}{1pt}$
4021 \begin_layout Standard
4028 can also be used for text when a line is inserted via the menu
4030 Insert\SpecialChar menuseparator
4031 Formatting\SpecialChar menuseparator
4033 \begin_inset space ~
4041 \begin_layout Standard
4043 \begin_inset CommandInset line
4054 \begin_layout Subsection
4056 \begin_inset CommandInset label
4058 name "subsec:Ellipses"
4063 \begin_inset Index idx
4066 \begin_layout Plain Layout
4075 \begin_layout Standard
4076 There are different types of ellipses available.
4080 \begin_layout Plain Layout
4081 In the math toolbar in the submenu of the button
4084 arg "math-insert \\ldots"
4092 For listings dots at the baseline are used (
4099 \begin_inset Index idx
4102 \begin_layout Plain Layout
4110 ), while for operations dots are needed that are on the same height as the
4118 \begin_inset Index idx
4121 \begin_layout Plain Layout
4130 When using the command
4137 \begin_inset Index idx
4140 \begin_layout Plain Layout
4148 , \SpecialChar LaTeX
4149 decides on the basis of the next character what type is used.
4150 \begin_inset Separator parbreak
4156 \begin_layout Standard
4158 \begin_inset Tabular
4159 <lyxtabular version="3" rows="9" columns="2">
4160 <features booktabs="true" tabularvalignment="middle">
4161 <column alignment="center" valignment="top" width="0pt">
4162 <column alignment="center" valignment="top" width="0pt">
4164 <cell alignment="center" valignment="top" topline="true" bottomline="true" usebox="none">
4167 \begin_layout Plain Layout
4173 <cell alignment="center" valignment="top" topline="true" bottomline="true" usebox="none">
4176 \begin_layout Plain Layout
4184 <cell alignment="center" valignment="top" usebox="none">
4187 \begin_layout Plain Layout
4189 \begin_inset space \textvisiblespace{}
4195 \begin_inset space \textvisiblespace{}
4203 <cell alignment="center" valignment="top" usebox="none">
4206 \begin_layout Plain Layout
4207 \begin_inset Formula $A_{1},\dots,A_{n}$
4217 <cell alignment="center" valignment="top" usebox="none">
4220 \begin_layout Plain Layout
4222 \begin_inset space \textvisiblespace{}
4228 \begin_inset space \textvisiblespace{}
4236 <cell alignment="center" valignment="top" usebox="none">
4239 \begin_layout Plain Layout
4240 \begin_inset Formula $A_{1}+\dots+A_{n}$
4250 <cell alignment="center" valignment="top" usebox="none">
4253 \begin_layout Plain Layout
4255 \begin_inset space \textvisiblespace{}
4261 \begin_inset space \textvisiblespace{}
4269 <cell alignment="center" valignment="top" usebox="none">
4272 \begin_layout Plain Layout
4273 \begin_inset Formula $A_{1},\ldots,A_{n}$
4283 <cell alignment="center" valignment="top" bottomline="true" usebox="none">
4286 \begin_layout Plain Layout
4288 \begin_inset space \textvisiblespace{}
4294 \begin_inset space \textvisiblespace{}
4302 <cell alignment="center" valignment="top" bottomline="true" usebox="none">
4305 \begin_layout Plain Layout
4306 \begin_inset Formula $A_{1}+\cdots+A_{n}$
4316 <cell alignment="center" valignment="top" usebox="none">
4319 \begin_layout Plain Layout
4327 <cell alignment="center" valignment="top" usebox="none">
4330 \begin_layout Plain Layout
4331 \begin_inset Formula $\vdots$
4341 <cell alignment="center" valignment="top" usebox="none">
4344 \begin_layout Plain Layout
4352 <cell alignment="center" valignment="top" usebox="none">
4355 \begin_layout Plain Layout
4356 \begin_inset Formula $\ddots$
4366 <cell alignment="center" valignment="top" usebox="none">
4369 \begin_layout Plain Layout
4377 <cell alignment="center" valignment="top" usebox="none">
4380 \begin_layout Plain Layout
4381 \begin_inset Formula $\iddots$
4391 <cell alignment="center" valignment="top" topline="true" bottomline="true" usebox="none">
4394 \begin_layout Plain Layout
4396 \begin_inset space \thinspace{}
4399 matrix with the different dots
4404 <cell alignment="center" valignment="top" topline="true" bottomline="true" usebox="none">
4407 \begin_layout Plain Layout
4408 \begin_inset Formula $\begin{array}{ccc}
4409 A_{11} & \cdots & A_{1m}\\
4410 \vdots & \ddots & \vdots\\
4411 A_{n1} & \cdots & A_{nm}
4428 \begin_layout Standard
4429 The ellipses available in menu
4431 Insert\SpecialChar menuseparator
4433 \begin_inset space ~
4447 \begin_layout Standard
4448 \begin_inset VSpace medskip
4457 , one of the options
4459 Use mathdots package (automatically)
4461 must be set in the document settings under
4464 \begin_inset space ~
4470 \begin_inset Newline newline
4475 Use mathdots package
4477 will improve the appearance of all dots in the documents if their font
4478 style or size is not the default.
4481 \begin_layout Standard
4482 \begin_inset VSpace medskip
4485 Specially for matrices there are ellipses that span over several columns.
4486 They are created with the command
4493 \begin_inset Index idx
4496 \begin_layout Plain Layout
4504 , that has the following scheme:
4507 \begin_layout Standard
4512 hdotsfor[distance]{number of columns}
4515 \begin_layout Standard
4516 The number of columns specifies how many columns should be spanned.
4517 Distance is a factor for the distance between the dots.
4520 \begin_layout Standard
4521 In the following matrix the command
4527 was inserted in the first box of the second line, to get an ellipsis with
4528 a dot distance twice as long as with the command
4535 \begin_inset Formula
4537 \left(\begin{array}{cccc}
4546 Note that the matrix fields that should be spanned must be empty, otherwise
4547 you get \SpecialChar LaTeX
4551 \begin_layout Standard
4552 \begin_inset VSpace bigskip
4555 Furthermore you can fill with the command
4562 \begin_inset Index idx
4565 \begin_layout Plain Layout
4573 the rest of a line with dots.
4574 The effect of these commands is the same as with
4581 \begin_inset CommandInset ref
4583 reference "subsec:Variable-Space"
4590 \begin_layout Standard
4591 For example the command
4596 \begin_inset space \textvisiblespace{}
4604 \begin_layout Standard
4605 \begin_inset Formula $A\dotfill B$
4611 \begin_layout Standard
4618 there is for a line the command
4625 \begin_inset Index idx
4628 \begin_layout Plain Layout
4639 \begin_layout Standard
4640 \begin_inset Formula $A\hrulefill B$
4646 \begin_layout Standard
4647 To use the commands for text, they have to be inserted in \SpecialChar TeX
4651 \begin_layout Section
4653 \begin_inset CommandInset label
4660 \begin_inset Index idx
4663 \begin_layout Plain Layout
4672 \begin_layout Standard
4673 Matrices can be inserted via the math toolbar button
4676 arg "dialog-show mathmatrix"
4681 Insert\SpecialChar menuseparator
4682 Math\SpecialChar menuseparator
4686 In the matrix dialog you can specify the number of columns and rows, the
4687 alignment and the decoration.
4688 The vertical alignment is only of importance for matrices in inline formulas:
4691 \begin_layout Standard
4692 The first matrix is top
4693 \begin_inset Formula $\begin{array}[t]{cccc}
4701 \begin_inset Formula $\begin{array}{cccc}
4708 and the third bottom
4709 \begin_inset Formula $\begin{array}[b]{cccc}
4719 \begin_layout Standard
4720 The horizontal alignment specifies how the column entries should be aligned.
4721 It is set by entering a letter for every column.
4726 denotes left aligned,
4735 To create for example a 4
4740 \begin_inset space ~
4743 matrix where the first column is left aligned, the second and third are
4744 centered and the last one is right aligned, one enters for the horizontal
4750 Normally in a matrix all columns are centered, therefore the default for
4758 \begin_layout Standard
4759 Horizontal alignment:
4762 \begin_layout Standard
4768 \begin_inset Formula $\begin{array}{lll}
4780 \begin_inset Formula $\begin{array}{ccc}
4792 \begin_inset Formula $\begin{array}{rrr}
4802 \begin_layout Standard
4803 To add or delete rows and columns subsequently, the math toolbar buttons
4807 arg "inset-modify tabular append-row"
4813 arg "inset-modify tabular delete-row"
4817 \begin_inset space \thinspace{}
4822 Edit\SpecialChar menuseparator
4826 New rows can also be created with
4829 arg "newline-insert newline"
4835 \begin_layout Standard
4836 \begin_inset VSpace bigskip
4843 adds parentheses in the selected style around the matrix.
4844 Alternatively, parentheses can can either be created with the commands
4852 \begin_inset Index idx
4855 \begin_layout Plain Layout
4870 \begin_inset Index idx
4873 \begin_layout Plain Layout
4884 \begin_inset space ~
4890 \begin_inset CommandInset ref
4892 reference "subsec:Automatic-Bracket-Size"
4896 , or by using the following commands:
4897 \begin_inset VSpace medskip
4903 \begin_layout Standard
4904 \begin_inset space \hfill{}
4908 \begin_inset Tabular
4909 <lyxtabular version="3" rows="4" columns="2">
4910 <features booktabs="true" tabularvalignment="middle">
4911 <column alignment="center" valignment="top" width="0pt">
4912 <column alignment="center" valignment="top">
4914 <cell alignment="center" valignment="top" topline="true" bottomline="true" usebox="none">
4917 \begin_layout Plain Layout
4923 <cell alignment="center" valignment="top" topline="true" bottomline="true" usebox="none">
4926 \begin_layout Plain Layout
4933 <row topspace="1.5mm">
4934 <cell alignment="center" valignment="top" usebox="none">
4937 \begin_layout Plain Layout
4941 \begin_inset space \textvisiblespace{}
4949 \begin_inset space \thinspace{}
4957 <cell alignment="center" valignment="top" usebox="none">
4960 \begin_layout Plain Layout
4961 \begin_inset Formula $\begin{bmatrix}\begin{array}{cc}
4962 0 & \textrm{-}\mathrm{i}\\
4964 \end{array}\end{bmatrix}$
4973 <row topspace="1.5mm" bottomspace="0.5mm">
4974 <cell alignment="center" valignment="top" usebox="none">
4977 \begin_layout Plain Layout
4981 \begin_inset space \textvisiblespace{}
4989 \begin_inset space \thinspace{}
4997 <cell alignment="center" valignment="top" usebox="none">
5000 \begin_layout Plain Layout
5001 \begin_inset Formula $\begin{Bmatrix}\begin{array}{cc}
5002 0 & \textrm{-}\mathrm{i}\\
5004 \end{array}\end{Bmatrix}$
5014 <cell alignment="center" valignment="top" topline="true" bottomline="true" usebox="none">
5017 \begin_layout Plain Layout
5021 \begin_inset space \textvisiblespace{}
5029 \begin_inset space \thinspace{}
5037 <cell alignment="center" valignment="top" topline="true" bottomline="true" usebox="none">
5040 \begin_layout Plain Layout
5041 \begin_inset Formula $\begin{pmatrix}\begin{array}{cc}
5042 0 & \textrm{-}\mathrm{i}\\
5044 \end{array}\end{pmatrix}$
5058 \begin_inset space \hfill{}
5062 \begin_inset Tabular
5063 <lyxtabular version="3" rows="4" columns="2">
5064 <features booktabs="true" tabularvalignment="middle">
5065 <column alignment="center" valignment="top" width="0pt">
5066 <column alignment="center" valignment="top">
5068 <cell alignment="center" valignment="top" topline="true" bottomline="true" usebox="none">
5071 \begin_layout Plain Layout
5077 <cell alignment="center" valignment="top" topline="true" bottomline="true" usebox="none">
5080 \begin_layout Plain Layout
5087 <row topspace="1.5mm">
5088 <cell alignment="center" valignment="top" usebox="none">
5091 \begin_layout Plain Layout
5095 \begin_inset space \textvisiblespace{}
5103 \begin_inset space \thinspace{}
5111 <cell alignment="center" valignment="top" usebox="none">
5114 \begin_layout Plain Layout
5115 \begin_inset Formula $\begin{vmatrix}\begin{array}{cc}
5116 0 & \textrm{-}\mathrm{i}\\
5118 \end{array}\end{vmatrix}$
5127 <row topspace="1.5mm" bottomspace="0.5mm">
5128 <cell alignment="center" valignment="top" usebox="none">
5131 \begin_layout Plain Layout
5135 \begin_inset space \textvisiblespace{}
5143 \begin_inset space \thinspace{}
5151 <cell alignment="center" valignment="top" usebox="none">
5154 \begin_layout Plain Layout
5155 \begin_inset Formula $\begin{Vmatrix}\begin{array}{cc}
5156 0 & \textrm{-}\mathrm{i}\\
5158 \end{array}\end{Vmatrix}$
5168 <cell alignment="center" valignment="top" topline="true" bottomline="true" usebox="none">
5171 \begin_layout Plain Layout
5175 \begin_inset space \textvisiblespace{}
5183 \begin_inset space \thinspace{}
5191 <cell alignment="center" valignment="top" topline="true" bottomline="true" usebox="none">
5194 \begin_layout Plain Layout
5195 \begin_inset Formula $\begin{matrix}\begin{array}{cc}
5196 0 & \textrm{-}\mathrm{i}\\
5198 \end{array}\end{matrix}$
5212 \begin_inset space \hfill{}
5218 \begin_layout Standard
5219 \begin_inset VSpace medskip
5223 \begin_inset space \thinspace{}
5227 \begin_inset space \space{}
5236 is inserted, a blue box appears between two vertical lines where the matrix
5238 \begin_inset Newline newline
5241 Note that decorated matrices ignore the vertical alignment.
5244 \begin_layout Standard
5245 \begin_inset VSpace bigskip
5248 As all multiline formulas are matrices, the length
5255 \begin_inset Index idx
5258 \begin_layout Plain Layout
5266 that is described in
5267 \begin_inset CommandInset ref
5269 reference "subsec:Column-Separation"
5273 can also be used to change the column separation of matrices.
5276 \begin_layout Standard
5277 To change the row separation, the command
5284 \begin_inset Index idx
5287 \begin_layout Plain Layout
5296 It is used as follows:
5299 \begin_layout Standard
5306 arraystretch}{stretch factor}
5307 \begin_inset Index idx
5310 \begin_layout Plain Layout
5321 \begin_layout Standard
5328 assigns the stretch factor to the predefined command
5336 \begin_inset space \thinspace{}
5340 \begin_inset space \space{}
5343 the row separation, use the factor 2.
5344 This is then used for all following matrices.
5345 To go back to the original separation, assign the factor 1 to
5354 \begin_layout Standard
5355 To set matrices into a text line, the command
5362 \begin_inset Index idx
5365 \begin_layout Plain Layout
5374 When it is inserted a blue box with two dashed lines appears.
5375 In this box the matrix is inserted.
5378 \begin_layout Standard
5380 \begin_inset Formula $\left(\begin{smallmatrix}A & B\\
5382 \end{smallmatrix}\right)$
5388 \begin_layout Section
5389 Brackets and Delimiters
5390 \begin_inset Index idx
5393 \begin_layout Plain Layout
5400 \begin_inset Index idx
5403 \begin_layout Plain Layout
5412 \begin_layout Subsection
5413 Vertical Brackets and Delimiters
5414 \begin_inset Index idx
5417 \begin_layout Plain Layout
5426 \begin_layout Standard
5427 \begin_inset space \hfill{}
5431 \begin_inset Tabular
5432 <lyxtabular version="3" rows="9" columns="2">
5433 <features booktabs="true" tabularvalignment="middle">
5434 <column alignment="center" valignment="top" width="0pt">
5435 <column alignment="center" valignment="top" width="0pt">
5437 <cell alignment="center" valignment="top" topline="true" bottomline="true" usebox="none">
5440 \begin_layout Plain Layout
5446 <cell alignment="center" valignment="top" topline="true" bottomline="true" usebox="none">
5449 \begin_layout Plain Layout
5457 <cell alignment="center" valignment="top" usebox="none">
5460 \begin_layout Plain Layout
5466 <cell alignment="center" valignment="top" usebox="none">
5469 \begin_layout Plain Layout
5470 \begin_inset Formula $($
5480 <cell alignment="center" valignment="top" usebox="none">
5483 \begin_layout Plain Layout
5489 <cell alignment="center" valignment="top" usebox="none">
5492 \begin_layout Plain Layout
5493 \begin_inset Formula $\{$
5503 <cell alignment="center" valignment="top" usebox="none">
5506 \begin_layout Plain Layout
5512 <cell alignment="center" valignment="top" usebox="none">
5515 \begin_layout Plain Layout
5516 \begin_inset Formula $[$
5526 <cell alignment="center" valignment="top" usebox="none">
5529 \begin_layout Plain Layout
5537 <cell alignment="center" valignment="top" usebox="none">
5540 \begin_layout Plain Layout
5541 \begin_inset Formula $\langle$
5551 <cell alignment="center" valignment="top" usebox="none">
5554 \begin_layout Plain Layout
5562 <cell alignment="center" valignment="top" usebox="none">
5565 \begin_layout Plain Layout
5566 \begin_inset Formula $\lceil$
5576 <cell alignment="center" valignment="top" usebox="none">
5579 \begin_layout Plain Layout
5587 <cell alignment="center" valignment="top" usebox="none">
5590 \begin_layout Plain Layout
5591 \begin_inset Formula $\lfloor$
5601 <cell alignment="center" valignment="top" usebox="none">
5604 \begin_layout Plain Layout
5610 <cell alignment="center" valignment="top" usebox="none">
5613 \begin_layout Plain Layout
5614 \begin_inset Formula $/$
5624 <cell alignment="center" valignment="top" bottomline="true" usebox="none">
5627 \begin_layout Plain Layout
5633 <cell alignment="center" valignment="top" bottomline="true" usebox="none">
5636 \begin_layout Plain Layout
5637 \begin_inset Formula $|$
5651 \begin_inset space \hfill{}
5655 \begin_inset Tabular
5656 <lyxtabular version="3" rows="9" columns="2">
5657 <features booktabs="true" tabularvalignment="middle">
5658 <column alignment="center" valignment="top" width="0pt">
5659 <column alignment="center" valignment="top" width="0pt">
5661 <cell alignment="center" valignment="top" topline="true" bottomline="true" usebox="none">
5664 \begin_layout Plain Layout
5670 <cell alignment="center" valignment="top" topline="true" bottomline="true" usebox="none">
5673 \begin_layout Plain Layout
5681 <cell alignment="center" valignment="top" usebox="none">
5684 \begin_layout Plain Layout
5690 <cell alignment="center" valignment="top" usebox="none">
5693 \begin_layout Plain Layout
5694 \begin_inset Formula $)$
5704 <cell alignment="center" valignment="top" usebox="none">
5707 \begin_layout Plain Layout
5713 <cell alignment="center" valignment="top" usebox="none">
5716 \begin_layout Plain Layout
5717 \begin_inset Formula $\}$
5727 <cell alignment="center" valignment="top" usebox="none">
5730 \begin_layout Plain Layout
5736 <cell alignment="center" valignment="top" usebox="none">
5739 \begin_layout Plain Layout
5740 \begin_inset Formula $]$
5750 <cell alignment="center" valignment="top" usebox="none">
5753 \begin_layout Plain Layout
5761 <cell alignment="center" valignment="top" usebox="none">
5764 \begin_layout Plain Layout
5765 \begin_inset Formula $\rangle$
5775 <cell alignment="center" valignment="top" usebox="none">
5778 \begin_layout Plain Layout
5786 <cell alignment="center" valignment="top" usebox="none">
5789 \begin_layout Plain Layout
5790 \begin_inset Formula $\rceil$
5800 <cell alignment="center" valignment="top" usebox="none">
5803 \begin_layout Plain Layout
5811 <cell alignment="center" valignment="top" usebox="none">
5814 \begin_layout Plain Layout
5815 \begin_inset Formula $\rfloor$
5825 <cell alignment="center" valignment="top" usebox="none">
5828 \begin_layout Plain Layout
5838 <cell alignment="center" valignment="top" usebox="none">
5841 \begin_layout Plain Layout
5842 \begin_inset Formula $\backslash$
5852 <cell alignment="center" valignment="top" bottomline="true" usebox="none">
5855 \begin_layout Plain Layout
5863 <cell alignment="center" valignment="top" bottomline="true" usebox="none">
5866 \begin_layout Plain Layout
5867 \begin_inset Formula $\|$
5881 \begin_inset space \hfill{}
5887 \begin_layout Standard
5890 \begin_inset Note Greyedout
5893 \begin_layout Plain Layout
5906 \begin_inset Index idx
5909 \begin_layout Plain Layout
5917 must be used for the backslash, because the command
5925 produces a line break there.
5933 \begin_layout Standard
5934 For all characters listed above the size can be adjusted with the commands
5935 described in the following two subsections.
5936 When using these commands, the characters < and > can directly be used
5937 instead of the commands
5952 \begin_layout Subsubsection
5954 \begin_inset CommandInset label
5956 name "subsec:Manual-Bracket-Size"
5961 \begin_inset Index idx
5964 \begin_layout Plain Layout
5965 Bracket size ! manual
5973 \begin_layout Standard
5974 The bracket size can be specified manually by the \SpecialChar LaTeX
5982 \begin_inset Index idx
5985 \begin_layout Plain Layout
6018 denotes the smallest and
6024 the largest bracket size.
6027 \begin_layout Standard
6028 These commands are used to emphasize levels of brackets:
6029 \begin_inset Separator parbreak
6035 \begin_layout Standard
6037 \begin_inset Tabular
6038 <lyxtabular version="3" rows="2" columns="2">
6039 <features tabularvalignment="middle">
6040 <column alignment="center" valignment="top" width="0pt">
6041 <column alignment="center" valignment="top" width="0pt">
6043 <cell alignment="center" valignment="top" usebox="none">
6046 \begin_layout Plain Layout
6047 all brackets in the same size:
6052 <cell alignment="center" valignment="top" usebox="none">
6055 \begin_layout Plain Layout
6056 \begin_inset Formula $((A+B)(A-B))^{C}\raisebox{-4mm}{}$
6066 <cell alignment="center" valignment="top" usebox="none">
6069 \begin_layout Plain Layout
6075 <cell alignment="center" valignment="top" usebox="none">
6078 \begin_layout Plain Layout
6079 \begin_inset Formula $\Big((A+B)(A-B)\Big)^{C}$
6093 \begin_inset Note Note
6096 \begin_layout Plain Layout
6103 is only used as spacer.
6111 \begin_layout Standard
6112 For the second formula the command
6119 \begin_inset space \textvisiblespace{}
6127 \begin_layout Standard
6128 Here is an overview about all bracket sizes:
6129 \begin_inset Separator parbreak
6135 \begin_layout Standard
6152 \begin_inset space \textvisiblespace{}
6160 \begin_inset space \textvisiblespace{}
6164 \begin_inset space \textvisiblespace{}
6174 \begin_layout Standard
6176 \begin_inset Formula $\Bigg(\exp\bigg<\Big[\big\{\ln(3x)\big\}^{2}\sin(x)\Big]^{A}\bigg>\Bigg)^{0,5}$
6182 \begin_layout Standard
6189 -commands there is the variant
6196 \begin_inset Index idx
6199 \begin_layout Plain Layout
6207 that adds a bit more space between the bracket and its content, and the
6221 \begin_inset Index idx
6224 \begin_layout Plain Layout
6234 , that don't add additional space.
6239 at the end of the command
6245 is for a left bracket; for a right bracket this will be replaced by an
6251 A left or right bracket can each be an opening or closing bracket.
6254 \begin_layout Standard
6255 In the following table is a comparison of the variants:
6256 \begin_inset Separator parbreak
6262 \begin_layout Standard
6264 \begin_inset Tabular
6265 <lyxtabular version="3" rows="5" columns="2">
6266 <features tabularvalignment="middle">
6267 <column alignment="center" valignment="middle">
6268 <column alignment="center" valignment="middle">
6270 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
6273 \begin_layout Plain Layout
6279 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
6282 \begin_layout Plain Layout
6284 \begin_inset Note Note
6287 \begin_layout Plain Layout
6294 is only used as spacer.
6306 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
6309 \begin_layout Plain Layout
6319 \begin_inset space \textvisiblespace{}
6329 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
6332 \begin_layout Plain Layout
6333 \begin_inset Formula $\raisebox{5.5mm}{}\Bigm(\bigm(\ln(3x)\bigm)^{2}\Bigm)\raisebox{-3.25mm}{}$
6343 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
6346 \begin_layout Plain Layout
6356 \begin_inset space \textvisiblespace{}
6366 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
6369 \begin_layout Plain Layout
6370 \begin_inset Formula $\raisebox{5.5mm}{}\Big(\big(\ln(3x)\big)^{2}\Big)\raisebox{-3.25mm}{}$
6380 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
6383 \begin_layout Plain Layout
6393 \begin_inset space \textvisiblespace{}
6403 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
6406 \begin_layout Plain Layout
6407 \begin_inset Formula $\raisebox{5.5mm}{}\Bigl(\bigl(\ln(3x)\bigr)^{2}\Bigr)\raisebox{-3.25mm}{}$
6417 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
6420 \begin_layout Plain Layout
6432 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
6435 \begin_layout Plain Layout
6436 \begin_inset Formula $\raisebox{4.5mm}{}\bigl)\ln(3x)\bigr(\raisebox{-2mm}{}$
6452 \begin_layout Subsubsection
6453 Automatic Bracket Size
6454 \begin_inset CommandInset label
6456 name "subsec:Automatic-Bracket-Size"
6461 \begin_inset Index idx
6464 \begin_layout Plain Layout
6465 Bracket size ! automatic
6473 \begin_layout Standard
6474 Brackets with variable size can be inserted with the commands
6481 \begin_inset Index idx
6484 \begin_layout Plain Layout
6499 \begin_inset Index idx
6502 \begin_layout Plain Layout
6510 or via the math toolbar button
6513 arg "dialog-show mathdelimiter"
6529 the wanted bracket must be inserted.
6530 The bracket size will then automatically be calculated for the output.
6531 \begin_inset Separator parbreak
6537 \begin_layout Standard
6539 normal bracket: The command
6546 \begin_inset space \textvisiblespace{}
6550 \begin_inset Formula $\downarrow$
6554 \begin_inset space \textvisiblespace{}
6560 \begin_inset Formula
6570 \begin_layout Standard
6572 multiline bracket: The command
6581 \begin_inset space \textvisiblespace{}
6585 \begin_inset Formula $\downarrow$
6589 \begin_inset space \textvisiblespace{}
6597 \begin_inset Formula
6599 \ln\left(\frac{A}{C}\right)
6607 \begin_layout Standard
6623 \begin_inset space ~
6629 This has the advantage that you can see in \SpecialChar LyX
6630 immediately the real bracket
6631 size and that the matching right bracket will be created too.
6632 \begin_inset Newline newline
6635 The command for the last example would then be:
6646 \begin_inset space \textvisiblespace{}
6650 \begin_inset Formula $\downarrow$
6656 \begin_layout Standard
6657 To omit a left or right bracket, a dot is inserted for the omitted bracket.
6658 For example the command
6665 \begin_inset space \textvisiblespace{}
6669 \begin_inset Formula $\downarrow$
6673 \begin_inset space \textvisiblespace{}
6683 \begin_inset Formula
6685 \left.\frac{A}{B}\right\}
6704 will be converted by \SpecialChar LyX
6705 to brackets in the right size when the document is
6706 reloaded and an omitted bracket will appear as dashed line.
6709 \begin_layout Standard
6710 \begin_inset VSpace bigskip
6713 Because all popular \SpecialChar LaTeX
6714 distributions use e\SpecialChar TeX
6715 , an extension to \SpecialChar LaTeX
6724 \begin_inset Index idx
6727 \begin_layout Plain Layout
6735 is additionally available for all brackets and limits.
6736 With this command the height of the following character is adapted to the
6737 one of the surrounding brackets, what is e.
6738 \begin_inset space \thinspace{}
6742 \begin_inset space \space{}
6745 needed for physical vectors:
6746 \begin_inset Formula
6748 \left\langle \phi\:\middle|\:J=\frac{3}{2}\,,\,M_{J}\right\rangle
6753 For physical vectors there is a special \SpecialChar LaTeX
6754 -package, described in
6755 \begin_inset CommandInset ref
6757 reference "subsec:Physical-Vectors"
6764 \begin_layout Subsection
6766 \begin_inset Index idx
6769 \begin_layout Plain Layout
6770 Brackets ! horizontal
6778 \begin_layout Standard
6780 \begin_inset Tabular
6781 <lyxtabular version="3" rows="4" columns="2">
6782 <features tabularvalignment="middle">
6783 <column alignment="center" valignment="top" width="0pt">
6784 <column alignment="center" valignment="top" width="0pt">
6786 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
6789 \begin_layout Plain Layout
6791 \begin_inset Note Note
6794 \begin_layout Plain Layout
6801 is only used as spacer.
6811 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
6814 \begin_layout Plain Layout
6822 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
6825 \begin_layout Plain Layout
6829 \begin_layout Plain Layout
6841 \begin_inset space \textvisiblespace{}
6845 \begin_inset space \textvisiblespace{}
6852 \begin_layout Plain Layout
6860 \begin_inset Index idx
6863 \begin_layout Plain Layout
6876 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
6879 \begin_layout Plain Layout
6880 \begin_inset Formula $\overbrace{A+B}^{3}$
6890 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
6893 \begin_layout Plain Layout
6897 \begin_layout Plain Layout
6909 \begin_inset space \textvisiblespace{}
6913 \begin_inset space \textvisiblespace{}
6920 \begin_layout Plain Layout
6928 \begin_inset Index idx
6931 \begin_layout Plain Layout
6944 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
6947 \begin_layout Plain Layout
6948 \begin_inset Formula $\underbrace{A+B}_{5}$
6958 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
6961 \begin_layout Plain Layout
6965 \begin_inset space \textvisiblespace{}
6971 \begin_inset space \textvisiblespace{}
6975 \begin_inset space \textvisiblespace{}
6979 \begin_inset space \textvisiblespace{}
6983 \begin_inset space \textvisiblespace{}
6987 \begin_inset space \textvisiblespace{}
6991 \begin_inset space \textvisiblespace{}
6999 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
7002 \begin_layout Plain Layout
7003 \begin_inset Formula $\overbrace{\underbrace{A+B_{w}}_{7}}^{C}$
7019 \begin_layout Standard
7020 In the last example it doesn't matter if
7032 is inserted at first.
7035 \begin_layout Standard
7036 \begin_inset VSpace medskip
7042 \begin_layout Standard
7043 If you set in the document settings under
7046 \begin_inset space ~
7056 \begin_inset Index idx
7059 \begin_layout Plain Layout
7060 Packages ! mathtools
7068 \begin_inset space ~
7073 , you have access to square backets:
7074 \begin_inset Separator parbreak
7080 \begin_layout Standard
7082 \begin_inset Tabular
7083 <lyxtabular version="3" rows="4" columns="2">
7084 <features tabularvalignment="middle">
7085 <column alignment="center" valignment="top" width="0pt">
7086 <column alignment="center" valignment="top" width="0pt">
7088 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
7091 \begin_layout Plain Layout
7093 \begin_inset Note Note
7096 \begin_layout Plain Layout
7103 is only used as spacer.
7113 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
7116 \begin_layout Plain Layout
7124 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
7127 \begin_layout Plain Layout
7131 \begin_layout Plain Layout
7167 \begin_inset space \textvisiblespace{}
7174 \begin_layout Plain Layout
7182 \begin_inset Index idx
7185 \begin_layout Plain Layout
7198 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
7201 \begin_layout Plain Layout
7202 \begin_inset Formula $\overbracket{A+B}^{3}$
7212 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
7215 \begin_layout Plain Layout
7219 \begin_layout Plain Layout
7255 \begin_inset space \textvisiblespace{}
7262 \begin_layout Plain Layout
7270 \begin_inset Index idx
7273 \begin_layout Plain Layout
7298 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
7301 \begin_layout Plain Layout
7302 \begin_inset Formula $\underbracket{A+B}_{5}$
7312 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
7315 \begin_layout Plain Layout
7321 \begin_inset space \textvisiblespace{}
7325 \begin_inset space \textvisiblespace{}
7329 \begin_inset space \textvisiblespace{}
7333 \begin_inset space \textvisiblespace{}
7337 \begin_inset space \textvisiblespace{}
7345 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
7348 \begin_layout Plain Layout
7349 \begin_inset Formula $\overbracket{\underbracket{A+B_{w}}_{7}}^{C}$
7365 \begin_layout Standard
7378 you can change the thickness of the bracket's stroke by specifying the
7379 desired thickness in square brackets behind the command:
7380 \begin_inset Separator parbreak
7386 \begin_layout Standard
7388 \begin_inset Tabular
7389 <lyxtabular version="3" rows="3" columns="2">
7390 <features tabularvalignment="middle">
7391 <column alignment="center" valignment="top" width="0pt">
7392 <column alignment="center" valignment="top" width="0pt">
7394 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
7397 \begin_layout Plain Layout
7399 \begin_inset Note Note
7402 \begin_layout Plain Layout
7409 is only used as spacer.
7419 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
7422 \begin_layout Plain Layout
7430 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
7433 \begin_layout Plain Layout
7437 \begin_layout Plain Layout
7475 \begin_inset space \textvisiblespace{}
7482 \begin_layout Plain Layout
7494 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
7497 \begin_layout Plain Layout
7498 \begin_inset Formula $\overbracket[3pt]{A+B}^{3}$
7508 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
7511 \begin_layout Plain Layout
7515 \begin_layout Plain Layout
7553 \begin_inset space \textvisiblespace{}
7560 \begin_layout Plain Layout
7572 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
7575 \begin_layout Plain Layout
7576 \begin_inset Formula $\underbracket[1pt]{A+B}_{5}$
7592 \begin_layout Standard
7593 \begin_inset VSpace bigskip
7596 When brackets should overlap each other, multiline formulas, as described
7598 \begin_inset CommandInset ref
7600 reference "sec:Multiline-Formulas"
7605 \begin_inset Formula
7607 A & = & \underbrace{gggg+bbqq}_{r}+\:dddd\\
7608 & & \hphantom{gggg+\:}\underbrace{\hphantom{bbqq+dddd}}_{s}
7613 In the first row the formula is inserted together with the first brace.
7614 It is hereby important that the space command
7618 \begin_layout Plain Layout
7619 Space commands are explained in
7620 \begin_inset CommandInset ref
7622 reference "subsec:Predefined-Space"
7637 is inserted before the first
7638 \begin_inset Formula $d$
7641 , because the brace that ends behind the
7642 \begin_inset Formula $q$
7645 prevents that the following
7646 \begin_inset Quotes eld
7650 \begin_inset Quotes erd
7653 is surrounded by space.
7657 \begin_layout Plain Layout
7658 because a bracket is not handled as a character, see
7659 \begin_inset CommandInset ref
7661 reference "subsec:Binary-Operators"
7670 In the second row the second brace is inserted.
7671 As it should begin before the
7672 \begin_inset Formula $b$
7687 \begin_layout Plain Layout
7695 \begin_inset CommandInset ref
7697 reference "subsec:Placeholders"
7706 This space is needed because the
7707 \begin_inset Quotes eld
7711 \begin_inset Quotes erd
7714 is also surrounded by space in the formula.
7715 The brace is placed under the command
7724 \begin_layout Standard
7725 It gets more complicated when brackets overlap each other above and under
7726 the formula, like in the following example:
7730 \begin_layout Plain Layout
7742 \begin_inset Formula
7744 & & \hphantom{gggg+\:}\overbrace{\hphantom{bbqq+dddd}}^{s}\\
7745 A & = & \underbrace{gggg+bbqq}_{r}+\:dddd
7754 \begin_layout Plain Layout
7765 The first formula row is the same as the second row of the previous example,
7766 with the difference that the brace is above.
7767 The second row contains the formula together with the second brace.
7768 To avoid that there is space between the upper brace in the first row and
7769 the formula, the row spacing needs to be reduced.
7770 This is not easily possible due to a bug in \SpecialChar LyX
7775 \begin_layout Plain Layout
7776 \begin_inset CommandInset href
7778 name "LyX-bug #1505"
7779 target "http://www.lyx.org/trac/ticket/1505"
7788 As a solution for the problem, the global formula row separation
7795 \begin_inset Index idx
7798 \begin_layout Plain Layout
7806 must be changed to -6
7807 \begin_inset space \thinspace{}
7810 pt before the formula with the command
7826 is set back after the formula to the standard value of 3
7827 \begin_inset space \thinspace{}
7830 pt using the same command.
7831 More about the row separation in formulas is explained in
7832 \begin_inset CommandInset ref
7834 reference "subsec:Line-Separation"
7841 \begin_layout Section
7843 \begin_inset Index idx
7846 \begin_layout Plain Layout
7855 \begin_layout Standard
7856 Arrows can be inserted via the math toolbar button
7859 arg "math-insert \\leftarrow"
7862 or the commands listed in the following subsections.
7865 \begin_layout Subsection
7867 \begin_inset Index idx
7870 \begin_layout Plain Layout
7879 \begin_layout Standard
7880 \begin_inset space \hfill{}
7884 \begin_inset Tabular
7885 <lyxtabular version="3" rows="8" columns="2">
7886 <features tabularvalignment="middle">
7887 <column alignment="center" valignment="top" width="0pt">
7888 <column alignment="center" valignment="top" width="0pt">
7890 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
7893 \begin_layout Plain Layout
7899 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
7902 \begin_layout Plain Layout
7910 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
7913 \begin_layout Plain Layout
7921 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
7924 \begin_layout Plain Layout
7925 \begin_inset Formula $\gets$
7935 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
7938 \begin_layout Plain Layout
7946 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
7949 \begin_layout Plain Layout
7950 \begin_inset Formula $\Leftarrow$
7960 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
7963 \begin_layout Plain Layout
7971 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
7974 \begin_layout Plain Layout
7975 \begin_inset Formula $\longleftarrow$
7985 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
7988 \begin_layout Plain Layout
7996 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
7999 \begin_layout Plain Layout
8000 \begin_inset Formula $\Longleftarrow$
8010 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
8013 \begin_layout Plain Layout
8021 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
8024 \begin_layout Plain Layout
8025 \begin_inset Formula $\leftharpoonup$
8035 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
8038 \begin_layout Plain Layout
8046 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
8049 \begin_layout Plain Layout
8050 \begin_inset Formula $\leftharpoondown$
8060 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
8063 \begin_layout Plain Layout
8071 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
8074 \begin_layout Plain Layout
8075 \begin_inset Formula $\hookleftarrow$
8089 \begin_inset space \hfill{}
8093 \begin_inset Tabular
8094 <lyxtabular version="3" rows="8" columns="2">
8095 <features tabularvalignment="middle">
8096 <column alignment="center" valignment="top" width="0pt">
8097 <column alignment="center" valignment="top" width="0pt">
8099 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
8102 \begin_layout Plain Layout
8108 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
8111 \begin_layout Plain Layout
8119 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
8122 \begin_layout Plain Layout
8130 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
8133 \begin_layout Plain Layout
8134 \begin_inset Formula $\to$
8144 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
8147 \begin_layout Plain Layout
8155 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
8158 \begin_layout Plain Layout
8159 \begin_inset Formula $\Rightarrow$
8169 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
8172 \begin_layout Plain Layout
8180 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
8183 \begin_layout Plain Layout
8184 \begin_inset Formula $\longrightarrow$
8194 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
8197 \begin_layout Plain Layout
8205 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
8208 \begin_layout Plain Layout
8209 \begin_inset Formula $\Longrightarrow$
8219 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
8222 \begin_layout Plain Layout
8230 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
8233 \begin_layout Plain Layout
8234 \begin_inset Formula $\rightharpoonup$
8244 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
8247 \begin_layout Plain Layout
8255 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
8258 \begin_layout Plain Layout
8259 \begin_inset Formula $\rightharpoondown$
8269 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
8272 \begin_layout Plain Layout
8280 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
8283 \begin_layout Plain Layout
8284 \begin_inset Formula $\hookrightarrow$
8298 \begin_inset space \hfill{}
8304 \begin_layout Standard
8305 \begin_inset space \hfill{}
8309 \begin_inset Tabular
8310 <lyxtabular version="3" rows="6" columns="2">
8311 <features tabularvalignment="middle">
8312 <column alignment="center" valignment="top" width="0pt">
8313 <column alignment="center" valignment="top" width="0pt">
8315 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
8318 \begin_layout Plain Layout
8324 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
8327 \begin_layout Plain Layout
8335 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
8338 \begin_layout Plain Layout
8346 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
8349 \begin_layout Plain Layout
8350 \begin_inset Formula $\leftrightarrow$
8360 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
8363 \begin_layout Plain Layout
8371 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
8374 \begin_layout Plain Layout
8375 \begin_inset Formula $\Leftrightarrow$
8385 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
8388 \begin_layout Plain Layout
8396 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
8399 \begin_layout Plain Layout
8400 \begin_inset Formula $\longleftrightarrow$
8410 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
8413 \begin_layout Plain Layout
8421 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
8424 \begin_layout Plain Layout
8425 \begin_inset Formula $\Longleftrightarrow$
8435 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
8438 \begin_layout Plain Layout
8446 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
8449 \begin_layout Plain Layout
8450 \begin_inset Formula $\rightleftharpoons$
8464 \begin_inset space \hspace{}
8469 \begin_inset space \hfill{}
8473 \begin_inset Tabular
8474 <lyxtabular version="3" rows="5" columns="2">
8475 <features tabularvalignment="middle">
8476 <column alignment="center" valignment="top" width="0pt">
8477 <column alignment="center" valignment="top" width="0pt">
8479 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
8482 \begin_layout Plain Layout
8488 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
8491 \begin_layout Plain Layout
8499 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
8502 \begin_layout Plain Layout
8510 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
8513 \begin_layout Plain Layout
8514 \begin_inset Formula $\mapsto$
8524 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
8527 \begin_layout Plain Layout
8535 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
8538 \begin_layout Plain Layout
8539 \begin_inset Formula $\longmapsto$
8549 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
8552 \begin_layout Plain Layout
8560 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
8563 \begin_layout Plain Layout
8564 \begin_inset Formula $\leadsto$
8574 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
8577 \begin_layout Plain Layout
8585 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
8588 \begin_layout Plain Layout
8589 \begin_inset Formula $\dasharrow$
8603 \begin_inset space \hfill{}
8609 \begin_layout Standard
8610 \begin_inset VSpace medskip
8613 Arrows used as accents like e.
8614 \begin_inset space \thinspace{}
8618 \begin_inset space \space{}
8621 vector arrows are listed in
8622 \begin_inset CommandInset ref
8624 reference "sec:Accents"
8631 \begin_layout Standard
8632 \begin_inset VSpace bigskip
8635 Furthermore there are the labeled arrows
8636 \begin_inset Index idx
8639 \begin_layout Plain Layout
8652 \begin_inset Index idx
8655 \begin_layout Plain Layout
8670 \begin_inset Index idx
8673 \begin_layout Plain Layout
8680 \begin_layout Plain Layout
8695 When inserting one of these commands in a formula, an arrow with two blue
8696 boxes appear where the label can be inserted.
8697 The length of the arrow adapts to the label width.
8700 \begin_layout Standard
8702 \begin_inset Tabular
8703 <lyxtabular version="3" rows="3" columns="2">
8704 <features tabularvalignment="middle">
8705 <column alignment="center" valignment="top" width="0pt">
8706 <column alignment="center" valignment="top" width="0pt">
8708 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
8711 \begin_layout Plain Layout
8717 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
8720 \begin_layout Plain Layout
8722 \begin_inset Note Note
8725 \begin_layout Plain Layout
8732 is only used as spacer.
8744 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
8747 \begin_layout Plain Layout
8751 \begin_inset space \textvisiblespace{}
8755 \begin_inset Formula $\downarrow$
8759 \begin_inset Formula $\to$
8767 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
8770 \begin_layout Plain Layout
8771 \begin_inset Formula $\raisebox{5.5mm}{}F(a)\xleftarrow[x>0]{x=a}F(x)\raisebox{-4mm}{}$
8781 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
8784 \begin_layout Plain Layout
8788 \begin_inset space \textvisiblespace{}
8792 \begin_inset Formula $\downarrow$
8796 \begin_inset Formula $\to$
8804 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
8807 \begin_layout Plain Layout
8808 \begin_inset Formula $\raisebox{5.5mm}{}F(x)\xrightarrow[x>0]{x=a}F(a)\raisebox{-4mm}{}$
8824 \begin_layout Standard
8825 \begin_inset VSpace medskip
8831 \begin_layout Standard
8832 If you set in the document settings under
8835 \begin_inset space ~
8845 \begin_inset Index idx
8848 \begin_layout Plain Layout
8849 Packages ! mathtools
8857 \begin_inset space ~
8862 , you have access to the following labeled arrows:
8865 \begin_layout Standard
8866 \begin_inset Newpage newpage
8870 \begin_inset Separator parbreak
8876 \begin_layout Standard
8878 \begin_inset space \hspace*{\fill}
8882 \begin_inset Tabular
8883 <lyxtabular version="3" rows="7" columns="2">
8884 <features tabularvalignment="middle">
8885 <column alignment="center" valignment="top" width="0pt">
8886 <column alignment="center" valignment="top" width="0pt">
8888 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
8891 \begin_layout Plain Layout
8897 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
8900 \begin_layout Plain Layout
8902 \begin_inset Note Note
8905 \begin_layout Plain Layout
8912 is only used as spacer.
8924 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
8927 \begin_layout Plain Layout
8947 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
8950 \begin_layout Plain Layout
8951 \begin_inset Formula $\raisebox{6mm}{}\xleftrightarrow[x=a]{x>0}\raisebox{-4mm}{}$
8961 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
8964 \begin_layout Plain Layout
8984 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
8987 \begin_layout Plain Layout
8988 \begin_inset Formula $\raisebox{6mm}{}\xLeftarrow[x=a]{x>0}\raisebox{-4mm}{}$
8998 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
9001 \begin_layout Plain Layout
9021 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
9024 \begin_layout Plain Layout
9025 \begin_inset Formula $\raisebox{6mm}{}\xRightarrow[x=a]{x>0}\raisebox{-4mm}{}$
9035 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
9038 \begin_layout Plain Layout
9058 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
9061 \begin_layout Plain Layout
9062 \begin_inset Formula $\raisebox{6mm}{}\xLeftrightarrow[x=a]{x>0}\raisebox{-4mm}{}$
9072 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
9075 \begin_layout Plain Layout
9095 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
9098 \begin_layout Plain Layout
9099 \begin_inset Formula $\raisebox{6mm}{}\xhookleftarrow[x=a]{x>0}\raisebox{-4mm}{}$
9109 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
9112 \begin_layout Plain Layout
9132 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
9135 \begin_layout Plain Layout
9136 \begin_inset Formula $\raisebox{6mm}{}\xhookrightarrow[x=a]{x>0}\raisebox{-4mm}{}$
9150 \begin_inset space \hspace*{\fill}
9154 \begin_inset Tabular
9155 <lyxtabular version="3" rows="7" columns="2">
9156 <features tabularvalignment="middle">
9157 <column alignment="center" valignment="top" width="0pt">
9158 <column alignment="center" valignment="top" width="0pt">
9160 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
9163 \begin_layout Plain Layout
9169 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
9172 \begin_layout Plain Layout
9174 \begin_inset Note Note
9177 \begin_layout Plain Layout
9184 is only used as spacer.
9196 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
9199 \begin_layout Plain Layout
9219 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
9222 \begin_layout Plain Layout
9223 \begin_inset Formula $\raisebox{6mm}{}\xleftharpoondown[x=a]{x>0}\raisebox{-4mm}{}$
9233 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
9236 \begin_layout Plain Layout
9256 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
9259 \begin_layout Plain Layout
9260 \begin_inset Formula $\raisebox{6mm}{}\xleftharpoonup[x=a]{x>0}\raisebox{-4mm}{}$
9270 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
9273 \begin_layout Plain Layout
9293 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
9296 \begin_layout Plain Layout
9297 \begin_inset Formula $\raisebox{6mm}{}\xrightharpoondown[x=a]{x>0}\raisebox{-4mm}{}$
9307 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
9310 \begin_layout Plain Layout
9330 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
9333 \begin_layout Plain Layout
9334 \begin_inset Formula $\raisebox{6mm}{}\xrightharpoonup[x=a]{x>0}\raisebox{-4mm}{}$
9344 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
9347 \begin_layout Plain Layout
9367 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
9370 \begin_layout Plain Layout
9371 \begin_inset Formula $\raisebox{6mm}{}\xleftrightharpoons[x=a]{x>0}\raisebox{-4mm}{}$
9381 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
9384 \begin_layout Plain Layout
9404 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
9407 \begin_layout Plain Layout
9408 \begin_inset Formula $\raisebox{6mm}{}\xrightleftharpoons[x=a]{x>0}\raisebox{-4mm}{}$
9422 \begin_inset space \hspace*{\fill}
9428 \begin_layout Standard
9429 The command scheme is for all these arrows:
9430 \begin_inset Separator parbreak
9436 \begin_layout Standard
9438 \begin_inset Tabular
9439 <lyxtabular version="3" rows="2" columns="2">
9440 <features tabularvalignment="middle">
9441 <column alignment="center" valignment="top" width="0pt">
9442 <column alignment="center" valignment="top" width="0pt">
9444 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
9447 \begin_layout Plain Layout
9453 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
9456 \begin_layout Plain Layout
9458 \begin_inset Note Note
9461 \begin_layout Plain Layout
9468 is only used as spacer.
9480 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
9483 \begin_layout Plain Layout
9486 xleftrightarrow[x=a]
9489 \begin_inset Formula $\to$
9497 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
9500 \begin_layout Plain Layout
9501 \begin_inset Formula $\raisebox{6mm}{}F(a)\xleftrightarrow[x=a]{x>0}F(x)\raisebox{-4mm}{}$
9517 \begin_layout Subsection
9518 Vertical and diagonal Arrows
9519 \begin_inset Index idx
9522 \begin_layout Plain Layout
9529 \begin_inset Index idx
9532 \begin_layout Plain Layout
9541 \begin_layout Standard
9542 \begin_inset space \hfill{}
9546 \begin_inset Tabular
9547 <lyxtabular version="3" rows="7" columns="2">
9548 <features tabularvalignment="middle">
9549 <column alignment="center" valignment="top" width="0pt">
9550 <column alignment="center" valignment="top" width="0pt">
9552 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
9555 \begin_layout Plain Layout
9561 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
9564 \begin_layout Plain Layout
9572 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
9575 \begin_layout Plain Layout
9583 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
9586 \begin_layout Plain Layout
9587 \begin_inset Formula $\uparrow$
9597 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
9600 \begin_layout Plain Layout
9608 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
9611 \begin_layout Plain Layout
9612 \begin_inset Formula $\Uparrow$
9622 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
9625 \begin_layout Plain Layout
9633 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
9636 \begin_layout Plain Layout
9637 \begin_inset Formula $\updownarrow$
9647 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
9650 \begin_layout Plain Layout
9658 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
9661 \begin_layout Plain Layout
9662 \begin_inset Formula $\Updownarrow$
9672 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
9675 \begin_layout Plain Layout
9683 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
9686 \begin_layout Plain Layout
9687 \begin_inset Formula $\Downarrow$
9697 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
9700 \begin_layout Plain Layout
9708 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
9711 \begin_layout Plain Layout
9712 \begin_inset Formula $\downarrow$
9726 \begin_inset space \hfill{}
9730 \begin_inset Tabular
9731 <lyxtabular version="3" rows="5" columns="2">
9732 <features tabularvalignment="middle">
9733 <column alignment="center" valignment="top" width="0pt">
9734 <column alignment="center" valignment="top" width="0pt">
9736 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
9739 \begin_layout Plain Layout
9745 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
9748 \begin_layout Plain Layout
9756 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
9759 \begin_layout Plain Layout
9767 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
9770 \begin_layout Plain Layout
9771 \begin_inset Formula $\nearrow$
9781 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
9784 \begin_layout Plain Layout
9792 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
9795 \begin_layout Plain Layout
9796 \begin_inset Formula $\searrow$
9806 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
9809 \begin_layout Plain Layout
9817 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
9820 \begin_layout Plain Layout
9821 \begin_inset Formula $\swarrow$
9831 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
9834 \begin_layout Plain Layout
9842 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
9845 \begin_layout Plain Layout
9846 \begin_inset Formula $\nwarrow$
9860 \begin_inset space \hfill{}
9866 \begin_layout Standard
9867 \begin_inset VSpace medskip
9870 Vertical arrows can be used also as delimiters together with the commands
9872 \begin_inset CommandInset ref
9874 reference "subsec:Manual-Bracket-Size"
9879 \begin_inset CommandInset ref
9881 reference "subsec:Automatic-Bracket-Size"
9888 \begin_layout Section
9890 \begin_inset CommandInset label
9897 \begin_inset Index idx
9900 \begin_layout Plain Layout
9909 \begin_layout Standard
9910 Accents can be inserted via the math toolbar button
9913 arg "math-insert \\hat"
9916 or the commands listed in the following subsections.
9919 \begin_layout Subsection
9920 Accents for one Character
9924 \begin_layout Plain Layout
9937 \begin_layout Plain Layout
9939 \begin_inset CommandInset ref
9941 reference "subsec:Accents-in-Text"
9954 \begin_layout Plain Layout
9962 \begin_inset Note Note
9965 \begin_layout Plain Layout
9972 is used to avoid that the footnote appears in the PDF-bookmark.
9975 \begin_layout Plain Layout
9983 \begin_inset CommandInset ref
9985 reference "subsec:Formulas-in-Section"
9995 \begin_inset CommandInset label
9997 name "subsec:Accents-for-one"
10002 \begin_inset Index idx
10005 \begin_layout Plain Layout
10006 Accents ! for one character
10014 \begin_layout Standard
10015 \begin_inset space \hfill{}
10019 \begin_inset Tabular
10020 <lyxtabular version="3" rows="8" columns="2">
10021 <features tabularvalignment="middle">
10022 <column alignment="center" valignment="top" width="0pt">
10023 <column alignment="center" valignment="top" width="0pt">
10025 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
10028 \begin_layout Plain Layout
10034 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
10037 \begin_layout Plain Layout
10039 \begin_inset Note Note
10042 \begin_layout Plain Layout
10049 is only used as spacer.
10061 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
10064 \begin_layout Plain Layout
10068 \begin_inset space \textvisiblespace{}
10076 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
10079 \begin_layout Plain Layout
10080 \begin_inset Formula $\raisebox{5mm}{}\dot{A}$
10090 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
10093 \begin_layout Plain Layout
10097 \begin_inset space \textvisiblespace{}
10105 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
10108 \begin_layout Plain Layout
10109 \begin_inset Formula $\raisebox{5mm}{}\ddot{A}$
10119 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
10122 \begin_layout Plain Layout
10126 \begin_inset space \textvisiblespace{}
10134 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
10137 \begin_layout Plain Layout
10138 \begin_inset Formula $\raisebox{5mm}{}\dddot{A}$
10148 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
10151 \begin_layout Plain Layout
10155 \begin_inset space \textvisiblespace{}
10163 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
10166 \begin_layout Plain Layout
10167 \begin_inset Formula $\raisebox{5mm}{}\ddddot{A}$
10177 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
10180 \begin_layout Plain Layout
10184 \begin_inset space \textvisiblespace{}
10188 \begin_inset Index idx
10191 \begin_layout Plain Layout
10202 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
10205 \begin_layout Plain Layout
10206 \begin_inset Formula $\raisebox{5mm}{}\vec{A}$
10216 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
10219 \begin_layout Plain Layout
10223 \begin_inset space \textvisiblespace{}
10231 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
10234 \begin_layout Plain Layout
10235 \begin_inset Formula $\raisebox{5mm}{}\bar{A}$
10245 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
10248 \begin_layout Plain Layout
10252 \begin_inset space \textvisiblespace{}
10260 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
10263 \begin_layout Plain Layout
10264 \begin_inset Formula $\raisebox{5mm}{}\mathring{A}$
10278 \begin_inset space \hfill{}
10282 \begin_inset Tabular
10283 <lyxtabular version="3" rows="7" columns="2">
10284 <features tabularvalignment="middle">
10285 <column alignment="center" valignment="top" width="0pt">
10286 <column alignment="center" valignment="top" width="0pt">
10288 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
10291 \begin_layout Plain Layout
10297 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
10300 \begin_layout Plain Layout
10308 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
10311 \begin_layout Plain Layout
10315 \begin_inset space \textvisiblespace{}
10323 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
10326 \begin_layout Plain Layout
10327 \begin_inset Formula $\raisebox{5mm}{}\tilde{A}$
10337 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
10340 \begin_layout Plain Layout
10344 \begin_inset space \textvisiblespace{}
10352 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
10355 \begin_layout Plain Layout
10356 \begin_inset Formula $\raisebox{5mm}{}\hat{A}$
10366 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
10369 \begin_layout Plain Layout
10373 \begin_inset space \textvisiblespace{}
10381 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
10384 \begin_layout Plain Layout
10385 \begin_inset Formula $\raisebox{5mm}{}\check{A}$
10395 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
10398 \begin_layout Plain Layout
10402 \begin_inset space \textvisiblespace{}
10410 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
10413 \begin_layout Plain Layout
10414 \begin_inset Formula $\raisebox{5mm}{}\acute{A}$
10424 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
10427 \begin_layout Plain Layout
10431 \begin_inset space \textvisiblespace{}
10439 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
10442 \begin_layout Plain Layout
10443 \begin_inset Formula $\raisebox{5mm}{}\grave{A}$
10453 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
10456 \begin_layout Plain Layout
10460 \begin_inset space \textvisiblespace{}
10468 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
10471 \begin_layout Plain Layout
10472 \begin_inset Formula $\raisebox{5mm}{}\breve{A}$
10486 \begin_inset space \hfill{}
10492 \begin_layout Standard
10493 \begin_inset VSpace bigskip
10499 \begin_layout Standard
10500 You can directly insert accents like é to formulas.
10502 will transform them to the corresponding accent command.
10504 \begin_inset Index idx
10507 \begin_layout Plain Layout
10513 it is better to insert a quotation mark before the vowel.
10514 These two characters are then treated by \SpecialChar LaTeX
10519 character when the formula part with the umlaut is marked as German.
10527 \begin_inset Quotes eld
10531 \begin_inset Quotes erd
10534 umlauts are created as demonstrated in the following example:
10537 \begin_layout Standard
10538 \begin_inset VSpace -2mm
10544 \begin_layout Standard
10546 \begin_inset Tabular
10547 <lyxtabular version="3" rows="3" columns="2">
10548 <features tabularvalignment="middle">
10549 <column alignment="center" valignment="top">
10550 <column alignment="center" valignment="top">
10552 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
10555 \begin_layout Plain Layout
10561 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
10564 \begin_layout Plain Layout
10566 \begin_inset Note Note
10569 \begin_layout Plain Layout
10577 \begin_inset space \thinspace{}
10580 pt space are only used as spacer.
10592 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
10595 \begin_layout Plain Layout
10598 \begin_inset Quotes grd
10606 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
10609 \begin_layout Plain Layout
10610 \begin_inset space \hspace{}
10617 \begin_inset Formula $"i$
10627 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
10630 \begin_layout Plain Layout
10634 \begin_inset space \textvisiblespace{}
10642 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
10645 \begin_layout Plain Layout
10646 \begin_inset Formula $\raisebox{5mm}{}\ddot{i}$
10662 \begin_layout Standard
10663 Another advantage to
10669 is that umlauts can directly be converted to mathematical text because
10670 the accent commands above are
10676 in mathematical text
10679 To convert an accented character to mathematical text, only the character
10680 under the accent may be converted.
10681 This applies also for all other conversions, e.
10682 \begin_inset space \thinspace{}
10686 \begin_inset space \space{}
10692 \begin_layout Standard
10693 In mathematical text, umlauts and other accented characters can directly
10697 \begin_layout Standard
10698 \begin_inset VSpace bigskip
10704 \begin_layout Standard
10706 also supports a tilde under the character if the \SpecialChar LaTeX
10712 \begin_inset Index idx
10715 \begin_layout Plain Layout
10716 Packages ! undertilde
10721 is installed on your system:
10724 \begin_layout Standard
10728 \begin_layout Plain Layout
10738 \begin_inset Note Note
10741 \begin_layout Plain Layout
10742 The following table will only be displayed when the \SpecialChar LaTeX
10753 \begin_inset Separator parbreak
10759 \begin_layout Standard
10762 \begin_inset Tabular
10763 <lyxtabular version="3" rows="2" columns="2">
10764 <features tabularvalignment="middle">
10765 <column alignment="center" valignment="top" width="0pt">
10766 <column alignment="center" valignment="top" width="0pt">
10768 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
10771 \begin_layout Plain Layout
10777 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
10780 \begin_layout Plain Layout
10788 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
10791 \begin_layout Plain Layout
10795 \begin_inset space \textvisiblespace{}
10803 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
10806 \begin_layout Plain Layout
10807 \begin_inset Formula $\raisebox{5mm}{}\utilde{A}$
10823 \begin_layout Standard
10827 \begin_layout Plain Layout
10837 \begin_inset Note Note
10840 \begin_layout Plain Layout
10841 The following will be displayed when the \SpecialChar LaTeX
10854 \begin_layout Standard
10855 You need to install the \SpecialChar LaTeX
10860 to see the rest of this subsection in the output.
10863 \begin_layout Standard
10867 \begin_layout Plain Layout
10879 \begin_layout Standard
10880 \begin_inset Newpage newpage
10886 \begin_layout Subsection
10887 Accents for several Characters
10888 \begin_inset Index idx
10891 \begin_layout Plain Layout
10892 Accents ! for several characters
10900 \begin_layout Standard
10901 \begin_inset space \hfill{}
10905 \begin_inset Tabular
10906 <lyxtabular version="3" rows="5" columns="2">
10907 <features tabularvalignment="middle">
10908 <column alignment="center" valignment="top" width="0pt">
10909 <column alignment="center" valignment="top" width="0pt">
10911 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
10914 \begin_layout Plain Layout
10920 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
10923 \begin_layout Plain Layout
10925 \begin_inset Note Note
10928 \begin_layout Plain Layout
10935 is only used as spacer.
10947 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
10950 \begin_layout Plain Layout
10954 \begin_inset space \textvisiblespace{}
10962 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
10965 \begin_layout Plain Layout
10966 \begin_inset Formula $\raisebox{6mm}{}\overleftarrow{A=B}\raisebox{-2mm}{}$
10976 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
10979 \begin_layout Plain Layout
10983 \begin_inset space \textvisiblespace{}
10991 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
10994 \begin_layout Plain Layout
10995 \begin_inset Formula $\raisebox{5mm}{}\underleftarrow{A=B}\raisebox{-3mm}{}$
11005 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
11008 \begin_layout Plain Layout
11012 \begin_inset space \textvisiblespace{}
11020 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
11023 \begin_layout Plain Layout
11024 \begin_inset Formula $\raisebox{6mm}{}\overleftrightarrow{A=B}\raisebox{-2mm}{}$
11034 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
11037 \begin_layout Plain Layout
11040 underleftrightarrow
11041 \begin_inset space \textvisiblespace{}
11049 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
11052 \begin_layout Plain Layout
11053 \begin_inset Formula $\raisebox{5mm}{}\underleftrightarrow{A=B}\raisebox{-3mm}{}$
11067 \begin_inset space \hfill{}
11071 \begin_inset Tabular
11072 <lyxtabular version="3" rows="5" columns="2">
11073 <features tabularvalignment="middle">
11074 <column alignment="center" valignment="top" width="0pt">
11075 <column alignment="center" valignment="top" width="0pt">
11077 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
11080 \begin_layout Plain Layout
11086 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
11089 \begin_layout Plain Layout
11097 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
11100 \begin_layout Plain Layout
11104 \begin_inset space \textvisiblespace{}
11112 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
11115 \begin_layout Plain Layout
11116 \begin_inset Formula $\raisebox{6mm}{}\overrightarrow{A=B}\raisebox{-2mm}{}$
11126 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
11129 \begin_layout Plain Layout
11133 \begin_inset space \textvisiblespace{}
11141 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
11144 \begin_layout Plain Layout
11145 \begin_inset Formula $\raisebox{5mm}{}\underrightarrow{A=B}\raisebox{-3mm}{}$
11155 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
11158 \begin_layout Plain Layout
11162 \begin_inset space \textvisiblespace{}
11170 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
11173 \begin_layout Plain Layout
11174 \begin_inset Formula $\raisebox{6mm}{}\widetilde{A=B}\raisebox{-2mm}{}$
11184 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
11187 \begin_layout Plain Layout
11191 \begin_inset space \textvisiblespace{}
11199 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
11202 \begin_layout Plain Layout
11203 \begin_inset Formula $\raisebox{6mm}{}\widehat{A=B}\raisebox{-2mm}{}$
11217 \begin_inset space \hfill{}
11223 \begin_layout Standard
11224 \begin_inset VSpace medskip
11227 With these commands as many characters as you like can be accented.
11240 will only be set in the output with a length of three characters, as shown
11241 in the following example:
11242 \begin_inset Formula
11244 \widetilde{A+B=C-D}
11252 \begin_layout Standard
11260 \begin_inset Index idx
11263 \begin_layout Plain Layout
11278 \begin_inset Index idx
11281 \begin_layout Plain Layout
11289 described in the previous subsection it is also possible to accent several
11296 \begin_inset space \textvisiblespace{}
11300 \begin_inset Formula $\downarrow$
11306 \begin_inset Formula
11308 \underset{***}{A=B}
11316 \begin_layout Section
11318 \begin_inset CommandInset label
11320 name "subsec:Space"
11325 \begin_inset Index idx
11328 \begin_layout Plain Layout
11337 \begin_layout Subsection
11339 \begin_inset CommandInset label
11341 name "subsec:Predefined-Space"
11346 \begin_inset Index idx
11349 \begin_layout Plain Layout
11350 Space ! horizontal ! predefined
11358 \begin_layout Standard
11359 Sometimes it is necessary to insert horizontal space into a formula.
11360 This is done by inserting a protected space (shortcut
11363 arg "command-alternatives space-insert protected ; math-space"
11368 \begin_inset Quotes eld
11374 \begin_inset space \textvisiblespace{}
11380 \begin_inset Quotes erd
11383 appears and by pressing
11387 several times one can select one of eight different space sizes.
11388 The spaces can also be inserted using the math toolbar button
11391 arg "math-insert \\space"
11394 or special commands.
11395 Independent from the inserted command, one can select the size again by
11401 \begin_inset Separator parbreak
11407 \begin_layout Standard
11410 \begin_inset Tabular
11411 <lyxtabular version="3" rows="6" columns="3">
11412 <features tabularvalignment="middle">
11413 <column alignment="center" valignment="top">
11414 <column alignment="center" valignment="top" width="15col%">
11415 <column alignment="center" valignment="top">
11417 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
11420 \begin_layout Plain Layout
11426 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
11429 \begin_layout Plain Layout
11439 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
11442 \begin_layout Plain Layout
11450 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
11453 \begin_layout Plain Layout
11461 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
11464 \begin_layout Plain Layout
11470 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
11473 \begin_layout Plain Layout
11474 \begin_inset Formula $A\,B$
11484 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
11487 \begin_layout Plain Layout
11495 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
11498 \begin_layout Plain Layout
11504 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
11507 \begin_layout Plain Layout
11508 \begin_inset Formula $A\:B$
11518 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
11521 \begin_layout Plain Layout
11529 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
11532 \begin_layout Plain Layout
11538 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
11541 \begin_layout Plain Layout
11542 \begin_inset Formula $A\;B$
11552 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
11555 \begin_layout Plain Layout
11563 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
11566 \begin_layout Plain Layout
11572 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
11575 \begin_layout Plain Layout
11576 \begin_inset Formula $A\quad B$
11586 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
11589 \begin_layout Plain Layout
11597 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
11600 \begin_layout Plain Layout
11606 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
11609 \begin_layout Plain Layout
11610 \begin_inset Formula $A\qquad B$
11624 \begin_inset space \hfill{}
11628 \begin_inset Tabular
11629 <lyxtabular version="3" rows="6" columns="3">
11630 <features tabularvalignment="middle">
11631 <column alignment="center" valignment="top">
11632 <column alignment="center" valignment="top" width="15col%">
11633 <column alignment="center" valignment="top">
11635 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
11638 \begin_layout Plain Layout
11644 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
11647 \begin_layout Plain Layout
11657 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
11660 \begin_layout Plain Layout
11668 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
11671 \begin_layout Plain Layout
11679 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
11682 \begin_layout Plain Layout
11688 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
11691 \begin_layout Plain Layout
11692 \begin_inset Formula $A\hfill B$
11702 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
11705 \begin_layout Plain Layout
11713 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
11716 \begin_layout Plain Layout
11722 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
11725 \begin_layout Plain Layout
11726 \begin_inset Formula $A\hspace*{1em}B$
11736 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
11739 \begin_layout Plain Layout
11747 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
11750 \begin_layout Plain Layout
11756 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
11759 \begin_layout Plain Layout
11760 \begin_inset Formula $A\hspace{1em}B$
11770 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
11773 \begin_layout Plain Layout
11777 \begin_inset space \textvisiblespace{}
11785 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
11788 \begin_layout Plain Layout
11794 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
11797 \begin_layout Plain Layout
11798 \begin_inset Formula $A\ B$
11808 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
11811 \begin_layout Plain Layout
11819 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
11822 \begin_layout Plain Layout
11828 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
11831 \begin_layout Plain Layout
11832 \begin_inset Formula $A\!B$
11848 \begin_layout Standard
11850 \begin_inset space ~
11854 \begin_inset space \thinspace{}
11858 \begin_inset space \thinspace{}
11861 7 are variable spaces which are explained in
11862 \begin_inset CommandInset ref
11864 reference "subsec:Variable-Space"
11870 \begin_inset space ~
11873 9 seems to produce no space.
11874 It is displayed red in \SpecialChar LyX
11875 contrary to the other sizes, because it is a negative
11877 There are two more negative spaces:
11878 \begin_inset Separator parbreak
11884 \begin_layout Standard
11886 \begin_inset Tabular
11887 <lyxtabular version="3" rows="3" columns="3">
11888 <features tabularvalignment="middle">
11889 <column alignment="center" valignment="middle" width="6.8cm">
11890 <column alignment="center" valignment="top" width="0pt">
11891 <column alignment="center" valignment="top" width="0pt">
11893 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
11896 \begin_layout Plain Layout
11902 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
11905 \begin_layout Plain Layout
11913 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
11916 \begin_layout Plain Layout
11926 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
11929 \begin_layout Plain Layout
11934 keystrokes after inserting the protected space
11939 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
11942 \begin_layout Plain Layout
11948 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
11951 \begin_layout Plain Layout
11959 <cell multicolumn="1" alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
11962 \begin_layout Plain Layout
11968 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
11971 \begin_layout Plain Layout
11972 \begin_inset Formula $A\negmedspace B$
11980 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
11983 \begin_layout Plain Layout
11984 \begin_inset Formula $A\negthickspace B$
12000 \begin_layout Standard
12001 Negative spaces can lead to characters overlapping each other.
12002 Thus they can be used to enforce ligatures, which are e.
12003 \begin_inset space \thinspace{}
12007 \begin_inset space \space{}
12010 useful for summation operators:
12011 \begin_inset Separator parbreak
12017 \begin_layout Standard
12019 \begin_inset Tabular
12020 <lyxtabular version="3" rows="3" columns="2">
12021 <features tabularvalignment="middle">
12022 <column alignment="center" valignment="top">
12023 <column alignment="center" valignment="top">
12025 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
12028 \begin_layout Plain Layout
12034 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
12037 \begin_layout Plain Layout
12039 \begin_inset Note Note
12042 \begin_layout Plain Layout
12049 is only used as spacer.
12061 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
12064 \begin_layout Plain Layout
12070 \begin_inset space \textvisiblespace{}
12078 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
12081 \begin_layout Plain Layout
12082 \begin_inset Formula $\raisebox{4.5mm}{}\sum\sum f_{kl}\raisebox{-2.5mm}{}$
12092 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
12095 \begin_layout Plain Layout
12103 \begin_inset space \textvisiblespace{}
12111 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
12114 \begin_layout Plain Layout
12115 \begin_inset Formula $\raisebox{4.5mm}{}\sum\negmedspace\sum f_{kl}\raisebox{-2.5mm}{}$
12131 \begin_layout Standard
12133 \begin_inset VSpace medskip
12139 \begin_layout Standard
12141 Relations like for example equal signs, are always surrounded by space.
12142 To suppress this, the equal sign is placed into a \SpecialChar TeX
12144 The following example demonstrates this:
12145 \begin_inset Separator parbreak
12151 \begin_layout Standard
12153 \begin_inset Tabular
12154 <lyxtabular version="3" rows="2" columns="2">
12155 <features tabularvalignment="middle">
12156 <column alignment="center" valignment="top" width="0pt">
12157 <column alignment="center" valignment="top" width="0pt">
12159 <cell alignment="center" valignment="top" usebox="none">
12162 \begin_layout Plain Layout
12168 <cell alignment="center" valignment="top" usebox="none">
12171 \begin_layout Plain Layout
12172 \begin_inset Formula $A=B$
12182 <cell alignment="center" valignment="top" usebox="none">
12185 \begin_layout Plain Layout
12186 \begin_inset Note Note
12189 \begin_layout Plain Layout
12196 is only used as spacer.
12202 \begin_inset Formula $\raisebox{5mm}{}$
12205 equation without space
12210 <cell multicolumn="1" alignment="center" valignment="top" usebox="none">
12213 \begin_layout Plain Layout
12214 \begin_inset Formula $A{=}B$
12230 \begin_layout Standard
12232 The command for the last formula is:
12237 \begin_inset Formula $\to$
12243 \begin_layout Standard
12244 \begin_inset VSpace bigskip
12250 \begin_layout Standard
12251 Spaces are needed for physical units, because the space between the value
12252 and the unit is the smallest one and not a normal space.
12253 For units in text, the smallest space is inserted via the menu
12255 Insert\SpecialChar menuseparator
12256 Formatting\SpecialChar menuseparator
12258 \begin_inset space ~
12266 arg "space-insert thin"
12272 \begin_layout Standard
12273 An example to visualize the difference:
12276 \begin_layout Standard
12277 \begin_inset Tabular
12278 <lyxtabular version="3" rows="2" columns="2">
12279 <features tabularvalignment="middle">
12280 <column alignment="left" valignment="top">
12281 <column alignment="left" valignment="top">
12283 <cell alignment="center" valignment="top" usebox="none">
12286 \begin_layout Plain Layout
12288 \begin_inset Formula $\cdot$
12296 <cell alignment="center" valignment="top" usebox="none">
12299 \begin_layout Plain Layout
12300 space between value and unit
12307 <cell alignment="center" valignment="top" usebox="none">
12310 \begin_layout Plain Layout
12312 \begin_inset space \thinspace{}
12316 \begin_inset Formula $\cdot$
12324 <cell alignment="center" valignment="top" usebox="none">
12327 \begin_layout Plain Layout
12328 smallest space between value and unit
12341 \begin_layout Subsection
12346 \begin_layout Plain Layout
12359 \begin_layout Plain Layout
12360 for vertical space in formulas see
12361 \begin_inset CommandInset ref
12363 reference "subsec:Line-Separation"
12376 \begin_layout Plain Layout
12384 \begin_inset Note Note
12387 \begin_layout Plain Layout
12390 texorpdfstring is used to avoid that the footnote appears in the PDF-bookmark.
12393 \begin_layout Plain Layout
12396 texorpdfstring is in section
12397 \begin_inset CommandInset ref
12399 reference "subsec:Formulas-in-Section"
12409 \begin_inset CommandInset label
12411 name "subsec:Variable-Space"
12416 \begin_inset Index idx
12419 \begin_layout Plain Layout
12420 Space ! horizontal ! variable
12428 \begin_layout Standard
12429 Space with a defined length can be inserted with the command
12436 \begin_inset Index idx
12439 \begin_layout Plain Layout
12449 \begin_inset Quotes eld
12455 \begin_inset space \textvisiblespace{}
12461 \begin_inset Quotes erd
12465 The length can be specified by left-clicking on the
12466 \begin_inset Quotes eld
12472 \begin_inset space \textvisiblespace{}
12478 \begin_inset Quotes erd
12482 The length may also be negative.
12483 When a space would be the first character in a line it would be omitted.
12484 To force its output use the command
12496 or left-click on the
12497 \begin_inset Quotes eld
12503 \begin_inset space \textvisiblespace{}
12509 \begin_inset Quotes erd
12512 and check the option
12517 \begin_inset Newline newline
12520 To insert as much space as is available, the command
12527 \begin_inset Index idx
12530 \begin_layout Plain Layout
12541 \begin_layout Standard
12542 \begin_inset VSpace -1mm
12548 \begin_layout Standard
12550 \begin_inset Tabular
12551 <lyxtabular version="3" rows="4" columns="2">
12552 <features tabularvalignment="middle">
12553 <column alignment="center" valignment="top">
12554 <column alignment="center" valignment="top">
12556 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
12559 \begin_layout Plain Layout
12567 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
12570 \begin_layout Plain Layout
12578 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
12581 \begin_layout Plain Layout
12585 \begin_inset space \textvisiblespace{}
12591 \begin_inset space \thinspace{}
12599 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
12602 \begin_layout Plain Layout
12603 \begin_inset Formula $A=B\hspace{3cm}A\not=C$
12613 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
12616 \begin_layout Plain Layout
12620 \begin_inset space \textvisiblespace{}
12626 \begin_inset space \thinspace{}
12634 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
12637 \begin_layout Plain Layout
12638 \begin_inset Formula $A\hspace{-1mm}A\not=A$
12648 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
12651 \begin_layout Plain Layout
12655 \begin_inset space \textvisiblespace{}
12663 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
12666 \begin_layout Plain Layout
12667 \begin_inset Formula $A=A\hfill B=B$
12683 \begin_layout Standard
12684 In the last example the available space is given by the longest column entry
12686 In an inline formula the space depends on the length of the line in which
12694 Thus, when the line uses the full width, no space will be created.
12701 only has an effect on displayed formulas when the formula style
12706 (Formula styles are explained in
12707 \begin_inset CommandInset ref
12709 reference "sec:Formula-Styles"
12716 \begin_layout Standard
12723 , there are the commands
12735 that fill the space with a pattern, see
12736 \begin_inset CommandInset ref
12738 reference "subsec:Ellipses"
12745 \begin_layout Standard
12746 For text, variable space can be inserted via the menu
12748 Insert\SpecialChar menuseparator
12749 Formatting\SpecialChar menuseparator
12751 \begin_inset space ~
12759 \begin_layout Standard
12760 This is a line with
12761 \begin_inset space \hspace{}
12766 \begin_inset space \thinspace{}
12772 \begin_layout Standard
12773 This is a line with
12774 \begin_inset space \hfill{}
12780 \begin_layout Subsection
12781 Space besides inline Formulas
12782 \begin_inset Index idx
12785 \begin_layout Plain Layout
12786 Space ! besides inline formulas
12794 \begin_layout Standard
12795 The space that surrounds inline formulas can be adjusted with the length
12803 \begin_inset Index idx
12806 \begin_layout Plain Layout
12815 The value of a length is set with the command
12822 \begin_inset Index idx
12825 \begin_layout Plain Layout
12833 which has the following scheme:
12836 \begin_layout Standard
12841 setlength{length name}{value}
12844 \begin_layout Standard
12852 \begin_inset space \thinspace{}
12858 \begin_layout Standard
12868 \begin_layout Standard
12869 is inserted in \SpecialChar TeX
12872 \begin_inset space \thinspace{}
12875 mm space will now be set around all inline formulas:
12879 \begin_layout Plain Layout
12893 \begin_layout Standard
12894 This is a line with an inline formula
12895 \begin_inset Formula $A=B$
12899 \begin_inset space \thinspace{}
12902 mm surrounding space.
12906 \begin_layout Plain Layout
12920 \begin_layout Standard
12921 To return to the predefined value,
12927 is set to the value 0
12928 \begin_inset space \thinspace{}
12934 \begin_layout Section
12936 \begin_inset Index idx
12939 \begin_layout Plain Layout
12946 \begin_inset Index idx
12949 \begin_layout Plain Layout
12954 \begin_layout Plain Layout
12965 \begin_layout Plain Layout
12980 \begin_layout Standard
12981 Boxes for text are described in chapter
12988 \begin_inset space ~
12996 \begin_layout Subsection
12998 \begin_inset CommandInset label
13000 name "subsec:Boxes-with-Frame"
13005 \begin_inset Index idx
13008 \begin_layout Plain Layout
13017 \begin_layout Standard
13018 It is possible to frame a formula or part of one with the commands
13025 \begin_inset Index idx
13028 \begin_layout Plain Layout
13043 \begin_inset Index idx
13046 \begin_layout Plain Layout
13057 \begin_layout Standard
13058 When one of these commands is inserted in a formula, a blue box appears
13059 within a frame to enter formula parts.
13066 an additional formula has to be created by
13070 within this box, because the box content will otherwise be treated as mathemati
13078 is used, a new formula is automatically created inside the frame.
13081 \begin_layout Standard
13088 is not suitable to frame displayed formulas because the formula will always
13089 be set in the size of the text.
13096 is in contrary not suitable to frame inline formulas, because the formula
13097 will always be set in the size of a displayed formula.
13100 \begin_layout Standard
13114 \begin_inset Index idx
13117 \begin_layout Plain Layout
13125 where additionally the frame width and the alignment can be specified.
13132 is used in the following scheme:
13135 \begin_layout Standard
13140 framebox[frame width][position]{box content}
13143 \begin_layout Standard
13144 The position can either be
13161 right aligns the formula in the box.
13162 When no position is given, the formula will be centered.
13163 \begin_inset Newline newline
13166 If no width is given, also no position can be given.
13167 In this case the frame width is adjusted to the box content like for
13176 \begin_layout Standard
13183 is inserted, a box appears containing three blue boxes.
13184 The first two boxes are surrounded by brackets and denote the two optional
13186 The third box is for formula parts like for
13193 \begin_inset Separator parbreak
13199 \begin_layout Standard
13201 \begin_inset Tabular
13202 <lyxtabular version="3" rows="5" columns="2">
13203 <features tabularvalignment="middle">
13204 <column alignment="center" valignment="top">
13205 <column alignment="center" valignment="top">
13207 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
13210 \begin_layout Plain Layout
13216 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
13219 \begin_layout Plain Layout
13221 \begin_inset Note Note
13224 \begin_layout Plain Layout
13231 is only used as spacer.
13243 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
13246 \begin_layout Plain Layout
13250 \begin_inset space \textvisiblespace{}
13260 \begin_inset space \textvisiblespace{}
13268 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
13271 \begin_layout Plain Layout
13272 \begin_inset Formula $\raisebox{6mm}{}\fbox{\ensuremath{\int A=B}}\raisebox{-4mm}{}$
13282 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
13285 \begin_layout Plain Layout
13289 \begin_inset space \textvisiblespace{}
13295 \begin_inset space \textvisiblespace{}
13303 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
13306 \begin_layout Plain Layout
13307 \begin_inset Formula $\raisebox{8.5mm}{}\boxed{\int A=B}\raisebox{-6.5mm}{}$
13317 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
13320 \begin_layout Plain Layout
13324 \begin_inset space \textvisiblespace{}
13332 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
13335 \begin_layout Plain Layout
13336 \begin_inset Formula $\raisebox{6mm}{}A+\fbox{B}\raisebox{-3mm}{}$
13346 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
13349 \begin_layout Plain Layout
13353 \begin_inset space \textvisiblespace{}
13357 \begin_inset Formula $\to$
13361 \begin_inset Formula $\to$
13371 \begin_inset space \textvisiblespace{}
13375 \begin_inset Formula $\downarrow$
13383 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
13386 \begin_layout Plain Layout
13387 \begin_inset Formula $\raisebox{6mm}{}$
13391 \begin_inset Formula $\framebox[20mm][]{\ensuremath{\frac{A}{B}}}$
13395 \begin_inset Formula $\raisebox{-4mm}{}$
13411 \begin_layout Standard
13412 The frame thickness can also be adjusted.
13413 To do this the following commands have to be inserted in \SpecialChar TeX
13418 \begin_layout Standard
13428 \begin_inset Quotes eld
13432 \begin_inset Quotes erd
13446 \begin_inset Quotes eld
13450 \begin_inset Quotes erd
13456 \begin_layout Standard
13457 \begin_inset Quotes eld
13461 \begin_inset Quotes erd
13464 specifies the minimal distance between the frame and the first character
13466 An example for this is the following framed formula:
13470 \begin_layout Plain Layout
13482 \begin_inset Formula
13489 Before this formula the commands
13492 \begin_layout Standard
13514 \begin_layout Standard
13515 were inserted in \SpecialChar TeX
13517 The given values are used for all following boxes.
13520 \begin_layout Standard
13521 To return to the standard frame size, the command
13524 \begin_layout Standard
13549 \begin_layout Plain Layout
13563 \begin_layout Standard
13564 is inserted in \SpecialChar TeX
13565 mode before the next formula.
13568 \begin_layout Subsection
13569 Boxes without Frame
13570 \begin_inset CommandInset label
13572 name "subsec:Boxes-without-Frame"
13577 \begin_inset Index idx
13580 \begin_layout Plain Layout
13581 Boxes ! without frame
13589 \begin_layout Standard
13590 For boxes without a frame there are the following box commands:
13597 \begin_inset Index idx
13600 \begin_layout Plain Layout
13615 \begin_inset Index idx
13618 \begin_layout Plain Layout
13633 \begin_inset Index idx
13636 \begin_layout Plain Layout
13647 \begin_layout Standard
13654 a box can be super- or subscripted.
13655 But in contrary to normal super- and subscripting, the characters in the
13656 box keep their font size.
13663 is used in the following scheme:
13666 \begin_layout Standard
13671 raisebox{height}{box content}
13674 \begin_layout Standard
13675 When the box should contain a formula, an extra formula is needed like for
13686 \begin_inset Note Greyedout
13689 \begin_layout Plain Layout
13700 this extra formula is created by pressing
13704 twice instead of once because \SpecialChar LyX
13705 doesn't yet support
13719 \begin_inset Separator parbreak
13725 \begin_layout Standard
13727 \begin_inset Tabular
13728 <lyxtabular version="3" rows="4" columns="2">
13729 <features tabularvalignment="middle">
13730 <column alignment="center" valignment="top">
13731 <column alignment="center" valignment="top">
13733 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
13736 \begin_layout Plain Layout
13742 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
13745 \begin_layout Plain Layout
13753 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
13756 \begin_layout Plain Layout
13760 \begin_inset Formula $\to$
13766 \begin_inset Formula $\to$
13774 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
13777 \begin_layout Plain Layout
13778 \begin_inset Formula $H\raisebox{2mm}{al}lo$
13788 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
13791 \begin_layout Plain Layout
13795 \begin_inset Formula $\to$
13801 \begin_inset Formula $\to$
13809 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
13812 \begin_layout Plain Layout
13813 \begin_inset Formula $H\raisebox{-2mm}{al}lo$
13823 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
13826 \begin_layout Plain Layout
13830 \begin_inset Formula $\to$
13846 \begin_inset space \textvisiblespace{}
13854 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
13857 \begin_layout Plain Layout
13858 \begin_inset Formula $A=\raisebox{-2mm}{\mbox{\ensuremath{\sqrt{B}}}}$
13874 \begin_layout Standard
13899 , with the difference that there is no frame.
13902 \begin_layout Subsection
13904 \begin_inset CommandInset label
13906 name "subsec:Colored-Boxes"
13911 \begin_inset Index idx
13914 \begin_layout Plain Layout
13923 \begin_layout Standard
13924 To be able to use all commands explained in this section, the \SpecialChar LaTeX
13933 \begin_layout Plain Layout
13934 The \SpecialChar LaTeX
13939 is part of every \SpecialChar LaTeX
13940 standard installation.
13946 \begin_inset Index idx
13949 \begin_layout Plain Layout
13955 has to be loaded in the \SpecialChar LaTeX
13956 -preamble with the line
13960 \begin_layout Plain Layout
13961 When text is colored somewhere in the document with a predefined color,
13963 loads the \SpecialChar LaTeX
13969 Thus it is possible that the package is loaded twice, but this does not
13976 \begin_inset Note Note
13979 \begin_layout Plain Layout
13980 To avoid that the package is loaded twice, a macro was inserted to the \SpecialChar LaTeX
13989 \begin_layout Standard
13997 \begin_layout Standard
13998 \begin_inset VSpace medskip
14001 To color boxes, the command
14008 \begin_inset Index idx
14011 \begin_layout Plain Layout
14019 is used in the following scheme:
14022 \begin_layout Standard
14027 colorbox{color}{box content}
14030 \begin_layout Standard
14031 The box content can also be a box and a
14037 can also be part of another box (see the 2nd and 3rd example).
14038 When the box should contain a formula, an extra formula has to be created,
14039 the same way as for
14049 \begin_layout Plain Layout
14050 This also applies for the command
14064 \begin_layout Standard
14065 One of the following predefined colors can be chosen:
14068 \begin_layout Standard
14102 \begin_inset Separator parbreak
14108 \begin_layout Standard
14110 \begin_inset Tabular
14111 <lyxtabular version="3" rows="4" columns="2">
14112 <features tabularvalignment="middle">
14113 <column alignment="center" valignment="top">
14114 <column alignment="center" valignment="top">
14116 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
14119 \begin_layout Plain Layout
14125 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
14128 \begin_layout Plain Layout
14130 \begin_inset Note Note
14133 \begin_layout Plain Layout
14140 is only used as spacer.
14152 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
14155 \begin_layout Plain Layout
14159 \begin_inset Formula $\to$
14169 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
14172 \begin_layout Plain Layout
14173 \begin_inset Formula $\raisebox{6mm}{}\colorbox{yellow}{A=B}\raisebox{-3mm}{}$
14183 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
14186 \begin_layout Plain Layout
14190 \begin_inset Formula $\to$
14198 \begin_inset space \textvisiblespace{}
14206 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
14209 \begin_layout Plain Layout
14210 \begin_inset Formula $\raisebox{6mm}{}\colorbox{green}{\fbox{A=B}}\raisebox{-3mm}{}$
14220 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
14223 \begin_layout Plain Layout
14227 \begin_inset space \textvisiblespace{}
14233 \begin_inset Formula $\to$
14249 \begin_inset space \textvisiblespace{}
14257 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
14260 \begin_layout Plain Layout
14261 \begin_inset Formula $\raisebox{7mm}{}\fbox{\colorbox{green}{\mbox{\ensuremath{\int C=D}}}}\raisebox{-5mm}{}$
14277 \begin_layout Standard
14284 only colors the box but not the characters in the box.
14285 To color all characters, the whole formula is highlighted and the desired
14286 color is chosen in the
14289 \begin_inset space ~
14295 The dialog can be called with the toolbar button
14298 arg "dialog-show character"
14303 Edit\SpecialChar menuseparator
14305 \begin_inset space ~
14308 Style\SpecialChar menuseparator
14312 The formula number then has the same color as the formula.
14313 When the formula number should get another color than the formula characters,
14314 the color must be changed within the formula.
14317 \begin_layout Standard
14321 \begin_layout Standard
14324 \begin_inset Formula
14326 \int A=B\label{eq:red}
14334 \begin_inset Formula
14336 \textcolor{red}{\int A=B}\label{eq:redgreen}
14344 \begin_layout Standard
14346 \begin_inset CommandInset ref
14352 is completely colored red.
14353 \begin_inset Newline newline
14357 \begin_inset CommandInset ref
14359 reference "eq:redgreen"
14363 was first completely colored green to set the color for the formula number.
14364 Subsequently the formula characters were colored red.
14367 \begin_layout Standard
14368 \begin_inset VSpace bigskip
14371 To color the frame different than the rest of the box, the command
14378 \begin_inset Index idx
14381 \begin_layout Plain Layout
14389 is used in the following scheme:
14392 \begin_layout Standard
14397 fcolorbox{frame color}{color}{box content}
14400 \begin_layout Standard
14407 is an extension of the command
14414 The frame width is set, like for
14437 \begin_layout Plain Layout
14449 \begin_inset Formula
14451 \fcolorbox{cyan}{magenta}{A=B}
14460 \begin_layout Plain Layout
14474 \begin_layout Standard
14475 This formula was created with the command
14476 \begin_inset Newline newline
14484 \begin_inset Formula $\to$
14490 \begin_inset Formula $\to$
14500 \begin_layout Standard
14501 \begin_inset VSpace bigskip
14504 To use other colors than the predefined ones, they have to be defined first.
14507 \begin_layout Standard
14508 One can for example define the color
14509 \begin_inset Quotes eld
14517 \begin_inset Quotes erd
14520 with the \SpecialChar LaTeX
14524 \begin_layout Standard
14529 definecolor{darkgreen}{cmyk}{0.5,
14544 \begin_inset Index idx
14547 \begin_layout Plain Layout
14558 \begin_layout Standard
14563 is the color space that denotes the colors
14580 The four comma separated numbers are the portion factor for the corresponding
14581 colors of the color space.
14582 The factors can be in the range of 0
14583 \begin_inset space \thinspace{}
14587 \begin_inset space \thinspace{}
14595 also the color space
14599 can be used for definitions.
14616 , so that there are in this case three portion factors for the corresponding
14618 Furthermore there is the color space
14622 with one portion factor for the gray value.
14625 \begin_layout Standard
14626 As example a framed box with the new defined color
14630 where the characters have been colored
14635 \begin_inset Formula
14637 \colorbox{darkgreen}{\color{yellow}\boxed{\int A\,\mathrm{d}x=\frac{\sqrt[5]{B}}{\ln\left(\frac{1}{3}\right)}}}
14645 \begin_layout Standard
14646 Self-defined colors can also be used for text with the help of the command
14654 \begin_inset Index idx
14657 \begin_layout Plain Layout
14666 \begin_layout Standard
14670 \begin_layout Plain Layout
14674 textcolor{darkgreen}{
14680 \begin_inset Quotes eld
14684 \begin_inset Quotes erd
14691 \begin_layout Plain Layout
14701 \begin_layout Standard
14709 \begin_inset Index idx
14712 \begin_layout Plain Layout
14720 is used in the scheme
14724 textcolor{color}{characters to color}
14729 \begin_layout Subsection
14731 \begin_inset CommandInset label
14733 name "subsec:Paragraph-Boxes"
14738 \begin_inset Index idx
14741 \begin_layout Plain Layout
14742 Boxes ! as paragraph
14750 \begin_layout Standard
14751 A box that can contain several lines and paragraphs, a so-called paragraph
14752 box (parbox), can be created with the menu
14754 Insert\SpecialChar menuseparator
14757 or the toolbar button
14766 \begin_layout Standard
14767 The following example shows a framed parbox in a line:
14770 \begin_layout Standard
14771 \begin_inset VSpace medskip
14775 \begin_inset Box Boxed
14785 height_special "totalheight"
14790 backgroundcolor "none"
14793 \begin_layout Plain Layout
14794 This is a paragraph box.
14796 \begin_inset space \thinspace{}
14799 cm long and can also contain formulas:
14800 \begin_inset Formula $\int A\,\mathrm{d}s=C$
14811 \begin_layout Standard
14812 \begin_inset VSpace medskip
14818 \begin_layout Standard
14819 Such a box is created by right-clicking on the gray box inset.
14820 A dialog pops up showing the box properties.
14834 \begin_inset space \thinspace{}
14839 Vertical Box Alignment
14844 \begin_layout Standard
14845 \begin_inset VSpace medskip
14848 In \SpecialChar LaTeX
14849 a parbox is created with the command
14856 \begin_inset Index idx
14859 \begin_layout Plain Layout
14867 which has the following scheme:
14870 \begin_layout Standard
14875 parbox[position]{width}{box content}
14878 \begin_layout Standard
14893 \begin_inset Quotes eld
14897 \begin_inset Quotes erd
14900 means that the box is aligned within the surrounding text with its last
14907 \begin_inset Quotes eld
14911 \begin_inset Quotes erd
14914 this is done with the first line.
14915 When no position is given, the box will be vertically centered, see section
14923 \begin_inset space ~
14928 manual for examples.
14931 \begin_layout Standard
14932 \begin_inset VSpace bigskip
14935 To frame formulas completely, including the formula number, the formula
14936 must be set into a parbox.
14937 To do this, the command
14951 is inserted in \SpecialChar TeX
14952 mode before the formula.
14960 \begin_inset Index idx
14963 \begin_layout Plain Layout
14971 is hereby the line width set for the document.
14972 Because the frame is outside the parbox, 2
14973 \begin_inset space \thinspace{}
14976 times the frame separation and the frame thickness must be subtracted from
14978 As this is not automatically done by \SpecialChar LyX
14983 \begin_layout Plain Layout
14984 \begin_inset CommandInset href
14986 name "LyX-bug #4483"
14987 target "http://www.lyx.org/trac/ticket/4483"
14997 mode has to be used.
14998 To be able to multiply and subtract in arguments, the \SpecialChar LaTeX
15007 \begin_layout Plain Layout
15012 is part of every \SpecialChar LaTeX
15013 standard installation.
15019 \begin_inset Index idx
15022 \begin_layout Plain Layout
15028 must be loaded in the \SpecialChar LaTeX
15029 -preamble with the line
15032 \begin_layout Standard
15040 \begin_layout Standard
15041 Behind the formula both boxes are closed by entering
15045 in \SpecialChar TeX
15047 Here is an example:
15051 \begin_layout Plain Layout
15065 \begin_layout Standard
15069 \begin_layout Plain Layout
15087 \begin_inset Formula
15089 \int A\,\mathrm{d}x=\frac{\sqrt[5]{B}}{\ln\left(\frac{1}{3}\right)}
15098 \begin_layout Plain Layout
15109 \begin_layout Plain Layout
15123 \begin_layout Standard
15124 \begin_inset VSpace medskip
15127 As a parbox is used as the argument of
15133 , there is in this case no difference between
15148 \begin_layout Standard
15149 \begin_inset VSpace bigskip
15152 Paragraph boxes are very useful to comment formulas directly.
15159 is used in combination with the command
15173 \begin_inset CommandInset ref
15175 reference "subsec:User-defined-Numbering"
15182 \begin_layout Standard
15183 An example of a formula commented with
15192 \begin_layout Standard
15196 \begin_layout Plain Layout
15209 This is a description.
15210 It is distinctly separated from the formula and multiline.
15214 \begin_layout Plain Layout
15226 \begin_layout Standard
15227 Such a formula must be inserted completely in \SpecialChar TeX
15228 mode because \SpecialChar LyX
15230 support the command
15237 The formula is created with the following command sequence:
15240 \begin_layout Standard
15253 is inserted in \SpecialChar TeX
15258 \begin_layout Plain Layout
15259 When the formula style
15271 can also be replaced by
15278 (formula styles see
15279 \begin_inset CommandInset ref
15281 reference "sec:Formula-Styles"
15290 Then the description follows as normal text and finally
15296 is inserted in \SpecialChar TeX
15310 hereby create a displayed formula.
15313 \begin_layout Standard
15320 can be seen in this example that was
15321 \begin_inset Quotes eld
15325 \begin_inset Quotes erd
15328 using the mathematical textmode:
15329 \begin_inset Formula
15331 5x-7b=3b\textrm{This is a description. It is not separated from the formula ...}
15339 \begin_layout Section
15341 \begin_inset Index idx
15344 \begin_layout Plain Layout
15353 \begin_layout Subsection
15355 \begin_inset CommandInset label
15357 name "subsec:Big-Operators"
15362 \begin_inset Index idx
15365 \begin_layout Plain Layout
15372 \begin_inset Index idx
15375 \begin_layout Plain Layout
15382 \begin_inset Index idx
15385 \begin_layout Plain Layout
15394 \begin_layout Standard
15395 To be able to use all integral operators listed here, the option
15397 Use esint package automatically
15399 must be set in the document settings under
15402 \begin_inset space ~
15410 \begin_layout Standard
15411 \begin_inset space \hfill{}
15415 \begin_inset Tabular
15416 <lyxtabular version="3" rows="11" columns="2">
15417 <features tabularvalignment="middle">
15418 <column alignment="center" valignment="top" width="0pt">
15419 <column alignment="center" valignment="top" width="0pt">
15421 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
15424 \begin_layout Plain Layout
15430 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
15433 \begin_layout Plain Layout
15441 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
15444 \begin_layout Plain Layout
15448 \begin_inset Index idx
15451 \begin_layout Plain Layout
15464 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
15467 \begin_layout Plain Layout
15468 \begin_inset Formula $\int$
15478 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
15481 \begin_layout Plain Layout
15489 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
15492 \begin_layout Plain Layout
15493 \begin_inset Formula $\oint$
15503 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
15506 \begin_layout Plain Layout
15514 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
15517 \begin_layout Plain Layout
15518 \begin_inset Formula $\ointctrclockwise$
15528 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
15531 \begin_layout Plain Layout
15539 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
15542 \begin_layout Plain Layout
15543 \begin_inset Formula $\ointclockwise$
15553 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
15556 \begin_layout Plain Layout
15564 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
15567 \begin_layout Plain Layout
15568 \begin_inset Formula $\sqint$
15578 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
15581 \begin_layout Plain Layout
15589 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
15592 \begin_layout Plain Layout
15594 \begin_inset Formula $\fint$
15604 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
15607 \begin_layout Plain Layout
15615 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
15618 \begin_layout Plain Layout
15620 \begin_inset Formula $\landupint$
15630 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
15633 \begin_layout Plain Layout
15641 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
15644 \begin_layout Plain Layout
15646 \begin_inset Formula $\landdownint$
15656 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
15659 \begin_layout Plain Layout
15667 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
15670 \begin_layout Plain Layout
15671 \begin_inset Formula $\bigcap$
15681 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
15684 \begin_layout Plain Layout
15692 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
15695 \begin_layout Plain Layout
15696 \begin_inset Formula $\bigcup$
15710 \begin_inset space \hfill{}
15714 \begin_inset Tabular
15715 <lyxtabular version="3" rows="11" columns="2">
15716 <features tabularvalignment="middle">
15717 <column alignment="center" valignment="top" width="0pt">
15718 <column alignment="center" valignment="top" width="0pt">
15720 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
15723 \begin_layout Plain Layout
15729 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
15732 \begin_layout Plain Layout
15740 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
15743 \begin_layout Plain Layout
15747 \begin_inset Index idx
15750 \begin_layout Plain Layout
15763 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
15766 \begin_layout Plain Layout
15767 \begin_inset Formula $\sum$
15777 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
15780 \begin_layout Plain Layout
15784 \begin_inset Index idx
15787 \begin_layout Plain Layout
15794 \begin_layout Plain Layout
15813 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
15816 \begin_layout Plain Layout
15817 \begin_inset Formula $\prod$
15827 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
15830 \begin_layout Plain Layout
15838 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
15841 \begin_layout Plain Layout
15842 \begin_inset Formula $\coprod$
15852 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
15855 \begin_layout Plain Layout
15863 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
15866 \begin_layout Plain Layout
15867 \begin_inset Formula $\bigodot$
15877 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
15880 \begin_layout Plain Layout
15888 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
15891 \begin_layout Plain Layout
15892 \begin_inset Formula $\bigotimes$
15902 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
15905 \begin_layout Plain Layout
15913 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
15916 \begin_layout Plain Layout
15917 \begin_inset Formula $\bigoplus$
15927 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
15930 \begin_layout Plain Layout
15938 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
15941 \begin_layout Plain Layout
15942 \begin_inset Formula $\bigwedge$
15952 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
15955 \begin_layout Plain Layout
15963 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
15966 \begin_layout Plain Layout
15967 \begin_inset Formula $\bigvee$
15977 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
15980 \begin_layout Plain Layout
15988 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
15991 \begin_layout Plain Layout
15992 \begin_inset Formula $\bigsqcup$
16002 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
16005 \begin_layout Plain Layout
16013 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
16016 \begin_layout Plain Layout
16017 \begin_inset Formula $\biguplus$
16031 \begin_inset space \hfill{}
16037 \begin_layout Standard
16038 All big operators can also be inserted via the math toolbar button
16041 arg "math-insert \\intop"
16047 \begin_layout Standard
16048 The operators are called big because they are bigger than the sometimes
16049 equal looking binary operators.
16050 All big operators can have limits as described in the next subsection.
16053 \begin_layout Standard
16054 For all integral operators there is a second version available, ending in
16072 These operators are different from
16079 \begin_inset space \space{}
16082 in the style the operator limits are displayed, see
16083 \begin_inset CommandInset ref
16085 reference "subsec:Operator-Limits"
16093 \begin_layout Subsubsection*
16094 Advice for Integrals
16097 \begin_layout Standard
16102 in an integral is an operator, that therefore has to be set upright.
16103 This is done by highlighting the
16107 and using the keyboard shortcut
16117 \begin_layout Plain Layout
16123 \begin_inset CommandInset ref
16125 reference "subsec:Font-Styles"
16135 Finally the smallest space is inserted before the
16139 , as this is usual for operators.
16143 \begin_layout Standard
16145 \begin_inset Formula $\int A(x)dx$
16149 \begin_inset Newline newline
16153 \begin_inset Phantom HPhantom
16156 \begin_layout Plain Layout
16163 \begin_inset Formula $\int A(x)\,\mathrm{d}x$
16169 \begin_layout Standard
16170 For multiple integrals there are the following commands:
16171 \begin_inset VSpace medskip
16177 \begin_layout Standard
16178 \begin_inset space \hfill{}
16182 \begin_inset Tabular
16183 <lyxtabular version="3" rows="4" columns="2">
16184 <features tabularvalignment="middle">
16185 <column alignment="center" valignment="top">
16186 <column alignment="center" valignment="top">
16188 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
16191 \begin_layout Plain Layout
16197 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
16200 \begin_layout Plain Layout
16202 \begin_inset Note Note
16205 \begin_layout Plain Layout
16212 is only used as spacer.
16224 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
16227 \begin_layout Plain Layout
16235 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
16238 \begin_layout Plain Layout
16239 \begin_inset Formula $\raisebox{4.5mm}{}\iint\raisebox{-2.5mm}{}$
16249 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
16252 \begin_layout Plain Layout
16260 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
16263 \begin_layout Plain Layout
16264 \begin_inset Formula $\raisebox{4.5mm}{}\oiint\raisebox{-2.5mm}{}$
16274 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
16277 \begin_layout Plain Layout
16285 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
16288 \begin_layout Plain Layout
16289 \begin_inset Formula $\raisebox{4.5mm}{}\sqiint\raisebox{-2.5mm}{}$
16303 \begin_inset space \hfill{}
16307 \begin_inset Tabular
16308 <lyxtabular version="3" rows="4" columns="2">
16309 <features tabularvalignment="middle">
16310 <column alignment="center" valignment="top">
16311 <column alignment="center" valignment="top">
16313 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
16316 \begin_layout Plain Layout
16322 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
16325 \begin_layout Plain Layout
16333 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
16336 \begin_layout Plain Layout
16344 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
16347 \begin_layout Plain Layout
16348 \begin_inset Formula $\raisebox{4.5mm}{}\iiint\raisebox{-2.5mm}{}$
16358 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
16361 \begin_layout Plain Layout
16369 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
16372 \begin_layout Plain Layout
16373 \begin_inset Formula $\raisebox{4.5mm}{}\iiiint\raisebox{-2.5mm}{}$
16383 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
16386 \begin_layout Plain Layout
16394 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
16397 \begin_layout Plain Layout
16398 \begin_inset Formula $\raisebox{4.5mm}{}\dotsint\raisebox{-2.5mm}{}$
16412 \begin_inset space \hfill{}
16418 \begin_layout Subsection
16420 \begin_inset CommandInset label
16422 name "subsec:Operator-Limits"
16427 \begin_inset Index idx
16430 \begin_layout Plain Layout
16439 \begin_layout Standard
16440 Limits are created by super- and subscripts:
16441 \begin_inset Separator parbreak
16447 \begin_layout Standard
16449 \begin_inset Tabular
16450 <lyxtabular version="3" rows="2" columns="2">
16451 <features tabularvalignment="middle">
16452 <column alignment="center" valignment="top" width="0pt">
16453 <column alignment="center" valignment="top" width="0pt">
16455 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
16458 \begin_layout Plain Layout
16464 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
16467 \begin_layout Plain Layout
16469 \begin_inset Note Note
16472 \begin_layout Plain Layout
16479 is only used as spacer.
16491 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
16494 \begin_layout Plain Layout
16500 \begin_inset space \textvisiblespace{}
16504 \begin_inset Formula $\to$
16508 \begin_inset Formula $\to$
16516 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
16519 \begin_layout Plain Layout
16520 \begin_inset Formula $\raisebox{5mm}{}\prod_{0}^{\infty}A(x)\raisebox{-2.5mm}{}$
16536 \begin_layout Standard
16537 Limits of inline formulas are set right beside the operator.
16538 Limits in displayed formulas are set above or below the operator, except
16539 for integral limits.
16542 \begin_layout Standard
16543 To force that the limits are set beside the operator, the cursor is set
16544 directly behind the operator and the limits type is changed with the menu
16547 Edit\SpecialChar menuseparator
16548 Math\SpecialChar menuseparator
16567 \begin_layout Standard
16568 The default limits type is this:
16569 \begin_inset Formula
16571 \sum_{x=0}^{\infty}\frac{1}{x^{2}}
16576 This is how it looks when the limits type was changed to
16583 \begin_inset Formula
16585 \sum\nolimits _{x=0}^{\infty}\frac{1}{x^{2}}
16590 For integrals, except those ending with
16606 etc., the limits are by default set beside the operator.
16607 But for multiple integrals the limits are often set below the operator.
16608 In the following example the limits type was therefore set to
16612 and so set below the integrals:
16613 \begin_inset Formula
16615 \iiint\limits _{V}X\,\mathrm{d}V=U\label{eq:VolInt}
16623 \begin_layout Standard
16624 \begin_inset VSpace medskip
16627 To specify conditions for limits, the commands
16634 \begin_inset Index idx
16637 \begin_layout Plain Layout
16652 \begin_inset Index idx
16655 \begin_layout Plain Layout
16664 To create for example this expression
16665 \begin_inset Formula
16667 \sum_{\begin{subarray}{c}
16671 \end{subarray}}^{n}k^{-2}\label{eq:substack}
16679 \begin_layout Standard
16680 the following has to be done:
16681 \begin_inset Newline newline
16693 \begin_inset space \textvisiblespace{}
16699 One is now in a blue box under the summation operator and insert there
16705 \begin_inset space \textvisiblespace{}
16711 The blue box is now within a purple box and now several lines can be written
16713 A new line is created by inserting a line break (
16716 arg "newline-insert newline"
16721 \begin_inset Newline newline
16726 0<k<1000 Ctrl+Return
16727 \begin_inset Newline newline
16732 is typed in, a new box appears below for the new line.
16735 \begin_layout Standard
16736 The alignment of the lines can be changed to left aligned with the
16746 Edit\SpecialChar menuseparator
16750 To get right alignment,
16755 \begin_inset space \textvisiblespace{}
16760 is inserted at the beginning of the line.
16763 \begin_layout Standard
16776 with the difference that the lines are always centered.
16779 \begin_layout Standard
16780 \begin_inset VSpace bigskip
16784 \begin_inset CommandInset ref
16786 reference "eq:substack"
16790 there can be too much space beside an operator, because the characters
16791 following the operator are set beside the limits.
16792 To avoid this the command
16799 \begin_inset Index idx
16802 \begin_layout Plain Layout
16811 To activate it, set in the document settings under
16814 \begin_inset space ~
16824 \begin_inset Index idx
16827 \begin_layout Plain Layout
16828 Packages ! mathtools
16836 \begin_inset space ~
16848 sets the space besides the operator to 0
16849 \begin_inset space \thinspace{}
16853 \begin_inset Newline newline
16857 \begin_inset CommandInset ref
16859 reference "eq:substack"
16863 , one uses the command
16866 \begin_layout Standard
16874 \begin_layout Standard
16875 and inserts the operator with its limits into the braces.
16876 Behind the brace one continues the formula:
16877 \begin_inset Formula
16879 \smashoperator{\sum_{\begin{subarray}{c}
16883 \end{subarray}}^{n}}k^{-2}
16891 \begin_layout Standard
16892 It is possible to set the space of only one side of the operator to 0
16893 \begin_inset space \thinspace{}
16897 To do this write either
16916 stands for the left and
16920 for the right side of the operator.
16921 Here is an example of the possible
16930 \begin_layout Standard
16931 \begin_inset Formula
16933 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}
16941 \begin_layout Standard
16942 \begin_inset VSpace bigskip
16948 \begin_layout Standard
16949 When several consecutive operators have limits the typesetting of the limits
16950 looks often imperfect in the output, see this example:
16951 \begin_inset Formula
16953 \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}
16958 To improve the typesetting set in the document settings under
16961 \begin_inset space ~
16971 \begin_inset Index idx
16974 \begin_layout Plain Layout
16975 Packages ! mathtools
16983 \begin_inset space ~
16989 Then insert into your formula the command
16996 \begin_inset Index idx
16999 \begin_layout Plain Layout
17007 directly before the first operator.
17008 The example will then look like this:
17009 \begin_inset Formula
17011 \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}
17019 \begin_layout Standard
17020 \begin_inset VSpace bigskip
17023 How to use one limit for several operators is described in
17024 \begin_inset CommandInset ref
17026 reference "subsec:Self-defined-Operators"
17033 \begin_layout Subsection
17034 Decoration for Operators
17035 \begin_inset Index idx
17038 \begin_layout Plain Layout
17039 Operators ! Decoration
17047 \begin_layout Standard
17055 \begin_inset Index idx
17058 \begin_layout Plain Layout
17073 \begin_inset Index idx
17076 \begin_layout Plain Layout
17084 characters can be placed above or below an operator, respectively.
17092 \begin_inset Index idx
17095 \begin_layout Plain Layout
17103 characters can be set before and behind a big operator.
17106 \begin_layout Standard
17108 \begin_inset space ~
17120 \begin_layout Itemize
17127 is used to set characters at the corners of the operator
17130 \begin_layout Itemize
17137 is used to set characters before and/or behind the operator (this variant
17138 represents \SpecialChar LaTeX
17148 \begin_layout Itemize
17155 is used to set characters at the left corners and/or behind the operator
17158 \begin_layout Itemize
17165 is used to set characters at the right corners and/or before the operator
17168 \begin_layout Standard
17169 For example the command
17174 \begin_inset space \textvisiblespace{}
17180 \begin_inset space \textvisiblespace{}
17184 \begin_inset Formula $\to$
17188 \begin_inset Formula $\to$
17192 \begin_inset space \textvisiblespace{}
17202 \begin_inset Formula
17204 \sideset{}{'}\sum_{k=1}^{n}
17212 \begin_layout Standard
17213 \begin_inset Note Greyedout
17216 \begin_layout Plain Layout
17223 can only be used to decorate big operators, binary operators are not allowed.
17231 \begin_layout Standard
17244 can also be used to decorate symbols and characters.
17245 For example, the command
17250 \begin_inset space \textvisiblespace{}
17256 \begin_inset space \textvisiblespace{}
17262 \begin_inset Formula $\uparrow$
17270 \begin_inset Formula
17272 \overset{a}{\maltese}
17280 \begin_layout Subsection
17282 \begin_inset CommandInset label
17284 name "subsec:Binary-Operators"
17289 \begin_inset Index idx
17292 \begin_layout Plain Layout
17301 \begin_layout Standard
17302 Binary operators are surrounded by space when there is a character before
17304 \begin_inset VSpace medskip
17310 \begin_layout Standard
17311 \begin_inset space \hfill{}
17315 \begin_inset Tabular
17316 <lyxtabular version="3" rows="13" columns="2">
17317 <features tabularvalignment="middle">
17318 <column alignment="center" valignment="top" width="0pt">
17319 <column alignment="center" valignment="top" width="0pt">
17321 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
17324 \begin_layout Plain Layout
17326 \begin_inset Note Note
17329 \begin_layout Plain Layout
17336 is only used as spacer.
17346 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
17349 \begin_layout Plain Layout
17357 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
17360 \begin_layout Plain Layout
17366 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
17369 \begin_layout Plain Layout
17370 \begin_inset Formula $+$
17380 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
17383 \begin_layout Plain Layout
17389 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
17392 \begin_layout Plain Layout
17393 \begin_inset Formula $-$
17403 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
17406 \begin_layout Plain Layout
17414 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
17417 \begin_layout Plain Layout
17418 \begin_inset Formula $\pm$
17428 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
17431 \begin_layout Plain Layout
17439 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
17442 \begin_layout Plain Layout
17443 \begin_inset Formula $\mp$
17453 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
17456 \begin_layout Plain Layout
17464 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
17467 \begin_layout Plain Layout
17468 \begin_inset Formula $\cdot$
17478 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
17481 \begin_layout Plain Layout
17489 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
17492 \begin_layout Plain Layout
17493 \begin_inset Formula $\times$
17503 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
17506 \begin_layout Plain Layout
17514 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
17517 \begin_layout Plain Layout
17518 \begin_inset Formula $\div$
17528 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
17531 \begin_layout Plain Layout
17535 \begin_layout Plain Layout
17548 \begin_layout Plain Layout
17560 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
17563 \begin_layout Plain Layout
17564 \begin_inset Formula $*$
17574 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
17577 \begin_layout Plain Layout
17585 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
17588 \begin_layout Plain Layout
17589 \begin_inset Formula $\star$
17599 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
17602 \begin_layout Plain Layout
17610 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
17613 \begin_layout Plain Layout
17614 \begin_inset Formula $\circ$
17624 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
17627 \begin_layout Plain Layout
17635 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
17638 \begin_layout Plain Layout
17639 \begin_inset Formula $\diamond$
17649 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
17652 \begin_layout Plain Layout
17660 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
17663 \begin_layout Plain Layout
17664 \begin_inset Formula $\bullet$
17678 \begin_inset space \hfill{}
17682 \begin_inset Tabular
17683 <lyxtabular version="3" rows="13" columns="2">
17684 <features tabularvalignment="middle">
17685 <column alignment="center" valignment="top" width="0pt">
17686 <column alignment="center" valignment="top" width="0pt">
17688 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
17691 \begin_layout Plain Layout
17697 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
17700 \begin_layout Plain Layout
17708 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
17711 \begin_layout Plain Layout
17719 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
17722 \begin_layout Plain Layout
17723 \begin_inset Formula $\nabla$
17733 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
17736 \begin_layout Plain Layout
17744 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
17747 \begin_layout Plain Layout
17748 \begin_inset Formula $\bigtriangledown$
17758 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
17761 \begin_layout Plain Layout
17769 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
17772 \begin_layout Plain Layout
17773 \begin_inset Formula $\bigtriangleup$
17783 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
17786 \begin_layout Plain Layout
17794 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
17797 \begin_layout Plain Layout
17798 \begin_inset Formula $\Box$
17808 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
17811 \begin_layout Plain Layout
17819 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
17822 \begin_layout Plain Layout
17823 \begin_inset Formula $\cap$
17833 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
17836 \begin_layout Plain Layout
17844 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
17847 \begin_layout Plain Layout
17848 \begin_inset Formula $\cup$
17858 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
17861 \begin_layout Plain Layout
17869 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
17872 \begin_layout Plain Layout
17873 \begin_inset Formula $\dagger$
17883 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
17886 \begin_layout Plain Layout
17894 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
17897 \begin_layout Plain Layout
17898 \begin_inset Formula $\ddagger$
17908 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
17911 \begin_layout Plain Layout
17919 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
17922 \begin_layout Plain Layout
17923 \begin_inset Formula $\wr$
17933 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
17936 \begin_layout Plain Layout
17944 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
17947 \begin_layout Plain Layout
17948 \begin_inset Formula $\bigcirc$
17958 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
17961 \begin_layout Plain Layout
17969 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
17972 \begin_layout Plain Layout
17973 \begin_inset Formula $\wedge$
17983 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
17986 \begin_layout Plain Layout
17994 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
17997 \begin_layout Plain Layout
17998 \begin_inset Formula $\vee$
18012 \begin_inset space \hfill{}
18016 \begin_inset Tabular
18017 <lyxtabular version="3" rows="13" columns="2">
18018 <features tabularvalignment="middle">
18019 <column alignment="center" valignment="top" width="0pt">
18020 <column alignment="center" valignment="top" width="0pt">
18022 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
18025 \begin_layout Plain Layout
18031 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
18034 \begin_layout Plain Layout
18042 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
18045 \begin_layout Plain Layout
18053 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
18056 \begin_layout Plain Layout
18057 \begin_inset Formula $\oplus$
18067 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
18070 \begin_layout Plain Layout
18078 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
18081 \begin_layout Plain Layout
18082 \begin_inset Formula $\ominus$
18092 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
18095 \begin_layout Plain Layout
18103 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
18106 \begin_layout Plain Layout
18107 \begin_inset Formula $\otimes$
18117 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
18120 \begin_layout Plain Layout
18128 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
18131 \begin_layout Plain Layout
18132 \begin_inset Formula $\oslash$
18142 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
18145 \begin_layout Plain Layout
18153 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
18156 \begin_layout Plain Layout
18157 \begin_inset Formula $\odot$
18167 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
18170 \begin_layout Plain Layout
18178 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
18181 \begin_layout Plain Layout
18182 \begin_inset Formula $\amalg$
18192 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
18195 \begin_layout Plain Layout
18203 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
18206 \begin_layout Plain Layout
18207 \begin_inset Formula $\uplus$
18217 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
18220 \begin_layout Plain Layout
18228 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
18231 \begin_layout Plain Layout
18232 \begin_inset Formula $\setminus$
18242 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
18245 \begin_layout Plain Layout
18253 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
18256 \begin_layout Plain Layout
18257 \begin_inset Formula $\sqcap$
18267 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
18270 \begin_layout Plain Layout
18278 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
18281 \begin_layout Plain Layout
18282 \begin_inset Formula $\sqcup$
18292 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
18295 \begin_layout Plain Layout
18303 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
18306 \begin_layout Plain Layout
18307 \begin_inset Formula $\triangleleft$
18317 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
18320 \begin_layout Plain Layout
18328 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
18331 \begin_layout Plain Layout
18332 \begin_inset Formula $\triangleright$
18346 \begin_inset space \hfill{}
18352 \begin_layout Standard
18353 All binary operators can also be inserted via the math toolbar button
18356 arg "math-insert \\pm"
18362 \begin_layout Standard
18363 To typeset the Laplace operator also
18380 \begin_inset Formula $\nabla^{2}$
18383 ) can be used instead of
18392 \begin_layout Standard
18399 Insert\SpecialChar menuseparator
18411 \begin_layout Subsection
18412 Self-defined Operators
18413 \begin_inset CommandInset label
18415 name "subsec:Self-defined-Operators"
18420 \begin_inset Index idx
18423 \begin_layout Plain Layout
18424 Operators ! self-defined
18432 \begin_layout Standard
18433 With the help of the command
18437 DeclareMathOperator
18440 \begin_inset Index idx
18443 \begin_layout Plain Layout
18448 DeclareMathOperator
18453 custom operators can be defined in the \SpecialChar LaTeX
18455 Its command scheme is:
18458 \begin_layout Standard
18463 DeclareMathOperator{new command}{display}
18466 \begin_layout Standard
18467 Display can be characters or symbols that define how the operator looks
18469 To define a big operator a * is set behind the command.
18470 All self-defined big operators can have limits as described in
18471 \begin_inset CommandInset ref
18473 reference "subsec:Operator-Limits"
18480 \begin_layout Standard
18481 For example the \SpecialChar LaTeX
18485 \begin_layout Standard
18490 DeclareMathOperator*{
18497 \begin_layout Standard
18498 defines the command
18504 , that inserts a big operator consisting of the lozenge symbol from
18505 \begin_inset CommandInset ref
18507 reference "subsec:Miscellaneous-Symbols"
18512 \begin_inset Formula
18514 \Lozenge_{n=1}^{\infty}
18519 The command for this formula is:
18530 \begin_inset Formula $\to$
18536 \begin_layout Standard
18537 \begin_inset VSpace bigskip
18540 When self-defined operators are not used several times in the document,
18541 they can also be defined with the commands
18548 \begin_inset Index idx
18551 \begin_layout Plain Layout
18566 \begin_inset Index idx
18569 \begin_layout Plain Layout
18577 , which have the following scheme:
18580 \begin_layout Standard
18594 \begin_layout Standard
18601 defines big operators,
18610 \begin_layout Standard
18618 \begin_inset space \thinspace{}
18622 \begin_inset space \space{}
18625 be used to use one limit for several operators:
18628 \begin_layout Standard
18629 \begin_inset Formula
18631 \mathop{\sum\negmedspace\sum}_{i,j=1}^{N}
18639 \begin_layout Standard
18640 The command for the formula above is:
18641 \begin_inset Newline newline
18657 \begin_inset space \textvisiblespace{}
18663 \begin_inset Formula $\to$
18669 \begin_inset space \textvisiblespace{}
18677 \begin_layout Section
18679 \begin_inset Index idx
18682 \begin_layout Plain Layout
18691 \begin_layout Subsection
18693 \begin_inset CommandInset label
18695 name "subsec:Font-Styles"
18700 \begin_inset Index idx
18703 \begin_layout Plain Layout
18712 \begin_layout Standard
18713 Latin letters in formulas can be set in one of the following font styles:
18716 \begin_layout Standard
18718 \begin_inset space \hfill{}
18722 \begin_inset Tabular
18723 <lyxtabular version="3" rows="6" columns="2">
18724 <features tabularvalignment="middle">
18725 <column alignment="center" valignment="top">
18726 <column alignment="center" valignment="top">
18728 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
18731 \begin_layout Plain Layout
18737 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
18740 \begin_layout Plain Layout
18748 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
18751 \begin_layout Plain Layout
18757 \begin_inset space \textvisiblespace{}
18767 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
18770 \begin_layout Plain Layout
18771 \begin_inset Formula $\mathbb{ABC}$
18781 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
18784 \begin_layout Plain Layout
18790 \begin_inset space \textvisiblespace{}
18800 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
18803 \begin_layout Plain Layout
18804 \begin_inset Formula $\mathbf{AbC}$
18814 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
18817 \begin_layout Plain Layout
18823 \begin_inset space \textvisiblespace{}
18833 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
18836 \begin_layout Plain Layout
18837 \begin_inset Formula $\boldsymbol{AbC}$
18847 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
18850 \begin_layout Plain Layout
18856 \begin_inset space \textvisiblespace{}
18866 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
18869 \begin_layout Plain Layout
18870 \begin_inset Formula $\mathcal{ABC}$
18880 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
18883 \begin_layout Plain Layout
18889 \begin_inset space \textvisiblespace{}
18899 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
18902 \begin_layout Plain Layout
18903 \begin_inset Formula $\mathfrak{AbC}$
18917 \begin_inset space \hfill{}
18921 \begin_inset Tabular
18922 <lyxtabular version="3" rows="6" columns="2">
18923 <features tabularvalignment="middle">
18924 <column alignment="center" valignment="top">
18925 <column alignment="center" valignment="top">
18927 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
18930 \begin_layout Plain Layout
18936 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
18939 \begin_layout Plain Layout
18947 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
18950 \begin_layout Plain Layout
18956 \begin_inset space \textvisiblespace{}
18966 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
18969 \begin_layout Plain Layout
18970 \begin_inset Formula $\mathit{AbC}$
18980 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
18983 \begin_layout Plain Layout
18989 \begin_inset space \textvisiblespace{}
18999 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
19002 \begin_layout Plain Layout
19003 \begin_inset Formula $\mathrm{AbC}$
19013 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
19016 \begin_layout Plain Layout
19022 \begin_inset space \textvisiblespace{}
19032 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
19035 \begin_layout Plain Layout
19036 \begin_inset Formula $\mathsf{AbC}$
19046 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
19049 \begin_layout Plain Layout
19055 \begin_inset space \textvisiblespace{}
19065 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
19068 \begin_layout Plain Layout
19069 \begin_inset Formula $\mathtt{AbC}$
19079 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
19082 \begin_layout Plain Layout
19088 \begin_inset space \textvisiblespace{}
19098 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
19101 \begin_layout Plain Layout
19102 \begin_inset Formula $\mathscr{ABC}$
19116 \begin_inset space \hfill{}
19122 \begin_layout Standard
19123 \begin_inset Note Greyedout
19126 \begin_layout Plain Layout
19149 can only be used for big letters.
19157 \begin_layout Standard
19158 Predefined is the style
19167 \begin_layout Standard
19168 The style commands work also for letters in mathematical constructs:
19169 \begin_inset Formula
19171 \mathfrak{A=\frac{b}{C}}
19179 \begin_layout Standard
19180 Characters in mathematical text don't appear in a math font style but in
19181 the text font style
19188 That their style can't be set correctly via the text style dialog is a
19189 bug in \SpecialChar LyX
19194 \begin_layout Plain Layout
19195 \begin_inset CommandInset href
19197 name "LyX-bug #4629"
19198 target "http://www.lyx.org/trac/ticket/4629"
19210 \begin_layout Standard
19211 Instead of the style commands the dialog
19213 Edit\SpecialChar menuseparator
19214 Math\SpecialChar menuseparator
19217 or the toolbar button
19220 arg "math-insert \\font"
19226 \begin_layout Subsection
19228 \begin_inset CommandInset label
19230 name "subsec:Bold-Formulas"
19235 \begin_inset Index idx
19238 \begin_layout Plain Layout
19247 \begin_layout Standard
19248 To make a complete formula bold, the command
19254 from the previous subsection cannot be used, because it doesn't work for
19255 small Greek letters.
19256 Furthermore it prints Latin letters always upright, like in the following
19260 \begin_layout Standard
19261 \begin_inset Formula
19263 \mathbf{\int_{n}^{2}f(\theta)=\Gamma}\qquad\textrm{equation with \textbackslash mathbf}
19271 \begin_layout Standard
19272 To display the formula correctly, the command
19279 \begin_inset Formula
19281 \boldsymbol{\int_{n}^{2}f(\theta)=\Gamma\qquad\textrm{equation with \textbackslash boldsymbol}}
19286 It is also possible to set the formula in a
19288 boldmath environment
19291 This environment is created by inserting the command
19298 \begin_inset Index idx
19301 \begin_layout Plain Layout
19309 in \SpecialChar TeX
19311 To end the environment, the command
19318 \begin_inset Index idx
19321 \begin_layout Plain Layout
19329 is inserted in \SpecialChar TeX
19334 \begin_layout Plain Layout
19344 \begin_inset Formula
19346 \int_{n}^{2}f(\theta)=\Gamma\qquad\textrm{equation in a boldmath environment}
19355 \begin_layout Plain Layout
19367 \begin_layout Subsection
19369 \begin_inset Index idx
19372 \begin_layout Plain Layout
19381 \begin_layout Standard
19382 Formulas can be colored like normal text: Highlight a formula or a formula
19388 Here is a formula in magenta:
19389 \begin_inset Formula
19391 {\color{magenta}\int A\,\mathrm{d}x=\frac{\sqrt[5]{B}}{\ln\left(\frac{1}{3}\right)}}
19399 \begin_layout Standard
19400 You can also define your own colors as described in
19401 \begin_inset CommandInset ref
19403 reference "subsec:Colored-Boxes"
19408 They can be used with the \SpecialChar TeX
19416 \begin_inset Index idx
19419 \begin_layout Plain Layout
19430 \begin_layout Standard
19435 textcolor{color}{characters or formula}
19438 \begin_layout Standard
19439 The following example was colored completely dark green and partly red:
19442 \begin_layout Standard
19446 \begin_layout Plain Layout
19450 textcolor{darkgreen}{
19456 \begin_inset Formula
19458 \int A\,\mathrm{d}x=\frac{{\color{red}\sqrt[5]{B}}}{\ln\left(\frac{1}{3}\right)}
19467 \begin_layout Plain Layout
19477 \begin_layout Standard
19478 Due to a bug in \SpecialChar LyX
19479 only complete formulas can be colored with self-defined
19484 \begin_layout Plain Layout
19485 \begin_inset CommandInset href
19487 name "LyX-bug #5269"
19488 target "http://www.lyx.org/trac/ticket/5269"
19500 \begin_layout Subsection
19502 \begin_inset CommandInset label
19504 name "subsec:Font-Sizes"
19509 \begin_inset Index idx
19512 \begin_layout Plain Layout
19521 \begin_layout Standard
19522 For characters in formulas there are, analog to characters in text, the
19523 following size commands:
19526 \begin_layout Standard
19570 \begin_inset Newline newline
19592 \begin_layout Standard
19593 The size produced by the commands depends on the document font size, which
19594 corresponds to the command
19601 The other commands produce smaller or larger sizes than
19608 The font size can however not exceed a certain value.
19609 Is for example the document font size 12
19610 \begin_inset space \thinspace{}
19619 switches to the same size as
19629 \begin_layout Standard
19630 A size command is inserted in \SpecialChar TeX
19631 mode before the formula and sets the size
19632 for all following formula and text characters.
19633 To switch back to the initial size, the command
19639 is inserted behind the formula in \SpecialChar TeX
19643 \begin_layout Standard
19644 Within a formula the size can be changed using the following size commands
19645 or the toolbar button
19648 arg "math-insert \\style"
19652 \begin_inset Separator parbreak
19658 \begin_layout Standard
19661 \begin_inset Tabular
19662 <lyxtabular version="3" rows="5" columns="2">
19663 <features tabularvalignment="middle">
19664 <column alignment="center" valignment="top">
19665 <column alignment="center" valignment="top">
19667 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
19670 \begin_layout Plain Layout
19676 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
19679 \begin_layout Plain Layout
19681 \begin_inset Note Note
19684 \begin_layout Plain Layout
19691 is only used as spacer.
19703 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
19706 \begin_layout Plain Layout
19710 \begin_inset Index idx
19713 \begin_layout Plain Layout
19726 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
19729 \begin_layout Plain Layout
19730 \begin_inset Formula $\raisebox{6.5mm}{}{\displaystyle E_{\mathrm{pot_{1}}}=\frac{K}{l+\frac{m}{n_{2}}}}\raisebox{-5.5mm}{}$
19740 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
19743 \begin_layout Plain Layout
19751 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
19754 \begin_layout Plain Layout
19755 \begin_inset Formula $\raisebox{4.5mm}{}{\textstyle E_{\mathrm{pot_{1}}}=\frac{K}{l+\frac{m}{n_{2}}}}\raisebox{-4mm}{}$
19765 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
19768 \begin_layout Plain Layout
19776 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
19779 \begin_layout Plain Layout
19780 \begin_inset Formula $\raisebox{4.5mm}{}{\scriptstyle E_{\mathrm{pot_{1}}}=\frac{K}{l+\frac{m}{n_{2}}}}\raisebox{-3.5mm}{}$
19790 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
19793 \begin_layout Plain Layout
19801 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
19804 \begin_layout Plain Layout
19805 \begin_inset Formula $\raisebox{4.5mm}{}{\scriptscriptstyle E_{\mathrm{pot_{1}}}=\frac{K}{l+\frac{m}{n_{2}}}}\raisebox{-3.5mm}{}$
19821 \begin_layout Standard
19822 After entering these commands, a blue box appears in which the formula parts
19826 \begin_layout Standard
19827 There is a further method to change the font size, that though only works
19828 for symbols or letters in mathematical text.
19829 To use it, one of the above text size commands is inserted in mathematical
19831 All following characters until the end of the mathematical text or until
19832 another size command will have the selected size.
19834 \begin_inset VSpace -2mm
19840 \begin_layout Standard
19844 \begin_layout Plain Layout
19854 \begin_inset Formula
19856 A=\frac{B}{c}\cdot\maltese
19862 \begin_inset Formula
19864 \maltese A\textrm{\Large\maltese\textit{A}}\textrm{\tiny\maltese\textit{A}}
19873 \begin_layout Plain Layout
19885 \begin_layout Standard
19886 \begin_inset VSpace medskip
19889 Before both formulas the command
19896 The command for the second formula is:
19897 \begin_inset Newline newline
19905 \begin_inset space \textvisiblespace{}
19911 \begin_inset space \textvisiblespace{}
19917 \begin_inset space \textvisiblespace{}
19923 \begin_inset space \textvisiblespace{}
19927 \begin_inset Formula $\to$
19931 \begin_inset Formula $\to$
19935 \begin_inset Newline newline
19939 \begin_inset space \hspace*{}
19950 \begin_inset space \textvisiblespace{}
19956 \begin_inset space \textvisiblespace{}
19962 \begin_inset space \textvisiblespace{}
19968 \begin_layout Standard
19969 If a symbol cannot be displayed in different sizes, it will always be displayed
19970 in the default size.
19973 \begin_layout Section
19975 \begin_inset Index idx
19978 \begin_layout Plain Layout
19987 \begin_layout Standard
19988 Greek letters can also be inserted via the toolbar button
19991 arg "math-insert \\alpha"
19995 All international typesetting norms purport that Greek letters in math
19996 have to be typeset italic/slanted.
19997 In some languages, like French or Russian, they are nevertheless sometimes
20001 \begin_layout Subsection
20003 \begin_inset Index idx
20006 \begin_layout Plain Layout
20007 Greek letters ! small
20015 \begin_layout Standard
20016 \begin_inset space \hfill{}
20020 \begin_inset Tabular
20021 <lyxtabular version="3" rows="11" columns="2">
20022 <features tabularvalignment="middle">
20023 <column alignment="center" valignment="top" width="0pt">
20024 <column alignment="center" valignment="top" width="0pt">
20026 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
20029 \begin_layout Plain Layout
20035 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
20038 \begin_layout Plain Layout
20046 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
20049 \begin_layout Plain Layout
20057 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
20060 \begin_layout Plain Layout
20061 \begin_inset Formula $\alpha$
20071 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
20074 \begin_layout Plain Layout
20082 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
20085 \begin_layout Plain Layout
20086 \begin_inset Formula $\beta$
20096 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
20099 \begin_layout Plain Layout
20107 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
20110 \begin_layout Plain Layout
20111 \begin_inset Formula $\gamma$
20121 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
20124 \begin_layout Plain Layout
20132 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
20135 \begin_layout Plain Layout
20136 \begin_inset Formula $\delta$
20146 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
20149 \begin_layout Plain Layout
20157 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
20160 \begin_layout Plain Layout
20161 \begin_inset Formula $\epsilon$
20171 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
20174 \begin_layout Plain Layout
20182 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
20185 \begin_layout Plain Layout
20186 \begin_inset Formula $\varepsilon$
20196 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
20199 \begin_layout Plain Layout
20207 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
20210 \begin_layout Plain Layout
20211 \begin_inset Formula $\zeta$
20221 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
20224 \begin_layout Plain Layout
20232 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
20235 \begin_layout Plain Layout
20236 \begin_inset Formula $\eta$
20246 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
20249 \begin_layout Plain Layout
20257 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
20260 \begin_layout Plain Layout
20261 \begin_inset Formula $\theta$
20271 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
20274 \begin_layout Plain Layout
20282 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
20285 \begin_layout Plain Layout
20286 \begin_inset Formula $\vartheta$
20300 \begin_inset space \hfill{}
20304 \begin_inset Tabular
20305 <lyxtabular version="3" rows="12" columns="2">
20306 <features tabularvalignment="middle">
20307 <column alignment="center" valignment="top" width="0pt">
20308 <column alignment="center" valignment="top" width="0pt">
20310 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
20313 \begin_layout Plain Layout
20319 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
20322 \begin_layout Plain Layout
20330 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
20333 \begin_layout Plain Layout
20341 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
20344 \begin_layout Plain Layout
20345 \begin_inset Formula $\iota$
20355 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
20358 \begin_layout Plain Layout
20366 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
20369 \begin_layout Plain Layout
20370 \begin_inset Formula $\kappa$
20380 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
20383 \begin_layout Plain Layout
20391 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
20394 \begin_layout Plain Layout
20395 \begin_inset Formula $\varkappa$
20405 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
20408 \begin_layout Plain Layout
20416 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
20419 \begin_layout Plain Layout
20420 \begin_inset Formula $\lambda$
20430 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
20433 \begin_layout Plain Layout
20441 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
20444 \begin_layout Plain Layout
20445 \begin_inset Formula $\mu$
20455 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
20458 \begin_layout Plain Layout
20466 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
20469 \begin_layout Plain Layout
20470 \begin_inset Formula $\nu$
20480 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
20483 \begin_layout Plain Layout
20491 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
20494 \begin_layout Plain Layout
20495 \begin_inset Formula $\xi$
20505 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
20508 \begin_layout Plain Layout
20514 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
20517 \begin_layout Plain Layout
20518 \begin_inset Formula $o$
20528 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
20531 \begin_layout Plain Layout
20539 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
20542 \begin_layout Plain Layout
20543 \begin_inset Formula $\pi$
20553 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
20556 \begin_layout Plain Layout
20564 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
20567 \begin_layout Plain Layout
20568 \begin_inset Formula $\varpi$
20578 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
20581 \begin_layout Plain Layout
20589 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
20592 \begin_layout Plain Layout
20593 \begin_inset Formula $\rho$
20607 \begin_inset space \hfill{}
20611 \begin_inset Tabular
20612 <lyxtabular version="3" rows="11" columns="2">
20613 <features tabularvalignment="middle">
20614 <column alignment="center" valignment="top" width="0pt">
20615 <column alignment="center" valignment="top" width="0pt">
20617 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
20620 \begin_layout Plain Layout
20626 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
20629 \begin_layout Plain Layout
20637 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
20640 \begin_layout Plain Layout
20648 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
20651 \begin_layout Plain Layout
20652 \begin_inset Formula $\varrho$
20662 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
20665 \begin_layout Plain Layout
20673 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
20676 \begin_layout Plain Layout
20677 \begin_inset Formula $\sigma$
20687 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
20690 \begin_layout Plain Layout
20698 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
20701 \begin_layout Plain Layout
20702 \begin_inset Formula $\varsigma$
20712 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
20715 \begin_layout Plain Layout
20723 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
20726 \begin_layout Plain Layout
20727 \begin_inset Formula $\tau$
20737 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
20740 \begin_layout Plain Layout
20748 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
20751 \begin_layout Plain Layout
20752 \begin_inset Formula $\upsilon$
20762 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
20765 \begin_layout Plain Layout
20773 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
20776 \begin_layout Plain Layout
20777 \begin_inset Formula $\phi$
20787 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
20790 \begin_layout Plain Layout
20798 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
20801 \begin_layout Plain Layout
20802 \begin_inset Formula $\varphi$
20812 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
20815 \begin_layout Plain Layout
20823 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
20826 \begin_layout Plain Layout
20827 \begin_inset Formula $\chi$
20837 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
20840 \begin_layout Plain Layout
20848 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
20851 \begin_layout Plain Layout
20852 \begin_inset Formula $\psi$
20862 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
20865 \begin_layout Plain Layout
20873 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
20876 \begin_layout Plain Layout
20877 \begin_inset Formula $\omega$
20891 \begin_inset space \hfill{}
20897 \begin_layout Standard
20898 \begin_inset VSpace medskip
20904 \begin_layout Standard
20905 How to create special upright Greek letters is explained in
20906 \begin_inset CommandInset ref
20908 reference "subsec:Upright-small-Greek"
20915 \begin_layout Subsection
20917 \begin_inset Index idx
20920 \begin_layout Plain Layout
20921 Greek letters ! big
20929 \begin_layout Standard
20930 \begin_inset space \hfill{}
20934 \begin_inset Tabular
20935 <lyxtabular version="3" rows="7" columns="2">
20936 <features tabularvalignment="middle">
20937 <column alignment="center" valignment="top" width="0pt">
20938 <column alignment="center" valignment="top" width="0pt">
20940 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
20943 \begin_layout Plain Layout
20949 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
20952 \begin_layout Plain Layout
20960 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
20963 \begin_layout Plain Layout
20971 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
20974 \begin_layout Plain Layout
20975 \begin_inset Formula $\Gamma$
20985 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
20988 \begin_layout Plain Layout
20996 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
20999 \begin_layout Plain Layout
21000 \begin_inset Formula $\Delta$
21010 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
21013 \begin_layout Plain Layout
21021 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
21024 \begin_layout Plain Layout
21025 \begin_inset Formula $\Theta$
21035 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
21038 \begin_layout Plain Layout
21046 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
21049 \begin_layout Plain Layout
21050 \begin_inset Formula $\Lambda$
21060 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
21063 \begin_layout Plain Layout
21071 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
21074 \begin_layout Plain Layout
21075 \begin_inset Formula $\Xi$
21085 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
21088 \begin_layout Plain Layout
21096 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
21099 \begin_layout Plain Layout
21100 \begin_inset Formula $\Pi$
21114 \begin_inset space \hfill{}
21118 \begin_inset Tabular
21119 <lyxtabular version="3" rows="6" columns="2">
21120 <features tabularvalignment="middle">
21121 <column alignment="center" valignment="top" width="0pt">
21122 <column alignment="center" valignment="top" width="0pt">
21124 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
21127 \begin_layout Plain Layout
21133 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
21136 \begin_layout Plain Layout
21144 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
21147 \begin_layout Plain Layout
21155 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
21158 \begin_layout Plain Layout
21159 \begin_inset Formula $\Sigma$
21169 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
21172 \begin_layout Plain Layout
21180 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
21183 \begin_layout Plain Layout
21184 \begin_inset Formula $\Upsilon$
21194 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
21197 \begin_layout Plain Layout
21205 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
21208 \begin_layout Plain Layout
21209 \begin_inset Formula $\Phi$
21219 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
21222 \begin_layout Plain Layout
21230 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
21233 \begin_layout Plain Layout
21234 \begin_inset Formula $\Psi$
21244 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
21247 \begin_layout Plain Layout
21255 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
21258 \begin_layout Plain Layout
21259 \begin_inset Formula $\Omega$
21273 \begin_inset space \hfill{}
21279 \begin_layout Standard
21280 \begin_inset VSpace medskip
21283 That the big Greek letters appear upright is caused by a design bug when
21286 To get correct italic big letters, begin every command with
21291 For example the command
21298 \begin_inset Formula $\varGamma$
21302 Another way is to load the package
21310 \begin_layout Plain Layout
21315 is part of the \SpecialChar LaTeX
21321 \begin_inset Index idx
21324 \begin_layout Plain Layout
21329 \begin_layout Plain Layout
21349 \begin_inset Index idx
21352 \begin_layout Plain Layout
21358 with the \SpecialChar LaTeX
21362 \begin_layout Standard
21367 usepackage{fixmath}
21370 \begin_layout Standard
21371 Then all big Greek letters in a document will automatically be typeset italic.
21374 \begin_layout Subsection
21376 \begin_inset Index idx
21379 \begin_layout Plain Layout
21380 Greek letters ! bold
21388 \begin_layout Standard
21389 Greek letters cannot be set with different font styles like Latin letters.
21390 They can only be made bold with the command
21397 \begin_inset Index idx
21400 \begin_layout Plain Layout
21409 \begin_inset Separator parbreak
21415 \begin_layout Standard
21417 \begin_inset Tabular
21418 <lyxtabular version="3" rows="3" columns="2">
21419 <features tabularvalignment="middle">
21420 <column alignment="center" valignment="top">
21421 <column alignment="center" valignment="top">
21423 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
21426 \begin_layout Plain Layout
21432 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
21435 \begin_layout Plain Layout
21443 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
21446 \begin_layout Plain Layout
21458 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
21461 \begin_layout Plain Layout
21462 \begin_inset Formula $\Upsilon\boldsymbol{\Upsilon}$
21472 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
21475 \begin_layout Plain Layout
21487 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
21490 \begin_layout Plain Layout
21491 \begin_inset Formula $\theta\boldsymbol{\theta}$
21507 \begin_layout Section
21512 \begin_layout Plain Layout
21525 \begin_layout Plain Layout
21526 A list with all symbols of most of the \SpecialChar LaTeX
21527 -packages can be found in
21528 \begin_inset CommandInset citation
21543 \begin_layout Plain Layout
21551 \begin_inset Note Note
21554 \begin_layout Plain Layout
21557 texorpdfstring is used to avoid that the footnote appears in the PDF-bookmark.
21560 \begin_layout Plain Layout
21563 texorpdfstring is in section
21564 \begin_inset CommandInset ref
21566 reference "subsec:Formulas-in-Section"
21576 \begin_inset Index idx
21579 \begin_layout Plain Layout
21588 \begin_layout Standard
21589 Many of the symbols listed in this section can also be inserted via the
21593 arg "math-insert \\nabla"
21599 arg "math-insert \\digamma"
21605 \begin_layout Subsection
21606 Mathematical Symbols
21607 \begin_inset CommandInset label
21609 name "subsec:Mathematical-Symbols"
21614 \begin_inset Index idx
21617 \begin_layout Plain Layout
21618 Symbols ! mathematical
21626 \begin_layout Standard
21627 \begin_inset space \hfill{}
21631 \begin_inset Tabular
21632 <lyxtabular version="3" rows="10" columns="2">
21633 <features tabularvalignment="middle">
21634 <column alignment="center" valignment="top" width="0pt">
21635 <column alignment="center" valignment="top" width="0pt">
21637 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
21640 \begin_layout Plain Layout
21646 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
21649 \begin_layout Plain Layout
21657 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
21660 \begin_layout Plain Layout
21668 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
21671 \begin_layout Plain Layout
21672 \begin_inset Formula $\neg$
21682 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
21685 \begin_layout Plain Layout
21693 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
21696 \begin_layout Plain Layout
21697 \begin_inset Formula $\Im$
21707 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
21710 \begin_layout Plain Layout
21718 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
21721 \begin_layout Plain Layout
21722 \begin_inset Formula $\Re$
21732 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
21735 \begin_layout Plain Layout
21743 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
21746 \begin_layout Plain Layout
21747 \begin_inset Formula $\aleph$
21757 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
21760 \begin_layout Plain Layout
21768 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
21771 \begin_layout Plain Layout
21772 \begin_inset Formula $\partial$
21782 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
21785 \begin_layout Plain Layout
21793 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
21796 \begin_layout Plain Layout
21797 \begin_inset Formula $\infty$
21807 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
21810 \begin_layout Plain Layout
21818 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
21821 \begin_layout Plain Layout
21822 \begin_inset Formula $\wp$
21832 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
21835 \begin_layout Plain Layout
21843 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
21846 \begin_layout Plain Layout
21847 \begin_inset Formula $\imath$
21857 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
21860 \begin_layout Plain Layout
21868 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
21871 \begin_layout Plain Layout
21872 \begin_inset Formula $\jmath$
21886 \begin_inset space \hfill{}
21890 \begin_inset Tabular
21891 <lyxtabular version="3" rows="10" columns="2">
21892 <features tabularvalignment="middle">
21893 <column alignment="center" valignment="top" width="0pt">
21894 <column alignment="center" valignment="top" width="0pt">
21896 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
21899 \begin_layout Plain Layout
21905 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
21908 \begin_layout Plain Layout
21910 \begin_inset Note Note
21913 \begin_layout Plain Layout
21920 is only used as spacer.
21932 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
21935 \begin_layout Plain Layout
21943 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
21946 \begin_layout Plain Layout
21947 \begin_inset Formula $\forall$
21957 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
21960 \begin_layout Plain Layout
21968 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
21971 \begin_layout Plain Layout
21972 \begin_inset Formula $\exists$
21982 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
21985 \begin_layout Plain Layout
21993 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
21996 \begin_layout Plain Layout
21997 \begin_inset Formula $\nexists$
22007 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
22010 \begin_layout Plain Layout
22018 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
22021 \begin_layout Plain Layout
22022 \begin_inset Formula $\emptyset$
22032 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
22035 \begin_layout Plain Layout
22043 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
22046 \begin_layout Plain Layout
22047 \begin_inset Formula $\varnothing$
22057 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
22060 \begin_layout Plain Layout
22068 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
22071 \begin_layout Plain Layout
22072 \begin_inset Formula $\dag$
22082 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
22085 \begin_layout Plain Layout
22093 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
22096 \begin_layout Plain Layout
22097 \begin_inset Formula $\ddag$
22107 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
22110 \begin_layout Plain Layout
22118 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
22121 \begin_layout Plain Layout
22125 \begin_layout Plain Layout
22135 \begin_inset Formula $\complement$
22142 \begin_layout Plain Layout
22156 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
22159 \begin_layout Plain Layout
22167 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
22170 \begin_layout Plain Layout
22171 \begin_inset Formula $\Bbbk$
22185 \begin_inset space \hfill{}
22189 \begin_inset Tabular
22190 <lyxtabular version="3" rows="10" columns="2">
22191 <features tabularvalignment="middle">
22192 <column alignment="center" valignment="top" width="0pt">
22193 <column alignment="center" valignment="top" width="0pt">
22195 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
22198 \begin_layout Plain Layout
22204 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
22207 \begin_layout Plain Layout
22215 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
22218 \begin_layout Plain Layout
22226 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
22229 \begin_layout Plain Layout
22230 \begin_inset Formula $\prime$
22240 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
22243 \begin_layout Plain Layout
22251 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
22254 \begin_layout Plain Layout
22255 \begin_inset Formula $\backprime$
22265 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
22268 \begin_layout Plain Layout
22276 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
22279 \begin_layout Plain Layout
22280 \begin_inset Formula $\mho$
22290 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
22293 \begin_layout Plain Layout
22301 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
22304 \begin_layout Plain Layout
22305 \begin_inset Formula $\triangle$
22315 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
22318 \begin_layout Plain Layout
22326 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
22329 \begin_layout Plain Layout
22330 \begin_inset Formula $\angle$
22340 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
22343 \begin_layout Plain Layout
22351 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
22354 \begin_layout Plain Layout
22355 \begin_inset Formula $\measuredangle$
22365 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
22368 \begin_layout Plain Layout
22376 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
22379 \begin_layout Plain Layout
22380 \begin_inset Formula $\sphericalangle$
22390 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
22393 \begin_layout Plain Layout
22401 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
22404 \begin_layout Plain Layout
22405 \begin_inset Formula $\top$
22415 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
22418 \begin_layout Plain Layout
22426 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
22429 \begin_layout Plain Layout
22430 \begin_inset Formula $\bot$
22444 \begin_inset space \hfill{}
22450 \begin_layout Standard
22451 \begin_inset Newpage newpage
22457 \begin_layout Subsection
22458 Miscellaneous Symbols
22459 \begin_inset CommandInset label
22461 name "subsec:Miscellaneous-Symbols"
22466 \begin_inset Index idx
22469 \begin_layout Plain Layout
22470 Symbols ! miscellaneous
22478 \begin_layout Standard
22481 \begin_inset Tabular
22482 <lyxtabular version="3" rows="10" columns="2">
22483 <features tabularvalignment="middle">
22484 <column alignment="center" valignment="top" width="0pt">
22485 <column alignment="center" valignment="top" width="0pt">
22487 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
22490 \begin_layout Plain Layout
22496 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
22499 \begin_layout Plain Layout
22507 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
22510 \begin_layout Plain Layout
22518 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
22521 \begin_layout Plain Layout
22522 \begin_inset Formula $\flat$
22532 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
22535 \begin_layout Plain Layout
22543 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
22546 \begin_layout Plain Layout
22547 \begin_inset Formula $\natural$
22557 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
22560 \begin_layout Plain Layout
22568 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
22571 \begin_layout Plain Layout
22572 \begin_inset Formula $\sharp$
22582 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
22585 \begin_layout Plain Layout
22593 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
22596 \begin_layout Plain Layout
22597 \begin_inset Formula $\surd$
22607 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
22610 \begin_layout Plain Layout
22618 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
22621 \begin_layout Plain Layout
22622 \begin_inset Formula $\checkmark$
22632 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
22635 \begin_layout Plain Layout
22643 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
22646 \begin_layout Plain Layout
22647 \begin_inset Formula $\yen$
22657 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
22660 \begin_layout Plain Layout
22668 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
22671 \begin_layout Plain Layout
22672 \begin_inset Formula $\pounds$
22682 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
22685 \begin_layout Plain Layout
22691 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
22694 \begin_layout Plain Layout
22695 \begin_inset Formula $\$$
22705 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
22708 \begin_layout Plain Layout
22714 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
22717 \begin_layout Plain Layout
22718 \begin_inset Formula $§$
22732 \begin_inset Tabular
22733 <lyxtabular version="3" rows="10" columns="2">
22734 <features tabularvalignment="middle">
22735 <column alignment="center" valignment="top">
22736 <column alignment="center" valignment="top">
22738 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
22741 \begin_layout Plain Layout
22747 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
22750 \begin_layout Plain Layout
22758 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
22761 \begin_layout Plain Layout
22769 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
22772 \begin_layout Plain Layout
22773 \begin_inset Formula $\hbar$
22783 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
22786 \begin_layout Plain Layout
22794 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
22797 \begin_layout Plain Layout
22798 \begin_inset Formula $\hslash$
22808 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
22811 \begin_layout Plain Layout
22819 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
22822 \begin_layout Plain Layout
22823 \begin_inset Formula $\clubsuit$
22833 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
22836 \begin_layout Plain Layout
22844 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
22847 \begin_layout Plain Layout
22848 \begin_inset Formula $\spadesuit$
22858 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
22861 \begin_layout Plain Layout
22869 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
22872 \begin_layout Plain Layout
22873 \begin_inset Formula $\bigstar$
22883 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
22886 \begin_layout Plain Layout
22894 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
22897 \begin_layout Plain Layout
22898 \begin_inset Formula $\blacklozenge$
22908 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
22911 \begin_layout Plain Layout
22919 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
22922 \begin_layout Plain Layout
22923 \begin_inset Formula $\blacktriangle$
22933 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
22936 \begin_layout Plain Layout
22944 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
22947 \begin_layout Plain Layout
22948 \begin_inset Formula $\blacktriangledown$
22958 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
22961 \begin_layout Plain Layout
22969 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
22972 \begin_layout Plain Layout
22973 \begin_inset Formula $\bullet$
22987 \begin_inset Tabular
22988 <lyxtabular version="3" rows="10" columns="2">
22989 <features tabularvalignment="middle">
22990 <column alignment="center" valignment="top" width="0pt">
22991 <column alignment="center" valignment="top" width="0pt">
22993 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
22996 \begin_layout Plain Layout
23002 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
23005 \begin_layout Plain Layout
23013 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
23016 \begin_layout Plain Layout
23024 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
23027 \begin_layout Plain Layout
23028 \begin_inset Formula $\diamondsuit$
23038 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
23041 \begin_layout Plain Layout
23049 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
23052 \begin_layout Plain Layout
23053 \begin_inset Formula $\Diamond$
23063 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
23066 \begin_layout Plain Layout
23074 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
23077 \begin_layout Plain Layout
23078 \begin_inset Formula $\heartsuit$
23088 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
23091 \begin_layout Plain Layout
23099 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
23102 \begin_layout Plain Layout
23103 \begin_inset Formula $\P$
23113 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
23116 \begin_layout Plain Layout
23124 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
23127 \begin_layout Plain Layout
23128 \begin_inset Formula $\copyright$
23138 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
23141 \begin_layout Plain Layout
23149 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
23152 \begin_layout Plain Layout
23153 \begin_inset Formula $\circledR$
23163 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
23166 \begin_layout Plain Layout
23174 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
23177 \begin_layout Plain Layout
23178 \begin_inset Formula $\maltese$
23188 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
23191 \begin_layout Plain Layout
23199 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
23202 \begin_layout Plain Layout
23203 \begin_inset Formula $\diagup$
23213 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
23216 \begin_layout Plain Layout
23224 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
23227 \begin_layout Plain Layout
23228 \begin_inset Formula $\diagdown$
23244 \begin_layout Standard
23245 \begin_inset VSpace medskip
23251 \begin_layout Standard
23252 Some symbols can be displayed in different sizes, see
23253 \begin_inset CommandInset ref
23255 reference "subsec:Font-Sizes"
23262 \begin_layout Subsection
23264 \begin_inset Index idx
23267 \begin_layout Plain Layout
23268 Symbols ! Euro-symbol
23274 \begin_inset Index idx
23277 \begin_layout Plain Layout
23284 \begin_layout Plain Layout
23301 \begin_layout Standard
23302 To use the Euro symbol in formulas, the \SpecialChar LaTeX
23308 \begin_inset Index idx
23311 \begin_layout Plain Layout
23317 must be installed and loaded with the \SpecialChar LaTeX
23321 \begin_layout Standard
23326 usepackage[gennarrow]{eurosym}
23329 \begin_layout Standard
23330 The Euro symbol can now be inserted with the command
23337 \begin_inset Index idx
23340 \begin_layout Plain Layout
23351 \begin_layout Standard
23352 The Euro symbol can directly be inserted with the € key in mathematical
23353 text, without having
23368 can also be inserted in \SpecialChar TeX
23370 The official currency symbol can then be inserted with the command
23377 \begin_inset Index idx
23380 \begin_layout Plain Layout
23388 , that is only available in \SpecialChar TeX
23392 \begin_layout Standard
23396 \begin_layout Plain Layout
23406 \begin_inset Note Note
23409 \begin_layout Plain Layout
23410 The following table will only be displayed when the \SpecialChar LaTeX
23423 \begin_layout Standard
23424 An overview about the different Euro symbols:
23425 \begin_inset Separator parbreak
23431 \begin_layout Standard
23433 \begin_inset Tabular
23434 <lyxtabular version="3" rows="4" columns="3">
23435 <features tabularvalignment="middle">
23436 <column alignment="center" valignment="top" width="0pt">
23437 <column alignment="center" valignment="top" width="0pt">
23438 <column alignment="center" valignment="top" width="0pt">
23440 <cell multicolumn="1" alignment="center" valignment="top" bottomline="true" usebox="none">
23443 \begin_layout Plain Layout
23449 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
23452 \begin_layout Plain Layout
23458 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
23461 \begin_layout Plain Layout
23469 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
23472 \begin_layout Plain Layout
23478 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
23481 \begin_layout Plain Layout
23489 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
23492 \begin_layout Plain Layout
23493 \begin_inset Formula $\euro$
23503 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
23506 \begin_layout Plain Layout
23512 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
23515 \begin_layout Plain Layout
23521 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
23524 \begin_layout Plain Layout
23525 \begin_inset Formula $\mbox{€}$
23535 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
23538 \begin_layout Plain Layout
23545 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
23548 \begin_layout Plain Layout
23556 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
23559 \begin_layout Plain Layout
23563 \begin_layout Plain Layout
23585 \begin_layout Standard
23589 \begin_layout Plain Layout
23599 \begin_inset Note Note
23602 \begin_layout Plain Layout
23603 The following will be displayed when the \SpecialChar LaTeX
23616 \begin_layout Standard
23617 You need to install the \SpecialChar LaTeX
23622 to see the rest of this subsection in the output.
23625 \begin_layout Standard
23629 \begin_layout Plain Layout
23641 \begin_layout Standard
23642 \begin_inset Newpage newpage
23648 \begin_layout Section
23650 \begin_inset CommandInset label
23652 name "sec:Relations"
23657 \begin_inset Index idx
23660 \begin_layout Plain Layout
23667 \begin_inset Index idx
23670 \begin_layout Plain Layout
23675 \begin_layout Plain Layout
23686 \begin_layout Plain Layout
23701 \begin_layout Standard
23702 All following relations can also be inserted via the toolbar button
23705 arg "math-insert \\leq"
23711 \begin_layout Standard
23712 \begin_inset space \hfill{}
23716 \begin_inset Tabular
23717 <lyxtabular version="3" rows="17" columns="2">
23718 <features tabularvalignment="middle">
23719 <column alignment="center" valignment="top" width="0pt">
23720 <column alignment="center" valignment="top" width="0pt">
23722 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
23725 \begin_layout Plain Layout
23731 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
23734 \begin_layout Plain Layout
23742 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
23745 \begin_layout Plain Layout
23751 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
23754 \begin_layout Plain Layout
23755 \begin_inset Formula $<$
23765 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
23768 \begin_layout Plain Layout
23776 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
23779 \begin_layout Plain Layout
23780 \begin_inset Formula $\le$
23790 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
23793 \begin_layout Plain Layout
23801 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
23804 \begin_layout Plain Layout
23805 \begin_inset Formula $\ll$
23815 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
23818 \begin_layout Plain Layout
23826 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
23829 \begin_layout Plain Layout
23830 \begin_inset Formula $\prec$
23840 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
23843 \begin_layout Plain Layout
23851 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
23854 \begin_layout Plain Layout
23855 \begin_inset Formula $\preceq$
23865 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
23868 \begin_layout Plain Layout
23876 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
23879 \begin_layout Plain Layout
23880 \begin_inset Formula $\subset$
23890 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
23893 \begin_layout Plain Layout
23901 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
23904 \begin_layout Plain Layout
23905 \begin_inset Formula $\subseteq$
23915 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
23918 \begin_layout Plain Layout
23926 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
23929 \begin_layout Plain Layout
23930 \begin_inset Formula $\sqsubseteq$
23940 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
23943 \begin_layout Plain Layout
23951 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
23954 \begin_layout Plain Layout
23955 \begin_inset Formula $\in$
23965 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
23968 \begin_layout Plain Layout
23976 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
23979 \begin_layout Plain Layout
23980 \begin_inset Formula $\vdash$
23990 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
23993 \begin_layout Plain Layout
24001 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
24004 \begin_layout Plain Layout
24005 \begin_inset Formula $\smile$
24015 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
24018 \begin_layout Plain Layout
24026 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
24029 \begin_layout Plain Layout
24030 \begin_inset Formula $\lhd$
24040 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
24043 \begin_layout Plain Layout
24051 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
24054 \begin_layout Plain Layout
24055 \begin_inset Formula $\unlhd$
24065 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
24068 \begin_layout Plain Layout
24076 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
24079 \begin_layout Plain Layout
24080 \begin_inset Formula $\gtrless$
24090 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
24093 \begin_layout Plain Layout
24101 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
24104 \begin_layout Plain Layout
24105 \begin_inset Formula $\mid$
24115 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
24118 \begin_layout Plain Layout
24126 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
24129 \begin_layout Plain Layout
24130 \begin_inset Formula $\nmid$
24144 \begin_inset space \hfill{}
24148 \begin_inset Tabular
24149 <lyxtabular version="3" rows="17" columns="2">
24150 <features tabularvalignment="middle">
24151 <column alignment="center" valignment="top" width="0pt">
24152 <column alignment="center" valignment="top" width="0pt">
24154 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
24157 \begin_layout Plain Layout
24163 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
24166 \begin_layout Plain Layout
24174 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
24177 \begin_layout Plain Layout
24183 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
24186 \begin_layout Plain Layout
24187 \begin_inset Formula $=$
24197 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
24200 \begin_layout Plain Layout
24208 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
24211 \begin_layout Plain Layout
24212 \begin_inset Formula $\not=$
24222 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
24225 \begin_layout Plain Layout
24233 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
24236 \begin_layout Plain Layout
24237 \begin_inset Formula $\equiv$
24247 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
24250 \begin_layout Plain Layout
24258 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
24261 \begin_layout Plain Layout
24262 \begin_inset Formula $\sim$
24272 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
24275 \begin_layout Plain Layout
24283 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
24286 \begin_layout Plain Layout
24287 \begin_inset Formula $\simeq$
24297 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
24300 \begin_layout Plain Layout
24308 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
24311 \begin_layout Plain Layout
24312 \begin_inset Formula $\approx$
24322 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
24325 \begin_layout Plain Layout
24333 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
24336 \begin_layout Plain Layout
24337 \begin_inset Formula $\cong$
24347 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
24350 \begin_layout Plain Layout
24358 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
24361 \begin_layout Plain Layout
24362 \begin_inset Formula $\bowtie$
24372 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
24375 \begin_layout Plain Layout
24383 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
24386 \begin_layout Plain Layout
24387 \begin_inset Formula $\notin$
24397 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
24400 \begin_layout Plain Layout
24408 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
24411 \begin_layout Plain Layout
24412 \begin_inset Formula $\perp$
24422 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
24425 \begin_layout Plain Layout
24433 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
24436 \begin_layout Plain Layout
24437 \begin_inset Formula $\propto$
24447 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
24450 \begin_layout Plain Layout
24458 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
24461 \begin_layout Plain Layout
24462 \begin_inset Formula $\asymp$
24472 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
24475 \begin_layout Plain Layout
24483 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
24486 \begin_layout Plain Layout
24487 \begin_inset Formula $\doteq$
24497 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
24500 \begin_layout Plain Layout
24508 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
24511 \begin_layout Plain Layout
24512 \begin_inset Formula $\circeq$
24522 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
24525 \begin_layout Plain Layout
24533 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
24536 \begin_layout Plain Layout
24537 \begin_inset Formula $\models$
24547 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
24550 \begin_layout Plain Layout
24558 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
24561 \begin_layout Plain Layout
24562 \begin_inset Formula $\widehat{=}$
24576 \begin_inset space \hfill{}
24580 \begin_inset Tabular
24581 <lyxtabular version="3" rows="17" columns="2">
24582 <features tabularvalignment="middle">
24583 <column alignment="center" valignment="top" width="0pt">
24584 <column alignment="center" valignment="top" width="0pt">
24586 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
24589 \begin_layout Plain Layout
24595 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
24598 \begin_layout Plain Layout
24606 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
24609 \begin_layout Plain Layout
24615 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
24618 \begin_layout Plain Layout
24619 \begin_inset Formula $>$
24629 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
24632 \begin_layout Plain Layout
24640 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
24643 \begin_layout Plain Layout
24644 \begin_inset Formula $\ge$
24654 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
24657 \begin_layout Plain Layout
24665 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
24668 \begin_layout Plain Layout
24669 \begin_inset Formula $\gg$
24679 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
24682 \begin_layout Plain Layout
24690 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
24693 \begin_layout Plain Layout
24694 \begin_inset Formula $\succ$
24704 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
24707 \begin_layout Plain Layout
24715 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
24718 \begin_layout Plain Layout
24719 \begin_inset Formula $\succeq$
24729 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
24732 \begin_layout Plain Layout
24740 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
24743 \begin_layout Plain Layout
24744 \begin_inset Formula $\supset$
24754 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
24757 \begin_layout Plain Layout
24765 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
24768 \begin_layout Plain Layout
24769 \begin_inset Formula $\supseteq$
24779 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
24782 \begin_layout Plain Layout
24790 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
24793 \begin_layout Plain Layout
24794 \begin_inset Formula $\sqsupseteq$
24804 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
24807 \begin_layout Plain Layout
24815 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
24818 \begin_layout Plain Layout
24819 \begin_inset Formula $\ni$
24829 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
24832 \begin_layout Plain Layout
24840 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
24843 \begin_layout Plain Layout
24844 \begin_inset Formula $\dashv$
24854 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
24857 \begin_layout Plain Layout
24865 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
24868 \begin_layout Plain Layout
24869 \begin_inset Formula $\frown$
24879 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
24882 \begin_layout Plain Layout
24890 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
24893 \begin_layout Plain Layout
24894 \begin_inset Formula $\rhd$
24904 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
24907 \begin_layout Plain Layout
24915 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
24918 \begin_layout Plain Layout
24919 \begin_inset Formula $\unrhd$
24929 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
24932 \begin_layout Plain Layout
24940 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
24943 \begin_layout Plain Layout
24944 \begin_inset Formula $\lessgtr$
24954 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
24957 \begin_layout Plain Layout
24965 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
24968 \begin_layout Plain Layout
24969 \begin_inset Formula $\parallel$
24979 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
24982 \begin_layout Plain Layout
24990 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
24993 \begin_layout Plain Layout
24994 \begin_inset Formula $\nparallel$
25008 \begin_inset space \hfill{}
25014 \begin_layout Standard
25015 \begin_inset VSpace medskip
25030 are bigger than the equal looking operators
25045 \begin_layout Standard
25047 supports also many special relations.
25048 Use the toolbar button
25051 arg "math-insert \\leqq"
25054 to see a list of these relations.
25057 \begin_layout Standard
25058 Relations are, in contrary to symbols, always surrounded by space.
25061 \begin_layout Standard
25062 Relations with labels can be created with the command
25069 \begin_inset Index idx
25072 \begin_layout Plain Layout
25081 \begin_inset Separator parbreak
25087 \begin_layout Standard
25089 \begin_inset Tabular
25090 <lyxtabular version="3" rows="2" columns="2">
25091 <features tabularvalignment="middle">
25092 <column alignment="center" valignment="top">
25093 <column alignment="center" valignment="top">
25095 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
25098 \begin_layout Plain Layout
25104 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
25107 \begin_layout Plain Layout
25109 \begin_inset Note Note
25112 \begin_layout Plain Layout
25119 is only used as spacer.
25131 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
25134 \begin_layout Plain Layout
25138 \begin_inset space \textvisiblespace{}
25146 \begin_inset space \textvisiblespace{}
25150 \begin_inset Formula $\downarrow$
25156 \begin_inset space \textvisiblespace{}
25160 \begin_inset space \textvisiblespace{}
25168 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
25171 \begin_layout Plain Layout
25172 \begin_inset Formula $\raisebox{5mm}{}A(r)\stackrel{r\to\infty}{\approx}B$
25188 \begin_layout Section
25192 \begin_layout Subsection
25193 Predefined Functions
25194 \begin_inset CommandInset label
25196 name "subsec:Predefined-Functions"
25201 \begin_inset Index idx
25204 \begin_layout Plain Layout
25205 Functions ! predefined
25213 \begin_layout Standard
25214 In general, variables are set
25218 in mathematical expressions, but not function names, because
25219 \begin_inset Formula $sin$
25222 could be misunderstood as
25223 \begin_inset Formula $s\cdot i\cdot n$
25227 Therefore there are predefined functionswhich are additionally a bit separated
25229 They are inserted as commands starting with a backslash before their name.
25230 \begin_inset Separator parbreak
25236 \begin_layout Standard
25238 \begin_inset Tabular
25239 <lyxtabular version="3" rows="2" columns="4">
25240 <features tabularvalignment="middle">
25241 <column alignment="center" valignment="top" width="0pt">
25242 <column alignment="center" valignment="top" width="0pt">
25243 <column alignment="center" valignment="top" width="0pt">
25244 <column alignment="center" valignment="top" width="0pt">
25246 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
25249 \begin_layout Plain Layout
25255 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
25258 \begin_layout Plain Layout
25264 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
25267 \begin_layout Plain Layout
25273 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
25276 \begin_layout Plain Layout
25284 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
25287 \begin_layout Plain Layout
25293 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
25296 \begin_layout Plain Layout
25297 \begin_inset Formula $Asin(x)+B$
25305 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
25308 \begin_layout Plain Layout
25316 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
25319 \begin_layout Plain Layout
25320 \begin_inset Formula $A\sin(x)+B$
25336 \begin_layout Standard
25337 The following functions are predefined:
25340 \begin_layout Standard
25341 \begin_inset VSpace -2mm
25347 \begin_layout Standard
25349 \begin_inset Tabular
25350 <lyxtabular version="3" rows="9" columns="4">
25351 <features tabularvalignment="middle">
25352 <column alignment="center" valignment="top" width="0pt">
25353 <column alignment="center" valignment="top" width="0pt">
25354 <column alignment="center" valignment="top" width="0pt">
25355 <column alignment="center" valignment="top" width="0pt">
25357 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
25360 \begin_layout Plain Layout
25366 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
25369 \begin_layout Plain Layout
25375 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
25378 \begin_layout Plain Layout
25384 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
25387 \begin_layout Plain Layout
25395 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
25398 \begin_layout Plain Layout
25406 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
25409 \begin_layout Plain Layout
25417 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
25420 \begin_layout Plain Layout
25428 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
25431 \begin_layout Plain Layout
25441 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
25444 \begin_layout Plain Layout
25452 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
25455 \begin_layout Plain Layout
25463 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
25466 \begin_layout Plain Layout
25474 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
25477 \begin_layout Plain Layout
25487 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
25490 \begin_layout Plain Layout
25498 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
25501 \begin_layout Plain Layout
25509 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
25512 \begin_layout Plain Layout
25520 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
25523 \begin_layout Plain Layout
25533 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
25536 \begin_layout Plain Layout
25544 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
25547 \begin_layout Plain Layout
25555 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
25558 \begin_layout Plain Layout
25566 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
25569 \begin_layout Plain Layout
25579 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
25582 \begin_layout Plain Layout
25590 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
25593 \begin_layout Plain Layout
25601 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
25604 \begin_layout Plain Layout
25612 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
25615 \begin_layout Plain Layout
25625 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
25628 \begin_layout Plain Layout
25636 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
25639 \begin_layout Plain Layout
25647 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
25650 \begin_layout Plain Layout
25658 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
25661 \begin_layout Plain Layout
25671 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
25674 \begin_layout Plain Layout
25682 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
25685 \begin_layout Plain Layout
25693 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
25696 \begin_layout Plain Layout
25704 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
25707 \begin_layout Plain Layout
25717 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
25720 \begin_layout Plain Layout
25728 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
25731 \begin_layout Plain Layout
25739 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
25742 \begin_layout Plain Layout
25750 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
25753 \begin_layout Plain Layout
25769 \begin_layout Standard
25770 They can also be inserted with the math toolbar button
25773 arg "math-insert \\functions"
25779 \begin_layout Subsection
25780 Self-defined Functions
25781 \begin_inset Index idx
25784 \begin_layout Plain Layout
25785 Functions ! self-defined
25793 \begin_layout Standard
25794 To use a function that is not predefined, like for example the sign function
25795 sgn(x), there are two possibilities:
25798 \begin_layout Itemize
25799 Define the function by inserting the following line to the \SpecialChar LaTeX
25804 \begin_layout Plain Layout
25809 DeclareMathOperator
25812 \begin_inset CommandInset ref
25814 reference "subsec:Self-defined-Operators"
25824 \begin_inset Newline newline
25828 \begin_inset VSpace -3mm
25832 \begin_inset Newline newline
25839 DeclareMathOperator{
25844 \begin_inset Index idx
25847 \begin_layout Plain Layout
25852 DeclareMathOperator
25858 \begin_inset Newline newline
25862 \begin_inset VSpace -2mm
25866 \begin_inset Newline newline
25869 Now the new defined function can be called with the command
25878 \begin_layout Itemize
25879 Write the formula as usual, mark the formula name, in our example the letters
25884 , and change it to mathematical text.
25885 Finally, a space is inserted between prefactor and function.
25888 \begin_layout Standard
25889 The result is the same with both methods as with a predefined function
25893 \begin_layout Plain Layout
25894 In \SpecialChar LyX
25895 self-defined functions are displayed red, predefined ones black.
25901 \begin_inset Separator parbreak
25907 \begin_layout Standard
25909 \begin_inset Tabular
25910 <lyxtabular version="3" rows="3" columns="2">
25911 <features tabularvalignment="middle">
25912 <column alignment="center" valignment="top" width="0pt">
25913 <column alignment="center" valignment="top" width="0pt">
25915 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
25918 \begin_layout Plain Layout
25924 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
25927 \begin_layout Plain Layout
25935 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
25938 \begin_layout Plain Layout
25946 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
25949 \begin_layout Plain Layout
25950 \begin_inset Formula $A\sgn(x)+B$
25960 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
25963 \begin_layout Plain Layout
25967 \begin_inset Formula $\underbrace{\textrm{sgn}}_{\textrm{Alt+M}\,\textrm{M}}$
25975 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
25978 \begin_layout Plain Layout
25979 \begin_inset Formula $A\,\textrm{sgn}(x)+B$
25995 \begin_layout Standard
25996 The first method is more suitable when the self-defined function should
25997 be used several times.
26000 \begin_layout Subsection
26002 \begin_inset Index idx
26005 \begin_layout Plain Layout
26014 \begin_layout Standard
26015 For limits, in addition to the commands
26022 \begin_inset Index idx
26025 \begin_layout Plain Layout
26045 the following functions are defined:
26046 \begin_inset Separator parbreak
26052 \begin_layout Standard
26054 \begin_inset Tabular
26055 <lyxtabular version="3" rows="5" columns="2">
26056 <features tabularvalignment="middle">
26057 <column alignment="center" valignment="top">
26058 <column alignment="center" valignment="top">
26060 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
26063 \begin_layout Plain Layout
26069 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
26072 \begin_layout Plain Layout
26074 \begin_inset Note Note
26077 \begin_layout Plain Layout
26084 is only used as spacer.
26096 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
26099 \begin_layout Plain Layout
26107 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
26110 \begin_layout Plain Layout
26111 \begin_inset Formula $\varliminf$
26121 <cell alignment="center" valignment="top" leftline="true" usebox="none">
26124 \begin_layout Plain Layout
26132 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
26135 \begin_layout Plain Layout
26136 \begin_inset Formula $\varlimsup$
26146 <cell alignment="center" valignment="top" leftline="true" usebox="none">
26149 \begin_layout Plain Layout
26157 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
26160 \begin_layout Plain Layout
26161 \begin_inset Formula $\varprojlim$
26171 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
26174 \begin_layout Plain Layout
26182 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
26185 \begin_layout Plain Layout
26186 \begin_inset Formula $\varinjlim$
26190 \begin_inset Formula $\raisebox{-2.5mm}{}$
26206 \begin_layout Standard
26207 \begin_inset VSpace medskip
26210 The limit is created by inserting a subscript.
26211 It is set right beside the function in an inline formula:
26214 \begin_layout Standard
26216 \begin_inset Tabular
26217 <lyxtabular version="3" rows="2" columns="2">
26218 <features tabularvalignment="middle">
26219 <column alignment="center" valignment="top" width="0pt">
26220 <column alignment="center" valignment="top" width="0pt">
26222 <cell alignment="center" valignment="top" usebox="none">
26225 \begin_layout Plain Layout
26231 <cell alignment="center" valignment="top" usebox="none">
26234 \begin_layout Plain Layout
26235 \begin_inset space \hspace{}
26240 \begin_inset Note Note
26243 \begin_layout Plain Layout
26250 are used here as spacer.
26262 <cell alignment="center" valignment="top" usebox="none">
26265 \begin_layout Plain Layout
26271 \begin_inset space \textvisiblespace{}
26275 \begin_inset space \textvisiblespace{}
26283 <cell alignment="center" valignment="top" usebox="none">
26286 \begin_layout Plain Layout
26287 \begin_inset Formula $\hspace{1cm}\raisebox{5mm}{}\lim_{x\to A}x=B$
26303 \begin_layout Standard
26304 In a displayed formula the limit is set below the formula, as usual:
26305 \begin_inset Formula
26315 \begin_layout Standard
26316 \begin_inset VSpace medskip
26322 \begin_layout Standard
26323 How to adjust the typesetting of the limits see
26324 \begin_inset CommandInset ref
26326 reference "subsec:Operator-Limits"
26333 \begin_layout Subsection
26335 \begin_inset Index idx
26338 \begin_layout Plain Layout
26339 Functions ! modulo-
26347 \begin_layout Standard
26348 The modulo-function is special, because it exists in four variants.
26349 The variants in a displayed formula are:
26350 \begin_inset Formula
26352 \underline{\textrm{Command}\raisebox{-0.9mm}{}} & & \underline{\textrm{Result}}\\
26353 \mathrm{a\backslash mod\textrm{␣}b} & & a\mod b\\
26354 \mathrm{a\backslash pmod\textrm{␣}b} & & a\pmod b\\
26355 \mathrm{a\backslash bmod\textrm{␣}b} & & a\bmod b\\
26356 \mathrm{a\backslash pod\textrm{␣}b} & & a\pod b
26364 \begin_layout Standard
26365 In an inline formula less space is set before the function names for all
26367 By default the modulo-functions take only the first following character
26369 To use more than one character, one has to put them into \SpecialChar TeX
26371 \begin_inset Formula
26373 \underline{\textrm{Command}\raisebox{-0.9mm}{}} & & \underline{\textrm{Result}}\\
26374 \mathrm{a\backslash pod\textrm{␣}bcd} & & a\pod bcd\\
26375 \mathrm{a\backslash pod\backslash\{bc\to d} & & a\pod{bc}d
26383 \begin_layout Section
26385 \begin_inset Index idx
26388 \begin_layout Plain Layout
26397 \begin_layout Standard
26398 The characters ^ and _ would normally create a superscript and subscript,
26400 To get these characters you have to insert them with a leading
26403 \begin_inset Separator parbreak
26409 \begin_layout Standard
26412 \begin_inset Tabular
26413 <lyxtabular version="3" rows="3" columns="2">
26414 <features tabularvalignment="middle">
26415 <column alignment="block" valignment="top">
26416 <column alignment="block" valignment="top">
26418 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
26421 \begin_layout Plain Layout
26427 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
26430 \begin_layout Plain Layout
26438 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
26441 \begin_layout Plain Layout
26445 \begin_inset space \textvisiblespace{}
26453 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
26456 \begin_layout Plain Layout
26457 \begin_inset Formula $\mathcircumflex$
26467 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
26470 \begin_layout Plain Layout
26478 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
26481 \begin_layout Plain Layout
26482 \begin_inset Formula $\_$
26498 \begin_layout Subsection
26499 Special Characters in Mathematical Text
26502 \begin_layout Standard
26503 The following commands can only be used in mathematical text or in \SpecialChar TeX
26507 \begin_layout Standard
26508 \begin_inset space \hfill{}
26512 \begin_inset Tabular
26513 <lyxtabular version="3" rows="8" columns="2">
26514 <features tabularvalignment="middle">
26515 <column alignment="block" valignment="top">
26516 <column alignment="block" valignment="top">
26518 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
26521 \begin_layout Plain Layout
26527 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
26530 \begin_layout Plain Layout
26538 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
26541 \begin_layout Plain Layout
26549 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
26552 \begin_layout Plain Layout
26553 \begin_inset Formula $\textrm{œ}$
26563 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
26566 \begin_layout Plain Layout
26574 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
26577 \begin_layout Plain Layout
26578 \begin_inset Formula $\textrm{Œ}$
26588 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
26591 \begin_layout Plain Layout
26599 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
26602 \begin_layout Plain Layout
26603 \begin_inset Formula $\textrm{æ}$
26613 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
26616 \begin_layout Plain Layout
26624 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
26627 \begin_layout Plain Layout
26628 \begin_inset Formula $\textrm{Æ}$
26638 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
26641 \begin_layout Plain Layout
26649 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
26652 \begin_layout Plain Layout
26653 \begin_inset Formula $\textrm{\aa}$
26663 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
26666 \begin_layout Plain Layout
26670 \begin_inset Index idx
26673 \begin_layout Plain Layout
26680 \begin_layout Plain Layout
26701 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
26704 \begin_layout Plain Layout
26705 \begin_inset Formula $\textrm{Å}$
26715 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
26718 \begin_layout Plain Layout
26726 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
26729 \begin_layout Plain Layout
26730 \begin_inset Formula $\textrm{ı}$
26744 \begin_inset space \hfill{}
26748 \begin_inset Tabular
26749 <lyxtabular version="3" rows="8" columns="2">
26750 <features tabularvalignment="middle">
26751 <column alignment="block" valignment="top">
26752 <column alignment="center" valignment="top">
26754 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
26757 \begin_layout Plain Layout
26759 \begin_inset Note Note
26762 \begin_layout Plain Layout
26764 \begin_inset space \thinspace{}
26767 mm is used for separation, because otherwise the output will be ¡ and ¿
26778 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
26781 \begin_layout Plain Layout
26789 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
26792 \begin_layout Plain Layout
26800 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
26803 \begin_layout Plain Layout
26804 \begin_inset Formula $\textrm{ø}$
26814 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
26817 \begin_layout Plain Layout
26825 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
26828 \begin_layout Plain Layout
26829 \begin_inset Formula $\textrm{Ø}$
26839 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
26842 \begin_layout Plain Layout
26850 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
26853 \begin_layout Plain Layout
26854 \begin_inset Formula $\textrm{ł}$
26864 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
26867 \begin_layout Plain Layout
26875 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
26878 \begin_layout Plain Layout
26879 \begin_inset Formula $\textrm{Ł}$
26889 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
26892 \begin_layout Plain Layout
26894 \begin_inset space \hspace{}
26899 \begin_inset space \textvisiblespace{}
26907 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
26910 \begin_layout Plain Layout
26911 \begin_inset Formula $\textrm{!`}$
26921 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
26924 \begin_layout Plain Layout
26926 \begin_inset space \hspace{}
26931 \begin_inset space \textvisiblespace{}
26939 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
26942 \begin_layout Plain Layout
26943 \begin_inset Formula $\textrm{?`}$
26953 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
26956 \begin_layout Plain Layout
26964 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
26967 \begin_layout Plain Layout
26968 \begin_inset Formula $\textrm{ȷ}$
26982 \begin_inset space \hfill{}
26988 \begin_layout Standard
26990 \begin_inset Formula $\textrm{\textrm{Å}}$
26994 \begin_inset Formula $\textrm{\textrm{Ø}}$
26997 can also be inserted via the math toolbar button
27000 arg "math-insert \\digamma"
27006 \begin_layout Standard
27007 An exception are the commands
27010 \begin_inset space \hspace{}
27019 \begin_inset space \hspace{}
27025 , because they can be inserted in \SpecialChar LyX
27029 \begin_layout Subsection
27031 \begin_inset CommandInset label
27033 name "subsec:Accents-in-Text"
27038 \begin_inset Index idx
27041 \begin_layout Plain Layout
27050 \begin_layout Standard
27051 With the following commands all letters can be accented.
27052 The commands must be inserted in \SpecialChar TeX
27056 \begin_layout Standard
27057 \begin_inset space \hfill{}
27061 \begin_inset Tabular
27062 <lyxtabular version="3" rows="8" columns="2">
27063 <features tabularvalignment="middle">
27064 <column alignment="block" valignment="top">
27065 <column alignment="block" valignment="top">
27067 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
27070 \begin_layout Plain Layout
27076 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
27079 \begin_layout Plain Layout
27087 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
27090 \begin_layout Plain Layout
27094 \begin_inset Quotes grd
27102 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
27105 \begin_layout Plain Layout
27109 \begin_layout Plain Layout
27125 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
27128 \begin_layout Plain Layout
27136 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
27139 \begin_layout Plain Layout
27143 \begin_layout Plain Layout
27159 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
27162 \begin_layout Plain Layout
27166 \begin_inset space \textvisiblespace{}
27174 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
27177 \begin_layout Plain Layout
27181 \begin_layout Plain Layout
27197 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
27200 \begin_layout Plain Layout
27208 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
27211 \begin_layout Plain Layout
27215 \begin_layout Plain Layout
27231 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
27234 \begin_layout Plain Layout
27238 \begin_inset space \textvisiblespace{}
27246 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
27249 \begin_layout Plain Layout
27253 \begin_layout Plain Layout
27269 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
27272 \begin_layout Plain Layout
27276 \begin_inset space \textvisiblespace{}
27284 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
27287 \begin_layout Plain Layout
27291 \begin_layout Plain Layout
27307 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
27310 \begin_layout Plain Layout
27314 \begin_inset space \textvisiblespace{}
27322 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
27325 \begin_layout Plain Layout
27329 \begin_layout Plain Layout
27349 \begin_inset space \hfill{}
27353 \begin_inset Tabular
27354 <lyxtabular version="3" rows="8" columns="2">
27355 <features tabularvalignment="middle">
27356 <column alignment="block" valignment="top">
27357 <column alignment="center" valignment="top">
27359 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
27362 \begin_layout Plain Layout
27368 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
27371 \begin_layout Plain Layout
27379 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
27382 \begin_layout Plain Layout
27386 \begin_inset space \textvisiblespace{}
27394 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
27397 \begin_layout Plain Layout
27401 \begin_layout Plain Layout
27417 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
27420 \begin_layout Plain Layout
27428 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
27431 \begin_layout Plain Layout
27435 \begin_layout Plain Layout
27451 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
27454 \begin_layout Plain Layout
27458 \begin_inset Index idx
27461 \begin_layout Plain Layout
27472 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
27475 \begin_layout Plain Layout
27479 \begin_layout Plain Layout
27495 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
27498 \begin_layout Plain Layout
27506 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
27509 \begin_layout Plain Layout
27513 \begin_layout Plain Layout
27529 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
27532 \begin_layout Plain Layout
27536 \begin_inset space \textvisiblespace{}
27544 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
27547 \begin_layout Plain Layout
27551 \begin_layout Plain Layout
27567 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
27570 \begin_layout Plain Layout
27574 \begin_inset space \textvisiblespace{}
27582 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
27585 \begin_layout Plain Layout
27589 \begin_layout Plain Layout
27605 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
27608 \begin_layout Plain Layout
27612 \begin_inset space \textvisiblespace{}
27620 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
27623 \begin_layout Plain Layout
27627 \begin_layout Plain Layout
27647 \begin_inset space \hfill{}
27653 \begin_layout Standard
27654 \begin_inset VSpace medskip
27663 also two different characters can be accented.
27669 \begin_inset space \textvisiblespace{}
27678 \begin_layout Plain Layout
27690 \begin_layout Standard
27703 can in combination with vowels directly be inserted with the keyboard without
27704 using \SpecialChar TeX
27706 The same applies for the tilde
27710 \begin_layout Plain Layout
27711 This only applies for keyboards where the tilde is defined as accent.
27720 in combination with
27735 \begin_layout Standard
27778 and accents that are inserted directly with the keyboard are also available
27779 in mathematical text.
27780 For the other accents there are special math commands to be used in formulas,
27782 \begin_inset CommandInset ref
27784 reference "subsec:Accents-for-one"
27791 \begin_layout Standard
27792 \begin_inset VSpace bigskip
27795 Furthermore, with the command
27802 \begin_inset Index idx
27805 \begin_layout Plain Layout
27813 all numbers and letters can be set into a circle, quasi accented with a
27814 circle, similar to the copyright symbol.
27817 \begin_layout Standard
27819 \begin_inset Tabular
27820 <lyxtabular version="3" rows="3" columns="2">
27821 <features tabularvalignment="middle">
27822 <column alignment="center" valignment="top">
27823 <column alignment="center" valignment="top">
27825 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
27828 \begin_layout Plain Layout
27834 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
27837 \begin_layout Plain Layout
27839 \begin_inset Note Note
27842 \begin_layout Plain Layout
27849 is only used as spacer.
27861 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
27864 \begin_layout Plain Layout
27872 <cell multicolumn="1" alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
27875 \begin_layout Plain Layout
27879 \begin_layout Plain Layout
27895 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
27898 \begin_layout Plain Layout
27909 raisebox{-1.5pt}{W}}
27914 <cell multicolumn="1" alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
27917 \begin_layout Plain Layout
27918 \begin_inset Formula $\raisebox{4.5mm}{}$
27925 \begin_layout Plain Layout
27943 \begin_inset Formula $\raisebox{-2mm}{}$
27959 \begin_layout Standard
27960 One has to take care that the character fits in the circle.
27971 \begin_layout Plain Layout
27973 \begin_inset CommandInset ref
27975 reference "subsec:Font-Sizes"
27984 specifies thereby the size of the circle.
27995 \begin_layout Plain Layout
27997 \begin_inset CommandInset ref
27999 reference "subsec:Boxes-without-Frame"
28008 the character can be centered.
28011 \begin_layout Subsection
28013 \begin_inset Index idx
28016 \begin_layout Plain Layout
28025 \begin_layout Standard
28026 Old-style figures (also known as old-style numerals) are created with the
28034 \begin_inset Index idx
28037 \begin_layout Plain Layout
28046 The command can be used in formulas and in \SpecialChar TeX
28048 The command scheme is:
28051 \begin_layout Standard
28056 oldstylenums{number}
28059 \begin_layout Standard
28064 oldstylenums{0123456789
28067 \begin_inset Formula $\oldstylenums{0123456789}$
28073 \begin_layout Section
28075 \begin_inset CommandInset label
28077 name "sec:Formula-Styles"
28082 \begin_inset Index idx
28085 \begin_layout Plain Layout
28094 \begin_layout Itemize
28095 There are two different alignment styles:
28096 \begin_inset Separator parbreak
28103 \begin_layout Description
28104 Centered is the predefined standard
28107 \begin_layout Description
28108 Indented for this the option
28112 must be inserted in the menu
28114 Document\SpecialChar menuseparator
28120 \begin_inset space ~
28126 \begin_layout Standard
28131 is used, the indentation can be adjusted with the length
28138 \begin_inset Index idx
28141 \begin_layout Plain Layout
28150 Should the distance be 15
28151 \begin_inset space \thinspace{}
28154 mm, the following command line is inserted in the \SpecialChar LaTeX
28158 \begin_layout Standard
28168 \begin_layout Standard
28169 When no length is specified, the predefined value of 30
28170 \begin_inset space \thinspace{}
28177 \begin_layout Itemize
28178 And two different numbering styles:
28179 \begin_inset Separator parbreak
28186 \begin_layout Description
28187 Right is the predefined standard
28190 \begin_layout Description
28191 Left for this the option
28195 must be inserted in the menu
28197 Document\SpecialChar menuseparator
28203 \begin_inset space ~
28210 \begin_layout Standard
28219 can also be used together.
28220 In this case both options are inserted, separated by a comma.
28223 \begin_layout Standard
28224 The chosen styles are used for all displayed formulas of the document.
28225 When both, centered and indented formulas should be created in a document,
28231 The indented formulas are then set in a flalign environment, see
28232 \begin_inset CommandInset ref
28234 reference "subsec:Flalign-Environment"
28241 \begin_layout Section
28243 \begin_inset CommandInset label
28245 name "sec:Multiline-Formulas"
28250 \begin_inset Index idx
28253 \begin_layout Plain Layout
28254 Formula ! multiline
28262 \begin_layout Subsection
28266 \begin_layout Standard
28267 In \SpecialChar LyX
28268 multiline formulas are created by pressing
28271 arg "newline-insert newline"
28275 This creates either an
28277 eqnarray environment
28279 that is described in
28280 \begin_inset CommandInset ref
28282 reference "subsec:Eqnarray-Environment"
28286 or, when the option
28288 Use AMS math package
28290 in the document settings is selected, an
28294 that is described in
28295 \begin_inset CommandInset ref
28297 reference "subsec:Standard-align-Environment"
28302 The align environment is recommended because it provides in any case a
28303 typographically correct output.
28306 \begin_layout Standard
28307 There are other multiline formula environments that can be created via the
28310 Insert\SpecialChar menuseparator
28314 These environments are described in the following sections.
28317 \begin_layout Standard
28318 In all multiline formula environments a new line is created by pressing
28322 arg "newline-insert newline"
28326 To add or delete lines, the math toolbar buttons
28329 arg "inset-modify tabular append-row"
28335 arg "inset-modify tabular delete-row"
28338 , respectively, or the menu
28340 Edit\SpecialChar menuseparator
28346 \begin_layout Subsubsection
28348 \begin_inset CommandInset label
28350 name "subsec:Line-Separation"
28355 \begin_inset Index idx
28358 \begin_layout Plain Layout
28359 Formula ! multiline ! Line separation
28367 \begin_layout Standard
28368 There is sometimes not enough space in multiline formulas between the lines:
28369 \begin_inset Formula
28371 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}\\
28372 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
28380 \begin_layout Standard
28381 In \SpecialChar LaTeX
28382 additional line space is specified as optional argument of the new line
28384 This is not yet possible in \SpecialChar LyX
28389 \begin_layout Plain Layout
28391 \begin_inset CommandInset href
28393 name "LyX-bug #1505"
28394 target "http://www.lyx.org/trac/ticket/1505"
28403 , therefore the whole formula must be inserted in \SpecialChar TeX
28405 To add in our example space, the command
28413 is inserted at the end of the first line.
28418 \begin_layout Plain Layout
28425 \begin_layout Plain Layout
28427 B^{2}(B^{2}-2r_{g}^{2}+2x_{0}^{2}-2r_{k}^{2})+4x_{0}^{2}x^{2}+4x_{0}xD &
28430 textrm{-}4x^{2}B^{2}+4x_{0}xB^{2}
28437 \begin_layout Plain Layout
28441 left(B^{2}+x_{0}^{2}
28449 left(B^{2}-2r_{g}^{2}+2x_{0}^{2}-2r_{k}^{2}
28454 \begin_layout Plain Layout
28466 \begin_layout Standard
28467 \begin_inset VSpace bigskip
28470 To set the line separation for all lines in a formula, the length
28477 \begin_inset Index idx
28480 \begin_layout Plain Layout
28490 \begin_inset Formula $\mbox{line separation}=\mathrm{6\,pt+\backslash jot}$
28501 \begin_inset space \thinspace{}
28506 \begin_inset space \thinspace{}
28509 mm additional line separation as in the previous example, the command
28512 \begin_layout Standard
28522 \begin_layout Standard
28523 is inserted in \SpecialChar TeX
28524 mode before the formula.
28525 This requires that the \SpecialChar LaTeX
28534 \begin_layout Plain Layout
28539 is part of every \SpecialChar LaTeX
28540 standard installation.
28546 \begin_inset Index idx
28549 \begin_layout Plain Layout
28555 was loaded in \SpecialChar LaTeX
28556 -preamble with the line
28559 \begin_layout Standard
28567 \begin_layout Standard
28572 \begin_layout Plain Layout
28584 \begin_inset Formula
28586 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}\\
28587 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
28595 \begin_layout Standard
28599 \begin_layout Plain Layout
28610 To get back to the predefined distance,
28616 is set to the value 3
28617 \begin_inset space \thinspace{}
28623 \begin_layout Subsubsection
28625 \begin_inset CommandInset label
28627 name "subsec:Column-Separation"
28632 \begin_inset Index idx
28635 \begin_layout Plain Layout
28636 Formula ! multiline ! Column separation
28644 \begin_layout Standard
28645 Multiline formulas form a matrix.
28646 A formula in the eqnarray environment is for example a matrix with three
28648 By changing the column separation in this environment, the space beside
28649 the relation sign can be changed.
28652 \begin_layout Standard
28653 The column separation is specified with the length
28660 \begin_inset Index idx
28663 \begin_layout Plain Layout
28672 \begin_inset Newline newline
28675 column separation = 2
28676 \begin_inset space \thinspace{}
28686 \begin_inset Newline newline
28692 \begin_layout Standard
28702 \begin_layout Standard
28703 inserted in \SpecialChar TeX
28704 mode, sets for all following formulas a column separation of
28706 \begin_inset space \thinspace{}
28710 To get back to the predefined distance,
28717 \begin_inset space \thinspace{}
28723 \begin_layout Standard
28725 \begin_inset space \thinspace{}
28728 cm column separation:
28732 \begin_layout Plain Layout
28744 \begin_inset Formula
28752 A formula with the predefined column separation for matrices of 10
28753 \begin_inset space \thinspace{}
28760 \begin_layout Plain Layout
28772 \begin_inset Formula
28783 \begin_layout Subsubsection
28785 \begin_inset Index idx
28788 \begin_layout Plain Layout
28797 \begin_layout Standard
28798 Long formulas can be typeset using these methods:
28801 \begin_layout Itemize
28802 When one side of the equation is much shorter than the line width, this
28803 one is chosen for the left side and the right side is typeset over two
28805 \begin_inset Formula
28807 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 \\
28808 & & -\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}
28813 The minus sign at the beginning of the second line does normally not appear
28814 as an operator because it is the first character of the line.
28815 Thus it would not be surrounded by space and could not be distinguished
28816 from the fraction bar.
28818 \begin_inset space \thinspace{}
28821 pt space was inserted behind the minus sign with the command
28831 \begin_layout Plain Layout
28839 \begin_inset CommandInset ref
28841 reference "subsec:Variable-Space"
28851 \begin_inset Index idx
28854 \begin_layout Plain Layout
28865 \begin_layout Itemize
28866 When both sides of the equation are too long, the command
28873 \begin_inset Index idx
28876 \begin_layout Plain Layout
28885 It is inserted in the first column of the first line and causes all further
28886 insertions to overwrite the following columns:
28887 \begin_inset Formula
28889 \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 \\
28890 & & -\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 \\
28891 & & =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}
28896 After the insertion of
28902 , the cursor is in a purple box that is a bit shifted to the left from the
28904 In this the formula is inserted.
28905 \begin_inset Newline newline
28908 The content of the further lines is inserted to the second or another formula
28910 The greater the column number where it was inserted, the larger the indentation.
28911 \begin_inset VSpace medskip
28915 \begin_inset Newline newline
28919 \begin_inset Note Greyedout
28922 \begin_layout Plain Layout
28923 Note the following when using
28932 \begin_layout Itemize
28933 The formula doesn't use the full page width.
28935 \begin_inset space \thinspace{}
28939 \begin_inset space \space{}
28943 \begin_inset Formula $-B^{2}$
28946 is added to the first line in the above example, it would have been outside
28948 To better use the width, negative space can be inserted at the beginning
28952 \begin_layout Itemize
28953 Due to a bug in \SpecialChar LyX
28954 the cursor cannot be set with the mouse into the first
28959 \begin_layout Plain Layout
28960 \begin_inset CommandInset href
28962 name "LyX-bug #1429"
28963 target "http://www.lyx.org/trac/ticket/1429"
28972 One can only set the cursor at the beginning of the line and move it with
28981 \begin_layout Itemize
28982 Other methods to set long formulas are offered by the environments described
28984 \begin_inset CommandInset ref
28986 reference "subsec:Multline-Environment"
28991 \begin_inset CommandInset ref
28993 reference "subsec:Multiline-Formula-Parts"
29000 \begin_layout Subsubsection
29001 Multiline Fractions
29002 \begin_inset CommandInset label
29004 name "subsec:Multiline-Fractions"
29009 \begin_inset Index idx
29012 \begin_layout Plain Layout
29013 Fractions ! multiline
29021 \begin_layout Standard
29022 There are cases where the denominator and/or the numerator of a fraction
29023 is so long that the fraction does not fit into one line.
29024 It is then necessary to add a line break within the fraction.
29025 This can be done using the command
29032 \begin_inset Index idx
29035 \begin_layout Plain Layout
29044 To activate it, set in the document settings under
29047 \begin_inset space ~
29057 \begin_inset Index idx
29060 \begin_layout Plain Layout
29061 Packages ! mathtools
29069 \begin_inset space ~
29084 \begin_layout Standard
29089 splitfrac{first line}{second line}
29092 \begin_layout Standard
29093 and is used as denominator and/or numerator:
29096 \begin_layout Standard
29097 \begin_inset Formula
29099 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}
29104 The command for the first numerator above is:
29107 \begin_layout Standard
29112 splitfrac{xy+xy+xy+xy+xy
29113 \begin_inset space \textvisiblespace{}
29121 \begin_layout Subsubsection
29123 \begin_inset CommandInset label
29125 name "subsec:Multiline-Brackets"
29130 \begin_inset Index idx
29133 \begin_layout Plain Layout
29134 Brackets ! for multiline expressions
29142 \begin_layout Standard
29143 For brackets spanning multiple lines the following problem occurs:
29144 \begin_inset Formula
29146 A & = & \sin(x)\left[\prod_{R=1}^{\infty}\frac{1}{R}+\cdots\right.\\
29147 & & \left.\cdots+B-D\right]
29155 \begin_layout Standard
29156 The closing bracket is smaller than the opening bracket because brackets
29157 with variable size may not span multiple lines.
29160 \begin_layout Standard
29161 To set the bracket size for the second line correctly, the first line is
29169 \begin_inset Index idx
29172 \begin_layout Plain Layout
29180 and the second line with
29188 \begin_layout Plain Layout
29202 \begin_inset CommandInset ref
29204 reference "subsec:Automatic-Bracket-Size"
29216 \begin_inset Index idx
29219 \begin_layout Plain Layout
29242 \begin_inset space \textvisiblespace{}
29252 \begin_inset space \textvisiblespace{}
29262 \begin_inset space \textvisiblespace{}
29268 \begin_inset Formula $\downarrow$
29274 \begin_inset Index idx
29277 \begin_layout Plain Layout
29285 is inserted, because the multiplication operator with its limits is the
29286 largest symbol in the first line and this should be the size for the bracket
29287 in the second line.
29290 \begin_layout Standard
29291 The result is this:
29292 \begin_inset Formula
29294 A & = & \sin(x)\left[\prod_{R=1}^{\infty}\frac{1}{R}+\cdots\right.\\
29295 & & \left.\vphantom{\prod_{R=1}^{\infty}}\cdots+B-D\right]
29303 \begin_layout Subsection
29307 \begin_layout Standard
29308 Align environments can be used for every kind of multiline formulas.
29309 They are especially useful to set several formulas side by side.
29312 \begin_layout Standard
29313 Align environments consist of columns.
29314 The odd columns are right aligned, the even ones left aligned.
29315 Every line in an Align environment can be numbered.
29318 \begin_layout Standard
29319 Align environments are created via the menu
29321 Insert\SpecialChar menuseparator
29327 Edit\SpecialChar menuseparator
29328 Math\SpecialChar menuseparator
29329 Change Formula Type
29331 already existing formulas can be converted to Align environments.
29334 \begin_layout Standard
29335 To add or delete columns, the math toolbar buttons
29338 arg "inset-modify tabular append-column"
29344 arg "inset-modify tabular delete-column"
29347 , respectively, or the menu
29349 Edit\SpecialChar menuseparator
29355 \begin_layout Subsubsection
29356 Standard align Environment
29357 \begin_inset CommandInset label
29359 name "subsec:Standard-align-Environment"
29364 \begin_inset Index idx
29367 \begin_layout Plain Layout
29368 Formula ! multiline ! align environment
29376 \begin_layout Standard
29377 This Align environment is created by pressing
29380 arg "newline-insert newline"
29383 in a formula or by the menu
29385 Insert\SpecialChar menuseparator
29386 Math\SpecialChar menuseparator
29387 AMS align Environment
29392 \begin_layout Standard
29393 An example for two formulas set side by side, that are created with a four
29394 column align environment:
29395 \begin_inset Formula
29397 A & =\sin(B) & C & =D\\
29398 C & \ne A & B & \ne D
29403 As it can be seen, the formulas in this environment are placed so as if
29412 \begin_layout Plain Layout
29420 \begin_inset CommandInset ref
29422 reference "subsec:Variable-Space"
29433 before the first and after every even column.
29434 When the formula style
29440 \begin_layout Plain Layout
29442 \begin_inset CommandInset ref
29444 reference "sec:Formula-Styles"
29455 is used, the formula is set without the
29461 before the first column.
29464 \begin_layout Subsubsection
29465 Alignat Environment
29466 \begin_inset Index idx
29469 \begin_layout Plain Layout
29470 Formula ! multiline ! alignat environment
29478 \begin_layout Standard
29479 The alignat environment has no predefined column separation.
29480 It can be inserted manually with the spaces that are described
29481 \begin_inset CommandInset ref
29483 reference "subsec:Space"
29490 \begin_layout Standard
29491 The above example in the alignat environment where 1
29492 \begin_inset space \thinspace{}
29495 cm space was inserted at the beginning of the second formula:
29496 \begin_inset Formula
29497 \begin{alignat*}{2}
29498 A & =\sin(B) & \hspace{1cm}C & =D\\
29499 C & \ne A & B & \ne D
29504 Because the column separation can be set separately for every column, this
29505 environment is especially suitable to set three and more formulas side
29509 \begin_layout Subsubsection
29510 Flalign Environment
29511 \begin_inset CommandInset label
29513 name "subsec:Flalign-Environment"
29518 \begin_inset Index idx
29521 \begin_layout Plain Layout
29522 Formula ! multiline ! flalign environment
29530 \begin_layout Standard
29531 In this environment the first two columns are always set as much as possible
29532 to the left and the last two ones to the right.
29534 \begin_inset Formula
29536 A & =1 & B & =2 & C & =3\\
29537 X & =\textrm{-}1 & Y & =\textrm{-}2 & Z & =4
29545 \begin_layout Standard
29546 By creating a flalign environment with an odd number of columns where an
29547 empty \SpecialChar TeX
29548 brace is inserted to the last column, several formulas in a document
29549 can be set to the left, although the formula style
29554 As example the indented formula
29555 \begin_inset CommandInset ref
29557 reference "eq:VolInt"
29562 \begin_inset Formula
29564 \hspace{30pt}\iiint\limits _{V}X\,\mathrm{d}V & =U & {}
29569 The first two columns contain the formula.
29570 To indent it as with the formula style
29575 \begin_inset space \thinspace{}
29578 pt space was inserted at the beginning of the first column.
29581 \begin_layout Subsection
29582 Eqnarray Environment
29583 \begin_inset CommandInset label
29585 name "subsec:Eqnarray-Environment"
29590 \begin_inset Index idx
29593 \begin_layout Plain Layout
29594 Formula ! multiline ! eqnarray environment
29602 \begin_layout Standard
29603 When this environment has been created, three blue boxes appear.
29604 The content of the first box is right aligned, the content of the last
29606 The content of the middle box appears centered and a bit smaller, because
29607 it is designed to insert there only relation characters.
29608 \begin_inset Formula
29610 \frac{ABC}{D} & \frac{ABC}{D} & \frac{ABC}{D}\\
29620 \begin_layout Subsection
29622 \begin_inset Index idx
29625 \begin_layout Plain Layout
29626 Formula ! multiline ! gather environment
29634 \begin_layout Standard
29635 This environment consists of only one centered column.
29636 Every line can be numbered.
29637 \begin_inset Formula
29648 \begin_layout Subsection
29649 Multline Environment
29650 \begin_inset CommandInset label
29652 name "subsec:Multline-Environment"
29657 \begin_inset Index idx
29660 \begin_layout Plain Layout
29661 Formula ! multiline ! multline environment
29669 \begin_layout Standard
29670 The multline environment consists, like the gather environment, of only
29672 But the first line is left aligned, the last one right aligned.
29673 All other lines are centered.
29674 Therefore this environment is suitable for long formulas.
29676 \begin_inset CommandInset ref
29678 reference "eq:lefteqn"
29682 in the multline environment:
29683 \begin_inset Formula
29685 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}\\
29686 -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}\\
29687 =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}}
29695 \begin_layout Standard
29696 In the output only the last (first) line of a multline environment appears
29697 numbered when the document numbering is right (left).
29701 \begin_layout Plain Layout
29702 numbering styles see
29703 \begin_inset CommandInset ref
29705 reference "sec:Formula-Styles"
29717 \begin_layout Standard
29725 \begin_inset Index idx
29728 \begin_layout Plain Layout
29743 \begin_inset Index idx
29746 \begin_layout Plain Layout
29754 a centered line can be right or left aligned, respectively.
29755 The commands are used as follows:
29758 \begin_layout Standard
29763 shoveright{line content}
29769 shoveleft{line content}
29772 \begin_layout Standard
29773 \begin_inset VSpace medskip
29783 \begin_inset Index idx
29786 \begin_layout Plain Layout
29794 specifies the distance of the first line from the left page margin.
29795 Predefined is the length 0
29796 \begin_inset space \thinspace{}
29802 \begin_layout Standard
29803 As example the above formula where the command
29806 \begin_layout Standard
29816 \begin_layout Standard
29817 was inserted in \SpecialChar TeX
29822 \begin_layout Plain Layout
29834 \begin_inset Formula
29836 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}\\
29837 \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}}\\
29838 =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}}
29847 \begin_layout Plain Layout
29858 The second line was left aligned using
29867 \begin_layout Subsection
29868 Multiline Formula Parts
29869 \begin_inset CommandInset label
29871 name "subsec:Multiline-Formula-Parts"
29876 \begin_inset Index idx
29879 \begin_layout Plain Layout
29880 Formula ! multiline ! formula parts
29888 \begin_layout Standard
29889 To display only parts of a formula with multiple lines, one of the following
29890 environments is used:
29907 They can be inserted via the menu
29909 Insert\SpecialChar menuseparator
29912 or by using the commands described in this section.
29915 \begin_layout Standard
29916 The first three have the same properties as the corresponding multiline
29917 formula environments, but it is possible to set further formula parts beside
29920 \begin_inset Formula
29922 \left.\begin{aligned}\Delta x\Delta p & \ge\frac{\hbar}{2}\\
29923 \Delta E\Delta t & \ge\frac{\hbar}{2}
29925 \right\} \textrm{Uncertainty relations}
29933 \begin_layout Standard
29934 To get this formula, a displayed formula is created where the command
29941 \begin_inset Index idx
29944 \begin_layout Plain Layout
29953 A purple box appears around the blue formula box where now columns and
29954 lines can be added.
29955 Outside the multiline environment other formula parts can be set, like
29959 \begin_layout Standard
29960 The aligned environment is also suitable for long formulas whose lines are
29961 horizontally aligned.
29962 Using aligned in a displayed formula has the advantage that the formula
29963 number is vertically centered behind the lines.
29965 \begin_inset CommandInset ref
29967 reference "eq:shortlong"
29971 in the aligned environment:
29972 \begin_inset Formula
29974 \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}|}\\
29975 & -\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}|}
29984 \begin_layout Standard
29985 To use the environments
30004 \begin_inset Index idx
30007 \begin_layout Plain Layout
30022 \begin_inset Index idx
30025 \begin_layout Plain Layout
30040 \begin_inset Index idx
30043 \begin_layout Plain Layout
30051 are inserted, respectively.
30052 The split environment has the same properties as the aligned environment
30053 but it can only have two columns.
30056 \begin_layout Subsection
30057 Text in multiline Formulas
30058 \begin_inset CommandInset label
30060 name "subsec:Text-in-multiline"
30065 \begin_inset Index idx
30068 \begin_layout Plain Layout
30075 \begin_inset Index idx
30078 \begin_layout Plain Layout
30079 Formula ! multiline ! text
30087 \begin_layout Standard
30088 In the Align environments, and the multline and gather environment, text
30089 can be inserted that will appear in a separate line and doesn't affect
30090 the column alignment.
30091 To do this, the command
30098 \begin_inset Index idx
30101 \begin_layout Plain Layout
30109 is used in the following scheme:
30112 \begin_layout Standard
30120 \begin_layout Standard
30121 The text should not be longer than a line because it cannot be hyphenated.
30122 As \SpecialChar LyX
30123 doesn't yet support
30129 directly, the text is written as mathematical text.
30136 must hereby be at the beginning of a line and appears in the output above
30138 An example where the text was inserted at the beginning of the second line:
30139 \begin_inset Formula
30141 I & =a\sqrt{2}\int_{0}^{2\pi}\sqrt{1+\cos(\phi)}\;\mathrm{d}\phi\\
30142 \intertext{\text{integrand is symmetric to \ensuremath{\phi=\pi}, therefore}} & =2a\sqrt{2}\int_{0}^{\pi}\sqrt{1+\cos(\phi)}\;\mathrm{d}\phi
30150 \begin_layout Standard
30157 always creates some vertical space between the text and the formula lines.
30158 To avoid this space, set in the document settings under
30161 \begin_inset space ~
30171 \begin_inset Index idx
30174 \begin_layout Plain Layout
30175 Packages ! mathtools
30183 \begin_inset space ~
30189 Then you can use the command
30196 \begin_inset Index idx
30199 \begin_layout Plain Layout
30216 \begin_layout Standard
30217 \begin_inset Formula
30219 I & =a\sqrt{2}\int_{0}^{2\pi}\sqrt{1+\cos(\phi)}\;\mathrm{d}\phi\\
30220 \shortintertext{\text{integrand is symmetric to \ensuremath{\phi=\pi}, therefore}} & =2a\sqrt{2}\int_{0}^{\pi}\sqrt{1+\cos(\phi)}\;\mathrm{d}\phi
30228 \begin_layout Section
30230 \begin_inset Index idx
30233 \begin_layout Plain Layout
30240 \begin_inset Index idx
30243 \begin_layout Plain Layout
30244 Formula ! numbering|see
30248 \begin_layout Plain Layout
30259 \begin_layout Plain Layout
30274 \begin_layout Subsection
30278 \begin_layout Standard
30279 Numbered formulas can be created with the menu
30281 Insert\SpecialChar menuseparator
30282 Math\SpecialChar menuseparator
30284 \begin_inset space ~
30292 \begin_inset space ~
30298 Existing formulas can be numbered with the menu
30300 Edit\SpecialChar menuseparator
30301 Math\SpecialChar menuseparator
30303 \begin_inset space ~
30311 arg "math-number-toggle"
30315 The formula number is displayed in \SpecialChar LyX
30316 behind the formula as a number sign
30318 The number sign is replaced in the output by the formula number.
30321 \begin_layout Standard
30322 When numbering is turned on in multiline formulas, all lines will be numbered.
30323 But the numbering can be controlled with the menu
30325 Edit\SpecialChar menuseparator
30326 Math\SpecialChar menuseparator
30328 \begin_inset space ~
30332 \begin_inset space ~
30336 \begin_inset space ~
30344 arg "math-number-line-toggle"
30350 \begin_layout Standard
30351 Except for inline formulas, all formulas can be numbered with two different
30353 \begin_inset CommandInset ref
30355 reference "sec:Formula-Styles"
30362 \begin_layout Subsection
30364 \begin_inset Index idx
30367 \begin_layout Plain Layout
30368 Cross-references ! to formulas
30376 \begin_layout Standard
30377 All labeled formulas can be cross-referenced.
30378 A label is added by the menu
30380 Insert\SpecialChar menuseparator
30383 or the toolbar button
30390 The cursor must hereby be inside a displayed formula.
30391 Alternatively you can right-click on the formula and choose
30396 A dialog pops up displaying the prefix
30401 The label is inserted there behind the prefix.
30402 The predefined prefix means
30403 \begin_inset Quotes eld
30407 \begin_inset Quotes erd
30410 and makes it easier to find labels in large documents because it marks
30411 it as formula label to divide it from e.
30412 \begin_inset space \thinspace{}
30416 \begin_inset space \space{}
30420 To change a label, the menu
30422 Insert\SpecialChar menuseparator
30425 is used again or you right-click on a formula and then on
30432 \begin_layout Standard
30433 The name of the label is displayed in \SpecialChar LyX
30434 within two parentheses behind formula.
30435 A formula with a label is always numbered.
30438 \begin_layout Standard
30439 Cross-references are inserted via the menu
30441 Insert\SpecialChar menuseparator
30444 or with the toolbar button
30447 arg "dialog-show-new-inset ref"
30451 A formula cross-reference appears in the output as formula number.
30452 When in the cross-reference dialog window the format
30456 is chosen, the cross-reference appears in the output as formula number
30458 \begin_inset Newline newline
30461 By right-clicking on a cross-reference in \SpecialChar LyX
30462 , one jumps to the formula that
30466 \begin_layout Standard
30467 Here are as examples cross-references to formulas of the following subsections:
30468 \begin_inset Note Note
30471 \begin_layout Plain Layout
30472 Note the different cross-reference types.
30480 \begin_layout Standard
30482 \begin_inset CommandInset ref
30489 \begin_inset CommandInset ref
30497 \begin_inset CommandInset ref
30503 ) big Latin letters are used for the numbering in contrary to (
30504 \begin_inset CommandInset ref
30513 \begin_layout Standard
30514 \begin_inset VSpace medskip
30517 When the argument of
30525 \begin_layout Plain Layout
30533 \begin_inset CommandInset ref
30535 reference "subsec:User-defined-Numbering"
30546 contains a box like in
30547 \begin_inset CommandInset ref
30549 reference "subsec:Paragraph-Boxes"
30553 , the formula cannot be referenced.
30556 \begin_layout Subsection
30558 \begin_inset Index idx
30561 \begin_layout Plain Layout
30562 Formula numbering ! subnumbering
30570 \begin_layout Standard
30571 With the help of the commands
30575 begin{subequations}
30583 formulas can be subnumbered.
30584 Both commands are inserted in \SpecialChar TeX
30588 \begin_layout Standard
30590 \begin_inset Formula
30601 \begin_layout Plain Layout
30605 addtocounter{equation}{-1}
30614 \begin_layout Plain Layout
30618 begin{subequations}
30624 \begin_inset VSpace -5mm
30628 \begin_inset Formula
30636 \begin_inset Formula
30646 \begin_layout Standard
30650 \begin_layout Plain Layout
30662 \begin_layout Standard
30663 To create the example, the following is done:
30666 \begin_layout Enumerate
30667 first formula is inserted
30670 \begin_layout Enumerate
30675 addtocounter{equation}{-1}
30677 begin{subequations}
30678 \begin_inset Index idx
30681 \begin_layout Plain Layout
30690 \begin_inset Newline newline
30695 is inserted after the first formula
30698 \begin_layout Enumerate
30699 second formula is inserted
30702 \begin_layout Enumerate
30703 third formula is inserted
30706 \begin_layout Enumerate
30713 is inserted after the third formula
30716 \begin_layout Standard
30717 Every formula between the commands
30729 is subnumbered as a, b,
30730 \begin_inset Newline linebreak
30733 c, \SpecialChar ldots
30734 For multiline formulas every line will be subnumbered.
30735 All subnumbered formulas are treated as
30740 But as every numbered formula increases the counter
30744 by one, the command
30750 is needed to decrease it.
30751 Otherwise the formulas
30752 \begin_inset CommandInset ref
30759 \begin_inset CommandInset ref
30766 \begin_inset CommandInset ref
30772 would be numbered as
30773 \begin_inset CommandInset ref
30780 \begin_inset CommandInset ref
30787 \begin_inset CommandInset ref
30796 \begin_layout Standard
30797 By inserting the commands in \SpecialChar TeX
30798 mode, a space is created between the first
30801 \begin_inset space \thinspace{}
30804 mm vertical space is inserted after the command
30808 begin{subequations}
30811 When the formula style
30817 \begin_layout Plain Layout
30819 \begin_inset CommandInset ref
30821 reference "sec:Formula-Styles"
30833 \begin_inset space \thinspace{}
30836 mm space is inserted instead.
30839 \begin_layout Standard
30840 Here is an example for a multiline formula where the numbering was turned
30841 off for the second line:
30845 \begin_layout Plain Layout
30849 begin{subequations}
30855 \begin_inset Formula
30857 A & = & (B-Z)^{2}=(B-Z)(B-Z)\label{eq:d}\\
30858 & = & B^{2}-ZB-BZ+Z^{2}\nonumber \\
30859 & = & B^{2}-2BZ+Z^{2}\label{eq:f}
30868 \begin_layout Plain Layout
30880 \begin_layout Subsection
30881 User-defined Numbering
30882 \begin_inset CommandInset label
30884 name "subsec:User-defined-Numbering"
30889 \begin_inset Index idx
30892 \begin_layout Plain Layout
30893 Formula numbering ! user-defined
30901 \begin_layout Standard
30902 \begin_inset Index idx
30905 \begin_layout Plain Layout
30906 Formula numbering ! self-defined delimiters
30911 With the standard numbering parentheses are set around the formula number.
30912 To replace the parentheses for example by vertical bars, the following
30913 line is added to the \SpecialChar LaTeX
30917 \begin_layout Standard
30929 \begin_inset Note Note
30932 \begin_layout Plain Layout
30933 This macro is already declared in the \SpecialChar LaTeX
30934 -preamble for testing.
30935 To activate it, remove the percent sign at the beginning.
30943 \begin_layout Standard
30944 To use other characters, the vertical bars besides the
30948 are replaced by one ore more characters.
30949 To get only the formula number the vertical bars are omitted.
30952 \begin_layout Standard
30953 \begin_inset VSpace bigskip
30956 When there should be an expression of your choice instead of the consecutive
30957 formula number in parentheses behind the formula, the command
30964 \begin_inset Index idx
30967 \begin_layout Plain Layout
30976 \begin_inset Formula
30978 A+B=C\tag{something}\label{eq:tag}
30983 In this example the command
30988 \begin_inset space \textvisiblespace{}
30993 was inserted in the formula.
30996 \begin_layout Standard
31002 \begin_inset space \textvisiblespace{}
31007 is inserted instead, the star prevents the parentheses around the expression:
31008 \begin_inset Formula
31010 A+B=C\tag*{something}
31018 \begin_layout Standard
31019 \begin_inset VSpace bigskip
31022 To restart the formula numbering with new document parts or sections, the
31023 following command is used:
31026 \begin_layout Standard
31031 @addtoreset{equation}{part}
31034 \begin_inset Index idx
31037 \begin_layout Plain Layout
31042 \begin_layout Plain Layout
31053 \begin_layout Plain Layout
31066 \begin_layout Plain Layout
31077 \begin_layout Plain Layout
31090 \begin_inset Newline newline
31094 \begin_inset Newline newline
31101 @addtoreset{equation}{section}
31104 \begin_layout Standard
31105 To be able to use these commands in \SpecialChar TeX
31107 \begin_inset Quotes eld
31111 \begin_inset Quotes erd
31114 character has to be made
31115 \begin_inset Quotes eld
31119 \begin_inset Quotes erd
31122 for \SpecialChar LaTeX
31137 So the command sequence in \SpecialChar TeX
31141 \begin_layout Standard
31147 \begin_inset Newline newline
31152 @addtoreset{equation}{section}
31153 \begin_inset Newline newline
31161 \begin_layout Standard
31162 In the \SpecialChar LaTeX
31175 can be omitted as they are automatically internally inserted by \SpecialChar LyX
31179 \begin_layout Standard
31194 \begin_layout Plain Layout
31199 is part of the \SpecialChar LaTeX
31205 \begin_inset Index idx
31208 \begin_layout Plain Layout
31209 Packages ! carlisle
31214 that is part of every \SpecialChar LaTeX
31215 standard installation.
31221 \begin_inset Index idx
31224 \begin_layout Plain Layout
31225 Packages ! remreset
31230 has to be loaded in the \SpecialChar LaTeX
31231 -preamble with the line
31234 \begin_layout Standard
31239 usepackage{remreset}
31242 \begin_layout Standard
31250 \begin_inset Index idx
31253 \begin_layout Plain Layout
31258 \begin_layout Plain Layout
31269 \begin_layout Plain Layout
31282 \begin_layout Plain Layout
31293 \begin_layout Plain Layout
31305 can be used with the same scheme as
31314 \begin_layout Standard
31315 \begin_inset VSpace bigskip
31318 Sometimes formulas should be numbered in the following form:
31321 \begin_layout Standard
31324 (section number.formula number)
31327 \begin_layout Standard
31328 The formula number should start with every section with
31329 \begin_inset Quotes eld
31333 \begin_inset Quotes erd
31339 \begin_layout Standard
31340 For this case there is the command
31347 \begin_inset Index idx
31350 \begin_layout Plain Layout
31358 , which is used with the following scheme:
31361 \begin_layout Standard
31366 numberwithin{counter}{sectioning}
31369 \begin_layout Standard
31370 Counter denotes what kind of numbering is affected, sectioning denotes what
31371 number is before the dot.
31374 \begin_layout Standard
31375 Thus in our case the following \SpecialChar LaTeX
31376 preamble or \SpecialChar TeX
31380 \begin_layout Standard
31385 numberwithin{equation}{section}
31388 \begin_layout Standard
31389 This is the result:
31393 \begin_layout Plain Layout
31397 numberwithin{equation}{section}
31403 \begin_inset Formula
31413 \begin_layout Standard
31415 \begin_inset space \thinspace{}
31419 \begin_inset space \space{}
31422 tables so that the number of the part is the sectioning,
31423 \begin_inset Newline newline
31430 numberwithin{table}{part}
31435 \begin_layout Standard
31436 To go back to the standard numbering or to prevent this kind of numbering
31437 when it is defined by the document class, the following command is inserted
31438 as \SpecialChar TeX
31439 code or to the \SpecialChar LaTeX
31443 \begin_layout Standard
31453 \begin_inset Index idx
31456 \begin_layout Plain Layout
31470 \begin_layout Plain Layout
31486 \begin_inset Newline newline
31494 \begin_inset Newline newline
31506 \begin_layout Standard
31513 uses internally the command
31519 , described above, that also needs to be reverted.
31523 \begin_layout Plain Layout
31530 \begin_layout Plain Layout
31534 @removefromreset{equation}{section}
31537 \begin_layout Plain Layout
31549 \begin_layout Subsection
31550 Numbering with Roman Numbers and Letters
31551 \begin_inset Index idx
31554 \begin_layout Plain Layout
31555 Formula numbering ! with letters
31561 \begin_inset Index idx
31564 \begin_layout Plain Layout
31565 Formula numbering ! with Roman numbers
31573 \begin_layout Standard
31574 Formulas can also be numbered with Roman numbers and Latin letters.
31575 To number for example with small Roman numbers, the command
31578 \begin_layout Standard
31590 \begin_layout Standard
31591 is inserted before the formula in \SpecialChar TeX
31600 \begin_inset Index idx
31603 \begin_layout Plain Layout
31611 redefines the predefined command
31627 \begin_layout Plain Layout
31634 has the same scheme like the command
31640 that is described in
31641 \begin_inset CommandInset ref
31643 reference "subsec:The-Command-newcommand"
31656 is the formula counter.
31663 is used as prefix for a counter, the value of the counter is output as
31665 When a formula is numbered, \SpecialChar LaTeX
31666 sets internally the command
31672 behind the formula.
31678 \begin_inset Index idx
31681 \begin_layout Plain Layout
31691 outputs the counter as small Roman number.
31694 \begin_layout Standard
31695 All formulas behind the command
31705 are now numbered Roman.
31706 To switch to numbering with big Roman numbers, the command is inserted
31720 \begin_inset Index idx
31723 \begin_layout Plain Layout
31735 \begin_inset Quotes eld
31739 \begin_inset Quotes erd
31742 with small Latin letters there is the command
31749 \begin_inset Index idx
31752 \begin_layout Plain Layout
31760 , for big ones there is the command
31767 \begin_inset Index idx
31770 \begin_layout Plain Layout
31783 \begin_layout Standard
31784 \begin_inset Note Greyedout
31787 \begin_layout Plain Layout
31794 \begin_inset space ~
31797 formulas can be numbered with Latin letters in one document.
31805 \begin_layout Standard
31809 \begin_layout Plain Layout
31825 \begin_layout Standard
31826 \begin_inset Formula
31828 A=\textrm{small roman}
31837 \begin_layout Plain Layout
31851 \begin_inset Formula
31853 B=\textrm{big Roman}\label{eq:Rom}
31862 \begin_layout Plain Layout
31876 \begin_inset Formula
31878 C=\textrm{small Latin}
31887 \begin_layout Plain Layout
31901 \begin_inset Formula
31903 D=\textrm{big Latin}\label{eq:Lat}
31911 \begin_layout Standard
31912 To switch back to the default numbering, insert the command:
31915 \begin_layout Standard
31925 \begin_inset Index idx
31928 \begin_layout Plain Layout
31939 \begin_layout Standard
31943 \begin_layout Plain Layout
31957 \begin_inset Formula
31967 \begin_layout Standard
31968 \begin_inset VSpace medskip
31971 As you see, formulas are numbered serially independent from the numbering
31973 When then numbering should start with
31974 \begin_inset Quotes eld
31978 \begin_inset Quotes erd
31981 when the style is changed, new equation counters have to be defined.
31982 A description about this can be found in the file
31983 \begin_inset CommandInset href
31985 name "Formula-numbering.lyx"
31986 target "run:Formula-numbering.lyx"
31993 \begin_layout Section
31994 Chemical Symbols and Equations
31995 \begin_inset CommandInset label
31997 name "subsec:Chemical-Symbols-and"
32002 \begin_inset Index idx
32005 \begin_layout Plain Layout
32006 Chemical characters ! Symbols
32012 \begin_inset Index idx
32015 \begin_layout Plain Layout
32022 \begin_inset Index idx
32025 \begin_layout Plain Layout
32034 \begin_layout Standard
32035 An example text from chemistry:
32038 \begin_layout Quote
32040 \begin_inset Formula $\mathrm{SO_{4}^{2-}}$
32043 -ion reacts with two
32044 \begin_inset Formula $\mathrm{Na^{+}}$
32047 -ions to sodium sulfate
32048 \begin_inset Formula $\left(\mathrm{Na_{2}SO_{4}}\right)$
32052 The chemical equation for this is:
32053 \begin_inset Formula
32055 \mathrm{2\,Na^{+}+SO_{4}^{2-}\longrightarrow Na_{2}SO_{4}}\label{eq:chem-reaction}
32063 \begin_layout Standard
32064 This chemical equation can directly be created as formula.
32065 To avoid that the symbols appear italic, everything is highlighted and
32066 changed by the shortcut
32072 to the upright font style.
32076 \begin_layout Plain Layout
32082 \begin_inset CommandInset ref
32084 reference "subsec:Font-Styles"
32096 \begin_layout Standard
32097 A more convenient way to typeset chemical formulas is to use the command
32105 \begin_inset Index idx
32108 \begin_layout Plain Layout
32116 that is available when the \SpecialChar LaTeX
32122 \begin_inset Index idx
32125 \begin_layout Plain Layout
32138 to a formula a new blue box appears where chemical formulas can be inserted
32139 in an intuitive way.
32140 \begin_inset Separator parbreak
32146 \begin_layout Standard
32148 \begin_inset Tabular
32149 <lyxtabular version="3" rows="10" columns="2">
32150 <features tabularvalignment="middle">
32151 <column alignment="center" valignment="top">
32152 <column alignment="center" valignment="top">
32154 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
32157 \begin_layout Plain Layout
32163 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
32166 \begin_layout Plain Layout
32168 \begin_inset Note Note
32171 \begin_layout Plain Layout
32178 is only used as spacer.
32190 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
32193 \begin_layout Plain Layout
32197 \begin_inset space \textvisiblespace{}
32205 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
32208 \begin_layout Plain Layout
32209 \begin_inset Formula $\raisebox{4.5mm}{}\ce{H2CO3}\raisebox{-2mm}{}$
32219 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
32222 \begin_layout Plain Layout
32226 \begin_inset space \textvisiblespace{}
32234 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
32237 \begin_layout Plain Layout
32238 \begin_inset Formula $\raisebox{5mm}{}\ce{SO4^{2-}}\raisebox{-2mm}{}$
32248 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
32251 \begin_layout Plain Layout
32255 \begin_inset space \textvisiblespace{}
32263 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
32266 \begin_layout Plain Layout
32267 \begin_inset Formula $\raisebox{4.5mm}{}\ce{(NH4)2S}\raisebox{-2mm}{}$
32277 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
32280 \begin_layout Plain Layout
32284 \begin_inset space \textvisiblespace{}
32292 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
32295 \begin_layout Plain Layout
32296 \begin_inset Formula $\raisebox{4.5mm}{}\ce{KCr(SO4)2.12H2O}\raisebox{-2mm}{}$
32306 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
32309 \begin_layout Plain Layout
32313 \begin_inset space \textvisiblespace{}
32319 \begin_inset space \textvisiblespace{}
32325 \begin_inset space \textvisiblespace{}
32333 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
32336 \begin_layout Plain Layout
32337 \begin_inset Formula $\raisebox{4.5mm}{}\ce{A-B\dbond C\tbond D}\raisebox{-2mm}{}$
32347 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
32350 \begin_layout Plain Layout
32354 \begin_inset space \textvisiblespace{}
32358 \begin_inset Formula $\downarrow$
32362 \begin_inset Formula $\to$
32370 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
32373 \begin_layout Plain Layout
32374 \begin_inset Formula $\raisebox{5mm}{}\ce{_{90}^{227}Th+}\raisebox{-2mm}{}$
32384 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
32387 \begin_layout Plain Layout
32391 \begin_inset space \textvisiblespace{}
32397 \begin_inset space \textvisiblespace{}
32403 \begin_inset space \textvisiblespace{}
32411 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
32414 \begin_layout Plain Layout
32415 \begin_inset Formula $\raisebox{4.5mm}{}\ce{\ensuremath{\mu\hyphen}Cl}\raisebox{-2mm}{}$
32425 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
32428 \begin_layout Plain Layout
32432 \begin_inset space \textvisiblespace{}
32436 \begin_inset space \textvisiblespace{}
32440 \begin_inset space \textvisiblespace{}
32444 \begin_inset space \textvisiblespace{}
32448 \begin_inset space \textvisiblespace{}
32456 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
32459 \begin_layout Plain Layout
32460 \begin_inset Formula $\raisebox{4.5mm}{}\ce{CO2 + C <=> 2CO}\raisebox{-2mm}{}$
32470 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
32473 \begin_layout Plain Layout
32477 \begin_inset space \textvisiblespace{}
32481 \begin_inset space \textvisiblespace{}
32485 \begin_inset space \textvisiblespace{}
32489 \begin_inset space \textvisiblespace{}
32497 \begin_inset space \textvisiblespace{}
32505 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
32508 \begin_layout Plain Layout
32509 \begin_inset Formula $\raisebox{5mm}{}\ce{CO2 + C ->[\alpha][\beta] 2CO}\raisebox{-4mm}{}$
32525 \begin_layout Standard
32526 \begin_inset Note Greyedout
32529 \begin_layout Plain Layout
32535 It is not possible in \SpecialChar LyX
32536 to use the character ^ to get an up-arrow as described
32542 One instead uses a negative thin space followed by the command
32549 \begin_inset Formula $\ce{Fe + 2H+ -> Fe^{2+} + H2\negthinspace\uparrow}$
32560 \begin_layout Standard
32567 the command for equation
32568 \begin_inset space ~
32572 \begin_inset CommandInset ref
32574 reference "eq:chem-reaction"
32579 \begin_inset Newline newline
32587 \begin_inset space \textvisiblespace{}
32591 \begin_inset space \textvisiblespace{}
32595 \begin_inset space \textvisiblespace{}
32599 \begin_inset space \textvisiblespace{}
32603 \begin_inset space \textvisiblespace{}
32607 \begin_inset space \textvisiblespace{}
32613 \begin_layout Standard
32614 To create multiline chemical equations first a multiline formula is created
32616 \begin_inset CommandInset ref
32618 reference "sec:Multiline-Formulas"
32623 Afterwards the command
32629 is used in every small blue box of the formula.
32631 \begin_inset CommandInset ref
32633 reference "eq:TEOS-reaction-1"
32638 \begin_inset CommandInset ref
32640 reference "eq:TEOS-reaction-2"
32644 are an example of a multi-stage chemical reaction where every equation
32645 has its own number.
32646 \begin_inset Formula
32648 \ce{TEOS + 4O} & \ce{->} & \ce{Si(OH)4 + 4C2H4O}\label{eq:TEOS-reaction-1}\\
32649 \ce{Si(OH)4} & \ce{->} & \ce{SiO2 + 2H2O}\label{eq:TEOS-reaction-2}
32657 \begin_layout Standard
32668 package provides the command
32675 \begin_inset Index idx
32678 \begin_layout Plain Layout
32686 that has to be used for special cases.
32687 For more information about
32693 and more examples have a look at the documentation of
32698 \begin_inset CommandInset citation
32707 \begin_layout Section
32711 \begin_layout Standard
32713 supports two types of commutative diagrams:
32721 that are explained in the following.
32724 \begin_layout Subsection
32726 \begin_inset Index idx
32729 \begin_layout Plain Layout
32738 \begin_layout Standard
32739 Diagrams of this type visualize relations by vertical and horizontal lines
32741 \begin_inset Formula
32743 \begin{CD}A@>>>B@>>>C\\
32754 \begin_layout Standard
32755 To get them, the command
32760 \begin_inset Index idx
32763 \begin_layout Plain Layout
32773 is inserted to a formula.
32774 A blue box appears with two dashed lines where further commands can be
32779 arg "newline-insert newline"
32782 a new line is created.
32783 Horizontal relations are inserted in odd, vertical in even formula lines.
32786 \begin_layout Standard
32787 To create the relations there are the following commands:
32790 \begin_layout Itemize
32795 creates a left arrow,
32806 \begin_layout Itemize
32811 creates an up arrow,
32819 a vertical equal sign
32822 \begin_layout Itemize
32828 is a placeholder for non-existent relations
32831 \begin_layout Standard
32832 All arrows can be labeled as follows:
32835 \begin_layout Itemize
32836 If text inserted between the first and second < or >, resp., it is placed
32838 When it is inserted between the second and third one, it appears under
32842 \begin_layout Itemize
32843 When text for vertical arrows is inserted between the first and second A
32844 or V, resp., it is placed left beside the arrow.
32845 When it is inserted between the second and third one, it appears right
32847 If the text contains an A or V, these letters must be set into a \SpecialChar TeX
32851 \begin_layout Standard
32852 As example a diagram with all possible relations:
32855 \begin_layout Standard
32856 \begin_inset Formula
32858 \begin{CD}A@>j>>B@>>k>C@=F\\
32869 \begin_layout Standard
32870 The command for this is:
32871 \begin_inset Newline newline
32879 \begin_inset space \textvisiblespace{}
32882 A@>j>>B@>>k>C@=F Ctrl+Return
32883 \begin_inset Newline newline
32887 \begin_inset Phantom HPhantom
32890 \begin_layout Plain Layout
32896 \begin_inset space \textvisiblespace{}
32909 \begin_inset Formula $\to$
32915 \begin_inset Newline newline
32919 \begin_inset Phantom HPhantom
32922 \begin_layout Plain Layout
32928 \begin_inset space \textvisiblespace{}
32939 \begin_layout Subsection
32941 \begin_inset Index idx
32944 \begin_layout Plain Layout
32945 Diagrams ! xymatrix
32953 \begin_layout Standard
32954 To be able to use xymatrices, the \SpecialChar LaTeX
32960 A xymatrix is created by inserting the command
32967 Then you are able to add new matrix columns and rows like for normal matrices,
32969 \begin_inset CommandInset ref
32971 reference "sec:Matrices"
32978 \begin_layout Standard
32979 In contrary to amscd diagrams, xymatrices supports diagonal and curved arrows,
32981 All possibilities to create commutative diagrams and decorations are explained
32986 that you find in the menu
32988 Help\SpecialChar menuseparator
32990 \begin_inset space ~
32998 \begin_layout Subsection
33004 \begin_inset Index idx
33007 \begin_layout Plain Layout
33016 \begin_layout Standard
33021 -diagrams, the \SpecialChar LaTeX
33031 -diagram is created by inserting the command
33038 Then you are able to add new matrix columns and rows like for normal matrices,
33040 \begin_inset CommandInset ref
33042 reference "sec:Matrices"
33049 \begin_layout Standard
33050 Examples how to create
33054 diagrams in \SpecialChar LyX
33057 Feynman-diagram manual
33059 that you find in the menu
33061 Help\SpecialChar menuseparator
33063 \begin_inset space ~
33071 \begin_layout Standard
33072 \begin_inset Newpage newpage
33078 \begin_layout Section
33079 User-defined Commands
33080 \begin_inset Index idx
33083 \begin_layout Plain Layout
33084 User-defined commands
33092 \begin_layout Standard
33093 \begin_inset Note Greyedout
33096 \begin_layout Plain Layout
33101 The names of user-defined commands and macros may only consist of Latin
33110 \begin_layout Subsection
33114 \begin_inset CommandInset label
33116 name "subsec:The-Command-newcommand"
33121 \begin_inset Index idx
33124 \begin_layout Plain Layout
33125 User-defined commands !
33133 \begin_inset Index idx
33136 \begin_layout Plain Layout
33147 \begin_layout Standard
33148 Many \SpecialChar LaTeX
33149 -commands are too long to be used frequently.
33150 But it is possible to define with the command
33156 new shorter commands.
33159 \begin_layout Standard
33160 The command scheme of
33169 \begin_layout Standard
33174 newcommand{new command name}[number of arguments][optional
33179 \begin_inset Newline newline
33183 \begin_inset Phantom HPhantom
33186 \begin_layout Plain Layout
33196 {command definition}
33199 \begin_layout Standard
33200 \begin_inset Note Greyedout
33203 \begin_layout Plain Layout
33208 Assure that the name of the new command is not already used in your document
33209 or by \SpecialChar LaTeX
33210 -packages that you use.
33211 When you for example define the command
33223 , you get an error message because
33229 is already defined as command for
33230 \begin_inset Quotes eld
33234 \begin_inset Formula $\le$
33238 \begin_inset Quotes erd
33249 \begin_layout Standard
33250 The number of arguments is an integer in the range 0
33251 \begin_inset space \thinspace{}
33255 \begin_inset space \thinspace{}
33258 9 and specifies how many arguments the new command should have.
33259 With the optional value a value for an optional argument can be predefined.
33260 When this is done, the
33268 rgument of the new command is automatically an optional one.
33271 \begin_layout Standard
33272 Here are some examples:
33275 \begin_layout Itemize
33276 To define the command
33288 , the \SpecialChar LaTeX
33290 \begin_inset VSpace medskip
33294 \begin_inset Newline newline
33308 \begin_layout Itemize
33309 To define the command
33321 , the argument (that should be underlined) must be taken into account.
33322 For this the preamble line is:
33323 \begin_inset VSpace medskip
33327 \begin_inset Newline newline
33341 \begin_inset VSpace medskip
33345 \begin_inset Newline newline
33352 acts as argument placeholder, the
33356 behind it denotes that it is the placeholder for the first argument.
33359 \begin_layout Itemize
33367 \begin_inset space \thinspace{}
33371 \begin_inset space \space{}
33381 \begin_inset VSpace medskip
33385 \begin_inset Newline newline
33396 framebox#1#2{$#3$}}
33399 \begin_inset VSpace medskip
33403 \begin_inset Newline newline
33406 The two Dollar signs creates the extra formula needed for
33413 \begin_inset CommandInset ref
33415 reference "subsec:Boxes-with-Frame"
33422 \begin_layout Itemize
33423 To create a new command for
33429 where the color for the box need not be specified, the argument for the
33430 color is defined optional:
33431 \begin_inset VSpace medskip
33435 \begin_inset Newline newline
33446 fcolorbox{#2}{#1}{$#3$}}
33449 \begin_inset VSpace medskip
33453 \begin_inset Newline newline
33456 When the color is not specified when using
33462 , the predefined color
33469 \begin_layout Standard
33470 A test of the new defined commands:
33471 \begin_inset Separator parbreak
33477 \begin_layout Standard
33479 \begin_inset Tabular
33480 <lyxtabular version="3" rows="6" columns="2">
33481 <features tabularvalignment="middle">
33482 <column alignment="center" valignment="top">
33483 <column alignment="center" valignment="top">
33485 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
33488 \begin_layout Plain Layout
33494 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
33497 \begin_layout Plain Layout
33499 \begin_inset Note Note
33502 \begin_layout Plain Layout
33509 is only used as spacer.
33521 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
33524 \begin_layout Plain Layout
33528 \begin_inset space \textvisiblespace{}
33536 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
33539 \begin_layout Plain Layout
33540 \begin_inset Formula $A\gr B$
33550 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
33553 \begin_layout Plain Layout
33561 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
33564 \begin_layout Plain Layout
33565 \begin_inset Formula $\raisebox{4.5mm}{}\us{ABcd}\raisebox{-2mm}{}$
33575 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
33578 \begin_layout Plain Layout
33582 \begin_inset Formula $\to$
33588 \begin_inset Formula $\to$
33596 \begin_inset space \textvisiblespace{}
33604 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
33607 \begin_layout Plain Layout
33608 \begin_inset Formula $\raisebox{6mm}{}\fb{[2cm]}{}{\int A=B}\raisebox{-4mm}{}$
33618 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
33621 \begin_layout Plain Layout
33625 \begin_inset Formula $\to$
33633 \begin_inset space \textvisiblespace{}
33641 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
33644 \begin_layout Plain Layout
33645 \begin_inset Formula $\raisebox{6mm}{}\cb{red}{\int A=B}\raisebox{-4mm}{}$
33655 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
33658 \begin_layout Plain Layout
33664 \begin_inset Formula $\to$
33672 \begin_inset space \textvisiblespace{}
33680 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
33683 \begin_layout Plain Layout
33684 \begin_inset Formula $\raisebox{6mm}{}\cb[green]{red}{\int A=B}\raisebox{-4mm}{}$
33700 \begin_layout Subsection
33702 \begin_inset Index idx
33705 \begin_layout Plain Layout
33706 User-defined commands! Math macros
33712 \begin_inset Index idx
33715 \begin_layout Plain Layout
33724 \begin_layout Standard
33725 User-defined commands are especially convenient for complex expressions.
33726 When you are for example dealing with a document that has quadratic equations,
33727 the same solution type occurs several times.
33728 The general form of a quadratic equation is
33729 \begin_inset Formula
33731 0=\lambda^{2}+p\lambda+q
33736 The general form of the solution is
33737 \begin_inset Formula
33739 \lambda_{1,2}=-\frac{p}{2}\pm\sqrt{\frac{p²}{4}-q}
33747 \begin_layout Standard
33748 To define a command for the solution formula where only the three parameters
33750 \begin_inset Formula $\lambda$
33754 \begin_inset Formula $p$
33758 \begin_inset Formula $q$
33761 need to be specified and the index of
33762 \begin_inset Formula $\lambda$
33765 can be given optionally, the \SpecialChar LaTeX
33767 \begin_inset Newline newline
33783 \begin_inset Newline newline
33787 \begin_inset Phantom HPhantom
33790 \begin_layout Plain Layout
33804 frac{#3^{2}}{4}-#4}}
33807 \begin_layout Standard
33808 To create with this the solution formula, the command
33809 \begin_inset Newline newline
33819 \begin_inset Formula $\to$
33825 \begin_inset Formula $\to$
33832 is inserted to a formula
33837 \begin_layout Standard
33838 The definition of the new command is unintuitive because one has to know
33839 the schemes of all used \SpecialChar LaTeX
33841 \begin_inset space \thinspace{}
33845 \begin_inset space \space{}
33848 that a fraction is inserted in \SpecialChar LaTeX
33853 frac{numerator}{denominator}
33856 Furthermore one can easily forget a brace in the definition and cannot
33857 see in \SpecialChar LyX
33858 what the new command is doing.
33859 To avoid these problems \SpecialChar LyX
33860 offers the possibility to use math macros instead
33870 \begin_layout Standard
33871 A math macro is created by using the menu
33873 Insert\SpecialChar menuseparator
33874 Math\SpecialChar menuseparator
33877 or the toolbar button
33880 arg "math-macro newmacroname_newcommand"
33884 The math macro toolbar appears together with the following box where the
33886 \begin_inset Newline newline
33890 \begin_inset space \hspace*{\fill}
33894 \begin_inset Graphics
33895 filename ../../../../LyX 2.2/Resources/doc/clipart/macrobox.png
33901 \begin_inset space \hspace*{\fill}
33905 \begin_inset Newline newline
33909 \begin_inset FormulaMacro
33910 \newcommand{\qG}[4][1,\,2]{#2_{#1}=-\frac{#3}{2}\pm\sqrt{\frac{#3^{2}}{4}-#4}}
33915 newmacroname is the default name of the macro that should be changed to
33916 something sensible.
33917 The wanted formula is inserted in the first blue box.
33918 An argument placeholder is inserted with the command
33925 \begin_inset space \thinspace{}
33929 \begin_inset space \space{}
33938 or by using the macro toolbar button
33941 arg "math-macro-add-param"
33945 Argument placeholders are displayed red.
33947 \begin_inset space ~
33950 arguments are possible.
33951 Optional arguments are created with the toolbar button
33954 arg "math-macro-add-optional-param"
33958 The first non-optional argument can be transformed to an optional one with
33962 arg "math-macro-make-optional"
33966 In the second blue box the appearance of the macro in \SpecialChar LyX
33968 Normally you want to see it as it is defined, so the box is kept empty.
33969 But when you have created a macro that needs lot of space on the screen,
33970 you can insert in the box for example
33971 \begin_inset Newline newline
34001 \begin_inset Newline newline
34006 For the macro only the arguments with the macro name in front of them will
34007 then be displayed in \SpecialChar LyX
34008 , leading to a better overview.
34009 The formula appears in the output as defined in the first box.
34010 \begin_inset Newline newline
34013 The appearance of macros in formulas can furthermore be changed for single
34014 macros by setting the cursor in the macro and using the menu
34016 View\SpecialChar menuseparator
34018 \begin_inset space ~
34022 \begin_inset space ~
34030 \begin_layout Standard
34031 To use a macro, the macro name is inserted as command to a formula, in our
34039 Our macro looks in \SpecialChar LyX
34041 \begin_inset Newline newline
34045 \begin_inset space \hspace*{\fill}
34049 \begin_inset Graphics
34050 filename ../../../../LyX 2.2/Resources/doc/clipart/macrouse.png
34056 \begin_inset space \hspace*{\fill}
34060 \begin_inset Newline newline
34063 Here is our macro example with the arguments
34064 \begin_inset Formula $x$
34068 \begin_inset Formula $\ln(x)$
34072 \begin_inset Formula $B$
34078 \begin_layout Standard
34079 \begin_inset Formula
34089 \begin_layout Standard
34093 Tools\SpecialChar menuseparator
34094 Preferences\SpecialChar menuseparator
34095 Editing\SpecialChar menuseparator
34098 different styles to edit macros.
34099 To find the style that suits you the most, choose a style and set the cursor
34100 in a macro formula to see the difference.
34103 \begin_layout Standard
34104 A math macro is transformed internally to a
34110 command when exporting the document.
34117 command is not placed in the \SpecialChar LaTeX
34118 -preamble, therefore macros can only be used
34119 in formulas that are in the document below the macro definition box.
34122 \begin_layout Standard
34123 Math macros can also be directly created from a
34130 When writing for example the command
34133 \begin_inset Newline newline
34142 xleftarrow[#2]{#1}}
34143 \begin_inset Newline newline
34148 in \SpecialChar LyX
34149 as normal text, highlighting it completely and using then the shortcut
34154 , the command will be transformed to a math macro.
34155 Using this method you need to be careful that the
34161 command is typed correctly, otherwise you get a faulty macro leading to
34166 \begin_layout Standard
34167 Math macros currently have the problem that further formulas in macro definition
34168 s are handled wrongly.
34169 Therefore the example
34176 \begin_inset CommandInset ref
34178 reference "subsec:The-Command-newcommand"
34182 cannot be created as macro.
34185 \begin_layout Standard
34186 When the cursor is in a macro definition box, you will see the macro toolbar
34187 in \SpecialChar LyX
34191 \begin_layout Standard
34192 \begin_inset VSpace defskip
34198 \begin_layout Standard
34199 \begin_inset Graphics
34200 filename ../../../../LyX 2.2/Resources/doc/clipart/MacroToolbar.png
34205 \begin_inset Index idx
34208 \begin_layout Plain Layout
34217 \begin_layout Standard
34218 \begin_inset VSpace defskip
34224 \begin_layout Standard
34225 The macro toolbar contains from left to right the following buttons:
34228 \begin_layout Standard
34229 \begin_inset VSpace defskip
34235 \begin_layout Standard
34236 \begin_inset Tabular
34237 <lyxtabular version="3" rows="9" columns="2">
34238 <features islongtable="true" longtabularalignment="center">
34239 <column alignment="left" valignment="top">
34240 <column alignment="left" valignment="top" width="85col%">
34241 <row interlinespace="2.5mm">
34242 <cell alignment="center" valignment="top" usebox="none">
34245 \begin_layout Plain Layout
34248 arg "math-macro-remove-param"
34256 <cell alignment="center" valignment="top" usebox="none">
34259 \begin_layout Plain Layout
34262 Edit\SpecialChar menuseparator
34263 Math\SpecialChar menuseparator
34265 \begin_inset space ~
34268 Definition\SpecialChar menuseparator
34269 Remove Last Argument
34275 <row interlinespace="2.5mm">
34276 <cell alignment="center" valignment="top" usebox="none">
34279 \begin_layout Plain Layout
34282 arg "math-macro-add-param"
34290 <cell alignment="center" valignment="top" usebox="none">
34293 \begin_layout Plain Layout
34296 Edit\SpecialChar menuseparator
34297 Math\SpecialChar menuseparator
34299 \begin_inset space ~
34302 Definition\SpecialChar menuseparator
34309 <row interlinespace="2.5mm">
34310 <cell alignment="center" valignment="top" usebox="none">
34313 \begin_layout Plain Layout
34316 arg "math-macro-make-optional"
34324 <cell alignment="center" valignment="top" usebox="none">
34327 \begin_layout Plain Layout
34330 Edit\SpecialChar menuseparator
34331 Math\SpecialChar menuseparator
34333 \begin_inset space ~
34336 Definition\SpecialChar menuseparator
34337 Transform First Non-Optional to
34338 \begin_inset Newline newline
34342 \begin_inset Phantom HPhantom
34345 \begin_layout Plain Layout
34348 Edit\SpecialChar menuseparator
34349 Math\SpecialChar menuseparator
34351 \begin_inset space ~
34354 Definition\SpecialChar menuseparator
34366 <row interlinespace="2.5mm">
34367 <cell alignment="center" valignment="top" usebox="none">
34370 \begin_layout Plain Layout
34373 arg "math-macro-make-nonoptional"
34381 <cell alignment="center" valignment="top" usebox="none">
34384 \begin_layout Plain Layout
34387 Edit\SpecialChar menuseparator
34388 Math\SpecialChar menuseparator
34390 \begin_inset space ~
34393 Definition\SpecialChar menuseparator
34394 Transform Last Optional to
34395 \begin_inset Newline newline
34399 \begin_inset Phantom HPhantom
34402 \begin_layout Plain Layout
34405 Edit\SpecialChar menuseparator
34406 Math\SpecialChar menuseparator
34408 \begin_inset space ~
34411 Definition\SpecialChar menuseparator
34417 Non-Optional Argument
34423 <row interlinespace="2.5mm">
34424 <cell alignment="center" valignment="top" usebox="none">
34427 \begin_layout Plain Layout
34430 arg "math-macro-remove-optional-param"
34438 <cell alignment="center" valignment="top" usebox="none">
34441 \begin_layout Plain Layout
34444 Edit\SpecialChar menuseparator
34445 Math\SpecialChar menuseparator
34447 \begin_inset space ~
34450 Definition\SpecialChar menuseparator
34451 Remove Optional Argument
34457 <row interlinespace="2.5mm">
34458 <cell alignment="center" valignment="top" usebox="none">
34461 \begin_layout Plain Layout
34464 arg "math-macro-add-optional-param"
34472 <cell alignment="center" valignment="top" usebox="none">
34475 \begin_layout Plain Layout
34478 Edit\SpecialChar menuseparator
34479 Math\SpecialChar menuseparator
34481 \begin_inset space ~
34484 Definition\SpecialChar menuseparator
34485 Insert Optional Argument
34491 <row interlinespace="2.5mm">
34492 <cell alignment="center" valignment="top" usebox="none">
34495 \begin_layout Plain Layout
34498 arg "math-macro-remove-greedy-param"
34506 <cell alignment="center" valignment="top" usebox="none">
34509 \begin_layout Plain Layout
34512 Edit\SpecialChar menuseparator
34513 Math\SpecialChar menuseparator
34515 \begin_inset space ~
34518 Definition\SpecialChar menuseparator
34519 Remove Last Argument
34520 \begin_inset Newline newline
34524 \begin_inset Phantom HPhantom
34527 \begin_layout Plain Layout
34530 Edit\SpecialChar menuseparator
34531 Math\SpecialChar menuseparator
34533 \begin_inset space ~
34536 Definition\SpecialChar menuseparator
34542 Spitting Out To The Right
34548 <row interlinespace="2.5mm">
34549 <cell alignment="center" valignment="top" usebox="none">
34552 \begin_layout Plain Layout
34555 arg "math-macro-append-greedy-param"
34563 <cell alignment="center" valignment="top" usebox="none">
34566 \begin_layout Plain Layout
34569 Edit\SpecialChar menuseparator
34570 Math\SpecialChar menuseparator
34572 \begin_inset space ~
34575 Definition\SpecialChar menuseparator
34577 \begin_inset Newline newline
34581 \begin_inset Phantom HPhantom
34584 \begin_layout Plain Layout
34587 Edit\SpecialChar menuseparator
34588 Math\SpecialChar menuseparator
34590 \begin_inset space ~
34593 Definition\SpecialChar menuseparator
34599 Eating From The Right
34605 <row interlinespace="2.5mm">
34606 <cell alignment="center" valignment="top" usebox="none">
34609 \begin_layout Plain Layout
34612 arg "math-macro-add-greedy-optional-param"
34620 <cell alignment="center" valignment="top" usebox="none">
34623 \begin_layout Plain Layout
34626 Edit\SpecialChar menuseparator
34627 Math\SpecialChar menuseparator
34629 \begin_inset space ~
34632 Definition\SpecialChar menuseparator
34633 Append Optional Argument
34634 \begin_inset Newline newline
34638 \begin_inset Phantom HPhantom
34641 \begin_layout Plain Layout
34644 Edit\SpecialChar menuseparator
34645 Math\SpecialChar menuseparator
34647 \begin_inset space ~
34650 Definition\SpecialChar menuseparator
34656 Eating From The Right
34669 \begin_layout Section
34670 Computer Algebra Systems
34673 \begin_layout Standard
34675 offers the exchange between mathematical expressions written in \SpecialChar LyX
34677 editor and external applications or user defined scripts.
34678 Currently supported applications are
34695 Note that the set of supported mathematical constructs is limited only
34696 to very simple cases.
34699 \begin_layout Subsection
34703 \begin_layout Standard
34704 Write some expression in a formula, go to the
34706 Edit\SpecialChar menuseparator
34707 Math\SpecialChar menuseparator
34708 Use Computer Algebra System
34710 menu and choose the application you have installed on the computer.
34711 After that the result of computation should show on the right side of the
34712 expression together with the
34713 \begin_inset Quotes eld
34717 \begin_inset Quotes erd
34723 \begin_layout Standard
34724 Here are few simple examples (with results from
34728 ) to show what kind of computations can be performed:
34731 \begin_layout Itemize
34732 \begin_inset Formula $\frac{37}{3}*2-\sum_{i=1}^{3}i^{i}=-\frac{22}{3}$
34738 \begin_layout Itemize
34739 \begin_inset Formula $\frac{37.0}{3}=12.33333333333333$
34745 \begin_layout Itemize
34746 \begin_inset Formula $\int_{1}^{2}\sin(x)dx=\cos1-\cos2$
34752 \begin_layout Itemize
34753 \begin_inset Formula $\det\left[\begin{array}{ccc}
34757 \end{array}\right]=-56$
34763 \begin_layout Itemize
34764 \begin_inset Formula $\lim_{x\rightarrow0}\left(\frac{\sin(x)}{x}\right)=1$
34770 \begin_layout Subsection
34774 \begin_layout Standard
34775 Currently there is no keyboard shortcut for calling the algebra applications.
34776 One can easily bind a shortcut to the
34790 \begin_inset space \thinspace{}
34794 \begin_inset space \space{}
34801 key inside the math editor.
34806 one would use this shortcut definition command:
34809 \begin_layout Standard
34812 command-alternatives paragraph-break;math-extern maxima
34815 \begin_layout Section
34817 \begin_inset Index idx
34820 \begin_layout Plain Layout
34829 \begin_layout Subsection
34831 \begin_inset Index idx
34834 \begin_layout Plain Layout
34843 \begin_layout Standard
34844 Negative numbers often look ugly in formulas because the minus sign before
34845 the number is set with the same length as the minus operator sign.
34846 When writing the negative number in normal text, the minus sign appears
34850 \begin_layout Standard
34851 Thus, the problem disappears when converting the minus sign to mathematical
34855 \begin_layout Standard
34856 An example to visualize the problem:
34857 \begin_inset Separator parbreak
34863 \begin_layout Standard
34865 \begin_inset Tabular
34866 <lyxtabular version="3" rows="3" columns="2">
34867 <features tabularvalignment="middle">
34868 <column alignment="right" valignment="top">
34869 <column alignment="left" valignment="top">
34871 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
34874 \begin_layout Plain Layout
34880 <cell alignment="center" valignment="top" topline="true" rightline="true" usebox="none">
34883 \begin_layout Plain Layout
34891 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
34894 \begin_layout Plain Layout
34900 <cell alignment="center" valignment="top" topline="true" bottomline="true" rightline="true" usebox="none">
34903 \begin_layout Plain Layout
34904 \begin_inset Formula $x=-2$
34914 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
34917 \begin_layout Plain Layout
34923 <cell alignment="center" valignment="top" topline="true" bottomline="true" rightline="true" usebox="none">
34926 \begin_layout Plain Layout
34927 \begin_inset Formula $x=\textrm{-}2$
34943 \begin_layout Subsection
34944 Comma as decimal Separator
34945 \begin_inset Index idx
34948 \begin_layout Plain Layout
34957 \begin_layout Standard
34958 In \SpecialChar LaTeX
34959 a comma inside a formula is used, according to the English convention,
34960 as number group separator.
34961 So there will be space added behind all commas in formulas.
34964 \begin_layout Standard
34965 To avoid this, the comma is highlighted and changed to mathematical text
34975 \begin_layout Standard
34976 To use all formula commas in the document as decimal separator, the file
34985 \begin_layout Plain Layout
34990 is part of the \SpecialChar LaTeX
34996 \begin_inset Index idx
34999 \begin_layout Plain Layout
35004 \begin_layout Plain Layout
35024 \begin_inset Index idx
35027 \begin_layout Plain Layout
35033 is loaded with the \SpecialChar LaTeX
35037 \begin_layout Standard
35045 \begin_layout Subsection
35047 \begin_inset CommandInset label
35049 name "subsec:Physical-Vectors"
35054 \begin_inset Index idx
35057 \begin_layout Plain Layout
35066 \begin_layout Standard
35067 Predefined vectors are offered by the \SpecialChar LaTeX
35073 \begin_inset Index idx
35076 \begin_layout Plain Layout
35082 that is loaded with the \SpecialChar LaTeX
35086 \begin_layout Standard
35094 \begin_layout Standard
35098 \begin_layout Plain Layout
35108 \begin_inset Note Note
35111 \begin_layout Plain Layout
35112 The following table will only be displayed when the \SpecialChar LaTeX
35125 \begin_layout Standard
35126 The following commands are defined:
35127 \begin_inset Separator parbreak
35133 \begin_layout Standard
35135 \begin_inset Tabular
35136 <lyxtabular version="3" rows="4" columns="2">
35137 <features tabularvalignment="middle">
35138 <column alignment="center" valignment="top">
35139 <column alignment="center" valignment="top">
35141 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
35144 \begin_layout Plain Layout
35150 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
35153 \begin_layout Plain Layout
35161 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
35164 \begin_layout Plain Layout
35174 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
35177 \begin_layout Plain Layout
35178 \begin_inset Formula $\Bra{\psi}$
35188 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
35191 \begin_layout Plain Layout
35201 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
35204 \begin_layout Plain Layout
35205 \begin_inset Formula $\Ket{\psi}$
35215 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
35218 \begin_layout Plain Layout
35230 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
35233 \begin_layout Plain Layout
35234 \begin_inset Formula $\Braket{\psi|\phi}$
35250 \begin_layout Standard
35257 assures that all vertical bars are set in the size of the surrounding brackets:
35258 \begin_inset Formula
35260 \Braket{\phi|J=\frac{3}{2}\,,\,M_{J}}
35269 \begin_layout Plain Layout
35279 \begin_inset Note Note
35282 \begin_layout Plain Layout
35283 The following will be displayed when the \SpecialChar LaTeX
35296 \begin_layout Standard
35297 You need to install the \SpecialChar LaTeX
35302 to see the rest of this subsection in the output.
35305 \begin_layout Standard
35309 \begin_layout Plain Layout
35321 \begin_layout Standard
35328 can also be achieved using the command
35334 , that is described in
35335 \begin_inset CommandInset ref
35337 reference "subsec:Automatic-Bracket-Size"
35344 \begin_layout Subsection
35345 Self-defined Fractions
35346 \begin_inset CommandInset label
35348 name "subsec:Self-defined-Fractions"
35353 \begin_inset Index idx
35356 \begin_layout Plain Layout
35357 Fractions ! self-defined
35365 \begin_layout Standard
35366 To define custom commands for fractions, the command
35373 \begin_inset Index idx
35376 \begin_layout Plain Layout
35383 \begin_layout Plain Layout
35397 is used in the following scheme:
35400 \begin_layout Standard
35413 bracket}{fraction bar thickness}{style}
35414 \begin_inset Newline newline
35418 \begin_inset Phantom HPhantom
35421 \begin_layout Plain Layout
35431 {numerator}{denominator}
35434 \begin_layout Standard
35435 The style is a number in the range of 0
35436 \begin_inset space \thinspace{}
35440 \begin_inset space \thinspace{}
35444 \begin_inset Separator parbreak
35450 \begin_layout Standard
35452 \begin_inset Tabular
35453 <lyxtabular version="3" rows="5" columns="2">
35454 <features tabularvalignment="middle">
35455 <column alignment="center" valignment="top">
35456 <column alignment="center" valignment="top">
35458 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
35461 \begin_layout Plain Layout
35467 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
35470 \begin_layout Plain Layout
35478 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
35481 \begin_layout Plain Layout
35487 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
35490 \begin_layout Plain Layout
35491 display style formula
35498 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
35501 \begin_layout Plain Layout
35507 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
35510 \begin_layout Plain Layout
35518 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
35521 \begin_layout Plain Layout
35527 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
35530 \begin_layout Plain Layout
35538 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
35541 \begin_layout Plain Layout
35547 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
35550 \begin_layout Plain Layout
35564 \begin_layout Standard
35565 When no style is given, the size is adjusted to the surrounding environment
35566 like for the command
35575 \begin_layout Standard
35576 When no fraction bar thickness is given, the predefined value of 0.4
35577 \begin_inset space \thinspace{}
35583 \begin_layout Standard
35584 \begin_inset VSpace medskip
35587 For example, the commands
35600 \begin_inset CommandInset ref
35602 reference "subsec:Fractions"
35606 are defined with the commands
35609 \begin_layout Standard
35618 genfrac{}{}{}{0}{#1}{#2}}
35621 \begin_layout Standard
35625 \begin_layout Standard
35634 genfrac{(}{)}{0pt}{1}{#1}{#2}}
35637 \begin_layout Standard
35638 \begin_inset VSpace medskip
35641 To define a fraction where the fraction bar thickness can be given as optional
35642 argument, the following line is inserted to the \SpecialChar LaTeX
35646 \begin_layout Standard
35655 genfrac{}{}{#1}{}{#2}{#3}}
35658 \begin_layout Standard
35660 \begin_inset Formula
35662 \text{Command} & & \mathrm{\backslash fracS[1mm]\backslash\{A\to\backslash\{B} & & \mathrm{\backslash fracS[5mm]\backslash\{A\to\backslash\{B}\\
35663 \text{Result} & & \fracS[1mm]{A}{B} & & \fracS[5mm]{A}{B}
35668 As one can see, the distance of the numerator and the denominator to the
35669 fraction bar is round about three times the bar thickness.
35672 \begin_layout Subsection
35674 \begin_inset Index idx
35677 \begin_layout Plain Layout
35686 \begin_layout Standard
35687 There are four ways to cancel formulas or parts of formulas:
35690 \begin_layout Standard
35694 \begin_layout Plain Layout
35704 \begin_inset Note Note
35707 \begin_layout Plain Layout
35708 The following table will only be displayed when the \SpecialChar LaTeX
35719 \begin_inset Separator parbreak
35725 \begin_layout Standard
35727 \begin_inset Tabular
35728 <lyxtabular version="3" rows="5" columns="2">
35729 <features tabularvalignment="middle">
35730 <column alignment="center" valignment="top">
35731 <column alignment="center" valignment="top">
35733 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
35736 \begin_layout Plain Layout
35742 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
35745 \begin_layout Plain Layout
35747 \begin_inset Note Note
35750 \begin_layout Plain Layout
35757 are used here as spacer.
35769 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
35772 \begin_layout Plain Layout
35776 \begin_inset space \textvisiblespace{}
35782 \begin_inset space \textvisiblespace{}
35790 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
35793 \begin_layout Plain Layout
35794 \begin_inset Formula $\raisebox{4.5mm}{}\cancel{\int A=B}\raisebox{-2.5mm}{}$
35804 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
35807 \begin_layout Plain Layout
35811 \begin_inset space \textvisiblespace{}
35817 \begin_inset space \textvisiblespace{}
35825 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
35828 \begin_layout Plain Layout
35829 \begin_inset Formula $\raisebox{4.5mm}{}\bcancel{\int A=B}\raisebox{-2.5mm}{}$
35839 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
35842 \begin_layout Plain Layout
35846 \begin_inset space \textvisiblespace{}
35852 \begin_inset space \textvisiblespace{}
35860 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
35863 \begin_layout Plain Layout
35864 \begin_inset Formula $\raisebox{4.5mm}{}\xcancel{\int A=B}\raisebox{-2.5mm}{}$
35874 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
35877 \begin_layout Plain Layout
35881 \begin_inset space \textvisiblespace{}
35887 \begin_inset space \textvisiblespace{}
35891 \begin_inset Formula $\to$
35899 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
35902 \begin_layout Plain Layout
35903 \begin_inset Formula $\raisebox{7mm}{}\cancelto{1}{\int A=B}\raisebox{-2.5mm}{}\hspace{3mm}$
35919 \begin_layout Standard
35926 is especially suitable to visualize the reduction of fractions within formulas:
35927 \begin_inset Formula
35929 \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}}}
35937 \begin_layout Standard
35938 To change the size of
35945 \begin_inset Quotes eld
35949 \begin_inset Quotes erd
35952 value one can add the \SpecialChar LaTeX
35956 \begin_layout Standard
35961 PassOptionsToPackage{option}{cancel}
35964 \begin_layout Standard
35973 which leads to the same size as for the canceled value, or
35977 which makes is it a bit smaller than normal.
35980 \begin_layout Standard
35981 To color the cancellation bar one adds this command as \SpecialChar TeX
35985 \begin_layout Standard
35997 \begin_layout Standard
36002 can be replaced by a color of your choice.
36005 \begin_layout Standard
36009 \begin_layout Plain Layout
36025 \begin_layout Standard
36026 \begin_inset Formula
36028 \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}}}
36036 \begin_layout Standard
36040 \begin_layout Plain Layout
36054 \begin_inset Note Note
36057 \begin_layout Plain Layout
36066 \begin_layout Standard
36067 For further customizations, see the documentation of the package
36072 \begin_inset CommandInset citation
36079 \begin_inset Index idx
36082 \begin_layout Plain Layout
36091 \begin_layout Standard
36095 \begin_layout Plain Layout
36105 \begin_inset Note Note
36108 \begin_layout Plain Layout
36109 The following will be displayed when the \SpecialChar LaTeX
36122 \begin_layout Standard
36123 You need to install the \SpecialChar LaTeX
36128 to see the rest of this subsection in the output.
36131 \begin_layout Standard
36135 \begin_layout Plain Layout
36147 \begin_layout Subsection
36148 Formulas in Section Headings
36149 \begin_inset CommandInset label
36151 name "subsec:Formulas-in-Section"
36156 \begin_inset Index idx
36159 \begin_layout Plain Layout
36160 Formula ! in section headings
36168 \begin_layout Standard
36169 When formulas are used in section headings, the following has to be taken
36173 \begin_layout Standard
36174 \begin_inset Note Greyedout
36177 \begin_layout Plain Layout
36183 \begin_inset Index idx
36186 \begin_layout Plain Layout
36187 Packages ! hyperref
36192 support is enabled in the document settings dialog under
36195 \begin_inset space ~
36200 , PDF-bookmarks are created for every section heading in the table of contents.
36201 If a section heading contains formulas, they are incorrectly displayed
36202 in the bookmark text, because formulas in bookmarks infringe the PDF convention
36211 \begin_layout Standard
36212 Both problems can be solved by inserting at the end of the section heading
36213 a short title with the menu
36215 Insert\SpecialChar menuseparator
36217 \begin_inset space ~
36223 Short titles are used as alternative for multiline section headings to
36224 keep the table of contents clearly arranged.
36225 Only the short title appears in the table of contents and therefore also
36226 in the PDF-bookmark.
36229 \begin_layout Standard
36230 When formulas should be used in the table of contents but
36234 is used, one can use the following command in \SpecialChar TeX
36238 \begin_layout Standard
36243 texorpdfstring{part}{alternative}
36244 \begin_inset Index idx
36247 \begin_layout Plain Layout
36258 \begin_layout Standard
36259 Part is the part of the heading that shouldn't appear in the PDF-bookmark.
36260 This can be characters, formulas, footnotes, but also cross-references.
36261 The alternative is used instead of the part for the bookmark.
36264 \begin_layout Standard
36265 Here are two example headings:
36266 \begin_inset VSpace -3mm
36273 \begin_layout Plain Layout
36285 \begin_layout Subsubsection
36286 Heading without formula in table of contents
36287 \begin_inset Formula $\sqrt{-1}=\mathrm{i}$
36291 \begin_inset Argument 1
36294 \begin_layout Plain Layout
36295 Heading without formula in table of contents
36303 \begin_layout Subsubsection
36304 Heading with formula in table of contents
36308 \begin_layout Plain Layout
36318 \begin_inset Formula $\sqrt{-1}=\mathrm{i}$
36325 \begin_layout Plain Layout
36335 \begin_layout Standard
36339 \begin_layout Plain Layout
36348 In the first heading a short title was used, in the second one
36357 \begin_layout Standard
36358 To get the same formatting as for the other headings, the complete heading
36367 \begin_layout Plain Layout
36369 \begin_inset CommandInset ref
36371 reference "subsec:Bold-Formulas"
36383 \begin_layout Subsection
36384 Formulas in multi-column Text
36385 \begin_inset Index idx
36388 \begin_layout Plain Layout
36389 Formula ! in multi-column text
36397 \begin_layout Standard
36398 Formulas in multi-column text are often too wide to fit into a column and
36399 thus need to be set over the whole page width.
36400 This is done by using the \SpecialChar LaTeX
36409 \begin_layout Plain Layout
36414 is part of every \SpecialChar LaTeX
36415 standard installation.
36421 \begin_inset Index idx
36424 \begin_layout Plain Layout
36425 Packages ! multicol
36430 , that is loaded with the \SpecialChar LaTeX
36434 \begin_layout Standard
36439 usepackage{multicol}
36442 \begin_layout Standard
36443 \begin_inset Note Greyedout
36446 \begin_layout Plain Layout
36447 Note that in this case the setting
36450 \begin_inset space ~
36457 Document\SpecialChar menuseparator
36463 \begin_inset space ~
36483 \begin_layout Standard
36484 Before the multi-column text the command
36487 \begin_layout Standard
36492 begin{multicols}{column number}
36495 \begin_layout Standard
36496 is written in \SpecialChar TeX
36498 The column number is a number in the range of 2
36499 \begin_inset space \thinspace{}
36503 \begin_inset space \thinspace{}
36507 Before the formula the multi-column text is ended by inserting the command
36510 \begin_layout Standard
36518 \begin_layout Standard
36519 in \SpecialChar TeX
36523 \begin_layout Standard
36524 Due to the command some space is automatically added before the formula.
36526 \begin_inset space \thinspace{}
36529 mm vertical space is inserted before the formula.
36530 When the formula style
36536 \begin_layout Plain Layout
36538 \begin_inset CommandInset ref
36540 reference "sec:Formula-Styles"
36552 \begin_inset space \thinspace{}
36555 mm space is inserted instead.
36558 \begin_layout Standard
36559 As example a multi-column text with a displayed formula:
36562 \begin_layout Standard
36568 \begin_layout Plain Layout
36572 begin{multicols}{2}
36577 Das Spektrum wird fouriertransformiert.
36578 Die Fouriertransformation wird verwendet, um die überlagerten Signale (Netzwerk
36579 , Lösungsmittel) zu trennen.
36580 Nachdem wir die Phasenverschiebung bestimmen konnten, interessiert uns
36581 nun das Aussehen des Ausgangssignals.
36582 Im Experiment haben wir es mit sehr vielen Teilchen zu tun, so dass man
36583 über alle Phasen integrieren muss.
36585 \begin_inset Formula $S$
36588 unser normiertes Ausgangssignal und
36589 \begin_inset Formula $P$
36592 die Phasenverteilungsfunktion, so ergibt sich die Beziehung
36596 \begin_layout Plain Layout
36606 \begin_inset VSpace -6mm
36610 \begin_inset Formula
36612 S(t)=S_{0}(t)\int_{-\infty}^{\infty}P(\phi,t)\mathrm{e}^{\mathrm{i}\phi}\,\mathrm{d}\phi
36621 \begin_layout Plain Layout
36625 begin{multicols}{2}
36631 \begin_inset Formula $S_{0}$
36634 das Signal ohne Gradient ist und die Normierungsbedingung
36635 \begin_inset Formula $\int_{-\infty}^{\infty}P(\phi,t)\,\mathrm{d}\phi=1$
36639 Nun dürfen wir aber nicht den Relaxationsprozess außer Acht lassen.
36641 \begin_inset Formula $\nicefrac{\pi}{2}$
36645 \begin_inset space \thinspace{}
36648 -rf-Puls beginnt sich die Magnetisierung zu entfokussieren, wodurch sich
36649 das Signal zusätzlich abschwächt.
36650 Diese Abschwächung verläuft exponentiell in Abhängigkeit der so genannten
36652 \begin_inset Formula $T_{2}$
36658 \begin_layout Standard
36664 \begin_layout Plain Layout
36676 \begin_layout Subsection
36677 Formulas with Description of Variables
36678 \begin_inset Index idx
36681 \begin_layout Plain Layout
36682 Formula ! with description of variables
36690 \begin_layout Standard
36691 To describe variables within a formula, like in formula
36692 \begin_inset CommandInset ref
36694 reference "eq:within"
36703 \begin_inset Formula $n$
36707 \begin_inset space ~
36710 matrix is used with left aligned columns for the
36711 \begin_inset Formula $n$
36718 \begin_layout Plain Layout
36720 \begin_inset CommandInset ref
36722 reference "sec:Matrices"
36731 To set the description in a smaller size, before the matrix e.
36732 \begin_inset space \thinspace{}
36736 \begin_inset space \space{}
36749 \begin_layout Plain Layout
36751 \begin_inset CommandInset ref
36753 reference "subsec:Font-Sizes"
36765 \begin_layout Standard
36766 When the formula style
36772 \begin_layout Plain Layout
36774 \begin_inset CommandInset ref
36776 reference "sec:Formula-Styles"
36797 \begin_layout Plain Layout
36804 only works in formulas with the style
36809 \begin_inset CommandInset ref
36811 reference "subsec:Variable-Space"
36820 is inserted before and after the matrix to have the same separation of
36821 the matrix from the equation and the side margin.
36824 \begin_layout Standard
36825 When the formula style
36829 is used, the method described in
36830 \begin_inset CommandInset ref
36832 reference "subsec:Flalign-Environment"
36836 is used to indent formulas.
36838 \begin_inset CommandInset ref
36840 reference "eq:within"
36844 consists of five columns where in the first two columns contain the equation,
36845 the third the matrix and the last one an empty \SpecialChar TeX
36847 \begin_inset Formula
36849 \hspace{30pt}F_{A} & =\rho·V·g & \footnotesize\begin{array}{ll}
36850 \rho & \textrm{density}\\
36851 V & \textrm{volume}\\
36852 g & \textrm{gravitational acceleration}
36853 \end{array} & & {}\label{eq:within}
36861 \begin_layout Subsection
36862 Upright small Greek Letters
36863 \begin_inset CommandInset label
36865 name "subsec:Upright-small-Greek"
36870 \begin_inset Index idx
36873 \begin_layout Plain Layout
36874 Greek letters ! upright
36882 \begin_layout Standard
36883 Most of the math fonts only provide italic small Greek letters.
36884 But for symbols of elementary particles like pions and neutrinos, upright
36885 Greek letters are needed.
36894 \begin_layout Plain Layout
36899 is part of the \SpecialChar LaTeX
36905 \begin_inset Index idx
36908 \begin_layout Plain Layout
36913 \begin_layout Plain Layout
36933 \begin_inset Index idx
36936 \begin_layout Plain Layout
36942 that is loaded with the \SpecialChar LaTeX
36946 \begin_layout Standard
36951 usepackage{upgreek}
36954 \begin_layout Standard
36960 \begin_layout Plain Layout
36970 \begin_inset Note Note
36973 \begin_layout Plain Layout
36974 The following table will only be displayed when the \SpecialChar LaTeX
36984 They are created when the command for a small Greek letter is started with
36990 For example the command
36997 \begin_inset Formula $\uptau$
37003 \begin_layout Standard
37004 With these commands reactions of elementary particles can be typeset:
37005 \begin_inset Formula
37007 \uppi^{+}\to\upmu^{+}+\upnu_{\upmu}
37015 \begin_layout Standard
37016 The upright letters are more bold and wider than the italic ones.
37017 They should therefore not be used for units like
37018 \begin_inset Quotes eld
37022 \begin_inset Quotes erd
37028 \begin_layout Standard
37032 \begin_layout Plain Layout
37042 \begin_inset Note Note
37045 \begin_layout Plain Layout
37046 The following will be displayed when the \SpecialChar LaTeX
37059 \begin_layout Standard
37060 You need to install the \SpecialChar LaTeX
37065 to see the rest of this subsection in the output.
37068 \begin_layout Standard
37072 \begin_layout Plain Layout
37084 \begin_layout Subsection
37085 Text Characters in Formulas
37086 \begin_inset Index idx
37089 \begin_layout Plain Layout
37098 \begin_layout Standard
37099 In some cases you might want to insert text characters directly into formulas.
37100 When for example the centered dot · is often used in formulas like
37101 \begin_inset Formula $\nu=5·10^{5}\,\mathrm{Hz}$
37104 , one would have to insert the command
37114 \begin_layout Plain Layout
37116 \begin_inset CommandInset ref
37118 reference "subsec:Binary-Operators"
37127 all the time, because this character is defined in all encodings as text
37129 But the encoding can be changed by this \SpecialChar LaTeX
37133 \begin_layout Standard
37138 Declare Inputtext{183}{
37148 f\SpecialChar ligaturebreak
37152 \begin_layout Standard
37153 The character encoding (menu
37155 Document\SpecialChar menuseparator
37156 Settings\SpecialChar menuseparator
37159 ) specifies what character appears when a keyboard key is pressed.
37160 When the key for the character '·' is pressed, internally the command
37167 But this command is not available in a formula so that you would get \SpecialChar LaTeX
37169 With the changed encoding the right command is chosen automatically, depending
37170 on if the character was inserted into a formula or not.
37173 \begin_layout Standard
37174 The encoding of several characters is saved in definition files.
37175 For example the encoding
37179 is defined in the file
37183 which is in the installation folder of \SpecialChar LaTeX
37185 Encodings should only be changed via the \SpecialChar LaTeX
37186 -preamble and not in the definition
37188 Otherwise documents could not be edited by other \SpecialChar LyX
37189 users working on other
37193 \begin_layout Standard
37194 \begin_inset VSpace medskip
37197 Besides the centered dot, in this document the degree sign ° is defined
37198 with the following \SpecialChar LaTeX
37199 -preamble line so that it can be directly inserted into
37203 \begin_layout Standard
37208 DeclareInputtext{176}{
37218 f\SpecialChar ligaturebreak
37222 \begin_layout Subsection
37224 -comments in formulas
37225 \begin_inset Index idx
37228 \begin_layout Plain Layout
37238 \begin_layout Standard
37239 In text you can insert a comment that will only be visible in the \SpecialChar LaTeX
37241 code of your file with the menu
37243 Insert\SpecialChar menuseparator
37244 Note\SpecialChar menuseparator
37248 This is not possible in a formula but you can insert \SpecialChar LaTeX
37253 \begin_layout Standard
37261 \begin_layout Standard
37262 This creates a box in which you can write your comment.
37263 Due to a bug in \SpecialChar LyX
37268 \begin_layout Plain Layout
37269 \begin_inset CommandInset href
37271 name "LyX-bug #9002"
37272 target "http://www.lyx.org/trac/ticket/9002"
37281 you cannot write normal text inside the comment, even when you use mathematical
37282 text, you will see its \SpecialChar LaTeX
37283 -commands in the \SpecialChar LaTeX
37285 \begin_inset Newline newline
37288 This a formula with a \SpecialChar LaTeX
37290 \begin_inset Formula
37292 A=B%\text{This is the comment}
37300 \begin_layout Standard
37301 \begin_inset Newpage newpage
37307 \begin_layout Section
37310 \begin_inset Index idx
37313 \begin_layout Plain Layout
37322 \begin_layout Standard
37323 This section is a summary of the most important typographic rules, listed
37328 \begin_layout Plain Layout
37329 This collection was partly taken from the German semi-official dictionary
37331 \begin_inset Quotes eld
37335 \begin_inset Quotes erd
37339 \begin_inset CommandInset citation
37345 that lists some of the ISO rules.
37346 More rules are listed in
37347 \begin_inset CommandInset citation
37361 \begin_layout Itemize
37370 \begin_layout Plain Layout
37371 done with font styles, see
37372 \begin_inset CommandInset ref
37374 reference "subsec:Font-Styles"
37383 , no matter if they appear in italic text: 30
37384 \begin_inset space \thinspace{}
37388 \begin_inset Newline newline
37391 Between the value and the unit is the smallest space, see
37392 \begin_inset CommandInset ref
37394 reference "subsec:Predefined-Space"
37399 \begin_inset Newline newline
37402 This convention is automatically fulfilled when the command
37409 When it is entered to a formula, two boxes appear.
37410 In the first one the value is inserted, in the second one the unit, and
37412 \begin_inset Formula $\unit[30]{km/h}$
37416 \begin_inset space \thinspace{}
37426 is not a real \SpecialChar LaTeX
37427 command but the command
37433 , therefore you cannot use it in \SpecialChar TeX
37437 \begin_layout Itemize
37438 Percent and perthousand signs are set like physical units:
37439 \begin_inset Newline newline
37443 \begin_inset space \thinspace{}
37449 \begin_layout Itemize
37450 The degree sign follows directly on the value: 15°, but not when it is used
37452 \begin_inset space \thinspace{}
37458 \begin_layout Itemize
37459 In numbers with more than four digits the smallest space is inserted before
37460 every third digit to group them:
37470 \begin_inset space \thinspace{}
37474 \begin_inset space \thinspace{}
37480 \begin_layout Itemize
37481 For dimensions like 120×90×40
37482 \begin_inset space \thinspace{}
37485 cm the multiplication sign
37486 \begin_inset Quotes eld
37490 \begin_inset Quotes erd
37494 It is available either via the command
37502 Insert\SpecialChar menuseparator
37503 Special Character\SpecialChar menuseparator
37509 \begin_layout Itemize
37510 Functions with names consisting of several letters are set upright to avoid
37512 \begin_inset CommandInset ref
37514 reference "subsec:Predefined-Functions"
37521 \begin_layout Itemize
37522 Indices consisting of several letters, are set upright:
37523 \begin_inset Formula $E_{\mathrm{kin}}$
37527 \begin_inset Newline newline
37530 Components of matrices are set italic:
37531 \begin_inset Formula $\hat{H}_{kl}$
37537 \begin_layout Itemize
37538 The differentiation/integration operator 'd', the Euler's number 'e' and
37539 the imaginary unit 'i' should be set upright, to avoid mixing them up with
37543 \begin_layout Itemize
37544 The character that denotes a
37548 transformation is inserted either by the command
37553 \begin_inset space \textvisiblespace{}
37560 Insert\SpecialChar menuseparator
37561 Special Character\SpecialChar menuseparator
37562 Symbols\SpecialChar menuseparator
37564 \begin_inset space ~
37570 \begin_inset Formula $\mathscr{F}$
37576 \begin_layout Standard
37577 \begin_inset Newpage newpage
37583 \begin_layout Section
37585 \begin_inset Index idx
37588 \begin_layout Plain Layout
37597 \begin_layout Standard
37598 Some characters and symbols can be created with several commands.
37599 Here is a list of the synonym commands:
37602 \begin_layout Standard
37603 \begin_inset VSpace bigskip
37607 \begin_inset space \hfill{}
37611 \begin_inset Tabular
37612 <lyxtabular version="3" rows="12" columns="2">
37613 <features tabularvalignment="middle">
37614 <column alignment="center" valignment="top" width="0pt">
37615 <column alignment="center" valignment="top" width="0pt">
37617 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
37620 \begin_layout Plain Layout
37626 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
37629 \begin_layout Plain Layout
37631 \begin_inset Note Note
37634 \begin_layout Plain Layout
37641 is only used as spacer.
37653 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
37656 \begin_layout Plain Layout
37664 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
37667 \begin_layout Plain Layout
37671 \begin_layout Plain Layout
37684 \begin_layout Plain Layout
37698 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
37701 \begin_layout Plain Layout
37709 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
37712 \begin_layout Plain Layout
37722 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
37725 \begin_layout Plain Layout
37733 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
37736 \begin_layout Plain Layout
37746 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
37749 \begin_layout Plain Layout
37757 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
37760 \begin_layout Plain Layout
37768 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
37771 \begin_layout Plain Layout
37779 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
37782 \begin_layout Plain Layout
37790 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
37793 \begin_layout Plain Layout
37801 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
37804 \begin_layout Plain Layout
37814 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
37817 \begin_layout Plain Layout
37825 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
37828 \begin_layout Plain Layout
37838 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
37841 \begin_layout Plain Layout
37849 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
37852 \begin_layout Plain Layout
37862 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
37865 \begin_layout Plain Layout
37873 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
37876 \begin_layout Plain Layout
37886 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
37889 \begin_layout Plain Layout
37897 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
37900 \begin_layout Plain Layout
37908 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
37911 \begin_layout Plain Layout
37919 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
37922 \begin_layout Plain Layout
37934 \begin_inset space \hfill{}
37938 \begin_inset Tabular
37939 <lyxtabular version="3" rows="12" columns="2">
37940 <features tabularvalignment="middle">
37941 <column alignment="center" valignment="top" width="0pt">
37942 <column alignment="center" valignment="top" width="0pt">
37944 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
37947 \begin_layout Plain Layout
37953 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
37956 \begin_layout Plain Layout
37964 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
37967 \begin_layout Plain Layout
37975 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
37978 \begin_layout Plain Layout
37990 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
37993 \begin_layout Plain Layout
38001 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
38004 \begin_layout Plain Layout
38014 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
38017 \begin_layout Plain Layout
38025 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
38028 \begin_layout Plain Layout
38038 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
38041 \begin_layout Plain Layout
38049 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
38052 \begin_layout Plain Layout
38060 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
38063 \begin_layout Plain Layout
38071 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
38074 \begin_layout Plain Layout
38082 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
38085 \begin_layout Plain Layout
38093 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
38096 \begin_layout Plain Layout
38106 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
38109 \begin_layout Plain Layout
38117 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
38120 \begin_layout Plain Layout
38130 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
38133 \begin_layout Plain Layout
38141 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
38144 \begin_layout Plain Layout
38154 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
38157 \begin_layout Plain Layout
38165 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
38168 \begin_layout Plain Layout
38178 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
38181 \begin_layout Plain Layout
38189 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
38192 \begin_layout Plain Layout
38202 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
38205 \begin_layout Plain Layout
38213 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
38216 \begin_layout Plain Layout
38230 \begin_inset space \hfill{}
38236 \begin_layout Standard
38237 \begin_inset Newpage newpage
38243 \begin_layout Bibliography
38244 \begin_inset CommandInset bibitem
38245 LatexCommand bibitem
38257 The \SpecialChar LaTeX
38261 Addison Wesley, 2004
38264 \begin_layout Bibliography
38265 \begin_inset CommandInset bibitem
38266 LatexCommand bibitem
38272 \begin_inset CommandInset href
38275 target "ftp://ftp.dante.de/tex-archive/info/math/voss/mathmode/Mathmode.pdf"
38279 of \SpecialChar LaTeX
38283 \begin_layout Bibliography
38284 \begin_inset CommandInset bibitem
38285 LatexCommand bibitem
38291 \begin_inset CommandInset href
38294 target "http://mirrors.ctan.org/macros/latex/required/amslatex/math/amsldoc.pdf"
38302 \begin_layout Plain Layout
38311 -\SpecialChar LaTeX
38315 \begin_layout Bibliography
38316 \begin_inset CommandInset bibitem
38317 LatexCommand bibitem
38323 \begin_inset CommandInset href
38326 target "ftp://ftp.dante.de/tex-archive/info/symbols/comprehensive/symbols-a4.pdf"
38330 of all symbols available with \SpecialChar LaTeX
38334 \begin_layout Bibliography
38335 \begin_inset CommandInset bibitem
38336 LatexCommand bibitem
38342 \begin_inset CommandInset href
38344 name "Documentation"
38345 target "http://mirrors.ctan.org/macros/latex/contrib/cancel/cancel.pdf"
38349 of the \SpecialChar LaTeX
38355 \begin_inset Index idx
38358 \begin_layout Plain Layout
38367 \begin_layout Bibliography
38368 \begin_inset CommandInset bibitem
38369 LatexCommand bibitem
38375 \begin_inset CommandInset href
38377 name "Documentation"
38378 target "http://www.tug.org/applications/hyperref/ftp/doc/manual.pdf"
38382 of the \SpecialChar LaTeX
38388 \begin_inset Index idx
38391 \begin_layout Plain Layout
38392 Packages ! hyperref
38400 \begin_layout Bibliography
38401 \begin_inset CommandInset bibitem
38402 LatexCommand bibitem
38408 \begin_inset CommandInset href
38410 name "Documentation"
38411 target "http://www.ctan.org/tex-archive/macros/latex/contrib/mhchem/mhchem.pdf"
38415 of the \SpecialChar LaTeX
38421 \begin_inset Index idx
38424 \begin_layout Plain Layout
38433 \begin_layout Bibliography
38434 \begin_inset CommandInset bibitem
38435 LatexCommand bibitem
38446 Auflage, Duden 2001
38449 \begin_layout Bibliography
38450 \begin_inset CommandInset bibitem
38451 LatexCommand bibitem
38457 \begin_inset CommandInset href
38460 target "http://physics.nist.gov/Document/checklist.pdf"
38464 for reviewing manuscripts
38467 \begin_layout Standard
38468 \begin_inset CommandInset index_print
38469 LatexCommand printindex